Scattering of phonons by density fluctuations and thermal conductivity of amorphous solids

Joshi, Y. P.

doi:10.1002/pssb.2220950137

Cited by 12 publications

(5 citation statements)

References 18 publications

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“…While a contribution of the lattice disorder to the density of states undoubtedly exists and can be very significant (see, for example, simulations of silica's heat capacity by Horbach at el. (Horbach et al, 1999)), we must note that if amorphous lattices were purely harmonic, the phonon absorption at the BP frequencies would be of the Rayleigh type and should be significantly lower than observed in the experiment (Anderson, 1981;Joshi, 1979). There must be internal resonances present in the bulk, that scatter phonons inelastically.…”

Section: Introductionmentioning

confidence: 77%

The Microscopic Quantum Theory of Low Temperature Amorphous Solids

Lubchenko¹,

Wolynes²

2007

Advances in Chemical Physics

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The quantum excitations in glasses have long presented a set of puzzles for condensed matter physicists. A common view is that they are largely disordered analogs of elementary excitations in crystals, supplemented by two level systems which are chemically local entities coming from disorder. A radical revision of this picture argues that the excitations in low temperature glasses are deeply connected to the energy landscape of the glass when it vitrifies: the excitations are not low excited states built on a single ground state but locally defined resonances, high in the energy spectrum of a solid. According to a semiclassical analysis, the two level systems involve resonant collective tunneling motions of around two hundred molecular units which are relics of the mosaic of cooperative motions at the glass transition temperature Tg. The density of states of the TLS is determined by Tg and the mosaic's length scale, which is a weak function of the cooling rate. The universality of phonon scattering in insulating glasses is explained. The Boson Peak and the plateau in thermal conductivity, observed at higher temperatures, are also quantitatively understood within the picture as arising from the same cooperative motions, but now accompanied by thermal activation of the mosaic's vibrational modes. The dynamics of some of the local structural transitions have significant quantum corrections to the semiclassical picture. These corrections lead to a deviation of the heat capacity and conductivity from the standard tunneling model results and explain the anomalous time dependence of the heat capacity. Interaction between tunneling centers contributes to the large and negative value of the Grüneisen parameter often observed in glasses.

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Section: Introductionmentioning

confidence: 77%

The Microscopic Quantum Theory of Low Temperature Amorphous Solids

Lubchenko¹,

Wolynes²

2007

Advances in Chemical Physics

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“…28,53,87 In the absence of such marginal stability, purely elastic scattering seems too weak to account for the apparent magnitude of phonon scattering at Boson Peak frequencies. 88,89 In contrast, the presence of structural degeneracy leads to an entirely distinct, resonant type of phonon scattering. The resonances are due to local transitions between distinct free energy minima of the aperiodic solid.…”

Section: Discussionmentioning

confidence: 99%

Self-consistent elastic continuum theory of degenerate, equilibrium aperiodic solids

Bevzenko

Lubchenko

2014

The Journal of Chemical Physics

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We show that the vibrational response of a glassy liquid at finite frequencies can be described by continuum mechanics despite the vast degeneracy of the vibrational ground state; standard continuum elasticity assumes a unique ground state. The effective elastic constants are determined by the bare elastic constants of individual free energy minima of the liquid, the magnitude of built-in stress, and temperature, analogously to how the dielectric response of a polar liquid is determined by the dipole moment of the constituent molecules and temperature. In contrast with the dielectric constant-which is enhanced by adding polar molecules to the system-the elastic constants are down-renormalized by the relaxation of the built-in stress. The renormalization flow of the elastic constants has three fixed points, two of which are trivial and correspond to the uniform liquid state and an infinitely compressible solid respectively. There is also a nontrivial fixed point at the Poisson ratio equal to 1/5, which corresponds to an isospin-like degeneracy between shear and uniform deformation. The present description predicts a discontinuous jump in the (finite frequency) shear modulus at the crossover from collisional to activated transport, consistent with the RFOT theory.

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“…These modes, which stem from a distribution in local elastic response [303][304][305], have been proposed as the cause of the Boson Peak, requiring however that the lattice be near its mechanical stability limit [21,304,306]. In the absence of such marginal stability, purely elastic scattering seems too weak to account for the apparent magnitude of phonon scattering at Boson Peak frequencies [23,307,308]. While the lack of periodicity in glasses undoubtedly contributes to the excess phonon scattering, the presently discussed structural resonances, which are inherently and strongly anharmonic processes, account quantitatively for the apparent magnitude of the heat capacity and phonon scattering in a (logarithmically) broad temperature range that covers both the two-level system and Boson peak dominated regimes.…”

Section: A Two-level Systems and The Boson Peakmentioning

confidence: 99%

Theory of the Structural Glass Transition: A Pedagogical Review

Lubchenko

2015

Preprint

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The random first-order transition (RFOT) theory of the structural glass transition is reviewed in a pedagogical fashion. The rigidity that emerges in crystals and glassy liquids is of the same fundamental origin. In both cases, it corresponds with a breaking of the translational symmetry; analogies with freezing transitions in spin systems can also be made. The common aspect of these seemingly distinct phenomena is a spontaneous emergence of the molecular field, a venerable and well-understood concept. In crucial distinction from periodic crystallisation, the free energy landscape of a glassy liquid is vastly degenerate, which gives rise to new length and time scales while rendering the emergence of rigidity gradual. We obviate the standard notion that to be mechanically stable a structure must be essentially unique; instead, we show that bulk degeneracy is perfectly allowed but should not exceed a certain value. The present microscopic description thus explains both crystallisation and the emergence of the landscape regime followed by vitrification in a unified, thermodynamics-rooted fashion. The article contains a self-contained exposition of the basics of the classical density functional theory and liquid theory, which are subsequently used to quantitatively estimate, without using adjustable parameters, the key attributes of glassy liquids, viz., the relaxation barriers, glass transition temperature, and cooperativity size. These results are then used to quantitatively discuss many diverse glassy phenomena, including: the intrinsic connection between the excess liquid entropy and relaxation rates, the non-Arrhenius temperature dependence of α-relaxation, the dynamic heterogeneity, violations of the fluctuation-dissipation theorem, glass ageing and rejuvenation, rheological and mechanical anomalies, super-stable glasses, enhanced crystallisation near the glass transition, the excess heat capacity and phonon scattering at cryogenic temperatures, the Boson peak and plateau in thermal conductivity, and the puzzling midgap electronic states in amorphous chalcogenides.

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Scattering of phonons by density fluctuations and thermal conductivity of amorphous solids

Cited by 12 publications

References 18 publications

The Microscopic Quantum Theory of Low Temperature Amorphous Solids

The Microscopic Quantum Theory of Low Temperature Amorphous Solids

Self-consistent elastic continuum theory of degenerate, equilibrium aperiodic solids

Theory of the Structural Glass Transition: A Pedagogical Review

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