P- V- T Data of hexagonal boron nitride h BN and determination of pressure and temperature using thermoelastic equations of state of multiple phases

Abstract

A synchrotron x-ray diffraction study on hexagonal boron-nitride (hBN) was conducted at simultaneous high pressures and temperatures. The pressure applied to the sample is pseudo-hydrostatic up to 9.0 GPa and the temperature was homogeneous in the range of 300 K to 1280 K. A modified Rietveld profile refinement has been applied to these diffraction spectra of low symmetry and multiple phases observed in the energy-dispersive mode. Thermoelastic parameters of hBN were derived by fitting a modified high temperature Birch-Murnaghan equation of state. The results are: bulk modulus K=17.6 GPa, pressure derivative K′=∂K/∂P=19.5, temperature derivative ḳ=∂K/∂T=−0.69 × 10−2 Gpa/K, volumetric thermal expansivity α=a+bT with values of a=4.38 × 10−5K−1 and b=1.75 × 10−8K−2, respectively. It is observed that the thermal expansion and compression along different crystal axes are significantly different. The crystal c-axis is much more expandable and compressible than the a-axis. This is attributed to the layered structure of the hBN. Because the thermoelastic equations of state of hBN and NaCl are quite different, the unit cell volumes of these two materials, derived from the same diffraction pattern, can be used to derive the experimental P-T conditions. The large intersection angle of isochoric lines of these phases in P-T space ensures a determination of P-T with satisfactory precision. The application and limitations of this method in obtaining experimental pressure and temperature using diffraction data and thermoelastic equations of state of multiple phases are discussed.