Ultrasonic study of the temperature and pressure dependences of the elastic properties of ceramic dimolybdenum carbide ( -Mo2C)

Abstract

Pulse-echo overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of ceramic samples of dimolybdenum carbide (α-Mo2C) as functions of temperature in the range 130–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. The temperature dependences of the shear elastic stiffness (μ) and Young's modulus (E) show normal behaviour and can be approximated by a conventional model for vibrational anharmonicity. The longitudinal elastic stiffness (CL) increases with decreasing temperature and shows a knee at about 200 K; the decrease in slope below the knee indicates longitudinal acoustic-mode softening. The adiabatic bulk modulus (BS) is also affected by the mode softening below 200 K. The values obtained for the acoustic Debye temperature (ΘD) for ceramic α-Mo2C agree well with the thermal Debye temperature determined previously from heat capacity measurements. The velocities of both the longitudinal and shear ultrasonic waves in ceramic α-Mo2C increase approximately linearly with pressure: both the long-wavelength longitudinal and shear acoustic modes stiffen under pressure. The values determined at room temperature for the hydrostatic-pressure derivative (∂μ/∂P)P=0 of the shear stiffness is similar to those found for ceramic TiC and TaC; while (∂CL/∂P)P=0 and (∂BS/∂P)P=0 have large values, possibly due to the defect microstructure of ceramic α-Mo2C.