Lower limit to the thermal conductivity of disordered crystals

Cahill, David G.; Watson, Susan K.; Pohl, Robert Wichard

doi:10.1103/physrevb.46.6131

Cited by 2,110 publications

(1,544 citation statements)

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“…where L is the boundary scattering mean free path in the bulk crystal sample, g p (o) is the phonon density of states, and the min function is used to ensure that the anharmonic relaxation time is not lower than half of the oscillation, p/o, consistent with the Ioffe-Regel limit 44,45 . For diffusons we assume a diffusivity…”

Section: Resultsmentioning

confidence: 99%

Twisting phonons in complex crystals with quasi-one-dimensional substructures

et al. 2015

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A variety of crystals contain quasi-one-dimensional substructures, which yield distinctive electronic, spintronic, optical and thermoelectric properties. There is a lack of understanding of the lattice dynamics that influences the properties of such complex crystals. Here we employ inelastic neutron scatting measurements and density functional theory calculations to show that numerous low-energy optical vibrational modes exist in higher manganese silicides, an example of such crystals. These optical modes, including unusually low-frequency twisting motions of the Si ladders inside the Mn chimneys, provide a large phase space for scattering acoustic phonons. A hybrid phonon and diffuson model is proposed to explain the low and anisotropic thermal conductivity of higher manganese silicides and to evaluate nanostructuring as an approach to further suppress the thermal conductivity and enhance the thermoelectric energy conversion efficiency. This discovery offers new insights into the structure-property relationships of a broad class of materials with quasi-one-dimensional substructures for various applications.

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Section: Resultsmentioning

confidence: 99%

Twisting phonons in complex crystals with quasi-one-dimensional substructures

et al. 2015

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“…Also, total ജ min =2/ . 9 The experimental results together with the calculated curves are shown in Fig. 1.…”

Section: ͑1͒mentioning

confidence: 99%

“…Both ODC and glass exhibit a temperature dependence of ͑T͒ characteristic of most amorphous solids. 2,9 ͑T͒ strongly increases with temperature up to about 5 K. A smeared-out plateau appears within 5 -10 K, above which ͑T͒ experiences a further increase. This increase lasts up to T = 50 K, from where ͑T͒ for both samples shows a very mild dependence on temperature up to both glass transition ranges at T g Ӎ 97 K. Data for the ODC closely follow those of the amorphous solid.…”

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confidence: 99%

Scattering of acoustic phonons in disordered matter: A quantitative evaluation of the effects of positional versus orientational disorder

et al. 2006

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The thermal conductivity of all three disordered solid phases of ethyl alcohol has been measured. That for the orientationally disordered bcc phase is found to be remarkably close to that for the structurally amorphous solid, especially at low temperatures. The results, which emphasize the role of orientational disorder in phonon scattering, are discussed with the aid of computer simulations on single-crystalline models of both bcc and monoclinic crystals. DOI: 10.1103/PhysRevB.74.060201 PACS number͑s͒: 66.70.ϩf, 61.43.Ϫj, 63.50.ϩx, 65.60.ϩa Our current understanding of the mechanisms of heat transport in disordered media rests upon concepts grounded on clean experiments showing that acoustic phonons, especially those having transverse polarization, are the main heat carriers. 1 Work carried out over the last couple of decades has evidenced striking quantitative similarities in the characteristic thermal conductivity of bulk amorphous materials 2 between, say, 0.1 and 10 K, independent of chemical composition. Furthermore, such similarity also extends to a good number of disordered crystals, including a quasicrystal, 2,3 and from the set of collected data it has been inferred that the ratio of the wavelength of the acoustic wave to the mean free path l of all these solids ranges within 10 −2 -10 −3 , which suggests the presence of "universal" behavior of some sort. On such grounds, it becomes clear that the presence of "glassy dynamics" cannot be attributed in full to the absence of static translational long-range order ͑LRO͒.Some molecular crystals where the individual molecules have random static orientations while their centers of mass are at the nodes of a three-dimensional crystalline lattice are also known to exhibit glasslike excitations. Of those, solid ethyl alcohol is perhaps the most convenient benchmark to carry out a quantitative comparison of the effects caused by the complete lack of LRO, 4 on the most sensitive property to explore the propagation of excitations in condensed matter, the thermal conductivity. The material, apart from the wellknown monoclinic ͑fully ordered͒ crystalline ͑FOC͒ modification, can be prepared in three long-lived phases, an amorphous solid or glass, an orientationally disordered crystal ͑ODC͒ ͑or orientational glass͒ showing static orientational disorder but having translational LRO since the molecules are at the nodes of a bcc lattice, and a crystal with dynamic orientational disorder ͓rotator-phase crystal ͑RPC͔͒ which retains LRO as a bcc lattice still exists. Two glass transitions take place about 97 K between the glass and supercooled liquid and the ODC and RPC. 4 Here we report on measurements of the thermal conductivity of ethyl alcohol for all the solid phases. The relevance of such an exercise is twofold. First and foremost, as stated in a recent review, 2 the measurements will provide additional tests on claims of quantitative universality of the properties of heat propagation at low and intermediate temperatures in disordered matter brought forward by a cl...

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“…[1][2][3]5,8,10 The validity of this assumption has been in many ways validated 5,[11][12][13][14][15][16][17][18][19][20] and consequently, the PGM has been used almost ubiquitously to understand phonon transport in all classes of solids. 13,18,19,[21][22][23][24][25] However, here we will examine more deeply the behaviors in a random alloy as a representative example, because its compositional disorder reveals a rather fundamental issue with the way phonons have been conceptualized, namely considering them to be plane waves/quasi-particles that travel and scatter. Our revision to this fundamental issue with the common PGM-based theory/conception of phonons is then tested by comparing to experiments.…”

Section: Introductionmentioning

confidence: 99%

Rethinking phonons: The issue of disorder

et al. 2017

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Current understanding of phonons treats them as plane waves/quasi-particles of atomic vibration that propagate and scatter. The problem is that conceptually, when any level of disorder is introduced, whether compositional or structural, the character of vibrational modes in solids changes, yet nearly all theoretical treatments continue to assume phonons are still waves. For example, the phonon contributions to alloy thermal conductivity (TC) rely on this assumption and are most often computed from the virtual crystal approximation (VCA). Good agreement is obtained in some cases, but there are many instances where it fails-both quantitatively and qualitatively. Here, we show that the conventional theory and understanding of phonons requires revision, because the critical assumption that all phonons/normal modes resemble plane waves with well-defined velocities is no longer valid when disorder is introduced. Here we show, surprisingly, that the character of phonons changes dramatically within the first few percent of impurity concentration, beyond which phonons more closely resemble the modes found in amorphous materials. We then utilize a different theory that can treat modes with any character and experimentally confirm its new insights.

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Lower limit to the thermal conductivity of disordered crystals

Cited by 2,110 publications

References 42 publications

Twisting phonons in complex crystals with quasi-one-dimensional substructures

Twisting phonons in complex crystals with quasi-one-dimensional substructures

Scattering of acoustic phonons in disordered matter: A quantitative evaluation of the effects of positional versus orientational disorder

Rethinking phonons: The issue of disorder

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