The pressure dependence of elastic constants and bond bending in HgTe

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Abstract
The elastic stiffness constants of HgTe have been obtained from ultrasonic wave velocities measured as a function of hydrostatic pressure up to 15·5 × 108 Pa, which is just below the pressure pt at which the structural transition from zinc blende to cinnabar takes place. The shear constants 1/2(C11 – C12) and C44, which are small even at atmospheric pressure, decrease linearly with pressure up to p t, but do not reach zero; all the shear acoustic mode Grüneisen gammas are negative in the long-wavelength limit. It is concluded that the densification phase transition is associated with collapse under a macroscopic shear which takes place when a modified Born stability criterion that 1/2C11−-C12)/B is 0·17 is reached. At pt the ratio βt/αt, of the bond-bending βt to stretching αt force constants is 0·075. The ionicity is found to increase under pressure towards the Phillips critical value of 0·785; as this happens, the bond-bending force constant β reduces until the crystal can no longer withstand shear. A complete set of third-order elastic constants has been measured; these are discussed in terms of a valence-force-field model and provide further evidence for the weakness of HgTe towards bond bending and shear. These third-order elastic constants are used to obtain the cubic invariants in the Hamiltonian with respect to strain. The small value found for 1/(C 111 + 2C 123−3C 112 supports the hypothesis that the transition involves a large component of shear in 〈110〉 directions on {110} planes; a shear component in 〈001〉 directions is also required. A topotactic scheme is suggested for the structural transition from zinc blende to rock salt or cinnabar which conforms with the pressure effects in the elastic shear constants measured for HgTe.