The third-order Birch–Murnaghan isothermal equation of state is given by P ( V ) = 3 B 0 2 [ ( V 0 V ) 7 / 3 − − ( V 0 V ) 5 / 3 ] { 1 + 3 4 ( B 0 ′ ′ − − 4 ) [ ( V 0 V ) 2 / 3 − − 1 ] } . where P is the pressure, V 0 is the reference volume, V is the deformed volume, B 0 is the bulk modulus, and B 0 ' is the derivative of the bulk modulus with respect to pressure. The bulk modulus and its derivative are usually obtained from fits to experimental data and are defined as B 0 = − − V ( ∂ ∂ P ∂ ∂ V ) P = 0 and B 0 ′ = ( ∂ ∂ B ∂ ∂ P ) P = 0 The expression for the equation of state is obtained by expanding the Helmholtz free energy in powers of the finite strain parameter f, defined as f = 1 2 [ ( V 0 V ) 2 / 3 − − 1 ] , in the form of a series. This is more evident by writing the equation in terms of f. Expanded to third order in finite strain, the equation reads, P ( f ) = 3 B 0 f ( 1 + 2 f ) 5 / 2 ( 1 + a f + h i g h e r o r d e r t e r m s ) , with a = 3 2 ( B 0 ′ − − 4 ) .