Session AAA08: V: Matter under Extreme Conditions

Planck Gravity and Its Relation to Relativity

2.5549..x10⁵⁹ in m³/JS⁴ and m/KgS² is a value derived from 2πc³/h = c³/h-bar = G/l_p² and it is a gravitational constant which should be known as Planck Gravity. This constant not only shows that gravity can be described as a rate of flow, but it can be used to normalize the derived Planck units in a way which expands out relativity.

 

This foundational expansion might give insight into the difficulty in reconciling aspects of quantum mechanics with relativity itself. Furthermore, the equations provided also hint at the possibility that the value for c in the equation E=mc² comes not from the speed of light, but from the frequency of time itself which is equal to the exact same value of 299792458² m/s but in units of angular work as m⁴Kg/jS⁴. Additionally, it predicts that either the mass of the graviton should theoretically be 3.5177..x10^-43 or mass is quantized in discreate quantities of that value.

 

Because of these potentials, there might exist a flawed understanding of time, gravity, energy, mass, and entrpy.  If true, then some adjustments might not only need to be made to some equations but also with the foundational understanding of our universe itself.

    

Building a database of thermoelastic properties using ab initio workflows

Materials computations of thermoelastic properties, especially of the ab initio kind, are intrinsically complex. These difficulties have inspired us to develop a workflow framework, express, to automate long and extensive sequences of ab initio calculations. Various materials properties can be computed in express, e.g., static equation of state, phonon density of states, thermal equation of state, and other thermodynamic properties. It helps users in the preparation of inputs, execution of simulations, and analysis of data. It also tracks the operations and steps that users perform and thus can restore interrupted or failed jobs.

In this release, we implemented new workflows: static elasticity and thermoelasticity workflows. With the integration of our cij code, which uses the Wu–Wentzcovitch semi-analytical method, we can calculate high-pressure and high-temperature thermoelastic coefficients and acoustic velocities of crystalline materials. These data are saved to a database for future predictions and searches.   

pgm: A Python package for free energy calculation

The quasiharmonic approximation (QHA) is a powerful method for computing the free energy and thermodynamic properties of materials at high pressures (P) and temperatures (T). However, anharmonicity, electronic excitations in metals, or both, introduce an intrinsic T-dependence on the phonon frequencies, making the QHA inadequate. Here we present a Python package, pgm, for free energy and thermodynamic property calculations. It is based on the concept of phonon quasiparticles and the phonon gas model (PGM). The free energy is obtained by integrating the entropy, which can be readily calculated for a system of phonon quasiparticles. This method is useful for computing the free energy in anharmonic insulators and harmonic or anharmonic metals. The current implementation offers properties in a continuum P,T range. The necessary inputs are ab initio T_el-dependent static energies and T-dependent phonon quasiparticle frequencies at several discrete volumes and the user-specified P,T range. We employ techniques like just-in-time (JIT) compiling and parallel computing to accelerate the numerical computation. We demonstrate successful applications of pgm to hcp-iron (ε-Fe) at extreme conditions [1] and cubic CaSiO3-perovskite [2], a strongly anharmonic system. Anharmonic free energies computed using thermodynamic integration (TI) agree with the results produced by this approach using an equivalent q-point mesh [3]. Therefore, a dense q-point mesh should produce anharmonic free energies equivalent to those obtained on TI simulations on 10⁴ atoms and beyond.

[1] Zhuang, J., Wang, H., Zhang, Q., & Wentzcovitch, R. M. (2021). Thermodynamic properties ε-Fe with thermal electronic excitation effects on vibrational spectra. Phys. Rev. B, 103(14), 144102.

[2] Zhang, Z., & Wentzcovitch, R. M. (2021). Ab initio anharmonic thermodynamic properties of cubic CaSiO3 perovskite. Phys. Rev. B, 103(10), 104108.

[3] Zhang, D. B., Sun, T., & Wentzcovitch, R. M. (2014). Phonon quasiparticles and anharmonic free energy in complex systems. Physical review letters, 112(5), 058501.

    

Plane-wave-based stochastic-deterministic density functional theory for extended systems

Traditional finite-temperature Kohn-Sham density functional theory (KSDFT) is one of the most popular quantum-mechanics-based methods in modeling materials since it balances the accuracy and efficiency well. However, traditional KSDFT based on the diagonalization method (DG) needs to solve all occupied bands, which increases fast as the temperature rises according to the Fermi-Dirac function. Thus, it is inefficient and also takes up a lot of memory at high temperatures, which limits its further applications. The evaluation of the ground-state density in KSDFT can be replaced by the Chebyshev trace (CT) method. Recently, stochastic density functional theory [Phys. Rev. Lett. 111, 106402 (2013)] (SDFT) and its improved theory, mixed stochastic-deterministic density functional theory [Phys. Rev. Lett. 125, 055002 (2020)] (MDFT) are developed based on the CT method and stochastic orbitals, which makes it possible to simulate high-temperature systems more efficiently. We have implemented the four methods based on the plane-wave basis set within the first-principles package ABACUS. In addition, all methods are adapted to the norm-conserving pseudopotentials and periodic boundary conditions with the use of k-point sampling in the Brillouin zone. By testing the Si and C systems from the DG method as benchmarks, we systematically evaluate the accuracy and efficiency of the SDFT, and MDFT methods by examining a series of physical properties, which include the electron density, free energy, atomic forces, stress, and density of states. We conclude that they not only reproduce the DG results with a sufficient accuracy but also exhibit several advantages over the DG method. We expect these methods can be of great help in studying high-temperature systems such as warm dense matter and dense plasmas.   

Ab initio melting temperatures of bcc and hcp iron under the Earth's inner core condition

There has been a long debate on the stable phase of iron under the Earth's inner core conditions. Due to the solid-liquid coexistence at the inner core boundary, the thermodynamic stability of solid phases directly relates to their melting temperatures, which remains considerable uncertainty. In the present study, we utilized a semi-empirical potential fitted to high-temperature ab initio data to perform a thermodynamic integration from classical systems described by this potential to ab initio systems. This method provides a smooth path for the thermodynamic integration and significantly reduces the uncertainty of determining the melting temperatures caused by the finite size effect down to 15 K. Our results suggest the hcp phase is the ground state of pure iron under the inner core conditions, while the free energy difference between the hcp and bcc phases is tiny, on the order of 10s meV/atom. It suggests the effect of nickel and light elements must be taken into account to get a complete picture of the crystalline structure of the solid inner core phase.

    

The epsilon phase of solid oxygen: The importance of the magnetic order

The epsilon phase of solid oxygen is a unique molecular crystal with C2/m space group symmetry being composed of the (O₂)₄ clusters. It has been a challenge for decades to elucidate   the   anomalous   pressure dependence of the lattice parameters at 10-20 GPa. In previous calculations [1, 2], the antiferromagnetic structure with 8-atom primitive unit cell of the C2/m has been assumed as the most stable structure (called AFM2). We show that the problems are remained due to the possible mismatch between the C2/m space group and the magnetic orders. To treat this problem, we use an extended conventional unit cell (16 atom/cell) instead of 8-atom primitive cell with spin-polarized SCAN-rVV10 functionals. We found that the anti-ferromagnetic structure with 16-atom unit cell (called AFM1), is more stable than the AFM2 in pressure range from 10 GPa to 20 GPa. In the AFM1 order, there are four oxygen molecules in the computational cell where the constituent O atoms have the same value for the magnetic moment, while there four oxygen molecules having non-equivalent magnetic moments. The former ones are arranged making the (anti-)ferromagnetic order in the b- (a-)direction, while the latter ones are arranged making the (anti-)ferromagnetic order in the a- (b-)direction. This AFM1 arrangement is inconsistent with the magnetic space group corresponding to the C2/m space group. This result also suggests that there is breaking of the time-reversal symmetry, prompting future experimental investigation. The observed lattice parameters [3] and neutron powder diffraction patterns [4, 5] are compared with the calculations considering of the AFM1 structure.

References:

[1] Y. Crespo et al., PNAS 111 (29), 10427-10432 (2014).

[2] A. Ramírez-Solís et al., Phys. Chem. Chem. Phys. 19, 2826-2833 (2017).

[3] H. Fujihisa et al., Phys. Rev. Lett. 97, 085503 (2006).

[4] I. N. Goncharenko Phys. Rev. Lett. 94, 205701 (2005).

[5] S. Klotz J. Low. Temp. Phys. 192, 1–18 (2018).   

Deep machine-learning potential for atomistic simulation of δ-AlOOH at high pressures and temperatures

δ-AlOOH (δ) is a critical high-pressure hydrous phase for understanding the Earth’s geological water cycle. Our earlier ab initio study [1] offered a practical multi-configuration model for understanding the pressure-dependent behavior of the H-bond, including H-bond disorder, tunneling, and symmetrization. Since H-bond behavior in δ is likely typical of H-bonds in other hydrous or nominally anhydrous phases, it would be helpful to develop a more complete understanding of its behavior beyond the symmetrization transition pressures. However, further simulations on δ require large-scale simulations that are prohibitive to ab initio calculations.

This study adopts the DP-GEN scheme [2] to develop a deep machine-learning potential (DP) for δ. Our DP potential predicts forces and energies accurately, and DP-based MD simulations reproduce detailed features found in ab initio pair-correlation functions and finite-T equation of states. The simulation with DP potential predicts the P-T region of the superionic state of AlOOH. It helps interpret the recently reported [3] instability of δ near the cold slab geotherm.

[1] C. Luo, K. Umemoto, and R. Wentzcovitch, Phys. Rev. Research 4, 023223 (2022).

[2] Y. Zhang et al., Computer Physics Communications 253, 107206 (2020).

[3] Y. Duan, et al., Earth and Planetary Science Letters 494, 92 (2018).