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TRANSCRIPT
II PARTI II
E.U. LIBR~y
"T'- ~0'8;3 Date- -~a .q. ~'5" .
General Introduction
General Introduction Chapter 1
1.1 Introduction
It is well established that characterization of crystal structure, microstructure,
crystallographic texture, flaw, defects, residual stress, mechanical properties, chemical
composition and corrosion properties are utmost essential for materials used in various
industrial applications. By controlling the defect related microstructural parameters like
small particle size as well as lattice strains, dislocation densities and stacking faults, it is
possible to obtain 'tailor made' materials with desired properties. Among various
techniques, diffraction method is widely used for the assessment of different types of
characteristics of material. Diffraction line profile of crystalline materials can be obtained
by using X-rays, electrons or neutrons. The electrons are strongly scattered by matter
through their electrostatic interactions and so are much Jess penetrating than X-rays. The
strong scattering makes electrons very suitable for examining surface films (oxide layers,
corrosion products etc.) and for examining small particle sizes by transmission through
the material. Neutrons, having magnetic moment, interact magnetically with the spinning
electrons in atoms and so are particularly used to examine the electronic structure of
magnetic materials.
X-ray diffraction method is the most useful and non-destructive tool for material
characterization, viz, crystal structure determination, quantitative estimation of different
phases present m a polycrystalline material, microstructure characterization,
measurement of residual stress and thereby mechanical properties and determination of
orientation in polycrystalline aggregates. In our present research work some
polycrystalline materials have been prepared by high energy ball milling and
conventional melting method in nanocrystalline form and special emphasis has been
given on quantitative analysis of samples containing a mixture of ph~ses and studies of
microstructural properties of prepared materials. In some cases structure property co
relations have been established also. All those studies will be discussed in detail in the
following sections with some relevance of such studies.
1.2 Historical background of X-ray crystallography
After the discovery of X-rays on I 895, X-ray crystallography was developed during
almost the span of the last century. In 1912, with Max Von Laue's discovery [I] of
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General Introduction Chapter 1
diffraction of X-rays by crystals a real understanding of the crystalline state in terms of
the distri~utions of atoms began. Further progress was achieved with W.L. Bragg's first
analysis of the structure of a crystal (rock salt) ~and with the determination of the
wavelength of monochromatic X-ray beam by his father W .H. Bragg.
Glorious advancement of this branch of science, X-ray crystallography, began with
the discovery of powder diffraction method of X-rays independently by Debye and
Scherrer in Germany in the year 1916 and by Hall in the United States in the year 1917.
In those days powder diffraction patterns were recorded photographically and basically
used to determine the atomic arrangement in metals and alloys. The technique developed
steadily and powder data have been used for the identification of unknown materials or
mixtures of phases since the late 1930s. Instrumentation for powder diffraction developed
over the years. from cameras to sophisticated diffractometers to produce diffractograms
indicating the positions of diffraction peaks and the intensity of reflections very
accurately within a short time period. Powder diffractionist gradually engaged their
attention to the problems associated with the behaviour of polycrysta11ine materials under
conditions of stress and strain, phase transformation in polycrystalline materials at high
temperature and/or pressure, the anisotropy in particle size and strain of the material and
analysis of structural imperfections. In the late 1960's the synthesis of materials by high
energy ball milling of powders was first developed by John Benjamin and his co-workers
at the International Nickel company [2]. It was found thatthis method termed mechanical
alloying could successfully produce powder materials having fine uniform particle size.
As the time goes on, mechanical alloying processing method becomes more important
with the invention that different kinds of materials e.g. solid solution alloys, dispersion
strengthened alloys, metal composites, compounds, nano-sized oxide ceramics could be
made by ball milling. There was a dramatic increase of interest in powder methods during
the I 970s, following the introduction by Rietveld in 1967 [3] of his powerful method for
refining crystal structures from powder data. Recently, X-ray powder diffraction methods
have been used to study the microstructure of different phases present in the nano-particle
sized polycrystalline sample.
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General Introduction Chapter 1
1.3 Atomic crystal structures ana microstructures: crystal imperfections
In a ·perfect cry star. atoms are arrayed in a pattern that repeats itself in three
dimensions throughout the interior of the crystal. The atomic crystal structure is based on
arrangement of the atoms in a crystal. The atoms arrange themselves in a regular and
homogenous manner to get a stable low energy configuration. The homogeneously
arranged portion of atoms is called a phase. Laue's discovery of the diffraction of X-rays
and consequent elucidation of the structures of different crystals greatly enhanced idea
about the properties of the crystalline material. It soon became apparent that, certain
properties like plasticity, electrolytic conductivity, crystal strength and some other
properties (mechanical, electrical, magnetic and optical) of materials also could not be
explained on the basis of differences in crystal structure alone. There always exist defects
in all real crystals. Consequently, it became necessary to postulate the departures from
the ideally perfect crystal structure. This departure from an ideal structure is generally
known as microstructure. Darwin in 1914 (4, 5] first postulated that there are optically
coherent regions within a real crystal such that all atoms within a region scatter X-rays in
phase with each other while some other regions are relatively tilted so that their phase
coherency is destroyed. Such an ideally imperfect crystal was thought to be like a mosaic
in which each part is perfect but slightly tilted relative to its neighbors. Hence the name
·mosaic crystal' has been introduced. But this purely imaginary concept failed to explain
many solid state phenomena and did not survive for long time.
In the middle of thirties, it was realized that the theory of ideal crystal was not able
to give a satisfactory explanation of the structure-sensitive properties of crystalline solids.
In 1928-1929, L. Prandtl (6] and U. Dehilinger [7] independently suggested that the
physical. mechanical and chemical properties of crystal were controlled. by the presence
of imperfections in the crystals. G. I. Taylor, M. Polanyi and E. Orwan (1934)
independently introduced the concept of dislocations into the theory of mechanical
properties without any direct proof of their existence [8]. In the same year (1934) Smekel
pointed out that some properties like electrolytic conductivity and diffusion in solids
could be explained properly by introducing the concept of another kind of imperfection,
namely point imperfection, due to lattice vacancy created by the displacement of one or
many atoms. The existence of dislocations in crystal was later established firmly by J.M.
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Genera/Introduction Chapter 1
Burger. Since then continued theoretical as well as experimental efforts were made to
detect. and characterize different kinds of imperfections which may exist in crystalline
materials under different conditions and play an important role in controlling several
structure-sensitive physical and mechanical properties. As a result of development of
impressive number of methods (etching by Gevers et al. [9] and Horn [10]; X-ray
techniques by Berg [11], Barrett [12], Lang [13] and Borrmam et al. (14]; decoration
techniques by Hedges et al. [15] and Amelinckx [16]; electron microscope techniques by
Bollman [ 17] and Hirsch et a!. [ 18]; Moire techniques by Hashimoto et a!. [ 19] and
Pashley et a!. [20] and field ion microscopy techniques by Muller [21-23] differentkinds
or dislocations become a observable and measurable quantity. In fact, every real
crystalline solid specimen is characterized by the crystal imperfection inherent in it and
possesses properties distinct from other specimens of same type because of these
characteristic crystal defects. It is because of this impelling reason that now-a-days study
of crystal imperfections by using various techniques has received so much attention.
Various types of crystal imperfections, lattice as well as electronic, may be classified in
the following way [24]:
Classification of crystal imperfections or defects
Defects/imperfections
1. Point imperfections
Interstitial
Vacancy
Schottky
Frenkel
2. Line imperfections
Edge dislocation
Screw dislocation
Formed by the introduction of an atom into non-atomic site.
Formed by the removal ofan atom from an-atomic. site.
Vacancy occurs in pairs of opposite ions.
Vacancy occurs in association with interstitials of same ion.
Boundary within the crystal of an extra plane of atoms.
Burgers vector is normal to the line of dislocations.
The crystal is not made up of parallel atomic planes one
above the other, rather it is a single atomic plane in the
form of a spiral. Burgers vector is parallel to the line of
dislocation.
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General Introduction
3. Plane imperfections
Line-age boundary :
Grain boundary
Stacking fault
Chapter 1
Boundary between two adjacent perfect regions in the same
crystal that are slightly tilted with respect to each other.
Boundary between two crystals in a polycrystalline solid.
Boundary between two parts of closest packing having
alternate stacking sequence.
4. Volume Imperfections
Voids and Precipitates
S.Transient
Generates from clusters of vacanc1es, interstitials and
solute/impurity atoms.
Generated and annihilated m a crystal due to phonon
phonon, phonon-atom and phonon-electron (exciton)
interactions.
Of all these imperfections present m crystals, let us briefly discuss one planar
imperfection namely. 'stacking fault' which arises from the considerations of
interruptions in the normal stacking sequence of close-packed crystallographic planes.
The detection as well as quantitative estimation of this particular type of lattice
imperfections is of prime interest in some of our present investigations on a number of
f.c.c. alloy system.
1.4 Stacking sequence: Plastic deformation and stacking faults
ln the face centered cubic structure, the atoms in the ( 111) planes are in the most
close-packed arrangement and the nearest neighbour distance is 'a/ ..fi '. For such close
packed planes, the interatomic forces are very strong and the atoms may be regarded as
hard spherical balls of uniform size held together by attractive forces. These close-packed
layers are stacked above each other in a regular manner to maintain the close packing
between them and to reduce the energy. In close-packed f.c.c. structure the normal
sequence of stacking of (Ill) planes is ABCABC. .... The planar imperfections, stacking
faults will be created when the normal stacking sequences are disturbed by any means.
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General Introduction Chapter 1
Let us discuss briefly how these sequences are generated and distributed inside a f.c.c
crystfll.
.... , \ . ,• .
(a) (b) (c)
Fig. 1.1 Close packing of equal spheres.
For the sake of simplicity, let us imagine a close-packed layer A. The second layer
B or C can go in either of the two sets of hollows on the A layer (Fig. 1.1 (a)). Therefore
every layer in the stack has to lie in one of the three positions -A, B or C - if the stack is
close-packed. Any sequence of A's, B's and C's is called a stacking order; it represents a
close packed structure provided it contains no example of AA, BB or CC. In f.c.c.
structure, slip occurs mostly on close-packed { 111} planes and the observed slip
direction is < 11 0>. Let us consider the movement of the layers when they are sheared
over each other to produce a displacement in the slip direction (plastic deformation). It
will be found that the B layer of atoms, instead of moving from one B site to the next B
site over the top of the A atoms, will move first to the nearby C site along the 'valley'
between two A atoms and then to the new B site via a second valley. Thus the B plane
will slide over the A plane in a zigzag motion. In other words, layers will be displaced
and dislocated from their normal sequences. The displacement from the normal position
is described by a vector known as Burgers vector (b). The direction of b with respect to
-the dislocation line and the length of b with respect to the identity distance in the
-direction of bare the fundamental characteristics of a dislocation. A dislocation in which
the Burgers vector is an identity period in the lattice is spoken of as 'complete', 'whole'
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General Introduction Chapter 1
or ·perfect·. Passage of such a dislocation leaves the crystal unchanged in its atomic
arrange1pent. A dislocation can be specified by giving its components along the three
crystal axes. The Burgers vector for slip in a f.c.c. crystal has the length and direction of
half a face diagonal and may be written as b = (/jJI 10].
Since the strain energy or a dislocation is proportional to b1, it is energetically
l~1vorable for dislocations in some crystals to form an 'extended dislocation' by splitting
-into two ·partial dislocations', each having smaller b than the whole dislocation. A unit
-dislocation with Burger vector b 1 thus splits up or dissociates into two partial
- -dislocations b 2 and b 3 according to the relation
( 1.1)
In f.c.c. close-packed structure, it is common to find the complete dislocation
(/jJ1 10] splits into two partials (}~121 1] and (1;;!121], with a consequent reduction in
shear strain energy [25].
(1.2)
In f.c.c. lattice, the partial dislocations may be either of the Shockley type, with Burgers
- -vector h lying on the plane of the fault or the Frank type, with b nonparallel to the fault
plane.
A decomposition of a full dislocation into partials results in a separation of partials.
The area between the partials is a discontinuity in the stacking sequence of the atom
layers and results in a stacking fault. In a f.c.c. crystal, the normal stacking sequence of
the atom layers ABCABC...... may be interrupted at a stacking fault and becomes
ABCA.j,.CABCAB ....... A fault of this type between two Shockley partials is called an
intrinsic stacking fault. It is equivalent to the removal of a close-packed layer of atoms, as
shown in Figure I .2(a).
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General Introduction Chapter 1
The result of inserting a layer, as indicated in Fig. 1.2(b), has been called an
extrinsic fault. In this fault type normal stacking sequence ABCABC...... become
A BCA .J..c.J.. BCABC .......
c c - -- B B A -..._ ./"
----~~--------A
------~-----------R ----___;~---- c
c B
............ A ../ c c --------~------A
c lJ -------+-----8 / .4 .......... A -------+-------A _/" c ......_
c -----~------c
B R ---~-----8
A A ------~-----------A A
((I) {b) (c)
Fig. 1.2 Faults in the stacking sequence of f.c.c. crystals. The lines represent the edges of (Ill) planes. (a) Intrinsic fault bounded by two Shockley partial dislocations. (b) Extrinsic fault, equivalent to an inserted plane (c) Twin fault or growth fault. Stacking sequences are indicated by dashed lines and by sequence of letters.
Another type of fault is created 111 the f.c.c. stacking sequence if the crystal
orientation on one side of a plane continues to be different from that on the other side in
the sequence shown in Fig. 1.2( c) . The fault is a twin fault or growth fault and the
~
stacking sequence in this fault type becomes ABC A CBA .....
Plastic deformation of a crystal takes place through a relative motion of the
constituent atoms under an applied stress and is related to the imperfections present in the
crystal. The main entities responsible for plastic deformation are line defects such as
dislocations, planar defects such as stacking faults and twin faults, point defects such as
vacancies and interstitial atoms. The distinguishing criterion of plastic deformation from
elastic deformation is that the normal equilibrium positions of the atoms are not restored
after the removal of external stress and as a result, a permanent change in shape occurs
without a concurrent deterioration in properties. Plastic deformation is conventionally
divided into two processes, e.g. hot-work and cold-work.
Plastic deformation on a polycrystalline material below its recrystallization
temperature is known as cold-work. The work on it above recrystallization temperature is
termed as hot-work. A polycrystalline material deformed by cold working process
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General Introduction Chapter 1
possesses high percentage of structural irregularities viz. fragmentation, distortion and
stacking faults. The cold worked tiny crystals retain a part of the mechanical energy
expended in the deformation process. In the cold-worked state, metals and alloys will, in
general. have a higher yield point and their ductility will be less than in the fully annealed
condition. Scattering of conduction electrons by dislocation arrays will increase their
electric resistance and their magnetic properties will be similarly affected.
In case of ceramics, plastic deformation introduces large number of dislocations,
which in turn increases the hardness of the material. But if plastic deformation proceed
too far then most ceramics fail in a brittle manner i.e. fracture occurs with little or no
plastic deformation.
Cold worked materials undergo the restoration process of recovery and
recrystallization by annealing during which the amount of deformation gradually
diminishes, the substance mostly recovers their elastic and electrical properties.
Crystallites in annealed polycrystalline materials grow in size. Thus, the study of one
cold worked and another fully annealed sample under the same condition will give the
idea of deformation produced in the crystals.
The usually adopted method for producing cold worked materials by plastic
deformation are rolling, hammering, filling, ball milling, wire drawing, etching,
stretching. bending, etc. The filling produces drastic cold work in a metal and
incorporates structural changes in a metal. In the ball milling process, powders are
plastically deformed and undergo three simultaneous phenomena-cold-working,
fracturing and annealing/re-welding.
There are some methods other than plastic deformation for producing cold worked
materials. These are: (a) interaction of energetic radiation with matters, causing
displacement of electrons, excitation of both electrons and atoms without displacement of
either, the displacement of atoms from lattice sites and transmutation of nuclei; (b)
quenching, producing a super saturation of point defects such as vacancies at high
temperature, stacking fault tetrahedra etc.; (c) phase transformation, such as precipitation
from a supersaturated solid solution, etc. However, detailed descriptions of all these
methods are beyond the scope of our present study.
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General Introduction Chapter 1
1.5 Stacking fault energy (y)
A·s mentioned in the earlier section, the normal stacking sequence out side the
dislocations of a f.c.c. metal is ABCABC......... and between the partial dislocations is
ABCI-AC!ABC ....... The region of the fault has a characteristic energy, called the
stacking fault energy y, which provides a force tending to pull the partial dislocations
together.
The stacking fault energy, SFE, of the close-packed metals has an important
influence on many of the physical properties of these materials. All mechanical
phenomena, which are related to dislocation motion and the resulting dislocation
configurations, are a strong function of the separation of partial dislocations, which is
determined mainly by the SFE. In addition, other phenomena such as stress corrosion
cracking and resistivity are probably related to SFE. Therefore, it is necessary to have
quantitative data on the variation of SFE with both composition and temperature.
1.6 Texture or preferred orientation
In a polycrystalline aggregate each grain normally has a crystallographic orientation
different from that of its neighbours. Considered as a whole, the orientation of all the
grains may be randomly distributed or they may tend to cluster, to a greater or lesser
degree, resulting in a disproportionately strong reflection intensity in that direction. Any
polycrystalline material characterized by the latter condition is said to have preferred
orientation or texture. Among different kind of textures, deformation textures are found
in cold-worked materials due to reorientation of the lattice of individual grains during
plastic deformation. The orientation change proceeds as plastic deformation continues,
until a texture is reached that is stable against further deformation. Annealing textures
develop in a specimen when recrystallization is permitted to occur by heating a cold
worked material at high enough temperature.
Preferred orientations are found to exist in cast metals, rolled metals, evaporated
films, electrodeposited metals, evaporated and sputtered metal films etc. Besides
metallurgical products, preferred orientations are also developed in many other materials,
including both organic and inorganic compounds, rocks, natural and synthetic fibrous
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General Introduction Chapter 1
materials. mineralogical specimen, etc. In fact, preferred orientation is generally a rule,
not exc.eption, and the preparation of a polycrystalline material with a completely random
crystal orientation is hardly possible.
The presence of preferred orientation often makes a metal or alloy industrially
important. For example. the steel sheet used for electrical transformer cores undergoes
repeated cycles of magnetization and demagnetization and requires a high permeability in
the direction of the applied magnetic field. Since the b.c.c. crystals of steel are most
easily magnetized in the [I 00] directions, rolling and the annealing treatment given in the
steel sheets are deliberately chosen to produce a high degree of preferred orientation and
maximize the number of grains having [100] in the rolling direction or (100) in the
rolling plane.
In the case of powder samples due to cleave or growth mechanism the grains and
crystallites tend to have a shape, which dose not approximate to a sphere. The crystallites
of such powders when compacted or deposited on a flat surface, tend to orient
preferentially into a particular crystallographic direction result in a disproportionately
strong reflection intensity in that direction. Thus, preferred orientation produces some
modification in the intensity distribution of Bragg reflection in the polycrystalline
materials either in the bulk or in the powder form and thus needs special attention in
microstructural analysis.
I. 7 Phase transformation
A phase may be defined as a physically distinct regwn of matter having
characteristic atomic structure and properties, which change continuously with
temperature, composition and any other thermodynamic variable. The phenomenon of
changing crystallographic structure in metals, alloys and ceramics under definite.
condition of temperature and/or pressure is known as phase transformation. The earlier
studies reveal that in order to transform one phase into another, the difference in crystal
structure requires formation of defects. Thus the defect structures give us some clues to
understand how phase transformations occur in various materials.
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General Introduction Chapter 1
In alloys, which are produced when different metals are mixed with an intention to
improv.e their mechanical and physical properties, three phases are formed as a result of
various physicochemical interactions of the components these are
(i) Solid solution,
(ii) Liquid solution,
(iii) Chemical compounds.
A solid solution consisting of two or more solid elements or compounds has a
single type of crystal lattice and constitutes a single phase. Generally two types of solid
solutions are found to exist: (i) Substitutional solid solution and (ii) Interstitial solid
solution. In the first case the atoms of the dissolved component (called solute atoms)
substitute some of the atoms of solvent (called matrix atoms) in its crystal lattice. In
interstitial solid solution the solute atoms are accommodated in the interstices of the
crystal lattice of the solvent. Generally, two types of interstitial sites are noticed. One is
octahedral interstice, which arises in the middle of the face-centered cube surrounded by
six atoms touching each other and the other is tetrahedral interstice, which forms between
four atoms [Figs. 1.3 and 1.4]. Carbon can dissolve upto 2% by weight in the face-
·a /./2
e Metal atoms e Metal atoms o Octahech·al interstices o T etrahech-al interstices
{a) (b)
Fig. 1.3 The interstitial voids in f.c.c. structure (a) Octahedral void and (b) Tetrahedral void.
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General Introduction Chapter 1
centered cubic form of iron and constitutes the most important example of interstitial
solid solution.
e 1'1etal atoms e Metal atoms
o Octahech·al interstices o Tetrahech·al interstices
(a) (.b)
Fig. 1.4 Interstitial void space in hcp structure (a) Octahedral void and (b) Tetrahedral void.
Liquid solution, unlike the solid solution is characterized by an extremely random
distribution of constituent atoms or molecules.
In chemical compounds atoms of each components arrange themselves in a regular
order at definite points of the lattice such that the crystal lattice of the newly formed
chemical compound differs completely from those of the components forming the
compound.
The new phase thus formed in alloys may or may not have the same crystal
structure as the original one. The most useful tool to judge what phases to be precipitated
out is to study "Phase Diagram". Phase diagram is a graphical representation of the
pressure. temperature and composition for which various phases are predicted under
specified condition. Mainly it is a plot of temperature vs. composition, divided into areas
where in a particular phase or mixture of phases is stable as such it forms a sort of map of
the alloy system involved.
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General Introduction Chapter 1
Two solid elements or compounds may mix together readily and thus form a one
phase solid solution. On the other hand, differences in crystal structure, valence, or
atomic size may prevent the complete interdissolution of the two components, and two
solid solutions (i.e., two solid phases) will be formed. Since the two-phase structure is, of
course. on the scale of the grain size of the solid, it is readily visible in the optical
microscope. In addition, any difference in crystal structure will show up readily in the X
ray diffraction patterns the material produces. The microhardness tester will measure any
difference in hardness of the two phases, and once again the two phases are, in principle,
mechanically separable.
1.8 Crystal imperfections investigated by X-ray and other methods: Direct and Indirect observations
A wide range of methods which exist for the studies of different types of lattice . imperfections have been reviewed by Byrne [26]. These methods can be categorized into
two groups: (i) direct observation (ii) indirect observation. The different tools that have
emerged so far to probe into the detection and characterization of various lattice
imperfections are listed below:
Direct observation
I. Etching and decoration technique
2. Field ion microscopy (FIM)
3. X-ray fluorescence (XRF)
4. X-ray and synchrotron X-ray topography (XRT AND SXRT)
5. Secondary ion mass spectrometry (SIMS)
6. Auger and photoelectron spectroscopy (AES, XPS)
7. High and low energy electron diffraction (HEED, LEED)
8. Transmission, scanning, scanning tunneling and high resolution electron
microscopy (TEM, SEM, STEM, HREM)
Indirect observation
I . Mechanical property studies
2. Electrical resistivity
3. Ultrasonic method
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General Introduction
4. Mossbauer spectroscopy
5. Solid state diffusion
6. Quenching and annealing phenomena
7. X-ray diffraction and small angle X-ray scattering
8. Neutron and Synchrotron irradiation
9. Replica-electron microscopy
I 0. Channeling studies
I I. Rutherford back scattering and positron annihilation techniques.
Chapter 1
A detailed discussion of all these techniques is difficult and also out of the scope of
the present dissertation, hence only a few important ones (direct method) are discussed
below in brief.
Some crystals are transparent to light and infrared radiation. The imperfections in
these crystals are not normally visible. However, following decoration technique it is
possible to decorate imperfections/ dislocations by introducing precipitation along the
I ine of dislocation. The position of the dislocation is revealed by the scattering of light at
the "beads" or precipitates, and can be observed in an optical microscope.
Field ion microscopy [21, 22] reveals the individual atoms in a crystal and uses ions
produced by field ionization of a suitable gas, preferably He or Ne, to project the
specimen radially on a fluorescent screen enabling the study of point defects, gram
boundaries, dislocations etc.
X-ray diffraction topography [27, 28] is an important and elegant tool to observe
directly lattice imperfections in as-grown single crystal. 'Lang' transmission topography
has been found to be a very powerful non-destructive method to characterize crystal . . microstructures involving dislocations, stacking faults, precipitates, grain boundaries.
Topography with the use of synchrotron radiation in recent years has become a powerful
and challenging method to study crystal imperfections.
When energetic ions collide with a specimen surface several phenomena occur. A
fraction of the ions sputter the atoms of the specimen surface. Some of them are back
scattered elastically. Collection and mass analysis of the sputtered secondary ions
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General Introduction Chapter 1
constitute the secondary ion mass spectroscopy (SIMS). The back-scattered sputtered
ions m:e analyzed to obtain chemical information about the specimen.
Auger and photoelectron spectroscopy CAES, XPS) techniques are used to identify
the presence of physical and chemical imperfections (interstitials, precipitates etc.) in the
surrounding matrix elements.
The scanning electron microscopy (SEM) provides a direct means of examining
surface topography of a sample at high magnifications with high resolution. The electrons
impinge on the sample and secondary as well as scattered electrons are ejected which can
be visualized on the cathode ray oscilloscope with a camera attachmept for
photographing the pictures to be used in further study.
Amongst the above listed direct methods the transmission electron microscopy
CTEM) is the most advanced and probably the most versatile technique available to
metallurgist for direct observations of high density of lattice imperfections. The
resolution of recently developed high resolution electron microscope (HREM) is even
less than l.SA 0. High Resolution Electron Microscope (HREM) is exactly the same as
TEM except that it has an even shorter wavelength or higher energy than that of TEM.
Based on the fundamental principles of wave~particle dualism and electron optics,
electron microscope was mainly developed at the Cavandish Laboratory in Cambridge by
Hirsch, Whelan and Howie [29] and independently by Bollmann [17] in order to look at
the dislocations (once considered as mere hypothesis) in a more direct and confirmative
manner. In TEM an electron beam is accelerated to 100 to 200 KV. This accelerated
beam impinges on the thin sample placed in ultra high vacuum chamber and gets
diffracted. From the sample two beams emerge, one direct and other diffracted beam. Out
of these two, the undesired beam is suppressed, while allowing the other beam to form an
image on the photographic plate. Electron microscope can be used in different ways (e.g.
for obtaining electron diffraction patterns from selected small areas of specimens; for
examining surface structures as imprinted in replica films of plastic, stripped off the
surface) but the most useful general technique involves the transmission of the electron
beam through dry and well distributed fine particles of the powder specimen over a
carbon grid. Structural details down to a size of about I nm can be observed from TEM
photograph. Due to the displacement of atoms from their ideal positions phase contrast is
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General Introduction Chapter 1
present in Bragg diffraction, which helps to locate defects in crystal. TEM is also able to
provi~e direct observation of dislocations, stacking faults, grain boundary structures, fine
precipitates, centers of strain and small clusters of point defect. In TEM dislocations
appear as dark lines and stacking faults give rise to interference fringes. A good electron
micrographs originating from diffraction contrast, reveals the position of dislocation,
stationary or moving extended nodes and even separation of partials resulting in weak
beam teclmique to estimate stacking fault energy [30, 31 ]. Under special condition, e.g.
by superposing a film of one crystal lattice on another to obtain a Moire effect it is even
possible to observe the lattice structure. In recent years, million-volt electron microscopes
have come into existence so that a thicker specimen, representative of bulk, may be
examined.
Electrons with energy 10 to 200 eV are supposed to have low energy. Low energy
electron diffraction (LEED) studies reveal the surface structure more clearly and form an
important tool in the thin film characterization. High-energy electron diffraction (HEED)
is generally carried out using electrons accelerated by potential of 50 to 100 kV. This
method gives valuable information on the arrangement of atoms in crystallites of the thin
film and their relative orientations.
The indirect techniques as mentioned above have round-wide application. We are,
directly concerned here with the X-ray diffraction method. There exist quite an
impressive number of methods to study lattice imperfections in single crystal as well as
polycrystals. Extinction [32,33], double- crystal diffractometer [34] X-ray interferometer
[35] and Kosselline studies can reveal respective lattice imperfections (mosacity, lattice
curvature etc.) in single crystals. Studies on size of precipitates (GP zones etc.), local
ordering and clustering of point defects to form large voids, increased concentration of
point defects etc. in single crystal and polycrystalline specimens can be made with the
help of small angle and diffuse scattering studies [36,37].
The method based on precise measurement of broadening, shift and asymmetry of
X-ray diffraction line profile from polycrystalline specimens were developed by Warren
school [38, 39] and have been extensively applied in the past decades [40] to elucidate
qualitatively the microstructure of the materials (deformed, vapor-grown etc.)
characterized by various types of imperfections, namely, intrinsic, extrinsic, twin or
18
General Introduction Chapter 1
growth faults, coherent domains, residual stresses, densities of dislocation and stacking
fault e1;ergies etc. In this method analysis is done considering each individual diffraction
lines and hence this method fails to characterize the materials having low symmetry
where diffraction lines are completely overlapped. In 1966 H.M. Rietveld [ 41] suggested
a total pattern fitting method, known as Rietveld method. This method has been
successfully applied for fitting the whole diffraction pattern, either overlapped or not,
' with a suitable function. In 1981, Powley suggested whole-powder-pattern
decomposition method [ 42] for refining unit cell parameters without reference to
structural method. These methods are very useful for studying the microstructures of
several materials having low or high symmetry. The following section will deal with
these methods in details.
1.9 X-ray studies on cold-worked polycrystalline materials: Consideration of stacking faults
It has been known for many years that the diffraction lines from cold worked
polycrystals are broadened and that the broadening increases with deformation.
Theoretical works of Bragg [ 43, 44] supported this view and results obtained up to 1952
have been reviewed by Greenough [45].
Improved algorithms and software for pattern decomposition and the availability of
good quality data from high resolution diffractometers have resulted in a revival of
interest in the use of 'integral breadth' in microstructural analysis. An advantage of this
approach is that, in principle, methods based on integral breadth can be applied to data
for any crystal system, but in practice the results can be inaccurate for materials with low
symmetry and large unit cells. This is due to the problem of obtaining meaningful line
profile parameters for severely overlapped reflections, but the situation may well change
as maximum entropy and other statistical methods are applied to the 'unscrambling' of
diffraction maxima. A feature of the integral method is that only average values of
microstructural parameters are obtained, which may be a disadvantage in some
application. Also, the analysis requires that an analytical function be ascribed to each
reflection which must clearly model the observed data as precisely as possible; should
allow for the breadths of convoluted functions to be readily separated and ideally should
have a physical significance. All these necessary criteria can be satisfied by using a
19
General Introduction Chapter 1
flexible function. The line profile due to size effects is often assumed to be Lorentzian
and the, form of strain profile is frequently taken as Gaussian. Being a convolution of
Lorentzian and Gaussian functions, V oigtian function introduced into by Langford [ 46] is
frequently used in line profile analysis.
Wilson has favored the 'variance' of line profile to be measured of line broadening
and subsequently theories have been developed by considering particle size, strain and
stacking fault effects (47, 48]. The method is, however, very sensitive to the range of line
profiles and therefore applicable only to these patterns where range of each reflection can
be determined properly.
The earlier X-ray studies were usually content to use peak widths but the effect of
precise peak shape, small peak displacements and slight peak asymmetry were
completely neglected during working with peak widths only (Scherrer). Warren and
Averbach [ 49, 50] were first adopted a Fourier analysis of line shapes for characterizing
microstructural properties of cold worked samples from two or more orders of a
reflection. The method appeared to be very powerful for elucidating the nature of
broadening as well as in giving information about the distribution of strain. But owing to
the difficulty in obtaining reliable Fourier coefficients for even moderate overlap of
reflections, the basic method is largely restricted to materials with high· symmetry and
even then serious errors due to unavoidable truncation of line-profile tails can occur. An
interesting alternative approach to the use of Fourier series, which to some extent.
overcomes the problem of line-profile overlap and thereby is applicable to materials
having low symmetry, was introduced by Enzo et al. in 1988 [51]. This uses pseudo
V oigt functions to model both particle size and lattice strain of crystalline material.
It is now well established that defect oriented microstructural parameters like small
coherently diffracting domains, lattice strains, dislocation density and stacking faults of a
polycrystalline material contribute to X-ray line broadening. Fourier analysis of line
profile [39] may be expected to yield valuable information about these parameters. Three
types of stacking faults are found to present in crystallographic structure, namely intrinsic
fault ( (i), extrinsic fault (c/1) and twin or growth fault(~). The peak broadening of a cold
worked profile is mainly due to combined effects of small coherently diffracting domain,
microstrains and stacking faults (a1, a11
, ~).·The asymmetry in cold-worked profile is
20
General Introduction Chapter 1
mainly due to presence of extrinsic stacking fault (a/1) and twin or growth fault (~).
Deforn:ation stacking faults ( a1 & a11) also produce a shift in the peak position of a cold
worked material from its annealed 'standard' specimen.
Conventional X-ray methods for particle size and strain analysis by the Scherrer
formula, integral breadth, Warren-Averbach's Fourier method suffer from the serious
problem of overlapping peaks in powder diffraction pattern since this methods are based
on single line profile analysis. In the mid-sixties, it became apparent to various
diffractionist that much more information could be obtained from a powder pattern if the
full power of computers could be applied to. full-pattern analysis. In 1967 [3] Rietveld
first worked out computer based analytical procedures (quite sophisticated ones for the
time as it turned out) to make use of the full information content of the powder pattern.
The method invented by him is appropriately referred to now as the 'Rietveld method' or
'Rietveld refinement' or 'Rietveld analysis'. This whole pattern fitting method was
originally applied for crystal structure refinement using neutron diffraction data [3, 158]
but now it is also used for analyzing X-ray diffraction pattern obtained from powder or
single crystal diffractometer. In the Rietveld method the least-squares refinements are
carried out until the best fit is obtained between the entire observed experimental pattern
and the entire calculated pattern based on the simultaneously refined models for the
crystal structure(s), diffraction optics effects, instrumental factors and other specimen
characteristics (space group symmetry, number of atoms, atomic position, site
occupancies, temperature factor, lattice parameters, etc.) as may be desired and can be
modeled. The refinement is conducted by minimizing the sum of the weighted, squared
differences of this calculated pattern and the observed intensities for every step in a
digital powder pattern. A key feature is the feedback, during refinement, between
improving knowledge of the structure and improving allocation of observed intensity to
partially overlapping individual Bragg reflection. The advantages of the method are of
many folds: (a) it does not requires any pure standard for quantitative anlyse; (b)
completely as well as partially overlapped reflections can be analyzed with sufficient
accuracy; (c) particle size and microstrain analysis are based on whole profile fitting
methodology; (d) structural parameters can be refined by this method and so on.
21
r-------------------~ B.U. LIBR~Y
1 F .,- ~CY63 .
Genera/Introduction Chapter 1
In Pawley method, developed by Pawley in 1981, whole-powder pattern fitting is
performed with a suitable analytical function to obtain information about microstructural
parameters [42]. The Pawley method was first proposed as a procedure for refining unit
cell parameters and providing a list of indexed integrated intensities. Either a pseudo
Voigt or Pearson VII function (introduced by Hallet a!. [52] and includes both Gaussian
and Lorentzian function) is used in most of the computer programs for Pawley and
Rietveld method to model diffraction line profile. Various works have been done till
today using psuedo-Voigt function in individual profile fitting method and Pawley
method to gather information about the microstructure of the crystalline materials [53,
54]. The individual profile fitting, the Pawley and the Rietveld methods are compared in
Table 1.1.
Table 1.1 Different features of the individual profile fitting, the Pawley and the Rietveld methods.
Individual profile-Fitting method Pawley method Rietveld method
Aim of analysis Pattern Pattern Structure decomposition decomposition refinement
Range of analysis Partial patterns Whole pattern Whole pattern
/Profile area Independent Independent Function of parameters parameters structural
<!) parameters -o ~ ---.Peak position Independent Function of unit- Function of unit-<!) parameters cell parameters ~ cell parameters 0
C: ---._Profile shape Independent of angle Angle-dependent Angle-dependent in small 28 range
A prior knowledge Null Approximate unit- · Initial cell and required to start the cell parameters structural
refinement Earameters
Recently, Rietveld and Pawley methods have also been used for ab initio structure
determination from powder data and over a hundred examples have been reported in the
literature to date.
22
General Introduction Chapter 1
1.10 A review on the study of microstructure by X-ray diffraction
From the past decades studies on the nature of structural imperfections introduced
into crystalline materials as a result of growth and plastic deformatione processes had been
the subjects of significant increasing interests to a large number of crystallographers. X
ray diffraction methods are very useful for investigation of high density of stacking fault
in heavily deformed materials. Experimental work in this field of study has been
adequately mentioned in the text of Wilson [48], Barrett and Massalski [55], Warren [39]
and Klug and Alexender [56]. In this section a short review on the significant
experimental and theoretical works made in the recent past on microstructural
characterization of materials is presented.
1.1 0.1 Early works on microstructural characterization using integral breadtlt, variance, Warren-A verbaclt method
Between 1950-1970 a large number of publications (theoretical as well as
experimental) based on comprehensive X-ray studies of crystallite size, microstrain,
stacking fault energies and dislocation densities in various metals, alloys and compounds
had been made adopting integral breadth, variance and Fourier methods. A detailed
description of those early works is almost impossible to present and beyond the scope of
our dissertation. Only a few significant references are mentioned here. These include:
Bertaut [57], Barrett [58], Warren and Averbach [49, 50], Warren and Warekois [59],
Williamson and Smallman [60], Wagner [61, 62], Michell and Hiag [63], Smallman and
Wesstmacott [64], Chtistian and Spreadborough [65], Cahn and Davies [66], Vassamillet
[67]. Davies and Cahn (68], Klein et al. [69], Welch and Otte [70], Alder and Wagner
[71 ]. Foley et al. [72], Vassamillet and Massalski [73], Howie and Swann [74], Sundahl
and Sivertsen [75], Koda et al. [76], Vassamillet and Massalski [i7], Nakajima and
Numakura [78], Wagner and Helion [79], Lele et al. [80, 81 ], Otte [82], Sengupta and
Quader [83], Goswami et al. [84], De and Sengupta [85], Rao and Rao [86], Delehouzee
and Deruyttere [87], Ahlers and Vassamillet [88].
23
General Introduction Chapter 1
1.10.2 Recent works on microstructural characterization using modified Warren A verbach method
The introduction of Rietveld method did not stop microstructural analysis by
Warren-A verbach method. Leine et al. (1980) investigated the microstructure of the
splat-cooled aluminium rich alloys using modified Warren-Averbach method [89].
Toneje and Bonefacic (1980) determined crystallite size, microstrain and stacking fault
probabilities for splat-quenched Ag -(6,8.2,11) at.% Sn alloys and compared the results
with cold-worked filings and bulk compressed alloys [90]. In many practical cases
crystallite size and microstrain are anisotropic and higher order reflections can not be
measured reliably. In such cases determination of crystallite size and microstrain from
single line analysis needs few additional assumptions compared to multiple line analysis.
Delhez et al. (1980, 1982) modified the classical theory of Warren (1969) for multi line
analysis and discussed about the errors involved in the analysis from theoretical aspects
[91. 92]. Ghosh et al. characterized the microstructure of Cu-Ge and Ag-Al alloys in
deformed state [93-95]. Ekstrom and Chafield using X-rays line profile broadening
analysis studied the milling behaviour of commercial alumina (Ab03) powders [96].
Reddy and Suryanarayana reported that the microstrain is the major source of line
broadening in Ag-Cd-In and Ag-Cd-Zn alloys [97]. Bhikshamaiah and Suryanarayana
determined the stacking fault energy in Ni and dilute Ni-Fe alloys as a function of
temperature [98]. Delhez et al. (1986) and Langford et al. (1988) made a detailed
discussion about systematic errors developed due to truncation of experimental line
profiles at a finite range [92, 99]. Pradhan et al. studied the microstructure of binary Cu
AL Cu-Si and ternary Cu-Mn-Si and Cu-Ge-Si alloys in the deformed state [53, 100-1 02].
David and Bonnet observed stacking-fault pyramid in the phase Ni73.5Al9 Ti 14Cr3.5 when
deformed at 7 40°C [ 103]. Yang and Wan studied the influence of Al on the stacking fault
energy in Fe-Al-Mn-C alloys [I04]. Balzer eta!. analyzed the line-broadening effects in
superconductors and reported that stacking fault energy increases with increasing Tc
[I 05). Vermeulen et al. suggested a method for correcting errors arising due to truncation
of line profiles [I 06, I 07]. Rosengard and Skriver made a comparative study of intrinsic,
extrinsic and twin fault probabilities found in 3d, 4d and 5d transitional metals [I 08]. Pal
et al. studied the microstructure of (Ag, Cu)-Zn and Cu-Ni-Sn alloys [I 09, II 0]. Drits et
al. studied thickness distribution and microstrain for illite and illite-smectite crystallites
24
General Introduction Chapter 1
[Ill]. Guerrero-Paz and Jaramillo-Vigueras [112] measured grain size in powders of the
Cu-15~t%Al. Cu-20at%Ni, Cu and Ni systems, milled for different times from X-ray
diffraction (XRD) pattern using Warren-Averbach method. Chatterjee et al. studied
microstructure of Pb(l-xlSnx alloys using the above method (113] and Mukherjee et al.
studied lattice imperfections in deformed zirconium based alloys [114]. Gubicza et al.
[ 115] investigated silicon nitride powders by high resolution X-ray diffraction and
obtained their particle size and dislocation density by the recently developed modified
Williamson-Hall and Warren-Averbach procedures from X-ray diffraction profiles.
Bhaumik et al. [ 116] studied microstructural parameters and stacking faults in thin films
of lead, vapour-deposited onto glass substrates, under high vacuum by detailed X-ray line
profile analysis using Warren-Averbach and Williamson-Hall method. Chatterjee et al.
[ 11 7] determined the strain and size induced broadening of the Bragg reflection from
vanadium pentoxide powders milled in a high-energy vibrational ball-mill by Warren
A verbach (W A) analysis, using a pattern-decomposition method based on pseudo-Voigt
function. Ungar et al. ( 118] analysed the breadths and the first few Fourier coefficients of
diffraction profiles of nanocrystalline powder of silicon nitride by modified Williamson
Hall and Warren-Averbach procedures and also fitted measured physical profiles of
deformed bulk copper specimen by Fourier coefficients of well established ab initio
functions of size and strain profiles. Chiriac et al. [119] measured the average crystallite
sizes of nanocrystalline FesoCo5(NbxZr1_x)7Bs (x = 0.3, 0.4 and 0.5) powders obtained by
high-energy ball milling using the Warren-Averbach method. Ungar et al. [120]
determined dislocation densities in nanocrystalline Ce02 powder by X-ray diffraction
profile analysis in modified Warren-Averbach method. Schafler et al. [121] determined
the types of dislocation for fine grained Cu 99.9% by the modified Williamson-Hall and
Warren-Averbach procedures. Ungar et al. [122] determined the density and the character
of dislocations and the size-distr~bution of grains in deformed copper specimens by the
modified Williamson-Hall and Warren-Averbach procedures. Dasgupta et al. [123]
thoroughly studied the applicability of the Warren-Averbach analysis for the case of
pseudo-Voigt (p-V) profiles. Garin et al. [ 124] determined the crystallite-size distribution
and microstrain in austempered ductile irons (ADI) subjected to cold deformation using
Warren-A verbach method.
25
General Introduction Chapter 1
1.1 0.3 Microstructural characterization by profile fitting method
Besides, the integral breadth, Variance, Fourier and Rietveld method, another very
popular method is the profile fitting method. In 1983 Turumen et a!. developed a new
method based on polynomial fitting of line profile, for interpretation of Warren -
A verbach mean square strain curve [ 125]. In 1986 Guerin et al. suggested an information
theory approach in order to obtain crystallite size distribution from X-ray line
broadening. This method reduces the errors arising due to truncation of line profile tails,
by 5% and gives better accuracy than those based on Fourier expansion [126]. Another
method was presented by Tokita and Kojima in 1987 for the separation of two or more
overlapping X-ray diffraction lines using narrowly distributed Gaussian function and one
dimensional fast Fourier transform pair. It was found that the observed diffraction lines
could be separated with accuracy of the order of I o-4 times the diffraction angles [ 127].
Line broadening analysis from synchrotron X-ray diffraction data was performed by
Huang et a!. ( 1987) for the first time and discussed in details the advantage of using
monochromatic and synchrotron X-ray in microstructural studies [128].
The use of an incident beam focusing monochromator (IBFM) m powder
diffractometry was proposed by Louer and Langford ( 1988) and discussed the advantage
of using IBFM in details [129].
The convolutive X-ray line profile fitting methodology was proposed by Enzo eta!.
(1988) [51]. This method has been applied to a series of milled fluorite samples and ultra
fine zirconia powders by Benedetti et a!. (1988) in order to study their microstructures
[130].
Recently Ungar et a!. [131] used a new procedure of X-ray line profile analysis to
study the dislocation structure and subgrain size-distributions in fatigued MANET steel.
Szekely et al. [ 132] investigated deformed copper single crystals by X-ray line profile
analysis. In another work by the same authors [133] the method of X-ray line profile
analysis was applied to obtain statistical parameters (average dislocation density, net
dislocation polarization and average dislocation density fluctuation) of the dislocation
structure developed in copper single crystals deformed in uniaxial compression.
Chatterjee and SenGupta [134] studied the strain caused by dislocation in ball-milled Ti
26
General Introduction Chapter I
sample using X-ray line broadening method. Lucks et a~. [135] characterized the
microstr~ctural imperfection in the milling products of molybdenum powder by X-ray
diffraction-line profile analysis. Boulle et al. [ 136] applied profile fitting procedures
associated with integral breadth studies and Fourier analysis for the study of the complex
Bi-containing layered perovskite SrBhNb209. Mahalingam et al. [137] studied the
variation of different microstructural parameters (crystallite size, rms strain, dislocation
density and stacking fault probability affecting the fraction of planes with film thickness)
of zinc telluride (ZnTe) thin films by the use of variance method. Recently in 2002 Sahu
et al. [138] studied microstructural characterization adopting X-ray profile fitting
techniques assuming pseudo-Voigt (p V) functions and evaluated different defect related
parameters (stacking fault densities, lattice parameter changes, rms strain, dislocation
densities etc.) for four compositions each of a-Cu-Ga and Ag-Ga alloys.
Pawley introduced a method, for refining unit-cell parameters and decomposing the
whole powder pattern in one step without reference to a structural model [ 42]. Pawley
method was extended to X-ray powder diffraction data by Toraya (1986). Various
computer programs, ALLHKL [139], WPPF [140], PROFIT [141], FULFIT [142],
ATRIB [143], LSQPROF [144], SIRPOW.92 [145], EXPO [146] were developed using
the concept of whole powder pattern fitting introduced by Pawley. The method is very
powerful in providing structure factor for Patterson or direct methods in ab initio
structure determination with powder diffraction data [147] and thus complements
Rietveld method as a combined technique for structure solution and refinement. Toraya
( 1989) refined the unit-cell parameters of Y 20 3-doped tetragonal Zr02 powders to extract
the crystallite and microstrain of the sample [139]. In 1990 Toraya et al. refined the
structure of N a2Ah Ti60 16 by Pawley method and extracted microstructural details for the
above mineral. He made a comparison of the atomic parameter. of monoclinic
Na2Ah Ti6016· refined under the same condition by Rietveld method and got a good
agreement with that obtained from Pawley method [148]. The other important work using
whole-powder-pattern fitting method includes determination of crystal structure from
poor-quality data using Patterson method by Wilson [149], crystal structure
determination from low-resolution X-ray powder diffraction data by WiJson et aJ. [150],
determination of accurate intensities from powder diffraction data and estimation of
intensities of overlapping reflections by Larson et al. [151], study of anisotropic
27
General Introduction Chapter 1
broadening in whole-powder-diffraction-pattern fitting by second-rank tensors by Le Bail
et a!. [ 152], application of the resonant scattering technique to ab initio structure solution
from powder data using SrS04 by Bergur eta!. [153], solution of crystal structures from
powder data by powder-pattern decomposition by Altomare et a!. [ 154], solution of
crystal structures from two-wavelength X-ray powder diffraction data breaking the phase
ambiguity in the non-centrosymmetric case by Gu eta!. [ 155].
Dong and Scardi [ 156] developed a new computer program (MarqX) for the
modeling of powder diffraction data which can be used for an unconstrained profile
fitting (pattern decomposition, PD or constrained modeling of the whole powder pattern
(Pawley method, PM), for single- as well as multiple-phase samples.
1.10.4 Microstructural characterization using Rietveld method
Rietveld method was first reported at the seventh Congress of the IUCr in
Moscow by H.M. Rietveld in 1966. [41, 157]. The response was slight, or, rather, non
existent, and it was not until the full implementation of the method was published
[55.93], that reactions came. In 1974, the Rietveld refinement using time-of-flight
neutron powder diffraction data was performed for the first time to analyze the
monoclinic phase of KCN by Decker et al. (159]. In 1975, Carpenter et al. attempted to
apply Rietveld method to spallation pulsed neutron source data and proposed a suitable
peak shape function based on a convolution of separate rising and falling exponential for
representing the time dependence of the initial neutron pulse [160]. In 1976, Windsor and
Sinclair obtained a good fit for nickel data from a pulsed neutron source at Harwell Linac
[ 161] using Rietveld refinement. In 1977 Mueller et a!. used a tabulated numerical peak
shape function to fit data for T~D1 5 from the ZING-P pulsed neutron source at Argonne
and got satisfactory result. Till 1977 the method was mainly used to refine structures
from data obtained by fixed wavelength neutron diffraction and a total of 172 structures
were refined in this way before 1977 [ 162].
The application of the Rietveld method to X-ray patterns slowly developed,
primarily because of the asymmetric and non-Gaussian nature and multiple spectral
components in most X-ray diffraction profiles. In the mid-1970's application of Rietveld
method was extended to X-ray data obtained with a diffractometer. Mackie and Young
28
General Introduction Chapter 1
[163], Malmros and Thomas [164], Young et al. [165], and Khattak and Cox [166] gave
the first. application of Rietveld method to X-ray data. The work of Wiles and Young in
1981 [ 167] marked the beginning of the much wider development of this method.
The popularity of the Rietveld method led to the development of many
sophisticated computer programs, usually based on Rietveld's original work [!58].
Among these most widely used are:
(i) The DBWS program written by Wiles, Sakthivel and Young for main frame
computers and later adapted for PC use [ 168]. It operates with X -ray and neutron
diffraction data in angle-dispersive mode. The other version of this program are LHPM
[169], ALFRIET1 [170] to refine only f (x) by deconvoluting a split Pearson VII
modeled g(x) from the observed data, ALFRIET2 [171] to refine structure with
incommensurate modulations and FULLPROF [172]. The latter version has been written
in to cover a variety of situations.
(ii) In 1987, Larson and Von Dreele [ 151] developed GSAS, which offers a high
flexibility and runs on a VAX-VMS machine and was recently adopted for PC use. It
works with angle dispersive and energy dispersive (time-of-flight) data. X-ray and
neutron diffraction data can be used simultaneously or independently in a structure
refinement. The program includes provisions for applying constrains on bond lengths and
angles.
(iii) XRS-82, The X-ray Rietveld System [173] is based on a collection of
crystallographic programs for the refinement of structures from single crystal data.
(iv) In 1992 Lutterrotti et al. developed a program, LSI for simultaneous refinement
of structural and microstructural parameters [174] using psuedo-Voig~ function. Izumi
( 1995) developed another program, called RIETAN for joint refinement with X-ray and
neutron data under non-linear constraints [ 175, 176]. Recently, Lutterotti et al. (1999)
developed a user-friendly software, the MAUD, based on Java platform, for material
analyzing using diffraction pattern. It can perform simultaneous crystal structure
refinement, measurement of line-broadening, texture and quantitative phase abundances
ofa mixed phase material [177-182].
29
General Introduction Chapter 1
Databases play a useful role in the course of structure determination for detecting
isostrucwral chemically related compounds. Among useful databases there are:
-PDF-2 maintained, updated and marketed by the International Centre for
Diffraction Data (ICDD, http://www.icdd.com). The PDF contains experimental data for
over 87.500 substances and more than 49,000 patterns calculated from the ICSD
database. It is consulted after collecting the powder data.
-NIST Crystal Data File (CDF) is a compilation of crystallographic and chemical
data on more than 200,000 entries and is marketed by ICDD. This is a useful database as
soon as the unit cell is known from pattern indexing.
-Inorganic Crystal Structure Database (ICSD) contains a complete crystallographic
information over 50,000 inorganic structures (http://barns.ill.fr/dif/icsd/).
-SDPD database contains references over 500 crystal structure determined ab initio
from powder diffraction data (http://sdpd.univ-lemans.fr/iniref.html).
Most programs used for Rietveld method incorporate as iterative procedure for
pattern matching [142] by fitting a calculated pattern to the observed data without the use
of a structure model, but using constraints on the positions of reflections allowed by the
space group conditions. The accuracy of results obtained as the output of refinement in
the programs available for Rietveld analysis depends on the judicious choice of the
profile function. One can use a single function or convolution of two or more functions
for approximating the observed diffraction profiles. Pearson VII [183], Split Pearson VII
[46), and psuedo-Voigt [184] functions have been demonstrated to give the best fit to the
observed X-ray profile fitting [185, 186] in structural and microstructural analysis using
Rietveld method. Dollase ( 1986) showed performance of March function in Rietveld
refinement [ 187] for preferred orientation measurement. Many authors then incorporated
March-Dollase function in Rietveld refinement codes and confirmed Dollases's
evaluation. Another interesting and apparently very powerful preferred orientation
function was given by Ahtee et al. (1989) in which the preferred orientation effect was
modeled by expanding the orientation distribution in spherical harmonies [188].
Recently, Wenk et al. introduced WIMV method for texture analysis and got tremendous
success [178].
30
General Introduction Chapter 1
The microstructural study by Rietveld method is now become very popular among
powde~ diffractionists. In 1988 Langford for the first time determined crystallite size and
microstrain using Rietveld method [ 189]. In 1993, Delhez et al. developed a theory for
the crystallite-microstrain separation [190] and reported that as long as microstructure
effects are isotropic, they can be accounted for easily in Rietveld refinements. Bokhimi et
al. [I 91] and Sanchez et al. [ 192] characterized the particle size of magnesium and
titanium oxides prepared by the sol-gel technique, by using DBDW and WYRIET. Xiao
et al. reported that the Rietveld refinement of nanostructured hollandite powders do not
converged well, due to anistropic effects associated with a fiber axis in the b direction
and fitted the powder pattern realized with a highly packed sample taking into account
the preferred orientation correction and reducing the contribution of the narrowest
reflections and reported a mean crystallite size of 108 A 0 with zero micros train [ 193].
The Rietveld method can determine the degree of crystallinity in semicrystalline
materials. Riello et al. modeling the crystalline peak profiles by psuedo-Voigt for a
sample of polyethylene terephtalate and simultaneously optimizing the background
contributions estimated quantitatively the volume fraction of silicate glass in ceramic by
RIETQUAN [194].
Pal et al. [195] prepared Fe-23Ni-3.8Mn by melting method and characterized
microstrcturally the isothermally transformed material, both in the bulk and powder
forms, by analyzing the X-ray diffraction line profile-related lattice defect parameters in
Rietveld method.
In 1998 Sriram et al. [I 96] synthesized the high-pressure cubic spinel modification
of Znln2S4 by chemical route and determine the crystallinity, phase purity and phase
transformation characteristics using X-ray diffraction data by Rietveld refinement
method.
Ungar et al. (1998) applied the dislocation based model of strain anisotropy in the
Fourier formalism of profile fitting and fitted the powder pattern of Li-Mn (spinel),
refining the parameters, namely the average dislocation density, the average coherent
domain size, the dislocation arrangement parameter and the dislocation contrast factor
[ 197]. In 1998, Popa developed a method especially for anisotropic crystallite shape
31
General Introduction Chapter 1
including the harmonic expansion [198) for better fitting of X-ray profiles. In 1999,
Scardi and Leoni reported that anisotropic line broadening of X-ray diffraction profiles
due to line and plane lattice defects can be Fourier modeled and a detailed information on
the defect structure (dislocation density and cut-off radius, stacking and twin fault
probabilities were refined together with the structural parameters) can be obtained when
applied to face-centered cubic structure materials [199]. Ungar et al. established a simple
preocedure for the experimental determination of the average contrast factor of
dislocations [200], in terms of a simple parameter q which can be used in Rietveld
structure refinement.
Studies on Rietveld refinement reveal that only size-effect is much easier to handle
than both size and microstrain. Being confirmed from the transmission electron
micrograph of the powder that only size effect is present, the size distribution of single
crystal nano particles can be estimated by two approaches. One approach consists in
Monte Carlo fitting of wide-angle X-ray scattering peak shape [201]. Another method
applies maximum entropy for determining the column-length distributions from size
broadened diffraction removing instrument broadening [202].
Line profile analysis is incorporated in Rietveld method for refinement of crystallite
size, microstrain, lattice distortion due to dislocations (edge/screw); planar defects (twin
and deformation faults) [203, 204]. Lutterotti et al. analyzed the material composed of
silicate glass in ceramic matrix by the Rietveld method and determined the content of
amorphous phase in ceramic materials [205] and characterized its defect structure.
Mello et al. [206] prepared samples of (FexCo1.x)Ta206 from pure FeTa20 6 and
CoTa206. From X-ray diffraction (XRD) measurements followed by Rietveld refinement,
it is demonstrated that the solid solution obeys the Vegard's law.
Bokhimi et al. [207] prepared samples in the Mg0-Ti02 system via the sol-gel
technique. Samples were characterized with X-ray powder diffraction and to quantify the
concentration and the crystallography of the phases in the samples, their crystalline
structures were refined using the Rietveld method.
32
General Introduction Chapter 1
Blouin et a!. [208] followed the kinetics of formation and structural evolution of
nanocrystalline phases by mechanochemical reaction between Ti and Ru02 by
performing a Rietveld refinement analysis of X-ray diffraction profile.
Sornadurai et a!. [209] prepared single phase pure TbZrAl samples by an arc
n1elting method and find out its structural parameters by Rietveld analysis of X-ray
powder-diffraction (XRD) profile.
Grey et a!. [21 OJ prepared a new high-pressure phase CaAlt2Si4027, in the Ca0-
Al203-Si02 system at high temperature and pressure. Its structure was refined using the
Rietveld method applied to powder X-ray diffraction data.
Rixecker et al [211] identified ternary phases with the cubic structure in both the
Fe-Nb-Si and Fe-Ta-Si systems fom1ed during the crystallization of mechanically alloyed
amorphous materials during heat treatments. The X-ray powder diffraction data were
evaluated both by loca1line fit and by Rietveld analysis.
Ortiz et a!. [212] applied the Rietveld and two line-broadening (variance and
integral breadth) methods to analyze a liquid phase-sintered SiC sample.
Yang et al. [213] synthesized a new compound CaGaB04 by solid state reaction at
high temperature and its structure was solved by direct methods from X-ray powder
diffraction data using the Rietveld method.
Wei et a!. [214] investigated phase relations of the ternary system SrO-Ti02-B203
by X-ray powder diffraction (XRD). The Rietveld refinement method was used to
determine the cell parameters and the structure of the compound Sr3B206 and found it to
be calcium-orthoborate structure.
Wang et al. [215] prepared Iron-doped titania photocatalysts with different iron
contents by using a sol-gel method in acidic media. The crystalline structures of the
various phases calcined at different temperatures were studied by using the Rietveld
technique in combination with XRD experiments.
Bose et al. [216] prepared five compositions of Cd-Ag alloy in different phases and
phase boundary regions have been prepared and analyzed both in the annealed and cold-
33
General Introduction Chapter 1
worked states employing Rietveld's powder structure refinement method and Warren
A verba~h' s method of X -ray line profile analysis.
In 2002 Bose et al. synthesized nanocrystalline Ni3Fe in sol-gel method [217] and
made X-ray microstructure characterization of the same material employing Rietveld's
powder structure refinement method, the Warren-Averrbach's method and the modified
Williamson-Hall method.
Pratapa et al. [218] made a comparative study of single-line and Rietveld strain-size
evaluation procedures using MgO ceramics. Strain-size evaluations from diffraction line
broadening for MgO ceramic materials have been compared using single-line integral
breadth and Rietveld procedures with the Voigt function.
Recently Bid et a!. [219] reported formation of fully stabilized c-ZrOz phase from
m-Zr02 phase in ball milling process without using any additive. Microstructural
parameters of ball milled Zr02 milled at four different BPMR (ball to powder mass ratio)
and different milling hrs were obtained by Rietveld powder structure refinement analysis.
A review article of Albinati and Willid in 1982 gives a good impression of the state
of the Rietveld method at that moment. Many more papers on the method have appeared
since, often with unexpected applications. It was mentioned in a review report by H.M.
Rietveld himself that a total of 172 structures were refined before 1977. In the period
January 1987 to May 1989 a total of 341 papers were published with reference to or using
the Rietveld method, of which nearly half using neutron diffraction. In the year 1991, the
number of papers published with reference to the Rietveld method is 257. In the year
1994 the number rises to 350. In a lecture in XVIIIth IUCR conference at Glasgow,
Scotland, H.M. Rietveld himself told that now-a-days Rietveld method is used in more
than 500 publication per year (220]. Recently Rietveld method is used in over 2000
publication per year.
1.11 Modern trend of research in powder diffraction
In the past two decades powder diffraction has made a very significant impact in
many areas of material science, especially in the more basic aspects of the research. The
list includes high Tc superconductors, magnetic materials, ferro and piezoelectrics,
34
General Introduction Chapter 1
electro-optics materials, battery electrodes, hydrogen storage, ceramics, polymers and
biomiqerals etc. A few important ones are discussed below in brief.
1.11.1 High Tc superconductivity
One of the great triumphs of Rietveld analysis has been in its crucial contribution to
the dizzyingly rapidly developing field of high temperature superconductor. After the
discovery of first high Tc superconductor [221, 222], the first important work on the
problem of delineating the crystal structure of YBa2Cu307-x was by the diffractionists at
the best neutron diffraction laboratories who solved the problem performing Ri~tveld
analysis with several different starting models [223]. Jorgensen et al. [224] reported the
change of the oxygen site-occupancy with preparation temperature for YBazCu301-x·
William et al. [225] determined the room temperature structure of YBazCu301-x which
includes a very precise set of atom positions and thermal-motion parameters and
conclusively demonstrated the absence of any cation disorder. Doped high Tc cuprates
are found to be an important candidate for crystal engineering [226-230]. The study of
structural chemistry for thallium cuprates TlzBa2Ca2Cu3010 (Tl-2223), featuring a critical
temperature (Tc) contributed in a deeper understanding of composition-structure-property
[231-232]. Subbarao et al. [233] investigated the influence of incorporation of Ca and Y
ions on the structural and superconducting properties of La3.s-x-y Y yCa2xBa3.s-xCu10z
system by Rietveld refinement using the neutron diffraction data as well as XRD data. Ha
et al. [234] have corrected the impurity effect on the characterization of Y t-xCaxBa2Cu30y
superconductors prepared by the solid state reaction method and analyzed by the Rietveld
analysis of the XRD pattern. In 2002, Cheng et al. [235] investigated the structural
properties and superconductivity of Mg (B 1.xCx)2 compounds by means of powder X-ray
diffraction and magnetization measurements. Rietveld analysis indicates about the
hexagonal structure and the change in lattice parameter of the sample.
1.11.2 Ferro and Piezo-electric materials
The study of ferro and piezo-electric materials are still popular now a days.
Stephens et al. reported that the application of an external field generates defects in the
structure and increases the internal stress in polycrystalline BaTi03 [236]. Kobayashi et
al. performing Rietveld analysis discovered a high-pressure phase having GdFe03 type
35
General Introduction Chapter 1
orthorhombic structure developed in ferroelectric KNb03 [237]. The synchrotron X-ray
powde1; diffraction measurements on perovskite like ferro-electric system PbZrt.x Tix03
(PZT) [238] have revealed a monoclinic phase between the previously established
tetragonal and rhombohedral regions. Noheda et al. further analysed the PbZro.s2 Tio.4s03
system performing a Rietveld refinement and reported positive shifts of the atoms in the
tetragonal phase along the polar [00 1} direction along with a local disordered shifts of the
Pb atoms of -0.2A perpendicular to the polar axis [239]. Ranjan and Pandey [240]
presented a detailed Rietveld analysis of the structure of paraelectric and antiferroelectric
phases of Sro. 70CaoJo Ti03 using powder XRD data.
1.11.3 Giant magneto resistance materials
In the last five years there has been a significant and rapid surge of interest for the
Mn + 3 /Mn +4 mixed-valanced oxides (magnitites) due to their colossal magneto resistance
(CMR)- a change in electrical resistance in a magnetic field and suitability for electronics
or information storage applications. Crystallographic techniques have given a paramount
contribution to magnetic research, mainly due to large electron-lattice coupling. The
initial emphasis on correlation between transport and average structural properties [241-
242] has gradually shifted towards local structural phenomena, associated with the Jahn
Teller polarons [242-245]. Guo et al. [246] investigated the crystal structures and giant
magneto resistance of CaF2-doped La213Ca 113Mn03 compounds by means of X-ray
powder diffraction (XRD) and magnetic measurements. Ganguly et al. [247] prepared
giant magnetoresistance samples with nominal compositions Lau (Sr 1 .xCa~)r. 8Mri207 and
characterized by X-ray diffraction (XRD) and ac susceptibility techniques.
1.11.4 Hydrogen in metals
Hydrogen in metals and metal hydrides is another subject of continuous interest
from the point of view of both fundamental properties and applications. Since hydrogen
is the fuel choice for the future, oil reserves are being squandered, and it thus becomes
essential from economic and safety point of view to know the structures and behavior of
these materials [248-250]. Nakamura et al. [251] investigated peak broadening in X-ray
powder diffraction (XRD) profiles of LaNi5-based alloys after hydriding and dehydriding
processes in order to clarify the mechanism of formation of lattice strain in hydriding and
36
General Introduction Cltapter 1
dehydriding. The Rietveld method was used to evaluate the degree of peak broadening
and to, determine anisotropic peak broadening axis for LaNis-based alloys before
hydriding, after activation and after 1000 hydriding-dehydriding cycles. Nakamura and
Akiba (252] investigated the hydriding mechanism of LaNis and LaNi4.7sAlo.2s by means
of in-situ X-ray diffraction measurements during their activation process. The XRD
profiles were analyzed by the Rietveld method to evaluate the lattice strain and the
crystallite size for both the solid solution phase ·and the hydride phase. Bououdina et al.
(253] made qualitative and quantitative X-ray analysis using the Rietveld method of the
as cast ZrCrO. 7Ni 1.3 alloy (Hydrogen absorbing materials). In 2002, Raman et al. [254]
investigated the synthesis, structural and microstructural characterizations of Mg-based
K2PtC16 type (Mg2FeH6) hydrogen storage material prepared by mechanical alloying.
1.11.5 Li-battery
Rietveld method has been contributing to the development of industrial inorganic
materials. One of the most outstanding example is cathode materials in rechargeable
lithium batteries i.e.LiNi02, LiMn204 and their related compounds. Vandates have
generated a new interest as a potential candidate for negative electrode material in Li-ion
battery [255, 256]. In order to explain the great acceptance of lithium ions within these
materials, recently special attention is being devoted to the characterization of these
materials by means of in-situ X-ray doffraction, Mossbouer, NMR and XANES
measurements etc. [257, 258]. Takada et a!. [259] carried out neutron and X-ray powder
diffraction and Rietveld refinements for structure and electrochemical characterization of
Li1+xMn2.x04 (0:::; x :$0.125) spinels for rechargeable lithium batteries. Andersson eta!.
[260] followed the extraction and insertion of lithium in solid-state synthesized LiFeP04
by in situ X -ray diffraction and Moss bauer spectroscopy. Hong et al. [261] prepared the
Lt /Co3+ -cod oped LiMn204 spinel using two-step synthesis method consisting of solid
state reaction method and citrate modified sol-gel method. The FT-infrared spectra,
chemical analysis, and Rietveld refinements of their XRD data revealed that the
manganese ions in the 16d sites were replaced by both lithium and cobalt ions which
enhanced the electrochemical cyclability of LiMn20 4 at the expense of a reduction in the
initial charge capacity. In a work of lithium-ion batteries, Prado et al. [262] studied the
structural modifications and redox processes occurring during lithium deintercalation
37
General Introduction Chapter 1
from the quasi-stoichiometric Lio.97(Nio.70Feo.tsCoo.ts)J.o302 phase by Rietveld refinement
of X-ray diffraction pattern and Mossbauer spectroscopy. Perner et al. [263] developed a
new MnOx cathode material for rechargeable lithium batteri Sources. Different
manganese oxide phases have been synthesized, Rietveld analysis of XRD profiles and
galvanostatic cycling in 2025 coin cells were performed for structural and
electrochemical characterization. Myung et al. prepared [264] LiNio.sMnu04 spinel by
an emulsion drying method which can intermix cations very homogeneously at the
atomic scale. The Rietveld refinement result clearly exhibited that the cubic spinel phase
was successfully formed without any secondary phases. They suggested that this mat.erial
can be used as a 4.5 V cathode material for Li-ion battery.
1.11.6 Magnetic intermetallics
Fundamental and applied researches are carried out in search for new materials
having interesting macroscopic magnetic properties. Sometimes addition of elements like
B. C. Si, Ge, N and P plays a crucial role in producing new compounds with improved
magnetic properties. The compound, Nd2Fe14B gained importance as a substitution for
SmCo05 as permanent magnet. Rigorous structural studies of the alloy using powdered
neutron diffraction were done by Herbst et al. [265] and using single crystal X-ray
techniques by Shoemaker et al. [266). In 1997 Raviprashad et al. reported the hardening
mechanism of nanocrystalline Nd2Fe14B, which plays a crucial role in the development of
exchange spring magnets and the effect of small amounts (0.1 at % addition of Cr, Cu,
Zr) of magnetic additions on the hardening behavior [267]. Recently, the systems
RMn6Ge6 in particular the compound TbMn6Ge6 is being studied by diffractionists for its
interesting rather complicated magnetic structure which varies with temperature [268,
269). On the other hand, the study of the AF2 magnetic structure of Mn5Si] is becoming
much popular today. Shah et al. [270] prepared and structurally characterized (Y1_
~GdxbF e27.5 Ti u by the Rietveld analysis of powder X-ray diffraction patterns.
1.11.8 Composites and technological materials: metals, alloys, interrmetallics, ceramics prepared by different routes
Different preparation routes have been used for obtaining composites and materiats
important for industrial application. In this section a review on this materials related to
38
General Introduction Chapter 1
the present thesis work is given.
Welham [271] examined mechanically induced chemical reactions between FeTi03
and silicon using X-ray diffraction and thermal processing. Reduction of FeTi03 by Si
during milling was observed with the formation of elemental iron and Ti02 or metal
silicidcs. In his another work [272) an ilmenite (FeTi03) concentrate had been milled
with sulphur in a laboratory-scale ball mill. X-ray diffraction and thermal processing
revealed that pyrite (FeS2) and rutile (Ti02) formed due to reaction occurred within the
mill. Welham et al. [273) also reported the fabrication of a homogeneous submicrometer
sized powder composed of nanocrystalline alumina and titanium nitride during ·high
energy ball milling. The starting materials were rutile and aluminium powder.
Kerr et al. [274] reported the formation of a sub-micron sized powder composed of
nanocrystalline alumina and titanium carbo nitride of two different stoichiometries during
high energy ball milling. The starting materials were rutile, graphite and aluminium
powder.
Cheng et al. [275] studied microstructures of melt-spun Ni-Al alloys with
compositions from 61-85at% Ni by means of transmission electron microscopy, X-ray
diffraction analysis and optical microscopy.
Fujimori et al. [276] used powder X-ray diffractometry and Raman scattering
measurements to study the structural changes of compositionally homogeneous
metastable Zr02 solid solutions induced by ScOu doping.
Gale et al. [277] investigated the microstructural development in as cast and aged
Ni-Al-Cr based alloys derived from the B2 type P-NiAl structure. Both the as-cast and
aged samples are examined using transmission electron microscopy.
Canton et al. [278] had shown the stability of the cubic form of zirconia in a
zirconia sample containing 3wt% sodium by analyzing the neutron diffraction pattern in
Rietveld method.
Shubin eta!. [279] studied milling ofV20 5 in a ball mill and reported the change in
colour. surface area, crystallite sizes and structure of the initial starting powder.
39
General Introduction Chapter 1
Filipek [280] used Differential thermal analysis (DTA) and X-ray powder
diffrac~ion (XRD) to study phase equilibria, established in air in the V20s-Sb204 system.
He reported the formation of a new phase approximate to SbV05 during the process of
preparation in two methods: by heating equimolar mixtures of V20s and alpha-Sb204 in
air and by oxidation of the known phase of rutile type obtained in pure argon.
Huneau eta!. [281] experimentally established phase relations in the ternary system
Al-Ni-Ti for the isothermal section at 900°C. The investigation was based on X-ray
powder diffraction, metallography, SEM and EMPA-techniques on about 40 ternary
alloys, prepared by argon-arc or vacuum-electron beam melting of proper elemental
powder blends.
Takasaki and Furuya [282) prepared three kinds of Ti-Al powders, TinAhs,
Ti57AI43 and Ti4sAl52, mechanically alloyed by a planetary ball mill in atmosphere of
argon or hydrogen and investigated the mechanical alloying (MA) process as well as the
phase variations of each powder after subsequent heating at 1173 K.
Berlouis et al. [283] investigated the hydriding properties of a senes of
nanocrystalline Mg-Ni based alloys prepared by high energy ball milling. ·
Trunec et al. [284] exposed agglomerated fine zirconia powder to dry and wet ball
milling and to wet mixing. The subject of study was the effect of powder treatment on the
disintegration of agglomerated particles, on the rheological properties of thermoplastic
ceramic mixtures, and on the properties of sintered yttria-stabilized tetragonal zirconia
polytrystalline ceramics (Y-TZP).
Itin et al. [285] reported that mechanical activation strongly influences the sintering
of pressed articles made of a powdered titanium-nickel alloy and its compositions with
dental porcelain.
Ren et a!. [286] investigated the enhanced reactivity, the polymorphic
transformation and the evolution of the powder characteristics of Ti02 and graphite
mixtures during high energy ball milling.
Begin-collin et a!. [287] investigated the effect of milling parameters, the powder
to ball weight ratio and the nature of the grinding media, on the kinetics of phase
40
General Introduction Chapter 1
transformations in anatase Ti02 powder during the process of ball milling.
Stubicar et a!. [288] synthesized ZrTi04 oxide powder from an equimolar Ti02-
Zr02 powder mixture by high energy dry ball mill and post-annealed processing. X-ray
diffraction was used to identify structural changes in the milled and the subsequently
post-annealed samples.
Apostolova et al. [289] synthesized V20 5 oxide compositions with glass-forming
oxides (Ge02, Te02, B20 3, P20 5, and B20 3) for intercalated cathodes of lithium batteries.
The obtained V20 5 glasses were analyzed by IR absorption spectroscopy and ~-ray
diffraction and thermal analyses.
Kim et al. [290] investigated the mixture behavior and microwave dielectric
properties of Ti02 doped with CuO sintered at around 900 degrees C for 2 h using X-ray
powder diffraction and a network analyzer.
Krivoroutchko et al. [291] prepared several Ni-Al-Ti-C compositions from different
areas of the Ni-Al phase diagram containing various amounts of Ti and C by mechanical
alloying. Synthesized samples were investigated by X-ray diffraction and differential
scanning calorimetry methods.
Huneau et a!. [292] prepared Ti-Ni-Al-N and Ti-Ni-Al-0 alloy samples by melting
method and studied phase diagrams of the alloy samples. The experimental investigation.
employed X-ray powder diffraction, metallography, SEM, and EMPA techniques in the
as-cast state as well as in annealed sample.
Cao et al. [293] investigated the mechanical alloying process of (Zr02)(0.8)-(alpha
Fe20J)(0.2) powder during high-energy ball milling at room temperature and studied the
thermal decomposition of the same powder at high temperature by XRD, TEM, and
differential thermal analysis. It was found that monoclinic zirconia transforms to cubic
zirconia stabilized by Fe3+ after a milling time of 60 h.
Rengakuji et al. [294] fabricated metal oxide thin films such as Ti02, Zr02 and
ZrTi04 from metal oxide precursor solutions by a dip-coating method, and were tested as
hydrocarbon gas sensors. The preparation method of the precursor solution was named
"advanced sol-gel method".
41
General Introduction Chapter 1
Tonejc et al. [295] used the Rietveld method and refined electron powder data
(recorded with selected area electron diffraction-SAED) on nanocrystalline Ti02-anatase
prepared by sol-gel route to investigate their structural parameters like lattice parameters
and grain sizes. They correlated refined lattice parameters with average gram stze
obtained from transmission electron microscopy (TEM) images.
Colon et a!. [296] studied a microcomposite powder in the system Ti02-Zr02 as a
precursor of zirconium titanate (ZT) materials by thermal methods (DT A-TG) and X-ray
diffraction (XRD). The microcomposite powder was prepared by chemical processing of
crystalline Ti02 (rutile, 10 mass% anatase), as inner core, coated with in situ precipitated
amorphous hydrated zirconia gel, as outer core.
Wilson et al. (297] applied the Bozzolo-Ferrante-Smith (BFS) method for alloys to
the study of NiAl-based materials to assess the effect of alloying additions on structure.
Ternary, quaternary and even pentalloys based on NiAl with additions of Ti, Cr and Cu
were studied and experimental verification of the theoretical predictions including the
phase structure of a Ni-Al~ Ti-Cr-Cu alloy was presented.
Madhuri et a!. (298] prepared Vanadium pentoxide thin films by the pulsed laser
deposition technique. X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD)
and atomic force microscopy (AFM) measurements were carried out in order to
understand the growth mechanism.
Bouzidi et al. (299] first time successfully deposited Vanadium oxide thin films by
spray pyrolysis technique at two substrate temperatures, 200 and 250 degreesC. The as
deposited films were studied as a function of spray solution concentrations, using X-ray
diffraction (XRD) and optical measurements. V20 5 and V40 9 polycrystalline films with
an orthorhombic structure were easily obtained under the different spraying conditions.
lvanova et al. [300] obtained a Ti02-V205 colloidal solution with a stability of
more than 2 years. Powder X ray diffraction (XRD) measurements showed that the
sample treated at 300 degreesC is amorphous and crystallization began after 450
degrees C.
42
General Introduction
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