Acentric crystal classes

Of the thirty-two crystal classes, twenty-two lack an inversion center and are therefore known as non-centrosymmetric, or acentric. Crystalline and polycrystalline bulk materials that belong to acentric crystal classes can exhibit a variety of technologically important physical properties, including optical activity, pyroelectricity, piezoelectricity, and second-harmonic generation (SHG, or frequency doubling). The relationships between acentric crystal classes and physical properties of bulk materials are summarized in Table 9.1.1. 

Eleven acentric crystal classes are chiral, i.e., they exist in enantiomorphic forms, whereas ten are polar, i.e., they exhibit a dipole moment. Only five (1,2, 3, 4, and 6) have both chiral and polar symmetry. All acentric crystal classes except 432 possess the same symmetry requirements for materials to display piezoelectric and SHG properties. Both ferroelectricity and pyroelectricity are related to polarity a ferroelectric material crystallizes in one of ten polar crystal classes (1, 2, 3,4, 6, m, mm2, 3m, 4mm, and 6mm) and possesses a permanent dipole moment that can be reversed by an applied voltage, but the spontaneous polarization (as a function of temperature) of a pyroelectric material is not. Thus all ferroelectric materials are pyroelectric, but the converse is not true. 

Table 9.1.1. Physical properties of materials found in acentric crystal classes...

Fig. 2.8 Some examples of chromophores forming acentric crystals. The space group and the crystal class are reported for each compound...

It may not be a coincidence that nitroanilines have been a useful class of compounds for second harmonic generation (12-13). They naturally associate into polar arrays, which are manifested in their crystal structures. The important question is whether or not these polar arrays are likely to bias the resulting crystal structures to be acentric. Although we do not have large enough data sets to make a statistically convincing case, from a set of 32 primary and secondary nitroanilines and analogs, about 40% of their crystal structures are acentric. These compounds are all capable of... 

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