In previous studies the average number of neighbors (n(avrg)) of an atom in the surface phase was found to increase by about 5-20 % between 0 K and the melting temperature for all solid chemical elements in the periodic table. These ideas are now used, along with the concept of surface free enthalpy excess, to describe the thermodynamic surface stability of solid chemical elements and a number of compounds. This increment makes the surface phase of solids "geometrically impossible" to exist at from a particular temperature, resulting the formation of vacancies in the surface layers. The latter results in the collapse of crystal structure, beginning with the formation of liquid in the surface layers a few atoms thick, in agreement with recently published experimental studies. The present derivation has resulted some important relationships between thermodynamic parameters as a function of the number of layers of the surface phase (m) and the average temperature slope of the surface free enthalpy excess (dgamma/dT). These are expressions for the heat of melting (DELTAH(m)), entropy of melting (DELTAS(m)), melting temperature (T(m)), and critical temperature (T(c)) in case of pure metals and compounds. The ratio of critical and melting temperature is also discussed. The melting and critical thermodynamic parameters are deduced from the same type of equation. The surface of the model 2D and the real 3D bulk are considered in detail, and finally comparison to the experimental results is given.