Thermodynamic properties and Debye-Waller factor of fee materials

We have calculated the equation of state and the various thermodynamic properties of monatomic fcc crystals by minimizing the Helmholtz free energy derived in the high temperature limit for the quasiharmonic theory, QH, and the lowest-order (cubic and quartic), 'A2, anharmonic terms of the perturbation theory, PT. The total energy in each case is obtained by adding the static energy. The calculation of the thermal properties was carried out for a nearest-neighbour central-force model of the fcc lattice by means of the appropriate thermodynamic relations. We have calculated the lattice constant, the thermal expansion, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the isothermal and adiabatic bulk moduli, and the Griineisen parameter, for the rare-gas solids Kr and Xe, and gold. Morse potential and modified Morse potential were each used to represent the atomic interaction for the three fcc materials. For most of the calculated thermodynamic properties from the QH theory, the results for Kr and Xe with the modified Morse potential show an improvement over the results for the Morse potential when compared with the experimental data. However, the results of the 'A 2 equation of state with the modified Morse potential are in good agreement with experiment only in the case of the specific heat at constant volume and at constant pressure. For Au we have calculated the lattice contribution from the QH and 'A 2 PT and the electronic contribution to the thermal properties. The electronic contribution was taken into account by using the free electron model. The results of the thermodynamic properties calculated with the modified Morse potential were similar to those obtained with the Morse potential. U sing the minimized equation of state we also calculated the Mossbauer recoilless fraction for Kr and Xe and the Debye-Waller factor (DWF) for Pb, AI, eu, Ag, and Au. The Mossbauer recoilless fraction was obtained for the above two potentials and Lennard-Jones potential. The L-J potential gives the best agreement with experiment for Kr. No experimental data exists for Xe. At low temperature the calculated DWF results for Pb, AI, and eu show a good agreement with experimental values, but at high temperature the experimental DWF results increase very rapidly. For Ag the computed values were below the expected results at all temperatures. The DWF results of the modified Morse potential for Pb, AI, eu and Ag were slightly better than those of the Morse potential. In the case of Au the calculated values were in poor agreement with experimental results. We have calculated the quasiharmonic phonon dispersion curves for Kr, Xe, eu, Ag, and Au. The calculated and experimental results of the frequencies agree quite well for all the materials except for Au where the longitudinal modes show serious discrepancies with the experimental results. In addition, the two lowest-order anharmonic contributions to the phonon frequency were derived using the Green's function method. The A 2 phonon dispersion curves have been calculated only for eu, and the results were similar to those of the QH dispersion curves. Finally, an expression for the Griineisen parameter "( has been derived from the anharmonic frequencies, and calculated for these materials. The "( results are comparable with those obtained from the thermodynamic definition.

J.R. Ai-6

Coarse grained sediment with clasts ranging from small to large. Clast shape ranges from angular to rounded. Lineations are abundant throughout the sample, along with rotation structures. Some comet structures and grain crushing can also be seen throughout the sample. Rotation structures can mainly be seen around larger clasts.

AI-2

Brown sediment with clasts ranging from small to large in size. Clast shape ranged from angular to rounded. Lineations and rotation structures can be seen throughout the sample. Rotation structures are common around medium and large sized clasts. Some comet structures , grain stacking, and crushed grains can also be seen in minor amounts. This sample also contains areas with clay and dark organic rich material.

AI-5

Brown sediment with clasts ranging from small to large in size. Grain shape ranges from angular to rounded. Edge-to-edge grain crushing and crushed grains are abundant throughout the sample. There are also many lineations and rotation structures present in this sample. It also contains many small patches of dark organic rich material.

AI-8

Brown sediment with clasts ranging from small to large in size. The grain shape ranges from angular to rounded. Grain crushing is abundant throughout the sample, along with rotation structures surrounding larger clasts. Lineations and and areas of clay can also be seen. A few necking structures are also present.

AI-9

Brown sediment clasts ranging from small to large in size. Clast shape ranges from angular to sub-rounded. Water escape pathways can be seen in this sample. It also contains a fine grained sand domain. Lineations are also commonly seen in this sample. Minor amounts of grain crushing and rotation structures can also be seen.

J.R AI-4

Brown sediment with clasts ranging from small to large in size. The grain shape ranges from angular to sub-rounded. Necking structures and lineations can commonly be seen throughout the sample. Rotation structures and minor amounts of grain crushing/stacking are also present.

J.R. Ai-3

Brown sediment with clasts ranging from small to large. The grain shape ranges from angular to sub-rounded. Rotation structures are abundant in this sample, along with necking structures. Some lineations and comet structures can also be seen. Crushed grains and grain stacks are present in minor amounts.

J.R. AI-5

Coarse brown sediment with clasts ranging from small to large in size. Clast shape ranges from angular to sub-rounded. Grain crushing is abundant throughout the sample. Crushed grains are present and there are also some examples of edge-to-edge grain crushing. Lineations and rotation structures can also be seen.

J.R AI-10

Brown sediment with clasts ranging from small to large. Grain shape ranges from angular to sub-rounded. Rotation structures and lineations are abundant in this sample. Comet structures and grain stacking can also be seen in this sample.