Temperature Dependent Lattice Constant Research Articles

Intrinsic thermal conductivity of ZrC from low to ultrahigh temperatures: A critical revisit

Current phonon transport theory based on ground-state calculations has been successful in predicting thermal conductivity at room and medium temperatures but may misrepresent behavior at high temperatures. In this work, we predict the thermal conductivity ($\ensuremath{\kappa}$) of ZrC including electronic and phonon contributions from 300 to 3500 K, by including high-order phonon scattering; lattice expansion; temperature-dependent (TD) second-, third-, and fourth-order force constants (2FC, 3FC, and 4FC); and interband phonon conduction by using first principles. For the phonon transport, we find that four-phonon scattering (4ph) significantly reduces the phonon thermal conductivity (${\ensuremath{\kappa}}_{\mathrm{ph}}$), by as much as $\ensuremath{\sim}75%$ at 3500 K. After including 4ph scattering and all other factors, ${\ensuremath{\kappa}}_{\mathrm{ph}}$ shows a $\ensuremath{\sim}{T}^{\ensuremath{-}1.5}$ rather than $\ensuremath{\sim}{T}^{\ensuremath{-}1}$ dependence. TD 2FC decreases three-phonon scattering rates but increases 4ph rates by decreasing and increasing the scattering phase spaces, respectively. For 4ph phase space, the TD 2FC flattens phonon bands, and allows more redistribution-4ph processes $(1+2\ensuremath{\rightarrow}3+4)$ to happen. The combination effect of TD 2FC and TD 4FC reduces 4ph rates of acoustic modes but increases those of optical modes. The TD 3FC and 4FC decrease the phonon scattering cross section and increase the ${\ensuremath{\kappa}}_{\mathrm{ph}}$ significantly (by 52% at 3500 K). The contribution from interband (Wigner) phonon conduction is small, even at ultrahigh temperatures. For electronic thermal transport, we find that it is sensitive to and can be changed by 20% by the TD lattice constants. The Lorenz number varies from 1.6 to $3.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.16em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$ at different temperatures. The theoretical prediction in the literature overpredicts ${\ensuremath{\kappa}}_{\mathrm{ph}}$ (e.g., $\ensuremath{\sim}28%$) and underpredicts the ${\ensuremath{\kappa}}_{\mathrm{el}}$ (e.g., $\ensuremath{\sim}38%$), resulting in an overall underprediction of $\ensuremath{\kappa}$ ($\ensuremath{\sim}26%$ at 1500 K). The impacts of grain size and defects are found to be strong, leading to the lower observed thermal conductivity in experiments.

High-temperature phonon transport properties of SnSe from machine-learning interatomic potential

As a promising thermoelectric material, tin selenide (SnSe) is of relatively low thermal conductivity. However, the phonon transport mechanisms in SnSe are not fully understood due to the complex phase transition, dynamical instability, and strong anharmonicity. In this work, we perform molecular dynamics simulations with a machine-learning interatomic potential to explore the thermal transport properties of SnSe at different temperatures. The developed interatomic potential is parameterized using the framework of moment tensor potential, exhibiting satisfactory predictions on temperature-dependent lattice constants and phonon dispersion, as well as phase transition temperature. From equilibrium molecular dynamics simulations, we obtained the thermal conductivity tensor from 200 K to 900 K. The origins of temperature-dependent thermal conductivity anisotropy and the roles of four-phonon scatterings are identified. The obtained interatomic potential can be utilized to study the mechanical and thermal properties of SnSe and related nanostructures in a wide range of temperatures.

Temperature Dependent Thermal and Elastic Properties of High Entropy (Ti0.2Zr0.2Hf0.2Nb0.2Ta0.2)B2: Molecular Dynamics Simulation by Deep Learning Potential

High entropy diborides are new categories of ultra-high temperature ceramics, which are believed promising candidates for applications in hypersonic vehicles. However, knowledge on high temperature thermal and mechanical properties of high entropy diborides is still lacking unit now. In this work, variations of thermal and elastic properties of high entropy (Ti0.2Zr0.2Hf0.2Nb0.2Ta0.2)B2 with respect to temperature were predicted by molecular dynamics simulations. Firstly, a deep learning potential for Ti-Zr-Hf-Nb-Ta-B diboride system was fitted with its prediction error in energy and force respectively being 9.2 meV/atom and 208 meV/Å, in comparison with first-principles calculations. Then, temperature dependent lattice constants, anisotropic thermal expansions, anisotropic phonon thermal conductivities, and elastic properties of high entropy (Ti0.2Zr0.2Hf0.2Nb0.2Ta0.2)B2 from 0 °C to 2400 °C were evaluated, where the predicted room temperature values agree well with experimental measurements. In addition, intrinsic lattice distortions of (Ti0.2Zr0.2Hf0.2Nb0.2Ta0.2)B2 were analyzed by displacements of atoms from their ideal positions, which are in an order of 10-3 Å and one order of magnitude smaller than those in (Ti0.2Zr0.2Hf0.2Nb0.2Ta0.2)C. It indicates that lattice distortions in (Ti0.2Zr0.2Hf0.2Nb0.2Ta0.2)B2 is not so severe as expected. With the new paradigm of machine learning potential, deep insight into high entropy materials can be achieved in the future, since the chemical and structural complexly in high entropy materials can be well handled by machine learning potential.

Phonon Anharmonicity in Few-Layer Black Phosphorus.

We report a temperature-dependent Raman spectroscopy study of few-layer black phosphorus (BP) with varied incident polarization and sample thickness. The Raman-active modes Ag1, B2g, and Ag2 exhibit a frequency downshift, while their line width tends to increase with increasing temperature. To understand the details of these phenomena, we perform first-principles density functional theory calculations on freestanding monolayer BP. The effect of thermal expansion is included by constraining the temperature-dependent lattice constant. The study of the temperature-induced shift of the phonon frequencies is carried out using ab initio molecular dynamics simulations. The normal-mode frequencies are calculated by identifying the peak positions from the magnitude of the Fourier transform of the total velocity autocorrelation. Anharmonicity induces a frequency shift for each individual mode, and the three- and four-phonon process coefficients are extracted. These results are compared with those obtained from many-body perturbation theory, giving access to phonon lifetimes and lattice thermal conductivity. We establish that the frequency downshift is primarily due to phonon-phonon scattering while thermal expansion only contributes indirectly by renormalizing the phonon-phonon scattering. Overall, the theoretical results are in excellent agreement with experiment, thus showing that controlling phonon scattering in BP could result in better thermoelectric devices or transistors that dissipate heat more effectively when confined to the nanoscale.

Revisiting lattice thermal transport in PbTe: The crucial role of quartic anharmonicity

We perform a first-principles study of lattice thermal transport in PbTe by explicitly considering anharmonicity up to 4th order. To determine the temperature-dependent lattice constant of PbTe beyond quasiharmonic approximation, we introduce a simple yet effective scheme to account for anharmonic phonon renormalization at finite temperature. Moreover, we explicitly compute mode-resolved phonon lifetimes by including both three- and four-phonon scatterings. We find that (1) anharmonic phonon renormalization leads to strong vibrational frequency shifts which improve the agreement between simulated and experimental lattice constants; (2) these frequency shifts lead to a significant increase in lattice thermal conductivity (κl) because of reduced phonon scattering phase space; and (3) four-phonon scatterings are responsible for severe reduction in κl on top of three-phonon scatterings, making κl consistent with experiments. Our results suggest that the predicted κl and its temperature dependence without considering thermal expansion, anharmonic phonon renormalization and four-phonon scatterings could accidentally agree with experiments due to error cancellation. Our study not only deepens the understanding of lattice thermal transport in PbTe but also exemplifies a widely applicable approach to investigate lattice dynamics and thermal transport properties from first-principles calculations including high-order anharmonicity.

First-principles modeling of the Invar effect in Fe65Ni35 by the spin-wave method

Thermal lattice expansion of the Invar Fe65Ni35 alloy is investigated in first-principles calculations using the spin-wave method, which is generalized here for the ferromagnetic state with short range order. It is shown that magnetic short-range order effects make substantial contribution to the equilibrium lattice constant and cannot be neglected in the accurate ab initio modeling of the thermal expansion in Fe-Ni alloys. We also demonstrate that at high temperatures, close and above the magnetic transition, magnetic entropy associated with transverse and longitudinal spin fluctuations yields a noticeable contribution to the equilibrium lattice constant. The obtained theoretical results for the temperature dependent lattice constant are in semiquantitative agreement with the experimental data apart from the region close the magnetic transition.

Anisotropic transport in the quasi-one-dimensional semiconductor Li0.33MoO3

Transport measurements (electrical resistivity, Seebeck coefficient, and thermal conductivity) in the temperature range 80–500 K are presented for single crystals of the quasi-one-dimensional (Q1D) semiconductor Li0.33MoO3. Opposite signs are observed for the Seebeck coefficient along the trinclinic a and c axes, with Sc − Sa ≃ 250 μV/K near room temperature and ≃100 μV/K at 380 K. The thermal conductivity at room temperature in the a-c planes was ∼2 W/m K and ∼10 times smaller along b*. A weak structural anomaly at Ts ≈ 355 K, identified in the temperature-dependent lattice constants, coincides with anomalies in the electrical properties. Analysis of the electronic transport at T > Ts favors an intrinsic semiconductor picture for transport along the most conducting Q1D axis and small-polaronic transport along the other directions, providing insight into the origin of the Seebeck anisotropy.

Temperature dependent lattice constant of InSb above room temperature

Using temperature dependent X-ray diffraction on two InSb single crystalline substrates, the bulk lattice constant of InSb was determined between 32 and 325°C. A polynomial function was fitted to the data: a(T)=6.4791+3.28×10−5×T+1.02×10−8×T2Å (T in °C), which gives slightly higher values than previously published (which go up to 62°C). From the fit, the thermal expansion of InSb was calculated to be α(T)=5.062×10−6+3.15×10−9×TK−1 (T in °C). We found that the thermal expansion coefficient is higher than previously published values above 100°C (more than 10% higher at 325°C).

Temperature dependence of stacking-fault and anti-phase boundary energies in AlSc from ab initio calculations

Temperature dependence of intrinsic stacking-fault energies (SFE) and anti-phase boundary energies (APBE) of AlSc is investigated in first-principles calculations using the axial Ising model and supercell approach. The temperature effect has been taken into consideration by including the one-electron thermal excitations in the electronic structure calculations, and vibrational free energy in the harmonic approximation as well as by using temperature dependent lattice constant. The latter has been determined within the Debye–Grüneisen model, which reproduces well the experimental data. The APBE and SFE are found to be reduced by about 10% in the temperature interval from 0 to 1000 K. It is shown that the inclusion of the free energy of lattice vibrations in the harmonic approximation increases the SFE further by about 4%. We also find a substantial contribution from local lattice relaxations in the case of APBE for the (1 1 1) plane and SFE leading to their reduction by about 30%.

Temperature dependent lattice constant of Al0.90Ga0.10AsySb1−y

Using x-ray diffraction, the in-plane and out-of-plane lattice constants of Al0.90Ga0.10AsySb1−y epilayers grown on GaSb and GaAs substrates were determined between 30 and 398 °C for y=0.003–0.059. The bulk lattice constant was then calculated from the in-plane and out-of-plane lattice constants. A polynomial function for the bulk lattice constant as a function of y and temperature was derived from a fit to the resulting data. Comparison to measured out-of-plane lattice constants of platinum-coated Al0.90Ga0.10AsySb1−y indicates that the polynomial function is valid up to around 550 °C. The polynomial function can be used to determine the lattice matching of Al0.90Ga0.10AsySb1−y to, e.g., GaSb at typical growth temperatures used for growth of cladding layers in laser structures. A formula is given for calculating the As mole fraction for lattice matching to GaSb at a given temperature.

Lattice Constants and Thermal Expansion Coefficient of Air Clathrate Hydrate in Deep Ice Cores from Vostok, Antarctica

We measured the temperature-dependent lattice constant of air hydrates in deep ice cores from Vostok, Antarctica, using single-crystal X-ray diffraction. Thus the thermal expansion coefficient was determined, the first for a structure II clathrate hydrate containing small guest molecules. Despite their high dissociation pressures, measurements were done at atmospheric pressure because the air hydrates had stabilized during their original residence at high pressure. At 200 K, the lattice constant and thermal expansion coefficient were 17.20 Å and 44 (±9) × 10-6 K-1, respectively. This thermal expansion coefficient is approximately equal to that from tetrahydrofuran hydrate, another structure II hydrate, but the lattice constant is 0.3% smaller. Crystal structure refinement determined that the total cage occupancy by air molecules was 0.9.

Temperature-dependent measurements on ZnSe heterostructures by high-resolution X-ray diffraction

Thermally induced strain in ZnSe epitaxial layers on GaAs occurs due to the different expansion coefficients of the single materials. This strain is directly investigated by high-resolution X-ray diffraction in the temperature range from 10 to 600 K. The strain is measured for a thick relaxed and a thin pseudomorphic layer. Furthermore, the lattice constants of ZnSe and GaAs bulk materials are determined at variable temperatures. It was observed that the thermal expansion is quite linear for GaAs and ZnSe only in the temperature range from 250 to 600 K. The measured temperature-dependent lattice constants and the derived expansion coefficients are input parameters for a model to calculate the thermally induced strain in the epitaxial layers. Good agreement could be obtained between the experimental data and the model.

Polymorphism and Superstructure in BaCoS2−δ

BaCoS2−δconsists of at least three different polymorphs: two that are stoichiometric and one that is potentially sulfur deficient with 0.0 ≤ δ ≤ 0.2. Two of these polymorphs were investigated here: a tetragonal single crystalP4/nmm,a= 4.568(1) Å,c= 8.942(2) Å (δ ≈ 0), and polycrystalline powderCmma,a= 6.4390(3) Å,b= 6.4909(3) Å,c= 8.9379(4) Å (δ ≈ 0.2). Room temperature TEM studies show that several classes of superstructures exist in the stoichiometric single crystals of this phase; on cooling the TEM diffraction patterns change and become more complex. Temperature-dependent lattice constants of polycrystalline BaCoS2−δshow anomalies near −60°C. BaCoS2−δis a metastable compound that is prepared above 850°C and subsequently quenched. Synthetic studies show that (1) at the preparation temperature BaCoS2is in equilibrium with S vapor at pressures on the order of an atmosphere, producing a nonstoichiometric phase BaCoS2−δ; (2) adding some excess sulfur can reduce δ to zero; and (3) too much excess sulfur results in partial or complete melting of the system (however, stoichiometric BaCoS2crystals can be obtained from those melts). Magnetic susceptibility measurements verify that the Co moments order antiferromagnetically at 310 K. At higher temperatures a Curie–Weiss fit to the data gives μeff= 2.14(4) μB/Co and θ = 150(20) K; these data are consistent with a low spin state for Co2+(d7).