Phonon conductivity correction term: Application to P-doped Ge

The role of the characteristic temperature θ¹ (which differentiates peripheral phonons from non-peripheral phonons) in the study of the phonon conductivity correction term due to three phonon normal processes, has been studied for the first time. The study is made for P-doped Ge in the temperature range 1–5 °K for the different values of θ¹ in the range 8–24 °K as an example.     

Theoretical study of the lattice thermal conductivity in Ge framework semiconductors

The lattice thermal conductivity of Ge clathrates is investigated by evaluating the linear response theory heat current correlation functions using molecular dynamics. Clathrate crystals with and without guest atoms in their fullerane cages are studied. In comparison with that of diamond-phase Ge, the clathrate conductivity is reduced by approximately 1 order of magnitude due to the open framework itself. The addition of an encapsulated (rattling) Sr guest atom produces a further order of magnitude reduction in the conductivity, making it comparable to that of amorphous Ge. Our results are consistent with experiments, and have impact on the search for improved thermoelectric materials.     

Characteristic temperature θ1 and lattice thermal conductivity of a doped sample: Application to P-doped Ge

Role of the characteristic temperature θ¹ which differentiates non-peripheral phonons from peripheral phonons, in the estimation of the total lattice thermal conductivity of the doped sample has been studied by calculating the total phonon conductivity of P-doped Ge in the temperature range 1–5 K for the different values of θ¹, for the first time.     

Modification of the lattice thermal conductivity in silicon quantum wires due to spatial confinement of acoustic phonons

Lattice thermal conductivity in silicon quantum wires is theoretically investigated. The bulk of heat in silicon structures is carried by acoustic phonons within a small region in the first Brillouin zone. Our formalism rigorously takes into account modification of these acoustic phonon modes and phonon group velocities in free- and clamped-surface wires due to spatial confinement. From our numerical results, we predict a significant decrease (more than an order of magnitude) of the lattice thermal conductivity in cylindrical quantum wires with diameter D =  200 Å. The decrease is about two times stronger in quantum wires than in quantum wells of corresponding dimensions. Our theoretical results are in qualitative agreement with experimentally observed drop of the lattice thermal conductivity in silicon low-dimensional structures.     

Contribution of thermal radiation in measurements of thermal conductivity of sandstone

The effective thermal conductivity of sandstone at high pressures of up to 400 MPa and temperatures of 273–523 K has been studied. It has been shown that the degree of crystallization of rock-forming minerals substantially influences the temperature and pressure dependences of the thermal conductivity. The contribution of the radiation heat transfer in measurements of the thermal conductivity of sandstone at various temperatures has been analyzed taking into account the reflection and attenuation of the thermal radiation. The results of measuring the reflection and absorption spectra of the thermal radiation have been presented.     

A unified treatment of the lattice Green function,generalized Watson integral and associated logarithmic integral for the d-dimensional hypercubic lattice

Using multinomial expansion theorems, a unified approximation for the lattice Green function, generalized Watson integral and associated logarithmic integral for the d-dimensional hypercubic lattice is presented. The validity of this approximation is tested by other calculation methods. The approximate formulas derived are satisfactory to all other approximations and are a most suitable solution for the study of related physical properties of solids. Some examples of the effectiveness of this methodology are presented.     

On the finite thermal conductivity of a one-dimensional rotator lattice

A heat transfer process is studied in a one-dimensional lattice of coupled rotators in which the orientation interaction between neighboring units is described by the periodic potential. Using this system as an example, it is demonstrated for the first time that one-dimensional lattices with a finite thermal conductivity in the thermodynamic limit can exist without substrate potential. As the temperature increases, the given system transforms from the state with an infinite thermal conductivity to the state with a finite thermal conductivity. The finiteness of the thermal conductivity stems from the existence of localized stationary excitations that interfere with heat transfer in the lattice. The lifetime and the concentration of these excitations increase with an increase in the temperature, which leads to a monotonic decrease in the thermal conductivity coefficient.     

Effect of dislocations on the lattice thermal conductivity of superconducting niobium

Thermal conductivity measurements on single crystal Nb samples in the superconducting state have demonstrated a resonant scattering of thermal phonons at roughly 5 × 10¹⁰Hz. The assumption of a mechanical resonance associated with the dislocation structure accounts for the present data and is consistent with other data found in the literature. The thermalization of phonons at an abraded sample surface, and the attendant failure of the relation l^?1 = ∑_jl_j^?1 for phonon mean free paths, was also observed.     

A correction to the Hamiltonian of the QCD string with quarks due to the rigidity term

The correction to the Hamiltonian of a quark-antiquark system due to the rigidity term in the action of the gluodynamics string is found using the action obtained by D. V. Antonov et al., Mod. Phys. Lett. A 11, 1905 (1996) with the Hamiltonian obtained by A. Yu. Dubin et al., Phys. At. Nucl. 56, 1745 (1993); Phys. Lett. B 323, 41 (1994) and E. L. Gubankova and A. Yu. Dubin, Phys. Lett. B 334, 180 (1994); preprint ITEP 62-94. This correction contains additional contributions to the orbital momentum of the system and several higher derivative operators. The resulting Hamiltonian is used to evaluate the rigid-string-induced term in the Hamiltonian of the relativistic quark model for the case of large masses of the quark and antiquark. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 9, 673–678 (10 May 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Effect of phonon scattering mechanisms on the lattice thermal conductivity of skutterudite-related compound

We have prepared the skutterudite-related compounds FeCo_3Sb_{12} and La_{0.75}Fe_3CoSb_{12} with different average grain sizes (about 0.8 and 3.9μm) by hot pressing. Samples were characterized by XRD, EPMA and SEM. The lattice thermal conductivity was investigated in the temperature range from room temperature to 200℃. Based on the Debye model, we analyse the change in lattice thermal conductivity due to various phonon scattering mechanisms by examining the relationship between the weighted phonon relaxation time τ(ω/ω_D)^2 and the reduced phonon frequency ω/ω_D. The effect of grain boundary scattering to phonon is negligible within the range of grain sizes considered in this study. The large reduction in lattice thermal conductivity of FeCo_3Sb_{12} compound contributes to the electron－phonon scattering. As for La_{0.75}Fe_3CoSb_{12} compound, the atoms of La filled into the large voids in the structure of the skutterudite produce more significant electron－phonon scattering as well as more substitute of Fe at Co site at the same time. Moreover, the point-defect scattering appears due to the difference between the atoms of La and the void. In addition, the scattering by the rattling of the rare-earth atoms in the void is another major contribution to the reduced lattice thermal conductivity. Introducing the coupling of the electron－phonon scattering with the point-defect scattering and the scattering by the rattling of the rare-earth atom is an effective method to reduce the lattice thermal conductivity of the skutterudite-related compounds by substitution of Fe for Co and the atoms of La filled in the large voids in the skutterudite structure.     

Calculation of lattice dynamical properties from electronic energies: Application to C,Si and Ge

It is shown that lattice dynamical properties of insulators can be calculated directly from the electronic band structure using the “special points” method. The shear modulii and zone boundary transverse acoustic phonon frequencies of C, Si and Ge are calculated with no adjustable parameters, with results in reasonable agreement with experiment.     

Application of SAXS to the study of particle-size-dependent thermal conductivity in silica nanofluids

Knowledge of the size and distribution of nanoparticles in solution is critical to understanding the observed enhancements in thermal conductivity and heat transfer of nanofluids. We have applied small-angle X-ray scattering (SAXS) to the characterization of SiO₂ nanoparticles (10–30 nm) uniformly dispersed in a water-based fluid using the Advanced Photon Source at Argonne National Laboratory. Size distributions for the suspended nanoparticles were derived by fitting experimental data to an established model. Thermal conductivity of the SiO₂ nanofluids was also measured, and the relation between the average particle size and the thermal conductivity enhancement was established. The experimental data contradict models based on fluid interfacial layers or Brownian motion but support the concept of thermal resistance at the liquid–particle interface.     

The temperature dependence of the conductivity and thermal emf due to multiphonon hopping in disordered semiconductors

Using transport theory, we studied the temperature dependence of the static conductivity and of the thermal emf due to multiphonon hopping in disordered semiconductors. In the low-temperature region when T < _m ( _m is the maximum phonon frequency), the temperature dependences of the conductivity and the thermal emf are the same as when single-phonon hopping is dominant. At higher temperatures (T _m), the hopping conductivity and thermal emf are characterized by a slower dependence on reciprocal temperature than in the low-temperature region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No.2, pp.42–47, February, 1976.The author is to V. L. Bonch-Bruevich and A. G. Mironov for discussing this work.     

Application of the multi distribution function lattice Boltzmann approach to thermal flows

Numerical methods able to model high Rayleigh (Ra) and high Prandtl (Pr) number thermal convection are important to study large-scale geophysical phenomena occuring in very viscous fluids such as magma chamber dynamics (10⁴ < Pr < 10⁷ and 10⁷ < Ra < 10¹¹). The important variable to quantify the thermal state of a convective fluid is a generalized dimensionless heat transfer coefficient (the Nusselt number) whose measure indicates the relative efficiency of the thermal convection. In this paper we test the ability of Multi-distribution Function approach (MDF) Thermal Lattice Boltzmann method to study the well-established scaling result for the Nusselt number (Nu ∝ Ra ^1/3) in Rayleigh Bénard convection for 10⁴ ≤ Ra ≤ 10⁹ and 10¹ ≤ Pr ≤ 10⁴. We explore its main drawbacks in the range of Pr and Ra number under investigation: (1) high computational time N _c required for the algorithm to converge and (2) high spatial accuracy needed to resolve the thickness of thermal plumes and both thermal and velocity boundary layer. We try to decrease the computational demands of the method using a multiscale approach based on the implicit dependence of the Pr number on the relaxation time, the spatial and temporal resolution characteristic of the MDF thermal model.     

The effects of different doping patterns on the lattice thermal conductivity of solid Ar

In order to investigate the effects of doping patterns on phonon transport, equilibrium molecular dynamics method is performed to calculate the lattice thermal conductivity of solid argon doped with krypton atoms in different geometrical distribution modes. Four different patterns are introduced through replacing Ar atoms with the same amount of Kr atoms in different volume and positions. The simulation results demonstrate that the impurity volume and distribution have significant effects on phonon transport in a crystal structure. The lowest thermal conductivity among the four doping patterns is achieved by introducing the impurity in a nanometer size cubic pattern distributed in the Ar matrix, which is roughly two times lower than that of pure argon at 17 K. The impurity strength on phonons is estimated through comparing the simulation results with those calculated from the Callaway model.