The elegance and beauty of crystals have always been a source of delight.What is a crystal? A crystal is defined as a solid that contains a very high degree of long-range three-dimensional internal order of the component atoms, molecules, or ions. This implies a repetitious internal organization, at least ideally. By contrast, the internal organization of atoms and ions within a noncrystalline material is totally random, and the material is described as "amorphous." Studies of crystal

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... , that is, of the external features of crystals, have been made since early times, particularly by those interested in minerals (for practical as well as esthetic reasons) (Groth, 1906–1919; Burke, 1966; Schneer, 1977). It was Max von Laue who realized in 1912 that this internal regularity of crystals gave them a grating-like quality so that they should be able to diffract electromagnetic radiation of an appropriate wavelength. From Avogadro's number (6.02 × 1023, the number of molecules in the molecular weight in grams of a compound) and the volume that this one "gram molecule" of material fills, von Laue was able to reason that distances between atoms or ions in a crystal were of the order of 10−9 to 10−10m (now described as 10 to 1 Å). A big debate at that time. was whether X rays were particles or waves. If X rays were found to be wavelike (rather than particle-like), von Laue estimated they would have wavelengths of this same order of magnitude, 10−9 to 10−10 m. Therefore, since diffraction was viewed as a property of waves rather than particles, von Laue urged Walther Friedrich and Paul Knipping to test if X rays could be diffracted by crystals. Their resulting diffraction experiment was dramatically successful. The crystal, because of its internal regularity, had indeed acted as a diffraction grating. This experiment was therefore considered to have demonstrated that X rays have wavelike properties (Friedrich et al., 1912). We now know that particles, such as neutrons or electrons, can also be diffracted.