Thermal Expansion and Atomic Vibrations of Zirconium Carbide to 1600 K
We have measured the lattice constants and Debye–Waller factors of ZrC from 12 to 1600 K using neutron diffraction. The data have been analyzed with the Grüneisen equation of state using an existing procedure for the Debye–Waller factors and a new procedure for the CTE that takes the temperature dependence of the elastic stiffness into account. The results of these measurements are in good agreement with previous measurements and with recent calculations. We have used the results of our measurements to estimate the melting point of ZrC with the Lindemann rule and obtain an estimate of 4000 K, in good agreement with the measured melting point of 3700 K of this highly refractory material. This last result demonstrates the importance of anharmonic effects in determining the melting point.
Lawson, A. C.; Butt, D. P.; Richardson, J. W.; and Li, Ju. (2007). "Thermal Expansion and Atomic Vibrations of Zirconium Carbide to 1600 K". Philosophical Magazine, 87(17), 2507-2519.