Linear dependence of the phonon thermal resistance of nonmetallic crystals on the isobaric thermal strain

This paper reports on the results of investigations into the thermal resistance W and thermal expansion coefficient β for single-crystal samples of Si, SiO₂, Al₂O₃, and NaCl. The available experimental data on the thermal resistance and thermal expansion coefficient for materials with different types of interatomic bonding and different Landau criteria for convection are analyzed. It is demonstrated that the reduced phonon thermal resistance is equal to the isobaric thermal strain at any temperature.     

Low-temperature thermal conductivity of highly enriched and natural germanium

Experimental data on the thermal conductivity K(T) of crystals of natural and highly enriched germanium (99.99%) ⁷⁰Ge with lapped and polished surfaces are analyzed in the temperature range ∼1.5–8 K. In all the samples in the temperature range ∼1.5–4 K the standard boundary mechanism of scattering dominates. As the temperature is raised, an isotopic scattering mechanism is observed in the natural samples. In the highly enriched samples the theoretical values of K(T) turn out to be much smaller than the experimental ones. It is conjectured that a Poiseuille viscous flow regime of the phonon gas emerges in this case. Zh. éksp. Teor. Fiz. 114, 1757–1764 (November 1998)     

Isotope effect in the thermal conductivity of germanium single crystals

The thermal conductivity of chemically, structurally, and isotopically highly pure germanium single crystals is investigated experimentally in the temperature range from 2 to 300 K. It is found that the thermal conductivity of germanium enriched to 99.99% ⁷⁰Ge is 8 times higher at the maximum than the thermal conductivity of germanium with the natural isotopic composition. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 463–467 (25 March 1996)     

Kondo anomalies of heat conductivity and Lorenz ratio in normal state (La,Ce) Al2

The thermal conductivity of LaAl₂ and of two dilute (La, Ce)Al₂ alloys was measured in the normal state between 0.4 and 8 K. From the lattice conductivity of LaAl₂ a high dislocation densityN _d caused by the arc melting process can be inferred. After annealingN _d is reduced by an order of magnitude. For the (La, Ce)Al₂ samples minima are observed at 5 K in theW ^e ·T vs.T curves (W ^e =electronic thermal resistivity). Below 1 K the quantityW ^e ·T is linear in (— lnT). The electronic Lorenz ratioL ^e (T)=ρ(T)/W ^e (T) ·T shows a maximum at 2 K with a value 23% aboveL ^e (0). It is for the first time that this Kondo anomaly is established in its full temperature dependence.     

On the role of the higgs mechanism in present electroweak precision tests

Based on the observablesM _W, Γ _l ,s _W ^?2 (M _Z ² ), we evaluate the parameters Δx, Δy and ε at one-loop level within an electroweak massive vector-boson theory, which does not employ the Higgs mechanism. The theoretical results are consistent with the experimental ones on Δx, Δy, ε. The theoretical prediction for Δy coincides with the standard-model one (apart from numerically irrelevant terms which vanish forM _H→∞). Nonrenormalizability only affects Δx and ε, which differ from the standard-model results by the replacement logM _H→log Λ for a heavy Higgs mass,M _H (where Λ denotes an effective UV cut-off).     

Study of thermal conductivity and specific heat of amorphous and partially crystalline poly(ethylene terephthalate) in relation to its structure

The thermal conductivity k(T) and the specific heat of amorphous and partially crystalline polyethylene terephthalate) were measured in the intervals 1.2–40K and 1.2–10K, respectively. For a quantitative study of the relation between the thermal conductivity and the structure and degree of crystallinity of the samples their small angle X-ray scattering was measured. For T > 20 K, k(T) increases with increasing degree of crystallinity φ, whereas for T < 10 K, k(T) decreases when φ increases. Amorphous PET shows a temperature dependence of k(T) which is typical for all amorphous materials. These results are compared with curves which were computed from experimental small angle structure functions using a model for phonon scattering in vitreous systems obtained by Klemens. It is shown that for T < 10 K the change in conductivity in the partially crystalline samples relative to that of the purely amorphous sample can quantitatively be explained by additional scattering of phonons from static long-range order fluctuations of the sound velocity which are due to the microscopic structure of the polymer. From a measurement of the optical extinction of the samples relative values of their thermal conductivity at 50 mK are estimated. The specific heat obeys a T³-law between 1.2 K and about 7 K and decreases linearly with φ. The Debye specific heat of the amorphous sample was computed from the sound velocities. It is only 85% of the measured value.     

Shape,size and phonon scattering effect on the thermal conductivity of nanostructures

A phenomological model is described here to study the effect of size, shape and phonon scattering on the thermal conductivity of nanostructures. Using the classical model proposed by Guisbiers et al (Phys. Chem. Chem. Phys. 12, 7203 (2010), J. Phys. Chem. C 112, 4097 (2008)) in terms of the melting temperature of nanostructures, the expression for variation of thermal conductivity is obtained in terms of shape and size parameter. An additional term is included in the expression of thermal conductivity to consider the impact of phonon scattering due to the surface roughness with a decrease in size. The expression of thermal conductivity is obtained for spherical nanosolids, nanowires and nanofilms. The thermal conductivity is found to decrease in nanostructures in comparison with the counterpart bulk material. The values of thermal conductivity obtained from the present model are found to be close to the available experimental data for different values of roughness parameter which verifies the suitability of the model.     

Photoinduced semiconductor-metal phase transition in the surface layer of vanadium dioxide

The photoinduced semiconductor-metal phase transition occurring for a time Δt < 1 ps in the surface layer of vanadium dioxide is studied theoretically. A nonthermal mechanism of instability development is considered. An equation for the order parameter ξ of the photoinduced semiconductor-metal phase transition is derived. It is shown that the transition of the surface layer of VO₂ to the metallic state requires irradiation by a laser pulse whose energy density W exceeds a critical value W _c. The phase transition is initiated at the surface, after which the interface propagates deep into the sample. The critical energy density W _c, the velocity of propagation of the metal-semiconductor interface, the thickness z ₀, and the characteristic time Δt of formation of the metal layer are calculated. The theoretical results obtained are in agreement with the experimental data on irradiation of vanadium dioxide single crystals by high-intensity laser pulses.     

Effect of isotopic disorder on the thermal conductivity of germanium in the region of the maximum

This paper discusses the question of how isotopic disorder affects the position of the thermal-conductivity maximum of germanium. The discussion is in terms of a Callaway-type model. Experimental data on the thermal conductivity of a natural Ge crystal and of highly enriched Ge⁷⁰ crystals are analyzed. Fiz. Tverd. Tela (St. Petersburg) 41, 1185–1189 (July 1999)     

Effect of dispersion and damping of thermal phonon states on the longitudinal ultrasonic absorption in germanium crystals

A method has been proposed for approximating a phonon spectrum of cubic crystals, which has been obtained from data on inelastic neutron scattering for symmetric directions, over the entire Brillouin zone in the form appropriate for studying relaxation characteristics of phonon systems. The effect of dispersion and damping of thermal phonon states on the longitudinal ultrasonic absorption in anharmonic processes of scattering with the participation of three longitudinal phonons has been investigated for germanium crystals. It has been shown that the inclusion of the dispersion leads to a decrease in the anisotropy of ultrasonic absorption in the LLL relaxation mechanism and makes it possible to fit the results obtained from calculations of the ultrasonic absorption coefficients to the experimental data in the low-temperature range. The temperature dependence and anisotropy of the relaxation rate of longitudinal thermal phonons in germanium crystals have been determined from experimental data on ultrasonic absorption. The performed analysis has refined values of the relaxation parameters obtained from the interpretation of the data on thermal conductivity of germanium crystals with different isotopic compositions in the isotropic-medium model.     

Specific features of thermal resistance of silicon in the temperature range 105–130 K

Careful experimental investigations into the behavior of the thermal resistance of single-crystal silicon are carried out in the immediate vicinity of the temperature of an anharmonicity sign inversion (T _i =121.1 K), where phonon thermal resistance approaches zero. An anomalous positive deviation of the total thermal resistance (W) from the linear part of the temperature dependence with a maximum at 121.1 K is found in the temperature range 105–130 K. The temperature behavior of W in this range indicates that the mean free path of phonons is limited by a characteristic size of structural defects and that its temperature dependence exhibits specific features in the vicinity of T _i . It is established that the character of the temperature dependence of W above and below T _i is different. A linear functional relation between the total thermal resistance and the isobaric thermal strain is revealed at positive and negative anharmonicities of atomic vibrations.     

Grain-size-dependent thermal conductivity of nanocrystalline materials

In order to study the influence of grain size and lattice strain on the thermal conductivity of nanocrystalline (NC) materials, both experimental and theoretical studies were carried out on NC copper. The NC copper samples were prepared by hot isostatic pressing of nano-sized powder particles with mean grain size of 30 nm. The thermal behaviors of the samples were measured to be 175.63–233.37 W (m K)^?1 by using a laser method at 300 K, which is 45.6 and 60.6 % of the coarse-grained copper, respectively. The average grain size lies in the range of 56–187 nm, and the lattice strain is in the range of ?0.21 to ?0.45 % (in the direction of 111) and ?0.09 to 0.92 % (in the direction of 200). In addition, a modified Kapitza resistance model was developed to study the thermal transport in NC copper. The theoretical calculations based on the presented theoretical model were in good agreement with our experimental results, and it demonstrated that the thermal conductivity of NC materials show obvious size effect. It is also evident that the decrease in the thermal conductivity of NC material can be mainly attributed to the nano-size effect rather than the lattice strain effect.     

Defect-induced increase in the phonon energy involved in the formation of Urbach tail in Cu-ternaries

From a combined analysis of the stoichiometric composition and Urbach tail in samples of CuInSe₂, CuInTe₂, and CuGaTe₂ of the I-III-VI₂ family of chalcopyrite semiconductors, it is found that the energy hν_p involved in the electron/exciton-phonon interaction is a linear function of a parameter Δz which is the sum of the deviations from ideal molecularity Δx and anion to cation ratio Δy. It gives evidence that in the copper ternaries hν_p is associated to the structural defects caused by cation-cation, cation-anion, and other intrinsic disorders. The high value of hν_p found in the studied samples, higher than the highest optical mode, is shown to come from the contribution of the additional phonon energy due to structural defects. This is in agreement with recently proposed models of the temperature dependence of the Urbach energy.     

Theory for anisotropic thermal conductivity of magnetic nanofluids

Effective thermal conductivity tensor for magnetic nanofluids containing magnetizable nanoparticles suspended in a base liquid is theoretically investigated with a two-step homogenization method. First, we adopt differential effective medium theory to determine the equivalent thermal conductivity of magnetizable nanoparticle chains. Second, we generalize self-consistent anisotropic effective medium theory to study the effective thermal conductivity tensors of magnetic nanofluids. Numerical results show that the aspect ratio of chain-like aggregated clusters plays an important role in enhancement of anisotropic thermal conductivity. In addition, our theoretical results on the elements of thermal conductivity parallel to the fields Kez and perpendicular to the fields Kex are in good agreement with experimental data. Furthermore, we predict the nonmonotonic dependence of effective thermal conductivity on magnetic field strength, in accordance with experimental reports.     

Memory switching of germanium tellurium amorphous semiconductor

The dc conductivity and switching properties of amorphous GeTe thin film of thickness 262 nm are investigated in the temperature range 303-373 K. The activation energy ΔE_σ, the room temperature electrical conductivity σ_RT and the pre-exponential factor σ₀ were measured and validated for the tested sample. The conduction activation energy ΔE_σ is calculated. The I-V characteristic curves of the thin film samples showing a memory switching at the turnover point (TOP) from high resistance state (OFF state) to the negative differential resistance state (NDRS) (ON state). It is found that the mean values of the threshold electrical field E_th decreased exponentially with increasing temperatures in the investigated range. The switching activation energy ΔE_th is calculated. Measurements of the dissipated threshold power P_th and the threshold resistance R_th were carried out at TOP point at different temperatures of the samples. The activation energies ΔE_R and ΔE_P caused by resistance and power respectively are deduced. The results obtained support thermal model for initiating switching process in this system.     

Thermal conductivity of gold and silver at high pressures

The thermal diffusivities of gold and silver have been measured under pressure up to 2.5 GPa at room temperature. From the measured data the pressure dependence of the thermal conductivity, λ, has been calculated. The values found for the pressure coefficient λ^?1$\text{δλ}\text{δP}$ were 3.9 × 10^?2GPa^?1 for gold and 4.0 × 10^?2 GP silver at atmospheric pressure. The results are compared to theoretical predictions of the pressure dependence and also to previous experimental results for copper and aluminium. For the noble metals, small angle or “vertical” scattering of electrons is shown to have a stronger volume dependence than “horizontal” scattering.     

73Ge NMR spectra in germanium single crystals with different isotopic composition

We have studied the influence of isotopic disorder on the local deformations in Ge single crystals from both experimental and calculation points of view. The nuclear magnetic resonance (NMR) spectra of⁷³Ge nuclei (the nuclear spin equals 9/2) in perfect single crystals of germanium with different isotopic content were measured at temperatures 80, 300 and 450 K. Abnormal broadening of the spectrum was found to occur when the magnetic field was aligned along the [111] axis of a crystal. The observed specific angular dependence of the quadrupole broadening was attributed to isotopic disorder among atoms of germanium sited around the⁷³Ge NMR probe. Local lattice deformations in germanium crystal lattice due to isotopic impurity atoms were calculated in the framework of the adiabatic bond charge model. The results obtained were applied to study random noncubic crystal field interactions with the nuclear quadrupole moments and corresponding effects in NMR spectra. Simulated second and fourth moments of resonance frequency distributions caused by the magnetic dipole-dipole and electric quadrupole interactions are used to analyze the lineshapes, theoretical predictions agree qualitatively with the experimental data.     

IR absorption and Raman spectra of single crystals of stable germanium isotopes

The Raman and IR absorption spectra of single crystals of germanium isotopes ⁷²Ge, ⁷³Ge, ⁷⁴Ge, and ⁷⁶Ge in the region of phonon absorption and interband electronic transitions are studied at room temperature. The dependence of the Raman peak position on the atomic mass has the form ν ~ M^–1/2. The shifts of the phonon absorption peaks of individual isotopes with respect to germanium of natural isotopic composition ^natGe are determined. With increasing average atomic mass of germanium, these peaks shift to longer wavelengths. In the region of interband electronic transitions, the intrinsic absorption edge of ⁷⁶Ge is observed to shift by 1 meV to higher energies with respect to Ge of natural isotopic composition. For isotopes with atomic masses close to that of natural germanium (⁷²Ge,⁷³Ge, ⁷⁴Ge), we found no significant difference in the band gap width at room temperature.     

Lattice thermal conductivity of compounds with inhomogeneous intermediate rare-earth ion valence

The thermal conductivity κ (within the range 4–300 K) and electrical conductivity σ (from 80 to 300 K) of polycrystalline Sm₃S₄ with the lattice parameter a=8.505 Å (with a slight off-stoichiometry toward Sm₂S₃) are measured. For T>95 K, charge transfer is shown to occur, as in stoichiometric Sm₃S₄ samples, by the hopping mechanism (σ ～ exp(?ΔE/kT) with ΔE ～ 0.13 eV). At low temperatures [up to the maximum in the lattice thermal conductivity κ_ph(T)], κ_ph ～ T ^2.6; in the range 20–50 K, κ_ph ～ T ^?1.2; and for T>95 K, where the hopping charge-transfer mechanism sets in, κ_ph ～ T ^?0.3 and a noticeable residual thermal resistivity is observed. It is concluded that in compounds with inhomogeneous intermediate rare-earthion valence, to which Sm₃S₄ belongs, electron hopping from Sm²⁺ (ion with a larger radius) to Sm³⁺ (ion with a smaller radius) and back generates local stresses in the crystal lattice which bring about a change in the thermal conductivity scaling of κ_ph from T ^?1.2 to T ^?0.3 and the formation of an appreciable residual thermal resistivity.     

Magnetization,magnetoelectric polarization,and specific heat of HoGa3(BO3)4

A comprehensive experimental and theoretical study of magnetic, magnetoelectric, thermal, and spectroscopic characteristics of HoGa₃(BO₃)₄ gallium borate single crystals has been performed. A large magnetoelectric effect exceeding its values found in all iron and aluminum borates except HoAl₃(BO₃)₄ has been observed. The magnetoelectric polarization of HoGa₃(BO₃)₄ equals ΔP _ba (B _a ) ≈ ?1020 μC/m² at T = 5 K in a magnetic field of 9 T. The theoretical treatment based on the crystal field model for rare-earth ions provides a unified approach for the consistent interpretation of all measured characteristics. The crystal-field parameters are determined. The temperature (in the 3–300 K range) and magnetic field (up to 9 T) dependences of the magnetization, the Schottky anomaly in the temperature dependence of the specific heat, and its shift in the field B ‖ c are described. To compare the thermal properties of HoGa₃(BO₃)₄ with those of HoAl₃(BO₃)₄ exhibiting record values of the polarization, the specific heat of HoAl₃(BO₃)₄ at various B values and the temperature dependence of the polarization ΔP _b (T) in the applied magnetic field of 9 T have been measured.