Physical properties and atomic arrangements in crystals

A survey is given of the relation between four physical properties of crystals and their structural characters. The properties discussed are the magnetic, optical, piezoelectric and elastic. The well-established relations between (a) diamagnetic anisotropy and molecular orientation and (b) paramagnetic anisotropy and the environment of complex ions are briefly reviewed. The more recent study of paramagnetic resonance absorption at high frequencies in a magnetic field is also included. The work on antiferromagnetic crystals is discussed in connection with the spinels. The study of optical activity and Raman spectra are considered under the heading of optical properties. The experimental confirmation by X-rays of the original convention concerning atomic configurations and the sign of optical activity in a molecule are described and also the connection between special features of the structures of tartrates, of sodium chlorate and of quartz and the handedness of the rotatory power is analysed. The piezoelectric properties of zinc blende, quartz, tourmaline, Rochelle salt and potassium dihydrogen phosphate are considered in relation to their structures. In the study of quartz and tourmaline the origin of the piezoelectric charge is attributed to tetrahedra of SiO₄ stressed in a direction from one corner to the opposite face. The spontaneous electric polarization of Rochelle salt and KH₂PO₄ is attributed to cooperative movements of hydrogen ions. Broad generalizations concerning the relation between elastic constants and the crystal structure are given. It is shown that the hardness increases in a regular way with the elastic constant c₁₁ (or an average of c₁₁, c₂₂, c₃₃) and also that there is a close connection between directions of strong interatomic bonds and a large value of the corresponding elastic constant.