István Orosz

Abstract

In his graphic art, István Orosz (1951–) often reaches out to science-related topics. He has prepared illustrations for several of our books and designed the cover for one of them. This book was about the interconnection of symmetry and scientific discoveries. Each chapter carried the name of a famous scientist and Orosz prepared the chapter opening portraits. One of them, “Complementary Kitaigorodsky” is shown above. Aleksandr I. Kitaigorodsky (1914–1985) announced his research program in the early 1940s. He addressed himself to determining the most advantageous symmetry conditions in the arrangement of molecules in crystals. The far-reaching goal was to predict the crystal structures of any newly synthesized compound. There was no theory helping researchers to make such predictions and Kitaigorodsky devised an empirical route to answer this question. He carved out a wooden model of arbitrary shape and used many such identical models for finding their most economical arrangement in three-dimensional space. He found that the best arrangement was in which the protrusion of one model fit the cavity of another—and that was a complementary way of filling the available space. Such an arrangement would not involve mirror symmetry between two models, that is, between two molecules. When there is mirror symmetry between two molecules, the cavities of the two molecules match up and so do their protrusions. Such an arrangement would not result in economical utilization of the available space. Kitaigorodsky’s conclusion was that crystal structures with mirror symmetry between its molecules should be rare, whereas crystal structures in which the arrangement of molecules would be complementary (characterized by rotational symmetry) should be frequent. On the basis of painstaking examination of all possible 230 symmetry possibilities, Kitaigorodsky set up a list of his predicted frequency occurrences starting with the highest probability and progressing toward the least probable. He did this when there were yet only very few known crystal structures. When decades later there were hundreds of thousands known crystal structures, they proved Kitaigorodsky’s predictions correct. The complementary arrangement of the molecules in crystals is indeed a fundamental characteristic of their structures.

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