Evaluation of pressure and volumetric modules in melted systems
In the article there were estimated the pair potential and pressure of bulk modules in molten systems. There are given appropriate formulas for calculating the compressibility of electron melts. The polytherms of compressibility for selenium, tellurium, germanium and silicon are calculated. For the calculation of bulk modules, melts of metals and semiconductors are considered as a two-component liquid consisting of ions and electrons. According to the virial theorem, a part of the pressure associated with the dynamics and interaction of the ion subsystem is estimated. Since the isothermal bulk modulus is a static exponent, we determined it under conditions where the pressure and volume in the system change slowly, and the temperature of the melt changes very slowly or remains constant. The adiabatic bulk modulus, i.e. dynamic, was determined under conditions of heating of the melt caused by compression. Under adiabatic compression a change in temperature and pressure is allowed. This phenomenon occurs in fast processes, i.e. when there is no heat exchange due to the inertia of the thermal properties of the melts. This behavior of adiabatic compressibility is characteristic of metallic melts. We have found that the instantaneous dynamic modulus calculated in the pair approximation model is identical to the dynamic modulus calculated in the full theory in the second order, and also differs markedly from the statistical module. The explanation of this fact consists in neglecting the members of the electron-ion interaction of a higher order than the second, and also the unsatisfactory modification of the pseudopotential by means of an amendment to the Hartree energy. We obtained the relationships that make possible to calculate the compressibility of melts. Theoretical calculated polytherms of compressibility for semiconductors are given in the article.