X-Ray Determinations of the Debye Temperatures and Thermal Expansions for the Pd–Ag–Au System

Abstract

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.

X-ray diffraction study of the structure and thermal parameters of the ternary Au–Ag–Pd alloys

“…1 The scientific understanding and technological importance of thermal expansion of the alloys has lead to the measurement of this property for various materials [3], e.g. the binary Au-Ag [4], Au-Pd [4][5][6][7] and Ag-Pd [4,[8][9] alloys, but the experimental data on the ternary Au-Ag-Pd alloys is rather limited [3][4].…”

“…Naidu and Houska in the pioneer work, studied the variations of the structure of highly deformed fillings of the Au-Ag-Pd alloys in order to explain the hardening mechanisms [3][4]. However, they have reported the values of the lattice parameter and the coefficient of thermal expansion on a few compositions only in the temperature range of 80-298 K. Later, the structure and thermal expansion of these alloys was investigated by Venudhar et al by the use of graphical extrapolation method [10][11].…”

A simple interpolation formula for the Debye temperatures of disordered alloys

“…Thus, there is a good chance of some kind of error in the measurement for x=,~. Naidu & Houska (1971) and as predicted by equation ( …”

“…To illustrate this for a ternary system, average values of r in Table 1 for Ag-Au, Ag-Pd, and Au-Pd were used in (8) with the pure-metal Debye temperatures to predict the Debye temperatures for the ternary alloys for which Naidu & Houska (1971) measured 0. The predicted and measured values of the Debye temperature are given in Table 2.…”

“…On balance, then, ~-does seem to reflect the strength of the unlike-atom force constant relative to the average of the likeatom force constants. Naidu & Houska (1971). (2) Shirley, Lally, Thomas & Fisher (1975).…”