Liquid-Liquid Phase Transitions in Silicon

Liquid-Liquid Crossover in Water Model: Local Structure vs Kinetics of Hydrogen Bonds

In equilibrium and supercooled liquids, polymorphism is manifested by thermodynamic regions defined in the phase diagram, which are predominantly of different short- and medium-range order (local structure). It is found that on the phase diagram of the water model, the thermodynamic region corresponding to the equilibrium liquid phase is divided by a line of the smooth liquid-liquid crossover. In the case of the water model TIP4P/2005, this crossover is revealed by various local order parameters and corresponds to pressures on the order of 3150 ± 350 atm at ambient temperature. In the vicinity of the crossover, the dynamics of water molecules change significantly, which is reflected, in particular, in the fact that the self-diffusion coefficient reaches its maximum values. In addition, changes in the structure also manifest themselves in changes in the kinetics of hydrogen bonding, which are captured by values of such quantities as the average lifetime of hydrogen bonding, the average lifetimes of different local coordination numbers, and the frequencies of changes in different local coordination numbers. An interpretation of the hydrogen bond kinetics in terms of the free energy landscape concept in the space of possible coordination numbers is proposed.

Observation of plasmon excitation in liquid silicon by inelastic x-ray scattering

Inelastic x-ray scattering (IXS) measurements were performed for observing the excitation of bulk plasmons in metallic liquid silicon (Si). The peak due to plasmon excitation was observed within the energy loss around 17 eV. Combined with IXS data of crystalline Si measured at several elevated temperatures, it was found that temperature dependence of the excitation energy in the crystalline solid state is explained by the electron gas including the band gap effect, whereas in the metallic liquid state near the melting point, it exhibits a departure from the electron gas; the plasmon energy takes a lower value than that of the electron gas. Such lowering of plasmon energies is reasonably explained by a model incorporating semiconducting component to the electron gas. Non-simple metallic nature in liquid silicon is highlighted by the observation of electron collective dynamics.

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Kohn-Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn-Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

Average-atom Ziman resistivity calculations in expanded metallic plasmas: Effect of mean ionization definition

We present calculations of electrical resistivity for expanded boron, aluminum, titanium, and copper plasmas using the Ziman formulation in the framework of the average-atom model. Our results are compared to experimental data, as well as to other theoretical calculations, relying on the Ziman and Kubo-Greenwood formulations, and based on average-atom models or quantum-molecular-dynamics simulations. The impact of the definition of ionization, paying particular attention to the consistency between the definition and the perfect free electron gas assumption made in the formalism, is discussed. We propose a definition of the mean ionization generalizing to expanded plasmas the idea initially put forward for dense plasmas, consisting in dropping the contribution of quasibound states from the ionization due to continuum ones. It is shown that our recommendation for the calculation of the quasibound density of states provides the best agreement with measurements.

Yukawa-Friedel-tail pair potentials for warm dense matter applications

Accurate equations of state (EOS) and plasma transport properties are essential for numerical simulations of warm dense matter encountered in many high-energy-density situations. Molecular dynamics (MD) is a simulation method that generates EOS and transport data using an externally provided potential to dynamically evolve the particles without further reference to the electrons. To minimize computational cost, pair potentials needed in MD may be obtained from the neutral-pseudoatom (NPA) approach, a form of single-ion density functional theory (DFT), where many-ion effects are included via ion-ion correlation functionals. Standard N-ion DFT-MD provides pair potentials via the force matching technique but at much greater computational cost. Here we propose a simple analytic model for pair potentials with physically meaningful parameters based on a Yukawa form with a thermally damped Friedel tail (YFT) applicable to systems containing free electrons. The YFT model accurately fits NPA pair potentials or the nonparametric force-matched potentials from N-ion DFT-MD, showing excellent agreement for a wide range of conditions. The YFT form provides accurate extrapolations of the NPA or force-matched potentials for small and large particle separations within a physical model. Our method can be adopted to treat plasma mixtures, allowing for large-scale simulations of multispecies warm dense matter.

Approximately 30 nm Nanogroove Formation on Single Crystalline Silicon Surface under Pulsed Nanosecond Laser Irradiation

Nanogrooves with a minimum feature size down to 30 nm (λ/26) can be formed directly on silicon surface by irradiation from two orthogonal polarized 1064 nm/10 ns fiber laser beams. The creation of such small nanogrooves is attributed to surface thermal stress during resolidification and supercooling with the double laser beams' irradiation. By varying the pulse number and laser fluence, the feature size of narrow grooves on silicon surface can be tuned. The experimental results and numerical calculation of surface thermal behaviors indicated that the high repetition rate of the nanosecond laser leads to the incubation effect and different silicon optical and thermal properties during laser irradiation. Resolution on this scale should be attractive in nanolithography, particularly considering that this method is available in far field and in ambient air.

Thermodynamics and kinetics of crystallization in deeply supercooled Stillinger-Weber silicon

We study the kinetics of crystallization in deeply supercooled liquid silicon employing computer simulations and the Stillinger-Weber three-body potential. The free energy barriers to crystallization are computed using umbrella sampling Monte Carlo simulations and from unconstrained molecular dynamics simulations using a mean first passage time formulation. We focus on state points that have been described in earlier work [S. Sastry and C. A. Angell, Nat. Mater. 2, 739 (2003)] as straddling a liquid-liquid phase transition (LLPT) between two metastable liquid states. It was argued subsequently [Ricci et al., Mol. Phys. 117, 3254 (2019)] that the apparent transition is due to the loss of metastability of the liquid state with respect to the crystalline state. The presence of a barrier to crystallization for these state points is therefore of importance to ascertain, which we investigate, with due attention to ambiguities that may arise from the choice of order parameters. We find a well-defined free energy barrier to crystallization and demonstrate that both umbrella sampling and mean first passage time methods yield results that agree quantitatively. Our results thus provide strong evidence against the possibility that the liquids at state points close to the reported LLPT exhibit slow, spontaneous crystallization, but they do not address the existence of a LLPT (or lack thereof). We also compute the free energy barriers to crystallization at other state points over a broad range of temperatures and pressures and discuss the effect of changes in the microscopic structure of the metastable liquid on the free energy barrier heights.

Ionization of carbon at 10-100 times the diamond density and in the 10^{6} K temperature range

The behavior of partially ionized hot compressed matter is critical to the study of planetary interiors as well as nuclear fusion studies. A recent quantum study of carbon in the 10-70 Gbar range and at a temperature of 100 eV used N-atom density functional theory (DFT) with N∼32-64 and molecular dynamics (MD). This involves band-structure-type electronic calculations and averaging over many MD-generated ion configurations. The calculated average number of free electrons per ion, viz., Z[over ¯], was systematically higher than from a standard average-atom quantum calculation. To clarify this offset, we examine the effect of the self-interaction error in such estimates and the possibility of carbon being in a granular plasma state containing Coulomb crystals with a magic number. The electrical conductivity, pressure, and compressibility of the carbon system are examined. The very low conductivity and the high-Z[over ¯] results of DFT MD point to the existence of carbon in a complex, nonuniform, low-conducting dispersed phase, possibly containing magic-number Coulomb crystals. The neutral pseudoatom estimate of Z[over ¯], conductivity, compressibility, and pressure reported here pertain to the uniform liquid.

Liquid-Liquid Critical Point in Phosphorus

The study of liquid-liquid phase transitions has attracted considerable attention. One interesting example of this phenomenon is phosphorus, for which the existence of a first-order phase transition between a low density insulating molecular phase and a conducting polymeric phase has been experimentally established. In this Letter, we model this transition by an ab initio quality molecular dynamics simulation and explore a large portion of the liquid section of the phase diagram. We draw the liquid-liquid coexistence curve and determine that it terminates into a second-order critical point. Close to the critical point, large coupled structure and electronic structure fluctuations are observed.

Thermodynamic anomalies in silicon and the relationship to the phase diagram

The evolution of thermodynamic anomalies are investigated in the pressure-temperature (pT) plane for silicon using the well-established Stillinger-Weber potential. Anomalies are observed in the density, compressibility and heat capacity. The relationships between them and with the liquid stability limit are investigated and related to the known thermodynamic constraints. The investigations are extended into the deeply supercooled regime using replica exchange techniques. Thermodynamic arguments are presented to justify the extension to low temperature, although a region of phase space is found to remain inaccessible due to unsuppressible crystallisation. The locus corresponding to the temperature of minimum compressibility is shown to display a characteristic 'S'-shape in thepTprojection which appears correlated with the underlying crystalline phase diagram. The progression of the anomalies is compared to the known underlying phase diagrams for both the crystal/liquid and amorphous/liquid states. The locations of the anomalies are also compared to those obtained from previous simulation work and (limited) experimental observations.