Thermal conductivity of glasses: first-principles theory and applications

Abstract

Predicting the thermal conductivity of glasses from first principles has hitherto been a very complex problem. The established Allen-Feldman and Green-Kubo approaches employ approximations with limited validity—the former neglects anharmonicity, the latter misses the quantum Bose-Einstein statistics of vibrations—and require atomistic models that are very challenging for first-principles methods. Here, we present a protocol to determine from first principles the thermal conductivity κ(T) of glasses above the plateau (i.e., above the temperature-independent region appearing almost without exceptions in the κ(T) of all glasses at cryogenic temperatures). The protocol combines the Wigner formulation of thermal transport with convergence-acceleration techniques, and accounts comprehensively for the effects of structural disorder, anharmonicity, and Bose-Einstein statistics. We validate this approach in vitreous silica, showing that models containing less than 200 atoms can already reproduce κ(T) in the macroscopic limit. We discuss the effects of anharmonicity and the mechanisms determining the trend of κ(T) at high temperature, reproducing experiments at temperatures where radiative effects remain negligible.

Temperature-invariant heat conductivity from compensating crystalline and glassy transport: from the Steinbach meteorite to furnace bricks

“…This implies the emergence of quasi-degenerate vibrational states (|ω(0) s −ω(0) s ′ |≪ 1 2 Γ(0) s +Γ(0) s ′ , s̸ =s ′ ), which can be coupled by off-diagonal velocity-operator elements and contribute to κ αβ C . We also note that in the harmonic disordered limit ℏΓ(0) s →ℏη→0 ∀s these wavelike mechanisms reduce to those described by the AF theory 11,15 . Most importantly, Eq.…”

“…7 shows that simple crystals such as α-quartz and AV tridymite, in which heat transport is mainly due to particle-like mechanisms (see Ref. 15 and Fig. 3), the artificial decrease (increase) of the linewidths directly translates into an increase (decrease) of the conductivity.…”

“…However, these case are promising for engineering materials with target conductivities, since the conductivities of ordered and disordered polymorphs can differ of several orders of magnitude. E.g., in silicon dioxide (SiO 2 ) crystalline α-quartz and vitreous silica have similar anharmonicity, but their conductivities have opposite trends in temperature and their magnitude at 80 K differs of about a factor 100 15 . While these paradigmatic cases have been extensively studied, the conductivities of hybrid polymorphs with intermediate degree of disorder have not received attention, due to rarity of samples and lack of theoretical methods capable to describe their conductivity below T D 15,24 .…”

“…E.g., in silicon dioxide (SiO 2 ) crystalline α-quartz and vitreous silica have similar anharmonicity, but their conductivities have opposite trends in temperature and their magnitude at 80 K differs of about a factor 100 15 . While these paradigmatic cases have been extensively studied, the conductivities of hybrid polymorphs with intermediate degree of disorder have not received attention, due to rarity of samples and lack of theoretical methods capable to describe their conductivity below T D 15,24 . Thus, we analyze them now using the WTE and experiments.…”

“…In order to simplify the analysis, we approximate the linewidths using the single-valued function of frequency 15,23,47 , i.e. Γ(q) s = Γ a [ω(q) s ]; using this approximation allows to recast Eq.…”