Transmission measurements can have a big problem due to
absorption
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Thin film – texture; YBCO/STO
Intensity
Omega (deg.)
14 15 16 17 18 19
0.4o
Intensity
0 90 180 270 360
Phi (deg.) fwhm = 1o
Intensity
10 20 30 40 50 60
2 theta (degrees)
002 003
004 005
006
007 STO 001 STO 002
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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
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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
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Inverse pole
figure
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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
70 CHAN PARK, MSE, SNU Spring-2019 Crystal Structure Analyses
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
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Pole Figure & Inverse Pole Figure
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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.
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Inverse pole figure
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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
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Inverse pole figure
The RD and TD inverse pole figures are obtained in a similar way
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Inverse pole figure
Negligible fraction of non-<111> fiber
Sample direction 3, or ND Strong <111>//ND Fiber Texture
Carnegie Mellon Univ.
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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
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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
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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.
80 CHAN PARK, MSE, SNU Spring-2019 Crystal Structure Analyses
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.
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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.
Cullity 3rdEd. Page 428
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Euler angle
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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
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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).85 CHAN PARK, MSE, SNU Spring-2019 Crystal Structure Analyses