Interpretation of Thermal Conductivity in the Ferromagnetic Metallic Phase of La0.83Sr0.17MnO3 Manganites: Scattering of Phonons and Magnons

The lattice contribution to the thermal conductivity (κ _ph) is theoretically analyzed within the framework of Kubo model in La_0.83Sr_0.17MnO₃ manganites. The theory is formulated when thermal conduction is limited by the scattering of phonons from defects, grain boundaries, charge carriers, and phonons. The lattice thermal conductivity dominates in La-Sr-MnO manganites and is artifact of strong phonon-impurity and -phonon scattering mechanism in the ferromagnetic metallic state. The electronic contribution to the thermal conductivity (κ _e) is estimated following Wiedemann-Franz law. This estimate sets an upper bound on κ _e, and in the vicinity of Curie temperature (T _c ) is about 1% of total heat transfer of manganites. Another important contribution in the metallic phase should come from spin waves (κ _m). It is noticed that κ _m increases with a T ² dependence on the temperature. These channels for heat transfer are algebraically added and κ _tot develops a broad peak at about 120 K, before falling off at lower temperatures. The behaviour of the thermal conductivity in manganites is determined by competition among the several operating scattering mechanisms for the heat carriers and a balance between electron, magnon, and phonon contributions. The numerical analysis of heat transfer in the ferromagnetic metallic phase of manganites shows similar results as those revealed from experiments.     

Thermal Conductivity of Small Nickel Particles

The thermal conductivity of nanoscale nickel particles due to phonon heat transfer is extrapolated from thin film results calculated using nonequilibrium molecular dynamics (NEMD). The electronic contribution to the thermal conductivity is deduced from the electrical conductivity using the Wiedemann–Franz law. Based on the relaxation time approximation, the electrical conductivity is calculated with the Kubo linear-response formalism. At the average temperature of T=300 K, which is lower than the Debye temperature Θ_D=450 K, the results show that in a particle size range of 1.408–10.56 nm, the calculated thermal conductivity decreases almost linearly with decreasing particle size, exhibiting a remarkable reduction compared with the bulk value. The phonon mean free path is estimated, and the size effect on the thermal conductivity is attributed to the reduction of the phonon mean free path according to the kinetic theory.     

Interpretation of Temperature-Dependent Resistivity of La–Pb–MnO3: Role of Electron–Phonon Interaction

The present paper deals with the theoretical investigation of temperature-dependent resistivity of the perovskite manganites La_0.78Pb_0.22MnO_3-δ within the framework of the classical electron–phonon model of resistivity, i.e., the Bloch–Gruneisen model. Due to inherent acoustic (low-frequency) phonons (ω_ac) as well as high-frequency optical phonons (ω_op), the contributions to the electron–phonon resistivity have first been estimated. At low temperatures the acoustic phonons of the oxygen-breathing mode yield a relatively larger contribution to the resistivity as compared to the contribution of optical phonons. Furthermore, the nature of phonons changes around T = 215 K exhibiting a crossover from an acoustic to optical phonon regime with elevated temperature. The contribution to resistivity estimated by considering both phonons, i.e., ω_ac and ω_op, when subtracted from experimental data, infers a T^4.5 temperature dependence over most of the temperature range. Deduced T^4.5 temperature dependence of ρ_diff = [ρ_exp − {ρ₀ + ρ_e-ph( = ρ_ac + ρ_op)}] is justified in terms of electron–magnon scattering within the double exchange (DE) process. Within the proposed scheme, the present numerical analysis of temperature dependent resistivity shows similar results as those revealed by experiments     

Low-Temperature Thermal Conductivity and Specific Heat of Plastically Deformed High-Purity Tantalum Single Crystals

The thermal conductivity and the specific heat of plastically deformed, high-purity tantalum single crystals have been measured together with an amorphous SiO₂ specimen in the temperature range between 50 mK and about 2 K. After plastic deformation, the thermal conductivity was reduced by a factor of more than 100 and had a magnitude comparable to that of the amorphous SiO₂ specimen. However, the specific heat measurements revealed a T³-relationship for the phonon contribution down to the lowest temperatures with a magnitude as in the case of undeformed crystalline solids. Thus, it must be concluded that the scattering of thermal phonons introduced by the plastic deformation has to be attributed to intrinsic properties of dislocations rather than to the interaction of phonons with tunneling systems. In the present paper the scattering mechanism is related to oscillations of geometrical kinks in non-screw dislocations.     

Thermal Conductivity of Carbon Aerogels as a Function of Pyrolysis Temperature

Amorphous carbon samples with a total porosity of about 85% were synthesized via pyrolysis of sol–gel derived resin precursors. Since the pores in the samples investigated have dimensions of a few tens of nanometers only, the gaseous contribution to the thermal conductivity is largely suppressed at ambient pressure. Values for the total thermal conductivity as low as 0.054 W·m⁻¹·K⁻¹ at 300°C are detected. However, the pyrolysis temperature has a great impact on the contribution of the solid backbone to the total thermal conductivity. From the same precursor a series of samples was prepared via pyrolysis at temperatures ranging from 800 to 2500°C. The thermal conductivity of this series of carbons at 300°cC under vacuum increases by a factor of about 8 if the pyrolysis temperature is shifted from 800 to 2500°C. To elucidate the reason for this strong increase, the infrared radiative properties, the electrical conductivity, the macroscopic density, the microcrystallite size, the sound velocity, and the inner surface of the samples were determined. Evaluation of the experimental data yields only a negligible contribution from radiative heat transfer and electronic transport to the total thermal conductivity. The main part of the increasing thermal conductivity therefore has to be attributed to an increasing phonon mean free path in the carbons prepared at higher pyrolysis temperatures. However, the phonon mean free path does not match directly the in-plane microcrystallite size of the amorphous carbon. Rather, the in-plane microcrystallite size represents an upper limit for the phonon mean free path. Hence, the limiting factor for the heat transport via phonons has to be defects swithin the carbon microcrystallites which are partially cured at higher temperatures.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

Electro- and Heat Transfer in $$\mathbf{Cd}_{\mathbf{0.22}}\mathbf{\hbox {Hg}}_{\mathbf{0.78}}{} \mathbf{Te}$$ Single Crystals in the Temperature Range of Their Practical Applications

The thermal and electrical conductivity of a single-crystal \(\hbox {Cd}_{0.22}\hbox {Hg}_{0.78}\hbox {Te}\) was studied in the temperature range of practical applications (77–300 K). The sample has impurity conductivity, which is limited by the scattering of charge carriers by phonons. Heat in the sample is transferred by phonons and thermal conductivity is limited by phonon–phonon scattering. The electron contribution to the thermal conductivity can be neglected.     

Structural and electrical properties of layered tetradymite-like compounds in the GeTe—Bi2Te3 and GeTe—Sb2Te3 systems

Analysis of the available crystallographic data shows that the GeTe-Bi₂Te₃ and GeTe-Sb₂Te₃ pseudobinary systems contain a wide variety of many-layered, long-period compounds belonging to the nGeTe · mBi₂Te₃ and nGeTe · mSb₂Te₃ homologous series. The Hall coefficient, thermoelectric power, and electrical conductivity of some of these compounds were measured over a wide temperature range. The temperature-dependent carrier mobility data suggest that both acoustic phonons and point defects contribute to the scattering of charge carriers. The lattice thermal conductivity of the many-layered, long-period compounds studied, κ_ph = 6–8 mW/(cm K), is notably lower than that of the constituent tellurides     

Thermal Conductivity of a Molecular Crystal with Rotational Degrees of Freedom: Orientational Defect Scattering

Measurements of thermal conductivity of solid methane-deuteromethane solutions at equilibrium vapor pressure in the temperature range 1.2÷20 K are reported. The obtained dependences of thermal conductivity on temperature and concentration can be explained qualitatively assuming that the dominant mechanism of phonon scattering is connected with the interaction of phonons with the rotational motion of the molecules in all of the three orientational phases of the CH₄-CD₄ system. The contribution of the orientational defect scattering to the thermal conductivity is discussed in frame of the model of local changes in the moments of inertia of molecules.      

Evaluation of Thermal Conductivity of Hyperstoichiometric UO<Subscript>2+<Emphasis Type="Italic">x</Emphasis></Subscript> by Molecular Dynamics Simulation

The thermal conductivity of UO_2+x has been investigated by an equilibrium molecular dynamics (EMD) simulation up to 2000 K using the Born–Mayer–Huggins interatomic potential with the partially ionic model. In the present EMD system with the Green–Kubo method, the thermal conductivity was determined by the auto-correlation functions of energy and charge currents and the cross-coupling term. The thermal conductivity of UO_2+x decreased with an increase of x and temperature. Its temperature dependence was relatively small for large x values, which was attributed to phonon scattering by excess oxygens. In addition, the heat capacity was calculated using the phonon-level density deduced by the velocity auto-correlation function for constituent ions. The phonon velocity was also evaluated by the phonon- dispersion relationship. Using these thermal properties obtained by EMD calculations, the effect of excess oxygens on the phonon mean free path was discussed.     

Electrical transport properties of Nd0.67−x Eu x Sr0.33MnO3 (0 ≤ x ≤ 0.67) manganites

A systematic investigation of electrical transport properties viz., electrical conductivity and thermopower of Eu-doped Neodymium-based colossal magnetoresistive manganites with compositional formula, Nd_0.67−x Eu _x Sr_0.33MnO₃ (x = 0–0.67) has been undertaken. These materials were prepared by citrate gel route and characterized by X-ray diffraction, scanning electron microscopy, AC susceptibility, and electrical resistivity measurements. With a view to understand the complex conduction mechanism of these materials, electrical resistivity and thermoelectric power (TEP) data have been analyzed using various theoretical models. It has been concluded that the ferromagnetic metallic part of the conduction mechanism is explained by grain/domain boundary, electron–electron, and magnon scattering mechanisms, while that of high temperature paramagnetic insulating region might be due to small polaron hopping mechanism. The sign change of charge carriers observed in TEP measurements is attributed to the oxygen deficiency of the samples.     

Thermal conductivity of solid hydrogen at low ortho-hydrogen concentrations

The interaction Hamiltonian of lattice vibrations and “impurity” ortho-hydrogen molecules of solid para-hydrogen has been derived from the potential of the anisotropic valence and dispersion forces. Below the thermal conductivity peak, along with boundary scattering, inelastic scattering of phonons by isolated ortho-hydrogen molecules has been shown to provide the principal contribution to the thermal resistivity at ortho concentrations c < 0.01. For c > 0.01 the heat flux in the lattice varies mainly through the resonant absorption and emission of phonons between rotational states of ortho-hydrogen molecular pairs. The thermal conductivity is calculated in the relaxation-time approximation for the equilibrium distribution of ortho-hydrogen molecules. The calculated dependences of the thermal conductivity on temperature and concentration are compared with those measured at temperatures up to 3.2 K and with c ≤ 0.05. The derived values are of the right order of magnitude and show good qualitative agreement with experiment.     

Nonuniform metallic state in manganites and cuprates

Local lattice distortions suggesting nonuniform charge distributions were found to be a common feature of manganites and cuprates in the metallic state by neutron scattering studies. The atomic pair-density function (PDF) determined by pulsed neutron powder diffraction showed that in La_1-xSr_xMnO₃ doped holes form lattice polarons which persist even in the metallic state. In La_1.85Sr_0.15CuO₄ the energy width of the LO phonons around (π,0) determined by inelastic neutron scattering reflects magnetic satellites indicative of spin charge stripe formation. The implications of such nonuniform charge distribution for metal-insulator transition and superconductivity are discussed.     

Phase diagram of the Pb-NiSb system and properties of (NiSb)<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Pb<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> solid solutions

The phase diagram of the Pb-NiSb system is presented. The system is pseudobinary, with a limited series of NiSb-based solid solutions: ≃1 mol % Pb at 300 K. In the temperature range ≃520–670 K, the system contains un unstable compound, Ni₃Pb₂Sb₃. At 1320 K, a monotectic transformation occurs (≃15–71 mol % NiSb). Electrical and thermal conductivity measurements reveal an additional contribution to the lattice thermal resistivity of the (NiSb)_{1 − x} Pb _x solid solutions and show that electrons and phonons in these materials are scattered elastically.     

Low-Temperature Internal Friction and Thermal Conductivity of Plastically Deformed, High-Purity Monocrystalline Niobium

The low-temperature internal friction Q ^–1 and thermal conductivity of plastically deformed, high-purity niobium monocrystals have been investigated and compared with measurements on an amorphous SiO₂ (a-SiO₂) specimen. After plastic deformation at intermediate temperatures, an approximately temperature independent internal friction Q ^–1 was observed with a magnitude comparable to that of the a-SiO₂ specimen. Plastic deformation at low temperatures leads to an internal friction Q ^–1 with a considerably smaller magnitude. In the temperature range between about 0.3 and 1.5K, the lattice thermal conductivity k of the deformed specimens decreases with increasing deformation. It is, however, nearly independent of the amount of deformation at the lowest temperatures investigated. In this temperature regime, the lattice thermal conductivity of the specimens varies proportional to T ³ and has a magnitude as would be expected for an undeformed sample. Additional heat release experiments on an undeformed sample clearly show no long-time energy relaxation effects. We conclude that the defects introduced by plastic deformation cannot be described with the tunneling model which had been proposed to describe the low temperature elastic and thermal properties of amorphous solids. The phonon scattering mechanisms observed in deformed niobium are tentatively related to the dynamic interaction of phonons with geometrical kinks in dislocations.     

A new heat transfer model of inorganic particulate-filled polymer composites

Thermal conductivity is an important parameter for characterization of thermal properties of materials. Various complicated factors affect the thermal conductivity of inorganic particulate-filled polymer composites. The heat transfer process and mechanisms in an inorganic particulate-filled polymer composite were analyzed in this article. A new theoretical model of heat transfer in these composites was established based on the law of minimal thermal resistance and the equal law of the specific equivalent thermal conductivity, and an relevant equation of effective thermal conductivity (K _eff) for describing a relationship between K _eff and filler volume fraction as well as other thermal parameters were derived based on this model. The values of K _eff of aluminum powder-filled phenol–aldehyde composites and graphite powder-filled phenol–aldehyde composites were estimated by using this equation, and the calculations were compared with the experimental measured data from these composites with filler volume fraction from 0 to 50% in temperature range of 50–60 °C and the predictions by Maxwell–Eucken equation and Russell equation. The results showed that the predictions of the K _eff by this equation were closer to the measured data of these composites than the other equations proposed in literature.     

Microscopic calculation of the heat transfer between a granular structure and liquid3He

A recent formula for the heat transfer coefficient between ³He quasiparticles and phonons of a sintered metallic powder is evaluated using the phonon density of states of a microscopic model of a granular structure. The microscopic model describes a simple crystalline granular structure and contains extended modes only. When the dominant phonon wavelength is less than a typical grain size, possesses a low-temperature enhancement typical of a sintered metallic powder and over a limited range exhibits a linear variation with temperature.     

Investigation of Al substitution on the thermoelectric properties of SrSi2

We report the results of aluminum substitution on the temperature-dependent electrical resistivity, Seebeck coefficient, as well as thermal conductivity of SrSi_2−xAl_x alloys with 0 ≤ x ≤ 0.20. It is found that the substitution of Al onto the Si sites of SrSi₂ causes a significant decrease in the electrical resistivity and the Seebeck coefficient. The observations are associated with the downward shift of the Fermi level, due to hole-doping via Al substitution within a rigid-band scenario. The low-temperature thermal conductivity decreases markedly with increasing Al content. Analysis of the lattice thermal conductivity from the contribution of various thermal scattering mechanisms reveals that the reduction in the lattice thermal conductivity mainly arises from the grain-boundary and point-defect scattering of the phonons through chemical substitution.     

Lattice Softening Significantly Reduces Thermal Conductivity and Leads to High Thermoelectric Efficiency

The influence of micro/nanostructure on thermal conductivity is a topic of great scientific interest, particularly to thermoelectrics. The current understanding is that structural defects decrease thermal conductivity through phonon scattering where the phonon dispersion and speed of sound are assumed to remain constant. Experimental work on a PbTe model system is presented, which shows that the speed of sound linearly decreases with increased internal strain. This softening of the materials lattice completely accounts for the reduction in lattice thermal conductivity, without the introduction of additional phonon scattering mechanisms. Additionally, it is shown that a major contribution to the improvement in the thermoelectric figure of merit (zT > 2) of high‐efficiency Na‐doped PbTe can be attributed to lattice softening. While inhomogeneous internal strain fields are known to introduce phonon scattering centers, this study demonstrates that internal strain can modify phonon propagation speed as well. This presents new avenues to control lattice thermal conductivity, beyond phonon scattering. In practice, many engineering materials will exhibit both softening and scattering effects, as is shown in silicon. This work shines new light on studies of thermal conductivity in fields of energy materials, microelectronics, and nanoscale heat transfer.     

Effect of piezoelectric polarization on phonon group velocity in nitride wurtzites

We have investigated the effect of piezoelectric (PZ) polarization property on group velocity of phonons in binary as well as in ternary wurtzite nitrides. It is found that with the presence of PZ polarization property, the phonon group velocity is modified. The change in phonon group velocity due to PZ polarization effect directly depends on piezoelectric tensor value. Using different piezoelectric tensor values recommended by different workers in the literature, percent change in group velocities of phonons has been estimated. The Debye temperatures and frequencies of binary nitrides GaN, AlN, and InN are also calculated using the modified group velocities. For ternary nitrides Al _x Ga_(1−x)N, In _x Ga_(1−x)N, and In _x Al_(1−x)N, the phonon group velocities have been calculated as a functions of composition. A small positive bowing is observed in phonon group velocities of ternary alloys. Percent variations in phonon group velocities are also calculated for a straightforward comparison among ternary nitrides. The results are expected to show a change in phonon relaxation rates and thermal conductivity of III-nitrides when piezoelectric polarization property is taken into account.     

Specific heat studies in Ho-Ba-CuO superconductors: Fermionic and bosonic contributions

The specific heats of superconducting HoBa₂Cu₃O_7-δ (T _c≅ 92 K) have been theoretically investigated in the temperature domain 70 ≤T ≤110 K. The bosonic (phonons) contribution to the specific heat is estimated from Debye model in the harmonic approximation for high temperature expansion (T > θ_D/2π) using the moments of the phonon density of states. The fermionic constituent as the electronic specific heat is deduced using a suitable trial function above and belowT _c. As a next step the contribution of specific heat by charge oscillations (plasmons) are obtained. The theoretical results from bosonic and fermionic terms are then compared with the experimental results. We find that the specific heats from electronic as well as plasmon term are only a fraction of lattice specific heat and in particular, plasmons do not influence the thermal conduction significantly. The implications of the above analysis are discussed.