II - Shodhganga : a reservoir of Indian theses @...

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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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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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.

4

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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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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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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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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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

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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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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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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

II


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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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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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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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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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

16


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

17


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


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


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


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 .


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


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


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


[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


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


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


[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


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


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


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


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


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


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


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


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


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


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


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


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


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