Third order elastic constants of bcc Cu-Al-Ni

We have measured the changes in the ultrasonic wave velocity, induced by the application of uniaxial stresses in a Cu-Al-Ni single crystal. From these measurements, the complete set of third-order elastic constants has been obtained. The comparison of results for Cu-Al-Ni with available data for other Cu-based alloys has shown that all these alloys exhibit similar anharmonic behavior. By using the measured elastic constants in a Landau expansion for elastic phase transitions, we have been able to give an estimation of the value of a fourth-order elastic constants combination. The experiments have also shown that the application of a stress in the [001] direction, reduces the material resistance to a (110)[110] shear and thus favors the martensitic transition.

Thermal resonance in signal transmission

We use temperature tuning to control signal propagation in simple one-dimensional arrays of masses connected by hard anharmonic springs and with no local potentials. In our numerical model a sustained signal is applied at one site of a chain immersed in a thermal environment and the signal-to-noise ratio is measured at each oscillator. We show that raising the temperature can lead to enhanced signal propagation along the chain, resulting in thermal resonance effects akin to the resonance observed in arrays of bistable systems.

Energy relaxation in nonlinear one-dimensional lattices

We study energy relaxation in thermalized one-dimensional nonlinear arrays of the Fermi-Pasta-Ulam type. The ends of the thermalized systems are placed in contact with a zero-temperature reservoir via damping forces. Harmonic arrays relax by sequential phonon decay into the cold reservoir, the lower-frequency modes relaxing first. The relaxation pathway for purely anharmonic arrays involves the degradation of higher-energy nonlinear modes into lower-energy ones. The lowest-energy modes are absorbed by the cold reservoir, but a small amount of energy is persistently left behind in the array in the form of almost stationary low-frequency localized modes. Arrays with interactions that contain both a harmonic and an anharmonic contribution exhibit behavior that involves the interplay of phonon modes and breather modes. At long times relaxation is extremely slow due to the spontaneous appearance and persistence of energetic high-frequency stationary breathers. Breather behavior is further ascertained by explicitly injecting a localized excitation into the thermalized arrays and observing the relaxation behavior.

Phonon spectra and thermodynamic properties of rare gas solids based on empirical and semi-empirical (ab initio) two-body potentials : a comparative study /

We study the phonon dispersion, cohesive and thermal properties of raxe gas solids Ne, Ar, Kr, and Xe, using a variety of potentials obtained from different approaches; such as, fitting to crystal properties, purely ab initio calculations for molecules and dimers or ab initio calculations for solid crystalline phase, a combination of ab initio calculations and fitting to either gas phase data or sohd state properties. We explore whether potentials derived with a certain approaxih have any obvious benefit over the others in reproducing the solid state properties. In particular, we study phonon dispersion, isothermal ajid adiabatic bulk moduli, thermal expansion, and elastic (shear) constants as a function of temperatiue. Anharmonic effects on thermal expansion, specific heat, and bulk moduli have been studied using A^ perturbation theory in the high temperature limit using the neaxest-neighbor central force (nncf) model as developed by Shukla and MacDonald [4]. In our study, we find that potentials based on fitting to the crystal properties have some advantage, particularly for Kr and Xe, in terms of reproducing the thermodynamic properties over an extended range of temperatiures, but agreement with the phonon frequencies with the measured values is not guaranteed. For the lighter element Ne, the LJ potential which is based on fitting to the gas phase data produces best results for the thermodynamic properties; however, the Eggenberger potential for Ne, where the potential is based on combining ab initio quantum chemical calculations and molecular dynamics simulations, produces results that have better agreement with the measured dispersion, and elastic (shear) values. For At, the Morse-type potential, which is based on M0ller-Plesset perturbation theory to fourth order (MP4) ab initio calculations, yields the best results for the thermodynamic properties, elastic (shear) constants, and the phonon dispersion curves.

An analysis of decoupling procedures in generating thermal Green's functions of O([lambda]â ´) by the Zubarev equation of motion method

The Zubarev equation of motion method has been applied to an anharmonic crystal of O( ,,4). All possible decoupling schemes have been interpreted in order to determine finite temperature expressions for the one phonon Green's function (and self energy) to 0()\4) for a crystal in which every atom is on a site of inversion symmetry. In order to provide a check of these results, the Helmholtz free energy expressions derived from the self energy expressions, have been shown to agree in the high temperature limit with the results obtained from the diagrammatic method. Expressions for the correlation functions that are related to the mean square displacement have been derived to 0(1\4) in the high temperature limit.

An application of cell-cluster theory to a rare gas crystal /|n[by] K. Westera. - 260 St. Catharines [Ont.] : Dept. of Physics, Brock University,

The Lennard-Jones Devonshire 1 (LJD) single particle theory for liquids is extended and applied to the anharmonic solid in a high temperature limit. The exact free energy for the crystal is expressed as a convergent series of terms involving larger and larger sets of contiguous particles called cell-clusters. The motions of all the particles within cell-clusters are correlated to each other and lead to non-trivial integrals of orders 3, 6, 9, ... 3N. For the first time the six dimensional integral has been calculated to high accuracy using a Lennard-Jones (6-12) pair interaction between nearest neighbours only for the f.c.c. lattice. The thermodynamic properties predicted by this model agree well with experimental results for solid Xenon.

A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

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.

On the formulation and the calculation of the harmonic contributions to the Debye-Waller factor in metals (sodium)

The algebraic expressions for the anharmonic contributions to the Debye-Waller factor up to 0(A ) and 0 L% ) £ where ^ is the scattering wave-vector] have been derived in a form suitable for cubic metals with small ion cores where the interatomic potential extends to many neighbours. This has been achieved in terms of various wave-vector dependent tensors, following the work of Shukla and Taylor (1974) on the cubic anharmonic Helmholtz free energy. The contribution to the various wave-vector dependent tensors from the coulomb and the electron-ion terms in the interatomic metallic potential has been obtained by the Ewald procedure. All the restricted multiple whole B r i l l o u i n zone (B.Z.) sums are reduced to single whole B.Z. sums by using the plane wave representation of the delta function. These single whole B.Z. sums are further reduced to the •%?? portion of the B.Z. following Shukla and Wilk (1974) and Shukla and Taylor (1974). Numerical calculations have been performed for sodium where the Born-Mayer term in the interatomic potential has been neglected because i t is small £ Vosko (1964)3 • *n o^er to compare our calculated results with the experimental results of Dawton (1937), we have also calculated the r a t io of the intensities at different temperatures for the lowest five reflections (110), (200), (220), (310) and (400) . Our calculated quasi-harmonic results agree reasonably well with the experimental results at temperatures (T) of the order of the Debye temperature ( 0 ). For T » © ^ 9 our calculated anharmonic results are found to be in good agreement with the experimental results.The anomalous terms in the Debye-Waller factor are found not to be negligible for certain reflections even for T ^ ©^ . At temperature T yy Op 9 where the temperature is of the order of the melting temperature (Xm) » "the anomalous terms are found to be important almost for all the f i ve reflections.

Phonon dispersion curves and atomic mean square displacement for several fcc and bcc materials

The atomic mean square displacement (MSD) and the phonon dispersion curves (PDC's) of a number of face-centred cubic (fcc) and body-centred cubic (bcc) materials have been calclllated from the quasiharmonic (QH) theory, the lowest order (A2 ) perturbation theory (PT) and a recently proposed Green's function (GF) method by Shukla and Hiibschle. The latter method includes certain anharmonic effects to all orders of anharmonicity. In order to determine the effect of the range of the interatomic interaction upon the anharmonic contributions to the MSD we have carried out our calculations for a Lennard-Jones (L-J) solid in the nearest-neighbour (NN) and next-nearest neighbour (NNN) approximations. These results can be presented in dimensionless units but if the NN and NNN results are to be compared with each other they must be converted to that of a real solid. When this is done for Xe, the QH MSD for the NN and NNN approximations are found to differ from each other by about 2%. For the A2 and GF results this difference amounts to 8% and 7% respectively. For the NN case we have also compared our PT results, which have been calculated exactly, with PT results calculated using a frequency-shift approximation. We conclude that this frequency-shift approximation is a poor approximation. We have calculated the MSD of five alkali metals, five bcc transition metals and seven fcc transition metals. The model potentials we have used include the Morse, modified Morse, and Rydberg potentials. In general the results obtained from the Green's function method are in the best agreement with experiment. However, this improvement is mostly qualitative and the values of MSD calculated from the Green's function method are not in much better agreement with the experimental data than those calculated from the QH theory. We have calculated the phonon dispersion curves (PDC's) of Na and Cu, using the 4 parameter modified Morse potential. In the case of Na, our results for the PDC's are in poor agreement with experiment. In the case of eu, the agreement between the tlleory and experiment is much better and in addition the results for the PDC's calclliated from the GF method are in better agreement with experiment that those obtained from the QH theory.

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.

Analysis Of The A11a22 X 11a11 And A 33a22 X 1 electronic transitions in selenocarbonyl difluoride

The absorption spectrum of F2CSe in the 18800-21900 cm-1 region has been recorded at -770 C and 220 C under the conditions of medium resolution. The responsible electronic promotion is TI* + n excitation which leads to 3A2 and lA2 excited states. Progressions in vI', v2', v3" v4' and v4" have been identified in the spectrum and have been analyzed in terms of vibronic transitions between a planar ground state and a nQnplanar excited state. The - 3 - 1 - 1 - 1 origins of the a A2 + X Al and A A2 + X Al systems were assigned to the bands at 19018 cm-l and 19689 cm-l . This has given a singlet-triplet splittl. n g lA2 - 3A2 P f 671 cm -1 The out-of-plane wagging levels were found to be anharmonic. 1 -1 Barrier heights of 2483 cm- and 2923 cm were obtained for the lA2 and 3A2 upper states from a fitting of the energy levels of a Lorentzian-quadratic function to the observed levels in the out-of-plane wagging modes. 1 3 For the A2 and A2 states nonplanar equilibrium angles of 30.10 and 31.40 have been evaluated respectively. i

Photothermal Investigations on Certain Plasma Polymerized Thin Films and Near IR Overtone Studies of Some Organic Molecules

Photothermal effect refers to heating of a sample due to the absorption of electromagnetic radiation. Photothermal (PT) heat generation which is an example of energy conversion has in general three kinds of applications. 1. PT material probing 2. PT material processing and 3. PT material destruction. The temperatures involved increases from 1-. 3. Of the above three, PT material probing is the most important in making significant contribution to the field of science and technology. Photothermal material characterization relies on high sensitivity detection techniques to monitor the effects caused by PT material heating of a sample. Photothermal method is a powerful high sensitivity non-contact tool used for non-destructive thermal characterization of materials. The high sensitivity of the photothermal methods has led to its application for analysis of low absorbance samples. Laser calorimetry, photothermal radiometry, pyroelectric technique, photoacoustic technique, photothermal beam deflection technique, etc. come under the broad class ofphotothermal techniques. However the choice of a suitable technique depends upon the nature of the sample, purpose of measurement, nature of light source used, etc. The present investigations are done on polymer thin films employing photothermal beam deflection technique, for the successful determination of their thermal diffusivity. Here the sample is excited by a He-Ne laser (A = 6328...\ ) which acts as the pump beam. Due to the refractive index gradient established in the sample surface and in the adjacent coupling medium, another optical beam called probe beam (diode laser, A= 6500A ) when passed through this region experiences a deflection and is detected using a position sensitive detector and its output is fed to a lock-in amplifier from which the amplitude and phase of the deflection can be directly obtained. The amplitude and phase of the signal is suitably analysed for determining the thermal diffusivity.The production of polymer thin film samples has gained considerable attention for the past few years. Plasma polymerization is an inexpensive tool for fabricating organic thin films. It refers to formation of polymeric materials under the influence of plasma, which is generated by some kind of electric discharge. Here plasma of the monomer vapour is generated by employing radio frequency (MHz) techniques. Plasma polymerization technique results in homogeneous, highly adhesive, thermally stable, pinhole free, dielectric, highly branched and cross-linked polymer films. The possible linkage in the formation of the polymers is suggested by comparing the FTIR spectra of the monomer and the polymer.Near IR overtone investigations on some organic molecules using local mode model are also done. Higher vibrational overtones often provide spectral simplification and greater resolution of peaks corresponding to nonequivalent X-H bonds where X is typically C, N or O. Vibrational overtone spectroscopy of molecules containing X-H oscillators is now a well established tool for molecular investigations. Conformational and steric differences between bonds and structural inequivalence ofCH bonds (methyl, aryl, acetylenic, etc.) are resolvable in the higher overtone spectra. The local mode model in which the X-H oscillators are considered to be loosely coupled anharmonic oscillators has been widely used for the interpretation of overtone spectra. If we are exciting a single local oscillator from the vibrational ground state to the vibrational state v, then the transition energy of the local mode overtone is given by .:lE a......v = A v + B v2 • A plot of .:lE / v versus v will yield A, the local mode frequency as the intercept and B, the local mode diagonal anharmonicity as the slope. Here A - B gives the mechanical frequency XI of the oscillator and B = X2 is the anharmonicity of the bond. The local mode parameters XI and X2 vary for non-equivalent X-H bonds and are sensitive to the inter and intra molecular environment of the X-H oscillator.

Third order elastic constants of bcc Cu-Al-Ni

We have measured the changes in the ultrasonic wave velocity, induced by the application of uniaxial stresses in a Cu-Al-Ni single crystal. From these measurements, the complete set of third-order elastic constants has been obtained. The comparison of results for Cu-Al-Ni with available data for other Cu-based alloys has shown that all these alloys exhibit similar anharmonic behavior. By using the measured elastic constants in a Landau expansion for elastic phase transitions, we have been able to give an estimation of the value of a fourth-order elastic constants combination. The experiments have also shown that the application of a stress in the [001] direction, reduces the material resistance to a (110)[110] shear and thus favors the martensitic transition.