Effect of Thermal Motion on the X-Ray Reflectivity of Quartz

Abstract

Two characteristic temperatures for quartz were determined which, when substituted into the Debye-Waller formula and then used to compute the ratios of temperature corrected integrated reflection coefficients of various pairs of sets of Bragg planes, gave results in best agreement with experimentally determined ratios. These temperatures are 508±16°K in the direction of the trigonal axis and 452±15°K in any perpendicular direction. Corresponding values obtained from an approximate formula relating characteristic temperatures with elastic constants were 448° and 398°K, respectively. The fairly good agreement between the characteristic temperatures obtained by the two methods seems to support the conjecture that the modification of the Debye theory used gives a fairly good approximate description of the effect of thermal motion on the x-ray reflectivity of quartz. Calculations based upon the experimentally determined characteristic temperatures indicate that when Bragg spacings are less than about 0.7 A, the reflectivity of quartz at room temperature is reduced to less than half the value that would be obtained if the atoms were rigidly fixed.