How to derive bulk modulus with the Birch Murnaghan equation of state?

Hello,

Currently I am doing some molecular modeling to calculate the bulk modulus of different materials. However, I am not very familar with fitting specific equations to a datafile. I need to fit the Birch Murnagan equation of state to the Volume-Energy data:

E(V) = E_0 + ((9*B_0*V_0)/16) * ((V/V_0)^(2/3)-1)^2*(6+B'_0((V/V0)^(2/3)-1)-4*(V/V_0)^(2/3))

How can I fit the curve to the equation without rewriting the complete EOS equation to E = Ax^3 + Bx^2 + Cx + D?

Answer 1

[Nick Hobbs]

Assuming you only need to fit your function to a dataset, one way to fit your equation is with the function fit from the Curve Fitting Toolbox. There is a provided example where they use a custom model. In your case, you could use your equation as an anonymous function like the provided example, and use the function to fit your data to your provided equation.