New method of calculation of the surface enthalpy of solids

Abstract

A new method of calculation of the surface enthalpy of solids E c in the so-called rigid lattice approximation is proposed. The formerly found [J. Solid State Chem. 57 (1985) 269, 291] empirical relationship between bond length and bond energy in oxide crystals is used for this purpose. It is sufficient to add the energies of all bonds cut in the process of surface formation over the surface unit cell and to divide the sum by double the unit cell area. The advantage of this widely applicable method consists in the fact that it is sufficient to know the structure of the considered crystal; for oxides all coefficients of the proposed equation have already been determined and listed in the quoted paper. Generalization of the method on the non-oxide (X) crystals is dependent on the determination of the respective coefficients for the element-X bonds. But at present the method is also applicable to non-oxide crystals of high symmetry (e.g. NaCl-type, CsCl-type, ZnS-type, fluorite-type). It is argued that E c may be thought of as active surface energy responsible for various aspects of the surface reactivity and cleavage, while the passive surface energy of the relaxed surface governs static phenomena. As the passive surface energy (or free energy) is not easy to be obtained either experimentally or theoretically, an attempt is made to predict the equilibrium form of crystals with Curie-Wulff plots using E c instead of the free energy. In most cases the predictions agree well with accessible literature data. Data involving cleavage planes and direct experimental determinations of the surface energy are also used in the evaluation of the proposed method. The paper is illustrated with numerical data of E hkl c calculated for a number of oxides and halides of the NaCl-type structure as well as for oxides of the rutile-type, TiO 2-anatase, V 2O 5 and MoO 3 including the reduced faces of the two latter oxides.