Phonon scattering from monovalent substitutional impurities in sodium chloride

This work was undertaken to investigate phonon scattering fl;'om monovalent substitutional impurities in sodium chloride using thefmal conductivity measurements as a tool. Similar work by other investi~ators on other alkali halides has shown that these defects scatter more strongly than the present theories allow. The eight impurities lithium, potassium, rubidium, silver, thallium, f1ourine, bromine, and iodine were used in this work. All of the crystals were grown in a purified argon atmosphere by the CzoGhra1ski technique. Thermal conductivity measurements were made over the temperature range 1.2°K to 300 oK. The range 1.2 to SOcK Was covered in a liquid helium cryostat using germanium resistance thermometer~ which had Peen previously calibrated against a gas thermometer and a vapol;' pressure thermometer. The range 65°K to 300 0K was covered in a liquid nitrogen cryostat using platinum resistance thermometers prev.iously calibrated against a standard. Not enough rubidium could be grown into the crystal to make a significant change in the conductivity but the other seven systems investigated showed depressions of the conductivity curves on eith~r .,side of the maximum, or on both. -2- In the present work, the Callaway analysis has been extende4 to be valid at higher temperatures by relaxing the Debye approximation. Using the shell model of the lattice, phonon data were c~lculated f~r 64000 points in the Brillouin zone. From this data a gensity of states a~9 frequency averaged group velocities were obtained which were then used in the Callaway expression. In addition, exact relaxation rates were obtained, through fprma1ism derived by Klein, within a simple model for the defect in the lat~ic~. The model assumed was a change of mass at the defe~t site and a change of force constant to the six nearest neighbors. With only nine degrees of freedom, the model allows the perturbation to be expressed as a 9 x 9 matrix. This matrix was partially diagonalized by transformin~ to symmetry coordinates. Within this new representation the perturbation matrix is diagonal in the three even parity configurations, an A1g breathing motion and two degenerate E tetragonal motions. In addition g there exists three degenerate sets of two coupled Tlu odd configurations. A transition or T matrix was determined from this p~r~urbation matrix and the Green's function matrix defined within the same representation. Exact relaxation rates were then obtained from this T matrix. The changes in force constant were obtained using a Born repulsive potential between the ions. New equilibrium positions of the surrounding ions were obtained from published literature and from a method using the static Green's function within the Alg configuration. The results for the change in force constant varied considerab~y so that this p~rameter was used as a semi-variable parameter in the analysis.The results of the analysis wer~ ~ncoura~ing cQnsid,ring the simple model and ~he fact that only one paramet~r was var~ed withi~ certain limits. Depressions of the conductivity qurve were pr¢4icted at approxi.,.. mately the same positions as found experimentally. Th~ Predicted high temperat~re depressions occurre~ at sli~htly lower temperatures than the experimental ones and the strengths did not agree very well with experiment. The degree to which the theory s~ccessfully predicted the experimental curves is related to the size of the strain field about ~he imp~rity so that it is hoped that a more sophisticateq ~pdel containing long range effects will improve the fit.U of I OnlyThesi