Ionic bulk modulus

Physical hardness can be defined to be proportional, and sometimes equal, to the chemical hardness (Parr and Yang, 1989). The relationship between the two types of hardness depends on the type of chemical bonding. For simple metals, where the bonding is nonlocal, the bulk modulus is proportional to the chemical hardness density. The same is true for non-local ionic bonding. However, for covalent crystals, where the bonding is local, the bulk moduli may be less appropriate measures of stability than the octahedral shear moduli. In this case, it is also found that the indentation hardness—and therefore the Mohs scratch hardness—are monotonic functions of the chemical hardness density. 

Strongly for the ionic crystals, yet the bulk modulus for the alkali halides varies as d. The cl trend for the bulk modulus will show up in the study of simple metals, and in terms of the pseudopotentials that will be used in the study of simple metals, d" -dependence takes on a particularly fundamental role. In Problem 15-3, the simple metal theory is used to give a good account of the bulk modulus in C, Si, and Gc. It should be noted also that the simple metal theory docs not give a good account of cohesive energy itself there is much cancellation between terms for that property, and there are important contributions (for example, that do not vary as... 

The appeal of this approach is in the small number of parameters which need be put into the calculation (those of Table 12-2, which are also given in the Solid State Table) as well as in the remoteness-of-origin of these parameters relative to the mechanical properties of the ionic crystals being studied. We use that approach though it is quite crude. Notice, in particular, that it predicts the same properties for complementary skew compounds such as NaCl and KF, which we shall see is far from true. Much higher accuracy could be obtained by fitting a and i to the observed spacing and bulk modulus for each compound. That choice is better... 

Let us then turn to the ionic solids themselves. Kim and Ciordon (1974) recalculated the total energy for the alkali halides that form rocksalt structures and thereby computed from first principles the lattice spacing, the separation energy (the energy per ion pair required to separate the solid into isolated ions -this comes from the theory more naturally than does the cohesive energy, which is relative to isolated neutral atoms), and the bulk modulus. For KCI, the agreement of the values for the three properties with experimental values is typical of the calculations. The calculated (and in parentheses, the experimental) values for KCI are 3.05 (3.15) A, 175 (166) kcal/mole, and 2.3 (1.9) x 10 dync/cmA Again we may say that the interactions are quite well understood in terms of the microscopic theory. We shall return to the interpretation of these properties in terms of simple models in Section 13-D. 

D. L. Anderson and O. L. Anderson (1970) showed that, for an ionic crystal with electrostatic attractive forces and a Born power-law repulsive potential, the bulk modulus K is given by... 

Elastic constants of solids can be related to the fundamental interaction energy terms. In fact it can be shown easily that the bulk modulus, K scales as the energy density, Ulr for an ionic material interacting through Bom-Mayer potential (see later in this section). Thus the molar volume which increases with the presence of larger ions in glasses can be expected to cause a decrease in Young s modulus. 

Table 6 Variation of lattice constant ao(A), bulk modulus Ko(GPa), ionic charge q(e), spin moments nins) iu " ith both composition of the hybrid functional and magnetic state ...

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