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ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-4/58/b/iii/solution

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Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 4 / 58 / b / iii / Solution by

Codex  0 2026-10-20

The third term is

2 F (11) cos [2 π (x + y)]

. To reinforce a maximum at

(x_{0}, y_{0})

from the preceding table, its sign should be

S (11) = (- 1)^{2 x_{0} + 2 y_{0}} = S (10) S (01) .

(1)

Hence the direct-methods triplet relationship is

S (10) S (01) S (11) ≃ + 1

for the strong reflections under consideration. This maximizes constructive density at shared atomic positions. For weak or competing reflections the relation is probabilistic rather than an unconditional algebraic theorem.

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