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18 19 the crystAlline World the stronghold of symmetrical order Of all natural objects, wellformed crystals make the closest approximation to the mathematical purity of the regular solids they can indeed assume some of these shapes, but not all. However, the fascinating, pristine beauty of specimen crystals is simply an externalisation of an even more impressive internal structure. In fact the crystalline state, with its constituent molecules lined up in tens, or even hundreds of millions, of obedient, identical molecules, is a realm of almost inconceivable orderliness. Crystals of different substances adopt a wide range of different and characteristic forms, but their regularities are based on the unit cell arrangements of one or other of just fourteen lattice structures below. These Bravais lattices, the equivalent of 2D graphs, enable the component molecules to repeat indefinitely in three different spatial directions, much like the repeat of a wallpaper pattern. The early scientific investigation of crystals was primarily concerned with classification, primarily in terms of the symmetries involved. By the mid19th century crystals had been placed in thirtytwo distinct classes, and by the end of that century all 230 possible spacegroups had been listed by the Russian crystallographer Federov. The discovery of Xray diffraction in the early 20th century, however, completely transformed the science. Systematic analysis of the symmetrical patterns thrown onto a photographic plate by this method revealed for the first time the extraordinary internal world of crystals.
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