A Physical Mechanics Paraphrase on Mie-Grüneisen Equation of State

A one-dimensional model of lattice physical mechanics was built up to study the atomic thermal vibration in a constant volume state.According to the lattice dynamics model, An equation of state of solids which is similar to the Mie-Grüneisen's, was deduced absolutely from vibration mechanics.The mechanical implication of thermal pressure was ascertained, that thermal pressure was the average value of thermal vibration force in time domain.The relationship between Grüneisen parameter and thermal vibration frequency shows that the Grüneisen parameter of a real solid corelates with its crystal structure.The differential expression between Grüneisen parameter derivated from a simple cubic crystal and cold pressure was obtained, which agrees with the D-M relation.