Mie-Grüneisen Equation of State Based on the Physical Mechanics Analysis of Three-Dimensional Lattice Thermal Vibration

According to crystal lattice structures, a three-dimensional lattice physical mechanics model in constant volume state was built up to study the atom thermal vibration.The equation of thermal energy and external force on the thermal vibrating lattice was deduced absolutely from the principle of mechanical vibration.By introducing macroscopic physical statics into microscopic atomic thermal vibration equation, Mie-Grüneisen equation of state for solids and the formula of Grüneisen parameter were deduced directly from the physical mechanical model.Finally, based on the arrangement of atoms in simple cubic, face-centered cubic, body-centered cubic, diamond cubic and close-packed hexagonal crystal, it was proved that the Grüneisen parameters of these symmetrical crystals can be expressed in a uniform formula, irrelevant to their actual arrangement of atoms.