Free Volume and Entropy in Condensed Systems I. General Principles. Fluctuation Entropy and Free Volume in Some Monatomic Crystals

In a system of atoms whose motions are classically excited, the change in entropy in any isothermal process can be written R ln (Vf₂/Vf₁) per mole, one such term for each kind of atom in the system. The free volume V_f used in this expression is the effective volume accessible to the centers of gravity of the atoms, corrected for fluctuation effects. Corresponding expressions can be written for the classical (translational or rotational) part of the motions of polyatomic molecules in real liquids and solids. In solids the free volume can be written V_f = Nvf, where v is a box, or cage, volume accessible to one particle, and f, the fluctuation factor, has a numerical value which depends on the way in which the box is defined. R ln f is a contribution to the entropy of the system, and the name ``fluctuation entropy'' is proposed for it. The fluctuation entropy includes what has been called ``communal entropy'' as well as a term due to the temperature variability of cell sizes. The free volume in a monatomic crystal can be determined from thermodynamic data, one convenient relationship being P_vap = (RT/V_f) exp (— ΔH/RT). When this is applied to the data for the vapor pressures of the solids A, Kr, Xe, Mg, Zn, Cd, Hg, values of V_f are obtained which are about ½ percent of the volumes of the solids. The values of f found for these crystals support Rice's view that solids should display a rather large fluctuation entropy.