Elastic Constants and Debye Temperature of TiC Using a New Ultrasonic Coherent Pulse/cw Technique

TLDR

The technique enables velocity measurements in both small and large samples without elaborate instrumentation. The study introduces a simple yet sensitive ultrasonic velocity measurement technique based on a coherent pulse/cw system. Using this technique, the authors measured the longitudinal and two transverse acoustic mode velocities along the (110) direction of a TiC single crystal and derived its elastic constants and Debye temperature. The measured velocities were vL = 9.23 × 10⁵ cm s⁻¹, vT1 = 6.43 × 10⁵ cm s⁻¹, vT2 = 5.93 × 10⁵ cm s⁻¹, yielding elastic constants c11 = 3.89 × 10¹² dyn cm⁻², c12 = 0.43 × 10¹² dyn cm⁻², c44 = 2.03 × 10¹² dyn cm⁻² and a room‑temperature Debye temperature of 935 K.

Abstract

A new simple but sensitive ultrasonic velocity measurement technique, using a coherent pulse/cw system, is described. The technique can readily be used for velocity measurements in either small or large samples, and does not require elaborate instrumentation. This technique has been used to measure the velocities of all three pure acoustic modes along a (110) direction of a single crystal of TiC. These velocities were then used to calculate the elastic constants and the Debye temperature for this sample. The measured velocities are vL = 9.230×105 cm sec−1, vT1 = 6.425×105 cm sec−1, and vT2 = 5.927×105 cm sec−1. The calculated elastic constants are c11 = 3.891×1012 dyn cm−2, c12 = 0.433×1012 dyn cm−2, c44 = 2.032×1012 dyn cm−2, and the room temperature Debye temperature is 935°K.