Lattice energies and unit cell volumes of complex ionic solids

We develop a powerful new limiting relation between lattice potential energ y, U-POT, and unit cell volume, V (hence, also, density), applicable to som e of the most complex ionic solids known (including minerals, and supercond uctive and even disordered, amorphous or molten materials). Our equation (w hich has a correlation coefficient, R = 0.998) possesses no empirical const ants whatsoever, and takes the following form: U-POT = AI(2I/V-m)(1/3). It is capable of estimating Lattice energies in the range 5000 < U-POT/kJ mol( -1) less than or equal to 70 000 and extending toward 100 MJ mol(-1). The r elation relies only on the following: (i) an ionic strength related term, I (defined as 1/2 Sigma n(i)z(i)(2) where ni is the number of ions of type i per formula unit, each bearing the charge z(i), with the summation extendi ng over all ions of the formula unit); (ii) a standard electrostatic conver sion term, A/kJ mol(-1) nm = 121.39 (the normal Madelung and electrostatic factor as found in the Kapustinskii equation, for example); and (iii) V-m t he volume of the formula unit (the "molar" or "molecular" volume). The equa tion provides estimates of U-POT to certainly within +/-7%; in most cases, estimates are significantly better than this. Examples are provided to illu strate the uses of the equation in predicting lattice energies and densitie s; the calculations require minimal data and can be performed easily and ra pidly, even on a pocket calculator. In the lower lattice energy range (i.e. , U-POT/kJ mol(-1) < 5000, corresponding to the simpler compounds and to ma ny inorganic salts possessing complex ions), our recently published linear correlation is more accurate. The linear equation, though empirically devel oped, is consistent with and can be rationalized following the approach dev eloped here.