Thermal Displacement in Copper-Gold Alloys
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The thermal displacements and Debye temperatures are determined for single crystals of copper and Cu-Au solid solutions including Cu3Au of four degrees of long range order (0.0, 0.53; 0.8, .98). Other solid solution compositions studied were .91Cu-.09Au and .2Cu-.8Au. At the .91Cu-.09Au composition a one week anneal produced a nonequilibrium structure. After a one month anneal the thermal displacements decreased to a value nearly equal to the value for pure Cu. The thermal displacements in the quenched .75Cu-.25Au crystal were also nearly equal to the value for pure Cu, but the thermal displacements increased as the Cu3Au crystal approached the equilibrium condition of full order. In the Cu3Au crystals, which were partially or fully ordered, the thermal displacements of the individual Cu and Au atoms were determined. It was observed that the vibration amplitudes of the Cu atoms are not isotropic in this diatomic cubic crystal. The vibrations of the Au atoms are equal in the  and  directions within experimental uncertainty. Also, the thermal displacements decrease as the crystal is changed from fully ordered to fully disordered. This is consistent with calculations of the vibrational spectrum for ordered and disordered Cu3Au. The static displacements for the partially ordered S = .80 crystal were also determined from the same experiments as the thermal displacements. An Einstein model was developed to calculate thermal displacements and Einstein frequencies from interatomic potentials. The calculated thermal displacements are 10 to 20 percent less than the experimental values. This is due to the simplifying assumptions in the model. The model calculation and the experimental results do agree on the changes in the thermal displacements with alloying. The Einstein model is also used to calculate the vibrational entropy in alloys.