Difference between revisions of "Twin index"
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| − | = | + | == Definition == |
A [[twinning|twin]] operation overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]). The reciprocal ''n'' of the fraction 1/''n'' of (quasi)restored nodes is called ''twin index'' | A [[twinning|twin]] operation overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]). The reciprocal ''n'' of the fraction 1/''n'' of (quasi)restored nodes is called ''twin index'' | ||
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where f depends on the [[direct lattice|lattice type]] and on the parities of ''X'', ''h'', ''k'', ''l'', ''u'', ''v'' and ''w'', as in the following table | where f depends on the [[direct lattice|lattice type]] and on the parities of ''X'', ''h'', ''k'', ''l'', ''u'', ''v'' and ''w'', as in the following table | ||
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<table border="1" cellspacing="2" cellpadding="2"> | <table border="1" cellspacing="2" cellpadding="2"> | ||
<tr> | <tr> | ||
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</table> | </table> | ||
| + | </center> | ||
| + | == References == | ||
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*Chapter 3.1.9 in ''International Tables for X-Ray Crystallography'' (1959) | *Chapter 3.1.9 in ''International Tables for X-Ray Crystallography'' (1959) | ||
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==History== | ==History== | ||
| + | |||
*Friedel, G. (1904). Étude sur les groupements cristallins. Extrait du Bullettin de la Société de l'Industrie minérale, Quatrième série, Tomes III e IV. Saint-Étienne, Société de l'imprimerie Thèolier J. Thomas et C., 485 pp. | *Friedel, G. (1904). Étude sur les groupements cristallins. Extrait du Bullettin de la Société de l'Industrie minérale, Quatrième série, Tomes III e IV. Saint-Étienne, Société de l'imprimerie Thèolier J. Thomas et C., 485 pp. | ||
*Friedel, G. (1926). Leçons de Cristallographie. Berger-Levrault, Nancy, Paris, Strasbourg, XIX+602 pp. | *Friedel, G. (1926). Leçons de Cristallographie. Berger-Levrault, Nancy, Paris, Strasbourg, XIX+602 pp. | ||
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| + | == See also == | ||
| + | |||
| + | Chapter 1.3 of ''International Tables of Crystallography, Volume C''<br> | ||
| + | Chapter 3.3 of ''International Tables of Crystallography, Volume D''<br> | ||
[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] | ||
Revision as of 16:41, 26 April 2006
Indice de macle (Fr). Indice di geminazione (It)
Contents
Definition
A twin operation overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent (twinning (effects of)). The reciprocal n of the fraction 1/n of (quasi)restored nodes is called twin index
Let (hkl) be the twin plane and [uvw] the lattice direction (quasi)-normal to it. alternatively, let [uvw] be the twin axis and (hkl) the lattice plane (quasi)-normal to it. The twin index is then:
n = X/f, X = |uh+vk+wl|
where f depends on the lattice type and on the parities of X, h, k, l, u, v and w, as in the following table
| Lattice type | condition on hkl | condition on uvw | condition on X | n |
|---|---|---|---|---|
| P | none | none | X odd | n = X |
| X even | n = X/2 | |||
| C | h+k odd | none | none | n = X |
| h+k even | u+v and w not both even | X odd | n = X | |
| X even | n = X/2 | |||
| u+v and w both even | X/2 odd | n = X/2 | ||
| X/2 even | n = X/4 | |||
| B | h+l odd | none | none | n = X |
| h+l even | u+w and v not both even | X odd | n = X | |
| X even | n = X/2 | |||
| u+w and v both even | X/2 odd | n = X/2 | ||
| X/2 even | n = X/4 | |||
| A | k+l odd | none | none | n = X |
| k+l even | v+w and u not both even | X odd | n = X | |
| X even | n = X/2 | |||
| v+w and u both even | X/2 odd | n = X/2 | ||
| X/2 even | n = X/4 | |||
| I | h+k+l odd | none | none | n = X |
| h+k+l even | u, v and w not all odd | X odd | n = X | |
| X even | n = X/2 | |||
| u, v and w all odd | X/2 odd | n = X/2 | ||
| X/2 even | n = X/4 | |||
| F | none | u+v+w odd | none | n = X | h, k, l not all odd | u+v+w even | X odd | n = X |
| X even | n = X/2 | h, k, l all odd | u+v+w even | X/2 odd | n = X/2 |
| X/2 even | n = X/4 |
</center>
References
- Chapter 3.1.9 in International Tables for X-Ray Crystallography (1959)
History
- Friedel, G. (1904). Étude sur les groupements cristallins. Extrait du Bullettin de la Société de l'Industrie minérale, Quatrième série, Tomes III e IV. Saint-Étienne, Société de l'imprimerie Thèolier J. Thomas et C., 485 pp.
- Friedel, G. (1926). Leçons de Cristallographie. Berger-Levrault, Nancy, Paris, Strasbourg, XIX+602 pp.
See also
Chapter 1.3 of International Tables of Crystallography, Volume C
Chapter 3.3 of International Tables of Crystallography, Volume D