Crystal dynamics and specific heat of copper doped alloys

Vibration of substitutional impurities in solids has been discussed using a Green's function technique. Within the general scheme of crystal impurity problem an expression has been derived for the change in lattice specific heat due to the presence of substitutional impurities. In the low concentration limit the theory has been employed to discuss the low temperature specific heat of α-phase alloys based on copper. Experimental results of low temperature lattice specific heat in Cu:Zn, Cu:Ga and Cu:Ge have been successfully explained and thus local variation in force constants between substitutional impurity and host atoms has been estimated taking nearest neighbour approximation. The lattice dynamics of pure crystal has been discussed in the harmonic approximation using Kreb's model; the eigen frequencies and eigen vectors are utilized to calculate the Green's function pertaining to the problem. The importance of force constant changes in addition to the changes in the mass at the impurity site has been brought out and it has been established that the enhanced or reduced (in some alloys) specific heats are dominated by force constants changes and in fact are very much sensitive to these changes. It has been found that at very low temperatures, the contribution to lattice specific heat due to even parity symmetry modes A1g, Eg, F1g and F2g are quite significant and, in fact, dominate over that of Fsub(1u) symmetry mode in which the impurity atom moves. However, it is observed that at higher temperatures more impurity modes appearing in the Fsub(1u) irreducible representation are excited and their contribution dominates over all others. (K.B.)