The mixed P, T derivative of isothermal bulk modulus for solids

摘要

Using the generalized Gilvarry J. Appl. Phys. 28, 1253 (1957) equation of state, we show that for the case where the Murnaghan equation of state holds, partial deriv~(2)B/partial derivTpartial derivP=0 where B is the isothermal bulk modulus. This leads to the following results: (1) The product αBδ is independent of volume and pressure at constant temperature, where α=(partial deriv In V/partial derivT)_(P) and δ is the Anderson-Gruneisen parameter. (2) The isothermal bulk modulus can be separated into two functions, B(T,P)=B(T)+B(P), where B(T) is a function of temperature only and B(P) is a function of pressure only, (3) (partial derivIn(αB)/partial derivIn η)_(T)=-(partial derivIn δ/partial derivIn η)_(T). where η=V/V_(0). (4) (partial derivIn(αB)/partial derivP)_(T)=-(partial derivIn δ/partial derivP)_(T). (5) If ψ=δ, where ψ=(partial derivB/partial derivP)_(T), then δ is independent of pressure and volume.