Lattice dynamics and specific heat of Al-Si and Al-Ge solid solutions

A simplified treatment has been proposed to study quantitatively the lattice dynamics of Al-Si and Al-Ge alloy systems by solid-solutioning under pressure. The volume and electron density effects on the lattice dynamics of the pure constituents aluminium, silicon or germanium are considered, and the phonon dispersion relations of the local and band modes were obtained. Then, the concentration dependence of the local and band mode frequencies were calculated for the Al_1–x Si _x and Al_1–x Ge _x systems. Using the local and band mode frequencies, the lattice specific heat at constant volume was determined theoretically, and results obtained for the temperature-dependent specific heat of matrix aluminium were found to be in good agreement with the experimental data. The concentration dependence of the specific heat could then be predicted quantitatively for Al_1–x Si _x and Al_1–x Ge _x alloy systems.     

Lattice dynamics and molecular dynamics simulation of complex materials

In this article we briefly review the lattice dynamics and molecular dynamics simulation techniques, as used for complex ionic and molecular solids, and demonstrate a number of applications through examples of our work. These computational studies, along with experiments, have provided microscopic insight into the structure and dynamics, phase transitions and thermodynamical properties of a variety of materials including fullerene, high temperature superconducting oxides and geological minerals as a function of pressure and temperature. The computational techniques also allow the study of the structures and dynamics associated with disorder, defects, surfaces, interfaces etc.     

Lattice dynamics and thermal expansion of lutetium

Dispersion relations, the lattice specific heat, third-order elastic constants, and the temperature variation of the lattice volume Grüneisen function of lutetium are determined on the basis of Keating's method. The lattice heat capacity is calculated using the frequency distribution function g(), and compared with the experimental values of Gerstein et al. The third-order elastic (TOE) constants are calculated using two anharmonic parameters. The low- and high-temperature limits _L and _H of the lattice thermal expansion are evaluated. The variation of lattice volume Grüneisen function with tempera- ture is presented. The pressure dependence of the lattice parameters and the compression ratio V/V ₀ of Lu are calculated using the theoretical TOE constants and Thurston's extrapolation formula.     

An interatomic potential for Ne2 derived from solid state data

Two sets of parameters for the Morse part of a Morse-Spline-van der Waals (MSV) interatomic potential appropriate to Ne ₂ have been derived using solid state data. The first assumes pairwise additivity of the interatomic potential, while the second assumes that the nonpairwise additivity can be approximated by the Axilrod-Teller-Muto three-body force. The second potential appears to be in better agreement with recent high-precision, low-temperature heat-capacity measurements on solid Ne.Issued as NRCC # 13328.Work supported by the Deutchesforsgemeinschaft.     

Lattice dynamics and the compression curves of cobalt

The phonon dispersion relations along symmetry directions in cobalt have been obtained using a nearest neighbor central force model for hcp lattices. The third-order elastic (TOE) constants obtained in this model have been used to determine the changes in the lattice parameters due to high pressure, using Thurston's extrapolation formula. The variation of volume with pressure has been calculated using Murnaghan's logarithmic equation. The agreement of the calculated values with the experimental shock wave data up to 1.2 Mbar pressure is remarkably good.Supported in part by the Council of Scientific and Industrial Research, Government of India, through the grant of a Research Fellowship to A.R.     

Channeling in solid Xe, Ar and Ne direct dark matter detectors

The channeling of the ion recoiling after a collision with a WIMP changes the ionization signal in direct detection experiments, producing a larger scintillation or ionization signal than otherwise expected. We give estimates of the fraction of channeled recoiling ions in solid Xe, Ar and Ne crystals using analytic models produced since the 1960s and 1970s to describe channeling and blocking effects.     

Studies of the dielectric constant in solid H2,4He,and Ne

Measurements of the static dielectric constant and of the resulting polarizability _CM defined by the Clausius-Mosotti relation are reported for several molecular solids under conditions of quasiconstant density. The range of measurements was between 0.4 and about 15 K, and pressures up to about 1 kbar were used. In solid H₂, the changes of as a function of ortho concentration are reported at 4.2 and 12 K, from which it is concluded that [(ortho)–(para)]/0.005, which is approximately 2 1/2 times larger than in the liquid phase. Furthermore the temperature change of _CM is studied for various densities at comparable ortho concentrationsX. Particular attention is paid to the orientational order-disorder transition in solid H₂ withX0.65, where _CM shows an abrupt change that appears to be a function ofX, density, and thermal history. In general _CM is lower in the ordered (cubic) phase than in the disordered (hexagonal) phase. The temperature change of _CM in almost pure para-H₂, measured between 4 and 0.4 K, is presented and is compared with other recently reported experiments. It is concluded that the mechanism that produces the change of _CM withT and at the order-disorder phase transition is not understood. In solid Ne, measurements of _CM are reported for one sample assumed to be at zero pressure and one where the density is quasiconstant. There is a strong temperature dependence in _CM for the former above 5 K (in agreement with previous findings), while for the latter _CM appears to be constant within the uncertainties introduced by strain-induced hysteresis effects. The sample of solid⁴He, investigated between its melting point at 4.3 and 0.8 K at constant density, shows a very weak temperature dependence of _CM, which is also consistent with previously reported measurements.Research supported by a grant of the U.S. Army Research Office (AROD) and from a contract with the Office of Naval Research. A preliminary account of this research was given inBull. Am. Phys. Soc. 20, 672 (1975).     

Triple-Point Temperatures of 20Ne and 22Ne

Interest in the triple points of neon isotopes has recently arisen as a result of the multi-institute project to understand how variations in the isotopic composition of natural neon influence the triple-point temperature of a particular sample. Given the challenges in determining with sufficiently low uncertainty both the relative isotopic concentrations, particularly of ²²Ne relative to ²⁰Ne, and the temperature differences among cells filled from different gas sources in order to determine the sensitivity coefficient with adequate confidence, modeling of the isotopic influence becomes an attractive alternative for correcting the triple points of ??natural?? neon samples to a common composition. The modeling requires, among other things, knowledge of the triple-point temperatures of ²⁰Ne and ²²Ne. The triple points of these pure neon isotopes have utility in their own right as secondary reference temperatures on the ITS-90, and one or both of these could replace ??natural?? neon in a revised International Temperature Scale or approximation to the ITS. The neon isotope triple-point temperatures (on the IPTS-68) reported by Furukawa, Kemp, and Sakurai in various publications from 1972 to 1986 predate the ITS-90, and so there is utility in contemporary measurements (on the ITS-90) with gas samples of recent production. At NRC, we find the triple point of ²⁰Ne to be at 24.54230?K (13.80?mK below the triple point of ??natural?? neon) and that of ²²Ne to be at 24.68889?K (132.79?mK above the triple point of ??natural?? neon), assuming the reference sample of ??natural?? neon realizes the ideal ITS-90 temperature of 24.5561 K.     

Lattice dynamics of colloidal crystals during photopolymerization of acrylic monomer matrix

The photoinitiated bulk polymerization process, which has been used recently in the manufacture of solid optical diffraction filters, is examined to understand the dynamics of both the crystalline colloidal arrays (CCA) and the host monomer species. Our analysis indicates that volume shrinkage of the monomer, changes in the dielectric properties of the monomer, and inhomogeneities of polymerization reaction rate across the dispersion during the polymerization process, are the major contributors for observed lattice compression and lattice disorder of the CCA of silica spheres in polymerized acrylic/methacrylic ester films. The effect of orientation of photocell with respect to the radiation source on Bragg diffraction of CCA indicated the presence of convective stirring in the thin fluid system during the photopolymerization that deleteriously affects the periodic array structures. To devise reproducible and more efficient optical filters, experimental methods to minimize or eliminate convective instabilities in monomeric dispersions during polymerization are suggested. © 1998 Chapman & Hall     

Lattice dynamics,thermal expansion,and bulk modulus of ruthenium

The lattice dynamics, third-order elastic (TOE) constants, and the temperature variation of the volume Grüneisen function of ruthenium have been calculated using the nearest neighbor central interaction model for hexagonal metals proposed by Srinivasan and Ramji Rao. The TOE constants have been employed to calculate the low-temperature limit of the lattice thermal expansion, the Anderson-Grüneisen (AG) parameter , and the second Grüneisen constantq of ruthenium. has the value 2.79 for ruthenium. The high-temperature limit has the value 3.31, which agrees well with the experimental value 3.25 obtained from thermal expansion and specific heat data of ruthenium. Anderson's theory has been used to explain the temperature dependence of the bulk modulus of ruthenium up to 923 K and has been compared with the experimental values obtained from the elastic constant data of Fisher and Dever. The variation of the lattice parameters of ruthenium with hydrostatic pressure up to 400 kbar has been calculated from its TOE constant data using the extrapolation formula of Thurston and has been compared with the experimental results of Clendenen and Drickamer. The fit is remarkably good.     

Lattice dynamics of layered ferroelectric semiconductor compound TlGaSe2

We present the first-principles calculation of the lattice dynamics of the TlGaSe₂ ternary semiconductor having highly anisotropic crystal structure. Calculations have been performed using open-source code ABINIT on the basis of the density functional perturbation theory within the plane-wave pseudopotential approach. Results on the frequencies of phonon modes in the centre of Brilloin zone and the dispersion of transverse shear acoustic branch of the phonon spectra agree well with the experimental data on Raman scattering, infrared reflectivity and ultrasound wave propagation in TlGaSe₂. The calculated and experimental temperature dependencies of heat capacity are in a good agreement up to the room temperature. Along the layer, the low-frequency acoustic branch displays the bending wave behavior which is characteristic of the layer crystal structures.     

Impact dynamics with applications to solid particle erosion

A reformulation and solution is presented of the equations of impulse and momentum for an arbitrarily shaped rigid body striking a flat massive surface. The model makes use of the classical coefficient of restitution, e, and tangential coefficient, μ. The latter is defined as the ratio of the tangential to normal impulse components. It is shown that a distinction between μ and friction coefficients, f, is necessary for a proper interpretation of impact data.The expression of impact energy loss is placed into a particularly convenient form. Comparisons are made of this impact model to others from the field of solid particle erosion and wear.     

Lattice dynamics of (Ba/K)BiO3

The Lattice dynamics of Ba_.6K_.4BiO₃ was investigated by inelastic neutron scattering on a superconducting single crystal (T _c =26 K (midpoint)). At low frequencies the dispersion curves are very similar to those observed in BaPb_.75Bi_.25O₃. Differences were found in the bond bending vibrations of the BiO₆ octahedra which indicate that the binding in the K-doped compound is more ionic. Rather anomalous features were observed in the high frequency Bi-O bond stretching vibrations which resemble those observed in the high T _c cuprates La_1.85Sr_.15CuO₄ and YBa₂Cu₃O₇. The observed frequency shifts are interpreted as the consequence from a strong electron phonon coupling. The data are compared to the results obtained on non superconducting Ba_.98K_.02BiO₃.     

Lattice dynamics in VO2 near the metal-insulator transition

We present a comprehensive experimental study of the lattice dynamics in the vicinity of the metal-insulator transition in VO₂ by means of combined use of Raman spectroscopy and ultrasonic microscopy. Single crystalline samples of high quality particularly allow quite a complete determination of all Raman modes in the insulating phase at the Γ-point and the observation of an optical soft mode. In addition, the elastic behavior has been successfully investigated by measuring the propagation velocity of ultrasonic surface waves microscopically excited in various crystal directions. Our study reveals a striking coincidence of strong lattice softening attributable to certain acoustic branches and the occurrence of the optical soft mode, which precedes the metal-insulator transition over more than 100 K on approaching the critical temperature.     

The temperature dependence of the dielectric constant in solid H2, D2,4He,and Ne

The dielectric constant ε of solid hexagonal close-packed H₂ (X?0), H₂(X?0.7), D₂(X=0.33), and He ⁴ at constant volume and of H₂(X=0.75) and Ne at saturated vapor pressure is studied as a function of temperature between 1.17 and 10 K. HereX is the fraction of molecules with angular rotational momentumJ=1, the fraction 1?X havingJ=0. These are the first reported measurements on van der Waals solids at constant volume. The experiments were carried out using a thick-walled capacitance cell, the measurement frequency being 14 MHz. The observed changes of ε withT are expressed in terms of the effective polarizability α_CM defined by the Clausius-Mosotti relation. A reduced polarizability α*=α_CM (T)/α_CM (T=1.17 K) is presented as a function of temperature. The initial purpose of the measurements was to observe the effect of rotational ordering of the(J=1) molecules in H ₂ , to be detected by a change in polarizability, as suggested by A. B. Harris. With increasing temperature it was found that α_CM decreased of the order of 0.1% for H ₂ and D ₂ . Also, differences were found between H₂(X=0) and H₂(X=0.75), which are briefly discussed. For He ₄ , α_CM decreased by about 3×10 ^?5 between 1.17 K and the melting point, 3.8 K. An analysis of the results showed that the temperature variation of α_CM could not be caused by the effect of lattice vibrations. Also, a simple calculation shows that the rearrangement of molecular positions in H ₂ and D ₂ at constant volume would have to be quite substantial to account for the observed temperature change in α_CM, which change is therefore not understood. The dielectric constant of Ne was measured at saturated vapor pressure and corrections were made to obtain the change of α_CM at constant volume. Rather different results were obtained for Ne than for the other solids: α_CM rose sharply with temperature, and this behavior also is not understood. Measurements of the diectric constant of H₂(X=0) and H₂(X=0.73) near the melting curve showed that the polarizability α_CM is the same within 0.1% in both the liquid and the solid phases. In the solid and liquid phases the density differences between H₂(X=0) and H₂(X=0.75) and also the differences in the respective melting pressures are in good agreement with the previous published work.     

Lattice dynamics and phonon dispersion in Hg2Br2 model ferroelastic crystals

Interatomic force constants have been determined, acoustic and optical phonon frequencies have been calculated, phonon dispersion curves have been constructed, and the density of states in the phonon spectrum has been obtained for Hg₂Br₂ model ferroelastic crystals. The effect of hydrostatic pressure on the acoustic and optical phonon frequencies and their dispersion has been theoretically analyzed. It is established that an increase in the pressure leads to significant softening of the slowest acoustic TA branch (soft mode) at the X point of the Brillouin zone, which agrees with the phenomenological Landau theory of phase transitions and is consistent with the available experimental data.     

Lattice dynamics of the Zn-Mg-Sc icosahedral quasicrystal and its Zn-Sc periodic 1/1 approximant

Quasicrystals are long-range-ordered materials that lack translational invariance, so the study of their physical properties remains a challenging problem. Here, we have carried out inelastic-X-ray- and neutron-scattering experiments on single-grain samples of the Zn-Mg-Sc icosahedral quasicrystal and of the Zn-Sc periodic cubic 1/1 approximant, with the aim of studying the respective influence of the local order and of the long-range order (periodic or quasiperiodic) on lattice dynamics. Besides the overall similarities and the existence of a pseudo-gap in the transverse dispersion relation, marked differences are observed, the pseudo-gap being larger and better defined in the approximant than in the quasicrystal. This can be qualitatively explained using the concept of a pseudo-Brillouin-zone in the quasicrystal. These results are compared with simulations on atomic models and using oscillating pair potentials, and the simulations reproduce in detail the experimental results. This paves the way for a detailed understanding of the physics of quasicrystals.     

Spin dynamics in U2D2 solid3He

Pulsed NMR experiments have been performed on U2D2 solid³He with a single domain at high magnetic fields. It was found that the frequency of the free induction signal changed with time. In some cases, a large negative frequency shift of about 2 kHz from the Larmor frequency was observed some time after the rf pulse, after which frequency returned to that observed for a small tipping angle. The tipping-angle-dependent frequency shift, which was taken to be the precession frequency immediately following the rf pulse, agreed with Namaizawa's theory. The free induction signal showed a decay behavior similar to that of superfluid³He-A. This can be attributed to the instability of the uniform precession due to the creation of spin wave modes, but does not agree with the instability criterion predicted by Ohmi et al. and Shopova.     

Real‐time direct integration of reduced solid dynamics equations

A new method is developed here for the real‐time integration of the equations of solid dynamics based on the use of proper orthogonal decomposition (POD)–proper generalized decomposition (PGD) approaches and direct time integration. The method is based upon the formulation of solid dynamics equations as a parametric problem, depending on their initial conditions. A sort of black‐box integrator that takes the resulting displacement field of the current time step as input and (via POD) provides the result for the subsequent time step at feedback rates on the order of 1 kHz is obtained. To avoid the so‐called curse of dimensionality produced by the large amount of parameters in the formulation (one per degree of freedom of the full model), a combined POD–PGD strategy is implemented. Examples that show the promising results of this technique are included. Copyright © 2014 John Wiley & Sons, Ltd.