Inversion of Pole Figures for Materials Having Cubic Crystal Symmetry

1966 ◽  
Vol 37 (5) ◽  
pp. 2069-2072 ◽  
Author(s):  
Ryong‐Joon Roe
Keyword(s):  
Crystal Symmetry ◽  
Cubic Crystal ◽  
Pole Figures

scholarly journals ODF Calculation by Series Expansion from Incompletely Measured Pole Figures Using the Positivity Condition Part I—Cubic Crystal Symmetry

1987 ◽  
Vol 7 (3) ◽  
pp. 171-185 ◽  
Author(s):  
M. Dahms ◽  
H. J. Bunge
Keyword(s):  
Series Expansion ◽  
Iterative Procedure ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Crystal Symmetry ◽  
Cubic Crystal ◽  
Positivity Condition ◽  
Pole Figures ◽  
Orientation Distribution Functions

The calculation of orientation distribution functions (ODF) from incomplete pole figures can be carried out by an iterative procedure taking into account the positivity condition for all pole figures. This method strongly reduces instabilities which may occasionally occur in other methods.

scholarly journals Texture Analysis From Incomplete Pole Figures in Low Symmetry Cases

1987 ◽  
Vol 7 (2) ◽  
pp. 115-129 ◽  
Author(s):  
F. Wagner ◽  
M. Humbert
Keyword(s):  
Computer Program ◽  
Texture Analysis ◽  
Crystal Symmetry ◽  
Harmonic Method ◽  
Pole Figures ◽  
Low Symmetry

From a classification of crystal symmetries involved in texture analysis we define a set of (low) crystal symmetries that can be similarly managed in the same computer program, using the harmonic method. A way of calculating the texture from incomplete pole figures is then proposed. Results are reported for two examples with hexagonal and trigonal crystal symmetry, respectively, and advantages and limitations of such texture analyses are discussed.

A square-shaped complex with an electron-acceptor ligand: unique cubic crystal symmetry and similarity to inorganic mineral katoite

CrystEngComm ◽  
2021 ◽  
Author(s):  
Kentaro Aoki ◽  
Kazuya Otsubo ◽  
Hiroshi Kitagawa
Keyword(s):  
Molecular Recognition ◽  
Electron Acceptor ◽  
Macrocyclic Complex ◽  
Macrocyclic Complexes ◽  
Crystal Symmetry ◽  
Cubic Crystal ◽  
Unique Structure ◽  
Inorganic Mineral ◽  
Significant Attention ◽  
Recognition Property

Square macrocyclic complexes have attracted significant attention due to their unique structure and molecular recognition property. Here we report a square macrocyclic complex using an electron-acceptor ligand N,N’-di(4-pyridyl)-1,4,5,8-naphthalenediimide (dpndi), [Pt(en)(dpndi)]4(SO4)4·20H2O...

Non-cubic crystal symmetry of CaSiO3 perovskite up to 18 GPa and 1600 K

2009 ◽  
Vol 282 (1-4) ◽  
pp. 268-274 ◽  
Author(s):  
Takeyuki Uchida ◽  
Yanbin Wang ◽  
Norimasa Nishiyama ◽  
Ken-ichi Funakoshi ◽  
Hiroshi Kaneko ◽  
...  
Keyword(s):  
Crystal Symmetry ◽  
Cubic Crystal ◽  
Casio3 Perovskite

scholarly journals Generalized Spherical Harmonics for Cubic-Triclinic Symmetry

1997 ◽  
Vol 29 (3-4) ◽  
pp. 235-239
Author(s):  
Peter R. Morris
Keyword(s):  
Spherical Harmonics ◽  
Orientation Distribution ◽  
Explicit Representation ◽  
Crystal Symmetry ◽  
Crystallite Orientation ◽  
Cubic Crystal ◽  
Triclinic Symmetry ◽  
Generalized Spherical Harmonics

An explicit representation is suggested for orthogonal generalized spherical harmonics with cubic-crystal and triclinic-sample symmetries. The representation employs sums and differences of orthogonal generalized spherical harmonics with cubic-crystal symmetry, previously described by Bunge for orthorhombic (or higher) sample symmetry, and is illustrated, for T∴iμυ, i = 4, 9, μ = 1, υ = 1 to 5. This representation facilitates crystallite orientation distribution (COD) analysis (aka ODF analysis) for these symmetries, using the Bunge formalism.

scholarly journals Generalized Spherical Harmonics for Cubic-Triclinic Symmetry

1995 ◽  
Vol 24 (4) ◽  
pp. 221-224
Author(s):  
Peter R. Morris
Keyword(s):  
Spherical Harmonics ◽  
Orientation Distribution ◽  
Explicit Representation ◽  
Crystal Symmetry ◽  
Crystallite Orientation ◽  
Cubic Crystal ◽  
Triclinic Symmetry ◽  
Generalized Spherical Harmonics

An explicit representation is suggested for orthogonal generalized spherical harmonics with cubic-crystal and triclinic-sample symmetries. The representation employs sums and differences of orthogonal generalized spherical harmonics with cubic-crystal symmetry, previously described by Bunge for orthorhombic (or higher) sample symmetry, and is illustrated, for T:.ιμν, ι=4, 9, μ=1, ν=1 to 5. This representation facilitates crystallite orientation distribution (COD)analysis (aka ODF analysis) for these symmetries, using the Bunge formalism.

scholarly journals An Improvement of Vector Method by Allocation of Intensities Based on the Crystallographic Symmetry

1989 ◽  
Vol 10 (2) ◽  
pp. 101-116 ◽  
Author(s):  
R. Shimizu ◽  
K. Ohta ◽  
J. Harase
Keyword(s):  
Texture Analysis ◽  
Crystal Symmetry ◽  
Residual Vector ◽  
Reflection And Transmission ◽  
Vector Method ◽  
X Ray ◽  
Textural Component ◽  
Pole Figures ◽  
Crystallographic Symmetry

An investigation has been carried out utilizing model and experimental pole figures made by X-ray technique in order to examine the use of the vector method as a means of the texture analysis. The main findings are as follows:• From crystal symmetry considerations positions and magnitudes of peaks along the ζ angle can be predicted. There are discrepancies in these intensity peaks and in some cases the peaks are missing altogether.• This problem was solved by the allocation of intensities such that equal intensities are obtained at the crystallographic symmetry positions.• Even a slightly mismatched combination of the reflection and transmission pole figures caused an increase in residual vector (R) resulting in the failure of the analysis for the minor textural component.

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