Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Chemistry and Pharmacology
It is assumed that a crystal structure in P1 is fixed and that the 15 non-negative numbers R1, R2, R3, R4, R5; R12, R13, R14, R15, R23, R24, R25, R34, R35, R45 are also specified. The random variables (vectors) h, k, l, m, n are assumed to be uniformly and independently distributed in the regions of reciprocal space defined by |Eh| = R1, |Ek| = R2, |El| = R3, |Em| = R4, |En| = R5; (1) |Eh + k| = R12, |Eh + l| = R13, |Eh + m| = R14, |Eh + n| = R15, |Ek + l| = R23, |Ek + m| = R24, |Ek + n| = R25, |El + m| = R34, |El + n| = R35, |Em + n| = R45: (2) and h + k + l + m + n = 0. (3) Then the structure invariant φ = φh + φk + φl + φm + φn, as a function of the primitive random variables h, k, l, m, n, is itself a random variable, and its conditional probability distribution, given (1) and (2), is derived. The distribution leads to estimates for cos φ in terms of the 15 magnitudes (1) and (2).
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