Quasi-harmonic Approximation 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.

The influence of site preference on the elastic properties of FCC_CoCrFeNi multi-principal element alloy

The influence of the existing site preference of the constituent elements on the sublattice on elastic properties is rarely explored in multi-principal element alloys (MPEAs). In this work, in order to explore the influence of the site preference of constituent atoms on the thermodynamic properties and elastic properties, the ordered configurations based on the previously predicted site occupying fractions (SOFs) and the disordered configuration based on a special quasi-random structure (SQS) were established, and the thermodynamic properties and elastic properties were predicted using the quasi-harmonic approximation (QHA) method first. It was found that the site preferring behaviors of atoms on the sublattices will not only improve the stability of the structure but will also lead to bigger elastic properties than its ideal disordered structure. Although the prediction of the temperature-dependent elastic properties using the QHA method shortens the time costs by only considering the effects of thermal expansion, it ignores the significant effect of lattice vibration on elastic properties at high temperatures. In order to explore the influence of lattice vibration on the temperature-dependent elastic properties further, the elastic properties of the ordered FCC_CoCrFeNi MPEA were predicted using the ab initio molecular dynamics (AIMD) method at several selective temperatures. The results show that except for the elastic constant C12 and bulk modulus, the lattice vibration reduces other elastic properties on the basis of thermal expansion. The predicted temperature-dependent shear and Young's moduli agree well with the limited experimental literature data. Thus, the temperature-dependent elastic properties can be reasonably predicted using the AIMD method based on site preference. The predicted polycrystalline elastic moduli B, G, and E of FCC_CoCrFeNi MPEA at 973 K are 146.68, 53.79, and 143.78 GPa, respectively.

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.

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.

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 $n$.

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.

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.

Novel high pressure structures and mechanical properties of rhenium diboride

The pressure-induced phase transition and mechanical properties of rhenium diboride (ReB2) have been investigated by using the particle swarm optimization algorithm in combination with density functional theory calculations. It was found that the P63/mmc structure of ReB2 (hP6-ReB2) is the most stable phase at ambient conditions, and it will transform to P6/mmm structure (hP3-ReB2) at about 300.7 GPa. Phonon dispersion curve calculations suggest that hP6-ReB2 and hP3-ReB2 possess dynamical stabilities in a wide range of 0–400 and 120–400 GPa, respectively. Moreover, the calculated hardness of hP6-ReB2 is 38.1 GPa at ambient conditions, suggesting it is a potential hard material. However, hP3-ReB2 just possesses the hardness value of 18.9 GPa at the pressure of 120 GPa. Finally, by means of the quasiharmonic approximation method, the high-pressure and finite-temperature phase diagram of ReB2 is proposed. It is found that the transition pressure of hP6-ReB2 to hP3-ReB2 decreases with increasing temperatures.

Predicting the structures and associated phase transition mechanisms in disordered crystals via a combination of experimental and theoretical methods.

Disordered materials make up a large proportion of condensed phase systems, but the difficulties in describing their structures and molecular dynamics limit their potential applications. Disordered crystalline systems, also known as plastic crystals, offer a unique perspective into these factors because the systems retain a degree of crystallinity, reducing the degrees of freedom that must be explored when interpreting the results. However, while disordered crystals do diffract X-rays, it is difficult to fully resolve meaningful crystalline structures, with the best scenario resulting in lattice parameters. In this study, we use a combination of experimental terahertz time-domain spectroscopy, and theoretical solid-state ab initio density functional theory and molecular dynamics simulations to fully elucidate the structures and associated dynamics of organic molecular solids. The results highlight that this combination provides a complete description of the energetic and mechanistic pathways involved in the formation of disordered crystals, and highlights the importance of low-frequency dynamics in their properties. Finally, with structures fully determined and validated by the experimental results, recent progress into anharmonic calculations, namely the quasi-harmonic approximation method, enables full temperature and pressure-dependent properties to be understood within the framework of the potential energy hyper-surface structure.

Thermo-mechanical properties of cubic titanium nitride

The equilibrium structure, elastic constants Cij and thermodynamic functions of cubic titanium nitride (TiN) were calculated within the temperature range of 0–3100 K and under a pressure range 0–60 GPa. Properties were computed using the generalised gradient approximations (GGA) exchange-correlation functional. Calculated mechanical properties (Elastic constants, Young’s modulus and shear modulus) and phonon spectra of TiN obtained via robust DFT-QHA algorithm, were generally in a good agreement with available experimental and theoretical analogous values. In particular, a well-examined quasi-harmonic approximation method implemented in the Gibbs2 code is utilised herein to provide accurate estimation of thermal expansion coefficients, entropies, heat capacity values (at different combinations of temperature/volume/pressure) and Debye’s temperature. Parameters calculated herein shall be useful to elucidate the superior performance of TiN at harsh operational conditions encompassing elevated temperatures and pressures pertinent to cutting machineries and surface coatings.

Study on the structural transition and thermal properties of Ni3Nb-D022 phase: First-principles calculation

The structural transition and thermal properties (thermodynamic and thermoelastic properties) of Ni3Nb-D022 phase are investigated by first-principles combined with quasi-harmonic approximation method. The computed results show that the structural transition from Ni3Nb-D022 to Ni3Nb-D0a primitively occurs at the temperature range of 950–960K. The phase structure is thermally stable but easily compressed. The heat capacity tends to Dulong-Petit limit when the temperature is higher than 900K. The computed thermoelastic properties of Ni3Nb-D022 phase reveal the slight softening trends with the increased temperature, indicating that the Ni3Nb-D022 phase is well heat-resistance. Additionally, Ni3Nb-D022 phase is ductile at the temperature range of 0–900K, and its hardness decreases with the increased temperature. Moreover, the Ni3Nb-D022 phase is anisotropic and has a distinct dependence on crystal orientations. The strengths of chemical bond along [100] and [010] orientations on (001) plane are slightly weakened with the increase of temperature.

First-Principles Predictions of Phase Transition and Mechanical Properties of Tungsten Diboride under Pressure

By using the particle swarm optimization algorithm, the crystal structures of tungsten diboride have been investigated up to 200 GPa at 0 K. We support that WB2 has an ReB2-type structure (hP6-WB2) with the space group P63/mmc at zero pressure and hP6-WB2 undergoes a phase transition to the MoB2-type phase (hR6-WB2) at about 10.8 GPa. Further, we predict that a tetragonal phase (tI12-WB2) with a space group of I41/amd will be the most stable structure above 133.6 GPa. Phonon dispersion curves suggest that these phases possess dynamical stabilities in a wide range of 0–200 GPa. The elastic constants and hardness are also estimated at 0 K and zero pressure. hP6-WB2 and hR6-WB2 have hardnesses of 37.3 and 29.2 GPa, respectively. However, tI12-WB2 just possesses the smallest hardness value of 7.9 GPa. Finally, a temperature–pressure phase diagram is derived within the quasi-harmonic approximation method, and the finite temperature phase boundaries are determined.

On the limitation of density functional theory (DFT) for the treatment of the anharmonicity in FCC metals

Abstract It has been already shown that the density functional theory (DFT) combined with the quasi-harmonic approximation (QHA) overestimates the specific heat capacity (and in general the thermal properties) of fcc metals. DFT + QHA seemingly shows a large anharmonic contribution to the heat capacity. However, in this article we show that this anharmonicity has no physical origin and it is a consequence of the deviation of the QHA from the Maxwell relations. We show that one can simply avoid this overestimation by enforcing the QHA method to obey the Maxwell relations throughout the thermodynamically self-consistent (TSC) method, instead of considering non-real local anharmonic effects.

First-principles study of the negative thermal expansion of PbTiO3

By using first-principles calculation and quasi-harmonic approximation method, we have systematically investigated the thermal expansion properties of tetragonal phase of PbTiO3, focusing on the correlation between the A1(TO) mode and negative thermal expansion (NTE). It is found that volume of the unit cell shows positive thermal expansion in a axis direction, and NTE in c axis direction from 0K to 900K. It is also found that the A1(TO) mode is softening when the volume shrinks by the phonon calculation. Calculating of Grüneisen parameters show that the A1(TO) mode makes a main contribution to the NTE, and this vibrational mode is the Pb, Ti and O atoms’ relative motion in c axis direction, which lead to a shrink of the unit cell in this direction. Our calculations clarify the correlation between the phonon mode and NTE of PbTiO3 in c axis direction at the atomic level, and provide an important theoretical basis for further understanding of the mechanism of the NTE.

Elastic and thermodynamic properties of Fe3Ga from first-principles calculations

Abstract First-principles calculations within the framework of density functional theory (DFT) are performed to investigate the elastic and thermodynamic properties of DO 3 -type Fe 3 Ga alloy. The obtained lattice constants and the bulk modulus are in good agreement with available experimental data. In terms of the calculated formation energy and Poisson’s ratio, the Fe 3 Ga alloy is mechanically stable and exhibit a negative Poisson’s ratio of −0.81 along the 〈110〉 direction. The thermodynamic properties such as the Gibbs free energy, thermal expansion, and the specific heat are obtained by the first-principles phonon calculations with the quasiharmonic approximation method. The predicted coefficient of linear thermal expansion and specific heat may provide a helpful reference for experimental work.

Temperature-dependent mechanical properties of alpha-/beta-Nb5Si3 phases from first-principles calculations

The temperature-dependent structural properties and anisotropic thermal expansion coefficients of α-/β-Nb5Si3 phases have been determined by minimizing the non-equilibrium Gibbs free energy as functions of crystallographic deformations. The results indicate that the crystal anisotropy of α-Nb5Si3 phase is much more temperature dependence than that of β-Nb5Si3 phase. The total/partial density of states of α-/β-Nb5Si3 phases are discussed in detail to analyze their electronic hybridizations. It is demonstrated that the bonding of the two phases is mainly contributed from the hybridization between Nb-4d and Si-3p electronic states. The temperature-dependent mechanical properties of α-/β-Nb5Si3 phases are further investigated via the quasi-harmonic approximation method in coupling with continuum elasticity theory. The calculated single-crystalline and polycrystalline elasticity shows that both phases are mechanically stable and exhibit the intrinsic brittleness. The results also suggest that α-Nb5Si3 phase possesses a superior ability of compression resistance but an inferior ability of high-temperature resistance of mechanical properties than those of β-Nb5Si3 phase. The bonding features of α-/β-Nb5Si3 phases are discussed by means of charge density difference analysis in order to explain the difference of the temperature-dependent mechanical properties between the two phases.