Thermal Expansion of Single Crystal Sapphire from 293 to 2000 K Standard Reference Material 732

Abstract

This single crystal sapphire is the fifth Standard Reference Material (SRM) to be certified for thermal expansion by the National Bureau of Standards. Expansion measurements to 1000 K on three samples indicate that the stock of material is of consistent quality suitable for certification. In the temperature range from 293 to 1000 K measurements were made using an interferometer apparatus resulting in

$$ \frac{{{L_{1000}} - {L_{293}}}}{{{L_{293}}}} = 5500 \times {10^{ - 6}} $$

with a standard deviation of 5 × 10^-6. Above 1000 K length measurements were made using twin tele-microscopes with the sample heated in a tungsten mesh furnace. From 293 to 2000 K

$$ \frac{{{L_{2000}} - {L_{293}}}}{{{L_{293}}}} = 15700 \times {10^{ - 6}} $$

with a standard deviation of 25 × 10^-6. Measurements were made parallel to the rod axis which is oriented 59° from the c-axis of the crystal. Smoothed values of the expansion and coefficients of expansion were obtained by fitting the expansion with a variation of Güneisen’s equation

$$ \frac{{{L_T} - {L_{293}}}}{{{L_{293}}}} = \frac{1}{{3a}}\;\quad \frac{{E\left( {\frac{ \odot }{T}} \right)}}{{{Q_o} - kE\left( {\frac{ \odot }{T}} \right)}} + \frac{{1 - a}}{a}\quad $$

Final values of the four parameters were obtained by minimizing the standard deviation in a least-squares analysis. The results of this study are generally in good agreement with expansion values found in the literature. Major differences, however, are observed in the comparison with x-ray diffraction studies and with extrapolated data appearing in the literature. No systematic deviations of the data from the final equation were observed. A comparison of the results of this study with data found in the literature will be presented.