Zur kinetischen Theorie der Wärmeleitung in Kristallen

Peierls, Rudolf

doi:10.1002/andp.19293950803

Cited by 946 publications

(542 citation statements)

References 5 publications

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“…Theoretical work in this area [9,10] was based on the application of the mode coupling theory [13,14]. Application of Peierls equation to the analysis of heat conduction in FPU lattices was limited to qualitative estimations [1,10,15]. It is therefore of interest to check if more careful analysis of * Electronic address: andrey.pereverzev@trinity.edu the Peierls equation can explain some of the anomalous properties of the FPU chains.…”

Section: Introductionmentioning

confidence: 99%

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

2003

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The Peierls equation is considered for the Fermi-Pasta-Ulam β lattice. Explicit form of the linearized collision operator is obtained. Using this form the decay rate of the normal mode energy as a function of wave vector k is estimated to be proportional to k 5/3 . This leads to the t −3/5 long time behavior of the current correlation function, and, therefore, to the divergent coefficient of heat conductivity. These results are in good agreement with the results of recent computer simulations. Compared to the results obtained through the mode coupling theory our estimations give the same k dependence of the decay rate but a different temperature dependence. Using our estimations we argue that adding a harmonic on-site potential to the Fermi-Pasta-Ulam β lattice may lead to finite heat conductivity in this model.

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Section: Introductionmentioning

confidence: 99%

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

2003

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“…As originally shown by Peierls 44 , phonon-phonon umklapp scattering is expected to exhibit a pronounced temperature dependence, on a scale comparable with the Debye temperature θ D ,…”

Section: Phonon-phonon Umklapp Scatteringmentioning

confidence: 69%

Phonon scattering rates and atomic ordering inAg1−xSb1+xTe2+x(
Ma
¹
,
Delaire
²
,
Specht
³

et al. 2014
Phys. Rev. B
15
0
12
0
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The phonon dispersions and scattering rates of the thermoelectric material Ag1−xSb1+xTe2+x (x = 0, 0.1, 0.2) were measured with inelastic neutron scattering, as function of both temperature T and off-stoichiometry x. In addition, detailed measurements of diffuse scattering were performed with both neutron and synchrotron x-ray diffraction. The results show that phonon scattering rates are large and weakly dependent on T or x, and the lattice thermal conductivity calculated from these scattering rates and group velocities is in good agreement with bulk transport measurements. We also find that the scattering rates and their temperature dependence cannot be accounted for with common models of phonon scattering by anharmonicity or point defects. The diffuse scattering measurements show a pervasive, complex signal, with several distinct components. In particular, broad superstructure reflections indicate a short-range ordering of the Ag and Sb cations on their sublattice. Single-crystal Bragg peak intensities also reveal large static atomic displacements, compatible with results from Rietveld refinement of neutron powder diffraction data. Our results indicate that a complex nanostructure, arising from multiple variants of nanoscale anisotropic superstructures of cations, and large atomic displacements, is likely responsible for the strong phonon scattering.

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“…where is the volume of the primitive cell, ω is the phonon frequency, e is the polarization vector, j is the polarization,n is the equilibrium phonon distribution, and 2 where M is the atomic mass of the host atoms in the crystal and M is the difference in mass between the impurity atoms of species i of concentration z and that of the host atoms. Equation (1) can be recast into the frequency domain by recognizing that ω j (q) = v p, j (q) q and dω j (q) = v g, j (q) dq, where v p,j and v g,j are the phase and group velocities of a phonon mode of polarization j, yielding…”

Section: Derivation Of Phonon-mass Impurity Scattering Ratesmentioning

confidence: 99%

Dispersion considerations affecting phonon-mass impurity scattering rates

Hopkins

2011

AIP Advances

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This work presents a derivation of phonon-mass impurity scattering rates applicable to dispersive phonon systems. This form of mass impurity scattering is compared with the previously accepted form assuming a nondispersive crystal by calculating the thermal conductivity of Si. The mass impurity scattering rate determined from this approach considering dispersion is in excellent agreement with theoretical calculations, where the scattering rates determined from the dispersionless model under predict the role of phonon-mass impurity scattering in thermal transport by over an order of magnitude

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Zur kinetischen Theorie der Wärmeleitung in Kristallen

Cited by 946 publications

References 5 publications

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

Phonon scattering rates and atomic ordering inAg1−xSb1+xTe2+x(
Ma
¹
,
Delaire
²
,
Specht
³

et al. 2014
Phys. Rev. B
15
0
12
0
View full text Add to dashboard Cite

Dispersion considerations affecting phonon-mass impurity scattering rates

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Zur kinetischen Theorie der Wärmeleitung in Kristallen

Cited by 946 publications

References 5 publications

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

Phonon scattering rates and atomic ordering inAg1−xSb1+xTe2+x(Ma1, Delaire2, Specht3 et al. 2014Phys. Rev. B150120View full textAdd to dashboardCite

Dispersion considerations affecting phonon-mass impurity scattering rates

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About

Phonon scattering rates and atomic ordering inAg1−xSb1+xTe2+x(
Ma
¹
,
Delaire
²
,
Specht
³

et al. 2014
Phys. Rev. B
15
0
12
0
View full text Add to dashboard Cite