Thermal Expansion of Diamond at Low Temperatures

Temperature variation of a lattice parameter of a synthetic diamond crystal (type IIa) was measured using high-energy-resolution x-ray Bragg diffraction in backscattering. A 2 order of magnitude improvement in the measurement accuracy allowed us to directly probe the linear thermal expansion coefficient at temperatures below 100 K. The lowest value measured was $2\times {10}^{-9}{\mathrm{K}}^{-1}$. It was found that the coefficient deviates from the expected Debye law ($T^3$) while no negative thermal expansion was observed. The anomalous behavior might be attributed to tunneling states due to low concentration impurities.

Figure 1

Experimental setup (see text for details).

Figure 2

Reflectivity of diamond from the (995) atomic planes. Filled circles, solid line: experimental dependence. Dashed line: calculations using dynamical theory of x-ray diffraction.

Figure 3

Relative change in the diamond lattice parameter with temperature. Circles: experiment 1; squares: experiment 2. Solid line is the sixth-order polynomial approximation. Dashed line is the approximation with $T^4$. The shaded area represents a region previously inaccessible due to the limited measurement accuracy.

Figure 4

Linear thermal expansion coefficient of diamond: obtained by point-by-point determination from experiment 1 (circles) and from experiment 2 (squares), calculated from the polynomial approximation (3) (solid line) and the Debye model approximation (4) (dashed line). The shaded area represents a region previously inaccessible due to the limited measurement accuracy.