4TH-ORDER ELASTIC-CONSTANTS AND 2ND 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 C-11 are positive. The second pressure derivatives C-12, C-13, and C33 are large suggesting that phase transformation will occur in white tin when subjected to hydrostatic pressure.