Fourth-order elastic constants and second pressure derivatives of white tin

The expressions for the 25 fourth-order elastic constants of a body-centered tetragonal crystal are derived with interactions extending to fifth neighbours. The expressions for its effective second-order elastic constants are obtained in terms of its natural second-, third-, and fourth-order elastic constants using the finite strain elasticity theory. The fourth-order elastic constants and the second pressure derivatives of white tin are evaluated using these formulae. All the second pressure derivatives of white tin except that of C11 are positive. The second pressure derivatives C12, C13, and C33 are large suggesting that phase transformation will occur in white tin when subjected to hydrostatic pressure.