SOME APPLICATIONS OF THERMODYNAMICS IN CRYSTAL-CHEMISTRY

The integrated study of polymorphic phase changes in crystals by combi ning thermodynamic and crystallographic data is illustrated for four o ne-component systems - tin, carbon, adamantane and fullerene C-60-I-h - Of increasing complexity. A brief review of the basic thermodynamics of the solid state (laws of thermodynamics, polymorphism, order of tr ansitions) reminds the reader that enthalpy (H) and entropy (S) are ex perimental quantities derivable from the values of the heat capacity a t constant pressure (C-P) measured as a function of temperature (T). C ombination of Hand S through the Gibbs function gives the free energy as a function of T (G = H - TS). For a one-component crystal with two polymorphic forms, the separate roles of the enthalpy and entropy diff erences between the polymorphs can be distinguished. This is illustrat ed in quantitative fashion for the two polymorphs of tin at atmospheri c pressure, where there is a first-order phase transformation from gre y (diamond) to white (metallic) at 286 K. Application of the Clausius- Clapeyron equation (dP/dT = Delta S/Delta V) shows that metallic tin i s the stable phase above approximate to 5 kbar at 0 K. This is entirel y analogous to the treatment of the pressure dependence of the melting point of ice. In the next stage, pressure is added as a variable in o rder to treat the graphite-diamond polymorphism of carbon. Adamantane, for which calorimetric, phase-diagram and crystallographic data are a vailable over a considerable range of temperature and pressure, is nex t reviewed in detail. The polymorphic change from tetragonal (stable b elow 208.6 K at atmospheric pressure) to cubic is almost, but not quit e, first-order in character. A somewhat similar analysis is applied to available calorimetric and crystallographic data for fullerene C-60-I -h, where the transition shows appreciable deviations from ideal first -order character. The next stage, not considered here, would be to pro ceed from the methods of thermodynamics to those of statistical mechan ics, involving consideration of the detailed vibrational spectra of th e solids.