Crystalline nature of materials TEXTURE

(1)

1 CHAN PARK, MSE, SNU Spring-2019 Crystal Structure Analyses

TEXTURE

Krawitz Chap 11 Hammond Chap 10 Cullity Chap 14 Dyson Ch 11

Klug & Alexander Chap 10

Crystal Structure Analysis

Materials Science & Engineering, Seoul National University CHAN PARK

Crystalline nature of materials

 Many solid materials are composed of crystals joined together

 The individual grains can fit together closely to form the solid

 XRD can determine macroscopic orientation of a collection of grains (individual grains using micro diffraction possible)

 EBSD can determine the orientation of individual grains and characterize grain boundaries

Crystallized copper oxide

Silicon iron alloy

(2)

Crystalline nature of materials - Grains

 A grain is a region of distinct crystal orientation within a polycrystalline material

 A grain boundary is the interface between two neighboring grains

 Grain boundaries have a significant influence on the properties of the material, dependent on the misorientation across boundaries

 Grain boundaries are regions of comparative

disorder, but special grain boundaries exist where a significant degree of order occurs  “CSL”

boundaries which have special properties

Crystalline nature of materials – CSLs

 Coincident site lattice boundaries (CSLs)

 A significant degree of order occurs at a CSL boundary, which leads to special properties

Schematic presentation of a

 ₃

boundary.

Where the two grain lattices meet at the boundary, 1 in every 3 atoms is shared or

coincident – shown in green.

Schematic presentation of a

 ₅

boundary. 1 in every 5 atoms is shared or coincident.

(3)

Crystalline nature of materials – properties

 If properties are equal in all directions, a material is termed

“isotropic”.

 If the properties tend to be greater or diminished in any direction, the material is termed “anisotropic”.

 Most materials are anisotropic.

 Anisotropy results from preferred orientation or texture.

Random orientation Preferred orientation Highly oriented - close to a single crystal

isotropic vs. anisotropic

Anisotropic structure of wood

Crystal structure - anisotropic arrangement of atoms

Photoelastic anisotropy used to visualize strains and

stresses Structure and Anisotropy

Prof. Jeong Hyo Tae, Kangnung National Univ.

(4)

Texture

 All orientations of crystallites possible

 1cc powder of 10um crystallites  10

⁹

particles

 1cc powder of 1um crystallites  10

¹²

particles

Texture

 Random powder – all crystallite orientations equally probable  flat pole figure

Loose powder

Metal wire

(100) random texture

(100) wire texture

 Crystallites oriented along wire axis - pole

figure peaked in center and at the rim

(5)

RD, TD, & ND

What is Texture?

Ks

K _s

ND

Normal direction

K _c

][001

[010]

[100]

RD Rolling direction TD

Transverse direction

K

_S

specimen reference frame sample coordinate system K

_C

crystal reference frame

crystal coordinate system

Orientation of Grains in Polycrystalline Solid

(6)

Texture

 In a polycrystalline body, the individual crystallites may have a random or non-random distribution of orientations.

 A body with a non-random distribution of orientation is said to be textured or to display preferred orientation.

 As materials properties are anisotropic (depend on the direction within a crystal), the presence of texture will alter the physical

properties of the polycrystalline material.

Texture

 Very common condition – difficult to prepare texture-free aggregate

 Can have a profound effect on diffracted intensities

 Many forming processes such as rolling & drawing introduce texture into a material  deformation texture

 On annealing, the texture can change, but not become random  Annealing texture

 Texture is well-studied because of its wide presence in real materials and its pronounced effect on physical properties

property

value in Zr along

c-axis a-axis

Young’s modulus 125 GPa 99 GPa CTE 11.4 x 10^-6 K^-1 5.7 x 10^-6 K^-1

Polycrystalline material with preferred orientation of the crystallites, can exhibit anisotropy in its physical properties, depending on the degree of preferred orientation

(7)

Where is texture observed ?

Geology Biology Metals Ceramics Polymers

Rocks Teeth Alloys Oxides Polyethylene

Soils Bones Intermetallics Silicates Polypropylene

Ores Shells Nitrides Liquid Crystals

Ice Carbides

Salt

Natural Materials Man-made Materials

Why texture is important?

 Each single crystal has anisotropic properties with respect to direction (e.g.

mechanical property, magnetic property…).

 When orientations of grains are randomly distributed, macroscopic property of the sample is isotropic.

 In textured materials, many macroscopic properties are anisotropic, i.e. they depend on direction.

 Sheet steel

 motors, transformers --- {110} // surface

 severe deformation (drawing, rolling) --- {111} ⊥ surface

 Control of texture  degree of deformation, annealing temperature

 Custom-made desired texture, is still difficult

(8)

Why texture research is important ?

 Texture is responsible for anisotropy of various properties

 plastic deformation

 mechanical properties

 corrosion and oxidation

 magnetic properties

 electrical conductivity

 ……….

 It allows to better understand various processes

 geological processes

 deformation of metals

 annealing processes

 electroplating

 oxidation of materials

 diffusion of atoms

 phase transformation

 …….

How is Texture formed & measured?

 How is Texture formed ?

 Solidification

 Metal forming

 Mechanical deformation

 Annealing

 Sintering

 Thin films

 How is Texture measured?

 Etch pits

 X-Ray diffraction

 Neutron diffraction

 EBSD

(9)

Deformation texture, Annealing texture

 Deformation texture

 Texture produced by forming process (wire drawing, sheet rolling)

 Grains undergo slip & rotation during plastic deformation.

 Annealing texture (recrystallization texture)

 When cold-worked materials with deformation texture is recrystallized by annealing, new structure can have a texture different from that of the un-annealed material.

 Results from the effect of the pre-existing texture on the nucleation &

growth of new grains in the material

Fiber texture, Rolling texture

A common direction parallel to the fiber or wire axis  [uvw]

Fiber texture

Defined by {hkl}<uvw>

{hkl} - planes // to sheet surface

<uvw> - direction // to rolling direction Rolling texture

(10)

Fiber texture

 In a sample with fiber texture, there is a preference for one (or more) directions within the grains [uvw] to lie close to the fiber axis

 Fiber axis lies along a wire or fiber

 Materials with fiber texture display rotational symmetry in the distribution of directions [uvw] about the fiber axis

 Fiber texture is common in wires and other materials formed by drawing or extrusion

 In some materials, there may be more than one direction that is preferentially oriented along the fiber axis

 Cu wire often has [111] + [100] texture

 Many grains have [111] orientation close to the fiber direction but there are also a lot of grains with [100] close to the fiber axis – typical example of double texture

Sheet (rolling) texture

 In a specimen showing sheet texture, grains prefer to have a set of planes (hkl) parallel to the sheet surface and a direction [uvw]

aligned with the rolling direction that was used during manufacture

 The ideal orientation is specified by (hkl)[uvw]

 In real materials, not all grains are oriented with planes (hkl) exactly parallel to the surface and direction [uvw] along the rolling direction.

The distribution of orientations that are present can be displayed by the use of a stereographic projection called a

pole figure

(11)

How to represent texture?

 Miller index

 Pole figure

 Inverse pole figure

 Orientation distribution function (ODF)

Miller index of crystal orientation; {hkl}<uvw>

 3 orthogonal directions as reference frame

 Most widely used ones

 Rolling direction (RD)

 Transverse direction (TD)

 Normal direction (ND)

 Can identify a crystal plane (hkl) normal parallel to ND and a crystal direction [uvw] parallel to RD, written as (hkl)[uvw]

{100}<110>

Oxford Instrument

Ks

{110}<001>

(12)

Pole figure vs. inverse pole figure

 Pole figure – intensity variation of one family of planes (poles) as a

function of sample orientation

 Inverse pole figure – intensity variation of several families of planes in a fixed sample orientation

 Data are plotted in “times random” unit --- in ratios of actual counts at a point to counts obtained from the corresponding random sample under the same experimental conditions

Pole Figure & Inverse Pole Figure

(13)

Pole figure

Pole

(14)

Pole figure

RD

TD ND

Pole figure

 Imagine a sample of a cubic material with only 10 grains. The orientation of the {100} directions for each grain (thirty of them) can be determined and plotted on a stereographic projection  (100) pole figure.

 No texture  poles will be uniformly distributed on the PF.

 Textured  poles will tend to group together in certain place on the PF.

Random orientation

Preferred orientation

(a) (b)

Uniform distribution of poles  the material is not textured

Cullity 3^rdEd. Page 405

Poles cluster close to the rolling direction and

⊥

_to

the sheet  (100)[010] texture. The cubic symmetry of the material requires that there should also be poles in the transverse direction

(15)

(100) Pole figure

(111)[011]

(100) Pole figure

(111)[011]

(16)

(100) Pole figure

(111)[011]

(100) Pole figure

(110)[001]

(17)

(100) Pole figure

(110)[001]

(110) Pole figure

(110)[001]

(18)

35 CHAN PARK, MSE, SNU Spring-2019 Crystal Structure Analyses Prof. Jeong Hyo Tae, Kangnung National Univ.

Top

Side

bi-axial texturing uni-axial texturing

no texturing

top view

side view I Texture - film

In-plane texture

Out-of-plane texture

(19)

Texture – film

no texturing

uni-axial T bi-axial T

film1 substrate

film2film3 film4

c a

out-of-plane texture in-plane texture

OMEGA scan - out-of-plane texture

ω

Oak Ridge National Lab

-15 0 15

ω (deg.)

Ni

(002) 7.0˚

If grain size is very large, sampling problems may inhibit accurate estimation

of pole densities Cube-textured Ni

(20)

PHI scan - in-plane texture

sample detector

θ

X-ray s ource

x 2θ z

y

sample detector

θ

X-ray s ource

x 2θ z

y x

z

y

x y

X sample D z X sample D

φ

x y

z x

y

X sample D z X samsampleple D

φ

x z y

sample

detector

sample

detector

x

χ

z

y x

z y

sample

detector

sample sample

detector

χ

φ(deg.)

0 90 180 270 360

Ni

(111) 8.5˚

φ(deg.)

0 90 180 270 360

Ni

(111) 8.5˚

Oak Ridge National Lab

θ(ω), 2θ, χ − fixed φ − zero to 360

^°

Pole figure

θ(ω), 2θ, − fixed

χ − zero to 70° (e.g. 5° step) φ − zero to 360° (e.g. 5° step)

0 .05 0 .12 0 .29 0 .69 1 .64 3 .90 9 .24 2 1.9 2 5 1.9 8

φ χ

φ(deg.)

0 90 180 270 360

Ni (111)

8.5˚

φ(deg.)

0 90 180 270 360

Ni (111)

8.5˚

θ(ω), 2θ, χ −fixed φ −zero to 360^°

Cube-textured Ni

(21)

Pole Figure

(111) pole figure of (100) oriented single crystal (or polycrystalline with in-plane orientation)

54.73°

Pole figure

 Probability function for texture

 A stereographic projection of a crystal axis down some sample direction

 A stereographic projection showing the orientation distribution of a certain direction (pole) within the crystals of the specimen

 A pole figure is scanned to measure the diffraction intensity of a given reflection (2θis constant) at a large number of different angular

orientations of the sample

 A contour map of the intensity is then plotted as a function of angular orientation of the specimen.

 The most common representation of the pole figures are stereographic or equal area projections

(22)

Pole figure

 The intensity of a given reflection (hkl) is proportional to the number of hkl planes in reflecting condition (Bragg’s law).  PF gives the probability of finding a given crystal-plane-normal as a function of the specimen orientation. If the crystallites in the sample have a random orientation, the recorded intensity will be uniform

 PFs tell you about the orientation of one direction in a crystal

 PFs does not fully specify the orientation of the crystals in the sample

 More than one PF is needed for this

 Which reflection to use in PF measurement (100 or 111 or …) has to be selected based on the material. (111) PF can be very informative for some materials, but may not be that useful in some other materials.

Texture analysis using XRD

 Reflection method

 α (or χ) : 0

^o

- 70

^o

 incomplete pole figure

 β (or φ) : 0

^o

- 360

^o

 Transmission method

 α (or χ) : 0

^o

- 50

^o

 incomplete pole figure

φ

χ α

φ(δ)

Reflection transmission

(23)

TD

α

RD

β

Back- reflection range

Pole Figure – reflection method

TD

α RD

β

Back- reflection range Pole Figure – reflection method

(24)

TD

α RD

β

Back- reflection

range Pole Figure – reflection method

TD

α RD

β

Back-reflection range

Pole Figure – reflection method

(25)

TD

β RD

90°-α

Transmission range Pole Figure – transmission method

TD

β RD

90°-α

Transmission range Pole Figure – transmission method

(26)

Back-reflection range

Transmission range

Overlapping Zone

TD

α β RD

Overlapping region

 Complete PF

 Incomplete PF

Pole figure measurement

 PFs are not typically determined by examining individual grains. They are determined by a combination of powder diffraction with either an area detector and/or a device for reorienting the whole polycrystalline material

 If a diffractometer is set at a θ_Bto record the (111) reflection, reorienting the sample while measuring the diffracted intensity will provide the required information to compute a PF as only those grains that have their (111) planes perpendicular to the diffraction vector will contribute to the recorded intensity

(27)

Four circle diffractometer > Relation between rotation axes

 The systematic change in angular orientation of the sample is normally achieved by utilizing a four-circle diffractometer

 The intensity data are collected for various settings of CHIand PHI

 Normally we measure all PHI values for a given setting of CHI, we then change CHI and repeat the process

θ(ω) 2θ

χ φ α: sample tilting (χ)

β: sample rotation (φ)

Bruker

Cube component {001}<100>

(28)

Pole figures – fiber texture

 In PFs for a materials with fiber texture, rotational symmetry around the fiber direction can be found

 The angle between the fiber axis and the peaks in the distribution of poles tells you what direction is preferentially aligned with the fiber axis

(111) Pole figure for a cubic material with imperfect [100]

fiber texture

The high probability shaded region makes an angle φ of ~54.7°to the fiber axis. This is the angle between [100] fiber axis and the (111) poles

Sheet texture by diffractometer

 In order to determine a PF using a diffractometer, the sample has to be reoriented in the beam.

Each different orientation gives an intensity that can be used to determine one point on a PF

 After absorption correction, the intensity is directly proportional to the density of poles on the PF

 Sheet texture can be measured in transmission and reflection. Both types of measurements are

needed for a complete PF α andδ are sample rotation angles. They are varied so that different points on the PF can be determined

(29)

Transmission method - diffractometer

 For α = 0, the diffraction vector is in the plane of the sheet. As α increases and we start to measure points closer to the center of the PF, the absorption goes up. This change in absorption has to be

corrected for, during the calculation of the PF

α

φ(δ)

Transmission method - diffractometer

 Absorption restricts the ability to measure PFs in transmission.

Need a sample with

µt ~ 1. This means 35um for iron or 75 um for

Al with Cu Kα radiation. Real samples usually have to be thinned and their surfaces etched so that a useful measurement can be made.

 Even after thinning, only the outer parts of the PF can be measured.

At α > 50°, absorption correction becomes inaccurate and specimen

holder frame obstructs the diffracted beam  a major problem for

some values of

α

(30)

Transmission method - Absorption correction

 The diffracted intensity has to be corrected for absorption.

This correction can be very large.

 Correction factor R for a sample with mt = 1 and θ = 19.25°

 The measured integrated

intensity has to be divided by the correction factor (R)

 For angles

α

> 50°, 1/R increases rapidly and the data is no longer usable

Schulz reflection method - diffractometer

 The center part of the PF can be measured by reflection

χ

: 0

^o

- 70

^o φ

: 0

^o

- 360

^o

φ χ

 This geometry allows

measurements over a large range of χ values without the

use of an absorption

correction

 Measurements at different χ

and

φ

values can be used to

determine the center portion

of the PF

(31)

Plotting pole figures

 If transmission and reflection measurements have to be combined, the two sets of data have to be carefully scaled together so that the PF is continuous.

 PFs can be drawn on an arbitrary scale or by comparing the

intensity that was actually measured with what you would expect for a sample with random grain orientations.  “times random”

contours

Pole figure with an “ideal texture”

 Sharp featured PFs may be

approximated with an ideal texture

 The maxima in the a brass PF correspond well with those expected for (110)[112] texture

 (111) poles of the single crystal are oriented so that its (110) planes are // to the sheet and the [112]

direction // to the rolling direction

(111) PF for cold-rolled a brass sheet

The probability of finding the crystal plane normal for the reflection is proportional to the

intensity

(32)

3-D display of pole figure

Problems with texture measurement

 If grain size is very large, sampling problems may inhibit accurate estimation of pole densities

 Surface of a sheet may not have the same texture as the bulk

 Transmission measurements can have a big problem due to

absorption

(33)

Thin film – texture; YBCO/STO

Intensity

Omega (deg.)

14 15 16 17 18 19

0.4^o

Intensity

0 90 180 270 360

Phi (deg.) fwhm = 1^o

Intensity

10 20 30 40 50 60

2 theta (degrees)

002 003

004 005

006

007 STO 001 STO 002

Textured film vs. single crystal

The amount of material properly oriented, in addition to ∆φ

and ∆ω, is needed to describe the degree of texture

(34)

Percentage cube texture

111

A B

Collect data

@ A

Collect data

@ B

At each point, I(A) – I(B) 

 I (blue)/ I (blue + yellow) = percentage cube texture

Theta

Inverse pole

figure

(35)

Direct pole figure vs. Inverse pole figure

 xyz sample coordinate system

 x’y’z’ crystal coordinate system

 Both are 2-D projections of the 3-D orientation distribution functions (ODF)  cannot completely describe the orientations present. 3-D ODF can do this.

z = ND x= RD

y= TD

x’ = [100] z’ = [001]

Y’ = [010]

z = ND x= RD

y= TD x’ = [100]

z’ = [001]

Y’ = [010]

Pole figure Inverse pole figure

Direct pole figure vs. Inverse pole figure

z = ND x= RD

y= TD

x’ = [100] z’ = [001]

Y’ = [010]

z = ND x= RD

y= TD x’ = [100]

z’ = [001]

Y’ = [010]

Pole figure Inverse pole figure

Dist. of selected xtallographic

direction relative to certain directions in the specimen

Dist. of selected direction in the specimen relative to xtal axes

Dist. of a, b & c relative to RD, TD & ND

Dist. of RD, TD & ND

relative to a, b & c

(36)

Pole Figure & Inverse Pole Figure

Inverse pole figure

 Choose a sample direction of

interest, e.g. the Normal Direction (ND or “3”)

 Choose a grain; determine which crystal direction the ND is parallel to; plot the result on a

stereographic projection.

 Repeat for all grains!

 If appropriate (large number of data points), plot contours

 Remember that the unit triangle is the fundamental zone for directions in cubic crystals

Carnegie Mellon Univ.

(37)

Inverse pole figure

Inverse PF

 The crystallographic direction // to ND plotted on a stereographic projection with axes // to the edges of the crystal unit cell

 The direction is repeated because, for cubic materials, it could be any one of 48

symmetrically equivalent crystal directions

a cubic crystal unit cell oriented w.r.t. sample axes

the same sample axes oriented w.r.t. the crystal unit cell

(38)

Inverse pole figure

The RD and TD inverse pole figures are obtained in a similar way

Inverse pole figure

Negligible fraction of non-<111> fiber

Sample direction 3, or ND Strong <111>//ND Fiber Texture

Carnegie Mellon Univ.

(39)

Direct PF vs. Inverse PF

 DPF

 Specify the poles of a specific crystal direction w.r.t. sample coordinate in stereographic projection

 Shows the distribution of a selected crystallographic direction relative to certain directions in the specimen

 IPF

 Specify the poles of sample coordinate system w.r.t. those of crystal coordinate system in stereographic projection

 Shows the distribution of a selected direction in the specimen relative to the crystal axes

Direct PF vs. Inverse PF

 DPF

 A normal PF indicates how likely it is that a specific direction in a grain will adopt some orientation relative to the external features of the sample

 IPF

 An inverse PF indicates how likely it is that some external feature of the sample, (e.g. the fiber axis) will be at some orientation relative to the crystallographic axes of the grains

 shows the distribution of crystallographic directions // to certain sample directions and can show some textures more clearly

(40)

Inverse pole figure

 In an inverse PF, the axes of the projection sphere are aligned with crystal directions.

 The directions plotted are the stereographic projection of crystal directions // to either the normal direction (ND), rolling direction (RD) or transverse direction (TD) in the sample.

 The inverse PF can help visualize certain types of textures.

Inverse pole figure

 Indicates the frequencies with which different crystal directions occur in a specified sample direction.

 Plays an important role in the calculation or estimation of physical properties of polyxtalline materials.

 Very informative for fiber samples as we are only interested in how the fiber axis is oriented.

 For sheet samples, it is less informative as we have to worry about the orientation of the sheet normal, the rolling direction and the transverse direction. This requires multiple inverse PFs.

(41)

Inverse pole figure of extruded Al rod

 Contours indicate how likely it is that the fiber axis will adopt a given orientation relative to the

crystallographic axes (directions) of a grain.

 IPF shows immediately the

crystallographic “direction” of the scatter.

Euler angle

(42)

Euler angles

TD(y)

RD(x) ND(z)

Rotation ϕ1about ND (z) axis

Rotation φ about new x axis bring ND to 001

Rotation ϕ2 about new z axis bring RD & TD to 100 & 010

Euler angles

TD(y)

RD(x) sample

crystal

ND(z)

Rotation ϕ1about ND (z) axis

Rotation φabout new x axis bring ND to 001

Rotation ϕ2about new z axis bring RD & TD to 100 & 010

 The orientation between 2 coordinate systems can be defined by a set of 3 successive rotations about specified axes.

 These rotation angles are called the Euler angles --- ϕ₁, φ, ϕ₂

(

Bunge’s notation).

(43)

Euler Angles, Animated

e

₁

=X

_sample

=RD e2=Y

_sample

=TD e

₃

=Z

_sample

=ND

e’

₁

e’

₂

φ

₁

Φ e”

₂

e”

₃

e’

₃

=

=e”

₁

y

_crystal

=e”’

₂

φ

₂

x

_crystal

=e”’

₁

z

_crystal

=e”’

₃

= [010]

[100]

[001]

Dr. Jongmin Baek

Orientation Distribution Function

(ODF)

(44)

Orientation distribution function (ODF)

sample

crystal

 Need to specify angles, ϕ

₁, φ, ϕ₂

between the crystallographic axes and the sample coordinate system.

 Probability function for texture

 A single PF does not completely describe the orientations of the grains in a sample.

 To fully specify grain orientation, we need to plot probability as a function of three angles.  This function or plot is ODF.

 The ODF is a function of three independent angular variables and gives the probability of finding the corresponding unit cell (lattice) orientation.

Orientation distribution function (ODF)

 Can be derived completely from two PFs for a cubic material.

 Once ODF is known, any PF can be calculated from it.

 Is often plotted as a series of sections.

ODF for cold rolled brass Sections are for constant ϕ

₂

ϕ

₁

φ

(45)

ODF Example (2D)

ODF

 ODF can give all the orientation information

 ODF does not give grain boundary information

 misorientation angle

 ODF together with EBSD can give all the orientation information + grain boundary information

 ODF, EBSD, grain size, grain shape can give complete microstructure

ODF Example (3D)

(46)

Electron Back Scattered Diffraction

(EBSD)

How is the signal generated & detected?

Each band in the pattern represents a crystal plane

(47)

EBSD is made of

Electron column focuses the

electron beam on the sample Sample is tilted using special holder or microscope stage

A special forward scatter electron detector is used to capture images of the sample

Microscope is used to select the point where the

measurement takes place

Pattern is formed on a phosphor screen

Phosphor screen is acquired on a low light Peltier cooled CCD camera Crystal orientation map

(48)

EBSD measurement

(49)

(50)

100CHAN PARK, MSE, SNU Spring-2019 Crystal Structure Analyses

(51)

(52)

Texture – XRD vs. EBSD

XRD EBSD

Featu res

Large penetrationdepth (few um) Spatial resolution 25um ~ 1mm

Small penetrationdepth (~20nm) – surface sensitive Spatial resolution tens of nm in FE-SEM

advan tages

Well-established technique

Relatively larger area scanned (< 10mm²) Large number of grains can be analysed in one experiment

Macroscopic samples can be examined

Direct calculation of ODF possible Superior spatial resolution (< tens of nm)

Texture measurement of microscopic area possible Can relate texture to microstructure

Can easily measure texture of multiphase materials

disad vanta ges

Calculation of ODF from PF is complex and can give erroneous information

Poor spatial resolution – unsuitable for microscopic samples and difficult to relate texture to microstructure

Requires relatively expensive SEM

May not work with heavily deformed materials Impractical with some samples (polymers, pharmaceuticals)

Need more sample prep

Less practical for texture measurements of large grained materials

(53)

EBSD vs. XRD

Misorientation angle “14” between grain 1 & grain 15

 does not make any difference in the current path

 is counted in XRD

 is not counted in EBSD 1°

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1° 1°

1°

7 ~ 8°  XRD 1°  EBSP

Texture analysis – overview 1

 Texture analysis - The determination of the preferred orientation of the crystallites in polycrystalline aggregates

 texture = preferred crystallographic orientation

 The preferred orientation is usually described in terms of pole figures

 A pole figure is scanned to measure the diffraction intensity of a given reflection (2- Theta is constant) at a large number of different angular orientations of the sample

 A contour map of the intensity is then plotted as a function of angular orientation of the specimen. The most common representation of the pole figures are stereographic projection

 The intensity of a given reflection (hkl) is proportional to the number of hkl planes in reflecting condition (Bragg’s law)

 Hence, the pole figure gives the probability of finding a given crystal-plane-normal as a function of the specimen orientation. If the crystallites in the sample have a

random orientation, the recorded intensity will be uniform

(54)

Texture analysis – overview 2

 The orientation of the unit cell can be used to describe crystallite directions

 The inverse pole figure gives the probability of finding a given specimen direction parallel to crystal (unit cell) directions

 By collecting data for several reflections and combining several pole figures, we can arrive at the complete orientation distribution function (ODF) of the crystallites within a single polycrystalline phase that makes up the material

 Considering a coordinate system defined in relation to the specimen, any orientation of the crystal lattice (unit cell) with respect to the specimen coordinate system may be defined by Euler rotation (three angular values) necessary to rotate the crystal coordinate system from a position coincident with the specimen coordinate system to a given position

Crystalline nature of materials TEXTURE

TEXTURE

Krawitz Chap 11 Hammond Chap 10 Cullity Chap 14 Dyson Ch 11

Klug & Alexander Chap 10

Crystalline nature of materials

 Many solid materials are composed of crystals joined together

 The individual grains can fit together closely to form the solid

Crystalline nature of materials - Grains

Crystalline nature of materials – CSLs

 Coincident site lattice boundaries (CSLs)

 A significant degree of order occurs at a CSL boundary, which leads to special properties

 3

 5

Crystalline nature of materials – properties

 If properties are equal in all directions, a material is termed

“isotropic”.

 If the properties tend to be greater or diminished in any direction, the material is termed “anisotropic”.

 Most materials are anisotropic.

 Anisotropy results from preferred orientation or texture.

isotropic vs. anisotropic

Anisotropic structure of wood

Crystal structure - anisotropic arrangement of atoms

Photoelastic anisotropy used to visualize strains and

stresses Structure and Anisotropy

Texture

 All orientations of crystallites possible

 1cc powder of 10um crystallites  10

particles

 1cc powder of 1um crystallites  10

particles

Texture

 Random powder – all crystallite orientations equally probable  flat pole figure

Loose powder

Metal wire

(100) random texture

(100) wire texture

 Crystallites oriented along wire axis - pole

figure peaked in center and at the rim

RD, TD, & ND

What is Texture?

Ks

K s

K c

K

specimen reference frame sample coordinate system K

crystal reference frame

crystal coordinate system

Orientation of Grains in Polycrystalline Solid

Texture

 In a polycrystalline body, the individual crystallites may have a random or non-random distribution of orientations.

 A body with a non-random distribution of orientation is said to be textured or to display preferred orientation.

 As materials properties are anisotropic (depend on the direction within a crystal), the presence of texture will alter the physical

Texture

Where is texture observed ?

Geology Biology Metals Ceramics Polymers

Rocks Teeth Alloys Oxides Polyethylene

Soils Bones Intermetallics Silicates Polypropylene

Ores Shells Nitrides Liquid Crystals

Ice Carbides

Salt

Natural Materials Man-made Materials

Why texture is important?

Why texture research is important ?

 Texture is responsible for anisotropy of various properties

 It allows to better understand various processes

How is Texture formed & measured?

 How is Texture formed ?

 How is Texture measured?

Deformation texture, Annealing texture

 Deformation texture

 Annealing texture (recrystallization texture)

Fiber texture, Rolling texture

A common direction parallel to the fiber or wire axis  [uvw]

Fiber texture

Defined by {hkl}<uvw>

{hkl} - planes // to sheet surface

<uvw> - direction // to rolling direction Rolling texture

Fiber texture

Sheet (rolling) texture

 In a specimen showing sheet texture, grains prefer to have a set of planes (hkl) parallel to the sheet surface and a direction [uvw]

 ₃

 ₅

K _s

K _c