An experimental investigation of dechanneling in copper single crystals

This investigation comprises a comparison of experimental and theoretical dechanneling of MeV protons in copper single crystals. Dechanneling results when an ion's transverse energy increases to the value where the ion can undergo small impact parameter collisions with individual atoms. Depth dependent dechanneling rates were determined as functions of lattice temperature, ion beam energy and crystal axis orientation. Ion beam energies were IMeV and 2MeV,temperatures ranged from 35 K to 280 K and the experiment was carried out along both the (lOa) and <110) axes. Experimental data took the form of aligned and random Rutherford backscattered energy spectra. Dechanneling rates were extracted from these spectra using a single scattering theory that took explicit account of the different stopping powers experienced by channeled and dechanneled ions and also included a correction factor to take into account multiple scattering effects along the ion's trajectory. The assumption of statistical equilibrium and small angle scattering of the channeled ions allows a description of dechanneling in terms of the solution of a diffusion like equation which contains a so called diffusion function. The diffusion function is shown to be related to the increase in average transverse energy. Theoretical treatments of increase in average transverse energy due to collisions of projectiles with channel electrons and thermal perturbations in the lattice potential are reviewed. Using the diffusion equation and the electron density in the channel centre as a fitting parameter dechanneling rates are extracted. Excellent agreement between theory and experiment has been demonstrated. Electron densities determined in the fitting procedure appear to be realistic. The surface parameters show themselves to be good indicators of the quality of the crystal.

Brillouin spectroscopy : measurement of elastic and photoelastic constants of some alkali holide crystals

The assembly and testing of apparatus for the measurement of elastic and photoelastic constants by Brillouin scattering, using a Fabry-Perot interferometer and with argon ion laser excitation is described. Such measurements are performed on NaCI, KBr and LiF using the A = 488.0 nm laser line. The elastic constants obtained here are in very good agreement with the ultrasonic data for all three materials. The discrepancy between ultrasonic and hypersonic sound velocities which was reported by some authors for KBr and LiF is not confirmed, and the elastic constants obtained for LiF are the most accurate to date. Also, the present photoelastic constants are in good agreement with the data obtained by ultrasonic techniques for all three crystals. The results for the KBr and LiF crystals constitute the first set of photoelastic constants obtained for these materials by Brillouin spectroscopy. Our results for LiF are the best available to date.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

Some electrical properties of semi-conductor crystals / |nPhyu Phyu Khin. -- 260 St. Catharines, Ont. : [s. n.],

SiC and AtB 12 have been prepared and their resistivities and Hall voltages measured. The resistivities and Hall voltages were measured by the Van der Pauw's method, using spring loaded tungsten contacts. In this method, the major requirement is to have samples of plane parallel surfaces of arbitrary shape with four small contacts at the circumference. Similar measurements were made with a number of SiC crystals obtained from the Norton Research Corporation (Canada)-Ltd., Carolina Aluminum Co., Exolon Co. and Carborundum Co. It was found that resistivity, carrier concentration and mobility of ions depend on the type of impurity. AtB 12 was prepared from the melt containing At and B in the ratio of 4:1. They formed amber-colour pseudo tetragonal crystals. As the crystals obtained were small for electrical measurements, hot pressed lumps have been used to measure their resistivity.

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.

Declaration from John Brown, culler who states that there are 1167 pieces which equal 75704 cubic feet of timber to be culled

Declaration from John Brown, culler who states that there are 1167 pieces which equal 75704 cubic feet of timber to be culled, April 9, 1878.