Ultraprecise studies of the thermal expansion coefficient of diamond using backscattering x-ray diffraction

The linear thermal expansion coefficient of diamond crystals of type IIa and type Ia was measured in the temperature range from 10 to 295 K. Neither negative thermal expansion nor any substantial difference in the thermal expansion coefficient in crystals of the different types were observed. An empirical expression was obtained that approximates the temperature dependence of the thermal expansion coefficient of diamond. The $T^3$ temperature dependence of a Debye solid holds below $\approx$100 K with an accuracy of $\approx$ ${10}^{-8}\hspace{0.5em}{\mathrm{K}}^{-1}$. A slight increase in the value of the lattice parameter was found for the Ia-type crystal, which suggests lattice dilatation by nitrogen impurity. The measurements were performed using Bragg diffraction in backscattering from diamond crystals of highly monochromatic 23.7 keV x rays with the recently demonstrated high relative accuracy of $1.2\times {10}^{-8}$ in the determination of the lattice parameter [S. Stoupin and Yu. Shvyd’ko, Phys. Rev. Lett. 104, 085901 (2010)].