Ultrasonic phase velocity and elastic modulus in isotopically enhanced manufactured diamonds

Abstract

We have performed ultrasonic pulse-echo experiments to measure the longitudinal and transverse acoustic velocities in nine single-crystal manufactured diamonds. The 13C concentration in the samples ranged from nearly 0% to 99%. Small (4%–5%) but distinct decreases in both the longitudinal and transverse 〈100〉 phase velocities with increasing 13C content were observed. Using these velocities and density data, values for the cubic elastic moduli c11 and c44 were determined. Within experimental uncertainty (typically <0.5%), c11 remained constant with 13C content. However, c44 was observed to decrease by 2% over the range 0%–99% 13C. Phase velocities in 〈111〉-oriented samples remained nearly constant with isotope content, implying a 2%–6% increase in 13C diamond’s effective elastic constants 1/3(c11+2c12+4c44) and 1/3(c11−c12+c44) over those of 12C diamond. Together with experimentally determined densities and crystalline orientations and the above results for c11 and c44, the 〈111〉 velocities were used to numerically invert the Christoffel equation for the elastic modulus c12. Surprisingly, c12 nearly doubled in the range 0% to 99% 13C, implying a 17% increase in the bulk modulus K=1/3(c11+2c12).