The Measurement of the Lattice Expansions and Debye Temperatures of Titanium and Silver by X-ray Methods

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Abstract
A high temperature diffractometer has been used to determine the lattice spacing-temperature relations for both α- and β-titanium. For α-titanium, the mean coefficients of thermal expansion over the temperature range 0-600°C are 9.55 x 10-6 deg-1 for the a spacing, and 10.65 x 10-6 deg-1 for the c spacing; for β-titanium, the mean expansion coefficient over the temperature range 900-1070°C is about 12.0 x 10-6 deg-1. The temperature variation of the (peak) intensities of diffracted powder lines for silver is in agreement with Debye-Waller theory, after applying a correction due to Paskin, and corresponds to a Debye temperature of 197°k. Corresponding results for α-titanium indicate that the Debye temperrature is about 270° ± 30°k. Analysis of the line shapes of cold-worked titanium indicates an appreciable density of basal plane stacking fault.