lecture2_louisa_v6

8/8/2019 lecture2_louisa_v6

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2.Phase diagrams


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Each material can be characterized by its elemental

composition and by itsphase content. Phase contentdefines the structure of the material. Structure of thematerial determines its properties.

Components and phases

Composition of thealloy79.1 wt%

Silver 20.9wt% Copper

Example: Phase content:

(darkerphase)

(lighter

phase) Ag

Cu


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Definition:

Phase is a homogeneous portion of asystem that has specific atomic

structure, physical and chemicalcharacteristics. If more than one phaseis present in a given system, each

phase will have its own distinctproperties and a boundaryseparatingthe phases.


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Changing T can change # of phases: path A to B

Phase content depends on T & Composition (co) of the

material.

Phase diagram represents this dependence.

A

B

C

Changing Co can change # of phases: path B to C


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Interstitial Solid

Solution: atoms witha small atomic radiidissolve in the lattice(they occupyinterstitial positions).Usually interstitialatoms are: N, C, H,B. In such solutionthere is a limit of asolubility.

Superlattice: soluteatoms occupy onlyparticular positions inthe lattice, creating

additional order superlattice. Thesephases called ordered phases.

Substitutional Solid

Solution: in this solidsolution solute atomssubstitute the solvent

atoms on randompositions. Limit ofsolubility in suchcase depends onseveral conditions(Hume Rotheryrules).

Types of solid phases.1) Solid solutions:


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Solubility - The amount of one component (solute) thatcan be completely dissolved in a second component(solvent) without creating a second phase. Thesolublity is the main characteristic of solid solution.

Unlimited solubility - When the amount ofsolute that can be dissolved in a solventwithout creating a second phase is unlimited.

Limited solubility - When only a some

maximum amount of a solute can be dissolvedin a solvent. This amount is called solubilitylimit.

Solubility


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2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used

herein under license.

Illustration: (a) Water exists in three states (phases):gas, liquid, and solid. (b) Water and alcohol haveunlimited solubility. (c) Salt and water have limitedsolubility. (d) Oil and water have no solubility.


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T

+

Solubility Limit:Max concentration forwhich only a solutionoccurs.

Ex: Phase Diagram:Pb-Sn System

Question: What is thesolubility limit of Sn in Pb at 100C?

Solubility limit increases with T:e.g., if T = 150C, solubility limit = 10wt% Sn.

Example of the Solubility Limit:

Answer: 5 wt% Sn.If Comp < 5 wt% Sn: (Pb)If Comp > 5 wt% Sn: (Pb) + (Sn) coexist

5 wt% Sn


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- Size factor when the difference between

the atomic diameter of the solvent and thesolute atoms is more than 15%, thesolubility is limited (due to high level ofdistortions in the lattice).

- Crystal structure factor if the crystalstructure of the two components isidentical, solubility will be higher.

- Valence factor atoms with higher valence

(those atoms that contribute moreelectrons) usually dissolve better than thoseatoms that have lower valence (atoms thatcontribute less electrons).

- Electronegativity factor if solute andsolvent stand close in the line of the

Hume-Rothery rules for solidsolubility:


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Examples:

rat

Cu =1.278, rat

Ni =1.243, both have FCC structure. Theseelements stand very close in the periodical table: ZNi =28,ZCu =29.

rat Pb =3.5, rat

Sn =2.81. Pb has FCC structure, Sn hastetragonal structure. ZPb =82, ZSn =50, both stand in the IV

column in the periodical table.


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Phase equilibria Phases can be stable (in equilibrium state) ormetastable

(non equilibrium). Phase is stable ifits structure and

characteristics do not change with time. Equilibrium is best described in terms of a thermodynamicquantity called the free energy (G). Free energy is afunction of the internal energy of a system and also functionof the entropy of the system (the degree of randomness or

disorder of the atoms in the structure). A system is atequilibrium if its free energy is at a minimum under somespecified combination of T (temperature), P (pressure) andC (composition).

Examples:

GAt a specific T

C in wt%

G

C in wt%

Intermetallicphase withnarrowrange ofstability

Phase withwide range of

stability


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Binary phase diagram- A phase diagram for a

system with two components.

Ternary phase diagram- A phase diagram for asystem with three components.

Isomorphousphase diagram- A phase diagram inwhich components display unlimited solid solubility.

Liquidustemperature- The temperature at whichthe first solid begins to form during solidification.

Solidus temperature - The temperature belowwhich all liquid has completely solidified.

Definitions:


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b

c

a

Solid solution

a) Isomorphous phase

diagram

b) Peritectic phasediagramc) Complex phasediagram

Examples of binary

phase diagrams:


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Phase diagrams are

also constructed forsystems with morethan 2 components.Usually these

diagrams arepresented atconstant pressureand at constanttemperature. Imageon the right presentU-Fe-Al phasediagram at 850C.

Ternary Phase Diagrams:


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Hypotheticalternaryphase

diagrampresented onthe left.

(c)2003Brooks/Cole,adivisionofThomsonLe a

rning,Inc.ThomsonL

earning

isatrademarkusedhereinunderlicense.


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Binary Phase Diagrams:

Binary phase diagramsrepresent the

relationships between temperature andcompositions, showing the phases existing atequilibrium. (Pressure is held constant normally 1atm.) In phase diagrams solubility limitsare clearlyseen.

Changes in the phases existing in the alloy and/orphase quantity will influence the microstructure ofan alloy.

Microstructure is subject of direct microscopic

observations, using optical or electronmicroscopes. In metal alloys, microstructure ischaracterized by the phases present, theirproportions, and the manner in which they aredistributed or arranged.


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b

c

a

Solid solution

a) Cu and Ni are mutuallysoluble in each other inthe solid state for allcompositions.(rat

Cu =1.27, ratNi =1.24,

both FCC, same valenceand closeelectronegativities.)

b) Solid solution rangeof B in A is wider thansolid solution range ofA in B.

c) Mg2Pb is anintermediate phase.Existence of valencecompound shortensthe range of solidsolution.


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This SEM image shows the lamellar eutecticstructure in the alloy Al77wt%-Cu33wt%. Theinterlamellar spacing is about one micron.

back2


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Intermediate Phases: For some systems intermediate compounds rather than solid

solutions may be found on the phase diagram and thesecompounds have distinct chemical formulas and crystalstructures; for metal-metal systems they are calledintermetallic compounds (bonded by metallic bonds).


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Intermediate Phases:

a) Valence Compounds Valence compounds are

created when the twocomponents stands far awayfrom each other in theperiodical table.

Valence compounds arebonded by ionic or covalentbonds.

Valence compounds can beeither strictly stoichiometric

(Mg2Pb previously) or to havesome range of stability ( and on the figure).

Valence compounds are brittleand have poor electrical

conductivity.


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Intermediate Phases:

b) Interstitial Compounds When concentration of interstitial atoms (C,B,N) is

more than solubility limit, interstitial compounds arecreated: Fe

3C, TaC, TiN, WC, MnN (r

at

C=0.77,rat

N=0.74, rat

B=0.80).

These compounds are very stable, they have highhardness and high melting temperature.

According to G. Hgg, when ,

composition of interstitial compounds is: MX, M2X,M

4X or MX

2.

Homogeneity range of interstitial compounds canbe quite wide.

59.0 Teutectoid


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This is the image of two-phase structure (alpha-Fe + Pearlite)

formed in Fe-0.4wt%C alloy

10 m

S


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Hypereutectoid Steel:


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Steel : Fe-1wt%CThis secondary electron SEM image shows the cementitedelineating prior austenite grain boundaries with a thin layer.

The majority of the area being taken by the pearlite eutectoid. Eachpearlite cell has a different orientation; the dark phase is a ferritephase.

E l l l ti f th


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Example: calculations of the

amounts according to lever rule


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TEutecto

id(C)

wt. % of alloying elements

Ti

Ni600

800

1000

1200

0 4 8 12

MoSi

W

Cr

Mn

wt. % of alloying elements

Ceutectoid(wt%C)

Ni

Ti

0 4 8 120

0.2

0.4

0.6

0.8

Cr

SiMn

WMo

Teutectoid changes: Ceutectoid changes:

Steel With Alloying Elements:

E l t i l t l


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Example: stainless steel.At first, let us review Fe-Ni and Fe-Cr binary phase

diagrams:

Fe


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This figure shows that an excessive amount of chromiumcan eliminate austenite at all temperatures, making itimpossible to achieve a to transition.

Without carbon, the limit beyond which austenite nolonger forms is about 13.5 wt% chromium. However,additions of carbon help stabilize the austenite andtherefore increase this limit.

Vertical section of Fe-Cr-Cdiagram for 0.1C wt%.
http://www.msm.cam.ac.uk/phase-trans/2005/Stainless_steels/figures/FeCrC.jpg


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2003Brooks/Cole,adivisionofThomsonLea

rning,Inc.ThomsonL

earning

isatrademarkusedhereinunderlicense.

The effect of 6%manganese on the

stability ranges ofthe phases in theeutectoid portion ofthe Fe-Fe3C phase

diagram.

Summary:


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Summary:Make sure you understand language and

concepts: Austenite Cementite Component Congruent transformation Equilibrium

Eutectic phase/reaction/structure Eutectoid reaction Ferrite Hypereutectoid alloy Hypoeutectoid alloy

Intermetallic compound Isomorphous

Lever ruleLiquidus lineMetastableMicrostructurePearlite

Peritectic reactionPhasePhase diagramPrimary phaseSolidus line

Solubility limitSystemTie line

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