We develop a powerful new limiting relation between lattice potential energy, U POT , and unit cell volume, V (hence, also, density), applicable to some of the most complex ionic solids known (including minerals, and superconductive and even disordered, amorphous or molten materials). Our equation (which has a correlation coefficient, R ) 0.998) possesses no empirical constants 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 e 70 000 and extending toward 100 MJ mol -1 . The relation relies only on the following: (i) an ionic strength related term, I (defined as 1 / 2 ∑n i z i 2 , where n i is the number of ions of type i per formula unit, each bearing the charge z i , with the summation extending over all ions of the formula unit); (ii) a standard electrostatic conversion 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 , the volume of the formula unit (the "molar" or "molecular" volume). The equation provides estimates of U POT to certainly within (7%; in most cases, estimates are significantly better than this. Examples are provided to illustrate the uses of the equation in predicting lattice energies and densities; the calculations require minimal data and can be performed easily and rapidly, 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 many inorganic salts possessing complex ions), our recently published linear correlation is more accurate. The linear equation, though empirically developed, is consistent with and can be rationalized following the approach developed here. Lattice potential energy (U POT ) is a dominant term in the thermodynamic analysis of the existence and stability of ionic solids. Direct experimental determination is generally not possible since, in practice, the crystalline solid dissociates into atoms and not into gaseous ions, as is required in the lattice energy evaluation. Therefore, its indirect experimental determination, computation, or estimation is of considerable interest in modern materials science; indeed, whenever the energetics of condensed-state materials are studied, the chemical processes under consideration may be rationalized if the appropriate lattice energy steps can be incorporated into the thermochemical cycle.A variety of estimation methods for lattice energies is available. These include the Born-Haber-Fajans thermochemical cycle 1 (which requires ancillary thermodynamic data) and modern computational methods (which generally require knowledge of the lattice constants and the coordinates of the ions as well as needing an established force field). The computational methods range from direct energy calculational procedures 2 through to programs that produce lattice energies in the course of their modeling of the solid. 3-5 Quantum mechanical procedures are also available, but are ...
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