Elastic and piezoelectric properties of minerals II. Structure-property relationships
Our knowledge of physical properties of crystals is rather limited compared to the number of solved crystal structures. Mainly the basic tensorial properties of numerous crystal species belonging to simple structure types like halite-, CsCl-, fluorite-, perovskite-, spinel- and garnet-type have been extensively studied over the years. On the basis of these data relations between chemical composition and certain physical properties could be established. For instance, the mean values of magnetic susceptibility of para- and diamagnetic crystals, dielectric constants, optical refractivity and the Faraday effect can be easily estimated by additivity rules as sums of quasi-persistent contributions of individual atoms, ions or molecules. A well-known example is the Clausius–Mosotti equation
which relates the mean dielectric constant ε of a crystal to the polarisabilities αj of its constituents. nj is the number of particles of type j per unit volume and ε0 denotes the permittivity of vacuum.
In contrast to such physical properties, elasticity exclusively arises from interactions between the constituents of a crystal. The mean elastic stiffness is therefore closely correlated to the lattice energy, and the elastic anisotropy directly reflects the anisotropy of the crystal’s bonding system. The modifications of carbon, SiO2 and Mg2SiO4 provide instructive examples (Fig. 1). Due to their higher tensorial rank, already the second-order elastic properties (Hooke’s law) behave anisotropically even in crystals possessing cubic symmetry (Fig. 2). Consequently, elasticity provides one of the most powerful probes for the investigation of structure-property relationships. Further, a series of rules on the qualitative interpretation of the structural dependence of many other physical properties can be derived from the elastic behaviour. Examples are listed in Table 1.