Volume and Pressure as Fundamental Variables Bulk Modulus

Volume and Pressure as Fundamental Variables Bulk Modulus 

The equation of state as a function of pressure and temperature describes perhaps the most fundamental property of condensed matter [1]. The stable structure of a solid at given pressure p and temperature T determines all other properties of a material. The total energy E at T = 0 as a function of volume V is the most convenient quantity for the theoretical analysis because it is the straightforward procedure to carry out the structure calculations at fixed volume. Comparison of theory and experiment is one of the touchstones of the ah initio research of interatomic forces. 

The fundamental quantities in these researches are pressure p, volume V, total energy of a solid E and bulk modulus B. Energy depends upon volume of the solid, 

In a crystal, E is the energy taken per cell of volume V = Vceii. The pressure p is given by 

In general, as the distance between the atoms decreases there is a tendency for all materials to transform to metallic structure, which is closely packed at the highest pressures. Thus, many interesting examples involve materials that have large-volume open structures at ordinary pressure, and which transform to more close-packed structures under pressure. 

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