Calculation of the Lattice Specific Heat of Very Dilute Al:Ag Alloys

A detailed study of the effects of force-constant changes due to impurity atoms on the lattice specific heat has been made in very dilute aluminum-silver alloys. Numerical computations have been performed for ${\mathrm{Al}}_{99.50}$ ${\mathrm{Ag}}_{0.50}$ and ${\mathrm{Al}}_{99.05}$ ${\mathrm{Ag}}_{0.95}$ alloys. Almost all of the of the contribution to the specific heat arises because of $F_{1u}$ resonance modes and the contribution increases with increase in temperature. A very good agreement between the theory and the experiment has been observed in both the alloys. The use of an effective force constant which has been defined earlier is found to be very appropriate in making simple calculations for the specific heat. The observed discrepencies between the results obtained in the frame work of effective force constant and those obtained in a realistic manner are seen to be less than 12% at very low temperatures and are even smaller at comparatively higher temperatures.