Kumar

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The Kumar (1995) EoS is based on the assumption that the product αKT is invariant with pressure, which enables Kumar to use the definition of the Anderson-Gruenesien parameter δ to arrive at:



This EoS is invertible:



From which one can obtain expressions for the bulk modulus and its pressure derivatives:


Thus, there is no obvious truncation of the EoS to second order with an implied value of K'0. Nor is there an obvious extension to 4th order with a refineable value of K''0. Therefore the Kumar EoS is only available in EosFit in 3rd-order form with refineable parameters V0, K0 and K'0.


The value of K'0 becomes zero at a pressure of

 

beyond which is becomes negative.


But the value of K''  asymptotes towards zero but never becomes zero. 


At P = 0 the value of K'' = -(K'0 +1)/K0 which is obviously more negative than the commonly-found value in minerals of  -K'0 /K0.