Quasiharmonic Method Research Articles

Pressure-induced evolution of structures and phase transition of technetium diboride

Using the particle swarm optimization algorithm, we conducted an extensive search for the high-pressure stable structure of technetium diboride (TcB2) within the pressure range of 0–400 GPa. At zero pressure, the P63/mmc (hP6-TcB2) structure is considered the ground state configuration. As the pressure increases, a structural transition from hP6-TcB2 to P6/mmm (hP3-TcB2) occurs at approximately 174.9 GPa. We discuss the bonding between the two distinct phases and analyze the contribution of different atomic bonds to maintaining their structural stability. Meanwhile, the temperature–pressure phase diagram of TcB2 was successfully determined for the first time through the quasi-harmonic approximation method. It is predicted that the transition pressure from hP6-TcB2 to hP3-TcB2 can be reduced to about 164 GPa at a room temperature of 300 K. These results provide valuable insights into the behavior of TcB2 under different temperature and pressure conditions and open up new possibilities for exploring its potential applications in a variety of environments.

Pressure and temperature effects on the Raman spectra of LLM-105

Currently, only one crystal structure of LLM-105 (2,6-diamino-3,5-dinitropyrazine-1-oxide) (P21/n) has been discovered, and there are still debates on its phase transition point and phase diagram. Based on previous work, we performed crystal structure, Raman spectra, and vibrational properties calculations on LLM-105 crystal. Our results indicate that the crystal structure of LLM-105 remains stable until compressed to 49 GPa, beyond which it may undergo two phase transitions at pressure intervals of 49.0–49.1 GPa and 51.4–51.5 GPa, respectively. Analysis of Raman shift results suggests that these two phase transitions may be reversible, with an intermediate phase possibly acting as a transition phase. Additionally, based on the quasi-harmonic approximation, we fitted the experimental data of LLM-105 lattice expansion state, obtaining the volume at zero pressure and using it for Raman spectra calculations. The results demonstrated the accuracy of this quasi-harmonic approximation method in describing the redshift of Raman peaks during the heating process and the excitation ratio of Raman peaks in different wavenumber ranges.

First-principles study on the high-pressure physical properties of orthocarbonate Ca2CO4

Orthorhombic Ca2CO4 is a recently discovered orthocarbonate whose high-pressure physical properties are critical for understanding the deep carbon cycle. Here, we study the structure, elastic and seismic properties of Ca2CO4-Pnma at 20–140 GPa using first-principles calculations, and compare them with the results of CaCO3 polymorphs. The results show that the structural parameters of Ca2CO4-Pnma are in good agreement with the experimental results. It could be the potential host of carbon in the Earth's mantle subduction slab, and its low wave velocity and small anisotropy may be the reason why it cannot be detected in seismic observation. The thermodynamic properties of Ca2CO4-Pnma at high temperature and high pressure are obtained using the quasi-harmonic approximation method. This study is helpful in understanding the behavior of Ca-carbonate in the Earth’s lower mantle conditions.

Study on the physical properties of Ca3CO5 polymorphs under lower mantle pressure

The physical properties of newly discovered orthocarbonate Ca3CO5 are of significant importance in understanding the carbon cycle and storage in the Earth's interior. Here, the structural, elastic, seismic, and thermal properties of Ca3CO5 polymorphs under the Earth's lower mantle pressure are investigated using first-principles calculations, and the results are compared with those of orthocarbonate Ca2CO4-Pnma. Our findings demonstrate that the pressure of the Cmcm phase of Ca3CO5 to the I4/mcm phase is 53.8 GPa, and the transition pressure and equation of state align with prior research. Additionally, the elastic moduli, densities, and wave velocities of Ca3CO5 polymorphs are similar to those of Ca2CO4-Pnma. However, the azimuthal anisotropies of Ca3CO5 polymorphs are greater than those of Ca2CO4-Pnma. Furthermore, the minimum thermal conductivity and diffusion thermal conductivity of Ca3CO5 polymorphs are smaller than those of Ca2CO4-Pnma. Ultimately, the thermodynamic properties of Ca3CO5 polymorphs are obtained utilizing the quasi-harmonic approximation method. These results provide valuable insight into the physical properties of Ca3CO5, which can aid in further understanding the carbon cycle and storage within the Earth's underground.

Nonharmonic contributions to the high-temperature phonon thermodynamics of Cr

Phonon densities of states (DOSs) of body-centered cubic chromium were measured by time-of-flight inelastic neutron scattering at temperatures up to 1493 K. Density functional theory calculations with both quasiharmonic (QH) and anharmonic (AH) methods were performed at temperatures above the N\'eel temperature. Features in the phonon DOSs decrease in energy (soften) substantially with temperature. A Born--von K\'arm\'an analysis using fits to the experimental DOSs reveals a softening of almost 17% of the high-transverse phonon branch between 330 and 1493 K. The low-transverse branch changes by approximately half this amount. The AH calculations capture the observed behavior of the two transverse phonon branches, but the QH calculations give some inverted trends. Vibrational entropies from phonons and electrons are obtained, and their sum is in excellent agreement with the entropy of chromium obtained by calorimetry, indicating that above 330 K, no explicit temperature-dependent magnetic contributions are necessary.

Electronic structure, elastic and thermodynamic properties of SnS from theoretical study

In this work, first-principles methods based on density functional theory are used to study the structural, electronic and elastic properties of rock-salt SnS in detail. Thermodynamic properties of SnS under high temperature and high pressure were studied by using the quasi-harmonic Debye model. The results show that the optimized structural parameters are in good agreement with the experimental and other theoretical values. The band structure and density of states of SnS are obtained by calculation and analysis. Based on the quasi-harmonic Debye method, the pressure and temperature dependencies of the equilibrium volume, the bulk modulus, the Debye temperature and so on are obtained.

An investigation on 3-hydroxybenzaldehyde for exploring terahertz low-frequency vibration modes with quasi-harmonic approximation method

3-Hydroxybenzaldehyde (3-HBA) was investigated in the range of 0.6–2.8 THz by terahertz time-domain spectroscopy (THz-TDS) and solid-state density functional theory (ss-DFT) with first-principles calculation. Four distinct peaks were found respectively, and among them, the intensity disparity between experiment and simulation spectra at 2.04 THz was recognized as the biggest inconsistency. Considering thermal behavior can be responsible for this, quasi-harmonic approximation (QHA) method was introduced to mimic the unit cell volume expansion. According to vibrational modes analysis, it was ascertained that the biggest vibrational modes discrepancy was also located at 2.04 THz. Molecules in 0% and 4% unit cell expansion exhibit an opposite rotational direction in a-b plane compared with 2% unit cell expansion. Noncovalent intermolecular interactions were investigated with independent gradient model (IGM), and the result indicates that hydrogen bonding is the dominating noncovalent interaction of 3-HBA. While calculating systematic potential energy to the displaced bonds stretching involving hydrogen atoms, it was found the anomalous potential energy variation to the bond stretching provides a possible explanation for the rotation direction divergence, that is, the rotation direction divergence can be related to some hydrogen atoms seeking lower overall potential energy around their equilibrium positions during bond stretching in response to the variational intermolecular van der Waals force. This research combined THz-TDS with the quasi-harmonic approximation method, elucidating the principle of vibrational characteristics in different volumes, which is beneficial to the investigation of the terahertz low-frequency vibration to thermal behavior as a reference in biochemistry and other fields.

Exploring high pressure structural transformations, electronic properties and superconducting properties of MH2 (M = Nb, Ta)

The high-pressure structures and properties of MH2 (M = Nb, Ta) are explored through an ab initio evolutionary algorithm for crystal structure prediction and first-principles calculations. It is found that NbH2 undergoes a phase transition from a cubic Fm3¯m structure with regular NbH8 cubes to an orthorhombic Pnma structure with fascinating distorted NbH9 tetrakaidecahedrons at 48.8 GPa, while the phase transition pressure of TaH2 from a hexagonal P63mc phase with slightly distorted TaH7 decahedron to an orthorhombic Pnma phase with attractive distorted TaH9 tetrakaidecahedrons is about 90.0 GPa. Besides, the calculated electronic band structure and density of states demonstrate that all of these structures are metallic. The Poisson’s ratio, electron localization function, and Bader charge analysis suggest that these phases possess dominant ionic bonding character with the effective charges transferring from the metal atom to H. From our electron–phonon calculations, the calculated superconducting critical temperature Tc of the Pnma-NbH2 is 6.903 K at 50 GPa. Finally, via the quasi-harmonic approximation method, the phase diagrams at pressure up to 300 GPa and temperature up to 1000 K of MH2 (M = Nb, Ta) are established, where the transition pressure of Fm3¯m-NbH2 → Pnma-NbH2 and P63mc-TaH2 → Pnma-TaH2 were found to decrease with increasing temperature.

Vibrational Enthalpies of Solid Crystalline Materials

Specific heat at constant pressure is traditionally a difficult thermodynamic quantity to obtain from first-principles calculations. While theoretical avenues to Cp(T) do exist—most notably, the quasi-harmonic approximation—there are many materials for which this approximation is not valid. One of those materials is Ge. In this paper, we demonstrate how a new method—termed the Beyond Quasi-Harmonic method—takes into account all anharmonic vibrations by showing how our results are significantly better than those achieved through using the quasi-harmonic model. In addition, we calculate Cp(T) for 3C-SiC, a material for which there are surprisingly few experimental results. For 3C-SiC, our results agree well with the available experiments, and for Ge, our results agree very well with the generally accepted values.

Enhancing efficiency and scope of first-principles quasiharmonic approximation methods through the calculation of third-order elastic constants

A novel computational strategy is presented to calculate from first principles the coefficient of thermal expansion and the elastic constants of a material over meaningful intervals of temperature and pressure. This strategy combines a novel implementation of the quasiharmonic approximation to calculate the isothermal-isochoric linear and nonlinear elastic constants of a material, with elementary equations of nonlinear continuum mechanics. Our implementation of the quasiharmonic approximation relies on finite deformations, the use of nonprimitive supercells to describe a material, a recently proposed technique to calculate generalized mode Gr\"uneisen parameters, and the numerical differentiation of the stress tensor to calculate both second- and third-order elastic constants. The combination of this method with nonlinear continuum mechanics is shown to yield accurate predictions of lattice parameters and linear elastic constants of a material over finite intervals of temperature and pressure, at the cost of calculating isothermal second- and third-order elastic constants for a single reference state. Here, the validity and limits of our novel methods are assessed by carrying out calculations of MgO based on classical interatomic potentials. To demonstrate potential, our methods are then used in conjunction with a density functional theory approach to calculate thermal expansion and elastic properties of silicon, lithium hydrate, and graphite.

Crystal structures and mechanical properties of tungsten monocarbide predicted by first-principles investigations

The crystal structure of tungsten monocarbide (WC) is researched from 0 to 650 GPa through first principles calculations. The results verify that the experimental structure (hP2-WC) with the space group P6¯m2 is the most stable phase in a wide range of pressure. Above 231 GPa, a new stable structure (space group P63/mmc, hP4-WC) is found to be the most stable phase, and it will transform to a CsCl-type phase (cF8-WC) around 582 GPa. Phonon calculations reveal that the hP4-WC phase is dynamically stable and may be a metastable structure at ambient conditions. The cF8-WC phase possesses dynamical stability above 20 GPa. The hP4-WC phase is a low compressible material with a large bulk modulus of 377 GPa at zero pressure. The hardness values of hP2-WC and hP4-WC at zero pressure are 32 and 21 GPa, respectively, while the cF8-WC phase possesses a hardness of 21 GPa at 20 GPa, implying that these phases are potential hard materials. The temperature–pressure phase boundary of WC is obtained by means of the quasi-harmonic approximation method. As the temperature increases, the transition pressure from hP2-WC to hP4-WC remained nearly unchanged. The transition pressure between hP4-WC and cF8-WC decreases with the increasing temperature.

Negative thermal expansion in the Ruddlesden-Popper calcium titanates

Materials exhibiting negative thermal expansion (NTE) are important for the fabrication and operation of microelectronic devices and optical systems. As an important group of Ruddlesden-Popper (RP) perovskites, calcium titanates ${\mathrm{Ca}}_{n+1}{\mathrm{Ti}}_{n}{\mathrm{O}}_{3n+1}$ [(CTO), $n=1,2,...,\ensuremath{\infty}$] have layered structures and may exhibit quasi-two-dimensional (quasi-2D) NTE within their three-dimensional structural architectures. In this paper, combining density-functional-theory calculations and the self-consistent quasiharmonic approximation method, we investigate the variation of the quasi-2D character of the phonon spectra and thermal expansion in the ${\mathrm{Ca}}_{n+1}{\mathrm{Ti}}_{n}{\mathrm{O}}_{3n+1}$ family ($n=1--3$, and $\ensuremath{\infty}$) with respect to $n$. We find that a quasi-2D NTE mechanism is active in the RP-CTOs at $n$ of 1--3, whereas a quasi-rigid-unit mode mechanism is active at $n=\ensuremath{\infty}$ (i.e., the perovskite phase). We find a NTE trend with layer number for the orthorhombic materials comprising the RP series, but the monoclinic polymorph is an outlier. For the orthorhombic members, we find the critical pressure for NTE increases with increasing $n$, but the NTE critical temperature decreases (when materials are compared at the same pressure). Additionally, the elastic moduli can be used as effective descriptors for this layer-dependent behavior of the NTE, i.e., the stiffer the RP-CTO then the lower its NTE. We also propose the integrated NTE capacity to capture the correlation between the quasi-2D NTE and $n$, and it monotonically decreases with increasing $n$.

Investigation of Grain Boundary Influence on the Thermodynamic Phase Stability of Nanocrystalline Iron by Using the Molecular Dynamics Simulation Method

The thermodynamics of allotropic transformation in nanocrystalline Fe is studied. For this purpose, the grain boundary structure is initially examined using a novel method based on molecular dynamics (MD) simulation, the results of which are exploited to determine grain boundary thickness and excess volume for different grain sizes. The dilated crystal model and the quasi-harmonic Debye approximation method are subsequently employed to calculate the values of Gibbs free energy for grain boundaries of different allotropic phases. Using the quantitative parameters obtained from the simulations, the relevant Gibbs free energy curves are plotted in terms of grain size and analyzed for different temperatures. This is followed by deriving stability curves for the γ-Fe and α-Fe phases in terms of grain size for different temperatures. Ultimately, the parameters obtained from MD simulation studies and the stability diagrams thus obtained are used to explore the changes in the γ→α allotropic transformation temperature of iron nanocrystal for different grain sizes. It will be that allotropic transformation temperature declines from 900 to 300 K with rising grain size from 4 to 33 nm.

Crystal structures and mechanical properties of osmium diboride at high pressure

We have investigated the crystal structures and mechanical properties of osmium diboride (OsB2) based on the density functional theory. The structures of OsB2 from 0 to 400 GPa were predicted using the particle swarm optimization algorithm structure prediction technique. The orthorhombic Pmmn structure of OsB2 (oP6-OsB2) was found to be the most stable phase under zero pressure and it will transfer to the hexagonal P63/mmc structure (hP6-OsB2) around 12.4 GPa. Meanwhile, we have discovered a new stable orthorhombic Immm structure (oI12-OsB2) above 379.6 GPa. After that, a thorough and comprehensive investigation on mechanical properties of different OsB2 phases is performed in this work. Further studies showed that the hardness of oP6-OsB2 and hP6-OsB2 at zero pressure is 15.6 and 20.1 GPa, while that for oI12-OsB2 under 400 GPa is 15.4 GPa, indicating that these three phases should be potentially hard materials rather than superhard materials. Finally, the pressure–temperature phase diagram of OsB2 is constructed for the first time by using the quasi-harmonic approximation method. Our results showed that the transition pressures of oP6-OsB2 → hP6-OsB2 and hP6-OsB2 → oI12-OsB2 all decreases appreciably with the increase of temperature.

Anharmonicity and Phase Diagram of Magnesium Oxide in the Megabar Regime.

With density functional molecular dynamics simulations, we computed the phase diagram of MgO from 50 to 2000GPa up to 20 000K. Via thermodynamic integration (TDI), we derive the Gibbs free energies of the B1, B2, and liquid phases and determine their phase boundaries. With TDI and a pseudo-quasi-harmonic approach, we show that anharmonic effects are important and stabilize the B1 phase in particular. As a result, the B1-B2 transition boundary in the pressure-temperature plane exhibits a steep slope. We predict the B1-B2-liquid triple point to occur at approximately T=10000 K and P=370 GPa, which is higher in pressure than was inferred with quasiharmonic methods alone. We predict the principal shock Hugoniot curve to enter the B2 phase stability domain but only over a very small range of parameters. This may render it difficult to observe this phase with shock experiments because of kinetic effects.

Efficient anharmonic lattice dynamics calculations of thermal transport in crystalline and disordered solids

Understanding heat transport in semiconductors and insulators is of fundamental importance because of its technological impact in electronics and renewable energy harvesting and conversion. Anharmonic lattice dynamics provides a powerful framework for the description of heat transport at the nanoscale. One of the advantages of this method is that it naturally includes quantum effects due to atoms vibrations, which are needed to compute the thermal properties of semiconductors widely used in nanotechnology, like silicon and carbon, even at room temperature. While the heat transport picture substantially differs between amorphous and crystalline semiconductors from a microscopic standpoint, a unified approach to simulate both crystals and glasses has been devised. Here, we introduce a unified workflow, which implements both the Boltzmann Transport equation and the quasi-harmonic Green-Kubo methods. We discuss how the theory can be optimized to exploit modern parallel architectures, and how it is implemented in κALDo: a versatile and scalable open-source software to compute phonon transport in solids. This approach is applied to crystalline and partially disordered silicon-based systems, including bulk silicon and clathrates, and on silicon–germanium alloy clathrates with largely reduced thermal conductivity.

Thermodynamic stability and vibrational anharmonicity of black phosphorene—beyond quasi-harmonic analysis

Thermodynamic stability and vibrational anharmonicity of single layer black phosphorene (SLBP) are studied using a spectral energy density (SED) method. At finite temperatures, SLBP sheet undergoes structural deformation due to the formation of thermally excited ripples. Thermal stability of deformed SLBP sheet is analyzed by computing finite temperature phonon dispersion, which shows that SLBP sheet is thermodynamically stable and survives the crumpling transition. To analyze the vibrational anharmonicity, temperature evolution of all zone center optic phonon modes are extracted, including experimentally forbidden IR and Raman active modes. Mode resolved phonon spectra exhibits red-shift in mode frequencies with temperature. The strong anharmonic phonon–phonon coupling is the predominant reason for the observed red-shift of phonon modes, the contribution of thermal expansion is marginal. Further, temperature sensitivity of all optic modes are analyzed by computing their first order temperature co-efficient (χ), and it can be expressed as B 2g > > > > B 1g > & B 2u > B 1u for Raman and IR active modes, respectively. The quasi-harmonic χ values are much smaller than the SED and experimental values; which substantiate that quasi-harmonic methods are inadequate, and a full anharmonic analysis is essential to explain structure and dynamics of SLBP at finite temperatures.

Exploring relationship of the state of N-dodecyl betaine in the solution monomer, at the interface and in the micelle via configurational entropy

Interfacial adsorption and bulk micellization of surfactant are common in natural world, and have prominent applications both in production and life. Surfactant molecules circularly flux among solution bulk, interface, and micelle in surfactant solution. Molecular dynamics (MD) simulations are carried out to compare the state of surfactant among solution monomer, interfacial monolayer, and micelle. Surface coverages from extremely dilute adsorption to saturated adsorption are all considered. Using the quasi harmonic approximation method, configurational entropies of N-dodecyl betaine (NDB) in different environments are obtained. The NDB monomers possess the largest freedom owing to spatial and non-aggregated superiorities. Entropy decomposition, including translational, rotational and vibrational entropies, is calculated to give further comparison and analysis. A new Born-Haber cycle is proposed to depict the state of NDB in different environments and to present entropy change of NDB itself in different mass transport processes. In particular, entropy changes of NDB in physical adsorption process below and above critical micelle concentration are obtained. The NDB molecule exhibits entropy decrease in interfacial adsorption, bulk micellization, and the transport of surfactant from micelle to surface layer.

First-principles study of bcc Fe-Cr-Si binary and ternary random alloys from special quasi-random structure

Using a combination of first-principles calculations with special quasi-random structure and quasi-harmonic approximation methods, we have calculated formation energy, magnetic moments, mechanical properties and thermodynamic properties of binary FeCr and ternary FeCrSi random alloys. The results agree well with available theoretical and experimental data. The body centered cubic structures and ferromagnetic phase are employed to calculate these properties in this work. The phase stability studies show that FeCr alloys are stable systems in Cr concentrations below 6% region. However, binary FeCr alloys are the systems with a miscibility gap for Cr concentrations above 6%. The ternary FeCrSi systems show much less formation energy than FeCr systems. For ternary FeCrSi alloys, Fe9Cr22Si1 shows maximum value of formation energy. Studies on magnetism have shown that Si is a kind of nonmagnetic material, it can be used to reduce magnetic moments of FeCr alloys. Doping a little Si into FeCr alloys can form more stable systems and improve bulk modulus, shear modulus and young's modulus in both low-Cr and rich-Cr concentration regions. Si element can generate effects on Debye temperature and volumetric thermal expansion coefficient of the alloy. But Si element can not generate obvious effects on constant volume heat capacity of FeCr alloys.

Specific heat at constant pressure from first principles: contributions from fully anharmonic vibrations

Specific heat at constant pressure (Cp) for diamond Si and wurtzite GaN is calculated using a novel, first principles method based on density functional theory. This method, termed the Beyond Quasi-Harmonic method, completely takes into account all anharmonic vibrations–both from changes in volume and phonon interactions. Our calculated values for Si show excellent agreement with the generally accepted experimental values. For GaN, however, there is a large discrepancy between two sets of experiments. From an analysis of the available literature, and our own data we develop a set of recommended values.