ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
A crystal structure in P{\bar 1} consisting of N identical atoms in the whole unit cell is fixed, and the four non-negative numbers R1, R2, R12/2, R_{1{\bar 2}/2} are also specified. The random variables (vectors) h, k are assumed to be uniformaly and independently distributed in the regions of reciprocal space defined by |Eh| = R1, |Ek| = R2, |E(h + k)/2| = R12/2, |Eh - k/2| = R_{1{\bar 2}/2}, (1), and h + k ≡ 0 (mod ωs), (2), where ωs, the seminvariant modulus for P{\bar 1}, is the three-dimensional vector ωs = (2,2,2), (3). Then the components of each of h ± k)/2 are integers. In view of (2) and (3) the linear combination of the phases φ = φh + φk, (4), is a structure seminvariant which, as a function of the primitive random variables h, k, is itself a random variable. Two approximations Q±, P±, of respective orders 1/N, 1/N2, to the conditional probability distribution of φ, given the four magnitudes (1), are derived and compared. In favorable cases, i.e. when the variance of the distribution happens to be small, they yield a reliable estimate (0 or π) for the structure seminvariant φ.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0567739476012333
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