Examination of the thermal variation of the mean square atomic displacements in zinc and evaluation of the associated Debye temperature.
Mean square atomic displacements variation with temperature in Zn, evaluating Debye temperature
Katz, J. L.↗
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Results for “Debye temperature”
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Machine learning the relationship between Debye temperature and superconducting transition temperature
Recently a relationship between the Debye temperature $Θ_D$ and the superconducting transition temperature $T_c$ of conventional superconductors has been proposed [Esterlis et al., npj Quantum Mater. 3, 59 (2018)]. The relationship indicates that $T_c$ ≤ $AΘ_D$ for phonon-mediated BCS superconductors, with $A$ being a prefactor of order ~ $0.1$. In order to verify this bound, we train machine learning (ML) models with 10 330 samples in the Materials Project database to predict $Θ_D$. Here, by applying our ML models to 9860 known superconductors in the NIMS SuperCon database, we find that the conventional superconductors in the database indeed follow the proposed bound. We also perform first-principles phonon calculations for $\mathrm{H_3S}$ and $\mathrm{LaH_{10}}$ at 200 GPa. The calculation results indicate that these high-pressure hydrides essentially saturate the bound of $T_c$ versus $Θ_D$.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Measurements of the thermal variation of the X-ray Debye temperature of pure nickel and chromium.
X-ray Debye temperature thermal variation measurements of pure nickel and chromium
SINGLE CRYSTAL↗
An empirical relationship between thermal conductivity and Debye temperature for silicates
Silicates thermal conductivity-Debye temperature relationship from thermal conductivity and acoustic data, applying to earth conductivity measurements
Horai, K.-I.↗
Equation Of State With Temperature Effects For Solids
Behavior at high temperature predicted from only four parameters. Equations derived to express thermodynamical properties of compressed solids at high temperatures. New equations based on fundamental considerations of thermodynamics, isothermal equation of state, and assumption thermal pressure independent of volume and varies linearly with temperature near and about Debye temperature. Using only four parameters (three are those of isothermal equation of state), new equations describe thermodynamic behavior of material over range of temperatures from approximately Debye temperature to melting point.
Vinet, Pascal↗
Structure, electrical and thermal properties of single-crystal BaCuGdTe 3
Single crystals of the quaternary chalcogenide BaCuGdTe 3 were obtained by direct reaction of elements allowing for a complete investigation of the intrinsic electrical and thermal properties of this previously uninvestigated material. The structure was investigated by high-resolution single-crystal synchrotron X-ray diffraction, revealing an orthorhombic crystal structure with the space group Cmcm. Although recently identified as a semiconductor suitable for thermoelectric applications from theoretical analyses, our electrical resistivity and Seebeck coefficient measurements show metallic conduction, the latter revealing strong phonon-drag. Temperature dependent hole mobility reveals dominant acoustic phonon scattering. Heat capacity data reveal a Debye temperature of 183 K and a very high density of states at the Fermi level, the latter confirming the metallic nature of this composition. Thermal conductivity is relatively high with Umklapp processes dominating thermal transport above the Debye temperature. The findings in this work lay the foundation for a more detailed understanding of the physical properties of this and similar multinary chalcogenide materials, and is part of the continuing effort in investigating quaternary chalcogenide materials and their suitability for use in technological applications.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Inelastic phonon transport across atomically sharp metal/semiconductor interfaces
Understanding thermal transport across metal/semiconductor interfaces is crucial for the heat dissipation of electronics. The dominant heat carriers in non-metals, phonons, are thought to transport elastically across most interfaces, except for a few extreme cases where the two materials that formed the interface are highly dissimilar with a large difference in Debye temperature. In this work, we show that even for two materials with similar Debye temperatures (Al/Si, Al/GaN), a substantial portion of phonons will transport inelastically across their interfaces at high temperatures, significantly enhancing interface thermal conductance. Moreover, we find that interface sharpness strongly affects phonon transport process. For atomically sharp interfaces, phonons are allowed to transport inelastically and interface thermal conductance linearly increases at high temperatures. With a diffuse interface, inelastic phonon transport diminishes. Our results provide new insights on phonon transport across interfaces and open up opportunities for engineering interface thermal conductance specifically for materials of relevance to microelectronics.
42 ENGINEERING↗
Impact of classical statistics on thermal conductivity predictions of BAs and diamond using machine learning molecular dynamics
Machine learning interatomic potentials (MLIPs) have greatly enhanced molecular dynamics (MD) simulations, achieving near-first-principles accuracy in thermal conductivity studies. In this work, we reveal that this accuracy, observed in BAs and diamond at sub-Debye temperatures, stems from an accidental error cancelation: classical statistics overestimates specific heat while underestimating phonon lifetimes, balancing out in thermal conductivity predictions. However, this balance is disrupted when isotopes are introduced, leading MLIP-based MD to significantly underpredict thermal conductivity compared to experiments and quantum statistics-based Boltzmann transport equation. This discrepancy arises not from classical statistics affecting phonon–isotope scattering rates but from its impact on the interplay between phonon–isotope and phonon–phonon scattering in the normal scattering-dominated BAs and diamond. In conclusion, this work underscores the limitations of MLIP-based MD for thermal conductivity studies at sub-Debye temperatures.
36 MATERIALS SCIENCE↗
The Debye-Waller factor of disordered solids: The case for amorphous silicon
This paper presents a first-principles study of the Debye-Waller factor and the Debye temperature for amorphous silicon (α-Si) from lattice-dynamical calculations and direct molecular-dynamics simulations using density-functional theory (DFT). The effects of temperature and structural disorder on the intensity of the diffraction maxima and the vibrational mean-square displacement (MSD) of Si atoms are studied in the harmonic approximation, with particular emphasis on the bond-length disorder, the presence of coordination defects, and microvoids in α-Si networks. It has been observed that the MSDs associated with tetrahedrally bonded Si atoms are considerably lower than their dangling-bond counterparts—originating from isolated and vacancy-induced clustered defects—and those on the surface of microvoids, leading to an asymmetric non-Gaussian tail in the distribution of atomic displacements. An examination of the effect of anharmonicity on the MSD at high temperatures using direct ab initio molecular-dynamics simulations (without the harmonic approximation) suggests that the vibrational motion in α-Si is practically unaffected by anharmonic effects at temperatures below 400 K, as far as the present DFT calculations are concerned. The Debye temperature of α-Si is found to be in the range of 488–541 K from specific-heat and MSD calculations using first-principles lattice-dynamical calculations in the harmonic approximation, which matches closely with the experimental value of 487–528 K obtained from specific-heat measurements of α-Si at low temperatures.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Ab initio studies of the impact of the Debye-Waller factor on the structural and dynamical properties of amorphous semiconductors: The case of a-Si
This paper presents a first-principles study of the Debye-Waller factor and the Debye temperature for amorphous silicon (a-Si) from lattice-dynamical calculations and direct molecular-dynamics simulations using density-functional theory (DFT). The effects of temperature and structural disorder on the intensity of the diffraction maxima and the vibrational mean-square displacement (MSD) of Si atoms are studied in the harmonic approximation, with particular emphasis on the bond-length disorder, the presence of coordination defects, and microvoids in a-Si networks. It has been observed that the MSDs associated with tetrahedrally-bonded Si atoms are considerably lower than their dangling-bond counterparts – originating from isolated and vacancy-induced clustered defects – and those on the surface of microvoids, leading to an asymmetric non-gaussian tail in the distribution of atomic displacements. An examination of the effect of anharmonicity on the MSD at high temperatures using direct ab initio molecular-dynamics simulations (without the harmonic approximation) suggests that the vibrational motion in a-Si is practically unaffected by anharmonic effects at temperatures below 400 K, as far as the present DFT calculations are concerned. The Debye temperature of a-Si is found to be in the range of 488–541 K from specific-heat and MSD calculations using first-principles lattice-dynamical calculations in the harmonic approximation, which matches closely with the experimental value of 487–528 K obtained from specific-heat measurements of a-Si at low temperatures.
36 MATERIALS SCIENCE↗
Vibrational Entropy of Crystalline Solids from Covariance of Atomic Displacements
The vibrational entropy of a solid at finite temperature is investigated from the perspective of information theory. Ab initio molecular dynamics (AIMD) simulations generate ensembles of atomic configurations at finite temperature from which we obtain the N-body distribution of atomic displacements, ρN. We calculate the information-theoretic entropy from the expectation value of lnρN. At a first level of approximation, treating individual atomic displacements independently, our method may be applied using Debye–Waller B-factors, allowing diffraction experiments to obtain an upper bound on the thermodynamic entropy. At the next level of approximation we correct the overestimation through inclusion of displacement covariances. We apply this approach to elemental body-centered cubic sodium and face-centered cubic aluminum, showing good agreement with experimental values above the Debye temperatures of the metals. Below the Debye temperatures, we extract an effective vibrational density of states from eigenvalues of the covariance matrix, and then evaluate the entropy quantum mechanically, again yielding good agreement with experiment down to low temperatures. Our method readily generalizes to complex solids, as we demonstrate for a high entropy alloy. Further, our method applies in cases where the quasiharmonic approximation fails, as we demonstrate by calculating the HCP/BCC transition in Ti.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Ab initio study of mechanical and thermal properties of GeTe-based and PbSe-based high-entropy chalcogenides
GeTe-based and PbSe-based high-entropy compounds have outstanding thermoelectric (TE) performance and crucial applications in mid and high temperatures. Recently, the optimization of TE performance of high-entropy compounds has been focused on reducing thermal conductivity by strengthening the phonon scattering process to improve TE performance. We report a first-principles investigation on nine GeTe-based high-entropy chalcogenide solid solutions constituted of eight metallic elements (Ag, Pb, Sb, Bi, Cu, Cd, Mn, and Sn) and 13 PbSe-based high-entropy chalcogenide solid solutions: Pb 0.99-y Sb 0.012 Sn y Se 1-2x Te x S x (x = 0.1, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, and y = 0) and Pb 0.99-y Sb 0.012 Sn y Se 1-2x Te x S x (y = 0.05, 0.1, 0.15, 0.2, 0.25 and x = 0.25). We have investigated the mechanical properties focusing on Debye temperature (Θ D ), thermal conductivity (κ), Grüneisen parameter (γ α ), dominant phonon wavelength (λ dom ), and melting temperature (T m ). We find that the lattice thermal conductivity is significantly reduced when GeTe is alloyed into the following compositions: Ge 0.75 Sb 0.13 Pb 0.12 Te, Ge 0.61 Ag 0.11 Sb 0.13 Pb 0.12 Bi 0.01 Te, and Ge 0.61 Ag 0.11 Sb 0.13 Pb 0.12 Mn 0.05 Bi 0.01 Te. This reduction is due to the mass increase and strain fluctuations. The results also show that Ge 0.61 Ag 0.11 Sb 0.13 Pb 0.12 Bi 0.01 Te solid solution has the lowest Young’s modulus (30.362 GPa), bulk and shear moduli (18.626 and 12.359 GPa), average sound velocity (1653.128 m/sec), Debye temperature (151.689 K), lattice thermal conductivity (0.574 W.m –1 .K –1 ), dominant phonon wavelength (0.692 Å), and melting temperature (535.91 K). Moreover, Ge 0.61 Ag 0.11 Sb 0.13 Pb 0.12 Bi 0.01 Te has the highest Grüneisen parameter with a reduced and temperature-independent lattice thermal conductivity. The positive correlation between Θ D and κ is revealed. Alloying of PbSe-based high-entropy by Sb, Sn, Te, and S atoms at the Se and Pb sites resulted in much higher shear strains resulted in the reduction of phonon velocity, a reduced Θ D , and a lower lattice thermal conductivity.
74 ATOMIC AND MOLECULAR PHYSICS↗
Superconducting compounds and alloys research
Resistivity measurements as a function of temperature were performed on alloys of the binary material system In sub(1-x) Bi sub x for x varying between 0 and 1. It was found that for all single-phase alloys (the pure elements, alpha-In, and the three intermetallic compounds) at temperatures sufficiently above the Debye-temperature, the resistivity p can be expressed as p = a sub o T(n), where a sub o and n are composition-dependent constants. The same exponential relationship can also be applied for the sub-system In-In2Bi, when the two phases are in compositional equilibrium. Superconductivity measurements on single and two-phase alloys can be explained with respect to the phase diagram. There occur three superconducting phases (alpha-In, In2Bi, and In5Bi3) with different transition temperatures in the alloying system. The magnitude of the transition temperatures for the various intermetallic phases of In-Bi is such that the disappearance or occurrence of a phase in two component alloys can be demonstrated easily by means of superconductivity measurements.
Otto, G.↗
Enhancing the accuracy and generality of the Debye–Grüneisen Model: Optimizing the volume dependence for accurate predictions across varied compositions
In this work, we have introduced an optimized Debye-Grüneisen model that revolutionizes the determination of the Debye temperature and Grüneisen parameters. Unlike conventional methods, our model requires only the 0 K energy volume data for a material as input, eliminating the need to determine the bulk modulus and its pressure derivative, which often pose challenges due to numerical uncertainties. This unique feature sets our model apart from existing approaches and streamlines the process, enabling accurate predictions of thermal expansion behavior across various materials. To demonstrate its effectiveness, we showcase its excellent agreement with measured coefficients of thermal expansion (CTE) for the nickel-cobalt-chromium-aluminum-yttrium (Ni-Co-Cr-Al-Y) bond-coating system. Additionally, we apply our approach by conducting a high-throughput search for potential bond-coating materials among 90,000 compositions within the aluminum-cobalt-chromium-iron-nickel (Al-Co-Cr-Fe-Ni) system. From this extensive search, four compositions are synthesized, and the measured CTE values agree very well with theoretical predictions, hence validating our approach. In conclusion, the current optimized Debye-Grüneisen model combined with Density Functional Theory (DFT)-based thermodynamic database enables reliable and efficient high-throughput calculations of CTE of of a material without expensive phonon calculations.
Bond coating materials↗
Thermal and Electronic Properties of Ba 2 MnSe 3
The structural, thermal, and electronic properties of Ba 2 MnSe 3 were investigated. Analysis of the low-temperature heat capacity revealed a low Debye temperature and a low average speed of sound that, together with the bonding in this material, result in a low thermal conductivity over a relatively large temperature range. Density functional theory and calculated electron localization were employed to investigate the electronic structure and bonding. Absorption and photoluminescence spectroscopy measurements corroborated our calculations and revealed a direct band gap of 1.75 eV. This study expands on our understanding of the physical properties of this material and reveals previously unascertained properties, the knowledge of which is imperative for any potential application of interest.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Low- and high-temperature heat capacity of metallic technetium
The heat capacity of technetium metal has been measured from 2.1 K to 293 K using relaxation calorimetry and the enthalpy increment up to 1700 K using drop calorimetry. The low-temperature calorimetry measurements revealed a superconducting transition temperature of T C = (7.76 ± 0.08) K. The zero-degree Debye temperature(θ E ) and the electronic heat capacity coefficient ($γ_{e}$) of the normal state were derived as (307 ± 5) K and (4.22 ± 0.20) mJ·K –2 ·mol –1 , respectively. The standard entropy of the superconducting standard state was derived as $S^{°}_{m}$ (298.15) = (36.8 ± 1.3) J·K –1 ·mol –1 . The fitting of enthalpy-increment data together with high-temperature heat capacity data reported in literature yielded a heat capacity equation up to 1700 K.
36 MATERIALS SCIENCE↗
Structure and disorder resulting in ultralow thermal conductivity in the defect chalcopyrite AgInSnSe 4
Quaternary chalcogenides are attractive for a variety of technological fields of interest due to the diverse physical properties these materials possess. Herein, the structural and thermal properties of the disordered chalcopyrite AgInSnSe 4 are reported revealing a distinct relation between its structure and physical properties. Modeling of the experimental temperature-dependent thermal properties revealed an ultralow thermal conductivity (0.47 Wm -1 K -1 at room temperature) due to lattice anharmonicity, a low speed of sound and a low Debye temperature. Moreover, first principles electronic structure calculations revealed that the Ag-Se tetrahedra within the crystal structure possess relatively weak bonds due to occupied antibonding states from p-d orbital hybridization, which suppress the thermal conductivity. Here, in order to further quantify our findings, we extended our analyses to include comparisons with other ternary and quaternary adamantine materials, all of which possess a fourfold tetrahedral coordination of atoms, in revealing the origin of the thermal properties in AgInSnSe 4 .
36 MATERIALS SCIENCE↗
Pressure and temperature dependences of the isotropic elastic moduli of polycrystalline alumina.
Pressure and temperature dependence of isotropic elastic moduli of polycrystalline alumina, noting Gruneisen parameter, equation of state and Debye temperature
Chung, D. H.↗