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Crystallographic quantitative texture analysis (QTA)
International Tables for Crystallography (2019). Vol. H, Section 5.3.2, pp. 555-567 [ doi:10.1107/97809553602060000968 ]
... is freeware. Two other programs, Material Analysis Using Diffraction (MAUD; Lutterotti et al., 1999 ) and the General Structure Analysis System (GSAS ... lambda] cannot be infinite and is limited to a value L, the maximum degree of series expansion, which fixes the angular ... crystal reference frame. The number of coefficients and the extension L to which the series in (5.3.14 ) has to be ...
Typical OD components
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.7.5, p. 566 [ doi:10.1107/97809553602060000968 ]
Typical OD components 5.3.2.7.5. Typical OD components Each of the previous texture types has corresponding OD descriptions as components of orientations, which can be represented, for example, using a Cartesian coordinate system for H space (Fig. 5.3.15 ) and isodensity surfaces for simplicity. An individual point g in this space represents an ...
Three-dimensional textures
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.7.4, pp. 565-566 [ doi:10.1107/97809553602060000968 ]
Three-dimensional textures 5.3.2.7.4. Three-dimensional textures Samples composed of crystallites which have had no opportunity to orient themselves in KA (zero degrees of freedom) will exhibit point poles for all of their pole figures. The pole figures will be similar to those of a single crystal. We call this a ...
Fibre textures
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.7.3, p. 565 [ doi:10.1107/97809553602060000968 ]
Fibre textures 5.3.2.7.3. Fibre textures If the crystallites lose another degree of freedom in their orientation ([infinity], [infinity]m, [infinity]/m, [infinity]2 or [infinity]/mm Curie groups), they are forced to align one of their <hkl>* directions with one direction y of KA, with all other directions being at random ...
Planar textures
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.7.2, p. 565 [ doi:10.1107/97809553602060000968 ]
Planar textures 5.3.2.7.2. Planar textures This kind of texture is exhibited by samples in which the crystallites have two degrees of freedom to orient and belong to the [infinity][infinity] Curie group. One specific <hkl>* direction family is allowed to rotate around one sample axis. The <hkl>* directions are then located ...
Random texture
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.7.1, pp. 564-565 [ doi:10.1107/97809553602060000968 ]
Random texture 5.3.2.7.1. Random texture A random texture (or random sample) belongs to the [infinity][infinity]/m Curie (limit) group and is simply a name given to the texture exhibited by a sample that has no preferred orientation. Its crystallites are randomly oriented. The same number of grains are diffracting at ...
Texture types
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.7, pp. 564-566 [ doi:10.1107/97809553602060000968 ]
Texture types 5.3.2.7. Texture types 5.3.2.7.1. Random texture | | A random texture (or random sample) belongs to the [infinity][infinity]/m Curie (limit) group and is simply a name given to the texture exhibited by a sample that has no preferred orientation. Its crystallites are randomly oriented. The same number of grains ...
Correlation between F2 and S
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.6.4, p. 564 [ doi:10.1107/97809553602060000968 ]
Correlation between F2 and S 5.3.2.6.4. Correlation between F2 and S From the definitions of F2 and S, their variations are restricted to the (1, [infinity]) and (0, -[infinity]) domains, respectively. Entropy and texture index are correlated, but it is not possible to obtain a general analytical expression for this correlation ...
Pole-figure and ODF strengths
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.6.3, p. 564 [ doi:10.1107/97809553602060000968 ]
Pole-figure and ODF strengths 5.3.2.6.3. Pole-figure and ODF strengths Both OD and pole-figure indexes are expressed in units that are not homogeneous with distribution density units (m.r.d.). To help with comparison and interpretation, it is more convenient to compare the square roots of these values, i.e. the ...
Texture entropy
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.6.2, p. 564 [ doi:10.1107/97809553602060000968 ]
Texture entropy 5.3.2.6.2. Texture entropy The second overall texture strength parameter is a measure of the texture disorder, evaluated by the calculation of the entropy (Shannon, 1948 ), References Shannon, C. E. (1948). A mathematical theory of communication. Bell Syst. Tech. J. 27, 379-423.GoogleScholar International Tables for Crystallography (2019). ...
International Tables for Crystallography (2019). Vol. H, Section 5.3.2, pp. 555-567 [ doi:10.1107/97809553602060000968 ]
... is freeware. Two other programs, Material Analysis Using Diffraction (MAUD; Lutterotti et al., 1999 ) and the General Structure Analysis System (GSAS ... lambda] cannot be infinite and is limited to a value L, the maximum degree of series expansion, which fixes the angular ... crystal reference frame. The number of coefficients and the extension L to which the series in (5.3.14 ) has to be ...
Typical OD components
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.7.5, p. 566 [ doi:10.1107/97809553602060000968 ]
Typical OD components 5.3.2.7.5. Typical OD components Each of the previous texture types has corresponding OD descriptions as components of orientations, which can be represented, for example, using a Cartesian coordinate system for H space (Fig. 5.3.15 ) and isodensity surfaces for simplicity. An individual point g in this space represents an ...
Three-dimensional textures
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.7.4, pp. 565-566 [ doi:10.1107/97809553602060000968 ]
Three-dimensional textures 5.3.2.7.4. Three-dimensional textures Samples composed of crystallites which have had no opportunity to orient themselves in KA (zero degrees of freedom) will exhibit point poles for all of their pole figures. The pole figures will be similar to those of a single crystal. We call this a ...
Fibre textures
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.7.3, p. 565 [ doi:10.1107/97809553602060000968 ]
Fibre textures 5.3.2.7.3. Fibre textures If the crystallites lose another degree of freedom in their orientation ([infinity], [infinity]m, [infinity]/m, [infinity]2 or [infinity]/mm Curie groups), they are forced to align one of their <hkl>* directions with one direction y of KA, with all other directions being at random ...
Planar textures
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.7.2, p. 565 [ doi:10.1107/97809553602060000968 ]
Planar textures 5.3.2.7.2. Planar textures This kind of texture is exhibited by samples in which the crystallites have two degrees of freedom to orient and belong to the [infinity][infinity] Curie group. One specific <hkl>* direction family is allowed to rotate around one sample axis. The <hkl>* directions are then located ...
Random texture
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.7.1, pp. 564-565 [ doi:10.1107/97809553602060000968 ]
Random texture 5.3.2.7.1. Random texture A random texture (or random sample) belongs to the [infinity][infinity]/m Curie (limit) group and is simply a name given to the texture exhibited by a sample that has no preferred orientation. Its crystallites are randomly oriented. The same number of grains are diffracting at ...
Texture types
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.7, pp. 564-566 [ doi:10.1107/97809553602060000968 ]
Texture types 5.3.2.7. Texture types 5.3.2.7.1. Random texture | | A random texture (or random sample) belongs to the [infinity][infinity]/m Curie (limit) group and is simply a name given to the texture exhibited by a sample that has no preferred orientation. Its crystallites are randomly oriented. The same number of grains ...
Correlation between F2 and S
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.6.4, p. 564 [ doi:10.1107/97809553602060000968 ]
Correlation between F2 and S 5.3.2.6.4. Correlation between F2 and S From the definitions of F2 and S, their variations are restricted to the (1, [infinity]) and (0, -[infinity]) domains, respectively. Entropy and texture index are correlated, but it is not possible to obtain a general analytical expression for this correlation ...
Pole-figure and ODF strengths
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.6.3, p. 564 [ doi:10.1107/97809553602060000968 ]
Pole-figure and ODF strengths 5.3.2.6.3. Pole-figure and ODF strengths Both OD and pole-figure indexes are expressed in units that are not homogeneous with distribution density units (m.r.d.). To help with comparison and interpretation, it is more convenient to compare the square roots of these values, i.e. the ...
Texture entropy
International Tables for Crystallography (2019). Vol. H, Section 5.3.2.6.2, p. 564 [ doi:10.1107/97809553602060000968 ]
Texture entropy 5.3.2.6.2. Texture entropy The second overall texture strength parameter is a measure of the texture disorder, evaluated by the calculation of the entropy (Shannon, 1948 ), References Shannon, C. E. (1948). A mathematical theory of communication. Bell Syst. Tech. J. 27, 379-423.GoogleScholar International Tables for Crystallography (2019). ...
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