Effect of Temperature on the Intensity of X-Rays Scattered by Powdered Sodium Fluoride

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Abstract
The ratio of the integrated intensities of a number of regularly reflected x-ray lines from powdered sodium fluoride crystals at room and liquid air temperatures has been studied by means of a photographic method. The results of the experiments show that the ratio varies with the angle as predicted by the Debye-Waller formula. The characteristic temperature of sodium fluoride was found to be equal to 442°K. This value agrees as well as one could expect with values calculated by the Lindemann melting-point formula and the known characteristic temperatures of sodium chloride or potassium chloride crystals. Using the known structure factor of sodium fluoride atoms at room temperature and assuming zero-point or no zero-point energy the structure factors of the atoms at rest have been calculated. A comparison with the theoretical structure factors of sodium fluoride and neon (sodium fluoride atoms are neon-like) and with the known experimental structure factor of gaseous neon atoms indicates that the assumption of zero-point energy is correct. The square root of the mean square amplitude of thermal vibration of the sodium and fluorine ions at room temperature was found to be equal to 0.182A.

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