Homometric Structures

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IN connexion with a recent discussion1 of the question of the uniqueness of an X-ray crystal analysis, Prof. Linus Pauling has directed my attention to a curious property of the point position2 Th7 - Ia3 - 24(d). Pauling and Shappell3 have shown that this point position, which involves a single parameter u, has a structure factor which is even in u, while parameter values + u and - u correspond to the structures which are not identical nor are they mirror-images of one another. An examination of this point position shows that these structures give identical sets of interatomic distances.

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  1. 1

    Patterson, A. L., Phys. Rev., 55, 682 (1939).

  2. 2

    cf. "Internationale Tabellen zur Bestimmung von Kristallstrukturen" 1, 322 (Berlin, etc. 1935); or R. W. G. Wyckoff, "Analytical Expression of the Results of the Theory of Space Groups" 127 (Washington 1930).

  3. 3

    Pauling, L., and Shappell, M. D., Z. Krist., 75, 128 (1930).

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PATTERSON, A. Homometric Structures. Nature 143, 939–940 (1939) doi:10.1038/143939b0

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