Evolution of Grain Boundary Character Distributions

in FCC and BCC Materials

Peter Keng-Yu Lin

A thesis submitted in conformity with the requirements for the Degree of Doctor of Philosophy

Department of MetalIurgy and Materials Science University of Toronto

O Copyright by Peter Keng-Yu Lin (1 997)

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Evolution of Grain Boundary Character Distributions in FCC and BCC Materials

Peter Keng-Yu Lin

Doctor of fhilosophy, June 1997 Department of Metallurgy and Materials Science, University of Toronto

Abstract

The structures of grain boundaries were characterized within the frarnework of Coincidence Site

Lattice (CSL) mode1 using Orientation Imaging Microscopy (OIMTM). The Grain boundary

character distribution (GBCD) in FCC low stacking fault energy materials susceptible to annealing

twinning, showed a preference of x3" boundaries (where n =1,2 and 3). The changes in the

distribution of the CSL boundaries during microstructural evolution were found to be influenced

by thermomechanical treatments. solute contents, texture and grain size. Moreover, the

contribution of twinning to the CSL distribution was further discussed in tems of the 'Twin

Limited Microstructure' whereby the frequencies of special grain boundaries (x129) were found to

lie within limits defined by (a) an upper lirnit based upon twin energetics leading to the creation of

additional special grain boundaries, and (b) a lower limit arising from isolated twinning events.

The preference for 23" grain boundaries was attributed to the geometric interaction of twin related

variants during grain growth.

The role of CSL boundaries in the development of Goss texture in BCC Fe-3% Si alloy was

investigated in pnmary recrystallized specimens and in specimens following the early stages of

secondary recrystallization. By utilizing the direct experimental crystallographic orientation

determination and the approach of 'Simulation by Hypothetical Nucleus (SH)', it was found that

(1) Goss grains do not have the size advantage or occur in clusters in the primary matrix (2) they

have a higher probability of forrning low 2 CSL boundaries, especially the ES coincidence relationships. Furthemore, the experimentdly detennined 'deficit' of CSL boundaries bounding a

growing Goss grain relative to the SH distribution. was rationalized on the basis of preferential

replacement of CSL boundaries by general boundaries due to the intrinsic enhanced mobility for

low grain boundaries. Such an interpretation supports the role of CSL boundaries in the

development of Goss texture and it is further estimated that the CSLs are on average, 10-20% more

mobile than generd boundaries during abnormal grain growth in Fe-3% Si alloy.

Acknowledgments

I am indebted to Professor K.T. Aust and Dr. G. Palumbo for giving me the opportunity to further

my education and for their genuine interest in my personal and professional development. With

their guidance and supervision, and at times much needed patience, 1 was able to further my

understanding in the field of grain boundaries.

I would like to extend my special thanks to Dr. J. Harase for providing silicon-iron samples and

invaluable discussions pertaining to many aspects of the investigation in Fe-3% Si alloys. Special

thanks are also due to Professor U. Erb for his critical review of this thesis.

The author is also grateful to Ontario Hydro Technologies, (Resource Integration - Materials

TechnoIogy Department), for providing access to the Orientation Imaging Microscopy (OIMm)

and for their generous financial support throughout the course of this work. The technical

assistance provided by the staff in the Materiais Technologies Department, Mr. A. Brennenstuhl,

Mr. E. Lehockey, Mr. R. Jarochowicz, Mr. D. Limoges, Mr. F. Smith, and Mr. A. Robertson, is

appreciated.

Graduate scholarships provided through ( 1) University of Toronto Open Fellowship and (2) the

Naniral Sciences and Engineering Research Council of Canada are gratefully acknowledged.

Table of Contents

............................................................................................ 1 Introduction 1

...................................................................................... 2 Literature Review 3

......... ..... 2.1 Fundamentals of Crystallographic and Geometncal Parameters ... 3 ................ 2.2 Geometrical Characterization of Grain Boundary Structure ........... 7

........................................... 2.2.1 Misorientation for Cubic Rotations 7

........... 2.2.2 The Coincidence Site Lattice (CSL) Mode1 of Grain Boundary 8

...................................... 2.2.3 Grain Boundary Dislocations (GBD's) 9

........................... 2.2.4 The Displacement Shift Complete @SC) Lattice 10

.................................... 2.2.5 Criterion for Allowed Angular Deviation 10

.................. 2.3 The RoIe of CSL Boundaries in Cubic (FCC and BCC) Materiais 14

........................................................... 2.3.1 Random Distribution 14

........................................... 2.3.2 Texture and the Frequency of CSL 15

............................ 2.3.3 Annealing Twinning and the Frequency of CSL 17

............. 2.3.4 Development of Recrystallization Texture and Grain Growth 24

......................... 2.3.4.1 Mobility and Grain Boundary Migration 24

2.3.4.2 Formation of Goss Texture by Secondary Recrystallization ... 29

.................................................................................. 2.4 Objectives 36

3 Experimental Procedure ............................................................................... 37

............................................................... 3.1 Characterization Technique 37

3 . 1 . 1 Pattern Formation ............................................................. 38

............................................ 3.1.2 O I M T M - Hardware Configuration 40

................................................ 3.1.3 O P - Software Capabilities 41

....................................................................... 3.2 Materials Processing 45

........................................................................ 3.2.1 Twinning 45

................................................................ 3.2.2 Fe-3% Si Alloys 46

................................. 3.3 Sample Preparation and SEM Operating Conditions 48

3.4 Grain Boundaries Statistics .............................................................. -49

.............................................................. 3.4.1 CSL Classification 49

......................... 3.4.2 Simulation by Hypotheticd NucIeus - SH method 49 ................................ 4 Results and Discussion - Evolution of GBCD in FCC Materiais 51

............................ 4.1 Twinning in Low Stacking Fault FCC Metals and Alloys 51

........................... . . 4 1 1 Grain Boundary Character Distribution (GBCD) 51

4.1.2 Role of Impurities .............................................................. 62

4 . I . 3 RoIe of Texture ................................................................. 63

4.1.4 Role of Grain Size .............................................................. 67

..................................... 4.2 Contribution of Twinning to the CSL Distribution 69

5 Results and Discussion - EvoIution of GBCD in BCC Materials ................................ 74

......................................................... . 5 I Primary Recrystallized Structure 74

5.1.1 Grain Boundary Character Distribution (GBCD) ........................... 74

.......................... ................... 5.1.2 Variation Through Thickness .. 79

...................................................... 5.2 Secondary Recrystallized Structure 87

5.3 CSL Formation During Secondary Recrystallization .................................. 96

5.4 MobiIi ty Consideration .................................................................... 103

6 Conclusions ............................................................................................ 107

6.1 Twinning .................................................................................... 107

.................................................................................... 6.2 Fe-3% Si 109

7 Recommendations for Future Work ................................................................ 1 1 1

Appendix .................................................................................................. 112

References ................................................................................................ 1 1 6

List of Tables

Table 2.1 : Experimental observations of lattice misorientation for the fast moving

boundaries ......................................................................................... .26

Table 3.1 : Impurity contents (ppm by wt.) for electronic grade (EG) and metallurgical

grade (MG) polycrystalline silicon.. ............................................................. 45

Table 3.2: Compositions (wt%) of nickel-base alloys and stainless steels.. .............. .45

Table 3.3: Summary of the thennomechanical parameters as shown in [121] .............. 46

Table 3.4: The applied thermomechanica1 matrices showing variation in % deformation and

number of strain-annealing steps. The temperature ( 1ûûû0C) and annealing time (Smins)

were kept constant. ............................................................................... -46

Table 3.5: Solutions and conditions used for specimen preparation. ...................... -48

Table 4.1 : Experimentaily determined grain boundary character distribution (GBCD) for

MG-Si, and EG-Si using the manuai EBSP mode ............................................. 52

Table 4.2: Experimentdly determined grain boundary character distribution (GBCD) for

............................................... SS 304 and Cu using the manual EBSP mode.. 52

Table 4.3: Experimentally determined GBCD for stainless steeis and various nickel-base

alloys using automated OIM.. ................................................................... -53

Table 4.4: Expenmentally determined GBCD for Alloy 600 using automated OIM. .... .54

Table 4.5: Grain boundary free energy, coherent twin boundary energy and stacking fault

energy of Cu, SS 304 and nickel [SI] ........................................................... 56

Table 4.6 : Simulated Grain boundary Energy of low 1 CSL boundaries in pure Ni [124].

Table 5.1 : CSL distributions in Fe-3% Si from the general pnmary recrystallized matrix.

...................................................................................................... -75

Table 5.2: CSL distributions calculated from onentation relationships between

experimentally measured orientations in the primary matrix and several reference main

texture components, including the Goss orientation.. ........................................ .76

Table 5.3: Experimental CSL distribution measured from grains directly bounding Goss

grains at 950°C and 1000°C ....................................................................... 99

Table 5.4: Percentage of CSLs (z 1-129) obtained from experimental measurement of interfaces bounding a growing Goss grain after onset of secondary recrystallization and the

potential CSL distribution with respect to Goss onentation as determined by SH method

(Table 5.2). ........................................................................................ - 1 û4

vii

List of Acronyms

CSL - Coincidence Site Lattice

GBCD - Grain Boundary Character Distribution

SH - Simulation by Hypothetical Nucleus

O P - Orientation Imaging Microscopy

GBD's - Grain Boundary Dislocations TEM - Transmission Electron Microscopy

DSC - Displacement Shift Complete

HVEM - High Voltage Electron Microscopy

TLM - Twin Limited Microstructure

ECP - Electron Channeling Pattern

SEM - Scanning Electron Microscopy

EBSD - Electron Backscattered Diffraction

EBSP - Electron Backscattenng Pattern

SIT - Silicon Intensified Target

GBEW - Grain Boundary Engineered

IQ - Image Quality

SFE - Stacking Fault Energy

List of Figures

Figure 2.1: Definition of Euler angles (Bunge's notation [15]) showing three successive rotations

and the three axes of x. y, z of the sample frarne and x', y', z' of the crystal frame. ............. .5

Figures 2.2: Representation of the Euler Space. ....................................................... .5

Figure 2.3: Formation of a CSL lattice (denoted by filled circle) by rotating lattice 2 so that certain

............................................................. of its points coincide with points of lattice 1 8

Figure 2.4: The maximum deviation angles (Ag) from CSL (Z) in 99.999% nickel displaying

.................................. selective immunity to intergranular corrosion in 2N H2S04 [33]. -12

Figure 2.5: Calculated values of random distribution for CSL's ranging from 1 through 29 using

four different variations in A8 dependence for LCSL. .............................................. .15

Figure 2.6: Illustration of Fullman and Fisher mode1 showing the formation of an anneaIing twin at

a grain corner. .............................................................................................. -19

Figure 2.7: The proposed relationship for the contribution of anneding twin (d) to special

boundary (d + 112 d) fraction on the basis of energetic and crystdIographic conditions [9]. ..... .22

Figure 2.8(a): A cornparison of rate of grain boundary migration for random and special

boundaries at 300°C in zone-refined lead doped with tin [23. ........................................ -25

Figure 2.8(b) The effect of tin on the activation energy for the migration of random and special

boundaries in lead [72]. ................................................................................... -26

Figure 2.9: Schematic diagram of a growing grain (Hypothetical Nucleus) advancing into the

................................... stable mavix forming new grain boundaries in the process[l04]. .32

Figure 2.10: A schematic illustration for the proposed mechanism of the texture evolution by grain

........................................... growth associated with the coincidence relationship [ 101.. .33

Figure 3.1 : Schematic diagram illustrating the geometric formation of a pair of Kikuchi lines from a

diffracting plane.. .......................................................................................... -39

Figure 3.2 : Schematic diagram showing the hardware components of the automated EBSP system

- O P system [ 1 11. ..................................................................................... -40

Figure 3.3: Typical EBSP pattern for nickel based Alloy 600 obtained after 16 frarne averaging and

background subtraction. .................................................................................. -43

Figure 3.4: Illustration of band identification for a h l l y indexed pattern shown above by Hough

trans form.. .................................................................................................. .43

Figure 3.5: Conventional SEM image of an intergranular crack. The image is compressed in the

Y-direction as a result of 70" tilt. ......................................................................... -44

Figure 3.6: illustration of OIM capability in reproducing a corresponding image of the

intergranular crack shown in Fig. 3.5.. ................................................................. -44

Figure 3.7: Schematic diagrarns of the orientation of the unit ce11 for each grain relative to the sheet

showing (left) Goss and (right) cube texture. .......................................................... .50

Figure 4.1 : A random distribution calculated based on Warrington and Boon[34]. . . . . . . . . . . . . . . . -56

Figure 4.2 (a): OIM image showing CSL distributions of a highly twinned Alloy 600. 2 3

boundaries are labeled in red and those in thin black lines correspond to 21; x5-29 are shown in

yellow and general randorn boundaries are depicted in black .......................................... 58

Figure 4.2 (b): OIM image showing CSL distributions of a conventional processed Ailoy 600. z3

boundaries are labeled in red and those in thin black lines correspond to 21 ; 15-29 are shown in

yellow and general random boundaries are depicted in black .......................................... 59

Figure 4.3 (a): The effect of defomation on the frequency of special CSL boundaries in Alloy

600.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60

Figure 4.3 (b): The effect of multiple steps of strain-annealing (at constant 10% deformation) on

the frequency of the special CSL boundaries in Alloy 600. . . .. . . .. .. . ... . . . . . . . . . . . . . . .. . . . . . . . . . . . . .60

Figure 4.4 (a-d): Illustration of the cumulative frequencies of CSLs for a relatively low (=3 1 %)

(a), an intermediate (45%) (b) and a relatively high ( ~ 6 0 % ) (c) twin density in contrat to that of a

random distribution (d) ..... . ... ..,...... .. ... .. .. .. .. .. .. ... . .. . ... ..... .. .. .. .. . .. .. . .. . .. . .. .. . ... .. . . . . .64

Figure 4.5: Pole figures obtained from OIM measurements showing (a) a highly random and (b)

weakly textured Alloy 600.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . - - - . - . . . -66

Figure 4.6: Frequency of CSLs as a function of grain size for the materials susceptible to

twinning ..... ..... .............. ... .... ... ....... .... ... ..... . ..... ... . ...... . ... ... . . ........ . ... . .. .. -.. ... -67

Figure 4.7: Contribution of annealing twins (U) to CSL (XSB). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 1

Figure 4.8: The effect of geometric interaction associated with twinning on the final CSL

....................................................................................... distribution (zS29). -72

Figure 5.1 : OIM image of primary recrystallized Fe-3% Si showing the specific locations of the

'Goss' grains (in blue) within IO0 deviation from exact Goss orientation and the low-1 CSL

boundaries (13 in red. x5-29 in yellow and 1 1 in black thick lines) ................................ 77

Figure 5.2: Frequency of coincidence grain boundaries in relation to an ideai Goss orientation and

its rotation about cûûb axis for a primary matnx.. .................................................. .78

Figure 5.3: Grain boundary character distributions of Fe-3% Si obtained at three depth levels from

the sheet surface ............................................................................................. 80

Figure 5.4 (a-c): OIM images showing distribution of the Goss nuclei in the primary recrystallized

Fe-3% Si alloys at various depth levels from the surface, (a) 30pm (b) 60pm and (c) 150pm. .8 1

Figure 5.5 (a-c): (200) Pole figures of pnmary recrystallized Fe-3% Si alloys obtained by OIM at

................................... various depth, (a) 30pm (b) 60vm (c) 150prn, from the surface. -82

Figure 5.6 (a): Frequency of coincidence grain boundaries in relation to orientations rotated

.... around Goss component for a primary matrix detennined at 30 pm from the sheet surface.. .84

Figure 5.6 (b): Frequency of coincidence grain boundaries in relation to orientations rotated

.... around Goss component for a primary matrix determined at 60 pm from the sheet surface.. .84

Figure 5.6 (c): Frequency of coincidence grain boundaries in relation to orientations rotated

... around Goss cornponent for a primary matnx detemined at 150 pm from the sheet surface. -85

Figure 5.7: OIM image of secondary recrystallized Fe-3% Si extracted at 965OC showing the

specific locations of the 'Goss' grains (in blue) within 10° deviation frorn exact Goss orientation

and the low-z CSL boundaries (x3 in red, 25-29 in yellow and El in thick black lines) ........ 87

Figure 5.8 (a-d): (200) pole figures of Fe-3% Si specimens showing (a) prirnary recrystal

texture and the subsequent sharpening of Goss texture during the course of secondary

recrystallization at various temperatures; (b) 875OC (c) 890°C and (d) 905OC. ..............

ized

..... -88

Figure 5.9: Grain boundary character distribution of pnmary and secondary recrystallized

.................................................................................................. specimens. -89

Figure 5.10 (a): Frequency of coincidence grain boundaries in relation to orientations rotated

............... around Goss component for a primary matrix prior to secondary recrystallization. -9 1

Figure 5.10 (b): Frequency of formation of coincidence grain boundaries in relation to orientations

rotated around Goss component following the onset of secondary recrystallization at 87S°C.. .. .9 1

Figure 5.10 (c): Frequency of formation of coincidence grain boundaries in relation to orientations

rotated around Goss component foliowing the onset of secondary recrystailization at 890°C.. .. .92

Figure 5.10 (d): Frequency of formation of coincidence grain boundaries in relation to orientations

.. rotated around Goss component following the onset of secondary recrystallization at 90S°C.. .92

Figure 5.1 1 (a): OIM image of a primary recrystallized specimen showing locations of Goss

grains (in blue) within 10 degree deviation and grains having 5 (in red) and 2 9 (in yellow)

.......................................................... coincidence relationship with Goss orientation 93

xiii

Figure 5.1 1 (b): O M image of a specimen extracted at 87S°C following secondary recrystallization

showing locations of Goss grains (in blue) within 10 degree deviation and grains having x5 (in

.......................... red) and Z9 (in yellow) coincidence relationship with Goss orientation.. .93

Figure 5.1 1 (c): OIM image of a specimen extracted at 8900C following secondary recrystallization

showing locations of Goss grains (in blue) within 10 degree deviation and grains having z5 (in

.......................... red) and 29 (in yellow) coincidence relationship with Goss orientation.. -94

Figure 5.12: (200) pole figures for primary recrystallized specimens following heat treatment at (a)

950°C and (b) 1000°C for two minutes ................................................................... 97

Figure 5.13: Orientation image of Fe-3% Si following the onset of secondary recrystallization at

1 OOO°C. The 'Goss' grains are labeled in blue (Le. within IO0 deviation frorn exact Goss

orientation) and the low-x CSL boundaries are denoted as x3 in red, 15-29 in yellow and 1 1 in

........................................................................................... black thick lines. -98

Figure 5.14: Illustration of the 'deficit' frorn experimentally determined low CSL's bounding a

growing Goss grain relative to that expected from SH predicted distribution. ..................... -100

Figure 5.15: Probability of CSL boundaries as function of migrating distance in grain diameters at

different velocity ratios between the CSLs and general boundanes (frorn EqS.1). ............... .105

xiv

Introduction

Grain boundaries have long k e n recognized as important microstmctural elements in engineering

rnaterials. Kronberg and Wilson [ I I first proposed the concept of a Coincidence Site Lattice (CSL)

in describing the structure of the grain boundary and its importance was indicated in their early

study of secondary recrystallization in copper. Aust and Rutter [2] further demonstrated that not dl

grain boundaries are created equal and the migration behavior of a particular boundary is strongly

influenced by the presence of solutes. Numerous studies on grain boundary structure and

properties have unequivocally established that many grain boundary properties, Le. segregation,

energy, corrosion etc.. are dependent upon the crystallographic characteristics of individual grain

boundaries as characterized on the basis of the CSL mode1 of grain boundary structure (see review

[3]). Consequently, the prospect for tailoring the specific properties associated with grain

boundaries (Le., with a view to obtain those boundary geometnes which are beneficial) is

definitely of interest.

The generic concept of 'Grain Boundary Design and Control' was first introduced by Watanabe

[4], whereby manipulation of the grain boundary character distribution (GBCD) of polycrystalline

materials to achieve a high fraction of stnicturally ordered low-z CSL grain boundaries, is thought

to be a viable means of obtaining a cornmensurate improvement in bulk material properties since

the CSL related interfaces have been shown to possess 'special' properties in contrat to 'general'

non-CSL interfaces [3,5]. The occurrence of these special boundaries is largely influenced by

fundamental material processing parameters involving recrystallization and grain growth and to

some extent, materials texture.

Annealing twinning was first identified by Aust et al. in a senes of studies in zone refined Pb [6],

Al [7] and Cu [8] as one of the mechanisms in which the frequency of low-z CSL grain

boundaries can be enhanced during grain boundary migration. Recently, in an effort to assess the

proportion of CSL boundaries during the rnicrostnictural evolution in low stacking fault energy

face centered cubic (FCC) materials, Palumbo et a1.[9] have proposed a geometrical mode1 which

y ields a theoretical Twin Limited Microstmcture' w here the interfacial constituent cm potentiall y

consist entirely of 'special' boundaries. The significance of annealing twins in this regard far

exceeds what is nominally accepted as a common microstructural constituent in FCC metals and

alloys.

A further area of interest associated with CSL boundaries lies within the changes of GBCD

accompanied by the process of abnomal grain growth (or secondary recrystallization). The

intrinsic mobile CSL boundaries have also been demonstrated by Harase et al. 1101 using a

statistical method, 'Simulation by Hypothetical Nucleus', to play an important role in developing a

strong secondary texture, ( 1 10), in Fe-3% Si electncal steel where a highly grain-oriented

steel is crucial for reducing the coercivity and, consequently, the core loss in transformer cores.

Recent advances in experirnental techniques. for instance, Orientation Imaging Microscopy

(OIMw)[l Il, for the characterization of grain boundaries have resulted in considerable

enhancernents by which the information on GBCD cm be readily obtained. The thmst for possible

industrial applications in producing a new class of 'Grain Boundary Engineered' materials has

necessitated the need for further understanding the dynamic change of the CSL boundaries in

materials during microstmc tural evolution.

Literature Review

A crystal orientation is the most important single quantity in descnbing the intemal structure of

polycrystalline materials and it forms the basis for al1 the subsequent microstructural

characterizations; for instance, misorientation between two adjoining crystais and description of a

preferred orientation (or texture) in materials. In this section, the fundamentals of these

crystallographic parameters are introduced.

2.1 Fundamentals of Crystallographic and Geometrical Parameters

In describing the grain orientation within a p l ycrystalline aggregate, numerous parameters such as

Miller indices, matrix representation and Euler angles, are commonly used. By definition, the

orientation of a crystai in the sample is defined as a rotation, g, which transforms the orientation

from a sample coordinate system (S) into that of the crystal coordinate system (C) [12].

= g S2 , where g describes the rotation of frarne S into frarne C [2.1] 13 [:) A traditional metallurgical representation of crystal orientation in materials consists of Miller

indices. By convention, for a rolled sheet materiai. the crystallographic plane (hkl) is chosen to be

parallel to the rolling plane and the crystallographic direction pardlel to the rolling direction:

v . k , where g = (hkl) c uvw > g = [ w 1 1

The notation of (hkl)cuvw> is specified as an ideal orientation and the grain orientations can be

conveniently displayed using a graphical representation known as a pole figure where a specified

orientation relative to the specimen is shown by a variation of pole density with pole orientations

for a selected set of crystal planes [13].

In matrix notation, the actual orientation of the two coordinate systems is represented by a 3x3

orientation matrix which consists of direction cosines which form between the base vectors

associated with both the sample and crystal frames. The components of the matnx are not

independent of each other which is an unfavorable condition when a continuous orientation

distribution function is desirable. However. the properties of an orthogonal matnx: (1) the sums

for the squares of each row and column vectors are unity, (2) the dot product between column or

row vectors are zero (3) the inverse of the matrix is equal to its transpose, dictate the number of the

direction of cosines defining a rotation which is effectively reduced from nine to three. One

direction cosine describes the rotation angle and two direction cosines indicate the rotation axis.

The main advantage of such representation is that the result of the two or more rotations cari be

readily calculated by matrix multiplication.

x ' y' crystal mis [S.3 J

z'

Another forrn of representation which is used predominantly in texture analysis of polycrystalline

materials is known as Euler angles and denoted by g(

only a two dimensional representation. The range of al1 the possible orientations are,

Figure 2.1: Definition of Euler angles (Bunge's notation [15]) showing three successive rotations and the three axes of x, y, z of the sarnple frame and x', y', z' o f the crystai frame.

Figures 2.2: Representation of the Euler Space.

Al1 three representations of a crystal orientation are, in principle, equivalent and can be convened

into one another. The choice of representation depends on the nature of the investigation where

one may be more appropriate than the other. A comprehensive mathematical description amongst

various foms of representations has been provided by Bunge [15]. For instance, Euler angles cari

be expressed in matrix form through matrix multiplication of the three consecutive rotations.

cosg, sin O

g(.;'z* = [-';.; Co;.' ] Therefore, the resulting matrix cm be expressed in terms of Euler angles as follows.

2.2 Geometricai Characterization of Grain Boundaries

A complete geornetrical description of a grain boundary requires five independent parameters: three

of which are associated with the misorientation between two adjoining crystals and the remaining

two define the normal of the grain boundary plane [16]. The pertinent information regarding grain

boundary structure on the bais of the geometrical criteria will be presented.

2.2.1 Misorientation for Cubic Rotations

The misorientation can be defined as the relative orientation between two adjoining crystals by

rotating one crystal with respect to the other into the same reference frarne. Such a rotation can be

described by a rotation matrix given by,

where gl and g2 represent the orientations of two individual grains in the polycrystal, respectively.

Mykura [17] has shown that the rotation matrix can also be expressed in the form of an angle-axis

pair. From the main diagonal of the matrix elements, the rotation angle and the direction of the

rotationai axis is given by equations [2.8] and [2.9] respectively.

Since the point group of the cubic lattice leads to 24 equivalent rotations by means of symmetry,

there are a total of 24-24-2=1152 different descriptions for the same relative orientation of two

cubic lattices [18]. Of dl the cubically equivalent rotations, only one with the minimal rotational

angle and axis pair pointing into the standard stereographic triangle ([Iûû], [ 1 101, [ 1 1 11) [19] is

needed to represent the whole set which is temed 'disorientation'.

2.2.2 The Coincidence Site Lattice (CSL) Model of Grain Boundaries

The concept of coincidence site in connection with grain boundaries was first proposed by

Kronberg and Wilson [l] where a 3-dimensional superlattice is constmcted by a rotation which

bnngs about the sites common to two interpenetrating lattices (see Figure 2.3). The CSL is

considered the smallest sublattice of the two adjoining grains. The degree of coincidence is

characterized by the reciprocal density of common lattice points, denoted as x, which is also the volume fraction of the coincidence unit ceil to the crystal lattice unit cell. The example shown in

Figure 2.3 corresponds to a x5 grain boundary relationship, (Le. 36.8"[001]).

Lattice 1 X

Figure 2.3: Formation of a CSL lattice (denoted by filled circle) by rotating lattice 2 so that certain of its points coincide with points of lattice 1.

Ranganathan [20] has shown that CSL's can be generated by a Function given by,

where x and y are non-negative integers representing the Cartesian coordinates on the lattice point.

For cubic matenals, many of the CSLs can be generated by a rotation of 180" about a rationai

direction e h k b and the valued determined must be repeatedly divided by 2 until an odd number

is obtained. The angle of the misonentation can be expressed by,

Since different sets of x, y and N can be generated by the same value of x, a letter designation (a, b, c . etc.,) is used in order to distinguish differences in disorientation angles where 'a' is the

smallest angle, 'b' is the next smallest, etc. Mykura [17] has provided a cornprehensive list of

'ideal' CSL orientation relationships for value up to 101e.

2.2.3. Grain Boundary Dislocations (GBD's)

The conventional method of appl y ing the coincidence relations hip to describe the structure of a

grain boundary is to consider the atoms that are common to both lattices at the boundary itself [2 11.

However, Chalmers and Gleiter [22] have proposed that the most important criterion for the

existence of CSL boundaries is not the exact position of the sharing of the atoms but rather, the

equivaience of the presence of a periodic structure which cm accommodate a slight deviation from

exact coincidence relationship. The long range elastic distortion of the lattice arises from the strain

field which can be expected to extend from the boundary to a distance cornmensurate with the

periodicity of the boundary. Such a boundary structure may be visualized as grain boundary

dislocations superimposed on the ideal coincidence boundary [23]. Grain boundary dislocations

(GBD's) are unique to grain boundary structures and distinct from lattice dislocations in terms of

the Burgen vector. The experimental observation of the strained images by transmission electron

microscope (TEM) has verified the existence of GBD's at CSL related boundaries [24,25] .

2.2.4. The Displacement Shift Complete (DSC) Lattice

As stated in the previous section, a network of 'grain boundary dislocations' can be produced by a

slight deviation in the relative orientation of the two crystals away from the exact coincidence

relationship provided that the translation of one lattice to the other preserves the periodicity of the

exact CSL. The framework of the Displacement Shift Complete (DSC) lattice is composed of al1

such translations that Ieave the structure of the periodic pattern unchanged [26]. The Burgers

vectors are translation vectors of the DSC lattice. Ishida and McLean [27] have shown that GBD's

with Burger vectors which are integral multiples of the unit Burgers vectors (bl, b2 and bg) are al1

geometrically possible. The magnitude of the unit Burgers vectors (bl and b2) at the interface is

shown to be proportional to ~ - 1 / 2 , while b j varies with the interplanar spacing in the direction of

a i s rotation f27]. The DSC can be defined as the reciprocal lattice of the CSL which consists of

the coarsest possible lattice containing the two adjoining crystals; the volume of the DSC lattice unit

is proportional to 2- 1 [ 161.

2.2.5 Criterion for Altowed Angular Deviation

Al1 grain boundaries can be classified as CSL boundaries; however, a CSL boundary with a very

high value is of no physical significance. In order to determine the proximity of a boundary to a

CSL relationship, the deviation angle from the exact CSL orientation can be calculated using a

rotation rnatrix method [28] where a deviation matrix (RM) can be obtained from rotation of an

exact CSL matrix (RCSL) to that of the boundary of concem(R);

The deviation angle extracted from the RM (Le. frorn diagonal elements of the matrix) is used to

compare with the critenon which gives rise to the maximum deviation angle allowed. Several

criteria, Brandon's [30], Dechamps [32], McLean's [27] and Palumbo's [33], have been proposed

to define the maximum allowed deviation for CSL grain boundaries. Al1 of them are generally

derived from the Read and Shockley relationship [29]. For a simple low angle boundary (El), the

angle (0) of deviation is expressed as a function of the Burgers vector (b) of the lattice dislocation

and minimal dislocation spacing (dmin),

However, in the case of high angle Z 1 boundaries and high angle general boundaries, dislocations

in the grain boundary core begin to overlap resulting in destruction of discemible dislocation

spacing. The deviation angle (AB) from an exact coincidence misorientation is then characterized

by the DSC lattice which requires vector translation in preserving the periodicity. Therefore, the

above expression can be modified as,

Brandon's critenon [30] is the rnost widely used criterion for classifying CSL boundaries where an

upper lirnit of 15' for the low angle boundary and the variation in magnitude of two minimal

Burger vectors (i.e. b l and b2 = z-112) in DSC lattice are considered,

Ishida and McLean [27] have considered the case of a symmetrical tilt boundq where periodicity,

p. is proportional to Z and ~ D S C a x- IR. This criterion gives rise to a x- 1 dependence for the maximum angle of deviation. Pumphrey [31] has considered the dislocation spacing to be

proportional to the grain boundary periodicity (p). Since Z represents the relative volume of the

CSL cell in relation to the lattice cell, p is proportional to the mean edge of the CSL cell. Hence, p

= d 5 ~ 1 1 3 . Furthemore, since the volume of the DSC primitive ceil is proportional to Z-1 [16],

~ D S C CC z- which give rise to the criterion.

Palumbo and Aust [33] have recently pointed out that Dechamps's assumption of Burger vectors in

the DSC lattice to be proportional to the mean edge of the DSC ce11 is erroneous. Grimmer et al.

[26] have demonstrated that only two of the Burger vectors (Le. b 1 and b2) Vary with X-I1* while

the third vector, b3, only changes with the interplanar spacing dong the rotational axis.

Figure 2.4: The maximum deviation angles (Ag) from CSL (Z) in 99.999% nickel displaying selective immunity to intergranular corrosion in 2N H2SO4 [33].

By applying b ~ s c = x-1/2 and the mean periodicity considered by Dechamps, p a

Palumbo and Aust [33] proposed a new criterion,

which yields a dependence of ~ - 5 ~ 6 for the maximum deviation angle allowed.

Palumbo and Aust [33] further assessed the applicability of the CSL/DSC mode1 to the structure of

the interfaces in their susceptibility to intergranular corrosion in high purity nickel (99.999%). It

was found that (1 ) the interfaces close to low CSL relationships were most resistant to the

initiation of localized corrosion and (2) the selective immunity was found to lie within a limiting

structure field (i.e. 1 and Ag) not exceeding the Z value 25 and an angular deviation defined by

eq42.171. Figure 2.4 illustrates the Z-dependence of the allowed angular deviation based upon

the experirnental observed A0 values for the interfaces displaying selective imrnunity. The z - ~ / ~ criterion showed the best fit with the experimental determined value amongst various criteria

[27,30,33] proposed. The geometric criteria for classification of CSL grain boundaries can be

considered to be largely dependent on the relative misorientation of adjoining crystals.

The Role of CSL Boundaries in Cubic (FCC and BCC) Materials

The acceptance of the CSL mode1 as a standard for the characterization of grain boundary structure

for both bicrystals and polycrystals has largely been based upon the preponderance of experimentai

observations between special properties and structural geometry (see review [3]). The frequency

of occurrence of any particular type of CSL grain boundary is inherently associated with the

fundamental materiais processing phenornena such as recrystallization, grain growth and texture.

2.3.1 Random Distribution

A random GBCD, as defined by Warrington and Boon[34], is the set of grain boundaries which

can be generated from a random polycrystalline aggregate where each grain orientation is equally

probable. In order to appreciate the occurrence of speciai boundaries, the randorn distribution must

first be determined as a reference state for subsequent comparisons. Warrington and Boon [34]

demonstrated that the probability of occurrence of any particular CSL is found by determining the

number of equivalent rotations leading to the same CSL and muitiplying the probability of a

boundary lying within the angular deviation (Ag) imposed by CSL. Because of cubic symmetry

and the number of distinct forms for each CSL, the number of equivalent rotations increases

significantly. As shown in Figure 2.5, the overall probability decreases with increasing 1. The

maximum value obtained is 2.28% for Zl (i.e. low angle grain boundaries) and the value for 1

to 29 (where x29 is the upper limit for consideration of being special [35]) ranges from 13.6% to

2.9% for the most lenient to the most stringent A8 criterion. The frequency of the random

distribution is well below the frequency of occurrence for many metallic systerns and it is strongly

affected by variation in the selected value of dependence.

- - e - - Ishida and McLean 1271 i' \ - PalurnboandAust[33]

\ * - Deschamps [32]

Figure 2.5: Caiculated values of random distribution for CSL's ranging from Z 1 through 29 using four different variations in A8 dependence for Z-CSL.

2.3-2 Texture and the Frequency of CSL

The occurrence of special boundaries has been linked to the overall texture associated with

polycrystailine materials since in many metals and alloys, grains are rarely randomly distributed. It

is also reasonable to extend the consideration that in polycrystalline aggregates, different types of

texture may lead to different CSL distributions on the basis of the localization of grain orientation

distribution associated with a common rotational axis. The existence of special boundaries rnay be

the cause or the result of the texturing process.

Howell et al. [36] found in their TEM study of grain boundary structure of highly textured

tungsten wires and rods a high frequency of low angle (XI) and low CSL boundaries. It was

suggested that the occurrence of the high frequency of CSL's is directly related to the sharpness

and type of texture. Watanabe et al. [37] demonstrated the effect of texture on CSL distribution

using randomly texnired Fe-6.5 wt.% silicon ribbons produced by a rapid solidification method

and subsequent annealing. It was found that the associated change in texture from an initial

randorn texture to a (100) texture resulted in a change of the CSL distribution. The 1 1 , z5. 13.

x17, x25 and z29 type boundaries were found to have preferentially occurred. Similarly, XI,

B, 29, 1 1, 2 19, 127 were found to be associated with the (1 10) texture. Moreover, a higher

frequency of 1 boundaries was observed for both textured materials (24.8% and 1796,

respectively) in cornparison to the random texture specimen (= 34%) . The incorporation of a

higher frequency of 1 boundaries in the sharply textured ribbon was attributed to grain boundary

migration and grain growth driven by orientation-dependent surface energy [38]. The experirnental

data generally supported the observation that low-angle boundaries and CSL boundaries are

associated with uniaxial texture on the basis that grains can rotate in relation to the preferred axial

direction.

In correlating macroscopic texture components with GBCD, Garbacz and Grabski [39,40]

calculated from computer simulations the frequencies of CSL boundaries for fiber texture and a

random texture. It was concluded that texture can strongly influence the CSL distribution when the

texture is sharp. With increasing deviation from ideal orientation (Le. dong the fiber axis) and

decreasing sharpness of the texture, the fraction of the CSL boundaries should decrease.

Doni et al. [41] also reported in their computer simulation study indicating that the number of the

low Z CSL grain boundaries increases when a strong 'fiber texture' has been imposed. The

crystal orientations lying within a 10° (AB) of the axes cl CO>, and cl 1 I > were considered

to be strong; while with a 20' (A@), the texture was considered to be weak. In addition, it was also

reported that there is also the tendency for the CSL boundaries to exhibit preferential symmetry in

the case of strong texture. Subsequently, a similar conclusion was also recently obtained by

Gertsman et al. [42].

However. Pan and Adams [43] recently demonstrated with experimental measurements that the

results of cornputer simulation are not universally applicable to al1 materials. It was shown in their

results that for a fiber-textured Al film, the simulated results are in accordance with the

experimental measurernents whereas for weakly textured Inconel 600, the discrepancy between

expenmental and predicted values is substantial. Moreover, Lin et al. [44] have recentiy reported

that the frequency of CSL boundaries can exceed 70% with a highly randomized texture for

specially processed Alloy 600. This was shown to be associated with the formation of annealing

g twins which increases the number of available texture components in the system [45].

2.3.3. Annealing Twinning and the Frequency of CSL

Various mechanisms conceming the formation of annealing twins in FCC metals have been

reviewed extensively in the literature(see review [46]). Fullman and Fisher [47] first concluded

that annealing twins can forni whenever there is a decrease in the overail interfacial free energy at

migrating grain corners. Dash and Brown [48] suggested that a packet of stacking faults at

migrating boundaries during pnmary recrystallization leads to the formation and the subsequent

growth of twins. Gleiter[49] subsequently offered an atomistic model detailing the formation of

twins by a two dimensional nucleation process on the (1 1 1) planes of growing grains based upon

electron rnicroscopic observation of migrating grain boundaries. Meyers and Murr [50] put fonh a

'pop out' mechanism describing the formation of annealing twins which does not depend on grain

boundary migration in contrat to the previous models and is pnmarily concemed with the partial

dislocations emitted from grain boundary ledges. Although no one single mechanism can satisfy

all the experimental observations, it is generaily accepted that annealing twins form only at grain

comers (or ledges) during recrystallization and grain growth at elevated temperature. Nonetheless,

the energetic criterion of the Fullman and Fisher model has been expenmentally established [5 11.

Figure 2.6 illustrates schematically the process of the formation of a coherent twin at a grain corner

as proposed by Fullman and Fisher [47]. The energetic conditions must satisfy the inequality

[2.18] where ifs and A's refer to the specific interfacial free energies and the specific areas,

respectively. In accordance with the proposed theory, the number of twin boundaries should

decrease with increasing ratio of twin boundary free energy to grain boundary free energy. Bolling

and Winegard [52] confirmed the hypothesis by measuring the annealing twin frequencies in both

zone refined lead and the same lead containing 0.1 at.% Ag.

Grain (3) Grain (3)

Figure 2.6: Illustration of Fullman and Fisher mode1 showing the fonnation of an annealing twin at a grain corner.

Various experimental studies have demonstrated that the formation of anneding twins c m alter the

structure of the grain boundary and the relative proportion of the twin boundaries can exceed that

of a random distribution. Aust et al. first demonstrated in zone-refined Pb [6], Al [7], Cu [8] that

when an annealing twin is fomed during grain boundary migration, a general boundary is replaced

at the growth front by a large angle Z boundary and in the event of repeated twinning, the high

grain boundary is replaced by one with a lower 1 vaiue. These observations in zone refined FCC

rnetals are indicative that the twinning process can significantly alter the frequency of low-Z CSL

boundaries on the basis of energetic preference.

Burger et al. [53] have also shown in their High Voltage EIectron Microscopy (HVEM) study of

the recrystallization process in deformed aluminurn single crystais that repeated twinning (even in

high purity aluminum) can lead to the creation of new orientations. A preference of the 2 7

orientation relationship was found to exist between the matrix and the recrystailized grains. The

final orientations of the recrystallized grains are favored by coincidence relationships and the

twinning process was found to be necessary in reducing the values of the boundaries. Similar

studies [54,55] were also reported on high purity copper single crystals and dilute copper-

phosphorus alloys where twinning frequently changes the orientations at the recrystallization front

until low grain boundaries are obtained.

Goodhew et al. [56,57] have shown in gold thin films that the process of grain boundary

dissociation cm contribute to a significant fraction of CSL interfaces in polycrystalline materials.

The tilt boundarïes near the 1 1. x 9 and x99 misorientations frequently dissociate and

give rise to a x 3 and a second boundary is often a z33 boundary. The possible reactions cm be

summarized as follows:

Forwood and Clarebrough [58] also demonstrated a sirnilar phenornenon in Cu with 6 at. 8 Si

alloy where x9. 27a and x8 1d were frequently found to dissociate.

Lim and Raj [59] analyzed the GBCD in polycrystalline nickel (grade 270) prepared by the strain-

annealing technique and showed an abundance of annealing twins and pronounced preference of

CSLs geometrically related to x 3 . It was concluded that the occurrence of related boundaries

is due to the impingement of growing grains having relationships during high temperature

annealing. The generation of other non-x3 related boundaries were rationalized as a random

occurrence as predicted by Wamngton and Boon [34].

In the study of creep cavitation in 304 stainless steel using the electron channeling pattern

technique, Don and Majumdar [60] observed a high fraction of 2 3 related boundaries and found a

drastic change in the cavitation process associated with twin interceptions. The change of

crystaIIographic characteristics associated with the interfaces were explained within the framework

of the CSL mode1 where the value of the resultant interface at a given triple junction is dictated

by the product or the quotient of the value associated with the other two interfaces. In the event

of twinning, the value of an interface equal to x can be operated by a factor of 3 to yield the new

interface with the 1 value having either x=x/3 or = 3x.

Randle and Brown [61] also observed a high proportion of 'twin related variants' (Le. 3n where

n=l, 2, and 3) in their GBCD study of austenitic steel altered by thennomechanical action and

attributed the formation of these interfaces as the main factor responsible for the increase in the

CSL population. It was suggested that due to the intrinsic high mobility of the low ): CSL

boundaries (with the exception of the coherent twin boundaries) during the grain boundary

migration penod, mutual impingement of these boundaries could lead to further multiplication of

these preferred interfaces. In a subsequent study [62], the influence of kinetics on the distribution

of GBCD in 99.98% pure nickel was demonstrated by specimens subjected to ( 1 ) fast heating and

cooling and (2) slow heating and cooling cycles. The 'slow' specimen showed a significantly

higher fraction of CSLs and it was attributed to the additional twinning was facilitated by grain

rotation evolving towards a lower energy configuration.

Palurnbo and Aust [63! investigated the influence of solute on GBCD in strain-annealed Ni

(99.999%) containing S in various amounts of 0.3, 3, and 10 ppm. The results also showed a

strong preference of twin(Z3) and twin related boundaries(Z9 and z27) in al1 of the Ni grades.

More significantly, in contrast to the conclusion of Lim and Raj [59], the generation of n0n-Z3~

low-x CSL interfaces was found to occur through twinning and its contribution is most significant

only at the very low impurity level. The relative contribution of solute to CSL related boundaries

was explained in terms of energetic, hinetic and geometric considerations. The energetic

contribution is only expected to be significant at a very low impurity level and is primarily

associated with the twinning event. The maximum kinetic contribution can only be expected to

occur when the mobility difference between CSL and non-CSL boundaries is maximized within a

certain concentration range for a given driving force. Only the geometnc influence was found to 4

be independent of solute.

O 0.1 0.2 0 .3 0.4 0.5 0.6 0.7 Frequency of B, (d)

Figure 2.7: The proposed relationship for the contribution of annealing twin (d) to special boundary (d +112 d) fraction on the bais of energetic and crystallographic conditions [9].

In an effort to quantify the overall contribution of the annealing twinning to CSL distribution in

FCC materials with relatively low stacking fault energy, a geornetrical model was proposed by

Palumbo et a1.[9] on the basis of energetic considerations and crystallographic constraints

associated with annealing twinning. This model. as illustrated in Figure 2.7, suggests that (1) as

an extension of the Fullman-Fisher model, every twinning event c m create the equivalent of one-

half of an 'additional' CSL special boundary, (2) the annealing twin density has a theoretical limit

of 2/3 and (3) as the twin density approaches 213, a distribution consisting entirely of 23n (with

O I n Q boundaries c m be achieved giving rise to a 'Twin Limited Microstructure'(TLM).

Gertsman et a1.[64] also showed by computer modeling that the experimentally observed

distribution of x3n boundaries can be rationalized on the basis of multiple twinning which is the

main process controlling the microstructural formation. It was concluded that only 2 3 boundaries

are energetically favored while other low CSLs exhibit no energetic preference and the

preponderance of 23" was attributed to geornetncal reasons only. However, it should be pointed

out that this mode1 cannot adequately address al1 the experimental microstructures studied

quantitatively since (1) GBCD is inherently sensitive to the stacking fault energy and history of

thermomechanical treatment, ( 2 ) the ideal orientations assumed in the modeling may not be

representative to those found in real microstructures. The maximum twin density reported was

43% [64] while several experimental studies[44, 621 have shown the occurrence of twin

boundaries at frequencies greater than 50%.

2.3.4 Development of Recrystallization Texture and Grain Growth

When a deformed rnetal undergoes the recrystallization process, the newly recrystallized grains

form a preferred crystallographic orientation relative to the deformed grains. The two prominent

mechanisms elucidating the occurrence of a unique anneaiing texture, oriented nucleation [65]

(preferred nucleation of grains with a particular orientation) and oriented growth [66] (preferred

growth of grains of specific orientations) have been the subject of controversy for more than 50

years. The rigid polarization between the two theories is untenable [67]. Nonetheless, recent

experimentai evidence [68,69] supports the oriented growth theory as the dominant but not the sole

cause of annealing texture. The recrystallization process begins with nucleation and as the nuclei

grow, the recrystallization texture may be related to deformation texture by certain rotation

relationships which correspond to grain boundaries with high mobility.

2.3.4.1 Grain Boundary Mobility and Migration

Migration of a grain boundary is defined as the displacement of the boundary perpendicular to the

tangent plane. Grain boundary migration is expressed by the rate equation,

where M is the boundary mobility and P is the driving force. The rate of migration has been

observed to be dependent on the misorientation, boundary inclination, temperature and impurities

(see reviews [70,7 1 1).

Much of the current understanding on the orientation dependence of grain boundary motion was

derived from the classic work of Aust and Rutter who studied the influence of solute (tin in zone-

refined lead) on the velocity [2] and activation energy of grain boundary migration [72] . Figures

2.8 (a) and (b) illustrate the most important results and the following conclusion cm be drawn: (1)

In the presence of solutes, the rate of migration for boundaries with misorientation close to the

coincidence relationships (Le., special boundaries) is substantially higher than for the random

boundaries. (2) The activation energy of the rnigrating 'random boundaries' increases with

increasing solute content while the activation energy for the 'special boundaries' is independent of

the soIute concentration studied.

0- O .O02 .m .m

WElGMT PERCENT ûF TIN

Figure 2.8(a): A cornparison of rate of grain boundary migration for random boundaries at 3ûû°C in zone-refined lead doped with tin [2].

and special

TIN COtlCENTRATlON MT.

Figure 2.8(b) The effect of tin on the activation energy for the migration of random and special boundaries in lead [72].

Table 2.1: Experimental observations of lattice misorientation for the fast moving boundaries

Kronberg and Wilson [ 2 ]

Beck [73] Liebmann et al. 174,751 Dunn and Koh [76] Aust and Rutter [2]

May and Erdmann [77] Frois and Dimitov [78] Rath and Gordon [79] Stiegler et ai. [80] Rutter and Aust [8 1 1

ibe and Lücke [82]

Rotation Axis Materials Nearest Coincidence Relationship

Table 2.1 lists several of the fast moving boundaries observed experimentally. Their rapid

migration rates are associated with the geometric characteristic of the low 1 CSL boundaries.

However, a few exceptions exist. For instance, the coherent twin boundaries (x3) in FCC show

no or very low mobility while the incoherent segments of the twin boundaries were shown to be

highly mobile [83]. The low angle boundary (1 1) has been shown to be relatively immobile

which is consistent with the structural character of such boundaries (i.e. Read-Shockley dislocation

arrays) [29].

The orientation dependence of grain boundary migration has direct implications for the texture

developed during recrystallization and grain growth. The high mobility of special boundaries

would account for their preferred growth and their special orientation relationship to deformed

grains could lead to the recrystallization texture. Kronberg and WiIson[l] showed a coincidence

relationship between secondary and primary recrystallized grains in their study of secondary

recrystallization of copper. It was concluded that the secondary grains grow abnormally larger

because they are surrounded by readily mobile CSL boundaries. In the expenment of cornpetitive

growth of recrystallized grains into striated single crystals of zone-refined Iead, Aust and Rutter

[84] also explained the development of the preferred orientations based upon the mobility

difference between the general and the CSL boundaries. In addition, the lower energy of the low

boundaries resulted in their introduction into the pure lead when twinning occurs during

annealing.

In the study of the early stage of secondary recrystallization in Fe-3% Si alloy, Watanabe [85]

reponed the preferential migration of a ( 1 10) plane-matching grain boundary using the Electron

Channeling Pattern (ECP) technique. The misorientation of the boundary is close to 50S0 C I 10>

(Le. corresponding to the 1 1 coincidence relationship). This is in accordance with Gleiter's step

mechanism of grain boundary migration [86] whereby a boundary is easier to transfer atoms from

one grain to the other on the close-packed plane.

Makita, Hanada and Izumi [87] studied the development of cube texture during recrystallization of

cold-rolled pure nickel using x-ray diffraction and ECP. The preferred rotational axes, CI 1 l> or

, are controlled by the rolling procedure and grains having identical orientations to

secondary grains are already present in the primary recrystallized specimen. The orientation *

relationships between pnmary cube texture and secondary grains were interpreted in terms of the

CSLs, x7. 1 3a, 1 3b, 25a. z37a. This evidence suggests that grains having the potential to

fom CSL boundaries are likely to be the nuc1ei for the secondary recrystallization.

Randle and Brown [88] studied the effect of post-recrystallization strain (2% and 7%) in austenitic

stainless steel using the EBSP technique and established a link between the observed anornalous

grain growth (Le. secondary recrystallization) and the evolution of the CSL boundaries. The

proportion of the CSL boundaries increases with small strain. Srolovitz, Grest and Anderson 1891

have previously indicated by Monte Carlo simulation that the presence of a large grain is

insufficient to initiate the onset of the secondary recrystallization and suggested that the residual

strain energy may be of importance. The CSL boundaries tend to occur in clusters and their

frequency increases toward the end of the grain growth incubation period. The clustering of the

mobile CSL boundaries can also contribute to the initiation of secondary recrystallization, in

addition to the residual strain energy as the dnving force, since the rate of boundary migration is a

function of both driving force and grain boundary mobility.

Parallel to the experimental work that measures the local mesotexnire change associated with the

initiation of secondary recrystallization, Rollett et al. [go] have employed a statistical approach to

snidy the influence of anisotropic grain boundary mobility in abnormal grain growth via cornputer

modeling. The authors assign a lower mobility to low angle grain boundaries than to the high

angle grain boundaries. The simulation indicates thzt abnorrnal grain growth can occur under the

influence of grain boundary mobility and the size of the abnormal grain is limited to a maximum

size which scales with the magnitude of the anisotropic mobility . In the event that only 1 in 106

grains is abnormal, a mobility ratio of 13 is sufficient to produce complete secondary

recrystallization.

The transition from normal grain growth to abnormal grain growth in Al- 1 wt.% Ga. was recently

studied by Sursaeva et a1.[91]. The ECP technique was used to determine the grain

misorientations of (1) grains in the recrystallized matnx and (2) between large abnormal grains and

rnatrix grains. It was concluded that the mobility factor predominates over the energy

consideration and the formation of new grain boundaries having high mobility is more important

for the onset of secondary recrystallization than the nucleation of new grains.

2.3.4.2 Formation of Goss Texture by Secondary Recrystallization

The ability of iron-silicon alloys to develop a strong Goss texture, ( 1 10), along with

characteristics such as high magnetic penneability, saturation magnetization and electrical

resistivity, have gained the universai acceptance of this alloy as the core material for transfomers.

The significant reduction achieved in total core loss over the years has been largely due to ( 1 ) the

improved crystal orientation thereby reducing the hysteresis loss and (2) the increased resistivity

and the thinner gages which decrease the eddy current loss. Driven by the potential economic

retums, the steel industries have fine-tuned the manufacturing process in producing the grain-

oriented silicon steel. The technique is based upon inhibition of normal grain growth by fine

precipitates of MnS and AIN in the primary matrix which subsequently leads to a strong secondary

Goss texture. However, the mechanism by which a weak primary recrystallized texture develops

into a strong single-component secondary texture still remains obscure.

Dunn [92,93] first proposed the oriented nucleation growth selectivity theory to explain the

experimentally observed orientation relationship between components in the secondary

recrystallization texture, ( 1 10)cOO 1 >, from the deformation texture, ( 1 1 1 )< 1 12>. in cold rolled

single crystals of silicon iron. The secondary nuclei were suggested to have larger grain size in

contrast to other pnmary grains. Within the weak components of pnmary recrystallized texture,

they cm grow into secondary grains via a rotation of 25" to 30' about c l 10> at the expense of

other prirnary grains in deviating orientations.

May and Tumbull [94] also studied the texture changes in high purity silicon iron with emphasis

on the impurity control. They found that larger primary grains can contribute to the evolution of

the secondary reciystailization texture and can be related by a 35' rotation about a common

mis. The presence of dispersed second phase, manganese sulfide, is necessary to maintain a stable

matnx of fine grains pnor to the development of a strong (1 10) texture. Moreover. the

influence of the surface energy on the migration of grain boundaries between ( 1 10) grains and

( 1 0 ) grains in high purity silicon iron was also demonstrated by Walter and Dunn [95]. The

direction of boundary migration was found to advance from (1 10) grains into the (100) grains in a

vacuum anneal and reverse back to the initial direction in impure argon atmosphere.

In the proposed grain growth equation for individual grains with grain size R in single phase

materials [96],

where Rcr is an average grain size and Z represents the impedance to growth by dispersion of

second phase particles, HilIert proposed that a grain having a size of 1.8 times the average size in

the matrix is predicted to be unstable with respect to growth. The materials with at least one very

large grain could instigate abnormal grain growth. Gladman [97] subsequentl y explained the

secondary recrystallization process in terms of unpinning of the grain boundaries from the

precipitate particles. During grain growth, the largest grains in the materials are likely to be

unpinned first as the agglomeration of the particles continues. The notion of the size advantage

was also supported by Dillarnore [98] who suggests that (1 10) grains are arnong the largest

grains present in the primary recrystallized structure and they are able to maintain the larger size by

geometrical coalescence[99] of two or more small grains of low misorientation. In contrast to the

above studies, the hypothesis of size advantage is not supported by the SEM-ECP study on the

origin of the Goss texture in Fe-3.25% Si alloys by Pease et al.[100] since the orientations of

selected large pnmary grains reveals a texture similar to those of primary recrystallized matenals

(i.e. a sharp Goss orientation for large grains was not observed).

In the investigation of the effects of impurities on grain growth in strain-anneal and secondary

recrystallization of Fe-3.25% Si alloy, Nakae and Tagashira [101], using the etch-pit technique,

reported the existence of colonies of three principal orientation components, (1 10),

( 1 1 1)< 1 1 O> and (1 1 1)< 1 12>, in the primary recrystallized structure. The abrupt growth of

( 1 10) grains into other colonies of recrystallized grains above the dissociation temperature of

sulfide contributes to the secondary recrystallized texture. Inokuti et a1.[102] supponed the

colonies theory and reported that Goss grains are larger than the matrix grains and the Goss grains

are formed as a result of inherited structure memory frorn the original hot rolling process.

Shinozaki et a1.[103] studied the orientation distribution of primaiy and secondary recrystallized

grains in 3% silicon steel using the three dimensional orientation distribution function. The

pnmary recrystallized grains were found to have peak orientation distribution near the (1 10)

and ( 1 11)c112> components. In cornparison with the distribution of secondary grains, the

authors explained the texture evolution by suggesting that in the pnmary recrystallized texture, the

( 1 10)cOO 1 > becomes the nucleus of secondary recrystallization and the ( 1 1 1 )< 1 12> components

have coincidence relationship concentrated near 3 5 O about c l 10> axis with the secondary grains

(i.e. including x9, x19a, z27). However, a considerably high orientation density of the two

components in the primaries is necessary for the occurrence of secondaries with ( 1 10)eOOb

orientation. The earlier concept [2,84] that the enhanced mobility of the CSL boundaries contribute

to the development of preferred orientation in FCC is likely to be applicable to BCC Fe-3% Si

alloys.

In an effort to clarify the role of CSL boundaries, Harase et al.[10] pioneered the concept,

'Simulation by Hypothetical Nucleus' - Le. calculating the frequency of CSL grain boundaries that

are likely to f o n with respect to a growing grain (hypothetical nucleus) from the pnmary matrix,

to further elucidate the mechanism of secondary recrystallization in Fe-3% Si alloys. The concept

advocates that in the investigation of the grain growth process, in addition to the boundary

relationship between grains that are in contact with each other pnor to the onset of abnormal grain

growth, the potential relationship when a growing grain cornes in contact with other matrix grains

must aiso be considered. This is illustrated schematically in Figure 2.9.

1 -fH (Hypothet ical nucleus) Figure 2.9: Schematic diagrarn of a growing grain (Hypothetical Nucleus) advancing in to the stable matrix forming new grain boundaries in the process[l04].

By applying the SH method, the calculation of the frequency of the CSL boundaries in relation to

hypothetical nuclei based on the direct experimental measurements of individual grains via ECP

shows that the frequency distribution of the grain boundaries having CSL relationship with respect

to secondary nuclei has a peak value near the (1 10)401> orientation. Figure 2.10 illustrates the

proposed mechanism describing the selective growth of grains of specific orientation associated

with the intensity of coincidence grains and the intensity of the secondary nuclei. It was found that

the specimens containing a critical number of grain boundaries having coincidence relationships

after primary recrystallization are able to complete secondary recrystailization. However, when the

CSL relationshi~s disappear in the primary rnatrix, no secondary recrystallization occurs.

c-+ Range of o r i ~ o c u evolvd by grain giowth

Orientation of hypothetical nucleus N

Figure 2.10: A schematic illustration for the proposed mechanism of the texture evolution by grain growth associated with the coincidence relationship [IO].

In view of the lengthy procedure required to obtain the orientation information of individual grains

via ECP, the application of the SH method to predict the secondary recrystallization was modified

by using the x-ray intensity values obtained during the course of standard pole figure

determinations instead. The new method is referred to as the SHG method [103]. Through

analysis of the x-ray intensity value, the 'likely' orientations are obtained using the 'vector

method1[l05]. In considering the intensity of hypothetical nucleus orientation in the matrix, IN.

and the intensity of coincidence oriented grains in relation to the hypothetical nucleus orientation,

Ic, the product of the two intensities, PCN, gives rise to the possibility of predicting grain growth

behavior in relation to the secondaries. It was demonstrated that a critical value of PCN is

necessary for secondary recrystallization and Goss grains were found to be closely related to 2 9

coincidence oriented grains in Fe-3% Si dloys produced by the single stage cold rolling method.

Yoshitomi et d.[106] recently investigated the secondary recrystallization of Fe-3% Si alloys with

special reference to the influence of the primary recrystallized grain growth on the secondary

recrystallization. The dominant grain growth in the higher temperature was marked by the

evolution of ( 1 10) secondaries; however. at a lower temperature, it is mainly evoIved by the

( 1 10)~227> secondaries frorn smaller primary recrystallized grains. The evolution of ( 1 10)cOO 1 >

secondary recrystallized grains was considered to be associated with the highest frequency of 2 9

coincidence boundaries while the evolution of (1 10) grains was attributed to the 25

coincidence relationship. The authors explained the evolution of secondary recrystalIization by the

assumption that Z5 coincidence boundaries are likely to be more mobile than 2 9 in the lower

temperature range. The pnmary recrystallized grain growth is considered to have an influence on

the secondary recrystailization temperature.

Moreover, in explainhg the mechanism of texture evolution of ( 100) cube onented texture

whereby the matenals are typically produced by cross rolling, Harase et a1.[107] found that the

secondary recrystallization of ( 1 00) texture shows the highest frequency of 1 7 coincidence

relationship with respect to cube orientation prior to the onset of secondary recrystallization. The

proposed mechanism of the texture evolution in Fe-3% Si can be surnrnarized in tems of the

distribution of the coincidence boundaries and their specific migration behavior under the influence

of precipitates in certain temperature ranges.

Rouag, Vigna and Penelle [IO81 shldied the role of the CSLs associated with the evolution of local

texture and grain boundary characteristics during secondary recrystallization of Fe-3% Si sheet.

The results on the evolution of the local texture are consistent with those related to the anisotropy

of grain boundary migration surrounding the growing Goss grains. It was found that the

percentage of the CSL boundaries decreases (Le. from 15% at 960°C to 5% at 975OC) in the

vicinity of a ( 1 10) grain when abnormal growth begins. This observation agrees with

previous reports [84, 1041 that the CSL boundaries are less dragged by solutes and consequently

move faster than general grain boundaries. At the early stage of the abnormal grain growth. the

Goss grains are able to grow by preferential migration of special boundaries which would explain

the decrease of the overall CSLs boundaries. It was assumed that in the later stage of growth, the

size effect then becomes the predominating factor. As first alluded by the Rouag et a1.[108], the

importance of the CSLs dunng secondary recrystallization is signified by the disappearance rather

the prevalence of the CSLs.

2.4 Objectives

The prirnary objectives of this investigation were to,

(1 ) Assess the relative proportion of low-x CSL boundaries and annealing twins in low

stacking fault energy materials in order to elucidate the role of twinning during microstructural

evolution.

(2) Utilize both the 'Simulation by Hypotheticd Nucleus' (SH) rnethod and direct experimental

crystallographic orientation detemination (OIMTM) in Fe-3% Si alloy to examine the role of CSL

boundaries in the texture development of Fe-3% Si alloy.

(3) Estimate the relative difference in mobility between the CSLs and the general boundaries

based upon the statistical changes in grain boundary population during the process of grain

growth.

3 Experimental Procedure

3.1 Characterization Technique

The scanning electron microscope (SEM) has been used extensively for materials characterization.

In addition to its superior imaging capability, a number of applications have been developed over

the years for particular materials science applications. These include x-ray fluorescence analysis,

electron beam induced current imaging, electron channeiing and electron diffraction. These

techniques can be applied to bulk specirnens with minimal sample preparation and the spatial

resolution of each technique depends on the diameter of the incident electron probe and the spread

of the electron bearn within the specimen.

The physics of the backscatter diffraction pattem was first described in 1953 by Alarn et al. [log]

who referred to these patterns as 'High-angle Kikuchi pattem'. Venables and Harland [110] were

the first to apply the same principles to the SEM in 1973 and termed the technique 'electron

backscattering pattem'. The acronyms, EBSD and EBSP, standing for electron backscattered

diffraction and electron backscattering patterns, are commonly used interchangeably. The main

attractions of the EBSP technique are ( 1 ) information can be obtained from a small grain size

range, (2) wide angular width (up to 60-70 degree) on one diffraction pattem and (3) minimal

modification to the SEM for observing the pattern. Subsequently, the technique was refined by

Dingley et al. [I 1 1.1 121 in the 1980's through implementation of real-time imaging of the Kikuchi

pattem with manual on-line computer interrogation. In the 1990ns, Adams and CO-workers [ I l ]

further improved the system by automating both the hardware configurations and computer

algorithms which enable rapid indexing of diffraction patterns and produce a micrograph

containing crystallographic information from the precise rneasurements of the local lattice which is

now known as Orientation Imaging Microscopy (OlMTM). This technique uniquely bridges the gap

between the conventional x-ray diffraction and the traditional thin foi1 transmission eiectron

diffraction methods. The x-ray technique provides global texture information but lacks the

resolution for the locaiized rneasurements. On the other hand, the thin foi1 transmission electron

diffraction offers detail resolutions; however, it is not an efficient technique for obtaining large data

sets for statisticaf purposes. Therefore, the information generated by OIM can be used to address

specific questions conceming the microstructural evolution both quantitatively and qualitatively. In

the following sections, a brief discussion of both the background and the operation of the

technique is presented.

3.1.1 Pattern Formation

When a narrowly focused electron bearn with an defined energy enters a crystalline material, the

stnking electrons disperse beneath the surface from a small interaction volume and subsequently

diffract from planes in the crystal lattice forming distinct bands in a systematic manner provided the

Bragg condition is satisfied. where h is the effective wavelength, d is the spacing between the

crystal planes and 0 is the angle of incidence.

h = 26 sin 8 C3.U

The diffracted electrons effectively fom a pair of cones for each set of crystal planes; Le., above

and below the diffracted plane corresponding to the reciprocal lattice vectors, t g . The mid-plane

between the cones is parallel to the plane from which the pattern aises. Hence, the geometrical

distribution of cones is identical to the crystal planes (see Figure 3.1) and therefore, possesses al1

the symmetry of the crystai (1 131 .

The stnking electrons lose energy rapidly upon penetrating the sarnple. The high energy electrons

can escape near the surface and the diffraction pattern is superimposed on background noise caused

by al1 the backscattered electrons that escaped the surface without being diffracted and/or

inelastically scattered after diffraction. The optimal angle between the incident beam and the

normal to the specimen surface should be in excess of 60 degrees to minimize absorption. The

intensity of the pattern aiso depends on the structure factor. The imaging screen should be

positioned in the forward scattering position. Only the high energy electrons (i.e., equal to the

incident beam energy) contribute to the illumination of phosphor which gives rise to the recordable

diffraction pattern.

Projection of Diffracting Plane

Phosphor Screen

Kikuchi

/

e of Intense Electrons

Electron Beam

PC - Pattern Center L - Specimen to Screen Distance

Figure 3.1 : Schematic diagram illustrating the geometric formation of a pair of Kikuchi lines from a diffracting plane.

3.1.2 OIMm - Hardware Configuration

Figure 3.2 illustrates the additional components necessary on the SEM in order to automatically

measure grain orientations. The computer is utilized to control the process of pattern collection, the

location on the sample from which diffraction occurs and deter