Showing papers on "Debye model published in 1995"
TL;DR: In this paper, it was shown that low temperature calorimetry is an efficient tool for scanning the distribution of the atomic vibrational states in real substances, and that the fractal dimension and Poisson's ratio in the elastic-isotropic multifractal model are related by a simple interdependence.
72 citations
TL;DR: In this paper, the authors have studied the elastic properties of the C15 compound NbCr{sub 2] in order to understand better the physical properties and deformation behavior of the compound, including load-deflection, thermoelastic stress, internal strain, sound velocities, dislocation core structure, and fracture toughness.
Abstract: Elastic properties of a solid are important because they relate to various fundamental solid-state phenomena such as interatomic potentials, equations of state, and phonon spectra. Elastic properties are also linked thermodynamically with specific heat, thermal expansion, Debye temperature, and Gruneisen parameter. Most important, knowledge of elastic constants is essential for many practical applications related to the mechanical properties of a solid as well: load-deflection, thermoelastic stress, internal strain (residual stress), sound velocities, dislocation core structure, and fracture toughness. In order to understand better the physical properties and deformation behavior of the C15 compound NbCr{sub 2}, the authors have studied its elastic properties in this paper. In Section 2, the experimental methods are described, including the preparation of the sample and the measurement of the elastic constants. In Section 3, the experimental results are presented and the implications of these experimental results are discussed. Conclusions are drawn in Section 4.
64 citations
TL;DR: Experimental results are in good agreement with theoretical calculations and Static and dynamic effects to the local disorder have been separately determined and compared with the results of previous studies.
Abstract: Anharmonic contributions to the pair potential of near-neighbor interactions of crystalline and amorphous germanium have been determined by temperature-dependent x-ray absorption fine structure measurements. The measurements have been carried out at the K edge of Ge in the temperature range 77\char21{}450 K and analyzed by the cumulant method. In c-Ge the temperature dependence of the first four cumulants has been determined for the first three coordination shells. The radial distribution function of the nearest-neighbor atoms has been found Gaussian in the examined temperature range; the second and third shell distance distributions show a symmetric but non-Gaussian behavior even below the Debye temperature. Cumulants have been related to the force constants of the effective pair potential. The harmonic contribution to thermal disorder has been extracted from the second cumulant for each coordination shell and compared with the mean square relative displacements calculated by harmonic models of lattice dynamics; experimental results are in good agreement with theoretical calculations. In amorphous germanium the first shell radial distribution function is asymmetric even at the lowest temperatures. Static and dynamic effects to the local disorder have been separately determined and compared with the results of previous studies.
62 citations
TL;DR: In this article, it is shown that, with exception of the alkali metals, such a law is only poorly fulfilled for other cubic elements and compounds, and a relation is often used that correlates Debye temperature and bulk modulus (c 11 + 2c 12 )/3 by a square-root law.
Abstract: Sophisticated methods have been put forward in the literature to calculate Debye temperatures from the elastic constants C ik . As a simple alternative method for cubic crystals, a relation is often used that correlates Debye temperature and bulk modulus (c 11 + 2c 12 )/3 by a square-root law. It is shown that, with exception of the alkali metals, such a law is only poorly fulfilled for other cubic elements and compounds. If one takes, however, elastic moduli such as [c 44 (c 11 - c 12 ) (c 11 + c 12 + 2c 44 )] 1/3 or {c 44 [(c 11 - c 12 ) c 44 /2] 1/2 (c 11 - c 12 + c 44 )/3} 1/3 instead of the bulk modulus the square-root law is established for various cubic material classes. This procedure eventually allows to easily evaluate hitherto unknown Debye temperatures from the elastic constants with high precision.
51 citations
28 citations
TL;DR: In this paper, a tetragonal zirconia was used to study the anomalous shock compression and release behaviors of yttria (Y2O3)-doped (3.0 mol %) tetragonia in the pressure range up to 125 GPa, where the velocity Us versus particle velocity Up relation of the final wave was given by Us=2.71+2.39Up km/s.
Abstract: Shock‐wave measurement and shock‐compression recovery experiments of yttria (Y2O3) ‐doped (3.0 mol %) tetragonal zirconia in the pressure range up to 125 GPa were performed to study the anomalous shock compression and release behaviors. The minute three‐wave structure with the transition points of 15–17 and 33–35 GPa was observed also by the inclined‐mirror method, which is consistent with the VISAR (velocity interferometer system for any reflector) data. The shock velocities of the second wave were so fast that the first transition could not be identified as a normal elastoplastic transition. The shock velocity Us versus particle velocity Up relation of the final wave was given by Us=2.71+2.39Up km/s. The equation of state of the final phase was analyzed by using a program based on the Debye model, the Mie–Gruneisen equation, and the Birch–Marnaghan equation. The volume change between the tetragonal phase and the final phase at zero pressure was estimated to be 18%, which was larger than that expected fo...
25 citations
TL;DR: In this article, the structure refinement of the room temperature X-ray powder diffraction data of ScMnO3 was carried out by Rietveld technique, based on the most probable space group P63cm.
24 citations
TL;DR: In this article, the authors used both conventional least squares fitting in reciprocal space and direct space fitting using the maximum-entropy method (MEM) for the analysis of the atomic thermal motion.
Abstract: Neutron diffraction measurements have been carried out on metallic magnesium at 11 different temperatures ranging from 125 to 755 K. The data, which were corrected for extinction and thermal diffuse scattering effects, were analysed with both conventional least-squares fitting in reciprocal space and direct-space fitting using the maximum-entropy method (MEM). Both the Gram-Charlier expansion of the harmonic displacement factor and the one-particle potential (OPP) model were used in the analysis of the atomic thermal motion. The reciprocal-space analysis as well as the direct-space analysis show the existence of cubic anharmonicity above 240 K. The cubic OPP anharmonic parameter could also be derived from values of almost forbidden reflections predicted from the MEM nuclear density distribution. The MEM further indicates fourth-order anharmonic effects in the atomic potentials above the Debye temperature (340 K).
23 citations
TL;DR: A nanocrystalline β-Sn film of 7 nm average grain size was prepared by inert gas condensation followed by ballistic consolidation, and was investigated by x-ray diffractometry at temperatures of 77 and 293 K.
Abstract: A nanocrystalline β–Sn film of 7 nm average grain size was prepared by inert gas condensation followed by ballistic consolidation, and was investigated by x-ray diffractometry at temperatures of 77 and 293 K. Although Sn normally undergoes a βα phase transformation at 286 K, this transformation was suppressed in the nanocrystalline film. Compared with large-grained β-Sn, a larger Debye–Waller factor and a lower Debye temperature were measured for nanocrystalline β-Sn; Θ D = 133 K for nanocrystalline material while Θ D = 161 K for large-grained material. The lower Debye temperature of the nanocrystalline β-Sn indicates that its vibrational entropy is increased by 0.6 k B /atom with respect to large-grained material.
22 citations
TL;DR: In this paper, the collective excitation of Zr67Ni33 amorphous and liquid alloys with a pair functional potential was studied and the spectrum and the correlation function of the particle current were calculated for longitudinal and transverse modes.
Abstract: Molecular dynamics simulations have been performed to study the collective excitation of Zr67Ni33 amorphous and liquid alloys with a pair functional potential. The spectrum and the correlation function of the particle current are calculated for longitudinal and transverse modes. The dispersion relation is estimated from the spectrum. It is related to the peak position of the static structure factor and is strongly dependent on temperature at large wavenumbers. The collective excitation is evident for the Zr-Zr correlation but not for the Ni-Ni correlation. The motion of the Zr-Zr correlation is non-localized but that of the Ni-Ni correlation is localized. The sound velocity and the Debye temperature are calculated from the dispersion relation. The calculated power spectrum agrees with the previously reported experimental result. The power spectrum of the Zr atom of the amorphous state is similar to that of the crystal state. On the other hand, the power spectrum of Ni shows an obvious difference between the amorphous and crystal states.
18 citations
TL;DR: In this article, the lattice dynamics of ReO3 were studied for the first time by X-ray absorption spectroscopy (XAS) in the temperature range from 77 to 350 K at the rhenium L3 edge.
Abstract: The lattice dynamics of ReO3 is studied for the first time by X-ray absorption spectroscopy (XAS) in the temperature range from 77 to 350 K at the rhenium L3 edge, The Debye-Waller factors are extracted for the first, fourth and sixth coordination shells of rhenium, and their temperature dependences are discussed on the basis of the Debye and Einstein vibrational models. The obtained characteristic temperatures Theta D and Theta E are compared with the ones found by other experimental techniques. The application of the Debye and Einstein models to the analysis of the XAS and X-ray diffraction data for compounds with different degrees of correlation in atomic motion is also discussed.
TL;DR: In this article, the molar heat capacity at constant pressure of the ternary chalcopyrites LiInSe2 and CuSe2 has been determined at temperatures from 2K to 300K with an adiabatic microcalorimeter.
Journal Article•
TL;DR: In this paper, the longitudinal wave velocity for glass series having general formulae (1) and (3) increases with increasing content of ZnO, and for series (2) that the velocity decreases linearly.
Abstract: Ultrasonic velocities, elastic constants and Debye temperature of ZnO, V 2 O 5 and B 2 O 3 composition glasses are reported at room temperature (303K). The three series of glasses used have general formulae: (1) xZnO.(100-x)B 2 O 3 ; (2) xZnO.10V 2 O 5 .(90-x)B 2 O 3 ; and (3) xZnO.(50-x)V 2 O 5 .50B 2 O 3 . It was observed that the longitudinal wave velocity for glass series having the general formulae (1) and (3) increases with increasing content of ZnO, and for series (2) that the velocity decreases linearly. The molar percentage of V 2 O 5 was kept constant. Similarly, all the elastic moduli were found to be ZnO content dependent except Poisson's ratio. The independent nature of Poisson's ratio suggests that the basic structure of the glass samples remains the same. The linear dependence of the Debye temperature with ZnO content is explained on the basis of mean atomic volume and mean sound velocity.
TL;DR: The possibility that crystal-to-amorphous phase transformations can be induced by one or more underlying instabilities of the crystalline phase has been investigated in highly supersaturated solid solutions of Nb--Pd.
Abstract: The possibility that crystal-to-amorphous phase transformations can be induced by one or more underlying instabilities of the crystalline phase has been investigated in highly supersaturated solid solutions of Nb--Pd. Several unusual properties were discovered that may be identified as precursor effects of the collapse of the bcc [alpha]--Nb terminal solution to the amorphous phase. Elastic neutron diffraction measurements of [alpha]--Nb solutions found, with increasing Pd concentration, an anomalously large increase of the average atomic root-mean-square displacement to about half of the value at which the Lindemann criterion predicts the lattice should melt. Low-temperature heat capacity measurements yielded a concomitant decrease in the Debye temperature, suggesting that supersaturation causes an elastic modulus to soften. Single crystals of [alpha]--Nb solutions at high supersaturations have a highly anisotropic structure that is visible in transmission electron microscopy images; it is consistent with the development of a soft phonon mode leading to a bcc-to-[omega] phase transformation. Considered together with the results of other recent experiments, these findings suggest that shear instability of the crystalline phase plays an important role in the crystal-to-amorphous transformation and that the average static mean-square displacement of atoms in the lattice acts as a useful parameter for the stability of themore » crystal with respect to amorphization.« less
TL;DR: In this article, the Seebeck coefficient, S, and electrical resistance, R, have been measured as functions of temperature at constant oxygen composition, z, for ceramic YBa 2 Cu 3 O z samples with 6.197 ≤ z ≤ 6.400 and at temperatures up to ≈ 1000 K, by means of a simple experimental device which allows us to change the temperature without changing the composition z.
Abstract: The Seebeck coefficient, S , and electrical resistance, R , have been measured as functions of temperature at constant oxygen composition, z , for ceramic YBa 2 Cu 3 O z samples with 6.197 ≤ z ≤ 6.400 and at temperatures up to ≈ 1000 K, by means of a simple experimental device which allows us to change the temperature without changing the composition z . S ( T ) z exhibits a large peak at T ≈ 200 K which decreases as z increases. The main object of the discussion is to understand the origin of this peak. At first, it is shown that this S peak is independent of the Neel transformation which occurs in the above composition range. The coupling between the Neel process and the transport properties is revealed, as for similar systems, by a λ point on the ( ϑ ln R / ϑT ) z versus T plot at T N and by a positive hump for ln R ( T ) z . Several possibilities are then discussed, notably antimagnon and phonon drag. A new experimental fact appears as a key argument in this discussion. The system exhibits a Fermi glass behavior with an Anderson transition occurring on changing z . At the transition which is observed between z = 6.350 and z = 6.400, the activated diffusion component of S disappears. However, for z = 6.400, on the metallic side of the transition, a T −1 term is still observed in S which is the signature of phonon drag. This phonon-drag effect appears to be unusually strong: the maximum temperature of the S peak, up to 250 K, is high as regards the Debye temperature, ≈ 350–400 K, and the phonon-drag contribution to S amounts to about 30% at 600 K for z = 6.400. This indicates a particularly strong electron-phonon coupling. As a consequence, the coupling parameter λ is expected to be high in these systems.
TL;DR: In this article, a mica sheet has been cleaved in situ in a UHV beam scattering apparatus, and diffraction of the helium atoms shows sharp Bragg peaks.
TL;DR: In this article, Debye temperature, electron-photon interaction parameter λ, plasma frequency and superconducting energy gap were derived for YNi 2 B 2 C samples prepared by inductive melting from the pure elements.
Abstract: New transport (resistivity versus temperature) and tunneling (low-temperature STM) measurements are reported on YNi 2 B 2 C samples prepared by inductive melting from the pure elements. Estimations of Debye temperature, electron-photon interaction parameter λ, plasma frequency and superconducting energy gap are given. Normal-state and superconducting data fit in a consistent picture of BCS superconductivity with λ ≤ 1.
TL;DR: In this article, the specific heat of (Sm2O3)0·19(P2O5) 0·81 and (Sm 2O3), 0·25(P 2O5), 0.75 glasses have been measured between 1·5 and 30 K using a calorimeter based on the thermal relaxation method.
Abstract: The specific heats of (Sm2O3)0·19(P2O5)0·81 and (Sm2O3)0·25(P2O5)0·75 glasses have been measured between 1·5 and 30 K using a calorimeter based on the thermal relaxation method. The results show an additional specific heat over that predicted from the Debye theory, which has been interpreted in terms of an excess of localized vibrational modes. To provide a basis for preliminary data analysis in terms of localized states, a phonon-fracton density of states has been used. The fit to the excess specific heat gives model parameters having the same magnitudes as those found previously for a wide range of glasses. The cross-over temperature from phonon to fracton behaviour estimated from the excess specific heat is similar to that obtained from recent low-frequency Raman scattering measurements.
TL;DR: In this article, the specific heat under constant pressure of intermetallic compounds Hf2Fe, hf2Co and hf 2Rh with the Ti2Ni structure was obtained by means of differential thermal analysis in the temperature range 275-740 K, and the results differ significantly from the Debye theory, even when a correction for optical phonons in Einstein approximation is considered, which indicates existence of a defect contribution to the heat.
Abstract: The specific heat under constant pressure, C
p, of intermetallic compounds Hf2Fe, Hf2Co and Hf2Rh with the Ti2Ni structure was obtained by means of differential thermal analysis in the temperature range 275–740 K. The results differ significantly from the Debye theory, even when a correction for optical phonons in Einstein approximation is considered, which indicates existence of a defect contribution to the specific heat. Relative entropy has been determined and the obtained results were fitted and analysed. The anomalous temperature behaviour of C
p is discussed, having in mind results of previous investigations of these and similar systems, obtained by other methods.
TL;DR: In this paper, the longitudinal and shear wave velocities of titanium substituted magnesium ferrites were determined at room temperature by the pulse transmission technique and the values of Young's modulus and rigidity modulus were corrected to theoretical density.
TL;DR: In this article, an analysis of the pressure and volume dependence of the Gruneisen parameter γ and the Debye temperature θ is presented for NaCl crystals using the model developed by Kumari and Dass.
Abstract: An analysis of the pressure and volume dependence of the Gruneisen parameter γ and the Debye temperature θ is presented for NaCl crystals using the model developed by Kumari and Dass. It is pointed out that the parameter q = d ln γ/d ln V should be taken nearly equal to unity for predicting γ and θ at different pressures. Various thermodynamic approximations implied in the analysis are discussed
TL;DR: In this article, the heat capacity of cobalt(II) bromate hexahydrate Co(H 2 O) 6 (BrO 3 ) 2 was measured at temperatures between 13 and 310 K.
TL;DR: Mosauer measurements of hexane-diammonium-tetrachloro-ferrate over the temperature range 78-320 K for powdered and single-crystal absorbers show a transition to the antiferromagnetic ordered state at (105.0 ± 0.2) K as mentioned in this paper.
Abstract: Mosauer measurements of hexane-diammonium-tetrachloro-ferrate over the temperature range 78–320 K for powdered and single-crystal absorbers show a transition to the antiferromagnetically ordered state at (105.0 ± 0.2) K. The center shift indicates an electronic ground state of 3d 6 4s 0.2 . The quadrupole splitting implies that Fe(II) exists in a distorted octahedral field and that the ground state is a doublet, with negative electric field gradient. The recoilless fraction, the center shift and the quadrupole splitting reveal the existence of a structural phase change at (235 ± 5) K. The Debye temperature of the lower temperature phase is (166 ± 5) K aand (155 ± 3) K for the higher. Transition to the ordered state takes place between 105 and 110 K where an increase of the spin correlation time is found. A three-dimensional transition associated with a weak ferromagnetic interaction as a result of canting of the spins is observed at about 102 K. At 77 K the effective magnetic field strength was found to be (225 ± 3) kOe and to make an angle of 80° ± 3° with the principle axis of the electric field gradient.
TL;DR: In this paper, the motion of a light particle in a solid coupled to conduction electrons and/or phonons is investigated within the framework of a two-state model, which may be taken as representing the particle ground states in two neighbouring potential wells.
Abstract: The motion of a light particle in a solid coupled to conduction electrons and/or phonons is investigated within the framework of a two-state model, which may be taken as representing the particle ground states in two neighbouring potential wells. With regard to the coupling of the particle to phonons, an important distinction arises between (i) special two-phonon processes, termed diphonon processes, which result from nonlinear particle-lattice coupling and which may give rise to quasielastic phase-destroying scattering and (ii) essentially inelastic processes which may arise from linear as well as from nonlinear particle-lattice coupling. An important parameter affecting particle motion is the static energy shift e between the particle ground states in the two wells. Under favourable conditions it may be experimentally controlled within certain limits. The two-state model allows us to estimate reliably the boundary in the e-T plane separating the regimes of incoherent hopping from that of coherent bandlike motion, and to discuss its dependence on the particle mass and the coupling parameters. Within the regime of incoherent motion a number of subregimes may exist. The situation becomes particularly interesting if a condensation of the electron system takes place, as in the case of a Bardeen-Copper-Schriefer superconductor. Then domains have to be distinguished in which the hopping rates are dominated by either quasiparticle coupling, diphonon processes, one-phonon processes, Cooper-pair breaking, coupling to normal-conducting electrons, or multiphonon-assisted processes. In the series of light particles carrying one positive elementary charge, which includes the positive muon (μ + ) and the nuclei of the hydrogen isotopes, the range of validity of the two-state description extends to rather high temperatures for the μ * but only to considerably lower temperatures for the heavier particles. Nevertheless, for protons the limiting temperature can be almost as high as the Debye temperature. Towards low temperatures the validity of the two-well description of unrestricted particle motion in a crystal is limited by the onset of coherent motion.
TL;DR: In this paper, the heat capacity of the ternary compounds RNiGe(R=Er, Dy, Gd, and Y) was studied in the temperature range between 2 and 40 K.
Abstract: The heat capacity of the ternary compounds RNiGe(R=Er, Dy, Gd, and Y) was studied in the temperature range between 2 and 40 K. From the heat capacity curves, Neel temperatures are found to be 3.3, 7.4, and 10.7 K for ErNiGe, DyNiGe, and GdNiGe, respectively. The heat capacity of YNiGe was well fitted with an average Debye temperature of 272 K in the temperature range between 2 and 40 K. The changes of magnetic entropy indicate a strong influence of the crystal field on the Er+3 and Dy+3 ion in ErNiGe and DyNiGe compounds. These results suggest the possibility of using these compounds as magnetic regenerator materials near the temperature of 4.2 K.
TL;DR: In this article, ScFe 10 Si 2 crystallizes in the ThMn 12 -type tetragonal structure with the space group I4/mmm and the lattice parameters: a = 0.8280 (1) nm, c = 0., 0.4706 (1), and c / a =0.57.
Abstract: ScFe 10 Si 2 crystallizes in the ThMn 12 -type tetragonal structure with the space group I4/mmm and the lattice parameters: a = 0.8280 (1) nm, c = 0.4706 (1) nm and c / a = 0.57. In the refinement performed for 317 independent reflections and 10 variable parameters, a final discrepancy factor R = 4.69% has been reached. The compound is ferromagnetic below 506 K ( 57 Fe ME) and 560 K (magnetic). The distribution of the Fe atoms in the 8( i ), 8( j ) and 8( f ) positions corresponds to 40, 31 and 29%, respectively. The Debye temperature determined from the temperature dependence of the isomer shift is 340 K.
TL;DR: In this article, measurements of low-temperature specific heat were presented for the metallic glasses Zr70Be30 and Zr67Cu33 in the as-quenched (cooling rate ∼ 106 K/s) and relaxed (annealing at T = 450 K for 2 h) states.
Abstract: Measurements of the low-temperature specific heat are presented for the metallic glasses Zr70Be30 and Zr67Cu33 in the as-quenched (cooling rate ∼ 106 K/s) and relaxed (annealing at T = 450 K for 2 h) states. Structure relaxation increases both electron density of states at the Fermi level and the Debye temperature, and at the same time the temperature of the superconducting transition decreases. The main parameters of the attractive interelectron interaction spectrum: coupling parameter, λ, and the effective frequency, ωph, have been determined.
TL;DR: In this article, the thermal conductivity of GdAl 2-like systems as a function of temperature has been calculated based on the variational method for transport coefficients, and the low-temperature limit obeys Matthiessen's rule 1/δ = 1/ κ = 1 δ + δ s + 1/γ imp where the three components are the contributions arising from e − -phonon, e − localized spin and e − impurity interactions.
TL;DR: In this paper, a model which describes trapping of inert gas atoms in the sputtered layer in terms of implantation and trapping, diffusion, growth, resputtering, and gas sputtering is presented.
Abstract: Amorphous Si layers were grown by krypton plasma sputter deposition at 310 °C. By pulsation of the substrate potential between 0 and 50 eV, the Kr concentration in the layers could be varied to a maximum of 5.5 at. %. A model which describes trapping of inert gas atoms in the sputtered layer in terms of implantation and trapping, diffusion, growth, resputtering, and gas sputtering is presented. High‐resolution electron microscopy, electrode‐probe (x‐ray) microanalysis, positron annihilation, Raman spectroscopy, Mossbauer spectroscopy, and bending and hardness measurements were performed on the deposited layers. It turns out that the ion assisted growth leads to a strong reduction of open volume defects. The experiments point to the presence of very small Kr agglomerates. From the Mossbauer experiments a lower limit of 250 K for the Debye temperature of the Kr agglomerates is derived. Molecular‐dynamic simulations from which the Debye temperatures of Kr mono‐, di‐, and trimers in amorphous Si can be derive...