Phonon Mean Free Path Research Articles

Suppressed Lone Pair Electrons Explain Unconventional Rise of Lattice Thermal Conductivity in Defective Crystalline Solids.

Manipulating thermal properties of materials can be interpreted as the control of how vibrations of atoms (known as phonons) scatter in a crystal lattice. Compared to a perfect crystal, crystalline solids with defects are expected to have shorter phonon mean free paths caused by point defect scattering, leading to lower lattice thermal conductivities than those without defects. While this is true in many cases, alloying can increase the phonon mean free path in the Cd-doped AgSnSbSe3 system to increase the lattice thermal conductivity from 0.65 to 1.05Wm-1K-1 by replacing 18% of the Sb sites with Cd. It is found that the presence of lone pair electrons leads to the off-centering of cations from the centrosymmetric position of a cubic lattice. X-ray pair distribution function analysis reveals that this structural distortion is relieved when the electronic configuration of the dopant element cannot produce lone pair electrons. Furthermore, a decrease in the Grüneisen parameter with doping is experimentally confirmed, establishing a relationship between the stereochemical activity of lone pair electrons and the lattice anharmonicity. The observed "harmonic" behavior with doping suggests that lone pair electrons must be preserved to effectively suppress phonon transport in these systems.

Synergistic role of Sn-doping on the thermal and electrical properties of sinnerite Cu6As4S9

Sinnerite Cu6As4S9 has been identified as a promising material for optoelectronic applications, with potential for other energy-related applications; however, knowledge of the electrical and thermal properties as well as the mechanisms underlying transport in sinnerite is lacking. We present an investigation of the synthesis, structural, thermal and electrical transport properties of stoichiometric and Sn-doped Cu6As4S9. Sinnerite has a triclinic lattice structure, with highly distorted local atomic coordination environments that, in part, results in its complex structure and bonding. Our results and analyses indicate As 4s2 lone pair-induced distortions and strong lattice anharmonicity that leads to a relatively short phonon mean free path, resulting in intrinsically very low thermal conductivity. The electrical resistivity for both compositions, Cu6As4-xSnxS9 (x = 0, 0.2), are relatively high and varies little with temperature, typical of degenerate semiconductors. An increase in mobility and electrical conductivity was obtained by Sn doping in Cu6As3.8Sn0.2S9. This work demonstrates an effective route to synthesize bulk sinnerite as well as advances the knowledge of the properties of sinnerite, as this and other ternary chalcogenides continue to be of interest for potential technologically significant applications.

Effective cross-plane thermal conductivity of metal-dielectric multilayers at low temperatures

Heat transfer in layered metal-dielectric structures is considered theoretically based on an analytical solution of the Boltzmann transfer equation for the phonon distribution function. Taking into account the size effect, the problem of effective cross-plane thermal conductivity of structures containing two metal layers is analyzed in detail. If the thickness of the metal layers is less than the phonon mean free path, interlayer heat transfer is carried out predominantly by phonons, and the effective cross-plane thermal conductivity is determined by the reflection of phonons from the metal/dielectric interfaces. In the opposite case of thick metal layers, the effective cross-plane thermal conductivity is determined both by the thermal conductivity of the metal layers and by the thermal resistance of the dielectric layers. The results obtained are generalized to multilayer structures and superlattices.

Efficient heuristic approach for minimization of phonon mean free path in large-area nanostructured thin films

Phonon transport simulations are conducted to unveil the design of nanostructured thin films with the lowest thermal conductivity for enhancing thermoelectric performance. An efficient and effective optimization method that utilizes simulated annealing is realized by tuning and switching a reduction rate of annealing temperature, which is a parameter to facilitate escaping local optima during the process. The superiority of this optimization approach is confirmed by demonstrating it in nanostructured thin films of various sizes. Furthermore, the characteristics of structures with lower thermal conductivities are identified from the optimization results for each size. Based on this, a large-area nanostructured thin film, in which the simulated annealing method is computationally costly, is designed and validated by comparing it with typical nanostructured thin films as a reference.

Resistivity size effect in epitaxial face-centered cubic Co(001) layers

Metastable face-centered cubic (fcc) Co layers are deposited by reactive magnetron sputtering in 5 mTorr N2 at 400 °C followed by vacuum annealing at 500 °C. The resulting phase-pure Co(001)/MgO(001) layers contain negligible nitrogen and exhibit a surface roughness <0.8 nm and a cube-on-cube epitaxial relationship with the substrate with Co[100]ǁMgO[100]. The measured resistivity vs thickness d = 10–1000 nm indicates a bulk resistivity ρo = 6.4 ± 0.3 μΩ cm for fcc Co at room temperature and ρo = 1.3 ± 0.1 μΩ cm at 77 K, and an effective electron phonon mean free path λ = 27 ± 2 nm and 79 ± 6 nm at 295 and 77 K, respectively. The resulting ρo × λ benchmark quantity is 3–5 times larger than that predicted from first principles, suggesting a breakdown of the Fuchs–Sondheimer model at small dimensions. The overall results indicate that fcc Co exhibits no intrinsic conductance benefit over stable hcp Co nor conventional Cu for narrow interconnects. The developed method for growth of epitaxial fcc Co(001) layers provides opportunities to study this metastable material for potential spintronic applications.

Heat transport in an angular-momentum-conserving lattice.

It is expected that the energy-diffusion propagator in a one-dimensional nonlinear lattice with three conserved quantities: energy, momentum, and stretch, consists of a central heat mode and two sound modes. The heat mode follows a Lévy distribution. Consequently, the heat diffusion is super, i.e., the second moment of the diffusion propagator diverges as t^{β} with β>1; and the heat conduction is anomalous, i.e., the heat conductivity is size dependent and diverges with size N by N^{α}, with α>0. In this paper, we study a one-dimensional lattice with two-dimensional transverse motions, in which the total angular momentum also conserves. More importantly, the diffusion of this conserved quantity is ballistic. Surprisingly, the above pictures and the values of the mentioned power exponents keep unchanged. The universality of the scalings is then further extended. On the other hand, the detailed strengths of heat transports are largely enhanced. Such a counterintuitive finding can be explained by the change of the phonon mean-free path of the lattices.

Phonon-drag in a graphite channel buried in diamond

While the phonon-drag effect can induce large Seebeck coefficients, it is associated with large mean free path phonons present in the vicinity of the maximum in temperature of the lattice thermal conductivity. In this paper, we initiate a new route by searching for the mutual drag between the electron and phonon-drag gases at the interface between two different media. In that respect, the temperature studies of the conductance and Seebeck coefficient of a model system consisting of an electrically conductive graphitic channel buried beneath the surface of a diamond crystal are shown. The observed behaviour is very similar to that of graphite, with a typical negative peak associated with the phonon-drag effect. Interestingly, this phonon-drag peak of the buried graphitic channel appears at a significantly higher temperature than that in pure graphite.

Engineering phonon transport through cation disorder in dimensionally constricted high entropy MXene

Designing materials with low thermal conductivity is a crucial objective for applications in thermal insulation and thermoelectrics. Traditional methods such as doping, mechanical strain and introducing defects in perfect crystals have been widely explored to impede the flow of heat. This work introduces dimensional constriction and cationic disorder as novel avenues to manipulate lattice thermal conductivity (LTC). High entropy materials characterized by random distribution of multiple elements, creates a suitable environment for thermal insulation due to its configurational disorder and local lattice distortions. On the other hand, MXenes, derived from MAX-phase, have garnered considerable attention due to their unique structural attributes, leading to potential applications in catalysis and energy storage. Ti2AlC MAX-phase is examined to understand the impact of dimensional constriction on phonon transport of Ti2C with cationic disorder, i.e., (Ti0.25Nb0.25Cr0.25Ta0.25)2C. The exponential reduction in LTC of HE-MXene is attributed to disorder scattering that significantly limits phonon mean free path (MFP) and relaxation time. The spread of mode-resolved LTC with MFP highlights the influence of disorder on phonon scattering. This work provides a systematic approach to engineer LTC through dimensional constriction and cationic disorder, laying the foundation for tailored materials with desired thermal properties.

Influence of boundary conditions on non-equilibrium heat transport under ultrafast laser action based on the lattice Boltzmann method

Based on the lattice Boltzmann method, this paper simulated the non-equilibrium heat transfer process in nano-silicon thin film under ultrafast laser irradiation. The influence of boundary conditions on heat transport was investigated. Results show that under rebound and diffuse boundary conditions, the energy distribution within the film is non-uniform due to interface effects. However, the specular boundary condition is equivalent to eliminating the interface, resulting in a smooth energy distribution. Under convective boundary conditions, the thermal wave phenomenon disappears owing to the open interface. When the energy tends to be stable, the energy density under convective boundary conditions is reduced to 50% of that under adiabatic boundary conditions. As the film size decreases, the differences between boundary conditions become more significant. Particularly when the film size is smaller than the phonon mean free path, the influence of boundary conditions cannot be neglected. Therefore, boundary conditions and size effects are important for the design of nanodevices. Furthermore, compared with the results obtained by the Cattaneo-Vernotte model, it is found that at smaller Knudsen numbers, the Cattaneo-Vernotte model has a better match with the lattice Boltzmann method.

Hydrogenation driven ultra-low lattice thermal conductivity in β 12 borophene

Borophene gathered large interest owing to its polymorphism and intriguing properties such as Dirac point, inherent metallicity, etc but oxidation limits its capabilities. Hydrogenated borophene was recently synthesised experimentally to harness its applications. Motivated by experimental work, in this paper, using first-principles calculations and Boltzmann transport theory, we study the freestanding β 12 borophene nanosheet doped and functionalised with hydrogen (H), lithium (Li), beryllium (Be), and carbon (C) atoms at different β 12 lattice sites. Among all possible configurations, we screen two stable candidates, pristine and hydrogenated β 12 borophene nanosheets. Both nanosheets possess dynamic and mechanical stability while the hydrogenated sheet has different anisotropic metallicity compared to pristine sheet leading to enhancement in brittle behaviour. Electronic structure calculations reveal that both nanosheets host Dirac cones (DCs), while hydrogenation leads to shift and enhancement in tilt of the DCs. Further hydrogenation leads to the appearance of additional Fermi pockets in the Fermi surface. Transport calculations reveals that the lattice thermal conductivity changes from 12.51 to 0.22 W m−1 K−1 (along armchair direction) and from 4.42 to 0.07 W m−1 K−1 (along zigzag direction) upon hydrogenation at room temperature (300 K), demonstrating a large reduction by two orders of magnitude. Such reduction is mainly attributed to decreased phonon mean free path and relaxation time along with the enhanced phonon scattering rates stemming from high frequency phonon flat modes in hydrogenated nanosheet. Comparatively larger weighted phase space leads to increased anharmonic scattering in hydrogenated nanosheet contributing to ultra-low lattice thermal conductivity. Consequently, hydrogenated β 12 nanosheet exhibits a comparatively higher thermoelectric figure of merit (∼0.75) at room temperature along armchair direction. Our study demonstrates the effects of functionalisation on transport properties of freestanding β 12 borophene nanosheets which can be utilised to enhance the thermoelectric performance in two-dimensional (2D) systems and expand the applications of boron-based 2D materials.

Anisotropic temperatures in multi-layered 2D materials

For multi-layered 2D materials, although its c-axis has a much lower thermal conductivity than the a-axis, its phonon mean free path has been confirmed to be very long, e.g., in the order of 100s nm at room temperature for multi-layered graphene. An anisotropic specific heat concept has been proposed in the past to explain this very long mean free path. This work carries out detailed atomistic modeling to quantify the anisotropic specific heat concept and reports the discovery of anisotropic temperatures in multi-layered 2D materials under ultrafast surface heating. Extremely fast c-phonon energy transport is discovered, and the non-Fourier effect is observed for both a-phonons and c-phonons. The energy coupling factor between these two modes of phonons is determined to be in the order of 1016 W K−1 m−3, with the specific number depending on the structure location. The anisotropic temperature concept is also quantitatively confirmed based on the lattice Boltzmann method simulation. The anisotropic temperature concept does not violate the physics that temperature is a scalar; rather, it is developed to distinguish the temperatures of phonons that travel in different directions. This concept is universally applicable to other 2D materials to describe the heat conduction in the in-plane and out-of-plane directions that feature different interatomic bonds.

Thermal transport in Yb-based 1-2-20 materials

Lattice thermal-transport properties of heavy-fermion YbT2Zn20-based (T = Co, Rh, and Ir) 1-2-20 compounds are calculated with the single-mode relaxation-time approximation and the full solution of the linearized phonon Boltzmann transport equation from first-principles anharmonic phonon calculations. We predict low lattice thermal conductivity κ L with a maximum value of ∼24.16 ·K at 85.14 K, 137.29 ·K at 9.67 K, and 23.55 ·K at 67.50 K and ∼12.02, 40.04, and 10.30 ·K at room temperature for YbCo2Zn20, YbRh2Zn20, and YbIr2Zn20, respectively. Based on the analysis of the cumulative κ L as a function of the phonon mean free path and the frequency-dependent joint density of states at various temperatures, we attribute the low κ L to a rattling mode with an average characteristic rattling frequency that enhanced phonon scattering processes, which reduced the phonon mean free paths, suppressed the phonon lifetime, and enhanced the probability of three-phonon scattering events. The predicted low κ L , especially in YbCo2Zn20 and YbIr2Zn20, makes them promising candidate materials for thermoelectric applications and thermal management.

Assessing Lattice Thermal Conductivity of Topological Insulator Bi2Se3 by Raman Thermometry

Lattice thermal conductivity (κL) of the hexagon‐shaped nanocrystals cluster of Bi2Se3, prepared by the hot‐injection technique using nontoxic solvents, is studied. From the temperature‐dependent Raman spectra of Bi2Se3 nanocrystals, the average Debye temperature (θD) and Gruneisen parameter (γ) are calculated by adopting the bond‐order–length–strength correlation theory. The average room temperature κL of Bi2Se3 nanocrystals evaluated from the Slack model using θD and γ is ≈1.1 Wm−1K−1. The κL of Bi2Se3 nanocrystals is larger than out‐of‐plane κL (≈0.4 Wm−1K−1) but close to the in‐plane κL (≈1.4 Wm−1K−1) simulated using the Boltzmann transport equation for phonon with three‐phonon scatterings. Nanostructuring introduces grain boundaries in the Bi2Se3 that block the long mean free path of phonons physically, reduces the phonon mean free path, and decreases the κL. The anisotropic phonon scattering introduced by the weak van der Waals force between adjacent quintuple layers in the out‐of‐plane direction, in addition to the acoustic–optical phonon scattering and anharmonicity, hinders the efficient transport of thermal energy in the Bi2Se3 and results in a lower κL. By utilizing materials with anisotropic thermal conductivity, thermoelectric devices can be designed to preferentially conduct heat in specific directions while minimizing heat loss in others.

Molecular dynamics study of thermal transport across diamond/cubic boron nitride interfaces

The thermal transport properties at the interface of diamond and cubic boron nitride (c-BN) heterostructures significantly influence heat dissipation in high-power electronic and optoelectronic devices. However, a fundamental understanding of the various parameters modulating the interfacial thermal conductance is still lacking. In this work, we employ non-equilibrium molecular dynamics (NEMD) simulations to systematically investigate the effects of system size, temperature, and defect density on the interfacial thermal conductance across diamond/c-BN interfaces. The results indicate a positive correlation between system length and interface thermal conductance when below the phonon mean free path threshold, attributable to ballistic phonon transport regimes in smaller domains. Additionally, we observe an incremental enhancement in interface thermal conductance with increasing temperature, stemmed from intensified phonon-phonon interactions and reduced boundary scattering of thermal energy carriers. The introduction of vacancy and twinning defects is found to hinder interfacial thermal transport due to heightened phonon scattering processes that impede phononic transmission. The interatomic interactions and lattice dynamics are analyzed to provide insights into the underlying thermal transport physics at the atomistic scale. By tuning the system length from 4 to 16 nm, temperature from 300 to 500 K, and defect density from 0 to 0.4%, we achieve tunable control of the interfacial thermal conductance. Our study elucidates the multiscale mechanisms governing thermal transport across diamond/c-BN and provides potential pathways to actively tailor interfacial thermal properties through structural and temperature engineering. The fundamental understandings are valuable for optimizing heat dissipation and enabling thermal management solutions in next-generation power electronics leveraging these materials.

Preparation, thermophysical properties, and thermal shock resistance of Yb2O3-doped YSZ coatings

The yttria-stabilized zirconia (YSZ) coatings were doped with various concentrations of Yb2O3 to build a multi-component solid solution system. The effects of concentration on the phase composition, microstructure, phase stability at high temperatures, thermal conductivity, thermal expansion, fracture toughness, elastic modulus, and other thermophysical properties of the coatings were systematically analyzed. Furthermore, the mechanism through which Yb2O3 doping impacts the thermal shock resistance of YSZ coatings was elucidated. The results reveal that doping with Yb3+, which has a similar radius to Zr4+, allows the YSZ coatings to retain the tetragonal phase structure at low doping concentrations. The Yb2O3 doping can reduce the thermal conductivity of YSZ coatings due to replacement atom and oxygen vacancy defects enhancing phonon scattering and decreasing the mean free path of phonons. The 1YbYSZ coating demonstrates better thermal shock resistance owing to its high CTE and high fracture toughness resulting from its tetragonal phase, high elastic modulus and high grain boundary density. The Yb2O3 doping can form defect clusters and increase the cation diffusion path due to oxygen vacancies, which inhibits the uneven diffusion of Y3+. Therefore, Yb2O3-doped YSZ coatings demonstrate remarkable phase stability at high temperatures of 1700 °C.

Ultralow thermal conductivity of amorphous silicon–germanium thin films for alloy and disorder scattering determined by 3ω method and nanoindentation

Abstract The ultralow thermal conductivity (1.3 W/(m∙K)) of amorphous silicon–germanium films for alloy and disorder scattering was investigated using the 3ω method and nanoindentation. The films exhibited the lowest phonon mean free path (MFP) of 0.5 nm compared to that of amorphous silicon (1.1 nm) and germanium (0.9 nm) films, owing to alloy scattering in the silicon–germanium films. Based on Matthiessen’s rule, the phonon MFPs of the amorphous silicon–germanium films contributing to alloy and disorder scattering were calculated to be 1.0 nm for both. Therefore, alloy and disorder scattering contribute equally to the reduction in the phonon MFP.

Role of phonon scattering and bonding in resolving lattice thermal conductivity ambiguities of β-Ga2O3.

Understanding the lattice thermal conductivity (κl) of β-Ga2O3 is very intriguing owing to its advantages in high-voltage and high-temperature applications. Despite several attempts, the underlying mechanism and causes of the notable discrepancies found in the κl values of β-Ga2O3 along [100] and [001] directions calculated using first principles remained unresolved. We demonstrate that the understanding of the nature of chemical bonding is crucial to overcome the inconsistency in theoretically reported κl values. In low-symmetry structures such as β-Ga2O3, the nature of the interactions is primarily long-range; therefore, a sufficiently large supercell inclusive of various bonding characteristics is required to capture relevant phonon wavelengths. Bonding nature-aware structure modeling allows precise estimation of acoustic and optical mode contributions towards κl. Additionally, phonon mean free path analysis confirms that considering only third-order interaction terms is adequate to determine the κl of β-Ga2O3. The calculated κl values are in excellent agreement with experimentally reported values in all three directions. Our results establish that the bonding nature and its influence on phonon scattering are essential to consider in calculating κl accurately.

Phonon mean free path of silicate glasses: a useful parameter to distinguish between framework and nonframework cations

Phonon mean free path of silicate glasses: a useful parameter to distinguish between framework and nonframework cations

Unveiling the ultralow in-plane thermal conductivity in 2D organic–inorganic hybrid perovskite (EA)2PbI4 single crystals

2D organic–inorganic hybrid perovskites EA2PbI4 exhibit ultralow in-plane thermal conductivity, approaching the amorphous limit, due to the exceptionally short phonon mean free paths comparable to the Pb–I bond lengths within the PbI6 octahedra.

Hidden structures: a driving factor to achieve low thermal conductivity and high thermoelectric performance.

The long-range periodic atomic arrangement or the lack thereof in solids typically dictates the magnitude and temperature dependence of their lattice thermal conductivity (κlat). Compared to crystalline materials, glasses exhibit a much-suppressed κlat across all temperatures as the phonon mean free path reaches parity with the interatomic distances therein. While the occurrence of such glass-like thermal transport in crystalline solids captivates the scientific community with its fundamental inquiry, it also holds the potential for profoundly impacting the field of thermoelectric energy conversion. Therefore, efficient manipulation of thermal transport and comprehension of the microscopic mechanisms dictating phonon scattering in crystalline solids are paramount. As quantized lattice vibrations (i.e., phonons) drive κlat, atomistic insights into the chemical bonding characteristics are crucial to have informed knowledge about their origins. Recently, it has been observed that within the highly symmetric 'averaged' crystal structures, often there are hidden locally asymmetric atomic motifs (within a few Å), which exert far-reaching influence on phonon transport. Phenomena such as local atomic off-centering, atomic rattling or tunneling, liquid-like atomic motion, site splitting, local ordering, etc., which arise within a few Å scales, are generally found to drastically disrupt the passage of heat carrying phonons. Despite their profound implication(s) for phonon dynamics, they are often overlooked by traditional crystallographic techniques. In this review, we provide a brief overview of the fundamental aspects of heat transport and explore the status quo of innately low thermally conductive crystalline solids, wherein the phonon dynamics is majorly governed by local structural phenomena. We also discuss advanced techniques capable of characterizing the crystal structure at the sub-atomic level. Subsequently, we delve into the emergent new ideas with examples linked to local crystal structure and lattice dynamics. While discussing the implications of the local structure for thermal conductivity, we provide the state-of-the-art examples of high-performance thermoelectric materials. Finally, we offer our viewpoint on the experimental and theoretical challenges, potential new paths, and the integration of novel strategies with material synthesis to achieve low κlat and realize high thermoelectric performance in crystalline solids via local structure designing.