Framework Of Quasi-harmonic Approximation Research Articles

On the role of intermolecular vibrational motions for ice polymorphs. IV. Anisotropy in the thermal expansivity and the nonaffine deformation for ice IX and III.

We explore anisotropic properties in the thermal expansivities of hydrogen-ordered ice IX and its hydrogen-disordered counterpart, ice III. The free energies of these ice forms are calculated to obtain the lattice constants for the tetragonal unit cell and the thermal expansivities at various thermodynamic conditions in the framework of quasi-harmonic approximation, taking account of their anisotropic nature. The thermal expansivities are also examined by applying a thermodynamic relation that connects them with the Grüneisen parameters and the elastic compliances. Both calculations suggest that ice III and IX exhibit a negative thermal expansion along the a-axis but have a positive one along the c-axis at low temperatures. It is found that nonaffine deformation in the variation of the lattice constant beyond affine transformation (the Born approximation) is essential in the theoretical calculation of the thermal properties of ice III and IX. We also find that the nonaffine deformation is described by the shift of the minimum energy positions in the potential manifold of hydrogen-ordered ice along a limited number of the normal mode coordinates, which is irrelevant to the system size. These modes become unstable against an applied strain, so that the potential minimum moves along those normal coordinates away from that of the affine-transformed structure. The unstable modes are all symmetry-preserving modes, and the space-group symmetry is an invariant under displacement along either of those normal coordinates. The number of the unstable modes in ice IX is 8 while it is 1 in another hydrogen-ordered ice VIII.

Effect of twin grain boundary on material thermal expansion

Based on first-principles phonon calculations within the framework of quasiharmonic approximation, we study the effect of twin grain boundary (TGB) on the thermal expansion of insulating materials. We select diamond-structure solids (C, Si, and Ge) and rutile $({\mathrm{SnO}}_{2})$ as representatives of the covalent and ionic bonding materials that are important systems commonly accompanied with TGB. We found distinct effects of TGB on thermal expansion in two types of materials. For diamond-structure solids, the thermal expansion of (111)-oriented twinning structure varies subtly from that of pristine material within the temperature range studied, which is primarily induced by the modification of vibrational phonon mode by the TGB effect. Distinctly, the thermal expansion of $\mathrm{SnO}_{2}$ twinnings increase substantially by comparison with the pristine case and depend strongly on the twin orientation. The (101) twinning shows much larger thermal expansion than the (301) twinning. Further analysis indicates the physical mechanism can be mainly attributed to the effect of rotational degree of freedom of the $\mathrm{SnO}_{6}$ octahedron motif and the stress induced by TGB. Our work reveals the physical mechanism underlying the distinct effect of TGB on thermal expansion caused by different chemical bonding, and meanwhile provides an insightful understanding of the relationship between specific structural features and thermal expansion in solid-phase materials.

Ab initio thermal expansion and thermoelastic properties of ringwoodite (<i>γ</i>-Mg<sub>2</sub>SiO<sub>4</sub>) at mantle transition zone conditions

Abstract. Thermal convection in the Earth's mantle is driven by lateral variations in temperature and density, which are substantially controlled by the local volume thermal expansion of the constituent mineral phases. Ringwoodite is a major component of the lower mantle transition zone, but its thermal expansivity and thermoelastic properties are still affected by large uncertainties. Ambient thermal expansion coefficient (αV0​​​​​​​), for instance, can vary as much as 100 % according to different experimental investigations available from the literature. In this work, we perform ab initio density functional theory calculations of vibrational properties of spinel-structured Mg2SiO4 ringwoodite in order to provide reliable thermophysical data up to mantle transition zone conditions. Temperature- and pressure-dependent thermal expansivity has been obtained by phonon dispersion calculations in the framework of quasi-harmonic approximation (QHA) up to 25 GPa and 2000 K. Theoretical analysis of vibrational spectra reveals that accurate prediction of IR and silent modes, along with their relative mode Grüneisen parameters, is crucial to define thermal expansivity. A six-parameter analytical function is able to reproduce ab initio values fairly well in the whole investigated P–T range, i.e., αV(P,T)=(1.6033×10-5+8.839×10-9T+11.586×10-3T-1-6.055T-2+804.31T-3) ×exp⁡(-2.52×10-2P), with temperature in kelvin and pressure in gigapascal. Ab initio static and isothermal bulk moduli have been derived for ringwoodite along with their P, T and cross derivatives, i.e., K0 = 184.3 GPa, KT,300 K = 176.6 GPa, K0′ = 4.13, KT,300K′ = 4.16, ∂KT∂TP = −0.0233 GPa K−1 and ∂2KT∂P∂T0=1.0×10-4 K−1. Computed thermal expansivity and thermoelastic properties support the evidence that QHA performs remarkably well for Mg2SiO4 ringwoodite up to mantle transition zone temperatures. Since volume thermal expansion of ringwoodite is strongly pressure-dependent and its pressure dependence becomes more marked with the increasing temperature, internally consistent assessments and empirical extrapolation of thermoelastic data to deep mantle conditions should be taken with care to avoid inaccurate or spurious predictions in phase equilibrium and mantle convection numerical modeling.

Density-functional-theory predictions of mechanical behaviour and thermal properties as well as experimental hardness of the Ga-bilayer Mo2Ga2C

Mo2Ga2C is a new MAX phase with a stacking Ga-bilayer as well as possible unusual properties. To understand this unique MAX phase structure and promote possible future applications, the structure, chemical bonding, and mechanical and thermodynamic properties of Mo2Ga2C were investigated by first-principles. Using the “bond stiffness” model, the strongest covalent bonding (1162 GPa) was formed between Mo and C atoms in Mo2Ga2C, while the weakest Ga-Ga (389 GPa) bonding was formed between two Ga-atomic layers, different from other typical MAX phases. The ratio of the bond stiffness of the weakest bond to the strongest bond (0.33) was lower than 1/2, indicating the high damage tolerance and fracture toughness of Mo2Ga2C, which was confirmed by indentation without any cracks. The high-temperature heat capacity and thermal expansion of Mo2Ga2C were calculated in the framework of quasi-harmonic approximation from 0 to 1300 K. Because of the metal-like electronic structure, the electronic excitation contribution became more significant with increasing temperature above 300 K.

Атомистическое моделирование решеточных свойств SnSe

We have performed a set of ab initio calculations of the ground state energy as a function of volume, elastic properties, and phonon spectra of tin selenide in its various crystalline modifications. Based on the obtained data set, the potential of interatomic interaction of SnSe is constructed using the atomic cluster expansion (ACE) method. The potential is further used to study the temperature dependences of thermal and elastic properties of SnSe in the framework of quasi-harmonic approximation.

Exploring the electronic structure and thermal properties of UAl3 using density functional theory calculations

Among the intermetallic compounds of uranium, U-Al alloy is found to be promising nuclear fuel for high-power research reactors due to its high thermal conductivity and structural stability. U-Al system can form three different intermetallic compounds namely, UAl2, UAl3 and UAl4. Here, we systematically explored the electronic structure and various thermal properties of the cubic UAl3 system. Pseudo-potential plane wave based DFT calculations are used along with the spin-orbit coupling. The structural parameter calculated using the generalised gradient approximation is comparable to the experimental results. The phonon dispersion plot indicates the dynamic stability of the structure. Thermophysical properties including free energy, molar specific heat, coefficient of thermal expansion, bulk modulus, etc. have been evaluated within the framework of quasi-harmonic approximation. Both the electronic and lattice contribution to thermal conductivity has been evaluated through the Boltzmann transport theory.

Calculation of Young’s Modulus of MoS2-Based Single-Wall Nanotubes Using Force-Field and Hybrid Density Functional Theory

A force field is proposed that reproduces with a high accuracy a large number of properties of the bulk crystal MoS2 phases, monolayers, and nanotubes. The reproduced values are both the experimental results and the results of quantum chemical calculations. The elaborated interaction potential can be useful primarily for investigation of multiwall MoS2 nanotubes and their thermodynamic properties, especially, since the potential is able to reproduce the frequencies of the crystal phonon spectrum. In this study the proposed potential is applied to simulate the temperature dependence of a number of properties of the armchair and zigzag nanotubes. The calculations have been performed using molecular mechanics method within the framework of quasi harmonic approximation which is carried out through the estimation of the temperature dependence of the Helmholtz free energy.

Electronic structure and thermophysical properties of U3Si2: A systematic first principle study

Uranium silicides are considered to be prominent accident tolerant fuel for the light water reactors due to their high metal density and high thermal conductivity. Among the uranium silicon binary compounds, U3Si2 is found to be advantageous. Here, we present a systematic first principles study of electronic structure and thermophysical properties of U3Si2 within the framework of quasi-harmonic approximation. The relativistic effects have been treated through incorporating the spin-orbit interactions for all the calculations. The optimized cell volume from PBE method is found to be slightly underestimated, however, from the PBE+U method, it is found to be slightly overestimated as compared to the experimental volume, all the electronic structure results are comparable to the reported results. Volume dependant phonon frequencies have been calculated using the density functional perturbation theory to incorporate the effect of anharmonicity indirectly through quasi-harmonic approximation. Various thermophysical properties like free energy, thermal expansion, heat capacity, bulk modulus, etc. have been evaluated. The vibrational contribution alone to molar specific heat is found to be underestimated as compared to the experimentally reported results. Interestingly, incorporation of the electronic contribution is found to improve the results significantly. Electronic component of thermal conductivity has been calculated using the Boltzmann transport theory. The computed results are comparable to the available experimental results, which supports the reliability of the present study. All these predicted properties are very much important to gain knowledge about the U3Si2 based fuel.

Internal and external thermal expansions of wurtzite ZnO from first principles

Many crystals contain “internal” structural parameters not completely constrained by symmetry. These vary with temperature T, similar to the variation of “external” structural parameters that describe the unit cell. The term “thermal expansion” most often refers to the external parameters, which are more easily and accurately measured. Here we use “thermal expansion” to mean both external and internal parameters. Internal thermal expansion impacts a wide range of applications, but has been given less attention. In this study, the thermal expansion behavior of wurtzite ZnO is studied from first principles with the generalized Grüneisen theory in the framework of quasi-harmonic approximation (QHA). Negative external thermal expansions are found below the temperature of 150 K. We demonstrate that the so-called “zero static internal stress approximation” (ZSISA) gives the correct external but incorrect internal thermal expansions, due to the neglect of the clamped-lattice internal contribution contained in the generalized Grüneisen theory. Although accurate at low T, at higher T the QHA may need to be supplemented by higher order anharmonic corrections.

Расчет модуля Юнга одностенных нанотрубок на основе MoS-=SUB=-2-=/SUB=- с использованием силового поля и гибридного метода теории функционала плотности

AbstractA force field is proposed that reproduces with a high accuracy a large number of properties of the bulk crystal MoS_2 phases, monolayers, and nanotubes. The reproduced values are both the experimental results and the results of quantum chemical calculations. The elaborated interaction potential can be useful primarily for investigation of multiwall MoS_2 nanotubes and their thermodynamic properties, especially, since the potential is able to reproduce the frequencies of the crystal phonon spectrum. In this study the proposed potential is applied to simulate the temperature dependence of a number of properties of the armchair and zigzag nanotubes. The calculations have been performed using molecular mechanics method within the framework of quasi harmonic approximation which is carried out through the estimation of the temperature dependence of the Helmholtz free energy.

Neutron total cross section calculation within the framework of quasi-harmonic approximation

The accuracy of neutron scattering cross sections is the gauge for the realistic outcome of a neutron transport simulation. To improve the traditional harmonic physics model used in such simulations, we revisit the slow neutron transport theory in crystalline materials and aim to develop a unified model that has good performance for neutron transport problems in crystals in a wide range of temperatures and pressures. The quasi-harmonic approximation (QHA) correlates phonon evolution explicitly with unit cell volume. Therefore, it is capable of evaluating a variety of material properties at finite temperatures. In this work, we show numerically that it is a very effective tool for our application as well. Within the framework of QHA, we calculate the temperature dependent characteristics of phonons in three elemental crystals, namely Be, Mg and Al. Based on the obtained results, our calculated neutron total cross sections agree closely with experimental transmission cross sections in a large temperature range below the melting point. We show that as the harmonic cross section model ignores the effects of phonon softening in these crystals, it underestimates the total inelastic cross sections at high temperatures. In the case of Al, we observe that such underestimation is up to 7% at room temperature. In addition, we study the phonon–phonon scatterings in Al. We observe that the cross section is insensitive to the finite phonon lifetimes even at 800 K.

Ab Initio Thermodynamic and Thermophysical Properties of Sodium Metasilicate, Na2SiO3, and Their Electron-Density and Electron-Pair-Density Counterparts.

Thermodynamic and thermophysical properties of Na2SiO3 in the Cmc21 structural state are computed ab initio using the hybrid B3LYP density functional method. The static properties at the athermal limit are first evaluated through a symmetry-preserving relaxation procedure. The thermodynamic properties that depend on vibrational frequencies, viz., heat capacities, thermal expansion, thermal derivative of the bulk modulus, thermal correction to internal energy, enthalpy, and Gibbs free energy, are then computed in the framework of quasi-harmonic approximation. Acoustic branches are computed by solving the Christoffel determinant and are assumed to follow sine wave dispersion when traveling within the Brillouin zone. The procedure generates several thermo-physical properties of interest in materials science and geophysics (transverse and longitudinal wave velocities, shear modulus, Young modulus, Poisson ratio) all consistent with experimentally determined properties. A representative cluster is then abstracted from the cell and a detailed electron localization/delocalization analysis is performed on it, in the ground state geometry, and on deformed states imposed by two peculiar mixed asymmetric stretching/bending modes affecting the silicate chain that, according to literature data, have anomalous mode Grüneisen parameters. A Bader analysis reveals an intriguing feature associated with these deformations: an increase in the covalence of the Si-O bond that strengthens the linkage opposing the weakening induced by thermal stress. Finally, on the same cluster, the Ramsey contributions to the JNM coupling are evaluated by the gauge-independent atomic orbital method. The calculated isotropic chemical shifts of both 23Na and 29Si are again in substantial agreement with observations.

Thermodynamic Properties of Rutile $$(\hbox {TiO}_{2})$$ ( TiO 2 ) Within the Phonon Calculations

Full phonon calculations have been performed to estimate the thermal properties of rutile (titanium dioxide). Calculations have been carried out using the pseudo-potential method within the local density approximation. Thermodynamic properties including the thermal expansion, thermal expansion coefficient, heat capacity and entropy were calculated as a function of temperature in the framework of quasi-harmonic approximation. Also, to compare the results with the results of other approaches, we apply Debye–Slater and Debye–Gruneisen approaches with the same parameters for electronic calculations. It is found that the phonon calculations provide more accurate estimates in comparison with the other two models.

High-pressure phase diagram of gold from first-principles calculations: Converging to an isotropic atomic stacking order

We reported the high pressure and temperature phase diagram of noble metal gold up to 500GPa and 7000K constructed from first-principles calculations. Using the unbiased multi-algorithm-collaborative (MAC) crystal structure prediction method, we discovered several metastable polymorphs of gold besides the previously known face-centered-cubic (fcc) structure. The phase boundaries of these polymorphs were located deliberately in the framework of quasi-harmonic approximation (QHA). The stability field of fcc-Au is almost identical to the experimental data. More importantly, we discovered and verified a new phase, the double hexagonal close-packed (dhcp) structure, before it transits to hcp under increasing compression. At room temperature, gold transforms from the fcc to the dhcp structure at 231.6GPa, and at further compression it transits to the hcp structure at 447.8GPa. From its elastic properties, an isotropy of atomic stacking order was observed in Au under increasing compression.

Phasego: A toolkit for automatic calculation and plot of phase diagram

The Phasego package extracts the Helmholtz free energy from the phonon density of states obtained by the first-principles calculations. With the help of equation of states fitting, it reduces the Gibbs free energy as a function of pressure/temperature at fixed temperature/pressure. Based on the quasi-harmonic approximation (QHA), it calculates the possible phase boundaries among all the structures of interest and finally plots the phase diagram automatically. For the single phase analysis, Phasego can numerically derive many properties, such as the thermal expansion coefficients, the bulk moduli, the heat capacities, the thermal pressures, the Hugoniot pressure–volume–temperature relations, the Grüneisen parameters, and the Debye temperatures. In order to check its ability of phase transition analysis, I present here two examples: semiconductor GaN and metallic Fe. In the case of GaN, Phasego automatically determined and plotted the phase boundaries among the provided zinc blende (ZB), wurtzite (WZ) and rocksalt (RS) structures. In the case of Fe, the results indicate that at high temperature the electronic thermal excitation free energy corrections considerably alter the phase boundaries among the body-centered cubic (bcc), face-centered cubic (fcc) and hexagonal close-packed (hcp) structures. Program summaryProgram title: PhasegoCatalogue identifier: AEVQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVQ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 837140No. of bytes in distributed program, including test data, etc.: 8816053Distribution format: tar.gzProgramming language: Python (versions 2.4 and later).Computer: Any computer that can run Python (versions 2.4 and later).Operating system: Any operating system that can run Python.RAM: 10 M bytesClassification: 7.8.External routines: Numpy [1], Scipy [2], Matplotlib [3]Nature of problem:Materials usually undergo structural phase transitions when the environmental pressure and temperature are elevated to high enough values. The phase transition process obeys the principle of lowest Gibbs free energy. In addition to the static energy, current density functional theory (DFT) calculations can easily give the phonon density of states of lattice vibrations, from which the Helmholtz free energy of phonons are reduced. Then Gibbs free energy can be achieved for the analysis of phase stability and phase transition at high pressure and temperature within the framework of QHA. The problem is to extract the Gibbs free energies from the DFT calculations and automatically analyze the high pressure and temperature phase boundaries among a number of structures.Solution method:With the help of numerical interpolation techniques, the Gibbs free energy as a function of pressure/temperature at fixed temperature/pressure can be obtained. Then the QHA based phase boundaries can be automatically determined and plotted by scanning the pressure/temperature at fixed temperature/pressure according to the principle of lowest Gibbs free energy.Restrictions:The restriction is from the QHA which takes partially into account the anharmonic effects.Unusual features:The phase boundaries among a number of structures can be automatically determined and plotted, which largely improve the efficiency of phase transition analysis. In addition to some basic thermodynamic properties of each single structure, the Hugoniot pressure–volume–temperature relations are also automatically reduced.Additional comments:This package can treat the phonon density of states data from many packages, such as PHON [4], PHONOPY [5], Quantum ESPRESSO [6], and ABINIT [7].Running time:The examples provided in the distribution take less than a minute to run.

Phase transition and thermodynamics of thorium from first-principles calculations

We report on the first-principles study of the phase transition and thermodynamic properties of the thorium metal (Th) within the framework of quasiharmonic approximation. The structural properties of Th under pressure are well reproduced. It is found that the fcc–bct phase transition occurs at 70 GPa. Based on our calculated phonon dispersion curve that is in good agreement with experiment, the thermal equation of state and thermodynamic properties, such as thermal pressure, heat capacity and entropy are obtained. All the properties of Th under high pressure and high temperature are predicted successfully.

Elastic Properties of Cu-Based Bulk Metallic Glass around Glass Transition Temperature

Temperature dependent elastic constants Cij(T) of Cu60Hf30Ti10 bulk metallic glass (BMG) have been investigated in a MHz frequency range using electromagnetic acoustic resonance (EMAR) up to 823 K. At room temperature, the BMG showed high Poisson’s ratio ν arising from low shear modulus G compared with that of constitutive crystalline elements. With increasing temperature, G showed usual linear temperature dependence while it suddenly drops around glass transition temperature, Tg. Within a framework of quasiharmonic approximation, Grüneisen parameter γ around Tg is estimated to be 10. This extremely large γ indicates the high anhramonicity of long wavelength limit acoustic mode phonon in the supercooled liquid state. The unusual elastic behavior can be interpreted on the basis of heterogeneous microstructure.