EMlistTC
Marc DeGraef edited this page Jan 14, 2019
·
1 revision
This program takes a crystal structure file and a texture component as input and lists all the equivalent texture components along with their various rotation representations.
The example below lists the equivalent texture components for the alpha-titanium crystal structure and the {1 0 -1 0}<1 1 -2 0> texture component. Note that there are 12 equivalent texture component symbols, and that TC 10 in the list corresponds to the rotation that fall inside the fundamental zone for this crystal system.
...
Enter xtal file name : Ti-alpha.xtal
Enter the texture component symbol {hk.l}<uvtw>
(This structure uses the hexagonal indexing system!)
Enter the three-index planar indices {hkl} 1,0,0
Enter the four-index direction indices <uvtw> 1,1,-2,0
---> in three index notation:[ 3 3 0]
Determining unique texture components
Multiplicity of {hkl} : 6
Multiplicity of <uvw> : 6
There are 12 equivalent texture components.
-------
TC 1 --> ( 1 0 . 0) [ 1 -2 1 0]
Euler angles : 0.0000000 90.0000000 60.0000000
Axis angle pair [n; angle] : -0.7745967 0.4472136 -0.4472136 ; 104.4775122
Rodrigues vector : -1.0000000 0.5773503 -0.5773503
Homochoric representation : -0.6680216 0.3856824 -0.3856824
Cubochoric representation : -0.6951007 0.5076187 -0.5076187
Quaternion : 0.6123724 -0.6123724 0.3535534 -0.3535534
Stereographic : -0.3798 0.2193 -0.2193
/ 0.5000 0.0000 0.8660 \
Orientation Matrix : | -0.8660 0.0000 0.5000 |
\ 0.0000 -1.0000 0.0000 /
-------
TC 2 --> ( 1 0 . 0) [ -1 2 -1 0]
Euler angles : 180.0000000 90.0000000 60.0000000
Axis angle pair [n; angle] : 0.3779645 0.6546537 0.6546537 ; 138.5903779
Rodrigues vector : 1.0000000 1.7320508 1.7320508
Homochoric representation : 0.4144098 0.7177788 0.7177788
Cubochoric representation : 0.5476194 0.8837143 0.8837143
Quaternion : 0.3535534 0.3535534 0.6123724 0.6123724
Stereographic : 0.2612 0.4524 0.4524
/ -0.5000 0.0000 0.8660 \
Orientation Matrix : | 0.8660 0.0000 0.5000 |
\ 0.0000 1.0000 0.0000 /
-------
TC 3 --> ( -1 1 . 0) [ 1 1 -2 0]
Euler angles : 0.0000000 90.0000000 300.0000000
Axis angle pair [n; angle] : -0.7745967 -0.4472136 0.4472136 ; 104.4775122
Rodrigues vector : -1.0000000 -0.5773503 0.5773503
Homochoric representation : -0.6680216 -0.3856824 0.3856824
Cubochoric representation : -0.6951007 -0.5076187 0.5076187
Quaternion : 0.6123724 -0.6123724 -0.3535534 0.3535534
Stereographic : -0.3798 -0.2193 0.2193
/ 0.5000 0.0000 -0.8660 \
Orientation Matrix : | 0.8660 0.0000 0.5000 |
\ 0.0000 -1.0000 0.0000 /
-------
TC 4 --> ( -1 1 . 0) [ -1 -1 2 0]
Euler angles : 180.0000000 90.0000000 300.0000000
Axis angle pair [n; angle] : 0.3779645 -0.6546537 -0.6546537 ; 138.5903779
Rodrigues vector : 1.0000000 -1.7320508 -1.7320508
Homochoric representation : 0.4144098 -0.7177788 -0.7177788
Cubochoric representation : 0.5476194 -0.8837143 -0.8837143
Quaternion : 0.3535534 0.3535534 -0.6123724 -0.6123724
Stereographic : 0.2612 -0.4524 -0.4524
/ -0.5000 0.0000 -0.8660 \
Orientation Matrix : | -0.8660 0.0000 0.5000 |
\ 0.0000 1.0000 0.0000 /
-------
TC 5 --> ( -1 0 . 0) [ 1 -2 1 0]
Euler angles : 180.0000000 90.0000000 240.0000000
Axis angle pair [n; angle] : 0.7745967 -0.4472136 -0.4472136 ; 104.4775122
Rodrigues vector : 1.0000000 -0.5773503 -0.5773503
Homochoric representation : 0.6680216 -0.3856824 -0.3856824
Cubochoric representation : 0.6951007 -0.5076187 -0.5076187
Quaternion : 0.6123724 0.6123724 -0.3535534 -0.3535534
Stereographic : 0.3798 -0.2193 -0.2193
/ 0.5000 0.0000 -0.8660 \
Orientation Matrix : | -0.8660 0.0000 -0.5000 |
\ 0.0000 1.0000 0.0000 /
-------
TC 6 --> ( -1 0 . 0) [ -1 2 -1 0]
Euler angles : 0.0000000 90.0000000 240.0000000
Axis angle pair [n; angle] : -0.3779645 -0.6546537 0.6546537 ; 138.5903779
Rodrigues vector : -1.0000000 -1.7320508 1.7320508
Homochoric representation : -0.4144098 -0.7177788 0.7177788
Cubochoric representation : -0.5476194 -0.8837143 0.8837143
Quaternion : 0.3535534 -0.3535534 -0.6123724 0.6123724
Stereographic : -0.2612 -0.4524 0.4524
/ -0.5000 0.0000 -0.8660 \
Orientation Matrix : | 0.8660 0.0000 -0.5000 |
\ 0.0000 -1.0000 0.0000 /
-------
TC 7 --> ( 0 1 . 0) [ -2 1 1 0]
Euler angles : 180.0000000 90.0000000 0.0000000
Axis angle pair [n; angle] : 0.0000000 -0.7071068 -0.7071068 ; 180.0000000
Rodrigues vector : 0.0000000 -0.7071068 -0.7071068 Infinity
Homochoric representation : 0.0000000 -0.9409258 -0.9409258
Cubochoric representation : 0.0000000 -1.0725147 -1.0725147
Quaternion : 0.0000000 0.0000000 -0.7071068 -0.7071068
Stereographic : 0.0000 -0.7071 -0.7071
/ -1.0000 0.0000 0.0000 \
Orientation Matrix : | 0.0000 0.0000 1.0000 |
\ 0.0000 1.0000 0.0000 /
-------
TC 8 --> ( 0 1 . 0) [ 2 -1 -1 0]
Euler angles : 0.0000000 90.0000000 0.0000000
Axis angle pair [n; angle] : -1.0000000 0.0000000 0.0000000 ; 90.0000000
Rodrigues vector : -1.0000000 0.0000000 0.0000000
Homochoric representation : -0.7536693 0.0000000 0.0000000
Cubochoric representation : -0.6074544 0.0000000 0.0000000
Quaternion : 0.7071068 -0.7071068 0.0000000 0.0000000
Stereographic : -0.4142 0.0000 0.0000
/ 1.0000 0.0000 0.0000 \
Orientation Matrix : | 0.0000 0.0000 1.0000 |
\ 0.0000 -1.0000 0.0000 /
-------
TC 9 --> ( 0 -1 . 0) [ -2 1 1 0]
Euler angles : 0.0000000 90.0000000 180.0000000
Axis angle pair [n; angle] : 0.0000000 0.7071068 -0.7071068 ; 180.0000000
Rodrigues vector : 0.0000000 0.7071068 -0.7071068 Infinity
Homochoric representation : 0.0000000 0.9409258 -0.9409258
Cubochoric representation : 0.0000000 1.0725147 -1.0725147
Quaternion : 0.0000000 0.0000000 -0.7071068 0.7071068
Stereographic : 0.0000 -0.7071 0.7071
/ -1.0000 0.0000 0.0000 \
Orientation Matrix : | 0.0000 0.0000 -1.0000 |
\ 0.0000 -1.0000 0.0000 /
-------
TC 10 --> ( 0 -1 . 0) [ 2 -1 -1 0]
Euler angles : 180.0000000 90.0000000 180.0000000
Axis angle pair [n; angle] : 1.0000000 0.0000000 0.0000000 ; 90.0000000
Rodrigues vector : 1.0000000 0.0000000 0.0000000
Homochoric representation : 0.7536693 0.0000000 0.0000000
Cubochoric representation : 0.6074544 0.0000000 0.0000000
Quaternion : 0.7071068 0.7071068 0.0000000 0.0000000
Stereographic : 0.4142 0.0000 0.0000
/ 1.0000 0.0000 0.0000 \
Orientation Matrix : | 0.0000 0.0000 -1.0000 |
\ 0.0000 1.0000 0.0000 /
---> THIS ROTATION LIES INSIDE THE FUNDAMENTAL ZONE.
-------
TC 11 --> ( 1 -1 . 0) [ 1 1 -2 0]
Euler angles : 180.0000000 90.0000000 120.0000000
Axis angle pair [n; angle] : 0.7745967 0.4472136 0.4472136 ; 104.4775122
Rodrigues vector : 1.0000000 0.5773503 0.5773503
Homochoric representation : 0.6680216 0.3856824 0.3856824
Cubochoric representation : 0.6951007 0.5076187 0.5076187
Quaternion : 0.6123724 0.6123724 0.3535534 0.3535534
Stereographic : 0.3798 0.2193 0.2193
/ 0.5000 0.0000 0.8660 \
Orientation Matrix : | 0.8660 0.0000 -0.5000 |
\ 0.0000 1.0000 0.0000 /
-------
TC 12 --> ( 1 -1 . 0) [ -1 -1 2 0]
Euler angles : 0.0000000 90.0000000 120.0000000
Axis angle pair [n; angle] : -0.3779645 0.6546537 -0.6546537 ; 138.5903779
Rodrigues vector : -1.0000000 1.7320508 -1.7320508
Homochoric representation : -0.4144098 0.7177788 -0.7177788
Cubochoric representation : -0.5476194 0.8837143 -0.8837143
Quaternion : 0.3535534 -0.3535534 0.6123724 -0.6123724
Stereographic : -0.2612 0.4524 -0.4524
/ -0.5000 0.0000 0.8660 \
Orientation Matrix : | -0.8660 0.0000 -0.5000 |
\ 0.0000 -1.0000 0.0000 /
Wiki pages are maintained by M. De Graef; they are part of the EMsoft package and fall under the same copyright (BSD2).
Information for Users
SEM Modalities
- Monte Carlo Simulations- EBSD Master Pattern Simulations
- EBSD Overlap Master Patterns
- EBSD Pattern Simulations
- EBSD Dictionary Indexing
- EBSD Spherical Indexing
- EBSD Reflector Ranking
- EBSD HREBSD
- ECP Master Pattern Simulations
- ECP Pattern Simulations
- TKD Master Pattern Simulations
- TKD Pattern Simulations
- ECCI Defect Image Simulations
TEM Modalities
- HH4- PED
- CBED Pattern Simulations
- STEM-DCI Image Simulations
- EMIntegrateSTEM utility
Utility Programs
- EMConvertOrientations- EMDisorientations
- EMHOLZ
- EMKikuchiMap
- EMOpenCLinfo
- EMZAgeom
- EMcuboMK
- EMdpextract
- EMdpmerge
- EMdrawcell
- EMeqvPS
- EMeqvrot
- EMfamily
- EMGBO
- EMGBOdm
- EMgetEulers
- EMgetOSM
- EMlatgeom
- EMlistSG
- EMlistTC
- EMmkxtal
- EMorbit
- EMorient
- EMqg
- EMsampleRFZ
- EMshowxtal
- EMsoftSlackTest
- EMsoftinit
- EMstar
- EMstereo
- EMxtalExtract
- EMxtalinfo
- EMzap
Complete Examples
- Crystal Data Entry Example
- EBSD Example
- ECP Example
- TKD Example
- ECCI Example
- CBED Example
- Dictionary Indexing Example
- DItutorial
Information for Developers