Thermal Electronic Contributions Research Articles

Full-Potential KKR Calculations for Interaction Energies in Al-Rich AlX (X = H～Sn) Alloys: I. Fundamental Features and Thermal Electronic Contribution due to Fermi-Dirac Distribution

We presented systematical ab-initio calculations for the n-body (n = 1-4) interaction energies (IEs) in Al-rich AlX (X = H～Sn) alloys, by using the full-potential Korringa-Kohn- Rostoker Green's function (FPKKR) method, and clarified the fundamental features and the thermal electronic contribution due to the Fermi Dirac (FD) distribution for these IEs. We show the calculated results for the IEs: (1) the 2-body IEs of the X = 3d and 4d impurities are strongly repulsive at the 1st-nearest neighbor (nn) and show the oscillating behavior with the interatomic distance; (2) the 1st-nn 2-body IEs of the X = Ne, Ar, and Kr (inert gas elements) impurities are strongly attractive; (3) the 1st-nn 2-body IEs around X = N (2sp element) are repulsive and relatively high; (4) the thermal electronic contribution due to the FD distribution is considerably high for the X = d impurities, while very low for the X = sp impurities; (5) the n-body (n = 1-4) IEs of the X = 3d and 4d impurities in Al and the thermal electronic contribution for these n-body IEs may be in general lower and lower with the increase in n. It is also discussed that the fundamental features (attraction or repulsion) of the calculated 2-body IEs may be understood by considering the strength differences among the X−X, Al−X, and Al−Al interactions.

The electronic structure, phase transition, elastic, thermodynamic, and thermoelectric properties of FeRh: high-temperature and high-pressure study

Abstract Using the projector augmented wave (PAW) within the Perdew, Burke, and Ernzerhof (PBE) form of generalized gradient approximation (GGA), We present a study of the electronic structure, phase transition, elastic, thermodynamic, and thermoelectric properties of FeRh. We find that FM structure exhibits the largest Fe magnetic moment, which is in accordance with the experimental data and Fe magnetic moment for A-AFM and G-AFM phases, c-AFM, A’-AFM and Ort phases show lower Fe local magnetic moment. Our most stable structure is orthorhombic phase. This conclusion is supported by Zarkevich and Johnson, but contrary to the results of Aschauer et al., Kim et al. and Gruner et al. The obtained phase transition of Ort → c-AFM occurs at ca. 116.5 GPa and c-AFM to A’-AFM phase transition pressure is 119.0 GPa. The compressional, shear and average velocities as well as the bulk and shear moduli increase monotonically with increasing pressure. It is also found that thermal electronic contributions to specific heat are not negligible and contribution rate of electrons to the total thermal conductivity dominant at high temperature. At lower temperature, lattice thermal conductivity KL increases rapidly with the increasing pressure and KL has a moderate increase under pressure at higher temperature. Whereas, electronic thermal conductivity Ke is opposite. Most of the heat is carried by phonons with mean free paths ranging from 10 to 300 nm at 300 K.

Thermodynamic analysis of the interface reaction and thermal stress of WCp/Fe composites

One of the key issues for composites is the formation mechanism and stability of the interface. Experimental technology and first-principles calculations with quasiharmonic approach considering the phonon and thermal electronic contribution are adopted to clarify the thermodynamics and thermal stress of the interface of tungsten carbide particle reinforced iron matrix (WCP/Fe) composites under finite temperature. The most favorable formation path of Fe3W3C at the interface is 3Fe+2WC + W2C→Fe3W3C+2C + W. For WCP/Fe and WCP/Co composites, the thermal stress of Co3W3C is smaller than Fe3W3C as the transition phase of the interface, and Fe is less suitable to be applied as the matrix of composites than Co. Our research provides significant guidance to improve the interfacial strength and stability of WCP/Fe composites.

Full-Potential KKR Calculations for Interaction Energies in Al-Rich AlX (X = H∼Sn) Alloys: I. Fundamental Features and Thermal Electronic Contribution due to Fermi-Dirac Distribution

Full-Potential KKR Calculations for Interaction Energies in Al-Rich AlX (X = H∼Sn) Alloys: I. Fundamental Features and Thermal Electronic Contribution due to Fermi-Dirac Distribution

Thermal electronic properties of aluminum under pressure: The role of sp to 3d electron transfer

As a simple metal, aluminum's valence band is usually described as a free-electron gas with three electrons per atom. The discrepancies between the experimental electronic Gr\uneisen parameter and heat capacity and their free-electron-gas counterparts are usually attributed to electron-phonon coupling. We recently calculated thermal electronic contributions to aluminum's internal energies with our average-atom code paradisio and obtained results that contradict this point of view. Our code also pointed out the overlap of the $sp$ valence band by the $3d$ one, resulting in an $sp$ to $d$ electron transfer. Applying Sommerfeld's temperature expansion method to the electron-electron Coulomb part of the internal energy, we relate the electronic Gr\uneisen parameter, $T=0$ K isotherm, and thermal contributions to the internal energy to a parameter $\ensuremath{\alpha}$ describing the fraction of $d$ electrons resulting from $p$ to $d$ transfer. Finally, we find a unique value of this parameter that provides a consistent explanation for the experimental Gr\uneisen parameter, for $T=0$ K energy deduced from experimental shock Hugoniot data, as well as for our average-atom thermal contributions to internal energy.

First-principles study of structural, elastic, electronic, vibrational and thermodynamic properties of uranium aluminides

The structural, elastic, electronic, vibrational and thermodynamic properties of uranium aluminides UAlx (x = 2, 3, 4) were studied by density functional theory calculations. The single crystal elastic constants of UAlx were predicted using the stress-strain method, which were further used to calculate the polycrystalline aggregate properties of UAlx, including bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio, etc. The calculated electronic density of states confirm that UAlx compounds are metallic phases with majority states at the Fermi level contributed by U 5f electrons. The phonon dispersion relations and density of states show that the low frequency acoustic phonon modes of UAlx are dominated by the lattice vibration of uranium atoms while high frequency optical phonon modes are from the vibration of aluminum atoms. Using quasiharmonic approximation, thermodynamic properties of UAlx, including Gibbs free energy, entropy, heat capacity, and linear thermal expansion coefficient, were predicted by including both lattice vibrational and thermal electronic contributions. The thermal electronic energy was found to be crucial for the description of the temperature dependence of the thermodynamic properties. The derived Gibbs energy functions of UAlx are expected to be useful to the thermodynamic modeling of the ternary U-Mo-Al system.

Exploring the intrinsic ductile metastable Fe-C compounds: Complex chemical bonds, anisotropic elasticity and variable thermal expansion

As the vitally important phases in iron and steel, the Fe-C binary compounds are investigated by first-principles calculations combined with quasi-harmonic approximation (QHA). The formation enthalpy and Gibbs free energy are positive, but the phonon dispersion are stable, indicating θ-Fe3C, o-Fe7C3, h-Fe7C3, γ-Fe23C6, χ-Fe5C2, η-Fe6C, η-Fe2C and ε-Fe3C are metastable phases in this binary system for the first time. The electronic structure indicates that the complex bonding behavior of these carbides are the combinations of covalent, ionic and metallic bonds, which determines the anisotropic elastic properties and novel intrinsic ductility of these carbides. The mechanical modulus is nearly proportional to the carbon content. o-Fe7C3 has the largest B value as 379 GPa and The anisotropic bulk modulus, shear modulus and Young's modulus are discussed by the anisotropic index and three-dimensional surface contours. The shear modulus range from 40 GPa to 204.2 GPa and the Young's modulus vary from 113.7 GPa to 512.6 GPa. Intrinsic hardness is predicted by semiempirical models. The thermal electronic contributions to thermodynamic properties are studied using the Mermin statistics for the dynamic stable phases. The volumetric thermal expansion coefficients of these Fe-C compounds vary between 1.0 × 10−5 K−1 to 5.0 × 10−5 K−1 at 1200 K. θ-Fe3C, h-Fe7C3 and η-Fe2C have the closest thermal expansion coefficient to α-Fe. Considering the thermal electronic contribution, the calculated heat capacity of θ-Fe3C is in good agreement with experimental results. η-Fe2C has the largest CP value as 0.72 J g−1 K−1 and η-Fe6C has the smallest CP value as 0.56 J g−1 K−1 at 1200 K.

First-principles calculations on elastic and entropy properties in FeRh alloys

First-principles calculations were employed to investigate elastic and entropy properties of B2 ferromagnetic and antiferromagnetic FeRh phases. We calculated lattice parameters, elastic constants, isotropic moduli like bulk modulus B, shear modulus G, Young’s modulus E, and Poisson’s ratio of two phases and compared these with other calculations and experiments. At finite temperatures, the values of vibrational (from both Debye model and phonon dispersion) and thermal electronic contributions to the total entropy change between the two phases are calculated about -50J/kg/K and 7.8J/kg/K comparable to the experimental results (−33±9J/kg/K and 8±1J/kg/K).

The pressure-temperature phase diagram of pure Co based on first-principles calculations.

We optimized the high pressure-temperature phase diagram of pure Co up to the liquidus temperature and 120 GPa, based on thermodynamic properties calculated using first-principles. The Gibbs energy for each phase was evaluated in the framework of a quasiharmonic approximation, with a consideration of the thermal electronic contribution at finite temperatures. Particularly, the liquidus temperature, as a function of pressure, was determined using classical Molecular Dynamics simulations. Our results in this work successfully integrated experimental observations and the previous theoretical predictions. The critical solid phase transitions of ε → γf and ε → β were clarified using the Gibbs energy as a function of pressure and temperature. In addition, the magnetism of β above 70 GPa was verified to be nonmagnetic. The difference between γp and β, which was unclear before, has been illustrated to be associated with the magnetic transformation from the paramagnetic state of the γp phase to the nonmagnetic state of the β phase rather than the structural transformation.

Crossing Thermal Lubricity and Electronic Effects in Friction: Vanadium Dioxide under the Metal–Insulator Transition

The remarkable turnover of friction on a vanadium dioxide (VO2) surface driven by the metal–insulator transition is revealed using temperature‐variable atomic force microscopy in ultrahigh vacuum. Phononic and electronic contributions are known as two major components in mediating friction energy dissipation. Here, a VO2 thin film is prepared on a silicon wafer with preferential orientations of (100) and (120) in the monoclinic phase using pulsed laser deposition. Corresponding friction and conductivity images show that friction decreases below the critical temperature, above which two trends are seen as the temperature increases: less friction on the insulating domains and higher friction on the metallic domains. This distinct temperature dependence of friction is attributed to the combined effects of thermal lubricity and electronic contributions. This study indicates the promising potential for vanadium oxide to tune friction in the electric regime as well as with temperature.

Pressure-induced phase transitions in UN: A density functional theory study

We studied the structural behavior and phase stability of UN under high pressures up to 200GPa and temperatures up to 1500K using density functional theory calculations in the generalized gradient approximation. The results show that a pressure-induced structural transition from the cubic to the rhombohedral phase occurs at 23.5GPa. The calculated structural and magnetic properties of the rhombohedral phase suggest that an isostructural transition occurs at 22.5GPa. The low-pressure rhombohedral phase has a fcc-like structure. We predict that under further compression, an antiferromagnetic to nonmagnetic transition occurs. This phase transition has been not observed by experiment yet. To evaluate conditions under which other new phase transitions might occur, we studied the phase stability of UN at finite temperature by taking into account the lattice vibrational and thermal electronic contributions to Gibbs energy. Based on the Gibbs energy models, the pressure–temperature phase diagram of UN was studied and the phase boundaries of the antiferromagnetic rhombohedral phase were also determined. We predict that, although metastable, the antiferromagnetic rhombohedral phase might be stabilized at low-temperature by quenching from the high-pressure phase.

First-principles investigation of electronic, mechanical and thermodynamic properties of L12 ordered Co3(M, W) (M = Al, Ge, Ga) phases

Studies were carried out on the equilibrium structural, temperature-dependent mechanical and thermodynamic properties of the Co3(M, W) (M=Al, Ge, Ga) phases in terms of first-principles calculations. The results of the ground-state elastic constants revealed that Co3(M, W) phases are mechanically stable and possess intrinsic ductility. It was found that the elastic heat-resistant properties of Co3(Ge, W) phase are inferior to those of Co3(Al, W) and Co3(Ga, W). Analyzing the charge density difference provides the explanation that the sharp decrease in mechanical properties is mainly due to the weakening of Co–Ge bonding at elevated temperatures for Co3(Ge, W). The elastic anisotropy as a function of temperature is discussed using a universal index. It is observed that Co3(M, W) phases show a high degree of elastic anisotropy. The degree of elastic anisotropy could be significantly decreased by an increase in temperature for Co3(M, W). The lattice vibration is treated with the quasiharmonic phonon approach, considering both the vibrational and thermal electronic contributions. The thermodynamic properties as a function of temperature are computed without any adjustable parameters, including heat capacity, entropy, enthalpy and thermal expansion coefficient.

First-principles study of structural, elastic, electronic, vibrational and thermodynamic properties of UN

Abstract The structural, elastic, electronic, phonon and thermodynamic properties of UN are studied by density functional theory (DFT) within local-density approximation (LDA) and generalized gradient approximation (GGA), and GGA + U . The GGA calculations of the ground state structural and elastic properties of UN show an overall better agreement with experimental data compared to LDA or GGA + U . The melting temperature of UN ( T m ) is estimated from the calculated elastic constant, with GGA predicting T m = 2944 ± 300 K, in excellent agreement with experimental data. The calculated phonon dispersions of UN agree well with the low temperature measurements. Furthermore, the thermodynamic properties of UN are studied using quasiharmonic approximation by including both lattice vibrational and thermal electronic contributions. The predicted thermodynamic properties, such as enthalpy, entropy, Gibbs energy, heat capacity and thermal expansion coefficient, agree well with experimental data. The derived thermodynamic functions of UN are useful to the thermodynamic modeling of phase stabilities in UN-based materials. This study shows that the thermal electronic energy and entropy due to U 5 f electrons are important to describe the free energy of UN, due to the metallic character of UN. The calculated thermodynamic properties also suggest that the anharmonic effects are less important in UN even at high-temperature.

Thermodynamics and elastic properties of Ta from first-principles calculations

Within the framework of the quasiharmonic approximation, the thermodynamics and elastic properties of Ta, including phonon density of states (DOS), equation of state, linear thermal expansion coefficient, entropy, enthalpy, heat capacity, elastic constants, bulk modulus, shear modulus, Young's modulus, microhardness, and sound velocity, are studied using the first-principles projector-augmented wave method. The vibrational contribution to Helmholtz free energy is evaluated from the first-principles phonon DOS and the Debye model. The thermal electronic contribution to Helmholtz free energy is estimated from the integration over the electronic DOS. By comparing the experimental results with the calculation results from the first-principles and the Debye model, it is found that the thermodynamic properties of Ta are depicted well by the first-principles. The elastic properties of Ta from the first-principles are consistent with the available experimental data.

Effects of alloying elements on thermal expansions of γ-Ni and γ′-Ni3Al by first-principles calculations

The effects of alloying elements (Al, Cr, Hf, Pt, Y, and Zr) on the coefficients of thermal expansion (CTE) of face-centered-cubic Ni (γ) and L12-Ni3Al (γ′) phases have been investigated in terms of the first-principles quasi-harmonic approach by considering both the vibrational and thermal electronic contributions. By combining the present CTE data and the compositions and phase fractions of γ and γ′, the CTE for some Ni–Al-base alloys are predicted and compared with available experimental measurements in the literature, showing good agreement. It is observed that the addition of Pt is effective in reducing the CTE of both γ and γ′ phases, resulting in lower expansion mismatch between the bond coat and the thermally grown oxide alumina layer, as shown by the predicted CTE of Ni–22 Al–x Pt (at.%) alloys (x=5, 10, 15, 20, 25, 30).

First‐principles study on the structural, phonon, and thermodynamic properties of the ternary carbides in Ti–Al–C system

AbstractThe structural, phonon, and thermodynamic properties of the ternary carbides Ti2AlC, Ti3AlC, and Ti3AlC2 in the Ti–Al–C system are investigated by using first‐principles calculations in this paper. Phonon dispersion curves and partial density of states have been investigated and revealed the different Ti–C bond characteristics between Ti3AlC and the two other compounds. The Gibbs energy, entropy, heat capacity, and thermal expansion coefficient of the three compounds are predicted by means of the quasi‐harmonic approximation. Furthermore, the thermal electronic contribution has been included in the thermodynamic properties. The obtained results of this study are in good agreement with the available experimental data.

Ab initiolattice dynamics and thermodynamics of rare-earth hexaboridesLaB6andCeB6

We have performed an ab initio study of structural, elastic, lattice-dynamical, and thermodynamical properties of rare-earth hexaborides ${\text{LaB}}_{6}$ and ${\text{CeB}}_{6}$. The calculations have been carried out within the density-functional theory and linear-response formalism using pseudopotentials and a plane-wave basis. Thermodynamical properties of ${\text{LaB}}_{6}$ and ${\text{CeB}}_{6}$ obtained from quasiharmonic approximation are in a good agreement with the available experimental data. We also present the complete phonon-dispersion curves, phonon density of states, and mode-Gr\"uneisen parameters and compared with the experimental measurements. A sizable difference between the vibrational contribution to entropy of ${\text{LaB}}_{6}$ and ${\text{CeB}}_{6}$ is found. The thermal electronic contribution to entropy and specific heat is found to be important for ${\text{CeB}}_{6}$.

First-principles thermodynamics from phonon and Debye model: Application to Ni and Ni3Al

Abstract Starting from first-principles projector-augmented wave method, finite temperature thermodynamic properties of Ni and Ni3Al, including thermal expansion coefficient, bulk modulus, entropy, enthalpy and heat capacity, have been studied in terms of quasiharmonic approach. The thermal electronic contribution to Helmholtz free energy is estimated from the integration over the electronic density of state. The vibrational contribution to Helmholtz free energy is described by two methods: (i) the first-principles phonon via the supercell method and (ii) the Debye model with the Debye temperatures determined by Debye–Gruneisen approach and Debye–Wang approach. At 0 K, nine 4-parameter and 5-parameter equations of state (EOS’s) are employed to fit the first-principles calculated static energy (without zero-point vibrational energy) vs. volume points, and it is found that the Birch-Murnaghan EOS gives a good account for both Ni and Ni3Al among the 4-parameter EOS’s, while the Murnaghan EOS and the logarithmic EOS are the worse ones. By comparing the experiments with respect to the ones from phonon, Debye–Gruneisen and Debye–Wang models, it is found that the thermodynamic properties of Ni and Ni3Al studied herein (except for the bulk modulus) are depicted well by the phonon calculations, and also by the Debye models through choosing suitable parameters. The presently comparative studies of Ni and Ni3Al by phonon and Debye models, as well as by different EOS’s, provide helpful insights into the study of thermodynamics for solid phases at elevated temperatures.

Density-functional study of the thermodynamic properties and the pressure–temperature phase diagram of Ti

The phonon spectra of $\ensuremath{\alpha}$, $\ensuremath{\beta}$, and $\ensuremath{\omega}$ Ti were studied using the supercell approach. The lattice vibrational energy was calculated in the quasiharmonic approximation using both first-principles phonon density of state and Debye model. The thermal electronic contribution to the free energy was evaluated from the integration over the electronic density of states. The Helmholtz energy was thus obtained by combining them with the 0 K total energy calculated within the framework of all-electron projector-augmented-wave method. The thermodynamic properties of $\ensuremath{\alpha}$ and $\ensuremath{\omega}$ Ti calculated by phonon and Debye model are very close to each other. The predicted enthalpy, entropy, bulk modulus, thermal expansion coefficient and heat capacity of $\ensuremath{\alpha}$ are in good agreement with experiments. By comparing with the experimental enthalpy of $\ensuremath{\beta}$, we found that the 0 K total energy calculated from bcc Ti is incorrect. This problem can be solved by shifting the total energy of $\ensuremath{\beta}$ down by $8\text{ }\text{kJ}\text{ }{\text{mol}}^{\ensuremath{-}1}$ to match the experimental value. With the Gibbs energy calculated from the Debye model as a function of pressure and temperature, the phase transformation conditions of $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}$, $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\beta}$, and $\ensuremath{\beta}\ensuremath{\rightarrow}\ensuremath{\omega}$ were identified. The predicted transition temperature between $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ at ambient pressure and the triple point are close to experiments. It was found that the entropy plays an important role in the $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\alpha}$ and $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\beta}$ transitions, and the thermal electronic contribution to the Gibbs energy cannot be neglected for studying the $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\beta}$ transition. Our calculations also showed that zero-point energy is crucial to predict the transition pressure of Ti at low temperatures.

Temperature dependence of the activity of Al in diluteNi(Al)solid solutions

Activities of dilute Al solid solutions in Ni are determined from a first-principles approach. Both thermal lattice vibration and electronic contributions to free energies are considered and compared. Vibrational contributions tend to dominate the temperature dependencies of the free energies, though electron thermal effects are significant. Calculations show opposing temperature trends for the formation enthalpies and entropies, leading to a partial cancellation of their role in the overall energetics. Nevertheless, their remaining temperature effects are strong. Over the temperature range, $400\phantom{\rule{0.3em}{0ex}}\mathrm{K}lTl1700\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the Al activity coefficient varies by 15 orders of magnitude, due to the relative strength of $\mathrm{Al}\text{\ensuremath{-}}\mathrm{Ni}$ and $\mathrm{Al}\text{\ensuremath{-}}\mathrm{Al}$ bonds. The Ni activity coefficient only varies less than 4% over the same range. Calculational results compare well with available experimental data. The thermodynamic principles elucidated from the calculations are used to provide a fundamental interpretation.