Quasiharmonic Lattice Dynamics Research Articles

CRYSTALpytools: A Python infrastructure for the Crystal code

CRYSTALpytools is an open source Python project available on GitHub that implements a user-friendly interface to the Crystal code for quantum-mechanical condensed matter simulations. CRYSTALpytools provides functionalities to: i) write and read Crystal input and output files for a range of calculations (single-point, electronic structure, geometry optimization, harmonic and quasi-harmonic lattice dynamics, elastic tensor evaluation, topological analysis of the electron density, electron transport, and others); ii) extract relevant information; iii) create workflows; iv) post-process computed quantities, and v) plot results in a variety of styles for rapid and precise visual analysis. Furthermore, CRYSTALpytools allows the user to translate Crystal objects (the central data structure of the project) to and from the Structure and Atoms objects of the pymatgen and ASE libraries, respectively. These tools can be used to create, manipulate and visualise complicated structures and write them efficiently to Crystal input files. Jupyter Notebooks have also been developed for the less Python savvy users to guide them in the use of CRYSTALpytools through a user-friendly graphical interface with predefined workflows to complete different specific tasks. Program summaryProgram Title: CRYSTALpytoolsCPC Library link to program files:https://doi.org/10.17632/p2bp3fsk86.1Developer's repository link:https://github.com/crystal-code-tools/CRYSTALpytoolsLicensing provisions: MITProgramming language: Python and Jupyter NotebookNature of problem: The Crystal code [1,2] is a powerful tool for the calculation of materials properties. It stands out in the condensed matter computational landscape because of the use of local basis sets, heavy parallelisation, efficient implementation of non-local Fock exchange, and extensive use of point and space symmetry. However, it currently lacks an easily programmable interface to access its input/output structure needed to be able to use Crystal calculations within computational materials science workflows. Historically, the use of Crystal in such workflows has been achieved through bespoke scripting implemented in a variety of languages which has hindered code reuse and sharing.Solution method: The CRYSTALpytools project will enable the automation of Crystal calculations in a modular code that can be co-developed by a wide community of users worldwide. It achieves this by transforming standardised input and output files into python objects and providing a suite of functionality to manipulate them. The core implementation is based on a set of data structures denoted the Crystal_objects. CRYSTALpytools, in its current implementation, contains a large variety of functions for input/output manipulation, vibrational and thermodynamic analysis, and visualisation.Additional comments including restrictions and unusual features: The exploitation of point group and space group symmetry is one of the strengths of the Crystal code, therefore, all the geometry modification functions have been developed to optimise the use of symmetry. When a structure is downloaded from a database or is modified by external code, such as pymatgen [3] or ASE [4], a symmetry analysis is performed before transforming the structure to be an optimised Crystal_object. All such objects can be directly transformed to standard structures periodic in 0, 1, 2 or 3 dimensions used by Crystal (ie: .gui or .f34 files).

Mode localization and suppressed heat transport in amorphous alloys

Glasses usually represent the lower limit for the thermal conductivity of solids, but a fundamental understanding of lattice heat transport in amorphous materials can provide design rules to beat such a limit. Here we investigate the role of mass disorder in glasses by studying amorphous silicon-germanium alloy (a-Si$_{1-x}$Ge$_x$) over the full range of atomic concentration from $x=0$ to $x=1$, using molecular dynamics and the quasi-harmonic Green-Kubo lattice dynamics formalism. We find that the thermal conductivity of a-Si$_{1-x}$Ge$_x$ as a function of $x$ exhibits a smoother U-shape than in crystalline mass-disordered alloys. The main contribution to the initial drop of thermal conductivity at low Ge concentration stems from the localization of otherwise extended modes that make up the lowest 8\% of the population by frequency. Contributions from intermediate frequency modes are decreased more gradually with increasing Ge to reach a broad minimum thermal conductivity between concentrations of Ge from $x=0.25$ to $0.75$.

Thermoelasticity of Flexible Organic Crystals from Quasi-harmonic Lattice Dynamics: The Case of Copper(II) Acetylacetonate.

A computationally affordable approach, based on quasi-harmonic lattice dynamics, is presented for the quantum-mechanical calculation of thermoelastic moduli of flexible, stimuli-responsive, organic crystals. The methodology relies on the simultaneous description of structural changes induced by thermal expansion and strain. The complete thermoelastic response of the mechanically flexible metal–organic copper(II) acetylacetonate crystal is determined and discussed in the temperature range 0–300 K. The elastic moduli do not just shrink with temperature but they do so anisotropically. The present results clearly indicate the need for an explicit account of thermal effects in the simulation of mechanical properties of elastically flexible organic materials. Indeed, predictions from standard static calculations on this flexible metal–organic crystal are off by up to 100%.

Role of phonons on phase stabilization of RE2Si2O7 over wide temperature range (RE = Yb, Gd)

Thermodynamic phase stabilities of α, β, γ and δ polymorphs of RE2Si2O7 (RE = Yb, Gd), promising candidates for environmental barrier coating systems of gas turbine engines in next generations, were investigated using harmonic and quasi-harmonic lattice dynamics in conjunction with ab initio calculations. By quantifying their Gibbs free energies with dynamics of atoms taken into account, we showed the phase stability of β-Yb2Si2O7 up to melting temperature under an ideal condition, and also under thermal stresses, ensuring the reliability of β-Yb2Si2O7 in environmental barrier coating systems. It was also found that the difference of anharmonic phonons in these polymorphs, which was measured as mode Grüneisen parameters, significantly changed their phonon free energies and invoked the formation of δ-Gd2Si2O7 at high temperature. These results enable a quantitative comprehension of the phase transformation of RE2Si2O7 and future discussions of other factors which may affect the phase stability such as lattice defects.

Frontiers in Modeling Metal–Organic Frameworks

Frontiers in Modeling Metal–Organic Frameworks

Lattice Dynamics: Quasi‐Harmonic Lattice Dynamics of a Prototypical Metal–Organic Framework (Adv. Theory Simul. 11/2019)

Quasi-harmonic lattice dynamics reveal the combined temperature and pressure effects on the structural and mechanical stability of a metal-organic framework, as discussed by Matthew R. Ryder, Alessandro Erba, and co-workers in article number 1900093. A group-subgroup phase transition is identified from phonon softening upon compression, resulting in a reduced bulk modulus and a corresponding change of the pressure derivative of the bulk modulus from positive to negative.

Capturing anharmonic and anisotropic natures in the thermotics and mechanics of Bi2Te3 thermoelectric material through an accurate and efficient potential

Force-field-(FF)-based molecular simulation is essential but challenging in the theoretical research of complex thermoelectric (TE) materials. As they are general and crucial in TE semiconductors, the structural natures of anharmonicity and anisotropy can help us understand the inherent relation between thermal and mechanical behavior, and therefore the reliability of FF studies can be assessed. In this paper, given prior knowledge of the structural, mechanical and thermal properties as well as the limitations and necessary approximations of the FF method, a feasible and detailed FF modeling scheme and simulation has been designed for Bi2Te3, which is a typical high-performance TE material. Using the complementary approach combining quasi-harmonic lattice and molecular dynamics, the obtained potential is systematically confirmed to be accurate and efficient for the prediction of anharmonic and anisotropic behavior in thermotics and mechanics over a wide temperature range compared with the present Bi2Te3 models. This reveals that the intrinsic anisotropy and anharmonicity can measure the asymmetry of crystal lattices and the interatomic force in the current state. In addition, the significant distinction of temperature-dependent anharmonic effects in different directions of Bi2Te3 stems from its layered hierarchical structure, in which weak van der Waals bonding will probably be the key structural factor in comprehensively improving performance for mass production and wearable application. This prior-knowledge-based FF study is also suggested as a bridge between the theoretical understanding of micro-mechanisms and the experimental measurement of TE material properties, leading to a general framework of molecular simulation for other complex energy materials.

Influence of the exchange-correlation functional on the quasi-harmonic lattice dynamics of II-VI semiconductors.

We perform a systematic comparison of the finite-temperature structure and properties of four bulk semiconductors (PbS, PbTe, ZnS, and ZnTe) predicted by eight popular exchange-correlation functionals from quasi-harmonic lattice-dynamics calculations. The performance of the functionals in reproducing the temperature dependence of a number of material properties, including lattice parameters, thermal-expansion coefficients, bulk moduli, heat capacities, and phonon frequencies, is evaluated quantitatively against available experimental data. We find that the phenomenological over- and under-binding characteristics of the local-density approximation and the PW91 and Perdew-Burke-Enzerhof (PBE) generalised-gradient approximation (GGA) functionals, respectively, are exaggerated at finite temperature, whereas the PBEsol GGA shows good general performance across all four systems. The Tao-Perdew-Staroverov-Scuseria (TPSS) and revTPSS meta-GGAs provide relatively small improvements over PBE, with the latter being better suited to calculating structural and dynamical properties, but both are considerably more computationally demanding than the simpler GGAs. The dispersion-corrected PBE-D2 and PBE-D3 functionals perform well in describing the lattice dynamics of the zinc chalcogenides, whereas the lead chalcogenides appear to be challenging for these functionals. These findings show that quasi-harmonic calculations with a suitable functional can predict finite-temperature structure and properties with useful accuracy, and that this technique can serve as a means of evaluating the performance of new functionals in the future.

Phonon spectra and temperature variation of bulk properties of Cu, Ag, Au and Pt using Sutton–Chen and modified Sutton–Chen potentials

Three potentials of the Finnis–Sinclair type are studied with regard to their suitability for predicting bulk thermal and elastic properties of fcc metals Cu, Ag, Au and Pt over a wide temperature range. We start with a particular parametrization of the Finnis–Sinclair model known as the Sutton–Chen potential and a later version of the same, known as the quantum Sutton–Chen potential. The quasiharmonic lattice dynamics method is used to study the temperature variation of the thermodynamic properties. Both models are found to yield poor results for thermal expansion, which can be traced to rapid softening of transverse phonon frequencies with increasing lattice parameter. The form of the Sutton–Chen potential is modified here to seek improvement in the agreement between quasiharmonic calculations and experimental data. It is found that the modified potential better predicts bulk properties in nearly all cases studied. Significant improvement is seen over the Sutton–Chen potential, while lesser but still substantial improvement is observed over the Quantum-Sutton Chen potential.

Magnetoelastic coupling in the cobalt adipate metal–organic framework from quasi-harmonic lattice dynamics

We explore how thermal expansion influences the magnetic interactions in hybrid frameworks.

Self-Consistent Real Space Free Energy Calculations for Polyethylene and Isotactic Polypropylene Crystals and Interfaces

Surface free energies for (100) and (010) orthorhombic polyethylene (PE) and α1 isotactic polypropylene (iPP) are calculated with self-consistent real space quasi-harmonic lattice dynamics methods. PE is used as a model system to systematically explore the accuracy of real space calculations versus traditional reciprocal space calculations for the bulk and interfacial properties of crystalline polymers. A linear potential is added to the atomistic Hamiltonian of the crystal to minimize the free energy of crystals with interfaces. (010) iPP is found to have a lower surface free energy than (100) iPP at temperatures relevant to crystallization. PE and iPP surface free energies are found to have opposite temperature dependences, ultimately because the PE slab stem packing becomes increasingly denser than the bulk as temperature increases while the opposite is true of iPP. Real space calculations give good agreement with experimental results and reciprocal space calculations for bulk PE and iPP lattice parameters, as well as calculated surface free energies of PE, with a reasonably sized crystal supercell and simpler calculations than in reciprocal space.

Efficient wide-range calculation of free energies in solids and liquids using reversible-scaling molecular dynamics

We elaborate a novel and efficient method to obtain multiphase Helmholtz free energies from molecular dynamics (MD) simulations over wide ranges of volume and temperature in materials that can be described by temperature-independent ion forces, with both higher accuracy and order-of-magnitude cost savings compared to direct thermodynamic-integration techniques. Our method leverages and significantly extends the technique of reversible-scaling molecular dynamics (RSMD) proposed by de Koning et al. [Phys. Rev. Lett. 83, 3973 (1999)], which allows a free-energy difference in a given phase at constant volume to be calculated as a function of temperature from a single MD simulation. In mechanically stable solid phases, our approach carefully combines quasiharmonic lattice dynamics at low temperatures with an accurate and fully isolated RSMD simulation of the anharmonic vibrational free energy at high temperatures to produce a seamless free energy from zero temperature to above melt along constant-volume isochores. In the liquid, we combine a unique calculation of the free energy along a high-temperature reference isotherm with isochoric RSMD simulations from that temperature to below melt. In metastable solid phases that are mechanically unstable at low temperature, we use two-phase MD melt simulations together with the liquid free energy to obtain the solid free energy along the solidus melt line and then perform isochoric RSMD simulations to temperatures above and below that point. While our free-energy method is general, we have specifically adapted it here to the case of metals in which the ion forces are well described by model generalized pseudopotential theory (MGPT) multi-ion interatomic potentials, and additive electron-thermal free-energy contributions can be included. Then using refined Ta6.8$x$ MGPT potentials, we have converged total free energies and their components to very high and unprecedented sub-milli-Rydberg (mRy) numerical accuracy in the stable-bcc, liquid, and metastable-fcc phases of tantalum for volumes ranging from up to 26% expansion to nearly twofold compression and for temperatures to 25 000 K. In turn, we have successfully used the free energies so obtained to calculate physically accurate thermodynamic properties and gain new insight into their behavior, including sensitive thermodynamic derivatives, bcc and fcc melt curves, and a multiphase equation of state for tantalum (Ta) over the same temperature range and for pressures as high as 600 GPa. We show that the anharmonic free-energy component in the bcc solid, although only 1--5 mRy in magnitude for Ta, can have a significant (15%--20%) effect on thermal expansivity, the Gr\uneisen parameter, and melt temperatures. We further show that the electron-thermal free-energy component can similarly impact the specific heat and thermal expansivity in both the solid and the liquid, while only minimally affecting (to$\ensuremath{\le}3$%) the bcc and fcc melt curves.

Structural phase transition of Ru at high pressure and temperature

The magnetism, stabilities and phase transition of Ru in hcp, fcc, bct and bcc structures are investigated with detailed first-principles calculations based on density-functional theory and quasiharmonic lattice dynamics approximation. Magnetic ground states and stability ranges of various phases are obtained. Calculated results indicate that the non-magnetic (NM)-hcp structure is the most stable in the entire pressure range at zero temperature, and the structural transition cannot be induced by pressure alone. NM-fcc structure is a metastable phase of bulk Ru, while both the NM-bcc and ferromagnetic (FM)-bct structures are dynamically unstable. At high pressure and temperature, a transformation from NM-hcp to NM-fcc structure will occur. Finally, the pressure-temperature phase diagram of Ru is presented.

Elastic stiffness coefficients of thenardite and their pressure and temperature dependence

AbstractThe elastic stiffness coefficients,cij, of orthorhombic Na2SO4thenardite (space group Fddd) were measäured with an ultrasonic plane wave technique at ambient temperature as a function of hydrostatic pressure in the range of 0.1–70 MPa. The variation of thecijin the range of 1–5000 MPa was studied with density functional theory (DFT) based calculations. The experimental results and the DFT calculations were used to derive a force-field model, which was then employed to compute lattice parameters and elastic stiffness tensors of thenardite and of two other Na2SO4polymorphs as functions of the temperature based on quasi-harmonic lattice dynamics. The structural parameters of the three polymorphs measured at high temperatures are reproduced to within 1.7% by the present calculations. Phases II (space groupPbnm) and III (Cmcm) appear to have significantly higher entropies than thenardite in agreement with their metastable formation at higher temperatures.

Structure of defective crystals at finite temperatures: A quasi-harmonic lattice dynamics approach

In this paper we extend the classical method of lattice dynamics to defective crystals with partial symmetries. We start by a nominal defect configuration and first relax it statically. Having the static equilibrium configuration, we use a quasi-harmonic lattice dynamics approach to approximate the free energy. Finally, the defect structure at a finite temperature is obtained by minimizing the approximate Helmholtz free energy. For higher temperatures we take the relaxed configuration at a lower temperature as the reference configuration. This method can be used to semi-analytically study the structure of defects at low but non-zero temperatures, where molecular dynamics cannot be used. As an example, we obtain the finite temperature structure of two 180° domain walls in a 2D lattice of interacting dipoles. We dynamically relax both the position and polarization vectors. In particular, we show that increasing temperature the domain wall thicknesses increase.

First-principles thermal equation of state and thermoelasticity of hcp Fe at high pressures

We investigate the equation of state and elastic properties of hcp iron at high pressures and high temperatures using first principles linear response linear-muffin-tin-orbital method in the generalized-gradient approximation. We calculate the Helmholtz free energy as a function of volume, temperature, and volume-conserving strains, including the electronic excitation contributions from band structures and lattice vibrational contributions from quasi-harmonic lattice dynamics. We perform detailed investigations on the behavior of elastic moduli and equation of state properties as functions of temperature and pressure, including the pressure-volume equation of state, bulk modulus, the thermal expansion coefficient, the Gruneisen ratio, and the shock Hugoniot. Detailed comparison has been made with available experimental measurements and theoretical predictions.

Ground-state structural and magnetic properties of solid α and β-O2

A pattern recognition optimization scheme coupled with a quasiharmonic lattice dynamics method is used to determine the minimum energy structures and magnetic orientations of solid oxygen. It is shown that the magnetic interaction is responsible for the stability of α-O2 with respect to β-O2 at zero temperature and pressure. The calculated α-O2 lattice parameters, magnetic orientations, and sublimation energy are in good agreement with experiment. Phonon dispersion curves are calculated at k ≠ 0 and the acoustic sound velocities are determined. The rms translational and orientational fluctuations from equilibrium are also calculated. The β-O2 phase is described by constraining the magnetic moments so that the magnetic Hamiltonian preserves the hexagonal symmetry of the crystal. The calculated lattice parameters are in good agreement with experiment and a three sublattice, quasihelical magnetic orientation is predicted from structural and energetic considerations.

Polymorphism and Phonon Dynamics of α‐Quaterthiophene

Low-frequency (10-150 cm(-1)) Raman spectra of the low-temperature (LT) and high-temperature (HT) polymorphs of the organic semiconductor alpha-quaterthiophene at 300 and 10 K are reported. Polarized spectra, assisted by quasi-harmonic lattice dynamics (QHLD) calculations, allow characterization of the lattice phonon dynamics and identification of the two phases spectroscopically. The experimental data can be explained by taking into account the coupling between intermolecular (lattice) and low-frequency intramolecular modes. Finally, Raman mapping is used to investigate the phase purity.

Predicting phonon properties and thermal conductivity from anharmonic lattice dynamics calculations and molecular dynamics simulations

Two methods for predicting phonon frequencies and relaxation times are presented. The first is based on quasiharmonic and anharmonic lattice dynamics calculations, and the second is based on a combination of quasiharmonic lattice dynamics calculations and molecular dynamics simulations. These phonon properties are then used with the Boltzmann transport equation under the relaxation-time approximation to predict the lattice thermal conductivity. The validity of the low-temperature assumptions made in the lattice dynamics framework are assessed by comparing to thermal conductivities predicted by the Green-Kubo and direct molecular dynamics methods for a test system of Lennard-Jones argon. The predictions of all four methods are in agreement at low temperature (20 K). At temperatures of 40 K (half the Debye temperature of Lennard-Jones argon) and below, the thermal-conductivity predictions from the two methods that use lattice dynamics calculations are within about 30% of those made using the more accurate Green-Kubo and direct molecular dynamics methods. The thermal-conductivity predictions using the lattice dynamics techniques become inaccurate at high temperature (above 40 K) due to the approximations inherent in the lattice dynamics framework. We apply the results to assess the validity of (i) the isotropic approximation in modeling thermal transport and (ii) the common assertion that low-frequency phonons dominate thermal transport. Lastly, we suggest approximations that can be made within the lattice dynamics framework that allow the thermal conductivity of Lennard-Jones argon to be estimated using two orders of magnitude less computing effort than the Green-Kubo or direct molecular dynamics methods.

THERMODYNAMICS AND HYDROGEN STORAGE ABILITY OF BINARY HYDROGEN + HELP GAS CLATHRATE HYDRATE

Storage of hydrogen as hydrogen hydrate is a promising alternative technology to liquefied hydrogen at cryogenic temperatures or compressed hydrogen at high pressures. In this paper, computer simulation is performed based on the solid solution theory of clathrates of van der Waals and Platteeuw with some modifications that include in particular the account of multiple cage occupancies and host relaxation. The quasiharmonic lattice dynamics method employed here gives the free energy of clathrate hydrate to first order in the anharmonicity of intermolecular potential and permits to take into account quantum zero-point vibration of host lattice and hydrogen in the cages. It is employed to study the thermodynamic functions of binary (mixed) H 2– CH 4 hydrates of cubic structure II (sII) and hexagonal structure H (sH). It is shown that at divariant equilibrium "gas phase–gas hydrate" with increasing pressure the filling of large cavities by hydrogen proceeds gradually from single filling to the maximal number of hydrogen molecules in clusters included in large cages (four in sII and five in sH) preserving stability of the hydrogen–methane hydrates sII and sH. The results show that mass fraction of hydrogen in the mixed sH hydrate is significantly lower than in the mixed sII hydrate. Pressure of monovariant equilibrium " IceI h–gas phase–mixed sII hydrate" with increasing methane concentration in the gas phase lowers in comparison with the pressure of pure hydrogen hydrate formation. For the mixed hydrogen + methane sH hydrates, it was demonstrated that thermodynamic stability depends on the filling degree of small cavities by methane molecules and stability area shifts to lower pressure with increasing filling.