Lattice parameters of rutile and anatase were determined from 30" to 6 5 0 T and from 28O to 712OC, respectively, using a high-temperature powder camera. These data were used to evaluate the coefficients of thermal expansion of rutile and anatase. The temperature dependence of the coefficients, aI, and parallel and perpendicular to the principal axis, respectively, are represented by the equations:Rutile: a , , = 8.816 X The relative magnitudes of the coefficients of thermal expansion of these polymorphs are explained in terms of the interionic distances.
The lattice parameters of Ni3AI have been determined accurately for the temperature range 25 to 594 "C by a high-temperature x-ray powder diffraction method. These data are used to evaluate the coefficients of thermal expansion at various tmperatures. The thermal expansion of Ni3AI has also been measured from 25 to 1000 "C by a dilation method. The thermal expansion values obtained by the dilation method are in good agreement with those determined by the x-ray diffraction method at around room temperature, but the agreement deteriorates with increase in temperature.
X-ray measurements of the Debye characteristic temperatures eM and the coefficient of thermal expansion for the Pd-Ag-Au ternary-alloy system are presented. The integrated intensities of Bragg reflections and lattice parameters were measured in the temperatures range 80-298'K. For all the alloys, the predominant lattice disturbance was due to thermal vibrations. No Significant effect due to static displacements was found. Debye temperatures were found to range from a low of 184'K for gold to a high of 290'K for palladium, with silver intermediate at 226 'K. The mean coefficient of thermal expansion was found to range from 9.8 x 10-6 for palladium to 17.9 x 10-6 for silver. Griineisen's relationship between the meansquare atomic-vibration amplitude and the thermal expansion for cubic solids has been found to be valid for these alloys and the constant YZ2 was found to be 0.167. The results suggest that a general weakening of the cohesive forces might be taking place as the smaller palladium atoms are replaced by silver and/or gold in the solid solution.
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