Solid Solutions of the Alkali Halides. II. The Theoretical Calculation of Lattice Constants, Heats of Mixing, and Distributions between Solid and Aqueous Phases

Abstract

In all previous attempts to calculate interionic distances and heats of mixing for alkali-halide solid solutions, uniform anion-cation distances throughout a given solution have been postulated. In the present paper, the more logical assumption is made that the ions are not at a constant nearest-neighbor distance, but take up positions of minimum potential energy relative to one another. A method making use of the Born-Mayer-Huggins equation for the lattice energies of the alkali halides is developed for the determination of these positions in a simplified model and for the calculation of the potential energy associated with the resultant lattice. From these values, the average lattice constant, the heat of mixing, and the activity-coefficient ratio in the solid solution are calculated; from the latter is obtained the theoretical distribution ratio between solid and aqueous solutions. Values of the listed properties have been calculated at various mole fractions for the solid solutions KBr–KCl, RbBr–RbCl, RbCl–KCl, RbBr–KBr at 25° and have been found to be in good agreement with the experimental data available.

Theories of Fused Salt Solutions

“…partial molar free energy of solution is given by ad = Aav -.-= RT In nAnD (15) o/Vad where AAv is Avogadro's number. Equations 14 and 15 give the same results as the Temkin11 d(Ax/T) , d(X2/T) , d(A,/ ) d(l/T) + 2 d(l/T) + "3 (1/ )fi-2 2 + tosAg(20) …”

“…11, 12, and 13 of Durham and Hawkins. 20 The potential constants used are summarized in Table IV. The Li-K dipoledipole constant was calculated, according to the method of Mayer21 and the (Li-K) dipole-quadrupole constant was taken as the geometric mean, of the (Li-Li) and (K-K) values.…”

“…"1 Cation---aniou' distance rLici = 2.909, /'kcl -3.437 A For at 40-60 mole1 % (Li-K) Cl• solution, we calculate AH = -172.10 + 0.4(192.90) + 0,6(164.23) = 3.60 kcal./mole where the cation-anion distance 7 = 3.246 A. was obtained by linear interpolation of the molar volume curve.9 The displacements and displacement energies for repulsion only then were calculated for each configuration and these results are summarized in Table V, where the notation of configurations is the same as Durham and Hawkins'. 20 The total displacement energy is calculated to be 2.16 kcal. and subtracting this from the unrelaxed heat of solution gives AH = 1.4.4 kcal.…”

A Green Function Estimation of Correction to Vegard's Law for isovalent Substitutional Defects in Alkali Halide Crystals

“…χ → Ο or χ → 1) and thus the concerned authors could not trace the above problem in their investigations for obvious reason. For high concentration of defects, different approaches, like Durham et al [3] from atomistic calculation, Hardy et al [4] from lattice static calculation, Fukai [5] from both semidiscrete and superlattice method, Fancher and Barsch [6] from semidiscrete method and present authors [7] from a self-consistent semidiscrete method, obtained a single value of relaxation for both types of nearest neighbour pairs indicating existence of a virtual crystal having lattice parameter r(χ), fairly close to the values suggested by Vegard's law.…”