Phonon Conductivity Research Articles

ANOMALOUS BEHAVIOUR OF THE LOW TEMPERATURE PHONON CONDUCTIVITY OF AN FeMnAl ALLOY

Measurements have been made at 4.2-30 K for the thermal conductivity of a poly-crystalline Fe-25Mn-5Al-0.2C sample with negative temperature coefficient of resistivity. It is found that the phonon conductivity is anomalously proportional to T. The suggested explanation is that this phenomenon results from the noneffectiveness of the scattering of phonons by electrons, when electrons have short mean free path caused by addition of Al.

Physical Properties of Ni3Al Containing 24 and 25 Atomic Percent Aluminum

ABSTRACTThermal conductivity, electrical resistivity, Seebeck coefficient and thermal expansion data were obtained on well-annealed Ni3Al containing 24 and 25 at. % Al. The results span the temperature range 300 to 1000 K. The expansion coefficients did not vary with composition and increased with temperature, reaching values of aIout 17 × 10−6 K−1 at 1000 K. The thermal conductivity and electrical resistivity changed rapidly with composition, and the thermal conductivity of 24 at. % Al is as much as 30% lower than that for stoichiometric Ni3A1. The electronic Lorenz function of Ni3Al was obtained by subtracting the estimated phonon conductivity component and found to be within about 5% of the Sommerfeld prediction from 300 to 1000 K. The electrical resistivity results for stoichiometric Ni 3Al are influenced by the loss of ferromagnetic order at lower temperatures and are not adequately described by the Bloch-Grüneisen equation.

Phonon Conductivity of Ice Single Crystals

AbstractThe phonon conductivity is analyzed of ice single crystals to study the role of the normal and the umklapp phonon‐phonon interaction processes.

Thermal conductivity of near-stoichiometric (U, Pu, Nd)O 2 and (U, Pu, Eu)O 2 solid solutions

The thermal conductivities of near-stoichiometric [(U 0.8Pu 0.2),R]O 2 solid solutions containing RO 1.5(R = Nd or Eu) up to 10 mol% were determined by the laser flash method in the temperature range 700–1900 K. The thermal conductivities for the solid solutions up to about 1550 K. satisfied the phonon conduction equation K = (A + BT) −1 . The thermal conductivity decreased gradually with the increase of the rare earth content. This decrease was mainly caused by the lattice defect thermal resistance. The measured defect thermal resistivities ( = A) were in good agreement with the calculated results based on the lattice defect model in which U 4+, U 5+, Pu 4+ and R 3+ ions were considered as phonon scattering centers. The lattice strain parameter ϵ = 97 and 103 were obtained for (U, Pu, Nd)O 2 and (U, Pu, Eu)O 2 solid solutions, respectively. The lattice strain effect on the thermal resistivity was about 15 times larger than the mass difference one.

Phonon thermal conductivity limited by electron scattering in amorphousZr70Cu30

The low-temperature thermal conductivity of amorphous ${\mathrm{Zr}}_{70}$${\mathrm{Cu}}_{30}$ is investigated. The lattice thermal conductivity as limited by electrons in the superconducting state has been obtained at temperatures close to ${T}_{c}$. This has allowed for the first time the verification of the temperature dependence of the phonon conductivity as predicted by Bardeen, Rickayzen, and Tewordt. The analysis of the data in the normal and superconducting state shows that Matthiessen's rule can be used in amorphous metals to separate the different scattering processes.

Thermal conductivity of germanium containing dislocations at low temperatures

AbstractTo study the frequency dependence of the phonon–dislocation scattering, the phonon conductivity of germanium with dislocations is analysed using Holland's model and Kumar and Sinha's relaxation time for the phonon–dislocation scattering processes. A reasonably good agreement is observed between present theory and experimental data of Sato and Sumino.

Thermal conductivity of ( Pu1− xNdx) O2− y and ( Pu1− xYx) O2− y solid solutions

The thermal conductivities of ( Pu 1− x R x ) O 2− y solid solutions (R = Nd and Y) containing RO 1.5 up to 10 mol% were determined in the temperature range 700–1450 K from thermal diffusivities measured by the laser flash method. The thermal conductivities satisfied the phonon conduction equation K = ( A + BT) −1 within ± 7%. The values of A, corresponding to the lattice defect thermal resistivity, increased linearly with the neodymium or yttrium content, while those of B were nearly constant. The increasing rate of A for ( Pu, Nd) O 2− y solid solutions was slightly larger than that for (Pu, Y)O 2−y. These increases were reasonably explained by the lattice defect model in wich Pu 4+, R 3+, O 2− ions, and oxygen vacancy in the solid solutions were considered as phonon scattering centers. For both solid solutions, the lattice strain effects on the lattice defect thermal resitivities were in preference to the mass effects. In addition, the stoichiometry effects on the additional defect thermal resistivities were about 1.3 times larger than the cation effects.

Thermal conductivity of near-stoichiometric (U, Nd)O 2, (U, Sm)O 2 and (U, Eu)O 2 solid solutions

The thermal conductivities of near-stoichiometric (U, R)O 2 solid solutions (R = Nd, Sm and Eu) containing RO 1.5 up to 15 mol% were determined in the temperature range 700–2000 K by the measurement of thermal diffusivity. The thermal conductivities satisfied the phonon conduction equation K = ( A + BT) −1 within ± 5%. The constant A corresponding to the lattice defect thermal resistivity increased linearly with the rare earth element content, while the temperature coefficient B was almost independent of it. The change in A with the rare earth element content increased in order of (U, Eu)O 2, (U, Sm)O 2 and (U, Nd)O 2 solid solutions. The increase of A was explained reasonably by the lattice defect model considering U 4+, U 5+ and R 3+ ions in the solid solutions as phonon scattering centers, using a common value for the strain parameter ( ϵ = 110). For all solid solutions, the lattice strain effect on the lattice defect thermal resistivities was much larger than the mass effect. In addition, the effect of U 5+ ions on the lattice defect thermal resistivity caused by the lattice strain effect was larger than that of R 3+ ions.

Thermal conductivity of stoichiometric (Pu, Nd)O 2 and (Pu, Y)O 2 solid solutions

The thermal conductivities of stoichiometric (Pu, R)O 2 solid solutions containing RO 1.5 (R = Nd and Y) up to 10 mol% were determined by the laser flash method in the temperature range 700–1400 K. The thermal conductivities for all solid solutions satisfied the phonon conduction equation K = ( A + BT) −1 within ± 6%. The lattice defect thermal resistivities (= A) increased gradually with the neodymium or yttrium content, while the intrinsic lattice thermal resistivities (= BT) were nearly equal to that measured for PuO 2. The measured thermal conductivities were consistent with the results of the lattice defect model calculation in which Pu 4+, Pu 5+ and R 3+ ions were considered as phonon scattering centers. The lattice strain parameters ϵ = 85 and 93 were obtained for (Pu, Nd)O 2 and (Pu, Y)O 2 solid solutions, respectively.

Phonon conduction in elastically anisotropic cubic crystals

Striking differences in the boundary-scattered phonon conductivity and effective phonon mean free path are predicted along the principal axes of cubic crystals. The results are shown to be the result of phonon focusing arising from elastic anisotropy. Normalized curves of boundary-scattered effective phonon mean free path and phonon conductivity have been calculated for samples of square cross section as a function of the elastic anisotropy, $A=\frac{2{C}_{44}}{({C}_{11}\ensuremath{-}{C}_{12})}$, and the elastic ratio, $\frac{{C}_{12}}{{C}_{11}}$. Normalized curves of phonon specific heat and effective velocity have been calculated as a function of the same variables. The effective phonon mean free path has also been calculated as a function of the sample side-face---thermal-length ratio, $\frac{D}{L}$. Anisotropies of more than 50% are possible for different rod axes. Silicon and calcium fluoride, materials in which this anisotropy was first reported, are shown to be very favorable materials to demonstrate this anisotropy. For silicon and calcium fluoride samples of rectangular cross section the thermal conduction is shown to depend upon the crystallogrphic orientation and width ratio of the side faces for samples with the same $〈110〉$ rod axis. Results are expressed in a convenient form for predicting the phonon conductivity of elastically anisotropic crystals, given the linear dimensions, the density, and the elastic constants.

Phonon Scattering in Plastically Deformed Ge

AbstractThe measurements of Sato and Sumino on the low temperature phonon conductivity of plastically deformed germanium single crystals are analysed quantitatively using a cooperative model for the scattering of phonons by static and vibrating dislocations. The discrepancies observed between the experimental and theoretical results around 20 and below 2.2 K are resolved by considering the scattering of phonons by dislocation induced point defects and by modifying the value of phonon scattering by crystal boundaries, respectively.

Lattice and radiative thermal conductivity variations through high p, T polymorphic structure transitions and melting points

A steady-state radial heat flux method is used to determine the apparent, lattice and radiative, thermal conductivity and its p, T-dependence up to 6 GPa and over a wide temperature range from 300 to 1600 K. The method employs a differential thermocouple to resolve small changes in temperature gradient due to a line source placed in a sample space subjected to well-defined uniform test temperatures. Measurements are made using an on-line computer. The method is shown to be eminently suitable for determining: (1) the p, T-dependence of the phonon conductivity of cubic single crystals and polycrystalline samples; (2) minima in the apparent thermal conductivity marking the onset of radiative contributions; (3) isolation of phonon and radiative components at high T; (4) conductivity variations caused by progressive polymorphic structure transformations; and (5) conductivity variations through high-pressure melting points into the liquid phase. Results for cubic structures such as MgO and NaCl give good agreement with existing standard values at low temperatures. The conductivity of MgO goes with the inverse of the temperature which is expected from 3-phonon processes. The conductivity of NaCl is of the form λ αT −1.32 with the deviation most likely due to thermal expansion effects. At higher temperatures, a radiative contribution was observed in NaCl and CaCO 3. Calculated values of the extinction coefficient of NaCl increase slightly with pressure.

The effect of gadolinium content on the thermal conductivity of near-stoichiometric (U,Gd)O 2 solid solutions

The thermal conductivities of near-stoichiometric (U, Gd)O 2 solid solutions containing CdO 1.5 up to 15 mol% were determined in the temperature range 700 to 2000 K from thermal diffusivities measured by the laser flash method. Temperature dependence of the thermal conductivities up to around 1600 K could be expressed by the phonon conduction equation K = (A + BT) −1 . The thermal conductivity decreased gradually with an increase of gadolinium content. Thermal resistivities caused by lattice defects were calculated from a theoretical model considering U 4+, U 5+ and Gd 3+ ions as phonon scattering centers. It was found that this model was in good agreement with the experimental results. The calculation based on this model indicates that the lattice strain effect on the lattice defect thermal resistivity is much larger than the mass effect.

Electron-phonon relaxation rates in the presence of internal strains and magnetic field in indirect-gapn-type semiconductors

We have studied theoretically the scattering of thermal phonons by neutral donors in $n$-type indirect-gap semiconductors with zinc-blende structure at low temperatures. The donor electron-phonon scattering relaxation rates are obtained in the presence of internal strains and an external magnetic field for resonance, elastic, and inelastic scattering. These expressions are used in explaining the phonon conductivity of $n$-type AlSb, SiC, ${\mathrm{Mg}}_{2}$Ge, and ${\mathrm{Mg}}_{2}$Si at low temperatures. A good agreement between theory and experiment is obtained.

Theory of thermal boundary resistance between small particles and liquid helium: Size effect on phonon conduction

The size effect for the heat transfer between small particles and liquid helium is theoretically investigated at low temperatures. The general expression is presented for the thermal boundary resistance due to phonon conduction between a small particle and liquid helium. The resistances are calculated under some experimental conditions, which exhibit a ${T}^{\ensuremath{-}3}$ variation above some temperature. Above this temperature the absolute magnitude of the calculated resistance also coincides with that of the acoustic mismatch theory for a bulk solid. Below its temperature the resistance increases exponentially with decreasing temperature. This temperature depends on both the size and the elastic properties of a small particle.

The effect of yttrium content on the thermal conductivity of near-stoichiometric (U,Y)O 2 solid solutions

The thermal conductivities of near-stoichiometric (U,Y)O 2 solid solutions containing YO 1.5 up to 15 mol% were determined in the temperature range 700–2000 K from thermal diffusivities measured by the laser flash method. The temperature dependence of the thermal conductivities up to around 1600 K could be expressed by the phonon conduction equation K = ( A + BT) −1. The thermal conductivity decreased gradually with an increase of yttrium content. Thermal resistivities caused by lattice defects were calculated from a theoretical model considering U 4+, U 5+ or U 6+ and Y 3+ ions as phonon scattering centers. It was found that this model agreed well with experimental results. The calculation based on this model indicated that the lattice strain effect on the thermal resistivity was much larger than the mass effect.

Additivity of relaxation times and thermal conductivity of nonmetals

The additivity of the inverse of the relaxation times as assumed by Callaway is observed to be valid to lowest approximation; otherwise, interference terms like Mattheissen's deviation term should be considered. It is also observed that the phonon-scattering processes due to lattice defects and chemical impurities can be included in an approximation with the phonon boundary scattering to analyze the phonon conductivity results at low temperatures.

Experimental determination of the phonon and electron components of the thermal conductivity of bcc iron

A study of the factors which affect the thermal conductivity of αFe and its solutions is described. The results of these experiments define the phonon and electronic components of the thermal conductivity of pure αFe fairly well between 90 and 400 K. Also, the phonon conductivity can be analyzed to identify the strengths of electron-phonon and phonon-phonon scattering, and the latter resistance is in good agreement with theoretical estimates. The scattering of phonons by electrons is intermediate between the small values for noble metals and the strong scattering found in Nb and Ta. An experimental estimate of the electron-phonon mass enhancement factor, 0.4, is derived from the results. Finally, reexamination of the data for ten solid solution alloys suggests that both phonon-scattering mechanisms are influenced by the alloying elements.

Phonon conductivity of p-type Ge-11 in the intermediate concentration region at low temperatures

Abstract The phonon thermal conductivity values for sample Ge-11 from 2 to 50°K for carrier concentration 2x1018 cm−3 is explained by borrowing an idea of holes being in mixed state i.e. both in localised bound state and in the free state in the intermediate concentration region. Since the above sample lie in the intermediate concentration region of metal-nonmetal transition, the theory of hole-phonon scattering in the mixed state is used (1). The density of states effective mass and deformation potential for the holes are calculated and are in good agreement with the experimentally known values. The impurity and isotope scattering parameters are also determined in the present calculations.

Peripheral phonons and phonon conductivity of a metal at low temperatures

The role of the peripheral and non-peripheral phonons in the estimation of the lattice thermal conductivity of a metal has been studied at low temperatures by calculating their separate contributions towards the total lattice thermal conductivity. The study is made in the temperature range 0.4–2.5 K with the help of the Ziman expression for the scattering of phonons by the charge carriers and the Callaway expression of the phonon conductivity, and Sb is taken as an example. The separate percentage contributions due to peripheral and non-peripheral phonons have also been studied and it is found that the percentage contribution due to peripheral phonons increases with increasing temperature while the percentage contribution due to non-peripheral phonons decreases with increasing temperature. The percentage contributions of the lattice thermal resistivities due to electrons and holes towards the total lattice thermal resistivity of Sb have also been reported in the present note.