Twin index
From Online Dictionary of Crystallography
Indice de macle (Fr). Indice di geminazione (It)
Twin index
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
</tr>
</tr>
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 |
References
Chapter 3.3 of International Tables of Crystallography, Volume D