Diffusion in the binary systems of molybdenum with nickel,iron and cobaltCitation for published version (APA):Heijwegen, C. P. (1973). Diffusion in the binary systems of molybdenum with nickel, iron and cobalt. TechnischeHogeschool Eindhoven. https://doi.org/10.6100/IR36206

DOI:10.6100/IR36206

Document status and date:Published: 01/01/1973

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DIFFUSION IN THE BINARY SYSTEMS

OF MOL YBDENUM WITH

NICKEL, IRON AND CO BALT

C. P. Heijwegen

DIPFUSION IN THE BINARY SYSTEMS

OF MOL YBDENUM WITH

NICKEL, IRON AND CO BALT

DIFFUSION IN THE BINARY SYSTEMS

OF MOL YBDENUM WITH

NICKEL, IRON AND COBALT

PROEFSCHRIFT

ter verkrijging van de graad van doctor

in de technische wetenschappen

aan de Technische Hogeschool Eindhoven,

op gezag van de rector magnificus,

prof. dr. ir. G . Vossers,

voor een commissie aangewezen door het college van dekanen

in het openbaar te verdedigen op dinsdag 29 mei 1973 te 16.00 uur.

door

Cornelis Petrus Heijwegen

geboren te Helmond

DRUK: HELSO BEDRIJVEN HELMOND

dit proefschrift is goedgekeurd door de promotoren

prof dr. G. D. Rieck en

prof dr. C. Zwikker.

Aan de nagedachtenis van mijn vader

Aan mijn moeder

Aan allen die bijgedragen hebben aan het tot stand

komen van dit proefschrift mijn dank.

CONTENTS

CHAPTER 1 INTRODUCTION

1.1 Interditfusion in roetal systems 1.2 The object of this thesis

CHAPTER 2 THEORY

2.1 Ditfusion mechanisms 2.2 Ditfusion equations 2.3 Approximating equations to calculate the

ditfusion coefficients 2.4 Ditfusion in multiphase binary systems

2.4.1 Determination of the ditfusion coefficients

2.4.2 Determination of the phase diagram by way of multiphase ditfusion

2.4.3 The kinetics of layer growth 2.5 The temperature dependenee of the diffu-

Page

11 11

13 14 1 6

17 17

1 8

18 1 8

sion process 2.6 Short-circuit ditfusion 19 2.7 The Kirkendall effect and its consequences 19

CHAPTER 3 CALCULATION OF THE INTERDIPFUSION COEFFICIENTS AND THE RATIO OF THE INTRINSIC DIPFUSION COEFFICIENTS

3.1 A computer program for the calculation of 21 interditfusion coefficients in binary systems

3.2 The ratio of the intrinsic diffusion coef- 26 ficients

CHAPTER 4 CONSTITUTION OF THE Mo-Ni, Mo-Fe AND Mo-Co SYSTEMS AND PROPERTIES OF THEIR PHASES

4.1 The equilibrium diagram of the Mo-Ni system 28 and the structure of the various phases

4.2 The equilibrium diagram of the Mo-Fe system 29 and the structure of the various phases

4.3 The equilibrium diagram of the Mo-Co system 30 and the structure of the various phases

CHAPTER 5 DIPFUSION IN THE Mo-Ni, Mo -Fe AND Mo-Co SYSTEMS

5.1 Ditfusion in the Mo-Ni systern 5.2 Diffusion in the Mo-Fe system 5.3 Diffusion in the Mo-Co system

32 33 35

CHAPTER 6 EXPERIMENTAL PROCEDURES

6.1 Introduetion 6.2 Preparatien of the ditfusion couples 6.3 Microscopie examinatien 6.4 Mieroprobe analysis 6.5 X-ray diffraction 6.6 Micro-indentation hardness testing

CHAPTER 7 DIFFUSION IN THE Mo-Ni SYSTEM

7.1 Experimental results 7.1.1 Layer growth measurements 7.1.2 Mieroprobe measurements 7.1.3 Hardness measurements 7.1.4 X-ray diffraction

7.2 Evaluation o f the results 7.2.1 Determination of the phase diagram

7.2.1.1 Introduetion 7.2.1.2 Experimental procedures 7.2.1 .3 Experimental results 7.2.1 .4 Discussion

7.2.2 Calculations of ditfusion data 7.2.3 Kirkendall effect

7.3 Conclusions

CHAPTER 8 DIFFUSION IN THE Mo-Fe SYSTEM

8.1 Experimental results 8.1.1 Layer growth measurements 8.1.2 Mieroprobe measurements 8.1.3 Hardness measurements 8.1.4 X-ray diffraction

8.2 Evaluation of the r e sults 8.2.1 Determination of the phase diagram 8.2.2 Calculations of ditfusion data 8.2.3 Kirkendall effect

8.3 Conclusions

CHAPTER 9 DIFFUSION IN THE Mo-Co SYSTEM

36 36 38 39 42 42

43 43 49 53 54 56 56 56 57 57 60 61 64 67

69 69 72 77 77 78 78 84 88 89

9.1 Experimental results 90 9.1.1 Layer growth measurements 90 9.1.2 Mieroprobe measurements 95 9.1.3 Hardness measurements 98 9.1.4 X-ray diffraction 98 9.1.5 Texture in the layer of the ~- 100

(Co 7 Mo~) phase formed in Mo-Co diffuslon couple s

9.2 Evaluation o f t he re sult s 105 9.2.1 Determi nation of t he phase d i agram 105 9.2.2 Calculations of ditfusion data 109 9.2.3 Kirkendall effect 113

9.3 Conclusions 114

CHAPTER 10 THE INFLUENCE OF CARBON ON THE INTER­DIPFUSION OF Mo AND Ni

1 0.1 Introduetion 10.2 Experimental procedures 10.3 Experimental results

10.3 .1 Layer growth measurements 10.3.2 X-ray diffraction 10.3.3 Hardness measurements 10.3.4 Mieroprobe measurements

1 0. 4 Discussion 1 0. 5 Conclusions

CHAPTER 11 DISCUSSION

115 116 117 117 122 124 125 130 132

SUMMARY 137

REPERENCES 140

C H A P T E R

INTRODUCTION

1.1 Interditfusion in roetal systems

If two metals are in contact with each other at a high temperature, they will interdiffuse, and then farm what is known as a diffusion couple; atoms of the one roetal move into the matrix of the other, and vice versa. During diffusion, the concentratien differences between the starting materials are levelled. A new concentratien distribution will set up. If for a system the inter­ditfusion coefficient is available as a function of concentratien and temperature, this new distribution at a certain time may be predicted.

Knowledge of diffusion data is important in many cases:

(a) in metallurgy many processes are controlled by diffusion, e.g. homogenisation, precipitation, sintering, oxidation, phase-transformations;

(b) in solid-state bonding and finishing techniques the interaction between substrate and coating at elevated temperatures must be known in cantrolling the joining process so as to ensure the reliability of the joints in service;

(c) in studying e.g. point defects in crystals and thermadynamie activities of the components;

(d) another important application of interditfusion experiments is the examinatien of the phase diagram of a system.

1.2 The object of this thesis

Molybdenum has a wide scope as a structural material for high-temperature applications. A very imposing barrier to its use, howe ver, is its poor oxidation resistance. The product of the oxidation reaction, which is Mo0 3 , volatilises above 730°c resulting in a loss weight. Mo can be protected from oxidation by applying a coating or by alloying withother elements.

Apart from the general reasans mentioned above the study of the interditfusion in the systems Ma-Ni, Mo-Fe, Mo-Co and Mo-Ni-C is carried out for seve ral reasons:

(a) Nickel~ iron-, and cabalt-base heat-resisting alloys often include Mo. This element is added to the base composition because it acts as a solid- 11

12

salution strengthener, participates in the formation of precipitates (carbides or intermetallic compounds) and even promotes certain phenomena such as order­disorder reactions. Knowledge of its diffusion kinetics in the alloys is useful in that it allows certain inferences to be made regarding the behaviour, especially at high temperatures, of the complex alloy.

(b) Nickel-, iron-, and cabalt-base alloy claddings are aften applied as coatings. Growth kinetics and mechanical properties of diffusion layers between the various starting materials have to be known.

(c) Carbon is almest always present in heat-resisting alloys and aften in coatings. The influence of carbon on the diffusion behaviour of Mo and Ni is, there­fore, investigated.

(d) The phase diagrams are also very important. The thesis wants to contribute to a better knowledge on this subject.

C H A P T E R 2

THEORY

2.1 Diffusion mechanisrns

The basic assumption·rnade to explain diffusion in any crystal is that each diffusing atorn makes a series of jumps between the various equilibrium lattice sites or interstitial positions. These jumps are in more or less random directions and allow the atoms to migrate through the crystal.

A number of possible mechanisms has been suggested. Manning 1 gives an excellent survey. The most important will be discussed briefly.

(a) The simplest mechanism is the direct interchange of two neighbouring atoms. This mechanism is unlike1y in crystals with tightly packed lattices, because of the large lattice distortions occurring with the mechanism. On the other hand the mechanism may be possible in very loosely packed crystals. A variation of the exchange mechanism is the ring type. Here, three or more atoms situated roughly in a ring move tagether so that the whole ring of atoms rotates over one atom distance. The lattice distortions required here are not as great as in a direct exchange mechanism. It is obvious that in an exchange mecha­nism no new lattice sites are formed, and, therefore, it is obviously impossible to obtain a nett displace­ment of atoms relative to the crysta l lattice. Furthermore, the activation energy necessary for this mechanisrn is much higher than the observed activation energies (Kirkendall effect, see later). Therefore, the exchange mechanisrn is unlikely in most metal systems.

(b) When t here are imperfections in the lattice, other rnechanisms requiring considerably less energy ma y o c cur. An example i s the interst i tial me chanism. Here, an atom (mostly a small impurity atom) moves through the crystal by jumping from one interstitial site to another. When the interstitial atom is nearly equal in size to the lattice atoms, diffusion is more likely to occur by the interstitia lcy mechanism, also calle d the indirect interstitial mecha nism. The i nte rstitial atom move s into a norma l lattice s ite and the a tom which o r iginally occupie d t he latt ice si t e is pushed i nto a neighbo uring inter s titial s ite.

(c) Any crystal in thermal equilibrium contains a certain number of vacant lattice sites. These vacancies 13

14

provide an easy path for diffusion. Each atom moves through the crystal by making a series of exchanges with the various vacancies which from time to time are in its vicinity. Mechanisms invalving vacancies are the most probable, explaining bath the Kirkendall effect and the observed low activation energies.

(d) Dislocation pipe, grain boundary and surface ditfu­sion mechanisms appear in regions where the regular lattice structure breaks down. Ditfusion should occur more easily in the open regions of the crystal at dislocations, grain boundaries and surfaces. Because of their low activation energies these mechanisms may be dominant at lower temperatures.

The first three are all mechanisms which describe volume diffusion i.e. diffusion in the bulk. The mechanisms mentioned at point (d) describe what is known as short­circuit diffusion.

2.2 Diffusion equations

Surveys on the theory of ditfusion are given by Den Broeder 2 , Van Loo 3 , and Bastin4 • We will give only the equations used in this thesis and we refer to refs 2, 3, 4 for their derivation.

The following general assumptions will be made:

(a) Ditfusion takes place only in the direction perpen­dicular to the contact interface between the two metals (this will be called the x-direction) .

(b) The diffusion process will nat extend to the end of the ditfusion couple ("infinite diffusion couple"). The concentration at the ends remains constant.

(c) The cross-section of the ditfusion couple remains constant.

(d) No pores are formed.

If the total volume of the ditfusion couple is constant, Fick's first law gives the definition of the interdit­fusion coefficient:

J i = Dv (a Ci ;a x) ( 1 )

where Ji = flux of atoms in moles/cm2

Ci = concentration of component i in moles/cm3

<lci/élx = the concentration gradient

Experiments show that Dv is a function of Ci and the temperature. Combina tion of Fick's first law a nd the law of conservation of matter leads to Fick's second law:

( 2)

Eqs. (1) and (2) only apply if the total volume of the diffusion couple remains constant during diffusion. In practice, this is rarely the case. In 1962, Sauer and Freise5 derived an equation which permits of calculating the interditfusion coefficient in the case of volume changes during diffusion. Recently, Wagner6 and Den Broeder2 obtained the same equation in a different way.

The equation is derived for a ditfusion couple, con­sisting of two "semi-infinite" rods of alloys with the composition Nb1 and Nb2 • During diffusion, volume changes occur. According to Den Broeder the interdit­fusion coefficient can then be written as:

(3)

in which vm is the molar volume in cm 3 /mole, as function of Nb; t is the diffusion time in seconds; Nb is the mole fraction of component B in at%; x is the coordinate in )Jm;

K n

(1-K ) n

If Va = Vb = vm, then vm is eliminated from eq. (3) and if the pure metals are used as starting materials, eq. (3) is transformed into:

Ref. 3 has derived an equation for the calculation of the intrinsic diffusion coefficients:

(4)

(5)

where xk is the position of the Kirkendall interface and Cb the concentrati en of component B in grammoles/cm3

With eq. (5) the mark e r displacement need not be measure d. In this thesis only the ratios of the intrinsic di ffusion coefficients have been calculated. For this reason eq.(S) is also written for the component A. Division of these two relations yields: 15

x 00

Ik Nb-;:{bl J N -N Nb2 ( v )dx - N ( b2 b)dx

Db bi V

vb -oo m xk m

n V xk N -N 00 (6)

a a J N -N N I ( b bi) dx N ( b2 b)dx a2 v al v

-oo m xk m

in which v~ and vb are the partial molar volumes for the concentrat1on in the Kirkendall interface.

2.3 Approximatinq equations to calculate the diffusion coefficients

If the molar volume is constant a solution of Fick's second law is given by Boltzmann 7 and Matano 8 ,

with the Matano condition

0

where Nb is the mole fraction of component b.

If D is a constant, and independent of concentration~ Fick's second law can be solved with the result:

eb + ca + eb - c -=~--=a erf ( x )

2 2 2(Dt)~

The error function erf( ___ x __ ~)is defined by: 2(Dt)

erf ( x ) 2(Dt)~

lJ!

~~ J exp (-n 2)dn

0

(7)

( 8)

( 9)

( 1 0)

where c ~s.t~e concentrati~n in moles/cm3 a~d ca and eb 16 are the 1n1t1al concentrat1ons of the start1ng materials.

The error function is available in tabular ferm. From eq. (10) it fellows that the penetratien curve is symmetrical with respect to the Matano interface, where the concentratien gradient reaches its maximum. Eq. (10) can be useful in predicting a penetratien curve in particular diffusion· problems using an average value of D (Lee9 , Van den Broek 10 ). Since in many systems the diffusion coefficient is a function of concentration, this seems to be a rather rough approximation.

Grube 11 has derived a salution of Fick's secend law with a constant D. This is:

2 c - cmin c - c . max m~n

-erf ( x ) 2(Dt)~

( 11 )

where Cmin is the initial concentratien of the diffusion element in the part of the couple that is poorer in this element. Cmax is the initial concentratien of the dif­fusion element in the part of the couple that is richer in it. x is the distance between a plane in the coupl~ and Grube's interface. The latter is defined as the plane along which after diffusion the concentratien Cg is such that:

c - c . g m~n

cmax - cmin 0,5 i.e. c

g ( 12)

C is the concentratien at a distance x from Grube's interface after a diffusion of t seconds. The erf is the s~e as in eq.(9). This me thad is aften applied to couples consisting of a pure roe tal a nd a dilute alloy of that metal.

2.4 Diffusion in multipbase binary systems

2.4.1 Q~t~E~!~~t!Q~_Qf_tt~_Q!ÉÉ~ê!Q~-~Q~fÉ!~!~~tê Jost 1 2 has shown that the Boltzmann-Matano analysis applies also to multipba se systems. The only condit i on is that the penetratien curve can be diff€rentiated and integrated. It is necessary that the diffusion process is the rate determining step. Approximations for calculating the Dy in these systems are give n in the literature. Heumann 3 has given a n e quation that appl i es to diffusi on in an intermeta llic phase if the concentrat i en profile i n this phase is l i near. The value of that Dy must be regarded as a n average value of the diffus1on coeff icients in the phase. Wagner 1 ~ derived a salution of Fick's secend law fora concentratien-independent diffusion coefficient. 17

2.4.2 Q~~~~~~~É~Q~_Qf_~b~_Qb~§~_Q!~g~~-QY_~~Y-QÉ_~~!É!: Qb~ê~_Q!!!~ê!Q~_(see also Chapter 7)

Multiphase diffusion is an important tool in investiga­ting phase diagrams. If two metals interdiffuse, a number of stable intermetallic compounds will be formed by chemica! reaction. The sequence of the layers is deter­mined by the sequence of the single-phase areas in the phase diagram at the diffusion temperature. The concen­tratien values at the· interfaces of the layers follow froro the phase diagram. But only if it is supposed that the equilibrium state is attained during layer growth. The literature gives a very great number of cases where the boundary concentrations of the layers are in agree­ment with results obtained in another way. The experimen­tal results gained in our laboratory are also very favourable (Van Loo 3 , Bastin4 ).

2.4.3 !b~-~~~~É~~ê-QÉ_!~Y~~-g~Q~Éb The parameter used in the Boltzmann-Matano analysis x/lt is very important. This parameter is at a particular temperature only a function of concentration. This means that all concentrations, also the phase boundary concen­trations, move parabolically with time. So the width of a particular layer increases ~arabolically with t i me, accor ding to the relations: d = kt or d = kàl t, where d is the layer thickness, t the diffusion time and k and kà are the penetratien constants in cm 2 /sec and cm/sec~ respectively. In practice, the observation of this law is aften used as a criterion for an undisturbed diffusion process. From equations derived by Kidson 1 5 it can be shown that k and kà depend on the compositions of the sta rt i ng mate­r ials and on all the interdiffusion coe fficients i n the entire diffusion region. k and kY are no material con­stants. However, in many practical problems, the values of k and kà can be of great use.

2.5 The temQerature dependenee of the diffusion process

The temperature depende nee of a di f fusion c oef f icie nt c a n aften be described by a n Arrhenius -type rela tionship :

D = D0 exp (-Q/ RT) ( 1 3)

where R is the gas constant, T the absolute t emperature, D0 is the frequency factor, i ndepe ndent of t empe r a ture, a nd Q the activatien energy. By platting log D v e rsus 1/T, Q a nd Do can be de termine d graphica lly. Dv is a linear f unction o f the i ntr i nsic diffusion coe fficients which are each dependent on temperature with an Arrhenius­type relationship. It is, therefore, remarkable that in

18 many experiments the Arrhe n i us' rule can yet be applied.

It is obvious that the value of Q and Do must be regarded as an empirica! one, which can easily describe the temperature dependenee of the ditfusion coefficient. The same remarks apply in a still larger measure for the penetratien constant. The latter depends on all the ditfusion coefficients throughout the whole ditfusion couple. Besides, at different temperatures, different equilibrium concentrations at the phase boundaries will arise.

2.6 Short-circuit ditfusion

Since the number of dislocation, grain boundaries and surfaces is more or less independent of temperature, ditfusion by these mechanisms might be expected to have a slighter temperature dependenee than that with mechanisms invalving point defects (e.g. vacancies), whose concentratien increases with temperature. The relation between the activatien energies is:

Qvolume > 0grain bounoary > Qsurface·

For the few systems in which these activatien energies are determined it appears that:

0vol : Qgr.b : Qsur ~ 4 : 2 : 1

At the same time one finds Dovol> Dogr > Dosur·

Transport along grain boundaries and surfaces becomes only important at low temperatures. A plot of log D vs. 1/T showing a bend, is an indication that short-circuit diffusion effects may be present. In sectien 2.4.3 it is stated that the layers grow para­bolically with time when there is only volume diffusion. This is always true if only one type of ditfusion mechanism is present. When two types of ditfusion mecha­nisms operate simultaneously the growth of a layer wil! be roughly proportional to t 1 /n, where n has a value between 2 and 4. The factor n can be calculated from log d vs. log t plots.

2.7 The Kirkendall effect and its consequences

Interditfusion is often accompanied by a nett displace­ment of atoms relative to the crystal lattice. This was first demonstrated by Kirkendall and Smigelskas 16 •

They marked the contact interface between the two diffu­sing materials, viz. copper and brass, with molybdenum wires. After a certain ditfusion time this marker inter­face showed a pronounced displacement relative to a point outside the diffusion zone. This phenomenon is called the Kirkendall effect. 19

20

This shift requires that the flux of zinc atoms that passes the markers in one direction is appreciably greater than that of capper atoms in the reverse direction. The phenomenon has proved to be quite general. The vacancy mechanism can explain this effect but it excludes the possibility of the ring mechanism. Besides, the formation of pores which is aften observed in the diffusion zone, and the agreement between the theoretically calculated activatien energy (Huntington and Seitz 17 ) for the vacancy mechanism with the observed activatien energy, show that this vacancy mechanism is the most probable.

C H A P T E R 3

CALCULATION OF THE INTERDIPFUSION COEFFICIENTS AND THE RATIO OF THE INTRINSIC DIPFUSION COEFFICIENTS

3.1 A computer program for the calculation of inter-ditfusion coefficients in binary systemsR

In almest all papers published up to now, the method used for the calculation of the interditfusion coeffi­cient is the classica! Boltzmann-Matano analysis 7 ' 8 ,

for which a computer program is given by Hartley19 •

It is well known, however, that such an analysis can oe applied only to systems with constant partial molar volumes. Van den Broek 10 has shown that the calculation of coefficients by this analysis rnay cause considerable errors. The concentratien dependenee of the partial rnolar volumes have been taken into account in an e~uation derived by Sauer and Freise 5 , Ballufi 20 , Wagner , and Den Broeder 2 •

Starting frorn this equation, a program is written in ALGOL 60, calculating the coefficients frorn the concen­tration-penetration curves of ditfusion couples. The forrnula used is given by Den Broeder,

00

I N -N J ( b ~ m b) dx ( 1 4)

x

vm is the rnolar volurne in cm 3 /rnole, as a function of Nb; t is the ditfusion time in seconds; Nb is the rnole fraction of component B in at%; x is the coordinate in ~rn; Nb 1 and Nbz are the starting compositions in at% of the two "serni-infinite" rods which forrn the ditfusion couple;

NbZ-Nb (1-K ) = N -N •

n b2 bi

The equation permits of the calculation of the chemical interditfusion coefficient Dv without the position of the Matano-interface being known.

publishe d in Scripta Metallurgica (ref.18). This paper is written in co-operation with Dr. G.J. Visser, of the Cornputing Centre of the University of Technology, Eindhoven, for whose help we feel greatly indebted.

21

22

To make it possible to calculate the ratio of the intrinsic ditfusion coefficients, Da and Db, in the Kirkendall interface, the integrals in the following equation are calculated by the program,

x N -N 00 N -N lN fk ( b b>)dx - N fk( b~m b)dxl Db vb b2 V bl

-"' m { 15} Da va x N -N "' N -N

N Jk { b bl}dx - N f { b2 b}dx a2 v al k vm -oo m

Vb and va are the partial rnalar volumes belonging to the concentratien at the Kirkendall interface.

'r!2L~!'Qg;:~IE

The program is structured in such a way that it can handle all possible cases in binary systems. The re is no limit to the number of compounds {and therefore to the number of phase boundaries} present in the concentration­penetration curve.

The program consists of the following steps:

1. smoothing of the experimental points;

2. polynomial curve fitting all these points;

3. calculation of the interditfusion coefficients at concentratien Nb. For each Nb this calculation implies: {a} determination of the coordinate x, {b} calculation of the integrals of eq.{14}, {c} determination of the gradient dx/dNb, {d} calculation of vm;

4. platting of a picture of the smoothed points and the polynomial through these points {this step is not necessary} .

All these steps will be considered in some detail in the following sections.

§:!:~E-1 In most cases the experimental points do not lie on a smooth curve. When a polynomial is drawn through the points, its degree should be relatively low to obtain a smooth curve. This is necessary to get a gradient which does not go up and down depending on the incidental gradient in a point of the curve. When the degree is too low, however, the curve does not fit the experime ntal points very well and the deviation from the true curve is very high {Fig.3.1} .The deviation hardly affects the values of the integrals, but fo r the calculation of the gradient dx/dNb it is disastrous. Therefore, it is necessary that the experimental points should be smoothed. The m experimental points are corrected by the formula:

~ i+3 -I x. -xk I l [ i+3 -I x· -xk I l r exp ( ~ 0 ) ilNbk I r exp ( ~ 0 ) k=~-3 k=~-3

( 1 6)

This is a 7-point forrnula, which corrects a point by the three preceding and the three following points. The weight of each point is deterrnined by an exponential function which decreases as the distance to the point which must be corrected increases. The value of the factor 10 in eq.(16) depends on the spacings of the experirnental points and also on the units of the coordi­nates. In our experirnents the factor 10 is excellent for this 7-point approach (Fig.3.2) .In this way the first and the last three points cannot be corrected and rernain unchanged.

Ta get an irnpression of the difference between the un­corrected and correcte d points, the r oot-rne an-square value

is calculate d.

5~0

54.5 6 1h dtgttt

54.0

53.5 AI .% Ni

53.0

52.5

52.0

51.5

51.0 / ' /

"' 49.5 .• ! .,.

50 .5

50.0

550

54.5

54.0

53.5

./.~r :::

52 .0

/ 51.5

/ 5 1.0

50.5

50.0

4 9.5

2 5 th dtgtee

At.%Ni

···~,~.~.~.~ .. ~~ .. ~.~ .. ~.~,.~ .. ~.~ .. ~.~ .. ~.~,~.~.~,~,. - ~m

49.ok2~0~4e;;0~6':-0 -'---:f.80~1~00::-'-:",7:,0,.....,.,,.!-::-0""-:-!,6~0 ~.~ •• ~,~00~22;".-0 -·~

Fig. 3.1 The 6th a n d 25t h degree po l ynomi al c ur v e fit t ing of a measured concentr ation pr o f i l e in the Ti-Ni system~ ( crosses represent the ex perimentaZ points )

îl This profile is taken frorn ref. (10) 23

55.0 5~0

54.5 54.5 SMOOTHED

54.0 UNSMOOTHED

54.0

At.~ .. Ni 53.5 ~3.5

At.% Ni

53.0 ~~ 53.0

",. ,./

/ 52.5 4' 52.5 .~

/ 52.0 / 52.0

51.5 //

~1.5

51.0 / '" 51.0 /

./" 50.5 ;-"'- 50.5

I ,..

50.0 50.0

.,.. U.5

•o.o'-:;2~0 ~.'::-o ~oo;-'-a;!;o;-'-;1,!"00.-'--:"12b0~14;;;-0~1 a"""o ._,,±ao"...._"2boo,....._",2 2!:::-'o 48·0'-2:-'0:~•"="o......"e'=-o --='ao:,-.-,..:1 o-=-o -1,.:.20::--:1-7:4o:-'-:"••O-:o~1 a~o~2~o7o ._,2,:.20=-' - ~m - ~m

Fig. 3.2 Th e 77th degPee polynomial cuPV e fitting of the uncorrecte d and correct e d points of the same concentration profil e as in Fig. 3. 7 (cposses r e present the uncorrected and cor­rected e xp e rimental p oint s

ê!:~I?-~ To get an impression of the difference between the un­corrected and the corrected points a polynomial curve fit is carried out on both series. The polynomial y=a0 +a 1 x+a 2 x 2 +a 3 x 3 + .... +anxn is adapted to the points using the procedure ORTHOPOL, described by Forsythe 2 1 and available in a similar form in nearly every computing centre. This is a least-squa res method using orthogonal polynomials. The degree of the poly­nomial is chosen to be the number of points divided by four. The result is rounded off downwards, but is at least three to obtain a reasonable curve even if only a few points are available. We chose this degree in order that the ratio of the number of points to the number of coefficients in the polynomial should be favourabl e . Experiments have shown that a h i gher degree does not yie ld a better curve. The fitt i ng of the points may b e better, but the curve also exhibits the me asuring errors. Therefore the error in the gradient cannot be reduced further.

The standard deviation in the Nb value s of the polynomial is give n by:

li,[Nbk(measured) - Nbk(calculated) ]'/(m- n-1)]\

24 n is the degree of the polynomial.

ê!:~E-~ In every measuring point a value of Nb (calculated) is determined by means of the polynomial using the YAPPROX procedure, which procedure calculates the y-value belonging to a certain x-value and belongs to the ORTHOPOL procedure.

The x is calculated by (reversed) interpolation between the two nearest values of Nb (calculated).

The integrals of eq.(14) are calculated with the rule of Simpson:

xn XOJ y(x)dx '\.(h/3) ryo+4y +2y +4y + ... +2y +4y +y J (17)

~ 1 2 3 n-2 n-1 n

where h is the step size in the x-direction (xi=Xi- 1+h), nis the number of steps, y 0 , y 1 , ... , Yn are the values of the functions

or

We divided the integration range in n=4m steps (h) ; other step sizes are also possible.

The gradient dx/dNb at a certain Nb is calculated with the derivative of the polynomial:

y = dNb/dx = a 1+2a 2x+3a 3 x 2 + ... +nanxn-l.

The POLCOEF procedure belonging to the ORTHOPOL proce­dure uses the coefficients of the polynomial. vm is calculated with the formula vm= A+BxNb·

This formula is used because the concentratien in a binary system can always be divided into steps where Vm is nearly linear. But other functions are also possible and usable.

ê!:~E-~ Using plot procedures, a graph of the polynomial through the corrected points (crosses) is drawn.

A few more details of the program are given in the flow diagram of Fig. 3.3

25

26

[START)

+ /Reading of the Nb's

r which the Dv has to calculated

+

at be

Calculation of Kn's Initialisation of lower and upper integral totals

+ ( Reading of time and

number of curves

For each curve Do A

For each Nb Do C

0 [Nb in region of this

+yes

curve\

Interpolation of x(Nf) between x [1] and x [m

+ Calculation of integrals x~x(Nb)+ lower integral x::l:x(Nb)+ upper integral

I

0 (~eading of A,B, number of points (m) , data points

+ Correcting data points and platting of corrected points

+ Polynomial curve fitting of corrected points and data points Platting curve

t For each Nb Do B

Calculation of d~ffusion coefficient

no no fNb in region )---\above this curve

t yes

ICalculation of I lower integral

ICalculation of upper integral

Add integral(s) to lower and upper integral totals

Fig. 3.3 Flow diagram of the computer program

3.2 The ratio of the intrinsic diffusion coefficients

Eq. (15) is used for the calculation of the ratio Db/Da.

x

When J -oo

Nb-Nbl -=:.._-=_,dx

vm is denoted by A

I

I

we can write:

( 1 8)

If pure metals are used as starting materials, eq.(18) yields:

A . B ( 1 9)

Eq. (18) enables us to see easily where the Kirkendall interface must lie, depending on whether only the A or B atoms move. From eq. (19) it is clear that the interface lies at the B-side if only B atoms move, and at the A-side if only A atoms move. If we have, for example, a couple consisting of the pure roe tal A and an alloy of the composition AB, sa that Nb 1 = 1 and Nb 2 = ~, eq.(18) is transformed into:

(20)

In eq. (20) neither the numerator nor the d e nominator can be negative. Sa 0 < A/B < 2. The r atio A/B can have values between 0 and 2 only. Sa it is clear that the Kirkendall interface lies at the A-side if only the A-atoms move, and if only the B-atoms move the position of the interface corresponds to B = ~A.

27

C H A P T E R 4

CONSTITUTION OF THE Mo-Ni, Mo-Fe AND Mo-Co SYSTEMS AND PROPERTIES OF THEIR PHASES

4.1 The eguilibrium diagram of the Mo-Ni system and the structure of the various phases

Casselton and Hume-Rothery22 have determined the whole diagram (see Fig. 7.19). The determinations were carried out by means of a combination of thermal analysis, microscopie, and X-ray methods.

~h~_§2~!9_§Q1~~!Q~-Q~-~!_!~-~Q The solubility of ~i in Mo is very slight; at most 1.8 at% Ni at 1362 C.

~h~-~=J~2~!lEh~~~ The homogeneity range is about 2-3 at% and is centred round 50.8 at% Ni according to Pearson23 and round 47 at% Ni according to Casselton et al. 22

The o-phase has a pseudo-tet~agonal unit cell with a= b = 9.108 and c = 8.852 Ä and contains 56 atoms pe r unit cell. However, the structure is orthohombic and the . 2 2 2 2~r25 space group ~s P 1 1 1 •

~h~-r=J~Q~!~lEh~§~ The homogeneity range is very narrow, probably less than 1 at%. The phase has an orthorhombic Cu Ti type of structure with the parameters a = 5.064 R, b = 4.244 R and c = 4.448 R. The phase contains 2atoms per unit cell. The space group is Pmmn 26

~h~-~=J~Q~!~lEh~§~ Casselton et al. did not succeed in obtaining a comple­tely homogeneaus alloy. The composition is in the range of 80.5-81.0 at% Ni. Harker 2 7 found that this phase has a tetragonal structure with a = 5.731 and c = 3.571 R, and showed that the tegragonal c e ll could b e regarded as a superlattice of the f.c.c. solid salution of Mo in Ni. Casselton et al. 22 found a tetragonal structure with a = 5.683 and c = 3.592 R. According to Guthrie and Stansbury2 e MoNi 4 is b.c. tetra­gonal with a= 5.727 and c = 3.566 R with spa ce group I 4/m.

!h~_§Q~!9_êQ!~~!Q~-Q~-~Q_!n_N!

The maximum solubility is 28.4 at% Mo at 1318°c. Casselton et al. 22 give also the lattice parameters as

28 a function of the composition (Table 4.1).

Alloys were prepared by sintering powders at 1250°C.

at% Mo

0 17.1 22.5 24.0 27.0

Table 4.1

a in R 3.5238 3. 5917 3.6179 3.6263 3.6373

Vlasova 29 , Spruiell 30 and Gordon Le Fevre 31 have studied the intermediate structures, formed during the conversion of solid solutions into MoNi 4 • The solid salution exhibits a tendency towards clustering, even at very low concentrations of Mo, which is typical of the ordered phase formed at higher Mo concentration. Saburi et al. 32 reported that alloys containing more than 20 at% Mo, when quenched from the high-temperature a­solid salution region, and subsequently annealed below the periteetic temperature (865°C), do not decompose into 8-MoNi 4 and y-MoNi 3 only, but at the beginning of the decomposition a Pt2 Mo type superlattice (possibly orde­red Ni2Mo) is also formed.

4.2 The equilibrium diagram of the Mo-Fe system and the structure of the various phases

The diagram given by Hansen 33 is essentially basedon work published befare 1930. In 1967 Sinha, Buckley and Hume-Rothery 34 determined a part of the phase diagram, namely the iron-rich side, up to 40 at% Mo (see Fig. 8.11).

~h§_§Q!i9_êQ!~~iQ~-Q~-E~-i~-~Q The solid solubility of Fe in Mo was established by lattice 8arameter measurements 35 . At 1100, 1200, 1300 and 1400 C the solubility is 4.5, 6.0, 7.9 and 11.0 at% Fe respectively.

~h~-<I=I?hèê~ The formula of the o-phase at the Mo-side is considered to be FeMo. The ether two boundaries are not exactly known. The phase is s~able in the temperature range between 1180 and 1540 C. The structure is tetragonal; a= 9.188 and c = 4.812 R, 30 atoms per cell. The space group is P4 2 /mnm36 . Wilsen and Spooner37 confirmed this structure, and calculated the parameters a = 9.218 and c = 4.813 R. ~h~-~=1[~2~Q~li?hèë~ The composition of the -phase has a concentratien range from about 60 to 61 at% Fe. The proper formula would 29

thus be Fe 3 Mo 2 • The crystal structure, however, is based on the A7 B6 type structure and is analogous to Fe 7 W6 and Co 7 Mo 6 and therefore called ~. The lattice parameters of the phase only determined for the Fe-rich side, are: for the rhombohedral cel! a= 9.001 Rand a= 30°38.6', containing 13 atoms per cel!, and for the corresponding hexagonal cel! a= 4.754 and c = 25.716 R3 ~, ~ontaining 39 atoms per cel!. The space group is R3m. Th5 periteetic temperature for the formation of ~ is 1370 c.

~g~-~:E~~~~ Sinha et al. 3 ~ have found a new phase, containing aboub 62.6 at% Fe. The phase is stable between 1245 and 1488 c. On cooling below 1245°C the R-phase decomposes only very slowly and very long annealing times are required to complete the decompositiQn. The space group is c;i-R3 and contains 53 atoms per unit cel!. The lattice para~eter for the rhombohedral cel! is a= 9.016 X and a= 74 27.8'. For the corresponding hexagonal cel! ~he lattice parameters would be a = 10.910 and c = 19.354 Ä.

~hê-~èYêê:2hèêê_~:irê~~QL Zaletaeva et al 38 claims to have isolated the compound Fe 2 Mo from 0.1C-16Cr-25Ni-6Mo steel by electrolytic separation and found it to be isostructural with Fe 2 W. This was confirmed by Elliot 39 •

Sinha et al. 34 , however, found that the À-phase has a hexagonal MgZn 2 -type structure with 12 atoms per cel!. For an alloy containing 66.7 at% Fe, the lattice para­meters are: a= 4.745 and c = 7.734 R. The formation of the phase is very slow. None of the other inve stigators have found this phase.

!h~_§Q1!Q_§Q!~!!Q~-Q~-~Q_!~_[ê

Hansen 33 reports a maximum solubility of Mo in Fe of 26 at% at 1450°C. The vertex of the Ó-loop was found to !ie at about 1.6 at% Mo at 1150 C.

4.3 The equilibrium diagram of the Mo-Co system and the structure of the various phases

Quinn and Hume-Rothery40 determined the diagram in 1963 except for the a/S Co transformation (see Fig. 9.14). The structure ofa-Co is f.c.c. and S-Co has the close­packed hexagonal structure. The alloys were pre pared from powders which were pressed into smal! bars, and these were subsequently sintered in hydrogen. After annealing and quenching, the alloys were examined

30 microscopically and by X-ray diffraction.

!h~_§Q1~Q_§Q1~~!Q~-Q~_ÇQ_!~-~Q

Quinn et al. 40 found the solub~lity of Co in Mo at the periteebic temperature of 1620 C to beat most 11.5 at%. At 1250 C the solubility was about 2 at% Co.

!h§_~:JÇQ2~Q~l2h~§~

The Mo-rich boundary of the O-phase lies between 63 and 64 at% Mo and is almast vertical. It decomposes eutec­toidally at 1250°C. Forsyth and d'Alta da Veiga 41 found that the a-phase is tetrag~nal with lattice parameters a = 9.2287 and c = 4.8269 Ä. The unit cel! contains 30 atoms and the space group is P4 2 /mnm.

!h~_g=JÇQz~QilQh~~~

This phase extends from 54.5 to 49.5 at% Co at 1335°C. With decreasing temperature the homogeneity range narrows on the Co-rich side. According to Forsyth and d'Alta da Veiga 42 the ~-phase (containing 46.15 at% Mo) has th5 rhombohedral Fe 7 W6 structure with a = 8.970 g, a = 30 47', 13 atoms per unit cel! and space group R3m, or for the ~orresponding hexagonal cel! a= 4.762 and c = 25.615 Ä.

!h§_~:JÇQl~Ql2h~§~

This phase is formed below 1030°C by a peritectoid reaction between the ~- and the 8-phases and possesses a narrow composition ran1e. In an alloy containing 75 at% Co, d'Alta da Veiga 4 found that the K-phase possesses the hexagonal Ni 3 Sn-type structure with a= 5.1245, c = 4.1125 and c/a = 0.8025 and 2 atoms per unit cel!. The space group is P6 3 /mmc. This is a super­lattice of the close-packed hexagonal structure with a doubled a-spacing and a halved axial ratio.

!h§_~:JÇQ1~Qll2h~§~

This phase has been found by Quinn et al. 40 and is not included in Hansen's 33 diagram. The 9-phase has roughly the composition Co 9 Mo 2 and is r e late d to the close­packed hexagonal structure. The diffraction lines of an alloy containing 18 a t % Mo were inde x e d by Quinn et al~ 0

as fitting a hexagonal cell with a = 2.5973, c = 4.2123 ~ and c/a = 1.6218 at 1100°C. The 8-phase is formed peritectoidally at 1200°C by reaction between the ~-phase and a-co and decomposes eutectoidally at 1080°c.

The sol i d salution of Mo in Co ------------------------------Quinn e t al. 40 observed that this solid salution when quenched from the f.c.c. area always partly transfarms into the close-packed hexagonal structure. The maximum solubility they found was about 17 at% Mo at 1335°C. 31

C H A P T E R 5

DIPFUSION IN THE Mo-Ni, Mo-Fe AND Mo-Co SYSTEMS

5.1 Diffusion in the Mo-Ni system

Davin et al. 44 investiga5ed the interditfusion of Mo and Ni between 1000 and 1300 C, using Ni-Mo91.3Ni diffusion couples. (Designations like Mo91.3Ni will be used throughout this thesis to denote a Mo-Ni alloy contai­ning 91.3 at% Ni.) The concentratien vs. penetratien curves were established by an electron microprobe. The diffusion coefficients were calculated by Grube's method. For Q and D0 , 64.4 kcal/mole and 0.853 cm 2 /sec, respectively, were found.

Swalin et al. 45 have also investigated the interdit­fusion of Mo and Ni, employing Ni-Mo99.07Ni diffusion coup6es. The temperature interval they used was 1150 to 1425 c. The concentratien in the diffusion zone was determined chemically by means of sectien analysis. The diffusion coefficients were also calculated by Grube's method, and from these Q was found to equal

2 68.9 kcal/mole and D0 3.0 cm /sec.

While the results of Davin et al. 44 and Swalin et al. 45

are in reasonably good agreement with each ether( there is a great discrepancy with the results of Budde 6 •

He calculated for the activatien energy a value of 50.8 kcal / mole and for the frequency factor a value of 0.0314 cm 2 /sec. He used diffusion couples of the type Ni-Mg79.2Ni and annealing4 tem~er~t~fe~ of 11f0 and 1290 C. Kalinovich et al. ' 4 ' ' ' 1 ' 21 have investigated the diffusion of Ni and Mo in a number of Mo-Ni alloy~ in an electric field (Table 5.1). They used Ni 63 and Mo 9 radio-active isotopes. Direct current heated the specimen and induced an electric field. From a great number of experimental values D were calcu­lated. In all cases log D vs. 1/T plots were straight lines so that Q and Do could be calculated.

The diffusion coefticients of Mo in Ni were determined by Bgrisov et al. at temperatures between 900 and 1200 C. Ni was electroplated with radio-active Mo. No marked boundary diffusion was observed. The found Q = 51 kcal/mole and D0 = 1.6x10- 3 cm2 /sec.

The same authors55 studied the diffusion of Ni in Mo. Mo slices were chemically plated with radio-active Ni.

32 Diffusion annealing was performed at temperatures between

Table 5.1

Ac ti vation energies and frequency factors for Ni and Mo ditfusion

in a number of Mo-Ni aZZoys in an electric field

Alloy Ni ditfusion Mo diffusion T 0 c Ref 0 Do Q Do

Ni 60.5 9.96 47 Mo92Ni 56.4 2.55 54.9 1. 31 1000-1400 48 Mo80Ni 48.8 0.1 9 50.3 0.25 950-1300 49,50 Mo84Ni 52.2 0.63 54.6 1 . 30 950-1300 51,52 Mo77Ni 47.4 0.12 49.5 0.20 1100-1300 53 Mo82Ni 50.4 0.34 52.2 0.45 950-1400 47

900 and 1200°C. Diffusion coefficients were determined by the technique of removing thin layers (2-10 w) and measuring the residual integral activity of the specimen. For the Ni diffusion in Mo, Q was calculated to be 85 kcal/male and D0 62 cm2 /sec. Hashimoto and Tanuma 56 have investigated recently the mutual diffusion welding of Mo using intermediate mate­rial, such as Ni and Fe. Belgw 900°C Ni appears to be more suitable than Fe. From 900 C the strength of the joint decreased with increasing welding temperature because gf the formation of an inter­metallic compound. Above 900 C Fe is preferable.

5.2 Diffusion in the Mo-Fe system

Krishtal et al. 57 have investigated the interditfusion of Mo and Fe in a d6ffusion couple consisting of the pure metals at 1250 C and after annealing for 10h. The ditfusion zone is 350w + 20w and the diffusion coeffi­cient of Mo in Fe was found to be 6.6x10- 9 cm2 /sec. Borisov et al. 58 studied the diffusion of Mo in pure Fe and in an Mo99.3Fe alloy. The specimens were poly­crystalline with a grain size of approximately 5-10 wm. The radio-active isotape Mo 99 was used, being electro­plated on the surface. The diffusion coefficients were determined in two ways, viz. by the absorption method and by layer-wise analysis. The latter me thod yielded mean coefficients (Dm) which characterised the total flow in the volume and gra in boundaries. In the absorp­tion method both the bulk and the boundary diffusion were determined separately. The results are summarised in Table 5.2. 33

34

Table 5.2

The aativation energies and frequenay factor s of the diJfusion of Mo 99 in pure Fe and in an Fe-Mo alloy,

using two different measuring me thods

Methad Q kcal/male ~0 cm 2 !_sec Remarks

Layer-wise 49.0 0.3 Dm in pure Fe Absarptien 73.0 7.8 x 1 0 3 Dvol i.n pure Fe Layer-wise 64.0 2.24 x 1 0 2 Dm in Fe-Mo alloy

1 0 4 Absarptien 75.0 1 . 3 x Dvol in Fe-Mo alloy

The temperature range was 750 to 900°C. The mean acti­vation energy determined by layer-wise analysis is seen to be lower than the corresponding energy for pure volume diffusion. This is due to the influence of grain boundaries, which is much less in the Fe-Mo alloy. Pivot et al. 59 studied the diffusion between Fe and Fe 15-20 wt% Mo alloys consisting of a(solid salution of Mo in Fe) and ~(Fe 7Mo 6 ). The penetratien curves were determined with a microprobe. The activatien energy was calculated to be 60.0 kcal/male and the freque ncy factor 10 cm2 /sec for the a-solid solution.

Rawlings and Newey 60 investigated the system using Fe-Mo

~!;!~s!~~ ~~~~~~!d !~et~~~~;:~u;:~eb:~~~:~i~~~ 1~n~r~~05°C. They were examined with a mieroprobe (see Table 5.3) and a micro-hardness analyser. The hardness of the R- and ~-phases were 955 and 1054 kg/mm 2 Hv· The authors do nat mention the solid solutions.

Table 5.3

Phases ident i fied in the diitusion couples (Rawling s et al. )

(th e aompositions of the phases are only averages )

Treatment R- phase d Jl-phase d o-phase d at% Fe ].lm at% Fe )llTl at% Fe )l ffi

192 days 800°C 60.0 6 81 days 900°C 57.2 11 12 days 1125°C 61 . 0 47 6 ~ days 1255°C 63.0 1 0 60.5 1 0 + 3

6 days 1320°C 69.4 10 58.4 15 + 3 H day 1405°C 62.3 3 50.3 5

+ present, but the layer was toa thin to allow proper determination of the concentration.

Seebold and Birks 61 have annealed a Fe-Mo sandwich couple at 1100°C for 66h and examined it with a microprobe. A 30 ~m thick diffusion zone with the composition 37-39 at% Mo (~-phase) was found to be present. The Fe-~ inter­face showed a continuous crack. The investigators con­cluded that no solid solutions were formed in the couple.

5.3 Diffusion in the Mo-Co system

Interdiffusion coefficients for mutual diffusion of Co and Mo were already determined in 1955 by B~ron and Lambert 62 at 900, 11go, 1275, 1500 and 1700 c. For runs at 900, 100 and 1275 C, Co-Mo couples were prepared by inserting a Co rod into a hollow Mo cylinder and the thickness of the diffusion layers was determined as a function of the time. The diffusion coefficients were determined, using the formula B2 = 4Dt, where B is the width of the diffusion zone. For runs at 1500 and 1700°C, the inner rod consisted of an ~1loy of Mo + 3.42 wt% Co. The couples were heated for 95h in an H2 atmosphere. The penetratien curves were determined by means of chemical analysis of machined chips of 250 ~m thickness. In these cases the Boltzmann-Matano method was used for calculation of the diffusion coefficient. Byron et al. derived an activatien energy of 34.8 kcal/mole, and a frequency factor of 2.82x10- 6 cm 2 /sec.

Davin et al. 44 have studied the interdiffusion of Mo and Co also gsing Co-Mo90.2Co diffusion couples between 1000 and 1300 C. Values of 62.8 kcal/mole for the activatien energy and 0.231 cm 2 /sec for the frequency factor were found. For the diffusion of Co in Mo (Mo was electroplated with radio-active Co) at temperatures between 1000 and 1300°C Borisov et al. 55 calculated Q to be 77.5 kcal/mole and D0 6 cm 2 /sec.

35

36

C H A P T E R 6

EXPERIMENTAL PROCEDURES

6.1 Introduetion

In principle the experimental procedure was as fellows:

(a) Preparatien of diffusion couples of pure metals or alloys.

(b) Annealing at a certain temperature. (c) Metallographic preparatien for investigation

purposes. (d) Continuatien of annealing, if necessary.

6.2 Preparatien of the diffusion couples

A large number of different diffusion couples were pre­pared. In fact, in a number of cases sandwich couples consisting of three different materials were prepared, e.g. Mo-Mo62.0Ni-Ni. Often two-phase alloys were used, because the single-phase alloys were mostly very brittle and difficult to handle, e.g. the 8-phase, and the ~­phases in the Mo-Fe and Mo-Co systems. In Tables 6.1 and 6.2 details are given about the purity of the metals used. The carbon present in Ni (MRC1) caused the hardness to increase from 175 to 270 kg/mmz. Annealing has a very great influence upon the hardness. No significant difference in diffusion behaviour between the nickel supplied by Halewood or (MRC2) was noticed.

Table 6.1

Vickers micro-hardness of the starting materials; load 50g

Me tal

Ni (MRC1) Ni (MRC2) Ni(halewood) Ni (MRC1) Ni(MRC2) Mo(Drijfhout) Fe (MRC) Co(MRC) Co(IviRC)

Treatment

as received as received as receiged 89h 1300 c 89h 1300°C as receive d as received as rece ived melted

!!v kg/mmz

271 175 177 11 8 11 6 304 208 218y 218à

à the identations have peculiar shapes. (all values are averages over 10 measurements).

Table 6.2

Typiaal analysis of the pure metals in ppm by weight

Element

c Mg Al Si s Ca Mn Fe Ni Cu Pb 0 N H Be Cr Co Mo Ag p Ta Sn w V Ti Zn Zr DR

Ni (Hal) 1l

50 < 2

25 < 7

< 8 <30 bal

6 <40

<70 <40

3

<30

Hal Balewood DH Drijfhout

Ni (MRC2)

50

5 <10

5 bal <15

20 < 5

1

2

10

Ni (MRC1) ik

600 15 45 45

250 bal

1 0

150

2

Mo (DH)

50

100

30 2 3

bal

200

Fe (MRC)

30 < 5 <10

35 30

< 5 20

bal 1 0 40

<10 78

< 3 < 2 < 5

1 0 10

<50

20 <10 <40 <10 <10

<10 <10

Co (MRC)

40 2 3

<10 < 8 <10

3 400 120

1 0 < 1

bal

ik perforrned by Analytical Laboratory, N.V. Philips, Eindhoven, Netherlands

DR distillation residues

The binary alloys were prepared by are rnelting Mo and either Ni (Hal or MRC2), or Fe or Co in the proper weight ratio and in an argon atrnosphere. Each sample was rernelted five tirnes in orde r to obtain the desired hornogeneity. The loss of weight was less than 0.2 wt%. Portions of 5 to 7g were melted. In larger portions (10g) pieces of Mo were still present. Three or four portions 37

of an alloy of 5 to 7g each were remelted in the same furnace in a special mould to obtain a bar of 10 mm in diameter. Each bar was annealed in a silica capsule for some period of time and at a certain temperature depen­ding on the temperatures at which the alloy was used as starting material in diffusion couples. Each bar was sawn into 1-2 mm thick slices, using a 1 mm carborondum or a diamond blade, dependent on the nature of the mate­rial. After this, the slices were ground on wet silicon carbide papers of various grades, the finest being 600.

Polishing after grinding caused no significant difference in the diffusion behaviour. After thorough degreasing, the slices of the couple constituents were subjected to a sli~ht pressure, and spot-welded in a vacuum of 1x1o- Torr. Electron probe micro-analysis of the asbounded specimens showed interditfusion due to this bonding treatment to be insignificant.

The diffusion couples were annealed at temperatures be­tween 800 and 1300°C in silica capsules in a vacuum of 10- 2 mm Hg. The temperatures were measured by means of a Pt-Pt (10 % Rh) thermocouple with an accuracy of~ 2°C and recorded continually. After the heat treatment the specimen was rapidly cocle d (Ni-Mo system) o r que nche d by dro pping the capsule into water and i mme dia t e ly breaking it (Fe-Mo and Co-Mo systems). The couple was mounted in epoxy resin. A cross-sectien of the diffusion zone, sufficiently remote from the edge to eliminate the effects of surface diffusion, was ground and polished in a plane parallel to the direc tion of diffusion using 0.05 ~m Al 2 0 3 on a soft cloth . The samples were washe d and e tched in a mixture of equal volume of c o ncentra t e d HN0 3 , H~SO~ and H3 PO in orde r to ma k e visible the phase beundarles for metaliographic analysis. To reveal the boundary Co-a solid salution in the Co-Mo system, the couple was first etched in a mixture of concentrated HN0 3 with water 1:1.

6.3 Microscopie e xaminatien

Microscopie examinatien of the diffusion layer and measurement of the layer thickness were carried out with a Reichert Neepan microscope using a calibra ted filar microme ter eyepiece. By this methad inf ormation was obtained regarding the number of pha s e s in the coup l e and the ir layer thickne sses in dependenee of time and tempe rature. Very aften the marker inte rface was also visible in t he microscope and the position of it was measured. Photo-

38 graphs were made u s ing a Re ichert MeF microscope .

6.4 Mieroprobe analysis

For determining concentratien versus penetratien profiles an AEI-SEM IIA electron probe micro-analyser was used. The X-ray intensities obtained with the mieroprobe have to be converted into concentratien units. Normally, one of the various theoretically based correction procedures is used. The conversion into concentratien units can also be carried out by using calibration standards 63 •

Up to now it is generally accepted that only single-phase standards can be used to set up a calibration curve, but as shown by Bastin, Heijwegen, Van Loo and Rieck 64 , poly­phase alloys can also be employed as standards, provided that some conditions (see below) are fulfilled. The main reasen why standards are used is the reliability of the methad and its independenee of possible instrument error.

The systems which have been investigated in our labora­toryare Ti-Ni 65 , Ti-Al 66 , Ti-Cu, Mo-Ni, Mo-Fe and Mo-Co. We shall mention here the results of the last three systems.

In all cases the Ziebold-Ogilvie relation 63 is shown to be valid:

where:

(21)

the relative intensity IA/I~ X-ray intensity of component A from a certain a rea of an a lloy A- B

X-ray intensity of component A from an equally large area of the pure reference metal A

weight fraction of component A in the alloy A-B MB

a cons tant equal to aA . ~ , where aA is a con-stant and MB and MA are th~ atomie we1ghts of the elements B a nd A, respective ly

male fraction of the component A iri an alloy A-B

The cons tant s aA and AA should be depende nt only on the a lloy s ystem and the epe r a ting c o ndi tions for the ana­l y s i s . A great numbe r of s tanda rds have been used. Only a minority were purely single-phase alloys. Whether poly­phase alloys are suitable as standards or not, depends on the following conditions: 39

(a) the alloys have to be macroscopically homogeneous, i.e. any cross-sectien has to be representative of the whole sample,

(b) microscopically, i.e. the grain size of the various phases has to be smaller than a certain value which is determined by (i) the measuring method, and (ii) the curvature of the calibration curve.

The region from which the X-rays originate may be a small area around the electron beam, focussed upon the samples (point measurement) , or a square of variable size over which the electron beam is scanned (scan measurement). If polyphase alloys are investigated, it will be clear that point measurements will not work be­cause of the tremendous number that is necessary to give a reliable average result. Therefore, scan measurements have to be performed. In fact, a calibration curve is required only to verify the validity of the Ziebold-Ogilvie relation. After this verification we can calculate the concentrations using this relation.

The alloys were melted as described in sectien 6.2. They were prepared for mieroprobe investigation by in­serting them in conducting resin and grinding up to 600 grit silicon carbide paper, followed by polishing. The alloys were not etched. In order to determine the value of KA, a representative value of IA for the alloy surface was obtained by scanning 30-100 different squares and counting the pulses of element A radiation for 10 seconds. Befere and a fter the measure ment, 10 squares of equal size of the pure roetal A were examined under the same conditions. The size of the scanned areas (100x 100 ~m to 25x25 ~m) was adapted to the microstructure of the alloy and the choice of the accelerating voltage. The results for our systems and eperating conditions are shown in Table 6.3 and in the Figures 6.1 (a, band c).

When recording the penetratien curve in a diffusion couple, point measurements were carried out under the same eperating conditions as in the calibration mea­surements. The steps in which the diffusion couple was movedunder the electron beam were at least 2.5 ~m. The movement was parallel to the direction of the diffusion, and the interface in the couple was oriented paralle l to the X-ray take-off path in orde~ to avoid absorption effects. Owing to several edge ,, ffects, however , the concentratien at the interface could not be determined accurately within a distance of about 2 ~m of the phase

40 interfaces (see also Chapter 7).

0.8

K

1 0.6

0.4

0.2

0.80 K

10.60

0.40

0.20

I I I

Mo-Ni ~

0.80 /: / Mo-Fe ;" K /? I I 0.60

/. ./ .Mo OAO

~.Ni 1

"1 20 40 60 ---at%Ni

80 100

• Co,25Kv o Co,30Kv

/ ' • Fe,20Kv

0.20 o Fe,JOKv

20 40 60 80 100 --at% Fe

Fig. 6.1

20 40 60 --at%Co

80 100 Calibration curv es for t he var ious sy st ems

Table 6.3

Surve y o f t he aalibra tion data in Mo -Ni , Mo - Fe and Mo - Co s y stems .

The X-ray take-off a ngZe is 22 . 5° ; the probe current is 0 . 2 WA.

Number of System standard Radiation Crystal KV ~A ~A

alloys

Mo-:tH 13 Ni Ka LiF 30 1 . 7 4 1. 06 7 MoL a Mica 30 1 .1 5 1 . 8 8

Mo-F'e 1 0 Fe Ka LiF 20 1 • 81 1 • 05 6 Fe Ka LiF 30 2.04 1 .1 9

Mo-Co 11 Co Ka LiF 25 1. 78 1 . 09 4 Co Ka LiF 30 1 . 89 1.16 41

42

6.5 X-ray diffraction

To identify the various phases formed in the diffusion couples by means of X-ray diffraction, the layers have been successively ground in a plane parallel to the contact interface in order to get diffractograms of the phases. After each abrasion of material, a CuKa diffrac­togram was made from the surface of the sample, using a Philips PW 1010 X-ray diffractometer. Slices of alloys were also investigated in a similar way, to identify the phases present in the alloy.

6.6 Micro-indentation hardness testing

Hardness measurements were carried out using a Leitz "Durimet" hardness tester applying a load of mostly 50g to the Vickers diamond . The hardness of the starting materials was measured and also in the diffusion zone in various couples in the systems. In this way the hard­ness in the various phases were measured and qualitative penetratien curves were obtained. The samples were not etched.

C H A P T E R 7

DIPFUSION IN THE Mo-Ni SYSTEM

7.1 Exoerimental results

7.1.1 ~~Y~E_gEQ~~~-~~~ê~E~~~~~ê We will discuss the layer growth of the a-solid solution, the 6-(MoNi) phase and the y-(MoNi 3 ) and B-(MoNi4 )

phases for various types of couple. The Ni uöed in cou­ples which were annealed at 800, 850 and 900 C was given a grain coarsening treatment at 1300°C for 64h, in order to diminish grain boundary ditfusion effects.

~~Yêf_gfQ~tb_Q~_tbê_~=êQ1!9_§Q!~t!QD

In a temperature range of 800 to 1295°C, the Mo-Ni, Ni-Mo62.0Ni, and Ni-Mo77.6Ni couples were investigated. In Chapter 2 it has been mentioned that grain boundary diffusion is only important at relatively low tempera­tures. This effect is clearly demonstrated in the growth of the a-solid salution in the various ditfusion couples. At 800 and 900°C grain boundary diffusion was the most important process, which yielded a very irregular solid salution layer (Fig. 7.1). Etching in dilute HN03 showed

Fig. 7.1

Optieal micrograph of a Mo-gi coupled annealed at 800 C for 282h. SOOx. Etchant was dilute HN0 3

that the Mo atoms penetrated the Ni via its grain boun­daries. Whe n no grain boundaries were pre s e nt along the interface, the a-solid salution layer as as good as absent: a lmest only volume ditfusion had take n place . Therefore , me asurements were always carrie d out at places of slight layer thickness in order to 0educe the effect of grain boundary diffusion. Above 900 C volume ditfusion became the most important mechanism. 43

In the Ni-Mo62.0Ni couples the diffusion behaviour of the a-solid salution was identical with that in the Ma-Ni couples, tgough the thickness of the a-solid salution below 1000 C was more regular. The Figs. 7.2 and 7.3 represent the results of the above measurements. The factor n (see sectien 2.6) can be 8alculated if log d is plotted against log t. Above 1oog C the n-values lie reasonably close to 2. Below 1000 C the n-values are larger than 2.

300

250

200

150

100

4 6 8 10 12 -1Y:.,hY2

Fig. 7. 2

Layer growth of the a­solid solution in Mo-Ni coupl es

300

12oo·c

250

200

115o•c 150

/,oo•c 100

1ooo·c

~t~.h% 10

Fig. 7. 3

Layer growth of the a­solid solution in Ni­Mo62.0Ni co upl es

15

In table 7.1 the penetratien constants (k), as calcula­ted from the d-It plots, are given. Below 1000°C, k

44 could not be calculated because of the curved lines.

Table 7.1

Penetration constants (k) of the a-solid salution in cm 2 /sec

T 0 c k in Mo-Ni k in Ni-Mo62.0Ni COUJ2les COUJ2les

1296 4.86 x 1 o-9 6.51 x 1 o-9 1250 2.56 x 1 o- 9 3.03 x 10- 9 1200 1. 22 x 10- 9 1 . 3 7 x 1 0-9 1150 5.92 x 1 o-1 o 5.92 x 1 0 -I 0

11 00 1. 9 8 x 1 o-1 o 2.53 x 1 o-1 o

1000 3.47 x 1 0 -I I 4 .17 x 1 0-I I

In Fig. 7.4 the logkvalues determined in Mo-Ni and Ni-Mo62.0Ni couples are plotted against 1/T; the acti­vation energies (Q) and the frequency factors (k0 ) were calculated by the least squares method. In the Mo-Ni couples Q = 67.1 kcal/mole and k 0 = 10.8 cm2 / sec; in the Ni;Mo62.0Ni couples Q = 67.7 kcal/mole and k0 = 15.2 cm /sec.

1öa,-_1_3ro_o __ 1_2ro_o ___ 1,1,oo ____ ~1o~o~o

\o 5 x

\o )(

2 \ )(

\ \

\ k,cm%ec

1

5

2

5

x Mo- Ni couples \

2 o Ni-Mo 62.0 at% Ni couples

10-11 '-----'-------L------'----' 6.0 6.5 7.0 7.5 8.0

-10-yT,K-1

Fig. 7.4

Pl ot of lo g k vs. 1/ T f or t he a-sol i d s alu t ion in two typ es o f c oup le 45

Ni-Mo77.6Ni couples were annealed at 800, 850 and 900°C. Only the a-solid salution was formed. In these cases d-(f plots yielded curved lines (Fig. 7.5). The diffu­sion is much faster than in the ether couples at these temperatures .

80

60

40

20

2 4 6 8

-~ time'12 ,days'l>

900'C

8so'c

10

Fig. 7. 5

Layer growth of the a­soZid salution in Ni ­Mo? ? .6Ni coupZes

The 600 ppm carbon present i n the Ni has no inf luence on the diffusion behaviour in the Ni-Mo626 0Ni couple with regard to the a-solid salution at 1295 C (see also Chapter 10).

~~Y§E_9EQ~~t_QÎ-~hê_§=l~2~!l2b~êê Mo-N~ couples have been investigated between 800 and 1295 C and Mo-Mo62.0Ni couples between 1100 and 1295°C. In Mo-Ni couples the variatien in the o-(MoNi) layer thickness was v e ry large at all temperature s. Same times there was a great difförence between two cogples at ene temperature (e.g. 1200 C). At 1100 and 1150 C the growth of the o-phase in Mo-Ni couples was equal to that in Mo-Mo62.0Ni couples, but above 1150°C the deviation was very large. Therefore, only the measurements of the o-(MoNi) layer growth in Mo-Mo62.0Ni couples have been used for the calculation of p e ne tra tien cons tants. I t fellows from Fig. 7.6 tha t forthe s e couples the layer thickness is proportional to /t, indicating a volume diffusion mechanism. The penetratien constants are given in Table 7.2.

In Fig. 7.7 log k is plotted against 1/T, yielding a straight line. The activatien e nergy (Q) a nd fr e que ncy factor (k0 ) have been calculated by the least squares me thod. Q is 83.9 kcal/male a nd k0 is 172. 3 cm 2/sec. Two different Mo-Mo62.0Ni couples were investigated at 1150°C. We found a rather great difference in the value

46 of k. The o-phase in the couple with the h i ghest k value

Fig. 7.6

Layer growth of the ö­(MoNi) phase in Mo-Mo62.0Ni couples

1300 1200 1100 1000 1Ö9r---~---,----~------TO

5

2

5

2

5

2

T,°C-

\ \

cm2/ k, /sec

1

\ ~2~----L-----L-----L---~

10 8.0 8.5 7.0 7.5 8.0

- 1oj''f. K-1

Fig. 7. 7

Plot of Zog k vs. 7 /T for the ö-(MoNi) Zayer in Mo­Mo62.0Ni couples

Ta:tle 7.2

Penetration constants (k) of the ö-(MoNi) phase in Mo-Mo62.0Ni couples

T oe k in cm 2 /sec

1295 3.95 x 1 o-1 o

1250 1. 50 x 1 o-1 o

1200 7.03 x 1 o-1 1

11 5{) 1 . 93 x 1 o-1 1

1100 9.31 x 1 o-1 2

appeared to contain isolated grains of another phase. At first these islands occurred at the MoNi-Mo62.0Ni phase boundary, but after some time they were found completely inside the ö-phase. Evidently, these islands 47

were present in the couple from the start. The Ni content in these islands was determined with the microprobe. The Ni content varied from 49.0-49.5 at% Ni.

Fig. 7.8

Optical micrograph of a Mo-Mo62.0Ni couple annealed at 120ooc for 85h. 500x. Island s of the n-(Mo 6 Ni 6 C) phase are visibl e i n the 8-(MoNi) Z2yer.

By comparison with the results given in Chapter 10, it was found that the islands consisted of the compound Mo 6Ni 6C (compare Fig. 7.8 with Fig. 10.5). The occurrence of this compound cannot be explained by the presence of carbon in the alloy, because the islands were nat present in all couples. We rather think that impuritie s on the surface of the couple constituents, perhaps SiC, intro­duced by abrasion, cause the formation of the carbide compound at the beginning. In spite of very good degrea­sing and ultrasonic cleaning of the surfaces of the specimens in alcohol these islands appeared in the o­layer from time to time and mostly at the edges of the couple. It is suggested that they are responsible for the greater layer thickness and indicate the very large influence of small impurities on the ditfusion behaviour in a ditfusion couple.

~~Y~E-SE~~~~-~f-~~~-Y:i~~~~ll_~~~-~:i~~~~~l_E~~~~~ The layer growth was studied at 800, 850 and 900°C. The layers formed in the various ditfusion couples (Mo-Ni; Ni-Mo62.0Ni and Mo77.6Ni-Mo62.0Ni) were very irregular and, therefore, we restriet ourselves to some remarks.

In Mo-Ni couples at 800 and 850°C we found, apart from the a-solid salution and the MoNi phase, an easily detectable MoNi 4 layer and sametimes only very thin layers of the MoNi 3 phase . At 900°C only the a-solid salution and the MoNi Bhase are formed. In Ni-Mo62.0Ni couples at 800 and 850 C a layer of MoNi 4 was formed tagether with the a-solid solution. 0 Mo77.7Ni-Mo62.0Ni in the couples, at 800 C only a very

48 thin and irregular MoNi 3 layer was visible. 57 Days of

annealing were required to ob~ain a regular layer of about 26 ~m thickness. At 850 C a regular and 31 ~m thick MoNi 3 layer was present after 28 days, and after 75 days the thickness was even 46 ~m (Fig. 7.9).

Fig. 7.9

OpticaZ miarograph of a Mo62.0Ni-Mo7?.6Ni coupZe anneaZed at 850°C for 75 days. y-(MoNi 3 ) is formed between the aZZoys. The aZZoy at the top of the micrograph is the Mo77.6Ni aZZoy. m is the marker interface. 500x.

The layer consisted of small grains at the Mo-rich side and of big grains at the Ni-rich side. The inter­face where the morphology'~hanges is the Kirkendali interfgce, which can also be observed in Fig. 7.9. At 900 C no layer was visible despite good contact.

7.1.2 ~~~~QE~Q~~-~~~§~~ê~~~t§ A very great number of concentration-penetration curves have been determined in all types of couples using NiKa radiation. These curves were used for the calculation of the interditfusion coefficients (Chapter 3) and for the determination of the phase diagram (section 7.2.1). MaLa radiation was nat used because of the very low intensity and the high background radiation.

~Q=~~-~Q~E!êê Penetratien curves of 20 diffusion couples were deter­mined. In Fig. 7.10 a few of them are represented. It is clear that the a-solid salution has a very large homogeneity range and that the boundary concentratien shifts to higher Mo contents with increasing temperature. The homogeneity range of MoNi is constant. A very small amount of Ni is soluble in Mo.

~~=~Q§~~Q~~-~Q~E!ê§ The concentratien curves of 17 ditfusion couples were determined. Same of them are represented in Fig. 7.11. Below 900°C a MoNi 4 layer was formed between the a­solid salution and the alloy.

~Q=~Q§~~Q~~-~~g-~Qi1~~~~=~Q§~~Q~~-~Q~E!~§­Penetration curves were determined in 15 Mo-Mo62.0Ni couples. Four of them are given in Fig. 7.12. In all 49

100

60

-o-o~.R=""---•T-'.,...,t:f.,:i;O-""t ·• ·r-·•-;.--• -o-o-o-o ~-~ .-•.:.-•4::1~• ·"

_.D_ o-o A·_!{·~----·- .~...-v6 !~ ,' , at%Ni __" ~.. ,~

- o-o •-•-:J"7 . Jt(,.. ! J ,../ I ....-o....-o __ • ...-.- .r"' / I 282 h goo·c 1 ~82 h

25ht29s'co-"""·---_:_....--.- f• 70h110o'c(' ' 1· "-... · 8oo·c

1

.- Î 81 h 12so·c h tt5o ·c --...-.... x 124 h tooo·c

1 I / Î j. t_.,..-J .- I 1

80

20

J 00~~~~~----~~~~~------~~~~--~~----_L--~~~~--~ 50 100 150 200 250 300 350

- dist•nce.jlm

Fig. 7.10 Penetration ourves in some Mo -Ni couples

40_L_ ______ l_ ______ ~ ______ _L ______ _J ________ l_ ______ ~ ______ _u

0 100 200 300 400 500 600 700

distance, ~m

Fig. 7.11 Pe n etrat ion curves i n some Ni-Mo62. 0Ni coupZes

cases a thin layer of solid salution of Ni in Mo was formed, tagether with the MoNi layer. At 100 and 1200°C penetratien curves were determined in Mo41.2Ni-Mo62.0Ni couples and in the Mo26.7Ni-Mo62.0Ni

50 couple annealed at 1237°c (see Fig. 7.12).

at %Ni

' 60 -~;h-,~;r-~-- ---- -------r-r ~,"i;Oh1200"C 44h1250"C ~

40

20

everege cucentretion of two-phue elloys

____ I_ ____ ----

J J 0o~~--~5~0~--~,~o~o~~~,~5~0~~~2~o~o----~2~5o~~--~3o~o~----3~5~o~---.4~oo

----- diatence.J'm

Fig. 7.12 Penetration curves in some Mo-Mo62.0Ni couples

~~:N922~§~~-~~9_NQ22~§~~:NQ§~~Q~~-QQ~E1~ê In Fig. 7.13 three curves determined in Ni-Mo77.6Ni couples are shown. Only the a-solid salution was formed. Its penetratien curve was mostly irregular6 perhaps caused by grain boundary diffusion. At BOO C the MoNi 4 phase was present at some places. The curve dete0mined in the Mo77.6Ni-Mo62.0Ni couple, annealed at BSOCis given in Fig. 7.14.

100

70

0

at% Ni

1

average concentration of two-phase alloys

50 100 15

-distance .pm

Fig. 7.13 Penetration curves in some Ni-Mo77.6Ni couples

200

51

100r---------------------~

ALLOY i 90 Mo62.0, y-MoNi3

at% Nii

: ALLOY : Mo77.6 I

:at% Ni z ~80 -"' o·b ·

,oooaoooaoooooooooaoooaO"b',. ·,b...J'/

ro i 60\ 7

b-.O·-o'

50

0 20 80 100

Fig. 7.14

Penetra tion ourve i n t he ooupl e gi ve n in Fig. ? . 9

Pe netra tien annealed at the couples formed. Two

~~~~~s 1 ~~~~ ~~~~~m~~;~ !~dt~~~~o~~ui~e~11 the phases a-solid salution and MoNi were examples are given in Fig. 7.15.

100 - - - - - - - - - - - - - - - - - - - - ~_:0::::.-.o =a - -~~-=-=-·-=-=--..=-=--

., /. Ni .--o.-o~_.----

1 40h12oo;.,..o-<>~ .........---.-• : ( ('""""' 40 --~ c ------------------- --20

j . average cancantrat1on of lwo-phaso olloys

0o~----~5~0------~1~00~----~15~0~----2~0~0~--~2~5~0~--~ disluco. pm

Fig. 7.15 Pe ne tration ourv e s in two 52 Ni - Mo 47.2Ni ooupl es

~~=~Q~Q~Q~~-fQYE!~ê Penetratien curves were determined in the cougles annealed at temperatures between 1100 to 1295 C and one example is given in Fig. 7.16. Only ~-solid solution of Mo in Ni is formed, because the alloy composition lies within the composition range.

100 at% Ni

I 95

--·-r·-"­.-o-o .-o­./

~Oh 1248"C

/ ~

90-•-·-·-·

100 200 300

--- distance, ~m 400 500

Fig. 7.16 Penetration aur.ve in a Ni-Mo90.0Ni aouple

7.1.3 li~fQ~~§§_~~~§~f~~~~!§ Vickers micro-hardness values (load SOg) were measured in the ditfusion zone of some couples. Fig. 7.17 is an example of a hardness against distance curve. In Table 7.3 the hardness values of the various phases are summa­rised.

1400r-----------------------------------------,

1200

1000

BOO

600

400

200

0

-O--o -o-o~o-Doo Mo

50 100 150 200

0

0 ()()COO~Ol

l Vo'o-o

'-o-o

- distance, pm

Fig. 7.17 Plot of the Viakers miaro-hardness vs. the distgnae in a Mo-Mo62.0Ni aoupZe anneaZed at 7200 C for 750h. Load was 50g. 53

Table 7.3

Vickers micro-hardness in some phases of the Mo-Ni system

Couple

Mo-Ni

Ni-Mo62.0Ni

Mo-Mo62.0Ni

Mo62.0Ni Mo41.2Ni averaged values:

Treatrnent

70h 1100°C 65~h 1200°C

20h 1295°C 98h 1100°C

57~h 1200°C 31h 1295°C

·150h 1200°C 23h 1295°C 67h 1200°C

282h 1100°C

Mo

230 230 280

242 230

240

Hv in

6-phase

1058: 1000+ 1200

1272 1200 1314 1250 1260

kg/mm 2

a-s.s.

280-121 300-120 338-125 307-118 327-128 350-131

Ni

1 21 120 125 11 8 128 131

124

+ The layer is too thin to allow accurate deterrnination of the hardness.

A hardness against distance curve was also de5errnined in the Mo77.6Ni-Mo62.0Ni couple, annealed at 850 C for 75 days. The hardness values for the alloys were about 575 and 1000 kg/mm 2 , respectively. The hardnessof the À­MoNi3 layer was 600-650 kg/mm 2 and was a little aniso­tropic. It is clear that anne alin? always decreases the hardness of Ni to about 120 kg/mm (see also Table 6.2) and the Mo frorn 300 to 240 kg/mm 2 •

7.1.4 ~:E~Y-~!ÉÉE~~!~~~ A nurnber of alloys ere investigated by X-ray diffraction. The results are listed in Table 7.4. These diffractograrns gave results as expected, except for the Mo77.6Ni alloy. In that case the reflections of the y-(MoNi 3 ) phase were easy to detect, but these of the ether ph~ses, such as ~-(MoNi 4 ), which was anyhow prese nt in the alloy (see sectien 7.2.1) or the a-solid solution, were not found.

The Mo73.7Ni and Mo91.0Ni alloys were not annealed after rnelting, so they consisted of pure a-solid solution. The reflections of Ni were shifted to smaller diffraction angles because the unit cell becomes large r by dissolving the larger Mo atorns. In the Mo62.0Ni alloy, anne aled at 1200°C for 48h, the equilibrated a-solid salution was present containing 24.9 at% Mo. We have calculated the lattice parameters for the a-solid salution in these

54 alloys (Table 7. 5) .

Table 7.4

Results of the diffractograms taken from various alloys

Alloy Treatrnent Phases present according to the diffractogram

Mo62. ON i 9d 855~C Y; ?? 37d 855 c Y; o?

Mo77. 6Ni 11 d 855°C y; ?? 39d 855°C y; ??

Mo5.9Ni Mo; 6 Mo16.9Ni Mo; 0 Mo47.0Ni 72h 1200°C 6 Mo73.7Ni a-s.s. Mo91 • ON i ik

1200°C a-s.s.

Mo29.0Niik 74h Moi 0 Mo41.2Ni 90h 1200°C Moi 0 Mo4 8. 4Niil 79h 1200°C 6 Mo62.0Ni 48h 1200°C 6. a-s.s. I

Table 7.5

Lattice parameters of the a-solid salution caleulated from the diffractograms of some of the alloys

given in Table 7.4

Alloy

Mo91 .ONi Mo73.7Ni Mo62.0Ni

Lattice parameter ~

3.57 + 0.01 3.634 + 0.003 3.643 + 0.003

Remarks

homoge neaus homogeneaus two-phase alloy

From the three alloys in Table 7.4 marked with an asterisk the lattice parameters of the 6-(MoNi) phase have been calculated. In the Mo62.0Ni alloy the 6-phase was satrirated with Ni, and in the Mo41.2Ni and Mo29.0Ni alloys saturated with Mo (se e Table 7.6).

Table 7.6

Lattiee parameters of ó-(MoNi) ealeulated from the diffractograms of some of the alloys giv en in Table 7.4

Alloy Treatment Lattice parameters ~

Mo62.0Ni 48h 1200°C a=b=9.16 + 0. 01 i c=8.87 + 0.01 1200°C

- -Mo41.2Ni 90h 9.16 + 0. 01 i 8.86 + 0. 01 Mo29.0Ni 74h 1200°C 9.16 0. 01 i 8.86

-0.01 + + - ss

The parameters seem to be independent of the composition of ê-MoNi. Shoemaker et al. 25 found for the MoNi phase (50.8 at~ Ni) the lattice parameters a=b=9.108 and c=8.852 Ä. In this case the composition of the MoNi phase lay within the homogeneity range of the phase and was nat saturated with either Mo or Ni. The a and bparameters deviate considerably from these of Shoemaker et al. 25

The values of the c-parameters however, agree very well. The parameters calculated for the a-solid salution are in agreement with these given by Casselton et al. 24

7.2 Evaluation of the results

7.2.1.1 !~!EQQ~g~!Q~

Theconventional me thad of determining the equilibrium diagram of two metals is to investigate the influence of variatien of the temperature on a number of alloys. The reverse, however, is also possible, and this methad has been used in the present investigation. If two metals are diffusing in each ether, generally a number of stable intermetallic compounds (phases) will be formed in layers parallel with the contact inte r f ace .

The sequence of the layers is determined by the sequence of the single-phase areas in the phase diagram of the two metals. The concentrations at the interfaces of the layers are in accordance with the phase diagram at the diffusion temperature, provided that equilibrium is attained during the layer growth. As to the a tta inment of equilibrium opini ons are divide d in the literature . Kirkaldy 67 believes that the conce pt of local equilibrium is at best an approximation since the displacement of an interface requires a free-energy difference and, hence, a departure from the equilibrium compositions at the interface. He feels, however, that the time taken to attain constant interface composit i ons (esse ntially the equilibrium values) will be short. Little e xperimental evidence of the occurrence of deviations from the equi­librium values is available (Eife rt 6 8 , Masing 6 9 ).

We agree with the concept of Kirkaldy, but we think that the deviations are so small that they cannot be deter­mined by the analytical methods now available. It seems to us that the deviations between interface concentratien

à This sectien is base d on a paper which is accepted for publication in "Zeitschrift ffir Me tallkunde ". The subsectien 7.2.1.2, viz. Experimental Procedures, has been reduced, because the procedures have already

56 been described in Chapter 6.

and equilibrium concentratien reported in the literature might well be due to experimental errors. However, stres­ses owing to volume changes can cause deviations in the phase boundary concentrations (Adda et al. 70 ).

But many examples in the literature mention the absence of equilibrium phases in diffusion couples. In most cases a very low growth rate of the phases in question will be the cause (Van Loo71 ).

A great difficulty is to check whether the boundary con­centrations in diffusion couples are equal to the equi­librium values, since very aften the phase diagrams are nat accurately known. In fact, verification is only possible if the results obtained from diffusion couples at a particular temperature can be compared with results obtained from two-phase alloys equilibrated under the same circumstances.

Because we were also interested in the phase diagram of the Mo-Ni system we have used this to check whether the boundary concentrations obtained from diffusion couples agree with those obtained from equilibrated two-phase alloys.

7.2.1.2 ~~E~~~~~D~~!_E~2~~g~~~~ The compositions chosen for the alloys in the two-phase fields were 7.9, 15.4, 29.0, 35.3, 41.2, 62.0, 71.0, 77.6, and 83.0 at% Ni. A number of alloys consistedof three phases even after very long annealing times, parti­cularly t8e Mo52.1Ni alloy. These alloys were only used below 900 c.

The alloys which were anne aled for 5h at 1295°C and for 20h at 1200°C and subsequently analysed with the micro­probe, were reannealed during 25 and 70h, respectively, to find out if there were deviations with time. This appeared nat to be the case; the concentrations remained constant. óhe longest annealing times were at 1295°C 30h, at 1200 C 14 days, at 1100°C 22 days and at

0 1000 C 28 days.

Because the electron beam of the electron probe micro­analyser has a finite diameter, the grain in which the concentratien is determined, must have a minimum jia­meter of about 5 ~m. The alloys with smaller grains are not usable for th~ determination of phase boundary con­centrations.

7.2.1.3 ~!E~E~ID~D~~!-~~êY!~ê The averaged boundary concentrations determined from the penetratien profiles of ditfusion couples and the averaged concentrations determined from equilibrated 57

58

alloys are given in table 7.7. The concentrations are plotted in Fig. 7.18 and the agreement is remarkable. For comparison, the boundary concentrations of the phases in this system as determined by Casselton and Hume-Rothery 22 (see Fig. 7.19) are also listed in Table 7.7. The determinations by Casselton et al. 22 were carried out by means of a combination of thermal analysis, microscopie and X-ray methods applied to annealed alloys.

T 0 e

1295 1275 1263 1250 1225 1200 1150 1100 1000 900 850 800

Table 7.7

Boundary concentrations in at% Ni, determined in diffusion couples and alloys,

and the r esul ts given by ref. 22

o-solid aolution 6-MoNi o - solid golution

couples alloya re!. 22 couples alloys ref .2 2 couples alloys

-72.3 {5) -72. ï (2) -72.0 52.1-47.7 (5) 52 .2 (2)-47,9(1) 46-48 2.2-0(4) 1.7 (5)--72.8 (l) -73. .. (1) 52.1-47.7(3 ) 52.0(1)-47.8(1) 1 . 6-0(2)

-72.7 (1) 51.9-47.5(1) 52.0(1)- 1.6-0(1) 2. 2*(1)--13.1 (2) -73 .0 ()) -72.7 51.9-47.4 (4) 51 . 6 (J) -47.6 (1) 46-48 1.4-0(4)

- 13.7 {l) 51.9-47.8(.)) -48.1 (1) t .4-0(2) -7·L1 (7) -75 . 1 {1) -7].5 51.9-49.0(8) 51 . 9(7) -48.0(12) 46-48 1.5-0(7) 1.3 (4)--74.8 {l) -74.9 {1) -7-4.3 52.0-47 . 7 (41 51.6(1)-47 . 7(1) 1 . 3-0()) 1.2 (4)--76. 4 {5) - 77.9 (6 ) -75 . 1 51 .8-47.8 (6) 51.7(5) -.0 . 9(9) .f6-48 1.1-0(6) 1.1 (2)--78.9 {4) -79 .J (6 ) -76.7 51.4-48.3 (3) 5 1.\(2)-48 . 0(1) 46-48 1.1-0(J) -80.5 (7) -79.5 ? -47 .61 2) 51 .9 (2)-48.1 ( 1) 46-48 -82. .. {3) -82 .5 ~5o 51.8 (1) - 46-48 -84.9 (7) -BJ .5 '50 51.8(3) -47. 9(1) 46-48

In brackets , the number of alloy• or diffuslon couples used for the determlnation .

. a, not accurate

T 0e 8-MoNl~ )'-MoNi 1

couples alloys ref . 22 couples alloys r~f .22

900 76 . 2-75 . 4 76.0-75 . 4 75 .S -74 . 5 850 80.5-80 . 0 8o. 5-80 . o 81.0-80 . 5 76.0-75 . 3 76.0-75 . 6 75.5-74.5 800 80 . 5 -80 . 0 80.7-80.3 81 .0- 80 . 5 76 . 2-75.4 76.2-75 . B 75.5-74.5

ref. 22

1.]-

1.0-

o. ,_

0.4-0. 2-

The boundar~ concentrations of MoNi 3 and MoNi 4 at 800, 850 and 900 C were determined in alloys with 62.0 and 77.6 at% Ni which were annealed up to 100 days.

Even after long annealing times it is necessary to examine whether equilibrium is attained in the alloy. This may be done by verifying the absence of a conce n­tratien gradient in the various grains of the alloy.

The alloys ~ith 77.6 at% Ni annealed for 100 days at 800, 850 and 900 C always contained three or even four phases viz. MoNi, MoNi 3 , MoNi 4 and sametimes a-solid solution. The MoNi 4 grains were very small and long, and were Widmanstätten rods at 800 and 850°C (see Fig. 7.20). The MoNi grains were too small to be analysed. The MoNil grains were big enough, and it was possible to dete rmir.e the concentratien range of a MoNi 3 grain between MoNi and MoNi 4 • The alloy with 77.6 at% Ni annealed at 900°C is Öntirely different from these annealed at 800 and 850 C. No Widmanstätten rods were visible.

5-MoNi y-MoNi 3 ~MoNi4 x alloys

o ditfusion couples • j ,----_':,-c :)-(

i i ~ • 0 ~ ' ' Oe

j ~ \ (Ni) • ll IJ/.

I I \

ii \ 900

800

i i ~\ ~ )(- - - - - - ---"' I I 1~-..-\

)( 1111\: wo I 11 11 \

x )( 0

0 10 20 30 40 50 60 70 80 90 100

-at%Ni

Fig. 7.18 The phase diagram of the Mo-Ni system acear­ding to the present work

1400

T,°C 1300

1200

1100

1000

900

800

-- (Mo)

0 10 20

5- MoNi y-MoNi 3 ~-MoNi4 t ~ (

'\/

(Ni)

,--

1\ 30 40 50 60 70 80 90 100

-----at% Ni

Fig. 7.19 The phase diagram of the Mo-Ni system acear­ding to CasseZton and Hume-Rothery 22

59

Fig. 7.20

Optioal miorograph of t he Mo77.6Ni alloy anneal ed at 850°C for 28 days. 500x .

In the Mo77.5Ni-Mo62.gNi couples a thick layer of MoNi 3

was found only at 850 C (see Figs. 7.9 and 7.14). At 800 and 900°C this layer was aften absent. The Ni-Mo77.6Ni couples contained only the a-solid solution. With Mo-Ni couples therÖ was always a-solid salution and MoNi and at 800 and 850 C only very thin layers of MoNi 3 and MoNi 4 were present. In view of these difficulties the determinations in the alloys and couples at 800, 850

0 and 900 C are not very accurate.

7.2.1.4 ~!§~~§§!2~ The 6-(MoNi) phase, the most important intermetallic compound in the system, has been observed at all annealing temperatures and has a homogeneity range of 4 at%. The MoNi phase includes the equiatomic composition in contradistinction to the results of Casselton and Hume-Rothery 22 • The solubility limit of Mo in Ni at 1318°c is 2~ at% Ni, decressing with temperature by 2.3 at%/ 100 C (1.6 at%/100 C found by Casselton e t al. 22

The solubility ob Ni in Mo is v e ry small and is about 2 at% Ni at 1295 C.

In diffusion couples at 850 and 800°C the layers of the three intermetallic phases, are mostly too thin to determine the concentratien ranges accurately. The value s give n for thes e phases are only indications. The accuracy was improved by u s ing annealed a lloys, this resulted in 75.6-76.1 at% Ni f or MoNi 3 and 80.1-80.6 at% Ni for MoNi 4 • These results do not differ much from those obtained by Casselton et al. 22 (see Table 7.7}. But, as said before, the determinations at this side of the diagram are not very accurate, and neither did Casselton et al. ever obtain a completely homogeneaus S-alloy. No important deviations were found when determining t he phase diagram by diffusio n couple s or by equi librate d alloys. A disadvantage of bath methods is the long annealing time needed to obtain sufficiently large grains

60 and sufficiently thick layers for an accurate concentra-

tion determination to be made. Another disadvantage is the fact that the concentration cannot be measured within 1-2 ~m from a phase interface. The resulting error in the phase boundary concentration can be decreased by inves­tigating thick ditfusion layers, obtained by using long annealing times or by means of incremental couples.

The great advantage of the ditfusion couple technique is that with one couple an isothermic cross-section through the phase diagram is obtained. For this reason it is a very rapid method. This is all the more important since at this moment many of the binary and most of the ternary phase diagrams are little known. In our labora­tory it has been found that in the Ti-Ni-Cu system 72 the ditfusion couple technique is very suitable for deter­mining ternary phase diagrams, toa. The methad deserves, therefore, more attention than it has at the moment.

7.2.2 Ç~1g~1~~!Q~ê_Qf_9!ff~ê!Q~-Q~~~

The rnalar volume Vm has been calculated from the lattice parameters of the a-solid solution22 , y-(MoNi 3 ) 22 ,

B-(MoNi4) 22 and o-(MoNi) 25 • In Fig. 7.21 Vm in cm 3 /mol is plotted against the male fraction (Nb) in at% Ni. The curve may be approximated by two linear parts, viz.:

9.0

7.0

0

for 0- 70 at% Ni 70-100 at% Ni

MoNi

20 40 60 ---at% Ni

~~§-~:êQ1~9_êQ1~~~Q~

80

9.39 - 0.029 Nb 9.03 - 0.024 Nb

100

Fig. 7.21

Molar volume vm in dependenee of the Ni aonaentration

The a-solid salution has a very large homogeneity range. The chemical ditfusion coefficient Dv was calculated in the whole range from each penetration curve. For the calculation the computer program as given in Chapter 3 was used. The a-solid salution was formed in the following eau- ~

62

ples: Mo-Ni; Ni-Mo41.2Ni; Ni-Mo62.0Ni and Ni-Mo90.0Ni. The diffusion coefficient in the a-solid solution is almest independent of the concentration. Approximating vm by an averaged constant value hardly affects the values of the calculated diffusion coefficients.

Depending on the type of couple, one concentratien (85 at% or 95 at% Ni) is chosen for calculating the activa­tien energy Q and the frequency factor 0 0 by the least squares method (see Table 7.8). At these concentrations the results are the most accurate. In Figs. 7.22 and 7.23 the logarithms of the diffusion coefficients are plotted against 1/T. Arrhenius' rule is obeyed in all cases. The values of the activatien energy agree very wel! with each ether. The same is true for the values of the frequency factor, as shown in Table 7.8. The conc lusion is justifiable that the se quantities a r e i n­dependent of the type of couple used for the determina­tion.

1ö 9r-__ 13~o_o ___ 1_2ro_o ___ 1_1ro_o ____ 1_oTo,o

5

2

5

2

5

2

cm2f ,.. /18<

• Ni-Mo 62.0 at% Ni couples A Ni-Mo 90.0 at %Ni couples

1Ö12L-----~----~----~----~ 6.0 6.5 7.0 7.5 8 .0

-1o"jT,K-1

Figs. 7.22, 7.23

1öer-__ 13,o_o ___ 1_2ro_o ___ 1_1To_o _____ 1o~o~o

5

2

5

2

5

2

cm2/ Dv. ;sec

t )(

)(

x Mo-Ni couples \

o Ni-Mo41.2at% Ni couples

1Ö12 ~----L-----~----~----~ 6.0 6.5 7.0 7.5 8.0

-1o4jT,K-1

P~ot o f log Dv vs . 7/T f or the a-solid salu t i on f or vari ous t yp e s o f coup le

Table 7.8

Activation energies and frequency factors in the a-solid salution

Couple Q(kcal/mole) D0 (cm 2 /sec) at%

Mo-Ni 66.3 0.97 85 Ni-Mo41.2Ni 66.4 1 . 14 85 Ni-Mo62.0Ni 62.5 0.30 85 Ni-Mo90.0Ni 67.5 1. 56 95

Ni

Our results are in excellent agreement with those of Davin et al. 44 and Swalin et al. 45 Davin et al. 44 found an activatien energy of 64.4 kcal/mole and a frequency factor of 0.853 cm2 /sec in the a-solid salution of a Ni-Mo91.3Ni couple. Shinyaev 73 has invesbigated the ditfusion of Ni 63 in Ni between 900 and 1300 C. The result was: 0 Ni 63 = 2.59 exp (-69.500/RT) cm2 /sec. Messner et al. 74 found: 0 Ni 63 = 0.84 exp (-66.300/RT) cm2 /sec. These results indicate that the activatien energy in the a-solid salution is nearly equal to that for self-diffusion in Ni.

~h§_~:J~QN~tEh~êê The MoNi phase was formed in the couples Mo-Mo62.0Ni; Ni-Mo41.2Ni and Mo-Ni. In the Mo-Ni couples the MoNi layer varied considerably in thickness and therefore, no ditfusion coefficients in the MoNi phase were calculated for that type of couple. The other two types of couple are used for the calculation of the ditfusion coeffi­cients. The results determined in the Mo-Mo62.0Ni cou­ples are the most accurate. In Fig. 7.24 the logarithm of the ditfusion coefficient is plotted agains 1/T, showing that the Arrhenius' rule is obeyed for both types of couple. The activatien energies and frequency factors were calculated using the least squares method, and they are represented in Table 7.9 at 50 at% Ni.

If at a certain temperature more than one penetratien curve have been determined, the resulting ditfusion coefficients are averaged. The accuracy of the Q and Do values is not as good as for the a-solid solution, because the scatter of the measuring data is larger. The results for the two diffe­rent types of couple are exactly the same (one straight line through all the points in Fig. 7.24). The high value of Q is an indication of the absence of grain boundary diffusion. o3

1300 1200 1100 1000

• Mo-Mo 62.0 at %Ni couples " Ni-Mo 41.2 at %Ni couples

1Ö12L-----L-----~----~----~ 6 .0 6.5 7.0 7.5 8.0

-1o4fT,K-1

Fig. 7. 24

Plot of log Dv vs. 7/T for the 6-(MoNi) phase in two types of couple

Table 7.9

Activation energy and frequency factor for the Ö-(MoNi) phase (at 50 at% Ni)

Couple

Mo-Mo62.0Ni Ni-Mo41.2Ni

Q(kcal/mole)

89.2 89.3

7.2.3 ~!r~~~9~11_~!!~~~

D0 (cm 2 /sec)

1180 11 56

We have used 2 artificial types of marker: tungsten wires with a diameter of 10 ~rn and zirconia particles suspended in alcohol. Tungsten wires as markers were not suitable because they reacted with the Mo and Ni and were held by the Mo, so that the position of the wires did not agree with that of the Kirkendall interface. In Mo-Ni couples the wires were situated in the MoNi

64 layer (Fig. 7.25) and disappeared after a certain, not

Ni

Fig. 7. 25

OpticaZ micrograph of a Mo-Ni coupZe anneaZed at 7200°C for ?h. 500x. The tungsten wire has reacted with the 6-(MoNi) phase.

very long, time (Bastin 4 has met with similar difficul­ties with tungsten markers in Ti-Ni couples). With Zr02 particles better results were obtained, but caution is required. Of course, diffusion may be obstructed by toa large a quantity of Zr0 2 particles. This type of marker has been used in, among other couples Ma-Ni and Ni-Mo90.0Ni couples. The particles were aften toa large in diameter or were spread over a certain area in the a-solid solution.

In Ni-Mo90.0Ni couples the determination of the position of the interface was generally more accurate than in Ma-Ni couples. With the Zr0 2 particles the position of the marker interface in Ma-Ni couples has been found at 82 at% Ni and then the ratio of DNi/DMo was 2. In Ni-Mo62.0Ni couples the Zr0 2 particles were also in the wrong position, viz. always toa far in the direction of the Ni. Probably, the particles were pushed into the Ni during the preparatien of the couples, because the hardness of Ni is much lower than that of Ma. In Ni-Mo90.0Ni couples the starting materials had nearly the same hardness and therefore the particles were pushed into bath materials in the same manner.

Another methad is to make use of the difference in morphology on bath sides of the Kirkendall interface, which is aften recognizable in a diffusion layer if there is a great difference in morphology between the starting materials.

The best methad was to make use of the impurities present on the original interface of the starting materials. These very small impurities became visible after pro­longed etching, particularly if one of the starting ma­terials was a two-phase alloy. We have tried to determine the Kirkendall interface in as many couples as possible. In nearly all of them the impurities at the interface 65

Fig. 7.26 Optical micrographs of various types of couple. The marker interfaces (m) are visible owing to impurities present on the surfaces of the starting materials. (a) Mo-Ni couple 25h 7295°C (b) Ni-Mo62.0Ni couple 43h 7700°C (c) Ni-Mo47.2Ni couple 40h 7200°C (d) Mo-Mo62.0Ni couple 22h 7250°C. SOOx.

were used for accurate microscopie determination of the Kirkendall interface. In Mo-Ni couples we found the markers after very long etching. In Fig. 7.26 (a,b,c,d) the marker interfaces in a Mo-Ni, a Ni-Mo62.0Ni, a Mo-Mo62.0Ni and a Ni-Mo41.2Ni couple are visible. In Table 7.10 the ratios DNi/DMo are given, calculated from eq. (15), tagether with the atomie percentage of Ni at the Kirkendall interface. The position of the Kirken­dall interface shifts from about 75 at% Ni in Mo-Ni couples, via about 79 at% Ni in Ni-Mo41.2Ni couples to about 83 at% Ni in Ni-Mo62.0Ni couples. In all these couples the interface is in the a-solid salution and DNi/DMo is almost equal, viz. about 0.4.

In the Ni-Mo90.0Ni couples the ratio has about the same value as in the ethers; the interface is situated at 95.1 at% Ni. However, the determination of its position is very critical, because 0.1 at% difference causes a variatien of 100% in the DNiiDMo ratio. The fact that Mo is the fastest component in the a-solid salution is a little surprising, because mostly the component with the lowest melting temperature is the fastest. There are only a few examples in the literature where the compo­nent with the highest melting point has the highest mobility. In fact, in the Ti-V system 75 the V atoms move

66 11 times as fast as Ti atoms at the Kirkendall interface

Table 7.1 0

The ratio of DNi/DMo at the KirkendalZ interface

marker marker treatment interface DNi/DMo treatment interface DNJDMo

at% Ni at!: Ni

Mo-Ni couples Ni-Mo62.0Ni couples

70h I I 00°C boundary 0. 8 124h 1000°C 84.7 0.3 6-a-s.s. 45h I I 00°C 84.9 0. I

Blh I I 50°C 76.4 0. 8 16h 1200°C 83.4 0.2 16h 1200°C 7 5. 3 0.4 57!h 1200°C 83.9 0.4 81 h 1250°C 7 3. 9 0. 6 28jh 1225°C 8 I . 5 0. 0 25h 1295°C 7 3. 7 0.4 Blh 1250°C 82.2 0. I

Ni-Mo41.2Ni couples 20h 1275°C 82.2 0.4

5h 1295°C 82.4 0.3 63h I I 48°C 79.5 0.4 Mo-Ni62.0Ni couples 40h 1200°C 7 9. 4 0. 5

28!h 1225°C 7 9. 0 0.4 45h I I 00°C 4 8. 9 I . 2 24h 1275°C 7 8. 5 0. 6 I08!h I I 00°C 48.3 I. 0

Ni-Mo90.0Ni couples 87h I I 50°C 48.5 I. 0 150h 1200°C 4 8. 8 6. 3

219h 1000°C a) 9 5. I I . 3 28jh 1225°C a) 4 9. I I. 8 b) 9 5. I 0. 3 b)48.7 3. 7

90h I I 5 0°C 95. 3 I. I 44h 1250°C 4 8. 7 I . 3 67h I I 9 8°C 9 5. I I. I lljh 1263°C a)48.9 I . 2

28jh 1225°C 95. 3 0. 3 b)48.8 I . 8 40h 1248°C 9 5. I 0.3 20h 1275°C 4 8. 8 0. 9 20h 1275°C 9 5. I numerator

< 0 20h 1295°C 95.2 numerator

< 0

at 3.5 at% V at 1250°C, and in the Cr-Fe system76 the Cr atoms move 1.5 times as fas~ as the Fe atoms in the temperature range of 1415-1440 C at 5.4 at% Cr.

In the Mo-Mo62.0Ni couples the marker interfaces were situated at 48.5-49.0 at% Ni in the MoNi phase. The ratio DNiiDMo varies largely, but is probably about 1 or somewhat larger. That means that Ni atoms move as fast as or a little faster than the Mo atoms in the MoNi phase.

7.3 Conclusions

a. The phase diagram of the Mo-Ni system has been deter­mined using diffusion couples and two-phase alloys. Both methods give identical phase diagrams.

b. The homogeneity range of the o-(MoNi) phase is 4 at% and is centred round 49.8 at% Ni. The hardness of 67

68

this phase is 1260 kg/mm 2 • The lattice ~arameters of the MoNi phase are a= b = 9.16 + 0.01 Ä and c = 8.86 + 0.01 R; they are independent of the composition of the phase. The solubility limit of Mo in Ni at 1318°C is 28 at% Mo, decreasing with temperature by 2.3 at%/ 100°C. The y-(MoNi 3 ) phase has a small homogeneity range and is situated at compositions higher than 75 at% Ni; the range of the 8-(MoNi 4 ) phase is also very small and includes perhaps the stoichiometrie composition. The solubility of Ni in Mo is very slight, being about 2 at% Ni at 1295°C.

c. The layer growth of the a-solid salution in Mo-Ni and Ni-Mo62.0Ni couples and the MoNi phase in Mo-Mo62.0Ni couples is parabalie and the activatien energies are 67.1, 67.7 and 83.9, respectively. The diffusion is governed by volume diffusion.

d. The interditfusion coefficients in the a-solid solu­tion and, ther~fore, also the activatien energies are independent of the concentratien and of the type of couple.

e. The Arrhenius' relation at 85 at% Ni in Mo-Ni couples is: Dv = 0.97 exp (-66,300/RT) cm 2 6sec for the tempe­rature range between 1000 and 1300 C. The Arrhenius' relation at 50 at% Ni in Mo-Mo62.0Ni couples is: Dv = 1180 exp (-89,200/RT) cm2 /söc for the tempera­ture range between 1100 and 1300 C.

f. Mo is the fastest component in the a-solid solution, viz. 2-3 times as fast as Ni. I n the MoNi phase (-49 at% Ni) the veloeities of the atom species are about equal. The prese nce of the Kirkendall e ffect in the a-solid salution is an indication that the volume diffusion is governed by a vacancy mechanism.

g. Only the very small impurities present on the contact surfaces of the starting materials act as good markers if there is a large diffe rence in hardness.

C H A P T E R 8

DIPFUSION IN THE Mo-Fe SYSTEM

8.1 Experimental results

8.1.1 1~Y~f_gfQ~th_~~~êYf~~~lltê Layer growth measurements were carried out mainly at couples consisting of the pure metals. After the prepa­ration of the couples no ditfusion zone was visible microscopically. The a-solid salution of Mo in Fe grew very fast. The boundaries of the colurnnar grains were parallel to the direction of the diffusion. During cooling from the annealing temperatures, the R- or ~­phase precipitated from the a-solid solution, yielding a Widmanstätten pattern (Fig. 8.1). Therefore, the couples had to be quenched.

Fig. 8.1 Optieal mierographs of an unquenehed Mo-Fe eouple annealed at 7J00°C (a) for 7~h and (b) for J5h. A phase is preeipitated from the a-solid solution.

Almast all the measurements were carried out using iron as received from MRC (see Table 6.1). In a recent ana­lysis, however, the carbon content appeared to be of the order of 0.05 to 0.1 wt% instead of 0.003 wt% as stated by the supplier. If iron is used as received in Mo-Fe couples, a layer of an n-carbide, viz. Mo 3 Fe 3 C, is always formed with a lat­tice parameter of 11.122 R, as has been determined by Fraker and Stadelmaier 77 • According tothese authors the ternary carbide phase is s table in a narrow composition range around Mo Fe C at 1000°C. The n-carbide layer

3 3 0 formed at all temperatures between 800 and 1300 C. It was detected by X-ray diffraction. At first we conside-red this layer to be the a-(FeMo) compound, because of 69

the practically identical concentratien range of 46 to 49 at% Fe. The n-layer was thin and always less than 3% of the thickness of the a-solid salution la~er. After long annealing the ~-layer - and above 1200 C also the R-layer - formed. Below 1000°c a peculiar layer "X", similar to the two-phase layer in Mo-Ni (+C) couples (seÖ Chapter 10, layer A), was formed. Particularly at 800 C this layer was relatively thick (about 8 ~m after 125h); at 1000°C the layer was thin (about 2 ~m after 64h).

Penötration curves measured in the couples annealed at 900 C after three different times, demonstrated that the boundary concentratien of the a-solid salution at the "X" layer side was time dependent. The concentratien determined in the couple annealed for 34d was equal to the value found in alloys and in the Fe-Mo55.4Fe couple annealed at 900°C. In Mo-Ni (+C) couples the boundary concentratien of the a-solid salution did not reach the equilibrium value either if the two-phase layer was present.

In order to campare the results with those obtained when no carbon was present, the iron was annealed at 1300°C for 24h in moist hydrogen. The C was oxidized to CO. No oxygen is soluble in solid iron, and only a thin oxide film of FeO was formed on the iron. This film was abra­ded. A nurnber of Mo-Fe couples were made and annealed at 800, 900, 1000, 1100, 1200 and 1300°C for different times6 No n-carbide was formed in these couples. Below 1200 c only the a-solid salution and the ~-phase were formed. AbovÖ 1200°C very thin layers of the R-phase- and at 1300 C now and then thin a-layers- were formed in addition to the a- and ~- phases. The carbon content did nat seem to have any influence on t8e results obtained for the a-solid salution above 1000 c. Below this tem­perature, however, the results differed appreciably. Therefore, in Fig. 8.2, in which the layer growth data of the a-solid salution in the Mo-Fe couples are given in dependenee of the square root of the annealing time, the data at 900 and 1000°C were take n from couples of which the iron was annealed in moist hydrogen.

Straight lines are found for all tempe5atures. The n-values at temperatures above 900 C are 2 or very close to that value, waich indicates a volume diffusion mechanism. Only at 900 C did we find a value different from 2, viz. 2.1. This indicates that at this tempera­ture mainly volume diffusion took place, but also to a slight extent grain boungary diffusion. Assuming the line at 900 c in Fig. 8.2 to be straight, the penetratien constant is not consistent with the

70 other values. The measurements of the thickness of the

1000 d,~m

I

500

4 8 1/ 1/ 12 -t'2. h/2

16

Fig. 8. 2

Layer growth of the a-solid salution in Mo-Fe couples

a-solid solution are reproducible. Table 8.1 gives the values of the penetratien constant k of the a-solid solution determined from Fig. 8.2. In Fig. 8.3 log k is plotted against 1/T. A satisfacto­rily straight line is found for temperatures between 1000 and 1300°C. The activatien energy Q and frequency factor k 0 have been calculated by the least squares method; the values are 58.2 kcal/mole and 17.5 cm /sec , respectively.

Table 8.1

Penetration oonstants (k) of the a-solid salution in Fe-Mo couples

T 0 c k(cm2 Lsec) T 0 c k(cm 2 Lsec)

900 1 • 09 x 1 o- 1 o 1216.f[ 5.14 x 10- 8

1000 2. 18 x 1 o- 9 1226.f[ 6.00 x 1 o-s 1100 1 • 02 x 1 o-s 1250.f[ 8.70 x 10-S 1120.f[ 1 • 11 x 1 o-s 1277.f[ 1 . 12 x 1 o- 7

1150 1 • 91 x 1 o-s 1300 1. 73 x 10- 7

1200 4.23 x 1 o-s

.ii only ene annealing time is used. 71

1300 1100

5

2

6.0 7.0

- 10/(K-1

0

8.0

Fig. 8.3

Plot of log k vs . 7/T for th e a - solid salu t ion in Mo-Fe coupl es

The ~-layer was thin (2-3% of the thickness of the a­solid salution layer) and, therefore, the thickness measurements were not very accurate. In general, the parabalie growth of the ~-phase was verified, but no penetration constants were calculated.

In incremental couples the layer growth of the ~-phase satisfied the parabalie relationship as was determined in the Mo55.4Fe-Mo67.7Fe couple, annealed at 1100°C. The growth of the a-solid salution in incremental cou­ples like Fe-Mo67.7Fe and Fe-Mo55.4Fe was also parabolic. The iron used in incremental couples and in alloys was not decarburised.

8.1.2 ~~~EQEEQe~-~~~ê~E~~~~ê A great number of concentration-penetration curves were determined. Most of them were used for the calculation of the interdiffusion coefficients with the computer program described in Chapter 3. The couples in which the curves were measured we re: Mo-Fe; Fe-Mo93.9Fe; Fe-Mo67.7Fe; Fe -Mo55.4Fe ; Mo-Mo67.7 Fe; Mo-Mo55.4Fe; Mo-Mo42.4Fe; Mo55.4Fe-Mo67.7Fe. The alloys were very brittle, particularly the Mo55.4Fe and

n Mo67.7Fe alloys.

20

~9:~~-f9!:!E!~ê

200 - distance, pm

300

Fig. 8. 4

Penetration curves of some quenohed Mo-Fe ooupZes. (a) 65h 900°CJ (b) ?O~h 7000°CJ (a) 4h 7200°C.

In Fig. 8.4 three curves are given for quenched couples, consisting of Mo and decarburised Fe. Only the w-phase was always formed in reasonably thick layers. As has been said before, the R- or w-phase precipitated from the ~-solid solution during cooling. The precipitated phase was partially formed as a layer, from which large protrusions penetrated into the grain boundaries of the a-solid solution. Inside the a-grains the phase was disp0rsed as very small particles (see Fig. 8.1). Above 1200 C, this phase was the R-phase; below this tempera­ture it seemed to be the w-phase. At the back of the Mo sheets in Mo-Fe couples, layers were also formed via vapour phase and surface diffusion. The boundary concentrations of the phases were the same as in solid-solid couples, but the layers were always much thicker and more regular. If present, the a-solid solution was visible as a series of swellings (Fig. 8.5).

~~:~9~~~~~~-~9!:!E!~ê Penetratien curves we5e determined in couples, annealed between 1000 and 1300 C. In all couples a-solid solution was formed. The formation of the y-solid solution, which was hardly detectable with the microprobe, was very slow. 73

74

Fig. 8.5 OptieaZ mie r ograph s of a Ma -Fe eoupZ e annea Ze d at 7000° C f o r 700h. Via the vapour phas e , i r on i s pZa ted upon th e baek of th e Mo she e t of t he soZid-soZid eoupZe and diffusion has oeeurred. (a) eross-seetion of the diffusi on zone at the baek of the Mo sheet. 200x. (b ) the surfaae of th e Mo shee t. The sweZZings show arystaZ Zi n e pZane s. 50x.

~~=~Q22~1~~-9Q~2!~2 Penetration curves werÖ determined in couples annealed at 1200, 1250 and 1300 C (Fig. 8.6). The a-solid salution and the ~-phase were formed. At 1250°C a very thin, and at 1300°C a reasonably thick, layer of the R-phase were formed.

0 The couples were annealed at 1120, 1216, and 1300 C (one example of a penetration curve in this type of coupleis given in Fig. 8.7). Only the a-solid salution was formed. This type of couple is similar to the Ni-Mo62.0Ni type of the couple.

~Q=~21~~1E~-~~9-~Q:~Q22~1E~-~Q~2!~ê In t hese types the s olubility o f Fe in Mo was measured. In the Mo-Mo55.4Fe couples the cr -phase was also f0rmed (Fig. 8.g). The annealing temperatures were between 1200 and 1300 C.

100

80

60

% ~ o=:sg-~--- ,. at o Fe ~o::e= ~ • .-------.-... l ® 0 .-..... ."..~ __.-.-·-·-

21 h 1250 C ·-•-•o...!$=-0 -·-•__. CL .-- 0-- ___.

-~~~::~-0- ~ ------------------~

Bh 130o·c 26Y2.h ©f ®r ~ : (i 1200 C c Ja 1.!11 , © I

R I

j / _j ......-J ~-·--· ~4 average J alloy composition

40L_--~----~----L---~--~s~o~o~--~--~----~----L---1~o~o~o----w

----distance ,flm

Fig. 8.6 Penetration curves of some Fe-Mo55.4Fe couples

60~---L----~----~---L----~--~

200 600 1000 -distance, pm

Fig. 8. 7

Penetration curve of a Fe-Mo67.7Fe couple anneal e d at 72 76° C for 30h.

~2=~2§1~1~§-~2~E!~2

60

at ,-. Fe

40 ( a 0

20

50 100 - distance,~m

Fig. 8. 8

Pe n e tra tion curve o f a Mo-Mo 55. 4Fe couple annealed at 7300°C for 24h.

Anne aling temperatures between 1100 and 1300°C were used. I n Fig. 8.9 three of the penetration curves are given. In all the couples the ~-phgse was formed, the a-phase only at 1100, 1277 and 1300 C and the R-phase above 1250°C. Above 1150°C porosity was visible in the diffu­sion layer near the alloy. This might have neen caused by the Kirkendall effect. 75

76

average al!oy composition

60

40

20

100 200 ---distance .~m

Fig. 8.9 Penetration curves of some Mo-Mo6?.7Fe couples

~Q~~~i[~=~Q§1~1[~-~Q~E!~ê The coupÓes were annealed at temperatures between 1100 and 1300 C (Fig. 8.10 gives two exarnples of penetratien curves). These couples were prepared because we wanted to know the diffusion behaviour in the ~- and R-phases. The couples were difficult to handle, because of the brittleness of the alloys. Aö all ternperatures the ~­phase was forrned and at 1250 C and higher also the R-phase. The range of the ~-phase decreased with increa­sing ternperatures.

70 f---.....-.

:: t·l averatalloy compositions -- -------------~

at/.Fe 70

60

soL_ _ _L __ ~~-_L-~~~ 100 200

- distance, ~m

Fig. 8.1 0

Penetration curves of two Mo55.4Fe-Mo6?.?Fe couples

8.1.3 ~êfQD~§§_~~ê§~!ê~êDtê The Vickers rnicro-hardness was rneasured in various dif­fusion layers (load 50g). In Table 8.2 the hardness values of the phases are listed. The iron used in the Mo-Fe couples was decarburised.

Table 8.2

Viakers micro-hardness (Hv) in various phases of the Mo-Fe system

Couple Treatrnent Hv in kg/rnm 2

Mo IJ R a-s.s. Fe

Mo-Fe 65h 1000°C 250 1254 208-150 11 0 Mo-Fe 64h 1200°C 250 1254 1 05 Mo-Fe 6~h 1300°C 239 396-145 11 0 Mo-Mo67.7Fe 40h 1277°C 1300 ? Mo55.4Fe-

1295°C Mo67.7Fe 7h 1380 1380 Mo55.4Fe-

1277°C Mo67.7Fe 40h 1300 1340

Pollanz 78 has deterrnined the Vickers hardness of the w- and o-phases in sintered alloys with a 100g load and four.d values of 1218 and 1116 kg/rnm 2 , respectively. The hardness of the n-Mo 3 Fe 3 C phase was found to be 1370 kg/rnm 2 •

8.1.4 ~=IêY_9!fff~gt!QD Sorne älloys and couples were investigated by X-ray dif­fraction and the results are listed in Table 8.3.

The lattice parameters of the a-solid solution in the Mo93.9Fe alloys (calculated frorn only three reflections) are both 2.885 R. (The lattice parameter for a-Fe at 20°c is 2.886 R.) The A-(Fe 2Mo) phase has never been found in any of the diffractograms (Sinha et al. 34 found it below 950°C). In Table 8.4 are listed the lattice parameters of the IJ-, R- and o-phases calculated frorn the diffractograms of the alloys, given in Table 8.4, together with those mentioned in the literature. The deviations of our r esults frorn those in the litera­ture are not large. The parameters calculated for the Mo-rich side of the IJ-phase are a little larger than those of the Fe-rich side of that phase found by Sinha et al. 77

Table 8.3

Results of the diffractograms taken from some Mo-Fe aZZoys and couples

Alloy or couple Treatment Phases

identified

Mo41.2Fe 124h 1200~C ]J i (Mo) cr? Mo51.3Fe 68h 12900 C (Mo)?; IJ; ]J

Mo55.4Fe 16d 1200 c (Mo); ]J

Mo55.4Fe 64h 1200°C ]J

Mo55.4Fe 63h 1150~C ]J

Mo66.4Fe 68h 1290 c R· ]J; a-s.s. 1200°C ' Mo67.7Fe 11 d R

Mo93.9Fe not annealed a-s.s. Mo93.9Fei'l 67d 900°C a-s.s.

Mo-Fe, back of Mo 22~h 1000°C ]J i Mo Mo-Fe, back of Mo 90h 850°C ]J i Mo Mo-Fe, back of Mo 64h 1200°C ]J i Mo

Mo-Mo55.4Fe 24h 1300°C cr; Mo?

f[ This alloy contains two phases; the ether Mo93.9Fe alloy was hornogeneous.

Table 8.4

Lattice parameters of the ]J-~ R- and a-phases

alloy ref. lattice in R phase and or treatment parameters structure

Mo55.4Fe 63 h I 150°C a•b• 4.767+0.002; c=25.77 +O. n 1 w. hexagonal Mo55.4Fe 16 d l200°C • 4.782+"0.002; ~25. 78 +o.ot w. hexagonal Mo67.7Fe ll d l200°C •10.921+"0.008; = 19. 34 +o.ot R, hexagonal MoS! .3Fe 68 h l290°C . 9.229~0.009; = 4. 823+"0. 007 a' tetragonal ref. 32 ~ 4. 7 54 =25.716 w ref. 32 ~ l 0. 9 l 0 =19.354 R ref. 37 ~ 9. I 88 = 4. 8 l 2 a

8.2 Evaluation of the results

8.2.1 Qgtg~~~D~t~QD_Qf_tb§_Qb§§§_Q~§g~§~

The phase diagram was deterrnined in two ways, using dit­fusion couples and two-phase alloys. The results of the rnethods were cornpared with each ether and with the re­sults given by,Hansen 33 and Sinha et al. 34 (Table 8.5

78 and F ig • 8 . 11 ) .

T 0 c

800 900

1000 1100 1200 1300

Table 8.5

Boundary concentrations of the various phases in the Mo-Fe system accordin& to Hansen 33

and Sinha et al. 34 (at% Fe)

À-a-s.s. phase

100-95.3 66.7 100-94.4 66.7

98.7-93.0 98.3-91.1 98.5-88.1 99.0-83.8

100 90 80 70

900 " À ... 1' ,,

800

0 10 20 30

R- ~,...

phase phase

61-60 61-60 61-60 61-60 61-60

62.6 61-60

60 50 40

0

40 50 60 __ ____,_ at% M o

(J-(Mo) phase

? ?

3.3-4.5-

50.0-49.9 5.2-50.0-49.6 7.9-

30 20 10 0

' ' (Mol

70 80 90 100

Fig. 8.11 The phase diagram of the Mo-Fe system acear­ding to Hansen 33 and Sinha et al. 34

QiffY2iQD_gQYQ1~§

The results from the diffusion couples taken tagether are listed in Table 8.6. They are represented in the phase diagram of Fig. 8.12. In the incremental couples the boundary concentrations of the a-solid salution were 79

80

determined in the couples: Fe-Mo93.9Fe; Fe-Mo67.7Fe; Fe---Mo55.4Fe; those of the ]..!- and R-phases in the couples: Mo-Mo67.7Fe; Fe-Mo55.4Fe; Mo55.4Fe-Mo67.7Fe; of the a-phase and (Mo) in the couples: Mo-Mo67.7Fe; Mo-Mo55.4Fe and of (Mo) also in Mo-Mo42.4Fe.

T oe

900

1000

1100

I I 20

I I 50

1200

I 2 I 6

1226

1250

1277

1300

1343

Table 8.6

Boundary concentrations in at% Fe, determined in diJfusion couples

in the Mo-Fe system

et-sol id solution R-phase

99.5-94.5(3)

98.1-92.5(3)

97.5-90.0(5)

97.5-89.4(2)

97.4-88.4(3)

97.6-86.5(9) "-67? (I)

97.9-85.8(2)

9 81 -86 (I)

98 -84.9(3) 65.5-64.S(2)

98 -82. 5(2) 65 -62.9 (I)

98.1-82. I (8) 65.0-61.8(5)

98.1-80.0(1) "-63 (I)

lJ-phase

60.5-56.3(3)

60.8-56 (3)

61.3-56.5(1)

62.5?-57 (4)

61.5-57 . 2(11)

(I)

61.3- 56.9(2)

61.3-57 (4)

60.5-57 ( 2)

60.0-56.7(8)

o-phase (Mo)

47.2-45.5(1)

1 . 0-0(3)

1.5-0(2)

I. 1-0(5)

2 -0(1)

).5-0(4)

4.5-0(10)

4 -0(1)

5 - 0(1)

5 . 4 - 0(3)

46? -44 (J) 6 . 6-0(4)

47 . 0-44.0(2) 8 -0(9)

8 -0(1)

(In brackets, the number of couples used for the determination)

The results below 1000°C are not quite reliable because of the presence of carbon in the iron. At these tempera­tures a two-phase layer was formed in Fe-Mo couples to­gether with a single-phase layer which contained 46-49 at% Fe. The latter turned out to be the n-Fe 3Mo C car­bide, having the Ti 2 Ni type of structure and a Iattice parameter of 11.122 ~ (see also Chapter 10). The other results in the Mo-Fe couples agreed with those in incre­mental couples. The layer containing ~45-47 at% Fe formed in incremental couples was indeed the a-layer, as was confirmed by X-ray diffraction. The a-phase was also present in some alloys.

?!!!2Yê The phases in the equilibrated and quenched alloys, used in the incremental couples, were analysed with the micro­probe, tagether with some alóoys, not used in couples and annealed at 1600 and 900 C. The annealing times were up to 11d at 1300 C; 16d at 1200°C; 25d at 1100°C; 67d

100 1400

\0

1300

T, °C 1200

1100

h ~ 0 I

0 0

t-Y I 0 0

I

80

OI I

0

a ó OI

o' 0

0

I 0 I

.0

/ 1000 0 0

I I 0

I 900

800 I

0 20

60 40

R P. 0

l ~JA.;

ti I '' I 0 0 0 0

V' 4 ~ 1 ~ 'I 0 0 0 00

1/

0 0

I 40 60

---at ~o Mo

20

~Mo) 0 I

~ 00

" \ OI

0

\ 0

I 0

I I

80 100

Fig. 8.12 The phase diagram of the Ma-Fe system aaaor­ding to the r e sults in the diffusion aoupl e s

100 80 60 40 20 0 1400.---.----.---.----.---.----r---,----.---.---~

1300

1200

T, oe t 1100

11000

900

800

0

! a ,l

J I .

l i

20

. I

40 60

------ at ro Mo

80

o(Mo) ~ ~ \ . I

100

Fig. 8.13 The phase d iagram o f t he Ma-Fe s y stem aaaor ­ding to the results in the two-phase alloys

at 900°C. Often, the alloys consisted of three phases, particularly the Mo42.4Fe alloy. In Table 8.7 the boundary concentrations in alloys are 81

Table 8. 7

Phase aonaentrations in at% Fe in annealed Mo-Fe alloys

T oe er.- so 1 id sol ut ion R+)J-phases a-phase (Ho)

900 -9 5. 0 (I) -5 5. 7 (I) 4 7. 8 (I)-

1000 -95.71(2)

1100 -89.5 (I) 66.3(1)-55.5(1) 47.1(1)-45.7(1)

I 120 -89.2 (I) 49.2?(1)-

I 150 -88.3(2) 66.9(2)-56.3(1) 47.1(1)-46.0(1) 1

1200 -86.9(2) 66.1 (2)-55.7(3) 46. 7 (I)- 7. 5 (I)-

I 2 16 -86.2(2) 65.9(2)-

1226 -86.0(2) 66.1(1)-55.5(1) 46.31(1)-

1250 -85.3(2) 65.5(2)-56.6(3) 8. I (I)

12 7 7 -82. 9 (I) 65.0(2)-56.8(3) 1 -45.0 (I) 9. 0 (I)

1300 -82.3(2) 64.7 (3)-56. 4 (4) 47.0(4)-44.5(3) 9. 5 (I)

?) the concentrations in the grains of the phase could net be determined accurately

(In brackets, the number of the alloys used for the determination)

listed; in brackets, the number of alloys used for the determination in question (see Fig. 8.13). The boundary concentrations of the ~-phase (Fe-rich side) and of the R-phase (Mo-rich side) could net be determined when using alloys. We failed in preparing alloys con­taining constituents of both phases.

Qi.ê2!:!.ê.ê!Q!} Generally, the diagrams determined by using diffusion couples and by using two-phase alloys agree satisfacto­rily. There are some discrepancies, viz.:

(a) The solid solubility of Fe in Mo found in alloys was somewhat higher than in couples.

(b) In couples, the R-phase was formed only above 1200°C, whereas in alloys it was present at all temperatures (although the results at 1000 and 900°C were net clear) . This is in accordance with the observation of Sinha et al. 34 that the R-phase does net decompose below 1245°C in slowly cocled alloys. The decomposi­tion of the phase requires very long annealing times.

(c) The o-phase is only found in some incremental cou­ples at only three temperatures, but in alloys at

82 nearly all temperatures.

The À-(Fe 2Mo) phase could net be detected at 900°C, even net in the Mo93.9Fe alloy annealed at 900°C for 67 days, only the ~-phase precipitated frorn the a-solid solution. We suppose that a "À-(Fe 2 Mo)" phase does net exist. In our apinion the ditfusion couple technique is the best tool in the investigation of phase diagrarns. As rnentioned before, the alloys aften contain more than two phases and despite long annealing treatrnents equilibrium is aften net attained.

Cernparisen of our results with these of previous werk: 1. The solid solubility of Mo in a-Fe differs frorn that

deterrnined by Sinha et al. 34

Sykes 79 considered Widrnanstätten pattern in a-grains to be due toa eutectic. Bechtoldt et al. 60 sup~osed it to be a rnetastable phase, while Takai et al. 1

proposed that the precipitate in the a-grains was due to the ~-phase precipitated frorn the a-solid solution. Our results with unquenched couples are in agreement with these of Takai et al. with the restrietion that in our apinion above 1200°C this precipitate is the R-phase.

2. The solubility of Mo in y-Fe is sornewhat larger than given in the literature 33 34

3. The hornogeneity range of the ~-phase is larger than deterrnined by Sinha et al. and Rawlings et al. 6 0

4. The R-phase is stable above 1200°C. The hornogeneity range becornes larger at increasing ternperatures (62.0-65.5 at% Fe at 1300°C). Sinha et al. and Rawlings et al. have found this phase above 1245°C at about 63 at% Fe.

5. Perhaps the o-phase is stable at lower ternperatures with a larger hornogeneity range than stated by Hansen. However, the results are questionable because of the carbon content of the iron.

6. Sinha et al. have found a À-(Fe Mo) phase, stable below 95ooc at the cornposition 66.7 at% Fe. Thornpson and West 82 believe that they have found this phase in an Fe-10% Cr-13% Co-5% Mo alloy at ageing ternperatures of 600 and 7oooc. In accordance with Rawlings et al. we have never found any evidence of the occurrence of that phase.

7. The solid solubiliti of Fe in Mo is nearly the sarne as given by Hansen. 3

8. As already mentioned in Chapter 7, Masing 69 in his paper describes sorne exarnples of deviations frorn the equilibrium values of boundary concentrations of phases growing during diffusion. One of the exarnples is the diffusion in the Mo-Fe systern. The Fe was ernbedded in Mo powder and annealed at 1200°C for 10h. The a-solid salution and the ~-phase were forrned. Layer sectioning (the sections were almest 100 ~rn thick) showed that the concentratien

of Mo in the a-solid solution in contact with the ~-phase was only 6.1 at% instead of the equilibrium concentratien of 13.5 at% Mo. Contrary to this rather inaccurate result, we have always found the equili­brium concentratien in all the Mo-Fe couples, even after 15 and 30 minutes of annealing at 1295°C (except for deviations at lower temperatures due to the pre­senee of carbon) . So we conclude that no deviation in this system is present and the deviation found by Masing must be due to experimental errors.

8.2.2 Calculations of diffusion data ------------------------------The molar volume vm, calculated from the experimentally determined densities, is nearly proportional to the concentratien over the whole range. The error introduced by this assumption is very small. The relation used in the calculations of the diffusion coefficients by the computer program described in Chapter 3 is:

vm = 9.41 - 0.023 Nb ,

where Nb is the at% Fe.

~hê-~:§91!9_§Q1~~!QD The a-solid solution has a very large homogeneity range. The chemical diffusion coefficient Dv was calculated at a number of concentrations from the penetratien curves. Carburised iron gives the same diffusion coefficient as decarburised iron. The a-solid salution was formed in the following couples: Mo-Fe; Fe-Mo67.7Fe; Fe-Mo55.4Fe; Fe-Mo93.9Fe.

The Fe-Mo67.7Fe and Fe-Mo55.4Fe types of couplewere annealed at only three temperatures; therefore, the results are plotted in the same Figure as those of the Mo-Fe couples. For all these types of couple the activa­tien energy (Q) and frequency factor (D0 ) have been calculated in two concentrations, viz. 90 (Fig. 8.14) and 95 at% Fe (Fig. 8.15). In the latter the results of the Fe-Mo93.9Fe couples arealso given. They are averaged values in the concentratien range formed in these couples, because there are large variations in the values of Dv. These variations are caused by the gentleness of the slope of the profile of the penetratien curve, so that minor irregularities in the curve give large deviations in the concentratien gradient. Even smoothing of the curve by our computer program is not enough to eliminate these effects. Arrhenius' rule is obeyed in a reasonable way in all cases. It is clear from the Figs. 8.14 and 8.15 that Q and D0 for the a-solid solution in the couples are identical at both concentrations except in the case of Fe-Mo93.9Fe

s4 couples, where they seem to be a little higher.

1300 1100

T ,°C

5 \\~ 2 \ -8

10 ~ 2 1\

5 cm/s Dv, sec à

\0

1 2 \ -9

10

à Fe- Mo

5 v Fe- Mo55.4Fe o Fe- Mo67.7Fe

2

6.0 7.0 4 ___ 1o/r.K-1

Fig. 8. 1 4

8.0

PZot of Zog Dv vs. 7/T for the a-soZid soZution at 90 at% Fe in various types of diJfusion aoupZe

1300 1100

T,°C

* 5

2 ~~ -8

10 ~\ 5

2 ,, cm7s Dv, sec

1 2 \

-9 10

5 o Fe- Mo ' Fe- Mo55.4 Fe • Fe- Mo67.7 Fe

2 • Fe- Mo93.9 Fe

6.0 7.0

10Î -1 ----- /T,K

Fig. 8.15

\ \

• 0

PZot of Zog Dv vs. 7 /T for the a-soZid soZution at 95 at% Fe in various types of aoupZe. The vaZues determined in the Fe-Mo93.9Fe coupZes are those averaged over the aonaentration range of the a-soZid soZution formed in the aoupZes.

8.0

Table 8.8 shows the values calculated for the Mo-Fe and Fe-Mo93.9Fe couples. The Q and D0 values at 96 at% Fe in Fe-Mo93.9Fe couples are 57.1 kcal/male and 4.16 crn 2 /sec, respectively, but the scatter of the values is larger than with the aver­aged results. So the conclusion seerns justifiable that in the a-solid salution these quantities are independent of the concentration. 85

Table 8.8

Aativation ener~ies Q(kaaZ/mole) and frequenay faotors D0 (am /sea) in the a-soZid salution

Couple

Fe-Mo Fe-Mo93.9Fe

90 at% Q Do

57.1 2.29

95 at% Q Do

56.7 2. 19

averaged over 95-97

at% Fe range Q Do

61.5 1 8 .1

Results of previous work about the diffusion at infinite dilution in a- and y-Fe are given in Table 8.9.

Table 8.9

Previous results for diffusion in a- and y-Fe

Diffusing a-Fe y-Fe Reference element Q Do Q Do

Fe 57.3 2.0 64.0 0.2 Tomlin et al. 8 3

Ni 56.0 1.3 67.0 0.77 Hirano et al. 8 4

Nb 82.3 5.30 Sparke et al. 8 5

Cr 59.9 8.52 69.7 10.80 Bowen et al. 8 6

V 57.6 3.92 63.1 0.25 Bowen et al. 8 6

Hf 69.3 1. 31 97.3 36.00 Bowen et al. 8 6

The differences in activatien energies for the ditfusion in a- and y-Fe can be explained qualitatively as being due to the differences in compressibility between the diffusing atom and the solvent atom (Bowen et al.). All the results of previous work indicate that the ditfusion in a-Fe (bcc) is much faster than in y-Fe (fee). Indeed, we have found a fast ditfusion of Mo in a-Fe (solid solution) and a very slow one in y-Fe (sec­tien 8.1.2). The radius of the Moatom is only a little shorter than that of Nb, but langer than that of Cr. Therefore, the activatien energy of Mo ditfusion in y-Fe will be probably close to the value of Nb ditfusion in y-Fe. Our results a~ree satisfactorily with these found by Pivot et al. 5 They found an activatien energy of 60.0 kcal/male and a frequency factor of 10 cm 2 jsec for

86 diffusion in the a-solid salution between 790 and 1185°C.

~~~-!~~~E~~~~~~!~-E~~ê~ê Assuming that the ~-(Fe 7 Mo 6 ) phase is growing paraboli­cally in the Mo55.4Fe-Mo67.7Fe; Mo-Mo67.7Fe and Fe­Mo55.4Fe couples, the interditfusion coefficients Dv in that phase have been calculated. Log Dv at 58, 59 and 60 at% Fe in Mo55.4Fe-Mo67.7Fe couples are plotted against 1/T (Fig. 8.16). There is considerable scatter in the Dv values, but a straight line can be drawn through the points. In Fig. 8.17 the log D values in Fe-Mo55.4Fe couples at 59 at% Fe (at only ~ temperatures) and in Mo-Mo67.7Fe couples at 58 and 60 at% Fe (6 temperatures) are plotted against 1/T. Arrhenius' rule can be considered to be obeyed.

1300 1100

-10 T,°C-

10

~~ 5

2 l~ • x

1"81

5 cm~ 0v• ;sec

2 t .5aat%Fe :\ 1d2 o 59 at%Fe .60 at%Fe

5 L_ ____ L-----~----~

6.0 7.0 _10~ -1

i'T,K

Fig 8.16

Plot of log Dv vs. 7 /T for the ~-(Fe 7 Mo 6 ) phase in Mo55.4Fe-Mo67.7Fe couples

1300 1100

T, oC -9

\ 10

5

\! 2

-10 10 \ 2 c'%

5 '\,, sec

2 1 \ \ -11

10

5

6.0 7.0 4 8.0

10/T K-1 '

Fig. 8.17

Plot of log Dv vs. 1/T for the ~-(Fe 7 Mo 6 ) phase formed in Fe-Mo55.4Fe couples (~, at 59 at% Fe) and Mo­Mo67.7Fe couples (•, at 58 at% Fe; o, at 60 at% Fe) 87

The activatien energies and frequency factors have been calculated with the least squares method. The averaged results of the Mo55.4Fe-Mo67.7Fe couples (7 values) give a Q of 71.0 kcal/mole and a D0 of 3.99 cm 2 /sec. The averaged values of the Mo-Mo67.7Fe and Fe-Mo55.4Fe cou­ples tagether (6 values) give a Q of 68.4 kcal/mole and a D0 of 1.48 cm 2/sec. No interditfusion coefficients have been calculated for the other phases.

8.2.3 ~~~~g~g~!!_~~~~gt

It was rather difficult to measure the position of the marker interface. In the Mo-Fe and Fe-Mo93.9Fe couples Zr0 2 particles had to be used, which often caused trouble (see Chapter 7). Of the couples of which at least one starting material was a two-phase alloy the Kirkendall interface was marked by small impurities In Table 8.10 the ratio of DFeiDMo is given for various couples. The difficulty in determining the position of the marker interface is evident from the negative values for the numerator or denominator of the quotient in eq. (15), which were found in some couples.

Table 8.10

The ratio of DpeiDMo at the Kirkendall interface

treatment treatment

Fe-Ho couples Fe-Mo93.9Fe couples

17 h l I 00°C 92.9 a I. 0 100 1000°C 96.7 a 2. 7 90 h 1 l 00°C 92.) a I • 3 42 I 1 50°C 96.5 a 8. 7. 90 h I I 00°C 9 I. 9 a 0.9 64 1200°C 96.6 a 2.4 6! h 1200°C 88.6 a 0.8 8 1)00°C 96. I a 0.0 24 h 1200°C 89.0 a 0. 7

Fe-Ho55.4Fe 64 h 1200°C 8 7. 0 a 0.4 couple

22 1226°C 87.4 a 0.8 26jh l200°C 89.2 a I. 4 I 6 1277°C 83.7 a 0.5

Fe-Mo67.7Fe 8 l300°C 83.9 a 0.6 couple 90 h I I 20°C 91 . I a 0.3

M.o-Mo67.7Fe couples Mo55.4Fe-Mo67.7Fe couple

63 l250°C 57.5 I 5. I 22 h 1226°C 60. I 40 1277°C 5 7. 5 I. 5

In the Mo-Fe couples the values are mostly a little less than one. This means, tgat in the Kirkendall igterface (from 93 at% Fe at 1100 C to 84 at% Fe at 1300 C) Mo diffuses a little faster than Fe. This is not found in the Fe-Mo93.9Fe couples. But in this type of couple the calculations are very inaccurate because 0.1 at% devia­tion in the position of the marker interface means a deviation of 100% in the DFe/DMo ratio. The ratio in the ~-phase is larger than 1.

Therefore, we can roughly conclude that:

88 (a) the ditfusion of Mo in the a-solid salution is

faster than of Fe (V, Cr and Au diffuse also faster than Fe in a-Fe);

(b) the ditfusion of Mo in the ~-phase is slower than of Fe.

8.3 Conclusions

(a) The phase diagram of the Ma-Fe system is determined by using ditfusion couples as wel! as two-phase alloys. Considerable differences occur between these methods. The phase diagram using ditfusion couples (Fig. 8.12) is the better one because in that case the phases are formed at the annealing temperature.

(b) In the system three intermetallic phases occur in addition to the a- and y-solid solutions and the solid salution of Fe in Ma, viz. (i) the ~-phase at all annealing temperatures, having a hardness of 1300 kg/mm 2 and a homogeneity rgnge of 56.6 to 61 at% Fe which narrows above 1250 C; (ii) the R-phase occurring above 1200°C, having a hardness of 1350 kg/mm 2 and a homogeneity range widening with increa­sing temperatures; (iii) the cr-phase which was p0e­sent in ditfusion couples at 1100, 1277 and 1300 C, having a homogeneity range at 1300°C of 44 to 47 at% Fe.

(c) If carbon is present as an impurity in iron, a layer of the Mo 3 Fe 3 C n-carbide phase was formed in Ma-Fe (+C) couples at all temperatures. Besides, after prolonged annealing at all temperatures the ~-phase

0 and, above 1200 C, the R-phase were also formed.

(d) The lattice paramete rs have been d e termined in the various phases occurring in this system. The para­meters of the ~-phase at the Mo-rich side are a little larger than at the Fe-rich side.

(e) The layer growth of the a-solid salution in Fe-Ho couples is parabolic, which mea ns that the ditfusion is governed by a volume ditfusion mechanism.

( f) The activatien energy in the a-solid solution, inde­pendent of the type of couple and of concentration, has a value of about 57 kcal/male and frequency factor of about 2 cm2 /sec. The value of the activa­tien energy in the ~-phase is about 70 kcaljmole and of the frequency factor about 3 cm 2 jsec.

(g) Ma is the fastest compone nt in the a-solid solution; in the ~-phase the reverse is true. This Kirkendall effect is an indication that the ditfusion is gover­ned by the vacancy mechanism. 89

C H A P T E R 9

DIPFUSION IN THE Mo-Co SYSTEM

9.1 Experimental results

9.1.1 ~èY~r_grg~~h-~~èê~r~~~~~§

Almost only Mo-Co couples were used for layer growta measurements. óhe temperature range was 800 to 1300 C. At 800 and 900 C thick layers of the K-phase were formed. The layers of the a-solid salution and of the ~-phase were very thin. The pronounced grain boundary ditfusion in Cabalt is shown in Fig. 9.1

Fig. 9.1

Optiaal micrograph of a Mo-Co couple annealed at B00°C for 207h. 100x. Etchant: dilute HN0 3 •

The dominating layer abgve 90o6c was the (Co Mo ) ~­phase. At 1000 and 1100 C this layer was everi t~icker than the a-solid salution layer. The ~-layer always consisted of thin and long needle shaped grains parallel to the direction of the ditfusion (Fig. 9.2).

Fig. 9. 2

Optical micrograph of a Mo-Co couple annealed at 1200°C for JOh. 500x. Grains are visible i n the ~-lay er.

At 1000°C four intermetallic layers were visible, but only the ~-layer had a reasonable thickness. Between the ~-layer and Mo a thin and regular white layer (cr-phase)

90 was formed. Between the ~-layer and the a-solid salution

two very irregular layers were present (K-phase and a phase containing about 84.5 at% Co (see 9.2.1)). The boundary of the g- and K-phases was very irregular. At 1100 and 1200 C the ~-layer and two very thin layers were formed, one (a) between Mo and the ~-phase and one (8) between the ~-phase and the a-solid solution. At 1300°C the ~-layer was very thick. Between this layer and Mo a very thin a-layer was formed. At 1200 and 1300°C the grains of the a-solid salution near the inter­metallic layers showed striations (Fig. 9.3).

Fig. 9. 3

OptieaZ mierograph of a Mo-Co eoupZe anneaZed at 7300°C for 3h. 500x. Striations are visible in the a-soZid solution.

No concentratien gaps were detected with the mieroprobe between the striated and non-striated areas. Possible explanations are that the situations are preci­pitations from the a-solid salution during cooling or deformation patterns.

The extent of the solid salution in Co was very difficult to determine. The typical deformation structure of the Co allowed us to reveal the Co a-solid salution boundary by etching with dilute HN0 3 • 0 The measurements at and above 1000 C were used for de­terminini the penetratien constants. The thickness d of the solid salution is plotted agains ft in Fig. 9.4. The lines through the points are straight. In Table 9.1 the penetratien constants are given.

Table 9.1

Penetration eonstante (kJ of the a-soZid salution

T 0 c k (cm 2 Lsec)

1ooo 1 • 6 3 x 1 o-1 1 11 00 1 . 4 0 x 1 o-1 o

1200 7.11 x 1 o-1 o

1300 3.38 x 10- 9 91

200

d,pm

t

100

2 10 12

Fig. 9. 4

-11 10

5

2

-1

1300 1100

106.0 7.0 -1o41 -1

!T,K

Fig. 9. 5

8.0

Layer growth of the a-soZid salution in Mo-Co coupZes

Plot of Zog k vs. 7/T for the a-soZid soZution in Mo-Co coup Zes

A plot of log k against 1/T yields a straight line (Fig. 9.5); Q is 71.2 kcal/male and k 0 is 26.9 cm 2 /sec.

The layer growth measurements of the ~-phase at 1000, 1100, 1200 and 1300°C and of the K-phase at 800 and 900°C are given in Fig. 9.6 in wh~ch the d-values are plotted against lt. Curvöd lines are obtained (except at 800 and perhaps at 1300 C). This means that the growth was not parabolic, and that during the growth of the phases a mixture of two diffusion mechanisms was present, viz. volume and grain boundary diffusion. In Fig. 9.7 logdis plotted against log t for the growth of the ~-phase. From the slopes of the lines the values of n (in equation dn = kt) have been calculated (Table 9.2).

It is clear from the n-values that with decreasing tem-92 perature the importance of the grain boundary diffusion

40

20

!. h

./ 0 / 0 l//1200C

I; 0

;;. /;" 0

!. • I. 0

5

----0 0 1100 c

6:K. ph a se at 9 oo" C

•

20 25

Fig. 9.6 Layer growth of the ~-(Co 7Mo 6 ) phase in Mo-Co coupZes

102 d,pm

5 I 2

1 10

5

2

1 2

-t,h

Fig. 9.7 Plot of Zog d vs. logt for the ~-(Co 1Mo 6 ) Zayer in Mo-Co coupl e s

mechanism increases. No activatien e ne rgy for thi s phase could, therefore, be determine d in Mo-Co couples.

Layer growtg measurements on the ~-phase were c arried out at 1150 C in a number of incremental diffusion cou­ples. The couples were: Co-Mo44.5Co; Mo-Mo86.5Co; Mo44.5Co-Mo62.0Co and Mo-Mo62.0Co; the growth of the e- 93

94

Table 9.2

SLopes (n) of the log d - log t plots

T oe n

1300 2.12 1200 2.32 1100 2.40 1000 2.53

phase was measured in the Mo79.0Co-Mo86.5Co couple. In Fig. 9.8 the d-values are plotted against IE. It is clear that the growth is parabalie in these types of couple. The ~-layer in the Mo-Mo62.0Co and Mo44.5Co­Mo62.0Co couples was difficult to measure, because the boundary with the Mo62.0Co alloy was not clear, particu­larly in Mo-Mo62.0Co couples. These measurements are omitted in Fig. 9.8. The ~-phase in the Mo44.5Co-Mo62.0Co couple consisted of big grains at the Co-rich side and of small grains at the Mo-rich side, which were not needle-shaped as in the Mo-Co couples. The Kirkendall interface was recognised by the change in morphology. The ~-phase in the Co-Mo44.5 couple also contained small but not needle-shaped grains and showed cracks.

150

' d,pm

t 100

o Co-Mo44.5Co

• Mo44.5Co- Mo62Co

50

Fig. 9.8

5 10 112 1f2 -t ,h

15 20

0 Layer growth of the ~-(Co 7Mo 6 ) phas e at 7750 C in the following aouples: Co-Mo44 .5Co , Mo44.5Co­Mo62.0Co and Mo-Mo86.5Co. Layer growth of the 6-(Co 9 Mo 2 ) phase at 7750°C in the Mo?9.0Co­Mo86.5Co aouple.

If Mo was one of the starting materials, the morphology of the ~-phase at the Mo-rich side of the Kirkendali interface was always the same. The grains were very thin and needle-shaped in the direction of the diffusion. The Kirkendali interface in Mo-Co couples was situated in the a-solid salution or at the boundary between the a­solid salution and 8-phase; therefore, the ~-layer con­sisted only of needle-shaped grains. In the 8-layer in the Mo86.5Co-Mo79.0Co couple no grains could be discerned.

9.1.2 ~!~~Q2~QQ~-~~~~~~~~~~~~ A great number of penetratien curves were determined. Most of them were used for the calculation of the dif­fusion coefficients by the computer program described in Chapter 3.

~Q=ç;;Q_~Q!:!2!~ê

Penetratien curves wÖre determined in couples annealed between 800 and 1300 c. In Fig . 9.9 a number of curves are given. The o-layer was always very thin; therefore, the concentratien gradient in that layer could not be determined.

40

I a 30

20

10

- J 100 200 300 400

- distance . pm

Fig. 9.9 Pe netr ation curves i n some Mo - Co couples 95

ÇQ:~Q22~§ÇQ_~gg_~Q:~Q22~§ÇQ_gQ~Qb~ê

The couples were annealed between 1050 and 1300°C. In Co-Mo93.6Co couples only a-solid salution was formed without any phase boundary. These couples are similar to the Ni-Mo90.0Ni and Fe-Mo93.9Fe couples.

ÇQ=~Q11~2ÇQ_~D9_ÇQ=~Q~2~QÇQ_QQ~Qb~ê

The couples of the bormer type were also annealed be­tween 1050 and 1300 C, these of the latter type only at 1250, 1273 and 1300°C. In the couples the a-solid solu­tion and the ~-phase layers were formed and below 1250°C thin 8-layers. An example of a penetratien curve of each type of couple is given in Fig. 9.10. The couples are similar to Ni-Mo41.2Ni and Fe-Mo55.4Fe types.

100

80 at%'Co

t 60

40

20

100 200 -distanca,pm

Fig. 9.1 0

Penetration curves in various types of coupZe

~Q11~2ÇQ=MQ§~~QÇQ_~D9_MQ=MQ§~~QÇQ_QQ~Qb~ê

The couples were annealed between 1050 and 1300°C. An example of a penetratien curve of each type is given in Fig. 9.11. In the Mo44.5Co-Mo62.0Co couples only the ~-phase was formed and in Mo-Mo62.0Co couples the ~­and o-phases. In the Mo62.0Co alloy and the ~-phase at the side of the alloy pores were formed.

MQ=MQZ2~QÇQ_QQ~Q!êê

The couples were annealed between 800 and 1150 to in­vest~gate the formation of the ~- and K-pgases below 1000 C and the ~- and 8-phases above 1000 C. One pene-

96 tratien curve is given in Fig. 9.11.

0 The couples were annealed at 1050, 1100 and 1150 C.They were prepared to investigate the formation of the e­phase. In Fig. 9.11 an example of a penetratien curve is given.

20

ct e ...---

__r·.-.1

I

J 20.Q...._distance. vm 40 0

Mo 79 Co-Mo86.5Co 145 h 1150° c

Fig. 9.11 Penetrat i on curves in various types of couple

~2=~211~2ÇQ_~QgQ!~§

In these couples, annealed at 1250, 1273 and 1300°C, the solid solubility of Co in Mo was measured.

ao.-----------~K~_r--~~~

at %Co _] .... _..

t r- Mo71 Co- Mo79 Co

60

40 Mo-Mo71Co

20

50 100 - distance. pm

Fig. 9.12

Pene tration curves in two types of couple annealed at 950°C for 7? da y s 97

~Q:~Q21~QÇQ_~~9-~221~QÇQ:~Q22~QÇQ_~Q~E!~2

The couples were ahnealed at 800, 850, 900 and 950°C . An example of a penetratien curve of each type of couple is given in Fig. 9.12. In the Mo71.0Co-Mo79.0Co couples only the K-phase was formed.

9.1.3 §~EQ~êêê-~ê~ê~~ê~ê~~§ The Vickers micro-hardness was determined in the diffu­sion zone of a number of diffusion couples. In Table 9.3 the hardness values of the various phases are given.

The hardnessof the K-phase, debermined in the Mo71.0Co­Mo79.0Co couple annealed at 900 C for 17~d, was 420 kg/

2 mm . Only the hardness of the ~-phase and of the K-phase was determined. The layers of the other intermetallic phases were toa thin.

Table 9.3

Viakers micro-hard n es s vaZues Hv (Zoad 50g) of some p hases i n the Mo-Co system

Couple Treatment Hv in kg/mm 2

Ma ~-phase a-s.s.n

Co-Mo 7h 1300°C 200 1200 495 Co-Ma 96h 1200°C 250 1250 450 Co-Mo44.5Co 145h 1100°C 1200 400 Mo-Mo62.0Co 280 1200x Mo44.5Co-

Mo62.0Co 1200x Co-Mo44.5Co 96h 1200°C 1300 532 Mo-Mo62.0Co 263 1280X Mo44.5Co-

Mo62.0Co 1268x

averaged 240 1240

con

255 233 232

250

243

à the indentations were aften deformed. x the layer of the ~-phase, at the Co-rich side was

poreus.

9.1.4 ~:f~Y-Q!ÉÉ~~~~!Q~ In Table 9.4 the results of the X-ray diffraction ana-

98 lysis for some alloys are summarised.

Alloy

Mo29.0Co Mo44.5Co Mo62.0Co Mo62. OCocb Mo71.0Co Mo79.0Co Mo79. OCo Mo86.5Co

Table 9.4

Results of the diffraatograms taken from various Ma-Co aZZoys

Treatment Phases identified

8h 1300°C (Mo); )J . 0

1200°C I

48h (Mo); )J 24h 1250°C )J ; (Co)? 3~d 11 00°C )J; (Co)? 20d 975°C (Co)~;)J?; K? 18d 975°C (Co)~; K 56h 1100°C (Co) !l

(Co)+ 6d 11 00°C (Co)~;

!l the solid salution of Ma in Co with a hexagonal structure.

+ the solid salution of Ma in Co with a cubic structure.

eb some reflections could nat be identified.

For the last four alloys, the lattice parameters of the a-solid salution of Ma in Co were calculated. 0 For the Mo62.0Co and Mo44.5Co alloys annealed at 1200 C, the lattice parameters of the )J-phase were calculated. The r esults are given in Table 9.5.

Table 9.5

Lattiae parameters aaZauZated from diffraatograms

all oy treatmen t phase l attice pärameters in R Mo62.0Co 24 h 1250°C w a 3 b ~ 4.731+0.003; c=25.34+0 .01 Mo44.5Co 48 h 1200°C w =4. 7 70"+0. 002.; =25.63"+0.01 Mo71.0Co 20 d 975°C (Co) he x ~2 . 575"+0. 00 I; =4 . 160"+0.00 1 Mo79.0Co 18 d 975°C (Co) he x •2 . 565"+0.001; =4 . 120"+0.00 1 Mo79.0Co 56 h I I 00°C (Co) he x =2.565"+0.005; =4 . 1 13+o.ooa Mo86 .5C o 6 d I I 00°C (Co) cub a• 3 .58 9"+0.003

The lJ-phases in the Mo62.0Co and Mo44.5Co alloys are saturated with Co (58.5 at% Co) and with Ma (51 at% Co), respectively. The structure is hexagonal. Thus going from the Co-saturated boundary to the Mo-saturated boundary the lattice parameters of the phase change for 99

a and Q from 4.731 to 4.770 ~ and for c from 25.34 to 25.63 ~. The lattice parameters calculated by Forsyth et al. 42 fora crystal containing 53.85 at% Co are almost equal to these we calculated for the Mo-saturated phase. In Table 9.6 the values of the lattice parameters obtai­ned by Henglein and Kohsok 87 and by Forsyth et al. are given for comparison.

Table 9.6

Lattice parameters (~) of the ~-(Co 7 Mo 6 ) phase as given in the literature

Forsyth et al. 42

53.85 at% Co a=4.762+0.001 c=25.61S+0.005

Hengleinet al. 87

53.7 at% Co a=4.767+0.005 c=25.6S+0.01

Hengleinet al. 87

Co-saturated a=4.725+0.005 c=25.42+0.02

To explain the shift in the lattice parameters in the ~-phase over the composition range, we must conclude that no compositional vacancies are found at the Co- and Mo-rich sides of the phase, because in that case the lattice parameters should have their maximum values at 54 at% Co (as has been found at 50 at% Ni in the NiAl­phase, where Ni vacancies were formed at the Al-rich side, and Ni atoms, which are smaller than Al atoms, dissolved substitutionally at the Ni-rich side 92 ).

In the ~-phase at the Co-rich side the Co atoms will occupy Mo places and at the Mo-rich side vice versa.

The (Co) is present in the alloys in the hexagonal form, except in the Mo86.5Co alloy annealed at 1100 C, where it is in the cubic ferm. The solid salution of Mo in Co transformed entirely or partly into the close-packed hexagonal structure if quenched from the f.c.c. area, as was also found by Quinn et al. A number of Mo-Co ditfu­sion couples have been investigated by X-ray diffraction in order to prove the texture in the ~-layer (se e for a description of this phenomenon sectien 9.1.5).

!~!~QQ~f!!Q~

Henglein and Kohsok 87 showed that the Co 7 Mo 6 a nd the Fe 7 W6 phases are isomorphous. The structure of the Fe 7 W6

phase had been determined by Westgren 88 using Arnfelt's 89

100 data. The structure parameters of Co 7 Mo 6 were recently

refined by Forsyth et al. 42 using single-crystal data. Positional parameters, very similar to those of Fe 7 W6 ,

were obtained. The structure of the ~-phase is based on the ideal stoi­choimetry A7 B6 • The prototype of thesecompoundsis Fe 7 W6 • It belongs to the C 3d5-R3m space group, and the rhombohedral unit cell contains 13 atoms.

Fig. 9.13 illustrates the relation between the rhombohe­dral unit cell and the equivalent hexagonal unit cell containing 39 atoms. The (Co7Mo 6 ) ~-phase appears to be completely ordered (Forsyth et al.); the smaller Co atoms occupy the two sites with 12-fold coordination (called CN12) and the Mo atoms occupy the 14-, 15- and 16-fold sites.

Fig. 9.13

Equivalent rhombohedral and hexagonal unit aells of the ~-phase (A 7 B6 )

struature. Th e A and B atoms are represented by the dots and airales , respeatively

These coordinationpolyhedraare joined toeach other along the three-fold axis. The CN16 atoms form graphite­like sheets and the CN14 atoms farm rows. It is generally accepted that texture may occur in layers growing in diffusion couples. Such a texture may appear when the structure of the phase i s such that the a toms move more e asily in one direction than in an other. The function of texture may be favoured by other factor s like epitaxial growth on the parent material and recrys­tallisation texture because of internal stresses in the diffusion zone.

102

Heumann et al. 90have found a texture in the Fe 2Al dit­fusion layer in a Fe-liquid Al couple. They found 5the layer to grow very fast and only the Al atoms diffuse in the phase. The needle-shaped crystals grow in the direction of their c-axis. The authors explained these facts by assurning that Al atoms can move very fast in the c-direction because of the high structural vacancy concentratien along the c-axis. Ayel et al. 91 found the same when the Fe 2Al 5 crystals were deposited from the gasphase. Van Loo 71 has also found texture in the TiA1 3 layer formed in Ti-Al couples. The study of the texture in this layer is still in progress. To our knowledge, no paper has yet been published in which a detailed descrip­tion is given of the occurrence of texture in ditfusion layers growing between two solid metals.

~~EêE!~~~i~!-Eê~~li~ In all the diffractograms of the Mo-Co couples the same reflections appeared. The annealbng temperatures were between 1032 and 1300°C. At 1300 C couples were examined after two different annealing times, viz. 8~ and SO~h, which gave the same diffractograms. Abviously, processes which are able to destray texture in a layer, e.g. re­crystallisation, had not taken place in the ~-layer after prolonged annealing at 1300°C. All couples were abraded perpendicularly to the diffusion direction until the ~­phase was exposed. Here and there were small areas where the base metal was visible. In most of the couples this was Mo, because it was easier to0 abrade the Co than the Mo. In the couple heated at 1032 C, Co was used as base material, but the diffractogram was identical with the ethers. Etching did not affect the diffractograrn very much.

In Table 9.7 the diffractograms of a number of couples are given. Most of them were recorded by CuKa radiation,

SO~h 1300°C

~ 1obs

2.37 vs

2.05 s 1.95 mw 1.91 w 1 . 37 m 1. 30 vw 1.18 s

v = very; 8 -

Table 9.7

Diffraatograms of the ~-phase formed in Mo-Co diJfusion couples

8\h 1300°C I 16h 1200°C 145h 11S0°c 16h 1100°C

~ 1obs ~ 1obs ~ 1obs

~ 1obs

2.37 vs 2.37 s 2.37 s 2.37 vs 2.07 w 2.08 w 2.07 w 2.07 w 2.05 s 2.05 m 2.04 wm 2. 04 m 1. 96 w 1. 95 vw 1. 95 vw 1.95 w 1. 91 vw 1. 92 vw 1. 91 w 1. 37 wm 1. 37 vw 1. 37 w 1. 37 w 1. 30 w 1. 30 w 1. 30 w 1. 30 wm

1.19 mw 1 .18 m 1 .18 m

strong; m z:::: me dium; w = weak.

48h 1032°C hkl

~ 1obs

2.38 vs 110 116

2.05 m 201 1. 96 w 204 1.92 vw 205 1 .37 wm 300 1. 31 w 306 1 .19 m 220

some by CoKa radiation. In the diffractograms reflec­tions caused by Mo were sametimes visible. For comparison, an alloy of the ~-phase containing 56.1 at% Co was melted and homogenised at 1270°C for 3h. The alloy was very brittle, and it was possible to grind it to powder. Of the finest powder fraction a Debye-Scherrer photograph was made and a diffractogram was taken by means of a counteó diffractometer, using CuKa radlation from 26: 25 to 54 • The results are listed in Table 9.8.

Table 9.8

ResuZts of the Debye-Scherrer photograph and the diffractogram of the Mo56. 7Co aZZoy

Debye-Scherrer EhotograEh

d I obs

2.37 m 2.17 m 2.12 w 2.08 s

2.02 m 1. 96 w 1 . 90 w 1. 83 vw 1. 78 vw 1. 3 7 w 1 . 33 w 1 . 3 0 vw 1 . 28 vw 1. 22 w 1 . 1 8 w

Q!§9~§§!Q!!

Diffractogram

d I obs

2.37 ms 2.16 s 2.12 ms 2.07 s 2.05 m 2.01 s 1. 96 w 1. 90 m 1 . 82 w

hkl

11 0 1 • 0. 1 0 0.012 11 6 201 1 . 0. 11 204 205, 118 0.0.14 1.0.13 300 2.1.10 306 1 • 0. 1 9 2. 1 .1 3 220

It was alre ady clear from the diffractograms of the two­phase alloys (Table 9.4) that all reflections found for the Fe 7 W6 phase, were also present in the X-ray patterns of the alloys. The positions of the reflections were calculated trom the lattice ~arameters given by Forsyth et al. 42 and Hengleinet al. 7

The ~-phase containing 56.1 at% Co also gives almast all r e flections of the Fe 7 W6 pattern. But camparisen of the results in Table 9.8 with these of Table 9.7 shows that in the diffractograms o f the ~-phase forme d in Mo-Co couples the reflections with high C-indices are absent, viz. (1.0.10); (0.0.12), (1.0.11), (0.0.14), (1.0.13), (2.1.10), (1.0.19) and (2.1.13). It is clear that tex- 103

ture is present in the ~-phase. We have calculated, therefore, the angles (~) of a number of reflecting planes with the plane (001) (Table 9.9).

Table 9.9

AngZes ~ of a number of refZeating pZanes of the ~-phase with the pZane (007)

plane hkl ~ plane hkl ~

11 0 90° 0.0.14 00 1.0.10 31° 15 I 1 . 0.13 33° 35 1

0.0.12 60 17 I 300 90° 116 60° 2.1 .1 0 58° 40 1

201 75° 38 1 306 71° 38 1

1.0.11 27° 52 1 1 . 0 .1 9 19° 37 1

204 72° 51 ' 2.1.13 oo 205 720 29 1 220 90° 11 8 52° 55 1

Comparison of the Tables 9.7, 9.8 and 9.9 shows that only the planes parallel to or making a small angle with the c-axis give reflections. The conclusion must be drawn that for most crystals in the layer the c-axis is perpendicular to the direction of the diffusion. From Fig. 9.13 it might follow indeed that more possibilities for atom movements exist in the direction perpendicular to the c-axis than in the c-direction. The layers consist of very small needle-shaped grains in the direction of the diffusion (Fig. 9.2). So the needle-axis is perpen­dicular to the c-axis of the ~-phase. Insection 9.1.1 it is mentioned that the mechanism of the layer growth of the ~-phase in Mo-Co couples is mainly volume diffu­sion with partly grain boundary diffusion (n >2). In the TiA1 3 layer grain boundary diffusion occurred also. 71

ÇQ!}S:!!:!.ê:!:2!:!.ê There is texture in the ~-(Co 7Mo 6 ) layer formed in solid Mo-Co couples annealed b e tween 1032 and 1300°C. The c-axis lies perpendicular to the direction of the diffusion. The texture is pronounced, and the angles of thÖ reflecting planes with the c-axis are less than 30 .

- We believe that in this phase a kind of pipes are present perpendicular to the c-direction, in which Mo or Co atoms will move easily.

- If there is texture in a diffusion layer, the grains are aften needle-shaped in the direction of the diffu­sion. This implies that grain boundary diffusion may

104 easily occur.

9.2 Evaluation of the results

9.2.1 Q~~~f~!~~~!Q~_QÉ-~~~-Q~~~~-g!~9f~~ The phase diagram was determined in two ways, using dif­fusion couples and two-phase alloys. The results are compared with each other and with those given by Quinn and Hume-Rothery~ 0 and Hansen 33 (Fig. 9.14 and Table 9. 1 0) •

0

e

tJ :.,. -- ----­./I f 4J I IJ

/,;' K I liJ ',, I/ I :1 I

10

30 20 10 0

100

Fig. 9.~4 The phase diagPam of the Mo-Co system aceoP­ding to Quinn and Hume-RothePy 40

Q!!!~~!Q~_gQ~Q1~ê

In Table 9.11 the averaged boundary concentrations de­termined in diffusion couples are listed and are shown in Fig. 9.15. At 1000°C only Mo-Co couples were used. The o-(Co Ma ) layer was mostly too thin (2-4 ~m) for accurate bon~entration determination. The concentrations of this layer are those as determined in about the middle of the layer.

The determination of the Mo-rich boundary concentratien of the ~-phase was more difficult than of the other, because the profile was more curved at the Mo-side. 105

800 900

1000 1100 1200 1300

T oe

I 300

1213

12 50

1200

l I 50

1100

I 050

I 000

950

900

850

800

Table 9.10

Boundary concentrations (in at% Co) of the phases in the Mo-Co s~stem

determined by Quinn et al. 0

a-solid 8- K-solution phase phase

100-96? 75 100-94? 75 100-91? 75 100-89.5 82 100-87 82 100-84

\1-phase

54.5-50.5 54.5,.-50.5 54.5-50.5 54.5-50.5 54.5-50.5 54.5-50.5

Table 9.11

o­phase

37-36.5

Boundary concentrations in at% Co, determined in diffusion couples

in the Ma-Co system

()-sol i <I sol ut ion 0-phase K-phase J,J-phase o-phase

100-80. 7(7) 58.8-51.)(10) '\. ] 6x {4)

100-80. 8( I) 59. o-s 1. s c 1) "- ) 7x ( l)

100-81.5(') 58 .6-51. 2(7) '\.)6x ( 3)

\00-82.7(7) "'8 1 x (6) 58 . 6 - 51 . 3(10) 40.0-36.8 ( 2)

1 00 - 84. 2 (5) 8 1 .4-80.6( 5 ) 58 . 5- 51.4(6) '1.. )6)( (2)

!00-8 5 . 9( 4) 82.7-81 . 4(2) 58 .4 - 5 1.6(6) '\.)6 (I)

100-86.5(4) 83 . 1- 81 .l.(4) 58 .4- 51.5(1) '\.) sx ( 2)

I 00-88.5 (I) 7).0-75.7(1) 58.5-51. S (I) '\..)61((1)

100-89.5(1) 76.6-7 5. I ( 2) ? -52. 0(3)

,x 76.0-H .S()) 58 -5 I. 5 (I)

I00-98.2?x(l) 76. 2-74.9 (2) "'SSx(2)

100-92 . Gx (2) 76.5-74.7(3) 59 -52( I)

x very th in

(in brackets the number of dilfusion coupl es used for the decermination)

(Mo)

1-1.2-1.4-1 • 7-2.0-3.0-

(Ho)

1. s-o (6)

I . 6-0 (I)

I. 6-0 ( s) I. J - O ( 7)

I. 1- 0 (4)

I. J -0( 4)

I . 2 - 0 (5)

I. 0-0 (I)

0.6-0(J)

0.9-0(3)

0.8-0(2)

0 . 9-0 (')

The Mo-Co couples annealed at 1000°C contained the a­phase, the \1-phase, the K-phase and the a-solid solution; furthermore a layer with a concentratien range of 84-84.8 at% Co (see Fig. 9.15). It is clear that this layer is not the e-phase.

~1J:QY.ê The alloys used in incremental couples were also investi­gated with the mieroprobe to determine the phase concen­trations. These are listed in Table 9.12, and are plotted

1o6 in Fig. 9.16. No equilibrium was attained in the ~-phase

1400

T, °C

11300

1200

1100

1000

900

at% Co----

?

(Mo)~

0 10 20 30 40 50 60 70 80 90 100 at% Mo

Fig. 9.15 The phase diagram of the Mo-Co system acear­ding to the results in th e diJfusion couples

14001-oc

1300f- t 1200

1100

at%Co---

ó è 9 ' '

-

70 80 90 100

Fig. 9.16 The phase diagram of the Mo-Co system acear-ding to the results in the two-phas e alloys 107

Table 9.12

Phase aonaentPations in at% Co in annealed Mo-Co alloys

T •c a-so lid aolut ioo e-phase K-phase u-phase cr-phue (llo)

I 300 -80.4 (I) 5 9.0( 1)-50.6(3) 37.9(3) 6. 9 (2)-

12 7 3 -50. 7 (2) 37.9 (2)

I 250 -79.5(1) 58.7(1)-50.5(3) 37.9(3)

1200 -79.6 ( I ) 58.5(1)-50.9(1)

I 150 -80.5(2) 58.9(2)-50.9(1)

1100 -80.6(2) 58.4(2)-50 .9(1 ) 36.3 (I)

lOSD -86.5 (I) 83.4(1)-80.8(2) 58.4 (2 )-5 I. I (I)

950 -89.2 (I) 76.7(1)-75 .3( 1)

850 76.8(1)-75 . 9(1) 58 . 0 ( 1)-

800 -96 . 1 ( 1 ) 76.9(1)-75 . 4(1) n. 5.( 1 >-

(In brackets, the nurnber of alloys used for the determination)

6. 4 (2 )-

6.8(3)-

6. 8 (I)-

5. 9 (I)-

6.9 (I)-

6. 0 (I)-

below 1000°C. The Mo44.5Co and Mo29.0Co alloys contained mostly three phases: ~. (Mo) and sometimes cr. The cr-phase was formed remarkably slowly from the other two phases; sometimes in the middle of the cr-grain (Mo) was still present. No concentratien gradient could be detected in the cr-grains. In the Mo29.0Co alloy annealed at 1300°C for Bh large grains of the cr-phase were formed. In the diffractogram of this alloy the three phases ~. cr and (Mo) were detected (seö section 9.1.3). In the Mo44.5Co alloy annealed at 1050 C the grains were too small to find out whether cr was present.

Discussion ----------The phase diagrams agree very well with each other. However, there are some differences. There were, as mentioned before, difficulties in the formation of the cr-phase in the alloys. This process was very slow, and equilibrium was not attained. The lowest tempörature at which we met the cr -phase in an alloy was 1100 c. But in ditfusion couples the a-phase was formed as a well detectable layer even at 1000°C. Another difference is the solid solubility of Co in Mo. In alloys it was about 6.5 at% and in ditfusion couples only about 1.5 at%.

Another difference is the solid solubility of Mo in Co at 1250°C. In the alloy the solubility was 2 at% higher than in couples. In our opinion the results obtaine d from diffusion couples are the mos t accurate.

Comparison of our results with those of previous work 108 shows a number of discrepancies:

1. The ~-phase, the most important intermetallic com­pound in the system, has been observed at all an­nealing temperatures and has a constant homogeneity range of 7 at% (51.5-58.5 at% Co). Quinn et al. 4 0

found a homogeneity range of only 4 at% (50.5-54.5 at% Co).

2. No details of the composition of the 6-phase are given up to now. We have found the Mo-rich boundary at 81 at% Co which is not affected by the temperature. The Co-rich boundary moves from 83 at% Co at 1050°C to 81 at% Co at 1200°C. At 1200°C no concentratien gradient was present. The desomposition temperature must lie a little above 1200 C.

0 3. The K-Co 3 Mo phase, found up to 1000 C, has a homo-geneity range of 75-76.5 at% Co. Quinn et al men­tioned no range.

4. The o-phase is found at and above 1000°C at about 38 at% Co. In alloys no concentratien gradient has beön detected. Quinn et al. found this phase above 1250 C at about 36.5 at% Co.

5. The solid solubility of Co in Mo found in diffusion couples was nearly the same as found by Quinn et al. In our apinion the (mo) grains in the alloys have not yet reached equilibrium. The fact that the solid solubility of Co in Mo, as determined in alloys (see Table 9.12), is hardly temperature-dependent can be taken as an indication that these alloys are not in equilibrium.

6. The solid solubility of Mo in Co is at 1300°C 19.5 at% Mo and 17.5 at% Mo at 1200°C. Quinn et al. found only 16 and 13 at% Mo, respectively. At all tempera­tures a higher solid solu8ility of Mo in Co is found in this study. Below 1000 C the results with regard to the solubility of Mo in Co are too inconsistent for conclusions to be made.

9.2.2 ~~l~~l~~i~~Q~-g~~~~§~Q~-g~!~ In this system the rnalar volume Vm is calculated from the lattice parameters of the phases (except for Mo, for which the experimentally determined density is used). Only a very small error is introduced when Vm is con­s idered to be linearly dependent on mole fraction Co (Nb) . The relation used, therefore, in the calculations of the diffusion coefficients by the computer program described in Chapter 3 is:

Vm = 9.41-0.027 Nb 109

110

~hê-~=êQ119_êQ1~~!Q~ Diffusion coefficients (Dv) were calculated in. a number of concentrations in the homogeneity range of the a­solid salution from the penetratien curves measured in the following couples: Co-Mo93.5Co; Co-Mo33.0Co; Co-Mo44.5Co; Mo-Mo93.5Co and Mo-Co. The diffusion coef­ficient is almost independent of the concentratien as is shown in Figs. 9.17 and 9.18 . In the Co-Mo93.5Co couples only a narrow range of the a-solid s alution is formed. In Fig. 9.18 log Dv at 95 and 97 at% Co is plotted against 1/T. The Dv at 97 at% Co are the best, because that concentratien lies in the middle of the range of the a-solid salution formed. In Fig. 9.17 log Dv at concentrations 90 and 95 at% Co in the Co-Mo29 . 0Co and Co-Mo44.5Co couples and at the concentratien 85 at% Co in the Mo-Mo93.5Co couple is plotted against 1/ T .

5

2

-1 10

1300 1100 0 r.c-

5 D c~ec v·

2 1 -11

10

x Mo-Mo93.6Co:85at%C 5 t. Co-Mo44.5Co]9oat'Yo

v Co-Mo29.0Coj v o Co-Mo44.5CoJ95at'7o o Co-Mo29.0Coj

2

5

2

0 -1 10

5

2

-1 10

1

5

2

2 -1 10

1300 1100

\ T,°C-

\ x

cm2 0\ Dv· ~ec

t

\. o 95 at%Co

0

\ x 97 at%Co

6.0 7.0 - - -104;. -1

i' T, K

8.0 6.0 7.0 8.0

F i g. 9 .1 7

Plot of Zog Dv vs . 7/T for v a r ious concentrations in t he a-s o lid salution i n v ar ious types o f co uple

,4_;: -1 - 1g,. T, K

Fig . 9 .18

Plot of Zog Dv vs . 7/T for the a - soZid salution formed i n Co - Mo 9 3 . 6Co co u ples

It is clear that Dv is also independent of the types of couple used. For the calculation of the activatien energy and the frequency factor the values for the Co-Mo33.0Co and Co-Mo44.5Co couples are averaged. In Table 9.13 the Q and D0 are given for the different couples, calculated by the least squares method. The Ma-Co couples have nat been taken into account because of the large scatter in their results.

Table 9.13

Activati on energies Q(kcal/mole) and frequency factors D0 (cm 2 / sec)

in the a-sol i d salution

couple 85 at% Co 90 at% Co 95 at% Co 97 at% Co Q Do Q Do Q Do Q Do

Co-Mo93.5Co 72.7 5.82 70.4 2.48 Mo-Mo93.5Co 69.7 2.31

~~=~~~~:~~~} 70.8 2.77 70.0 2.03 67.6 1.07

Our results differ somewhat from those found by Davin et al. 44 They found an activatien energy of 62.8 kcal/ male and a frequency factor 0.231 cm 2 /sec in the a­solid salution between 1000 and 1300°C. The data found by Byron et al. 62 , viz. 34.8 kcal/male and 2.82x10- 6

cm 2 /sec are typical of the occurrence of grain boundary diffusion. Our activatien energie s agree well with those for self­diffusion in Co found by Mead et al. 93 , Nix et al. 94

and Hassner et al. 95 They found values of 67.7, 67.0 and 68.7 kcal/male respectively. Ruder et al. 96 , however, found an activatien energy of 61.9 kcal/male. The tem­perature range in all studies was well above 1000°C.

~~~-i~i~E~~i~11i~-E~~~~ê The ~-phase was formed in the Eollowing couples Co­Mo29.0Co; Co-Mo44.5Co; Mo44.5Co-Mo62.0Co; Mo-Mo62.0Co; Mo-Co; Mo-Mo93.5Co. In the Ma-Co and Mo-Mo93.5Co couples the ~-phase did nat grow parabolically. No ditfusion coefficients were calculated in these two types of cou­ple. In the Mo-Mo62.0Co couples the boundary between the alloy and the ~-phase was very difficult to locate. This resulte d in large v a riations in the ditfusion coef­ficients. The results determined in the Mo44.5Co-Mo62.5Co couple, in which only the ~-phase was formed, are, there­fore, the most accurate. In Fig. 9.19 the averaged values of log Dv in the ~-phase are plotted against 1/T 111

112

showing that Arrhenius' rule is obeyed. This rule is also obeyed for the Co-Mo29.0Co couples, which were annealed at only 4 temperatures.

1300 1100 2~~~---r----~-----.-.

-9 10

5 ~~ !?\

2 \à -10 2 \ \

1 o Dy.cm/sec ~

5 I \~

_: R \. 10 0

• Co-Mo29Co o\ 5 o Mo44.5Co-Mo62Co

x Co-Mo44.5Co AMo-Mo62Co

6.0 7.0 -1~ -1

T.K BD

Fig . 9. 1 9

PZots of Zog Dv vs. 7 /T for the ~-(Co 7Mo 6 ) phas e in various types of coupZe

The results of the Mo-Mo62.0Co and the Co-Mo44.5Co cou­ples are in reasonable agreement with those of the other two types of couple. Of the Mo44.5Co-Mo62.0Co and Co-Mo33.0Co couples only the activatien energies and frequency factors were calculated with the least squares me thod (Table 9.14).

Table 9.14

Activation energies {Q) and fr equency factors (D 0 )

in the ~-phase

couple

Mo44.5Co-Mo62.0Co Co-Mo33.0Co

Q(kcal/mole)

64.4 62.0

D0 (cm 2 /sec)

0.24 0.1 8

The 6-phase was formed in Mo79.0Co-Mo86.5Co couples in reasonably thick layers. Bu~ these couples were annealed only at 1050, 1100 and 1150 C and at the last tempera­ture the phase has a very narrow concentratien range, so no Q and D0 values could be calculated. The diffusion coefficient in the phase at 82 at% at 1050°C and 1100°C are 8.1x10- 12 and 1.4x10-11 cm2 /sec, respectively.

9.2.3 ~1f~ê~9~11_êÉÉê2~ In the Co-Mo and Co-Mo93.5Co couples Zr02 particles were used as markers. In incremental couples mostly small impurities revealed the Kirkendall interface. When the interface lies in the ~-phase the morphology on both sides of the Kirkendall interface mostly differed. Needle-shaped grains were always found between Mo and the Kirkendall interface and normal grains at the ether side of the interface (Fig. 9.20).

Fig. 9.20 Optical micrographs of the (a) Mo44.5Co­Mo62.0Co c ouple ann eal e d at 7200°C for 96h (750x) and (b) Mo-Mo 79.0Co couple annealed at 950°C f o r 72 days (50 0x). Th e ma r ke r inter­fa ces ar e v i s ib l e (m).

In Table 9.15 the ratios Dc0 /DM0 , calculated from eq. (15) are given, tagether with the concentratien at the Kirkendall interface.

The results are very inconsistent a nd hardly interpre­table. In t he Mo44. 5Co-Mo62.0Co; Mo79.0Co-Mo86.5Co and Co-Mo93.5Co couples small de viations in the position of the Kirkendall interface cause large deviations in the Dc0 /DMo ratio. 113

Table 9.15

The ratio Dc0 /DM0 at the Kirkendall interface

treatment treatment

Co-Ho couples Ho-Ho62. OCo couples

196 I 050°C 82. 2 l. 4 196 h I 050°C 5l. 0 16) 145 I I 00°C 85. l l. 5 145 I I 00°C 52. 7 denominator<O 96 1200°C 81. 2 2. 8 50 I I J00°C 52. 8 11

l h I J00°C 82.6 a 2. 8 50 lh 1300°C u - a u-a I. 4 Mo79. 0Co-Mo86. SCo coup l es

Co-H.o44. 5Co coup Ie 196 h 1 nso0 c 82. 5 0. 64 145 h I I 00°C a 1. a numerator<O

50 lh I 300°C 81.2 0. I 2 145 h l I 50°C 84 . 0 0. 91

Mo-Ho79.0Co coup 1 e Co-Ho93. SCo couples

196 h I 050°C 56.0 0. 74 145 h l l 00°C 96.4 a numerator<O

Ho-Ho86 . SCo coup ie 14 5 h I I 50°C 97. l 5. 6 96 h 1 200°C 97.4 13.6

I 45 h I 150°C 8-a 0. 65 96 h I 250°C 96. 7 a numerator<O

Mo44. 5 Co-Ho62. 0 couples 50 l h l 300°C 96.9 I . 9

I 96 h I 050°C 55. 7 " denominutor<O 145 h I I 00°C .H . 5 nume-rator<O I 4 5 h I I 50°C 55. 4 0 . lO

96 h 1200°C 55 . ) 0. 54 96 h I 2 50°C 55. 5 4. 87 so I h I 300°C 55. 2 0. 24

9.3 Conclusions

a. The phase diagram of the Mo-Co system has been de­termined using ditfusion couples and two-phase alloys. The phase diagram based on the results of diffusion couples is probably the best and certainly the most detailed (see Fig. 9.15).

b. The lattice parameters of the ~-(Co 7Mo 6 ) phase have been determined for both boundary concentrations.

c. The layer growth of the a-solid salution in Mo-Co couples is parabolic. The ~-layer in the Co-Mo44.5Co, Mo-Mo86.5Co and Mo44.5Co-Mo62.0Co couples and the 8-layer in the Mo86.5Co-Mo79.0Co couple at 1150°C also grow parabolically, indicating that the ditfu­sion is governed by a volume diffusion mechanism.

d. The layer growth of the ~-phase in Mo-Co couples is net parabolic. Tagether with volume diffusion, grain boundary diffusion also occurs, especially at lower temperatures.

e. A pronounced texture is found in the ~-layer formed in Mo-Co diffgsion couples at temperatures between 1032 and 1300 C. The c-axis of the hexagonal unit cell lies perpendicular to the direction of the diffusion.

f. The activatien energy in the a-solid salution is in­dependent of the type of couple and of the concentra­tion, and is about 70 kcal/mole; the frequency factor is about 2.5 cm2 /sec.

g. The activatien energy in the ~-phase is about 64 kcal/ mole; the frequency factor is about 0. 2 cm 2 /sec.

h. No conclusions can be drawn from the results obtained 114 from the marker experiments in this system.

C H A P TE R 10

THE INFLUENCE OF CARBON ON THE INTERDIPFUSION OF Mo AND Ni

10.1 Introduetion

During our solid-state diffusion investigation into the binary Mo-Ni system we have come across the important changes in diffusion behaviour which are caused by small amounts (0.06-0.4 wt%) of carbon present in the nickel. Totally different diffusion zones were built up at some temperatures, and two-phase diffusion layers often occur­red. It turned out that the n-carbides (Mo,Ni) 6 C and (Mo,Ni) 12C were formed. These carbides arealso very im­portant as precipitates in many heat-resistant Ni-based superalloys, which contain roughly equal amounts of carbon. We have, therefore, investigated in more detail the relevant part of the ternary phase diagram Mo-Ni-C by the diffusion couple technique to get more insight in the kinetics of carbide formation. Data about diffusion in this kind of systems are lacking in the literature. The general features of this study can be extended to systems as (Ni,Fe,Co)-W-C and Co-Mo-e with, of course, appropriate differences.

Fig. 10.1 shows an isothermal sectionat 1000°C of the Mo-Ni-C system according toFrakerand Stadelmaier 77 •

Fraker et al. and Ettmayer and Suchentrunk 98 investi­gated the phase boundaries of stable n-carbides in the Mo-Ni-C system. These are two n-carbide phases which are basically (Mo,Ni) 6 C and (Mo,Ni) 12 C. Mo 3 Ni 3 C and Mo 4 Ni 2 C are the boundary formulae of the M9C carbide which is saturated with Ni and Mo, respect1vely. So the metal ratio in M6 C varies widely but there is only a small variatien in the carbon content. The n-carbides belong to the space group Fd3m, Ti 2 Ni-type, having 96 metal and 16 carbon atoms in a f.c.c. lattice, with variable cubic spacings. The structure consists of octahedral and tetrahedral units. The carbon atoms occu­py the eentres of slightly distorted Mo octahedra.

Leciejewisz 99 has studied the (Mo,Ni) 12 C compound with neutron diffraction and found as its space group again Fd3m. The possibility of substitution of Mo by W and of Ni by Co and Fe clearly exists, similarly that of C by N and 0 for corresponding variatien of metal ratios.

fl This Chapter is based on a paper submitted to Metallurgical Transactions. 115

Fraker et al. 77 have giveh the variatien in lattice pa­rameters with the composition of the n-carbides (Table 10.1).

I

ll><l),.a l l),•a •Mo,C ~

At.% C

Fig. 1 0.1

Mo-Ni-C, isothermal sec­tion at 1000°C, according to Fraker and Stadelmaier 11

Table 10.1

Compositions and lattice parame t ers of the n-phas es 71

Phase comp., at% Lattice Constant, A

40Mo 48Ni 12C 11.161 42Mo 46Ni 12C 11.141 42Mo 45Ni 13C 11.143 50Mo 35Ni 15C 11.188 54Mo 30Ni 16C 11.216 56Mo 28Ni 16C 11 . 255 45Mo 47Ni se 10.894

10.2 Experimental proceduresàà

Mo-Ni diffusion couples were prepared from high-purity Molybdenum sheet and 3/8 inch Nickel rod. Spectographic

tkà Th" b . h ~s su sect~on as been reduced because the 116 procedures have already been described in Chapter 6.

analysis of the Ni rod indicated the following impurity levels (in ppm), (the carbon content is determined by a conductimetric technique)~ Si: 40, Al: 40, Fe: 250, Mg: 10, Cr: 150, Cu: 10, 0: 20, C: 600 ppm. The Mo sheet had a thickness of 0.5 mm and a purity of 99.99%.

The ditfusion couples were sealed in silica capsules under vacuum of 10-2 mm Hg, and were subjected to diffu­sion annealings at temperatures between 800 and 1295°C.

The alloy Ni+0.4 wt% C was ar8 melted in an argon atmos­phere and homogenised at 1200 C. To get the carbon in the Ni, a few holes were drilled in the Ni-disc and filled with very pure carbon powder. The couples of this alloy with Mo were annealed at 900, 1100, 1195 and 1295°C and examined with the microprobe. The couples were investigated with microscope, hardness tester, X-ray diffractometer and electron microprobe.

For the determination of penetratien curves in the electron mieroprobe NiKa, MoLa, and Cka characteristic X-ray radiation was utilised. The measurements were taken at an accelerating voltage of 30, 30, 12 kV and a probe current of 0.2, 0.2, 1.0 ~A. The counting rates of the X-rays integrated over 10 seconds were measured either in steps (stepscanning) or with a recorder (continuous scanning) across the ditfusion zone. The intensity ratio for Ni and Mo were converted to concentrations via the calibration curves given in Fig. 6.1a.

10.3 Experimental results

10.3.1 ~~yg~-g~Q~th_~g~§~rg~g~t§ If there is only one type of diffusion, the layers grow parabolically with time. A penetratien constant k, defined for a layer as kà= d/lt, where d is the thick­ness of the layer and t is the ditfusion time, can be calculated. Measurements ~ere performed at 800, 900, 1000, 1100, 1200 and 1295 C and the Ni discs were 2 to 3 mm thick. Fig. 0 10.2 gives the layer growth results at 1100 and 1295 C as examples. At 800 and 900°C a layer A is formed, consisting of a grey matrix with long thin needles. The needles become thicker at higher temperatures. In the photographs in Fig. 10.3 one can see that above 900°C two other layers exist. The one nearest to the Ni is called layer C, the

The analysis are performed by the Analytica! Labora­tory of N.V. Philips, Eindhoven, Netherlands. 117

110 o ·c

"7 • a-s. s. x layer A • a-s. s.

100 11 laye r B 11 layer B

'V laye r c 'V laye r C •

•

80 • I • d.~m 150 d.~m

t • • t

I I •

6 8 10

Fig. 10.2 Growth of the Zayers in Mo-Ni (with 600 ppm C) couples at 7000 and 7295°C. Th e thicknesses of the Ni discs are 2 and 3 . 3 mm~ respectively.

ether one is called layer B. At all temperatures a layer of the a~solid salution of ~o in Ni is formed, which grows parabolically at 1000 C and higher. Below 1000°C there is considerable grain boundary diffusion; in that case only the thickness of the thinnest part of the layer is taken into account in ordör to reduce the grain boundary diffusion. At 800 and 900 C none of the layers grows parabolically. After 231h at 9og0 c layer C becomes visible. At 1000, 1100, 1200 and 1295 C layer C having a short incubation timÖ, grows parabolically. Layer A is not visible above 1100 C. In Table 10.2 the behaviour of the layers in the diffusion couples consisting of Mo-Ni (0.06 wt% C) is described. For all these measurements one couple was used at each temperature. After each mea­surement the couple was taken out of the resin and annealed again.

To find out the influence of the re-annealing of the 118 couples, layer measure~ents in dependenee of time were

~ s. s.

·.- 's . s .

B

Fig. 10.3 Optical micrographs of diffusion c o uples con­sistin g of Mo and Ni (with 6go ppm C). The 0 tr eatments ar e : (a) 754h 800 C ( b) 237h 900 C {a) 50h 11oo0 c (d J 72h 120 0°c ( e J 77h 7295°C. 6 00x.

temperature

800°C

900°C

1000°C . 1100°C

1200°C

1295°C

Table 10.2

Lay e r growth r e sults of Mo-Ni (wit h 600 ppm c arbon) coupl e s

layer A laye r B l a ye r C

prese nt - -present - pres ent aftel:

231h

maxa at 1- 2h; present present af ter disappears af ter 66h 11h; klit.: 0 . 848

af ter 900h

disappears almost con- present af t e r af ter 145h s tant in 4h; klit.: 2 . 4

thickne ss

- d i s appears prese nt a f t e r af t e r 70h 4h; ka= 4. 0

- consta.nt pres ent af ter thickness 6h; klit.: 4.3

a -solid s o lution

presen t

pr e s ent

ka= 4.2

ka= 8 .43

klit.: 23. 7

klit.: 38.6

119

carried out at two ternperatures, 1295 and 11og0 c, using a new couple for each annealing time. At 1295 C the a­solid solution, growing parabolically, and layer B, which has a constant thickness, are present. Layer C is not occurring in these couples. This is in accordance with the findings in Fig. 10.2 that layer C does not gppear unless a secend heating had taken place. At 1100 C the results are identical with the results obtained with one couple for all annealing times.

To find out whether the layer growth is dependent on the total arnount of carbon present in the Ni-disc (which is of course a function of the thickness) three Mo-Ni-Mo couples were prepared with different thicknesses of the Ni discs. These thicknesses wÖre 2, 10 and 20 rnrn. The couples were annealed at 1295 C using periods of 25h after which the layers were rneasured. The measurements of the a-solid salution frorn these couples, and from the couple with Ni 3.3 rnrn thick, lie satisfactorily upon one straight line. The measurernents of the ether layers are drawn in the Fig. 10.4a-c. With Ni 2 rnrn thick, the incu­bation time of layer C is 25h and layer B has a maximurn at 16h. With Ni 10 rnrn thick, the incubation time of layer C is 41h and layer B has a maximurn thickness at about 40h. With Ni 20 rnrn thick, layer C is still not forrned after 150h. We assurne that the maximurn of layer B is obtained after 150h. Layer A occurs also, reachinq its

Mo-Ni(+

Table 10.3

X-ray diagrams of lay er A in three different diJfusion couples and of Mo 2 C

600 pprn C) Mo-Ni(+ 600 ppm C) Mo-Ni (+ 0. 4 wt% C) Mo2C 196h 8000C 46h 900°c 140h 11 oooc (ref .1 00)

d,~ l.a obs d,~ 1 obs d,~ 1 obs d,S1 I rel

2.60 w 2.60 w 2.60 rn 2.59 30 - - 2.37 w 2.36 30 2.28 rn 2.29 rn 2.29 s 2.27 100 2.23 rn 2.23 rn 2.23 w

2.10 w 2.07 vw 2 . 07 vw 2.04 vw 2.03 vs 1. 99 vw 1. 75 w 1. 76 s 1. 75 w 1. 75 40 1. 5 7 vs 1. 57 s 1.58 rn 1. 50 s 1. 51 rn 1. 50 s 1.50 50 1. 35 vw 1.35 w 1. 35 70 1. 28 w 1. 28 vw 1. 27 vw 1. 27 vw 1.27 w 1. 27 60

1 • 25 vw 1. 26 w 1. 25 60

120 .R s strong; rn = medium; w = weak; v very.

maximurn thickness within 25h. The occurrence of láyer A in the couple with 20 rnrn thick Ni, and a shift frorn the maximurn in the layer growth plot of layer B ~o langer annealing tirnes with greater thicknesses of the Ni disc, show clearly the dependenee of the diffusion behaviour on the total arnount of carbon present.

80 f- (a) IJ. -layer B 9 -layer A

601-d.pm

1 /

40

~. / 20 ;- >·.

/~ ·~ A'-._

"-............ 0 I

2 4 6 8 10 12 tY> hY>

Fig. 10.4

Growth of lay e rs A, B and C in Mo-Ni (with 600 ppm C) couples with different Ni 0 disas thiaknesses at 7295 C; ((a) Ni 2 mm, (b) Ni 70 mm, (a) Ni 2 0 mm) .

80

60

80

60

40

IJ. -layer B (b)

\I -layer c

d,pm

1

/V /A\ V/

V ""'--li....._b, __ /l_

2 4 6 8 10 12

-tY2,hY>

( c) A _..-t.-

x layer A A/ A layer B

A/

I d.pm

A

1 x

x

\ x \,_

x......,_x ........

2 4 6 8 10 12

- tl'> . hY> 121

122

10.3.2 ~:~èY-~~~~~è~t~~~ A number of Mo-Ni couples, in which layer A is present, were investigated by X-ray diffraction. The resulting diffractograms of three of these are tabulated (Table 10.3). The diagram of the MoF from the ASTM system is also given. The Mo 2 C, Ni and Mo phases can be identified. With the microscope were seen which phase was exposed to the X-rays. It appears that layer A, formed in the cou­ples, is respbnsible for the Mo 2 C lines.

The diffractogram of layer ~ was determined in the cou­ples Mo-Ni annealed at 1295 C for 25 and 70h. Those two

Table 10.4

Measured and aalaulated (MGC n-aarbide). The Mo-Ni whiah layer B is measured~

hkl 28 28 .:::ale. 1 oba me•s

222 27.60 27. 58 vv 400 32.00 31.95 " 331 34.9 1 34 .90 ms 422 39. 39 39 . 39 8

511 41.90 41.85 VS

333 440 45. 7 7 45.75 . 531 4 7. 96 4 7. 98 vw 6 00 48 . 71 48. 70 wm H2 6 22 54.25 54. 23 vm 444 56. 90 56.85 vv 711 58 . 68 58 . 77 m 551

731 63. 72 63. 70 vm 553 800 66. 70 66.68 " 733 68.45 6"8. 44 m 822 71. 30 7 1. 32 8

660 75 1 73.02 73 . 02 m 555 662 7 3 . 60 73 . 58 " 840 75.80 75.82 vw 91 I 7 7 . 48 77.4 9 " 753 842 78 .08 78.04 vv 664 80.24 80.2 5 vv

771 86. 23 86.23 me 933 755

10. 2. 88. 90 88.94 " 862 951 90.55 90.56 V

773 10. 2 . 9 1 . 10 91-.10 m 666

I I. I. I 99. 23 99.25 V

775 11. 3 . 1 103. 70 103.66 vv 97 1 955

X-ray diagram of layer B (+ 600 ppm aarbon) gouple is annealed at 7295 C for

28(Ti 2Ni) l/t0 (ri 2Ni)

13. 52 20 22. 32 10 27 . 24 20 31 . 48 10 34.46 20 38.96 50 41. 58 100

45.32 50 4 7. 56 10 48.38 20

53 . 22 20 56.40 20 57. 96 20

61 . 34 20 62. 96 20

65.90 10 6 7. 58 20 70.36 50

72. 16 20

76 . 54 I 0

77.12 20

80. 92 10 85. 20 50

87. 78 I 0

89. 20 10

90.0 2 I 0

97. 94 10

I 02. 02 20

Lattice parameter of the 8-phase is I 1.216 X. Lattice pa rameter of Ti 2 Ni ia 11.310 i.

in 25h

diagrams, which are completely identical, are used for the calculation of the lattice parameters. In Table 10.4 one of these diagrams is given tagether with the diagram of Ti2 Ni (Duwez and Taylor101 ), for comparison. It is clear that layer B has a Ti 2 Ni-type structure with a lattice parameter of 11.216 ± 0.004 A.

The diffractogram of layer C was determined in the Mo-Ni couple annealed for 34h at 1200°C. Ni and the a-solid salution layer were abraded and layer C, was exposed to the X-rays. Because layer C was thin, layer B and Mo also occur in the diffractogram (see Table 10.5). All the lines (apart from the four strengest lines of layer B and the strengest line of Mo) can be identified,

Table 10.5

Measured and calculated X-ray diagram of layer C (M~ 2 C n-carbide). The Mo-Ni (+ 600 ppm carbon) couple in wh~eh layer C is measured~ is annealed at 7200°C for 34h

hkl 28 28 meas calc 1obs Line belengs to

400 32.68 32.78 mw layer c 331 35.80 35.83 m layer c

3 9 .1 0 vw layer B 422 40.42 40.47 s layer c

41.60 mw layer B 511 43.00 43.05 vs layer c

45.50 w layer B 440 47.06 47.06 s layer c 600 50.15 50.11 vw layer c 442

58.45 s Mo 711 60.60 60.57 layer c 551 731 65.70 65.71 mw layer c 553 733 70.70 70.66 w layer c

71.00 mw layer B 660 73.65 73.67 s layer c 822 751 75.50 75.45 w layer c 555 771 89.35 89.37 m layer c 933 755

Lattice parameter of C-phase is 10.885 R 123

124

according to the same f.c.c. lattice as Ti2 Ni. The lat­tice parameter is calculated as 10.885 ± 0.007 A. As will be mentioned in the discussion the B- and C-layers are M6 C and M12 C n-carbides, respectively.

6-(moNi) compound was nat present in any of the couples. Therefore, a Mo-Ni (with 600 ppm eb couple was annealed for a very long time, 352h at 1200 C. A two-phase layer and a-solid salution are present now in the couple (Fig. 10.5). Diffractograms of the layer were made and the C- and 6-(MoNi) phase can be identified.

,. s.s.

...

Optical micrograph of Ma­Ni (with 600 ppm C) cou­

o ple annealed at 7200 C for 352h; 200x.

10.3.3 g~EQ~~~~-~~~ê~E~~~~tê In Table 10.6 the micro-hardness measurements, perforrned on four couples, are given. The hardness value of layer A is sornewhat higher than that of Mo2 C for which Samsonov et al. 102 give a value of about 1450 kg/rnm2 • The hard­ness values of layers B and C in these couples are about 1450 kg/rnm2 • That of the 6-(MoNi) phase in Mo-Ni (with­out carbon) couples is about 1300 kg/rnm2 • Fig. 10.6 gives the hardness as function of the distance going from Mo over layers A and B and the a-solid salution to the Ni.

Table 10.6

Vickers micro-hardness values in kg/mm 2 (load 50g) in layers formed in Mo-Ni (with carbon ) couples

thickness of Ni

wt% C tr eatment Ni a-solid so luti on A C ! ~lo

20 mm 0.06 50 h 1295 °e 128 128- 300 2009 1500 - 2 3 0

3 mm 0 . 06 26 h 129 5 °e 123 123- 300 - 1450 l•so 220

2 mm

2 mm

0.4

0.4

IS h 1295 °e 1Shi19S 0 e

; 1790 14 90

i I 7 50 I 4 70 - i

Hv. kgj• • 2

2000- I

1500 .....

10001-

500>--

,...

.~

O~M~o~~~j-.A~lB~j~~a~-1 ~s~ol~id~so~l-ut~ii-on~'~'-'L'-'~'-'~~N-i~ 0 120 240 360 480 600 720

- distance, ~m

Fig. 10.6 The hardness (Hv) in kg/mm 2 in the dijfusion sone of the Mo-Ni (with 600 ppm C) 0 aoupl e (Ni 20 mm thiak)~ annea l ed at 7295 C for 50h.

10.3.4 ~!~~Q~~Q~~-~~~ê~~~~~~tê The penetratien of Ni was determined quantitatively by stepscanning. The carbon concentratien was determined only qualitatively, because local quantitative determi­nation of carbon was not possible. From the curves obtained by stepscanning the Ni concentrations at the phase boundaries were measured and are given in Table 10.7. In all the phases present in the diffusion couples the carbon concentratien is assurned to be zero to make it possible to calculate the Ni concentration. Thus in all the curves given here, the (Mo+Ni) concentratien is assurned to be 100%. This assurnption is valid for the a­solid solution and 0-(MoNi), but not for the ether phases. However, the ratio of Mo a nd Ni concentratien in the n­carbides is not influenced by the carbon because of the very low wt% carbon. A nurnber of concentratien curves is given in the Fig. 10.7 and 10.8. 125

126

Table 10.7

Boundary concentrations in at% Ni in Mo-Ni (with carbon) diJfusion couples assuming that Mo+Ni=700%

0

thickness ~t% c treatment

ex-se lid c B A of Ni salution

I 0 mm 0.06 50 h 1295 oe -72.5 too thin 38. 5-36. I -2 mm 0.06 73 h 1295 oe -72 . 5 49 . 4-46.6 37.5-35.9 -

20 mro 0.06 70 h 1295 oe -75.5 -.

38.5-35.4 var

3. 3 mm 0.06 26 h 1295 oe -72.5 49.2-46.9 37 .2-35.7 -

2 mm 0.4 IS h 1295 oe -78 - 40.5-38.0 var

3 mm 0.06 109 h 1200 oe -75 50.0-49.2 - -

3 mm 0.06 24 5 h 1200 oe 49 . 5-49.1 - -

3 mm 0.06 352 h 1200 oe 49.5-49.0. - -2 mm 0.04 15 h I I 95 oe -66 - - var

I . 8 mm 0 . 06 92 h I I 00 oe -78 . 5 49 . 6-49.0 35.9 - 33.9 thin

2 mm 0.4 20 h I I 00 oe -85 - - var

2 mm 0.06 I I 4 h 1000 oe -BI 49.8-48.8 too thin var

3 mm 0.06 231 h 900 oe -84.5 too thin - var

2 mm 0.4 20 h 900 oe -93.5 - - var

3 mm 0.06 244 h 800 oe -94 - - var

3 mm 0.06 32 d 800 e -8 7. 5 - - var

~ in C-layer i s ó-MoNi present having a homogeneity ran ge of 48- 52 at Z ~i. + var • variable

40 80 - distance. pm

120 160

Fig. 10.7

Penetra ti on curves of Mo-Ni (with 600 ppm C) couples

100 At.% Ni 73h 129s·c

80 Ni20mmthick

60

c oooo

40 J ... .,.....--

I B . 20

j~ 0

0 80 160 240 320 - distance, ~m

Fig. 10.8 Penetration curves of MoÖNi (with 600 ppm C) couple s ann ealed at 7295 C and with different thickne sses f or Ni

In the Mo-Ni couple anneale d at 1295°c for 25h the total composition in about 10 points in the middle of layer B was determined with the microprobe. Only the a-solid solution and a 30 ~m thick B layer were present. The Mo determination was much more inaccurate than the Ni de­termination and, therefore, was carried out twice as often. The X-ray signals we re measured in the order: pure Ni, Ni in layer B, Mo in layer B, and pure Mo. Assuming that the carbon concentratien is z e ro, the Ni concentratien is 37.2 (+ 0.2) at%, and the Mo concentra­tien is 62.3 (+ 1) at%.-The atomie ratio of Mo:Ni in the B layer is 62.3:37.2 or about 1.7:1. Hereafter wetried to determine the carbon concentratien in the B layer. This was not possible because of the streng background ràdiation and the low scattering of carbon. To check this procedure of determination of the atomie ratio Mo:Ni the concentrations in the ó- (MoNi) and the a -solid solution we re determined in the same way in an alloy of 50 wt% Ni and 50 wt% Mo. For ê -(MoNi) we found 39.8 wt% Ni and 60.9 wt% Mo and for the a-solid solution 63.4 wt% Ni and 36.4 wt% Mo. 127

Examining the concentration-penetration curves using Ni containing 600 ppm carbon (Figs. 10.7 and 10.8) we find in layer A a very low and variable Ni concentration, which becomes higher with increasing temperature. The concentratien gradient of Ni in layer C is very small, only 0.5%. Above 1000°C the influence of carbon appears to be less if the contact is bad or at the edge of the couple. The concentratien curve is different from that taken in the centre of the couple, layer A is not exis­ting, layer B is very thin and layer C very thick. At 1295°C concentratien curves were measured in many couples with Ni containing 600 ppm carbon. The gradient in layer C is small. The concentratien gradient in layer B is dependent on the Ni thickness. Only in couples with 20 mm thick Ni or more, layer A, which consists of dark and white grains, appear (Fig. 10.9) illustrating the two-phase character of the layer. In' the small. white grains the Ni concentration, which is higher than in the black ones, tends to that in layer B. The Ni boundary concentratien of the a-solid salution in couples with 20 mm thick Ni is somewhat higher than in couples with thinner Ni.

Fig. 1 0. 9

OpticaZ micrograph of Ma­Ni (with 600 ppm C) cou­pl e annealed at 7295°C for 25h, with a Ni thick­ness of 20 mm; 200x.

In Fig. 10.10 the curves are given for the couples of Mo and Ni with 0.4 wt% carbon, annealed at 1195 and 1295°C, (see also Fig. 10.11). At both temperatures the Ni con­centration in the a-solid salution has shifted to higher values. At 1195°C only layer A is present with the a­solid salution and this layer A shows at the Mo side a variable Ni concentration, but close to the a-solid so­lution there exists an area in the layer which contains almest no Ni. This seems to be the pure Mo 2 C phase. At 1295°C layer A has a somewhat higher Ni concentratien and the area of the pure carbide is thin. Also layer B is present, but the Ni concentratien in layer B is some­what higher than with less carbon in the Ni. At the edge of the couple layer A is not present but layer B is very thick and has the same Ni concentratien as in the ether

128 couples.

60

15h1195°C

...--·---·-·-·-·-· ...... • -·-"' 15 h 1295 ·c

/,/

At.%Ni

/

. ~·' nil J t" . '·/ G ~

80 160 - distance.pm

15 h 1295°C

at the edge

of the couple

240 320

Fig. 10.10 Pen e tration c urves of Mo-Ni (w i t h 0.4 wt% C) coupl e s

s;s.

Fig. 1 0.11

Op t iea l miar ograph of a d i Jfu s i on aouple e on­sist i n g of Mo and Ni (with 0.·4 wt % C) 0 and annealed at 7795 C for 75h; 600x.

X-ray ernission and electron picture s of the Mo-Ni (with 0 600 pprn carbon) couple s annealed for 154h at 800 c and

for 20h at 900 + 20h at 1200 C, r espectively, illustrate the higher carbon concentratien in layer A (Fig. 10.12 a-b) . The B and C layers in the last couple show also a higher carbon concentratien than the rest of the couple. 129

S.& A Mo

a

&S. C B

b

Mo

Fig. 10.12 E~ectron and X-ray emi ss ion pictur es of two dijfusion couples consisting of Mo and Ni (with 600 gpm C) (a) 754h 800°C (b) 20h 900 + 20h 7200 C. Radiation CKa; 7200x.

10.4 Discussion

The 600 ppm carbon present in the Ni used he re, trans ­form a binary diffusion system into a system which i s in fact ternary. Since the concentration of the carbon in the diffusion zones could not be determined quantita­tively, calculations of diffusion coefficients or acti­vation energies are not possible.

The layer growth results show that the a-solid solution of Mo in Ni is the only phase which i s independent of the presence of carbon. The formation of the other com­pounds is ~nfluenced by carbon in a complicated way. Below 1200 C and with thin Ni discs there exists a two­phasÖ layer (=A), consisting of Mo 2 C and a mixed carbide. 1000 C is the lowest temperature at which this mixed carbide, which is an n-carbide o f the type M6 C with a lattice parameter of 11.216 A, is f o rmed as a single­phase layer. Comparing this para me t e r with the parame t e rs given by Fraker et al. 77 the compound is probably Mo 54 Ni 30 C16 (Table 10.1) giving anatomie ratio Mo:Ni of 1.8:1 and a carbon concentration of 2.7 wt%. We found an

130 atomie ratio between 1.8:1 and 1.6:1. So only the M6 C

n-carbide near the composition Mo 4Ni 2 C is formed in the couples. The Mo-Ni-Mo couple annealed at 1295°C for 25h has n-carbide layers of 30 ~m thickness on bath sides. Assurning that all the carbon present in the Ni has dif­fused into the n-carbide, the carbon concentration can be 3.2 wt% in that compound. With thick Ni discs (e.g. 20 rnm), i.e. with higher total amount of carbon, Mo 2 C is formed in the reaction zone at 1295°C. Qualitatively is shown that carbon is present in the diffusion zone. Another proof that the formation of A, B and C layers is caused by the presence of carbon may be found in experiments in which the carbon is ex­tracted from thÖ Ni. This extraction is carried out by heating at 1300 C in moist hydrogen. The couples of Ma with Ni, treated in this way, annealed at1100°C, do nat show any evidence of the A, B ar C layers.

Above 1000°C the M6 C (= B) layer becomes thicker at in­creasing temperatures. This layer consists of many small grains (Fig. 10.13) which become visible by interference contrast microscopy. The thicknesses of the A and B layers are rela~ed to each other. The layer growth expe­riments at 1295 C with different thicknesses for the Ni disc show this relationship very well.

Fig. 1 0.13

OpticaZ micrograph of a Mo-Ni (with 600 ppm C) coupZe, Ni t hickness 20 mm, anne aZed at 7295°C for ?Oh; 200x; interJe­renee contrast.

The so-called layer C has a composition which lies in the region of 6-(MoNi) and is, according to X-ray measu­rements, an n-carbide of the type M12 C having a lattice parameter of 10.885 A. Frake r et al. have found for this carbide a lattice parameter of 10.894 A (Table 10.1). It is clear that these are the same phases. The homo­geneity range is very narrow and lies between 49 and 49.5 at% Ni. Thus the formula of the phases is almast Mo 6 Ni 6 C. The calculated carbon concentration in this phase is 1.4 wt %. The M6 C and M12 C layers are closely connected. At increasing annealing times the M6 C layer becomes thinner and the M1 2 C layer thicker (see Fig. 10.2 and 10.4). The formation of the M6 C phase is almost instantly. A maximum exists in the layer thickness-lt curve only with thick Ni discs at 1295°C. That is, when the amount. of carbon is high enough to maintain the supply of carbon for some time. 1~

132

The following reaction scheme is proposed to explain all these phenomena. The carbon diffuses very rapidly to the reaction zone so that a sharply increased carbon concentratien is built up in a very short time. This carbon reacts with the Mo and Ni, and it farms, depending on the temperature and carbon content, Mo 2C and/or MGC n-carbide. When the carbon has run out of the Ni the M12 C n-carbide can be formed. While the process is going on, the M12 C layer becomes thicker and the Mo 2C, if present, will be trans­formed into M6 C phase and this into M12 C ghase. On pro­longed annealing of Mo-Ni couples at 1100 C and 1200°C the o-(MoNi) phase is formed, in which M12 C phase is present as islands. The o-(MoNi) reaches the same con­centration range as in the Mo-Ni system without carbon. In Table 10.8 a survey of the successive stages is re­presented. It must be noted that all stages can be found at all temperatures depending on the annealing time.

Table 10.8

Successive stages in Mo-Ni(+C) diffusion couples

Mo Ni(+C)

Mo Mo 2C+M 6 C ct-s.s. Ni

Mo Mo 2C+M 6 C M6 C ct-s.s. Ni

Mo Mo 2C+M 6 C M6 C Ml zC ct-s.s. Ni I Mo M6 C Ml 2c a-s.s. Ni

Mo Ml2c ct-s.s. Ni

Mo M12 C+o-MoNi ct-s.s. Ni

The boundary concentratien of the ct-solid solgtion in the Mo-Ni (0.4 wt% C) couple annealed at 1295 C, is 78 at% Ni instead of 72 at% Ni in the binary Mo-Ni system and at 1195°C 86 at% Ni instead of 75. This effect is found in all couples in which so much carbon i s present that Mo 2 C can be formed and is more pronounced at lower annealing temperatures and higher carbon concentrations.

10.5 Conclusions

Small amounts of carbon in Ni (0.06-0.4 wt%) complete­ly change the ditfusion behaviour in the binary Mo- Ni system.

- Dependent on the amount of carbon, the temperature and the annealing time, the phases Mo 2C, n-(Mo,Ni) 6 C and

n-(Mo,Ni) 12 C occur in single-phase or two-phase layers.

- It turned out that the ternary Mo-Ni-C phase diagram as proposed by Fraker and Stadelmaier for 1000°C is essentially valid between 900 and 1300°C. The n-(Mo,Ni) 12C phase did not show up below 900°C, although it might have been present in layers too thin to be microscopically detectable.

- The same layers occur in the diffusion couples at all temperatures. The particular time of occurring, how­ever, is dependent on the annealing time and the total amount of carbon present in the Ni. Obviously, M12 C is the most stable carbide phase occurring in the diffu­sion zone of the Mo-Ni(+C) couples.

133

134

C HAPTER 11

DISCUSSION

In the foregoing chapters the experimental results and calculations of the diffusion data in the Mo-Ni, Mo-Fe, Mo-Co and Mo-Ni-C systems have been given and discussed separately. In this chapter we shall campare the results obtained in these systems.

In the Mo-Ni, Mo-Fe and Mo-Co systems the diffusion couple technique has proved to be an accurate, fast and simple technique for the determination of phase diagrams of two metals. It gives results which are often more reliable than those determined in "equilibrated" alloys. Systematic deviations from the equilibrium concentrations at the interfaces in diffusion couples as mentioned by, among others, Masing and Eifert et al. 68 , have never been met in all the systems investigated by us. On the con­trary, it has been found that an example of such a deviation in a Fe-Mo diffusion couple as given by Masing was not correct.

The a-solid salution areas in the three systems are very extensive. The solid solubility of Mo in Fe is the highest in the three systems and that of Ni in Mo the smallest. Only the a-solid salution of Mo in Fe showed a streng tendency towards precipitation. Quenching was, therefore, necessary. o-phases are formed in the Mo-Fe and Mo-Co systems, but not in Mo-Ni. The Mo-Fe and Mo­Co systems both give rise to A7 B 6 type phases (~),

having the same crystal structure but different composi­tions. This phase is not detected in the Mo-Ni system.

With respect to the binary systems, mentioned above, the R-phase is found only in the Mo-Fe system. The a-, 8-, ~- and R-structures are related to each other. The common link is the presence of exclusively tetrahedral interstices. Only a limited number of coordination en­vironments are allowed. 97 The Ni-rich and Co-rich parts of the two phase diagrams are very similar. Each shows a MoX 3 phase. The 8-Co 9 Mo 2 phase has an ordered close-packed hexagonal structure, which may be regarded as derived from the close-packed hexagonal modification of cobalt, whilst the structure of the S-MoNi 4 at almast the same composi­tion may be regarded as a superlattice derived from the f.c.c. structure of Ni.

The layer growth gf the a-solid solutions was parabalie at and above 1000 c. Below this temperature grain boun-

dary diffusion became more important. The intermetallic phases: o-(MoNi), ~-(Fe 7Mo 6 ), ~-(Co Mo ) and e-(Co Mo ) also grew according to the parabolit r~lation, whi~h 2

means that the diffusion was governed by a volume dif­fusion mechanism.

An important exception was the growth of the ~-(Co .;to 6 )

layer formed in Mo-Co diffusion couples, in which both volume and grain boundary diffusion occurred. The layer consisted of long needle-shaped grains, in which a texture was present. The c-axis of the hexagonal cell was perpendicular to the direction of the diffusion. The grains in the ~-layers formed in incremental couples were equiaxed. Only if Mo was one of the starting mate­rials were needle-shaped grains formed. In the layer of the ~-phase in the Fe-Mo couples no indications were found for the presence of texture.

From the concentration-penetration curves of the various ditfusion couples in which the phases grew parabolical­ly, the interditfusion coefficients (Dv) have been cal­culated and from these the activatien energies (Q) and frequency factors (D0 ) •

Camparing the activatien energies calculated for the a-solid solutions, it is clear that the Q value in the a-solid salution of the Mo-Fe system is much lower than in the other two systems. This is not surprising because the solid salution of Mo in Fe in the a-state possesses the b.c.c. structure, which is less close-packed than the f.c.c. structure of the a-solid solutions in the ether two systems. It is remarkable that in all systems the ditfusion coefficient in the a-solid salution is independent of concentration, and that the activatien energies in the solid solutions agree very well with those of the self­diffusion in the transition metals.

The activatien energies determined from layer growth experiments agree with those calculated from the inter­ditfusion coefficients. This 'is surprising because the activiation energy determined from the layer growth experiments is not only dependent on the diffusion coef­ficients in the phase in question, but also on the dit­fusion coefficients of all other phases in the couple and of the homogeneity ranges of the solid solutions. As shown in the phase diagrams these ranges increase very fast with increasing temperature.

The investigations into the Kirkendall effect gave re­markable results. It has been found that in the a-solid salution of the Mo-Ni and Mo-Fe systems the Mo is the fastest diffusing component. It is a pity that in the Mo-Co system the results are so inconsistent that no conclusions can be drawn. In the intermetallic o-(MoNi) 135

136

and ~-(Fe 7Mo 6 ) phases the diffusing velocity of the species is nearly equal, or Mo is slower.

The diffusion in the three systems is fast. If the metals Ni, Fe and Co are yet used as coatings on Mo, a diffusion barrier must, therefore, be applied. A dis­advantage might be that all systems contain brittle phases. Ni seems to be the best metal for a coating, because the diffusion is slowest and at high temperatures only one intermetallic phase is formed. Carbon present as an impurity in Ni or Fe changes the binary diffusion couple Mo-Ni (or Fe) into a ternary diffusion system. In the Mo-Ni(+C) couples the kinetics of the carbide formation was studied in more detail than in the Mo-Fe(+C) couples. In the Mo-Ni(+C) couples one two-phase layer and two n-carbide (M 6 C and M12 C) layers were formed. In Mo-Fe(+C) couples one two-phase layer and one n-carbide layer, viz. Mo 3 Fe 3 C with a narrow homogeneity range round this composition were formed. The M6 C carbide in the Mo-Ni(+C) couples had a narrow range round Mo 54 Ni 30 C16 •

SUMMARY

Interditfusion phenomena have been investigated in the Mo-Ni, Mo-Fe, Mo-Co and Mo-Ni-C systems using the dit­fusion couple technique. After preparation, the ditfusion cougles were annealed at temperatures between BOO and 1300 C in evacuated silica capsules to prevent oxidation. Afterwards the couples were examined using the experimental techniques: microscopy, mieroprobe analysis, X-ray diffraction and micro-indentation hardness testing.

The layer growth of the a-solid solutions obeys the parabalie law above 1000°c. Below this temperature grain boundary ditfusion also occur. The layer growth of the intermetallic phases o-(MoNi) and ~-(Fe 7Mo 6 ) is parabo­lic. The layer growth of the ~-(Co 7Mo 6 ) phase is para­bolie only in incremental couples. In Mo-Co couples this phase is formed by bath volume and grain boundary diffu­sion.

The phase diagrams of the three binary systems have been determined using bath ditfusion couple technique and equilibrated, two-phase alloys. It is shown that the ditfusion couple technique gives more detailed results in less time than the investigation of equilibrated two-phase alloys. No deviations of the equilibrium concentrations at the interfaces in ditfusion couples were found.

The phase diagram of the Mo-Ni system deviates not essentially from that given by Casselton et al. 22

However, the boundary concentrations of the phases are somewhat different. The phase diagram of the Mo-Fe system is found to be more or less in accordance with the results of Sinha et al. 34 There are, however, important deviations in the composition ranges of the various phases. The ~­phase is formed at all annealing temperatures, the R-phase above 1200°C, and the a-phase already at 1100°C. The À-(Fe2 Mo) phase found by Sinha et al. has not been detected by us.

The phase diagram of the Mo-Co system differs not essen­tially from that given by Quinn et al. 40 The composition ranges, however, differ considerably. The ~-phase is found at all annealing temperatures, the 8-phase between 1050 and 1200°C, the K-Co 3 Mo phase below 1000°C and the a -phase above that temperature.

The lattice parameters of the Co-rich and the Mo-rich sides of the ~-phase have been calculated and are found to increase with increasing Mo content. It is concluded 137

138

that Co and Mo can replace each other. In the ~-layer formed in Mo-Co couples texture was present, in which the c-axis of the hexagonal unit cell is orientated perpendicular to the ditfusion direction.

A computer program has been written in co-operation with Dr. G.J. Visser to calculate ditfusion coefficients from the concentration-penetration curves determined with the mieroprobe using an equation given by Den Broeder. 2

It is shown that the ditfusion coefficients of the a­solid solutions of the three binary systems are inde­pendent of concentration. Arrhenius' relation applies in all cases. For temperatures between 1000 and 1300°C, it has been found that:

Dv = 0.97 exp(-66,300/RT) cm 2 /sec in Mo-Ni couples at 85 at% Ni;

Dv 2.29 exp(-57,100/RT) cm 2 /sec in Mo-Fe couples at 90 at% Fe;

Dv = 2.31 exp(-69,700/RT) cm2 /sec in the Mo-Mo93.5Co couples at 85 at% Co.

The ditfusion coefficient at the composition of 50 at% Ni in the ó-(MoNi) phase formed in Mo-Mo62.0Ni couples can be written as:

Dv = 1180 exp(-89,200/RT) cm 2 /sec for temperatures between 1100 and 1300°C.

The ditfusion coefficient in the ~-(Fe 7Mo 6 ) phase formed in Mo55.4Fe-Mo67.7Fe couples averagedover the homoge­neity range can be written as:

Dv = 3.99 exp(-71,000/RT) 8m2 /sec for temperatures between 1100 and 1300 C.

The ditfusion coefficient in the ~-(Co 7Mo 6 ) phase formed in Mo44.5Co-Mo62.0Co couples averaged over the range can be written as:

Dv = 0.24 exp(-64,400/RT) cm 2 /sec for temperatures between 1050 and 1300°C.

Marker experiments show that the Mo atoms diffuse faster than Ni or Fe atoms in their a-solid solutions. In the intermetallic ó-(MoNi) and ~-(Fe 7 Mo 6 ) phases the species Mo and Ni and Mo and Fe respective ly, move in about the same velocity or Mo somewhat more slowly. From the ex­periments in the Mo-Co system no conclusions are drawn.

In the Mo-Ni(+C) couples the kinetics of the carbide formation was studied in detail. The carbon content of the Ni samples was mostly 0.06 wt%. Dependent on the amount of carbon, the temperature and the annealing time, the Mo 2 C, n-(Mo,Ni) 6 C and n-(Mo,Ni) 12C phases occur in single-phase or two-phase layers. The M C carbide phase had a narrow range round the compositie~ Mo 54 Ni 30 C16 ,

whereas the M12 C layer consistedof Mo 6 Ni 6 C. Also in Mo-Fe couples small amounts of carbon present in the iron change the diffusion behaviour. One two-phase layer was formed at low temperatures, and at all temperatures a single-phase layer consisted of the n-carbide Mo 3 Fe 3 C. After prolonged annealing single-phase layers of the ~- and R-phase also ferm.

13 9

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2.

3. 4.

5.

6. 7. 8. 9.

10. 11 .

12. 13. 14. 15. 16.

17.

1 8.

19. 20. 21. 22.

23.

24.

25.

26.

27. 28.

29. 30. 31 .

32.

140

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143

2 jan. 1946

1963

1969

1969 - heden

LEVENSBERICHT

Geboren te Helmond

Diploma HBS-B behaald aan het Carolus Borromeus College te Helmond

Ingenieursexamen afgelegd aan de Technische Hogeschool Eindhoven

Wetenschappelijk ambtenaar in dienst van de Nederlandse Organi­satie voor Zuiver-Wetenschappelijk Onderzoek.

STELLINGEN

1. Het vaak door onderzoekers aangehaalde artikel van Masing, waarin experimenten worden beschreven over afwj.jkingen van de evenwiehts-concentraties aan de fasengrenzen in diffusiekoppels, berust wat betreft het Mo-Fe systeem op experimentele fouten.

G. Masing~ Proc.Int. Symposium on Reactivity of SoZids~ Gothenburg~ Part II, 947 (7952 )

Dit proefschrift, hoofdstuk 8.

2. De diffusiezones in de Cu-Au koppels, onderzocht door Pinnel c.s., zijn zo dun dat geen diffusie coefficient met redelijke nauwkeurigheid berekend kan worden. De activeringsenergie door hen berekend heeft dan ook weinig waarde, ondanks de toevallige goede overeenkomst met eerder werk.

M.R. Pinne l en J.E. Bennett, MetaZ Z. Trans., ~~ 7989 (7972).

3. De zeer lage activeringsenergie, door Funamizu c.s. gevonden voor de diffusie in de S-Al 3 Mg 2 fase, wordt door voornoemde auteurs toegeschreven aan het op­treden van structurele vacatures. Deze verklaring is twijfelachtig; veeleer kan men denken aan zuivere korrelgrens diffusie.

Y. Funamizu enK . vlatanabe, Tran s. J.I.M., !...1.> 278 (7972).

4. Tegen de methode, die Matthias in ZlJn proefschrift hanteert om te bewijzen dat alleen Si diffundeert in MoSi 2 fase, zijn ernstige bedenkingen aan te voeren.

K. Matthias, proefschrift~ Universiteit van KarZsruhe, 7969.

5. De diffusie coefficienten berekend door Shamblen c.s. in a-Ti-Ti 3 Ga diffusiekoppels zijn fout, wegens ge­bruik van een verkeerde concentratie-eenheid, waar­door een foutieve bepaling van de plaats van het Matano-vlak volgt.

C.E. ShambZen en C.J. Rosa, MetaZZ .Trans., ~~ 7925 (7977).

6. De analysemethode, die Blöch c.s. toepassen op complexcarbiden, geeft alleen inlichtingen over de verhoudingen waarin de metallische elementen voor­komen in de betreffende carbiden. Het bepalen van de juiste chemische formule is met de door hen gebruikte methode niet mogelijk.

R. Blöeh en A. Kulmburg, Mikrochimica Aeta, 7 240 (7970).

7. De interpretatie die Walch geeft aan de resultaten van het onderzoek naar de samenhang van de specifieke weerstand met de kristalstructuur in het systeem mangaanoxide-nikkeloxide is wat betreft het fasen­diagram onjuist.

H. Waleh, Siem e n s Z., i?_, 65 (7973).

8. Bij de berekening van de defocussering in de textuur­goniometer hebben Couterne c.s. aangenomen dat de intensiteit van de reflectie in het diffractievlak constant blijft. Een veel betere benadering is dat deze intensiteit volgens een Gausse curve verloopt.

J.C. eauterne en G. Cizeron, J.Appl.Cryst., i• 467 (7977).

9. Dat Inoguchi c.s. met behulp van röntgendiffractie de percentages Mo0 3 , NiO en CoO, neergeslagen op een alumina drager, tot in tienden van gewichts procenten nauwkeurig hebben kunnen bepalen, lijkt overdreven.

M. Inoguahi a.s., Bull. Jap . Petr. I nst ., ~, 3 (7977).

10. Het verdient aanbeveling, gezien de werkloosheid onder pas-afgestudeerde academici, kooklessen op te nemen in het na-kandidaats studieprogramma.

Eindhoven, 29 mei 1973 C.P. Heijwegen