Session R17: Matter in Extreme Environments: Theoretical Methods and Applications II

New directions for random search

Genuinely new knowledge and scientific insight can be obtained about dense matter by combining random numbers with reliable and efficient first principles methods. Diverse ensembles of initial structures can be generated, and structurally optimized. The resulting low energy structures are candidates for stable, and metastable, phases and/or defects that might be experimentally realized. This, of course, depends on a sufficiently broad and thorough sampling of configuration space.

Algorithms which attempt to learn from (computational) experience are necessarily sequential, and correlated. A purely random strategy, as employed by Ab Initio Random Structure Searching (AIRSS),[1,2] is entirely parallel, and a natural fit to the high throughput computation (HTC) paradigm. The absence of correlation between the independent random samples ensures that it is possible to estimate when a sufficiently dense sampling has been achieved (or at least, has not been achieved). Challenging cases can be tackled by designing the initial random structures so that they focus the search in regions of configuration space that are anticipated to yield success.

The design of these random “sensible” structures will be explored, along with some new directions which promise to accelerate random search, and recent applications to materials under extreme compression.

[1] C. J. Pickard, and R. J. Needs, Phys. Rev. Lett., 97 (4), 045504 (2006) & Journal of Physics-Condensed Matter, 23(5), 053201 (2011)
[2] Released under the GPL2 license: http://www.mtg.msm.cam.ac.uk/Codes/AIRSS   

Theoretical Prediction of Superhard Materials with the XtalOpt Evolutionary Algorithm

The XtalOpt evolutionary algorithm for crystal structure prediction has been extended to enable the prediction of superhard stable materials. The hardness is calculated via a linear relationship with the shear modulus (originally discovered by Teter) as reported by Chen. The shear modulus is obtained via AFLOW-ML (Automatic FLOW for Materials Discovery - Machine Learning). A new fitness function has been implemented wherein the user can denote the percent contribution that hardness and enthalpy have on the fitness function. We have used XtalOpt to search for hard and stable carbon allotropes and found 44 hitherto unpredicted phases whose Vickers Harnesses were calculated to be greater than 45 GPa. The structural motifs in these phases were analyzed. We also discuss the thermodynamic and kinetic stability of the predicted structures, and potential ways in which they can be synthesized under pressure.   

Meta GGA (SCAN) + van der Waals functionals (rvv10) calculation for K-edge X-ray Raman Spectrum of the epsilon and zeta phase of solid oxygen

Previous theoretical studies could not predict precisely the epsilon-zeta transitional pressure which was measured at 96 GPa by experiments (Weck et al., PRL 2009, 102, 255503). The GW calculation showed the transitional pressure at 50 GPa (Kim et al., RPRB 2008, 77, 092104) while the B3LYP hybrid functional could estimate the co-existence range of epsilon-zeta from 75 GPa to 145 GPa (Ochoa-Calle et al., PRB 2015 92, 085148). The combination of meta GGA(SCAN) and van der Waals functional (rvv10) was demonstrated to enhance the direct epsilon-zeta transition at 70 GPa while the lattice parameters were very closed to the experimental data (in manuscript). On the other hand, the Inelastic X-ray Scattering (IXS) was successfully used to study epsilon phase of solid oxygen (Meng et al., PNAS 2008, 105, 33). In this talk, we will discuss the evolution of calculated IXS K-edge spectra from epsilon phase to zeta phase using SCAN+rvv10. The calculated spectra will be compared to the experimental data.   

Dynamic non-equilibrium chemical bonding pathways under thermomechanical compression

The most urgent need in the explosion science of chemical reactions is about time-resolved non-equilibrium processes on when and how mechanical work and thermal heat are deposited into molecules to initiate reactions. Using quantum solid-state chemistry calculations, multi-resolution and multi-scale dynamic non-equilibrium simulations were recently developed for chemical reactions under compression. The non-equilibrium reaction processes are characterized by the lowest resolution in reactant and resultant conformations, the intermediate resolution in energy, enthalpy, mechanical stress, and chemical shear flows, and the highest resolution in reactive modes selected by compression. The dynamic motion of these flows is governed by a number of equations with respect to time, including the conservation of momentum and energy together with effects of mechanical endothermic bond compression, thermal heat transfer, and exothermic energy release of bond breaking related to irreversible Arrhenius kinetics with volume change and energy barriers. It provides details of dynamic non-equilibrium chemical bonding pathways from quantum to continuum scales. Simulations agreed well with experimental observations such as shock compressed graphite transformed into hexagonal diamond.   

phq: a Fortran code to compute phonon quasiparticle properties and dispersions

Intrinsic thermal shifts of phonon frequencies due to lattice anharmonicity may be significant in solids at high temperatures. As such, the calculation of phonon dispersions incorporating anharmonic effects is critical for predictive studies of vibrational, thermodynamic, and lattice transport properties. Here we introduce the phq code to compute anharmonic phonon dispersions of crystals that combines molecular dynamics (MD) and lattice dynamics calculations. The method invokes the concept of phonon quasiparticles to extract thermal shifts and phonon lifetimes from velocity autocorrelation functions projected into normal modes sampled by MD simulations. With the renormalized frequencies, it is possible to construct an effective harmonic force constant matrix that allows us to calculate the anharmonic phonon dispersion over the whole Brillouin Zone. Due to the nature of phonon quasiparticles, this approach is applicable not only to simply crystals, but also to complex crystal structures with many atoms per primitive cell with extra effort. We demonstrate successful applications of this code to weakly and strongly anharmonic systems. In addition to temperature-dependent anharmonic phonon dispersions, the vibrational entropy and free energy at constant volume can also be obtained.   

Evolutionary optimized PAW (EPAW) data-sets across the periodic table

<div>We have recently designed and implemented a method named “Evolutionary Generator of projector augmented wave datasets” (EPAW-1.0) [1,2] to produce optimized projector augmented-wave (EPAW) data-sets. The generated EPAW data-sets are transferable and can be employed in Quantum ESPRESSO and ABINIT distributions for the accurate prediction of materials properties at the scalar relativistic level. The accuracy level is very close to the highly precise calculations by the all-electron full potential linearized Augmented-plane-wave (AE-FLAPW) approach as implemented in the WIEN2k code. The EPAW performance level in solid-state studies is nearly uniform over an enlarged pressure region and outperforms other standard PAW dataset libraries, ultra-soft, and norm-conserving pseudopotentials mentioned in the reported effort by Lejaeghere et al. [3]. Employing EPAW-1.0, we generate both LDA and GGA EPAW libraries especially for low-pressure calculations for elements across the periodic table.

1) K. Sarkar et al., J COMPUT PHYS,347 (2017), 39.
2) K. Sarkar et al., COMPUT PHYS COMMUN,233 (2018), 110.
3) K. Lejaeghere et al., Science (80), 351 (2016).</div>   

qha: A Python package for quasi-harmonic free energy calculation for multi-configuration system

The quasi-harmonic approximation (QHA) offers an effective way of calculating the thermodynamic properties of many crystalline solids at high pressures and temperatures. In some cases, e.g., solid solutions or partially disordered systems such as H₂O ice-VII, the system has numerous symmetrically distinct configurations. Here we present a Python package, qha, which can calculate the equation of state and various thermodynamic properties of both single- and multi-configuration crystalline systems in the framework of the QHA. This code has a wide range of applications, including, but not limited to, order-disorder phase transitions ^[1], solid solutions ^[2], complex defect stability ^[3], etc. Apart from its versatility, qha has been tested to be both accurate and computationally efficient. It can also be used as an all-in-one executable or taken apart into stand-alone functions, increasing its usability.

[1] K. Umemoto et al., Chemical Physics Letters. 499, 236–240 (2010).
[2] G. Shukla, R. M. Wentzcovitch, Physics of the Earth and Planetary Interiors. 260, 53–61 (2016).
[3] T. Qin et al., American Mineralogist. 103, 692–699 (2018).   

Intrinsic Lattice anharmonicity and thermal conductivity of PbTe at High Temperature: Breakdown of the Phonon Minimal Mean Free Path Theory

We investigated the vibrational property of lead telluride (PbTe) with a focus on lattice anharmonicity at relatively high temperatures using the phonon quasiparticle approach. The calculated anharmonic phonon dispersions are strongly temperature dependent and some phonon modes adopt giant frequency shifts. As a result, we witness the avoided crossing between transverse optical modes and longitudinal acoustic modes at elevated temperature, in good agreement with experimentation. These results reveal strong anharmonic effects in PbTe. The obtained phonon lifetimes allow studies of transport properties. For considered temperatures, the phonon mean free paths can be shorter than lattice constants at relatively high temperature, especially for optical modes. This finding goes against the widely employed minimal phonon mean free path concept. As such, the calculated lattice thermal conductivity of PbTe, which is indeed relatively small, does not have the prescribedminima at high temperature, showcasing the breakdown of the minimal mean free path theory. Our study provides a basis for delineating vibrational and transport properties of PbTe and other thermoelectric materials within the framework of the phonon gas model.   

Thermodynamics and Thermal Conduction at Extreme Conditions Based on Phonon Quasiparticles

Predictions of materials properties at extreme conditions of pressures and temperatures are exceedingly important because it is challenging to obtain them experimentally. At the atomistic level, the accuracy of these predictions relies essentially on a satisfactory characterization of lattice anharmonicity which is generally pronounced at high temperatures. This has stimulated the development of several ab initio approaches to address anharmonic effects on lattice vibrations.

In this talk we present an overview of an ab initio method to address lattice anharmonicity based on the concept of phonon quasiparticles and illustrate its applications to some complex systems, e.g., (i) the vibrational and thermodynamic stabilization of cubic CaSiO3-pv at high temperatures, (iii) the hcp-bcc pre-melting transition in beryllium, and (iii) the irregular thermal shifts of IR frequencies and the breakdown of the well-known minimal phonon mean free path theory in MgSiO₃-perovskite. We also introduce a computational package for high pressure and high temperature computational studies that interfaces with popular ab initio packages.

References:
Z. Zhang, D.-B. Zhang, T. Sun, and R. M. Wentzcovitch, Computer Physics Communications (2018, under review)
D.-B. Zhang, P. B. Allen, T. Sun and R. M. Wentzcovitch, Physical Review B RC, 96, 100302 (2017).
Y. Lu, T. Sun, Ping Zhang, P. Zhang, D.-B. Zhang, and R. M. Wentzcovitch, Physical Review Letters 118, 145702 (2017).
D.-B. Zhang, T. Sun and R.M. Wentzcovitch, Physical Review Letters 112, 058501 (2014).
T. Sun, D.-B. Zhang, and Renata M. Wentzcovitch, Physical Review B 89, 094109 (2014).