Formulation of the third-order Grüneisen parameter at extreme compression

Higher order derivatives of bulk modulus of materials at infinite pressure

“…The theory of materials at infinite pressure originally due to Stacey [1,2] and further developed by Shanker et al [17,18] has been extended in the present study to determine the n-th order pressure derivatives of bulk modulus at extreme compression. Using some basic principles of calculus it has been found that the higher order pressure derivatives of bulk modulus can be determined only with the help of first and second pressure derivatives of bulk modulus at infinite pressure.…”

“…Equations (15) and (16) The left hand side of equation 18can be written as (19) where K"' = d 3 K/dP 3 . It has been found [17,18,20] that the right hand side of Eq. (19) is positive finite equal to the third order Grüneisen parameter at infinite pressure…”

“…The third order Grüneisen parameter ∞ λ is given by Eq. 20for the materials at extreme compression [17,18]. It should be…”

“…In order to derive thermodynamic relationships and identities at infinite pressure, we make use of some basic principles of calculus [17,18] which are written as follows. If y is a function of x such that y remains positive finite at x tends to zero, then…”

A comparative study of Burakovsky's and Jacobs's volume dependence Grüneisen parameter for fcc aluminum

“…0 q  in the limit V tends zero or P tends to infinity [11][12][13].Obviously, q deduced from Eq. (1) doesn't satisfy this boundary condition.…”