The elastic behaviour of orthorhombic sulphur under pressure

Abstract

Orthorhombic, α -sulphur comprises S 8 rings strongly bound by covalent, intramolecular forces but held together by much weaker intermolecular bonds. To examine the vibrational anharmonicity of the long-wavelength acoustic modes in a molecular crystal of this type, the effects of hydrostatic and uniaxial pressures upon the velocities of ultrasonic modes propagated in a single crystal of orthorhombic sulphur have been measured. From the experimental results at room temperature 19 of 20 third-order elastic constants and also the hydrostatic pressure derivatives of the 9 second-order elastic constants have been obtained. The elastic stiffnesses and their hydrostatic pressure derivatives have also been calculated from an intermolecular potential of the 6-exp variety. Good agreement between the results obtained from this lattice dynamical calculation and the ultrasonic experiments establishes that the potential model provides a reasonable description of the elastic behaviour of this molecular crystal. The compression estimated from the Murnaghan equation of state agrees well with that estimated theoretically from the lattice dynamic calculations. The Debye temperature determined from the ultrasonic-wave velocities is 187.5 ± 2 K. Ultrasonic-wave velocities are linear up to about 100°C; the crystals do not undergo the transition to a monoclinic (β) phase which can take place at 95°C. There is no indication of softening of the long-wavelength acoustic phonon modes. Vibrational anharmonicity is discussed in terms of the long-wavelength acoustic-mode Grüneisen parameters obtained from the generalized Grüneisen theory in the quasiharmonic approximation. The mean high-temperature long-wavelength acoustic-mode Grüneisen parameter γ̄ el H (= 2.72) is much larger than the room-temperature thermal Grüneisen parameter γ th (=0.54). In this molecular crystal the intermolecular volume is much more compressible than the intramolecular volume; the mode Grüneisen parameters for purely internal vibrational modes are small, whereas those for the external modes are large. At room temper­ature all phonon modes contribute so that γ th is made small by the small internal-mode contributions. In contrast, the weak, strongly pressure dependent intermolecular forces dominate the zone-centre acoustic modes and lead to a large mean Grüneisen parameter γ̄ el H .