Showing papers on "Debye model published in 2001"

Phonon Density of States of Iron up to 153 Gigapascals

Abstract: We report phonon densities of states (DOS) of iron measured by nuclear resonant inelastic x-ray scattering to 153 gigapascals and calculated from ab initio theory. Qualitatively, they are in agreement, but the theory predicts density at higher energies. From the DOS, we derive elastic and thermodynamic parameters of iron, including shear modulus, compressional and shear velocities, heat capacity, entropy, kinetic energy, zero-point energy, and Debye temperature. In comparison to the compressional and shear velocities from the preliminary reference Earth model (PREM) seismic model, our results suggest that Earth's inner core has a mean atomic number equal to or higher than pure iron, which is consistent with an iron-nickel alloy.

Electronic and elastic properties of the light actinide tellurides

Abstract: The elastic constants c11, c12 and c44 of U, Np, Pu, and Am telluride single crystals have been obtained by Brillouin scattering from the measured sound velocities in prominent crystallographic directions. In case of the U chalcogenides also by ultrasound techniques. The Cauchy pressure, the Poisson ratio, the anisotropy ratio, the bulk modulus and the Debye temperature have been derived from these data. U and Pu telluride have a negative c12, implying intermediate valence. AmTe has a very low bulk modulus, but a positive c12. It is extremely soft, with a very low sound velocity. For AmTe also the LO and TO phonon frequencies could be determined. The elastic data point to a divalent Am state. The optical reflectivity of the light actinide tellurides (and sometimes of all chalcogenides) has been measured between UV and infrared wavelengths, in the case of AmTe down to the far infrared. The plasma edge of the free carriers has been determined, which yields the ratio of n/m*. Together with the γ value of the specific heat and magnetic data a consistent proposal for the electronic structure of the light actinide chalcogenides can be given. Thus, the Pu chalcogenides are intermediate valent and represent the high-pressure phase of the corresponding Sm chalcogenides. AmTe, as judged by the electronic, optic and magnetic properties seems to be in the 5f7 configuration, i.e. divalent Am, but with a narrow, half-filled (24 meV) wide 5f band, about 0.1 eV below the bottom of the 6d conduction band. We thus propose a new kind of unhybridized heavy fermion. Also AmTe seems to represent a high-pressure phase of EuTe.

Nature of small-polaron hopping conduction and the effect of Cr doping on the transport properties of rare-earth manganite La0.5Pb0.5Mn1−xCrxO3

Abstract: The conductivity and magnetoresistance of La0.5Pb0.5Mn1−xCrxO3 (0.0⩽x⩽0.45) measured at 0.0 and 1.5 T magnetic field have been reported. All the oxide samples except x=0.45, showed metal insulator transition (MIT) between 158–276 K, depending on x. In contrast to the behavior of a similar sample La0.7Ca0.3Mn1−xCrxO3 showing no (MIT) for x⩾0.3, the Pb doped samples showed MIT even with x=0.35. The MIT peak temperature (Tp) shifts towards lower temperature with increasing x while magnetic field shifts Tp to the high temperature regime. The metallic (ferromagnetic) part of the temperature dependent resistivity (ρ) curve (below Tp) is well fitted with ρ(T)=ρ0+ρ2.5T2.5 indicating the importance of electron–magnon interaction (second term). We have successfully fitted the high temperature (T>θD/2, θD is Debye temperature) conductivity data, both in presence and in absence of magnetic field, with small polaron hopping conduction mechanism. Adiabatic small polaron hopping conduction mechanism is followed by the s...

Detailed electronic structure studies on superconducting MgB 2 and related compounds

Abstract: Our recent electronic structure studies on series of transition metal diborides indicated that the electron phonon coupling constant is much smaller in these materials than in superconducting intermetallics. However experimental studies recently show an exceptionally large superconducting transition temperature of 40 K in MgB2. In order to understand the unexpected superconducting behavior of this compound we have made electronic structure calculations for MgB2 and closely related systems. Our calculated Debye temperature from the elastic properties indicate that the average phonon frequency is very large in MgB2 compared with other superconducting intermetallics and the exceptionally high Tc in this material can be explained through BCS mechanism only if phonon softening occurs or the phonon modes are highly anisotropic. We identied a doubly-degenerate quasi-two dimensional key-energy band in the vicinity ofEF along -A direction of BZ (having equal amount of B px and py character) which play an important role in deciding the superconducting behavior of this material. Based on this result, we have searched for similar kinds of electronic feature in a series of isoelectronic compounds such as BeB2, CaB2 ,S rB 2 ,L iBC and MgB 2C2 and found that MgB2C2 is one potential material from the superconductivity point of view. We have also investigated closely related compound MgB4 and found that its EF is lying in a pseudogap with a negligibly small density of states at EF which is not favorable for superconductivity. There are contradictory experimental results regarding the anisotropy in the elastic properties of MgB2 ranging from isotropic, moderately anisotropic to highly anisotropic. In order to settle this issue we have calculated the single crystal elastic constants for MgB2 by the accurate full-potential method and derived the directional dependent linear compressibility, Young’s modulus, shear modulus and relevant elastic properties from these results. We have observed large anisotropy in the elastic properties consistent with recent high-pressure measurements. Our calculated polarized optical dielectric tensor shows highly anisotropic behavior even though it possesses isotropic transport property. MgB2 possesses a mixed bonding character and this has been veried from density of states, charge density and

Characterization of the native Cr2O3 oxide surface of CrO2

Abstract: Using photoemission and inverse photoemission, we have been able to characterize the Cr2O3 oxide surface of CrO2 thin films. The Cr2O3 surface oxide exhibits a band gap of about 3 eV, although the bulk CrO2 is conducting. The thickness of this insulating Cr2O3 layer is twice the photoelectron escape depth which is about 2 nm thick. The effective Cr2O3 surface layer Debye temperature, describing motion normal to the surface, is about 370 K. From a comparison of CrO2 films grown by different techniques, with different Cr2O3 content, evidence is provided that the CrO2 may polarize the Cr2O3.

Ab initio thermodynamics of metals: Al and W

Abstract: We present an ab initio pseudopotential calculation of thermodynamic properties of aluminum and tungsten. The difference of almost one order of magnitude of the experimental linear thermal expansion coefficients of these materials is well reproduced by our calculations and explained in terms of microscopic quantities. The specific heat is reported and compared with available experimental data. Mode-Gr\"uneisen parameters, Debye temperature, and temperature dependence of isothermal and adiabatic bulk modulus as well as the pressure dependence of compressibility complete the work.

The temperature dependence of the Young's modulus of MgSiN2, AlN and Si3N4

Abstract: The temperature dependence of the Young's modulus of MgSiN2 and AlN was measured between 293 and 973 K using the impulse excitation method and compared with literature data reported for Si3N4. The data could be fitted with . The values of the fitting parameters E0 and T0 are related to the Debye temperature, and the parameter B to the harmonic character of the bond.

Experimental vibrational Grüneisen ratio values for ϵ‐iron up to 330 GPa at 300 K

Abstract: Experimental values for the vibrational Gruneisen ratio, γυ, for hexagonal close-packed (hcp) iron, called epsilon (ϵ)-iron, were obtained over a large compression range corresponding to Earth's inner-core pressure. This was done by measuring the intensity change in x-ray diffraction lines under pressure, P. X-ray structural refinement using the Rietveld method on powder diffraction data yielded information on mean square displacement used to obtain the Debye temperature, Θ, as a function of compression, V/V0. The value of Θ was determined from the measured intensity of the diffraction lines, which arises from the mean squared amplitude measured in-situ in the diamond cell. From the Debye relationship, γυ=−(∂ ln Θ/∂ ln V)T, we determined experimental data on γυ versus V of Fe (hcp) up to 330 GPa at 300 K. The measured value of γυ(V) is 1.18 at 330 GPa and 1.41 at 135 GPa.

Localized vibrational mode analysis of the resistivity and specific heat of LaB 6

Abstract: ${\mathrm{LaB}}_{6}$ and other hexaborides are inclusion compounds in which the rare earth or other metal ion is weakly bound and sits in an oversized ``cage'' of boron ions Here we show that a simple model that treats the La ions as independent harmonic (Einstein) oscillators embedded in a Debye framework of boron ions successfully accounts for the anomalies in the specific heat and resistivity of ${\mathrm{LaB}}_{6}$ One of the nice features of the model is that the Einstein temperature of the La atoms and the Debye temperature of the boron framework are derived from room-temperature x-ray crystallography data This feature makes the model easy to apply to other hexaborides and other materials that can be treated as inclusion compounds The results from this work imply that local modes are likely to be important for understanding the physical properties of all the hexaborides

Melting of iron and other metals at earth's core conditions: A simplified computational approach

Abstract: In order to study melting of metals at high pressure, we propose a different method which can be thought of as a generalization of the well-known Lindemann law. One essential interesting feature is that neither the Debye temperature nor the Gr\"uneisen coefficient are used in the theory. We find that the method based on first-principles calculations can be used to model the pressure dependence of the melting properties of metals very well. Predictions of the melting along the principal Hugoniot are calculated for Cu and Ta. In the case of Fe, the melting temperature is calculated at geophysically interesting pressures.

Magnetic properties of ordered perovskites Ba2LnTaO6 (Ln = Y, lanthanides)

Abstract: Magnetic properties of the quaternary oxides Ba2LnTaO6 (Ln = Y or lanthanides) are reported. Their powder x-ray diffraction measurements and Rietveld analysis show that they have an ordered perovskite structure and are monoclinic (Ln = La-Tb) with space group P21/n or cubic (Ln = Y, Dy-Lu) with space group Fmm. Magnetic susceptibilities of Ba2LnTaO6 were measured. All compounds in this work are paramagnetic down to 5 K. Ba2EuTaO6 and Ba2SmTaO6 show Van Vleck paramagnetism; their spin-orbit coupling constants are determined to be 331 cm-1 and 287 cm-1, respectively. 151Eu Mossbauer measurements for Ba2EuTaO6 were carried out at 12, 100, 200 and 300 K. The Eu ion is in the trivalent state, and the symmetry of the Eu site is distorted from the octahedral symmetry. The Debye temperature of Eu3+ was determined to be 335 K from the temperature dependence of the absorption area of intensity curves.

The spin-crossover complex [ Fe(tpa)(NCS)2] - Investigated by synchrotron-radiation based spectroscopies

Abstract: The temperature-induced spin crossover of iron(II) in the [ Fe ( tpa )( NCS ) 2 ] complex has been investigated by nuclear forward scattering (NFS), nuclear inelastic scattering (NIS), extended X-ray absorption fine structure (EXAFS) spectroscopy, conventional Mossbauer spectroscopy (MS) and by measurements of the magnetic susceptibility (SQUID). The various measurements consistently show that the transition is complete and abrupt and exhibits a hysteresis between 102 and 110 K. The dependence of the hyperfine parameters of the high-spin (HS) and of the low-spin (LS) phase on temperature is gradual while the effective thickness (determined by the Lamb-Mossbauer factor f LM ) shows a step at the transition temperature. This step could be identified clearly because the effective thickness is measured directly by NFS. The Lamb-Mossbauer factor, the Debye temperature and the mean-square displacement of iron(II) could be determined for the HS and for the LS phase. When comparing the NIS data with the results from density functional theory (DFT), the Fe-N stretching vibrations of both LS and HS phases could be unambiguously identified and the f LM could be factorized for both phases into a lattice and a molecular part. The structural information from EXAFS and DFT geometry optimization are in reasonable agreement.

Ultrasonic characterisation of ferroelectric BaTiO3 doped lead bismuth oxide semiconducting glasses

Abstract: Ferroelectric BaTiO3 doped lead bismuth xPbO–(100−x)Bi2O3–5BaTiO3 semiconducting oxide glasses with different PbO contents (x=20,30,40 and 50 wt%) have been prepared by the rapid quenching method. The ultrasonic velocity and attenuation measurements have been made at room temperature (298 K) at frequencies 2.25–10 MHz. From the measured density and ultrasonic velocity data, elastic moduli, Debye temperature, Poisson's ratio and other related physical parameters have been determined. At lower PbO content ( PbO wt %) , a monotonic decrease in velocity, elastic moduli and Debye temperature was noted. A further increase in PbO content ( PbO >40 wt %) lead to an increase in all the above parameters, after showing a minimum at 40 wt% of PbO. In addition, the effect of ultrasonic frequency on velocity and attenuation has also been studied in these glasses. The observed results have been explained in terms of the change in the structure and physical properties of the glass network with change in PbO content.

Acoustic investigations on PbO-Al2O3-B2O3 glasses doped with certain rare earth ions

Abstract: Elastic moduli (Y, η), Poisson’s ratio (σ), microhardness (H) and some thermodynamical parameters such as Debye temperature (θD), diffusion constant (D i),latent heat of melting (ΔH m) etc of PbO-Al2O3-B2O3 glasses doped with rare earth ions viz. Pr3+, Nd3+, Sm3+, Eu3+, Tb3+, Dy3+, Ho3+, Er3+ and Yb3+, are studied as functions of temperatures (in the temperature range 30–200°C) by ultrasonic techniques. All these parameters are found to increase with increasing atomic numberZ of the rare earth ions and found to decrease with increasing temperature of measurement. From these results (together with IR spectra of these glasses), an attempt is made to throw some light on the mechanical strength of these glasses.

An improved lattice mechanical model for FCC transition metals

Abstract: A lattice mechanical model for transition metals, recently proposed by Antonov et al. has been improved. This improved model has been tested against its ability to reproduce a large number of lattice mechanical properties like binding energy, P–V relations, elastic constants and their pressure derivatives, interatomic interactions, phonon dispersion curves, temperature variation of Debye temperature, Debye–Waller factor and temperature variation of mean square displacement with fairly good success.

Low-temperature specific heat and critical magnetic field of α-uranium single crystals

Abstract: The current work reports on the specific heat and the electrical resistivity of {alpha}-uranium at cryogenic temperatures. Measurements were made on {alpha}-uranium single crystals that have some unexpected mechanical properties. Despite the fact that {alpha}-uranium normally work hardens and often fails in a brittle manner, these crystals bend easily. Presumably, the combination of flexibility and strength comes from twinning in response to stress, and these twins can run freely during deformation. Because grain boundaries are not present, we anticipated that the characteristics of the charge density wave (CDW) might be more prominent in these crystals. For these reasons, the specific heat was measured from T{approximately}0.5 to 110 K, using semiadiabatic calorimetry in zero field, and the electrical resistivity was measured from T{approximately}0.1 to 0.50 K, in magnetic fields up to 80 mT using a standard four-probe ac technique. An abrupt resistance drop typical of a superconducting transition was observed as the temperature fell below 0.78 K, a temperature at which the resistance fell to 90% from its original value. A residual resistivity ratio RRR{approximately}115 was measured from the low-temperature resistivity data. In addition, three phase transitions were clearly seen in the specific-heat data, located at T=23, 36, and 42 K.more » These transitions are consistent with the {alpha}{sub 3}, {alpha}{sub 2}, and {alpha}{sub 1} CDW structures that have been previously observed in uranium metal. Analysis of the specific-heat data give an electronic specific heat ({gamma})=9.13mJK{sup {minus}2}mol{sup {minus}1} and a low-temperature limiting Debye temperature ({Theta}{sub D})=256K({+-}0.25K). The highest calorimetric value measured previously was 218 K. Our value of 256 K is in favorable agreement with that previously obtained from elastic constants 250 K ({+-}2 K). The agreement between calorimetric and elastic {Theta}{sub D} values, ductility at room temperature, and a RRR that is three times larger than previously reported values highlight the properties of these {alpha}-uranium single crystals.« less

Electronic transport in Cd–Yb and Y–Mg–Zn quasicrystals

Abstract: Electronic transport properties of the stable binary Cd5.7Yb quasicrystal and a quasicrystal in the Y–Mg–Zn family is presented. Electrical conductivity in these systems is an order of magnitude higher than other quasicrystals, resulting in larger thermal conductivity values due to enhanced electronic contributions (λE=L0σT). Room temperature Hall measurements provide a charge carrier density of 2.3×1021 and 3.1×1020 cm−3 in Cd5.7Yb and Y–Mg–Zn, respectively, indicating these materials have a higher carrier concentration and are better conductors than other quasicrystalline counterparts. Thermoelectric power in both Cd5.7Yb and Y–Mg–Zn have relatively small magnitudes (16 and 8 μV/K, respectively). Despite many similarities between these two systems, low temperature specific heat reveals a low Debye temperature in Cd5.7Yb(140 K) while the Debye temperature of Y–Mg–Zn and other quasicrystals is at least twice as large. Consequences of the electrical transport in these systems will be discussed.

Characteristics of the glass transition and supercooled liquid state of the Zr 41 Ti 14 Cu 12.5 Ni 10 Be 22.5 bulk metallic glass

Abstract: Acoustic velocities and their temperature dependence of ${\mathrm{Zr}}_{41}{\mathrm{Ti}}_{14}{\mathrm{Cu}}_{12.5}{\mathrm{Ni}}_{10}{\mathrm{Be}}_{22.5}$ bulk metallic glass (BMG) have been measured up to 773 K by using an ultrasonic pulse-echo overlap method. The temperature dependence of density, Vicker's hardness, elastic constants, and thermodynamic parameters of the BMG are determined. A rapid change of the density, acoustic velocities, elastic constants, and Debye temperature near the glass transition temperature, and anomalous density, acoustic and elastic behaviors in the supercooled liquid region are observed. A striking softening of long-wavelength transverse acoustic phonons in the glassy state relative to the supercooled liquid state is found. The glass transition process is delayed to high temperature with an increase of heating rate. Our results provide evidence that the glass transition in the BMG can be regarded as a kinetically modified thermodynamic phase transformation.

Ultrasonic study of the elastic and nonlinear acoustic properties of ceramic aluminum nitride

Abstract: Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of aluminum nitride (AlN) ceramic samples as functions of temperature in the range 100–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. Aluminum nitride is an elastically stiff but light ceramic: at 295 K, the longitudinal stiffness (C L), shear stiffness (μ), adiabatic bulk modulus (B S), Young's modulus (E) and Poisson's ratio (σ) are 373 GPa, 130 GPa, 200 GPa, 320 GPa and 0.234, respectively. The temperature dependences of C L and B S show normal behaviour and can be approximated by the conventional model for vibrational anharmonicity. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to determine the hydrostatic-pressure derivatives of elastic stiffnesses and the acoustic-mode Gruneisen parameters. The values determined at 295 K for the hydrostatic-pressure derivatives (∂C L/∂P) P=0, (∂μ/∂P) P=0 and (∂B S/∂P) P=0 are 4.7 ± 0.1, 0.22 ± 0.03 and 4.4 ± 0.15, respectively. The adiabatic bulk modulus B S and its hydrostatic-pressure derivative (∂B S/∂P) P=0 are in good agreement with the results of recent high pressure X-ray diffraction measurements and theoretical calculations. The longitudinal (γL), shear (γS), and mean (γel) acoustic-mode Gruneisen parameters of AlN are positive: the zone-centre acoustic phonons stiffen under pressure. The shear γS (=0.006) is much smaller than the longitudinal γL (=1.09) accounting for the low thermal Gr¨neisen parameter γth (=0.65) obtained for this ceramic: since the acoustic Debye temperature ΘD (=980 ± 5 K) is so high, the shear modes play an important role in acoustic phonon population at room temperature. Hence knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic AlN.

Measurement of low temperature specific heat of crystalline TeO2 for the optimization of bolometric detectors

Abstract: The optimization of bolometric detectors, like those that will be developed for the rare event experiment CUORE, requires a complete knowledge of the detector's thermal parameters. Since the CUORE detecting elements will consist of TeO2 crystals, we have measured the specific heat of this material down to 60 mK with the thermal relaxation method. Previous available data were taken at temperatures higher than 0.6 K. Our results are clearly consistent with a lattice dominated specific heat. The Debye temperature, evaluated to be (232±7) K, is in excellent agreement with the elastic constant values measured by other authors. The knowledge of the Debye temperature allows a simple prediction of the pulse amplitude of presently working bolometers.

Isotope effects on the lattice dynamics of crystals

Abstract: It seems likely that isotope effects are most clearly manifested in crystal lattice dynamics, which is evidenced by works in this field that have been published for more than half a century. A great number of stable isotopes and well-developed methods of their separation has made it possible to date to grow crystals of C, LiH, ZnO, ZnSe, CuCl, GaN, GaAs, CdS, Cu2O, Si, Ge and α-Sn with a controllable isotopic composition. The accumulated voluminous theoretical and experimental data suggest that the isotopic composition of a crystal lattice exerts some influence on the thermal, elastic, and vibrational properties of crystals. These effects are quite large and can be readily measured by modern experimental techniques (ultrasound, Brillouin and Raman scattering, and neutron scattering). For example, the change in the lattice constant is Δa/a=10−3 to 10−4, while the change δcik in the elastic constants amounts to several percent. The maximum km (where km is the maximum of thermal conductivity) measured for the most highly enriched 70 Ge (99.99%) sample is 10.5 kW/mK, one order of magnitude higher than for the natural Ge (analogous for C and Si). In addition, crystals of different isotopic compositions possess different Debye temperatures. This difference between a LiH crystal and its deuteride exceeds hundred degrees. Of the same order of magnitude is the difference between Debye temperatures for diamond crystals. Very pronounced and general effects of isotopic substitution are observed in phonon spectra. The scattering lines in isotopically mixed crystals are not only shifted (the shift of LO lines exceeds 100 cm−1) but are also broadened. This broadening is related to the isotopic disorder of a crystal lattice. It is shown in this review that the degree of change in the scattering potential is different for different isotopic mixed crystals. In the case of germanium and diamond crystals, phonon scattering is weak, which allows one to successfully apply the coherent potential approximation (CPA) for describing shift and broadening of scattering lines. In the case of lithium hydride, the change in the scattering potential is so strong that it results in phonon localization, which is directly observed in experiments. Capture the thermal neutrons by isotope nuclei followed by nuclei decay produces new elements in a very large number of possibilities for isotope selective doping of different materials. The review closes with a section describing future developments and applications of isotope technology and engineering.

Electrical conductivity and magnetic susceptibility of titanium monoxide

Abstract: Conductivity and magnetic susceptibility of disordered cubic titanium monoxide TiO y (0.920 ≤ y ≤ 1.262) are studied. Temperature dependences of the conductivity of TiO y monoxides with y ≤ 1.069 are described by the Bloch‐Gruneisen function with Debye temperature 400‐480 K, and temperature dependences of the susceptibility include Pauli paramagnetism of conduction electrons. The behavior of conductivity and susceptibility of TiO y with y ♢ 1.087 is typical of semiconductors with nondegenerate charge carriers obeying Boltzmann statistics. The band gap Δ E between the valence and conduction bands of TiO y ( y ♢ 1.087) is 0.06‐0.17 eV, and effective mass of charge carriers is equal to 7‐14 electron masses. © 2001 MAIK “Nauka/Interperiodica”.

Static Dielectric Constant and Relaxation Time for the Binary Mixture of Water, Ethanol, N. N-Dimethylformamide, Dimethylsulphoxide, and N, M-Dimethylacetamide with 20Hethoxyethanol

Abstract: Frequency spectra of the complex permittivity of 2-methoxyethanol (2-ME) with water, ethanol, dimethylsulphoxide (DMSO), N,N-dimethylformamide (DMF) and N,N-dimethylacatamide (DMA) have been determined over the frequency range of 10 MHz to 20 GHz at 25 , using the Time domain reflectometry method, for 11 concentrations for each system. The static dielectric constant, dielectric constant at microwave frequency, relaxation time, excess dielectric parameters, and Kirkwood correlation factor have been determined. The relaxation in these systems within the frequency range can be described by a single relaxation time constant, using the Debye model. The parameters show a systematic change with the concentration.

Heat capacity of germanium crystals with various isotopic composition

Abstract: The heat capacity of three pure (n, p≤2×1016 cm-3) germanium crystals with different isotopic compositions was measured in the temperature range from 2.8 K to 100 K. These samples, one made of enriched 70Ge (95.6%), Ge of natural isotopic composition and n, p < 1014 cm-3, and one of the largest possible isotopic mass variance 70/76Ge (43%/48%) with n, p<1014 cm-3, show a change of the molar heat capacity (and corresponding Debye temperature, θD) as expected from the average mass variation, corresponding to θD∝M-0.5 (M = molar mass) at low temperatures. The mass effect is best visible around 21.5 K, at the minimum of the corresponding Debye temperatures θD, and amounts to ΔθD = 5.3 K for the difference between the Debye temperatures of 70Ge and 70/76Ge. The specific heat capacity of the natural Ge crystal agrees within 2% with the best data available in the literature taken on much larger masses of Ge.

Ultrasonic determination of the temperature and hydrostatic pressure dependences of the elastic properties of ceramic titanium diboride

Abstract: Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of titanium diboride (TiB2) ceramic samples as functions of temperature in the range 130–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. TiB2 is an elastically stiff but light ceramic: at 295 K, the longitudinal stiffness (CL), shear stiffness (μ), adiabatic bulk modulus (BS), Young's modulus (E) and Poisson's ratio (σ) are 612 GPa, 252 GPa, 276 GPa, 579 GPa and 0.151, respectively. The adiabatic bulk modulus BS is in good agreement with the results of recent theoretical calculations. All elastic moduli increase with decreasing temperature and do not show any pronounced unusual effects. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to determine the hydrostatic-pressure derivatives of elastic stiffnesses and the acoustic-mode Gruneisen parameters. The values determined at 295 K for the hydrostatic-pressure derivatives (∂CL/∂P)P=0, (∂μ/∂P)P=0 and (∂BS/∂P)P=0 are 7.29 ± 0.1, 2.53 ± 0.1 and 3.91 ± 0.1, respectively. The hydrostatic-pressure derivative (∂BS/∂P)P=0 of the bulk modulus of TiB2 ceramic is found to be larger than that estimated previously from uniaxial shock-wave loading experiments. The longitudinal (γL), shear (γS), and mean (γel) acoustic-mode Gruneisen parameters of TiB2 are positive: the zone-centre acoustic phonons stiffen under pressure in the usual way. Since the acoustic Debye temperature ΘD (=1190 K) is very high, the shear modes provide a substantial contribution to the acoustic phonon population at room temperature. Knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic TiB2.