Empirical Calculation of the Bulk Modulus for the Alkali Halide Crystals

Abstract

Cohen [l] predicted that the zero pressure isothermal bulk modulus B, of group IV, III-V, and V-VI semiconductor crystals, near the center of the periodic table, with the diamond and zincblende structures, should scale as B, = where d is the nearest neighbor distance (in A) and a = 1761 GPa w3.'.Subsequently Lam et al. [2] found that the bulk modulus scaled as B , = (1971 -2202) x = 1 for III-V, and 1 = 2 for II-VI semiconductors. The accuracy of the above formula in predicting the bulk modulus is remarkably good with only small percentage error for most of the materials examined.Recently Schlosser [3] found a similar scaling for the NaCl and CsCl structure in alkali halide crystals; the product P = Bod -35 is, to a good approximation, constant within each family with a common cation (Li, Na, K, Rb, Ag, Cs, T1) and a common crystal structure.Nevertheless, Schlosser [3] did not give any physical explanation for this occurrence, in particular for the dependence of P on the kind of cation. Recently, in color center as well as in defect physics, we adopted [4] the Sanderson model for nonmolecular structures which utilizes an unequivocal scheme in determining the ionic radii; we obtained predictions for off-center configurations of impurity ions in alkali halides and oxides [4], for FA (II-type) center formation [5] and for F-center luminescence quantum yield [6] in alkali halides (incidentally, it should be remembered that we found [7] also a correlation between the Sanderson partial charge and the Szigeti effective charge).Thus, we looked for a dependence of B, not only on the lattice parameter d but also on the ionic radius (the latter plays the role of a corrective effect).Indeed, since the applicability of the Cohen relationship is essentially restricted [l, 21 to covalent compounds, we expect a dependence of B, on the ionic bonding, which implies, in the framework of the Sanderson model, the dependence on the partial charge and on the ionic radius.In Table 1 . We restricted our attention to NaCl structure crystals since, unfortunately, only few accurate values for ionic radii have been obtained for CsCl structure crystals [4] by using with 1 = 0 for group IV,

Calculation of the Bulk Modulus of Simple and Complex Crystals with the Chemical Bond Method

“…An accurate determination of bulk modulus is a complicated issue involving a careful analysis of elastic parameters, plastic deformation, and even experiment measurement processes. Therefore, many experimental and theoretical attempts have been made to determine the bulk moduli of various crystals, − and some relations between the bulk modulus and physical parameters have been obtained, for example, the correlation between the bulk modulus and the Debye temperature, , the bulk modulus−volume−ionicity relationship, , a simple relation between the bulk modulus and the bond length for some binary semiconductors, ,, a linear relation between the bulk modulus and plasma energy, and so on. ,, A number of researchers have focused upon the bulk modulus in their search for new superhard materials because the hardness correlates roughly with the bulk modulus for group IV, III−V, and II−VI materials; the bulk modulus results were used to predict the hardness of a new material. However, for the complex crystals, it is well-known that quantum mechanics does not easily accommodate this picture; the theoretical study is more difficult.…”