Acentric crystal

Papoular, R.J. and Delapalme, A. (1994) Model-free polarised neutron diffraction study of an acentric crystal metamagnetic UCoAl, Phys. Rev. Lett., 72(10), 1486-1489. 

Giacovazzo, C. and SUiqi, D. (2001). The method of joint probability distribution functions apphed to MAD techniques. The two-wavelength case for acentric crystals. Acta Crystallogr. A 57, 700-707. 

In this case, the phase problem reduces to a question of the sign of the structure factor. Since the sign of the structure factor can be evaluated more reliably than the phase angle, the electron density in a centrosymmetric crystal can be evaluated more accurately than that in an acentric crystal (93), Equation (2) implies that total, time-averaged electron density can be determined by the diffraction method. 

Accurate X-ray analyses have been carried out for the acentric crystals of (i75-C5H5Ni)2C2H2. As shown in Fig. 18 the diamagnetic binu-... 

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...

Boyd GD, Bridges TJ, Pollack MA, Turner EH. Microwave nonlinear susceptibilities due to electronic and ionic anharmonicities in acentric crystals. Phys Rev Lett 1971 26(7) 387. 

Friedel s Law Georges Friedel noted that F(hkl) / values for centrosymmet-rically related Bragg reflections are equal, even for an acentric crystal structure. 

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

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