Ab initio calculation of properties of carbon in the amorphous and liquid states

Influence of nuclear quantum effects on the electronic properties of amorphous carbon

In crystalline solids, atoms are arranged in periodic patterns on regular lattices. Amorphous solids, instead, lack long-range order; namely, a regular array of atoms beyond first or second nearest neighbors is absent. The lack of periodicity influences many properties of amorphous materials, including the coupling of electronic and nuclear motion. Here we study amorphous carbon, a system composed of a relatively light atom. We show that to understand its electronic properties, a quantum mechanical treatment of electron–nuclear coupling is essential, and we illustrate a simulation framework based on first principles to do so. We also discuss the role of specific defect states in the disordered network in determining the physical properties of amorphous carbon.

We carry out quantum simulations to study the physical properties of diamond-like amorphous carbon by coupling first-principles molecular dynamics with a quantum thermostat, and we analyze multiple samples representative of different defective sites present in the disordered network. We show that quantum vibronic coupling is critical in determining the electronic properties of the system, in particular its electronic and mobility gaps, while it has a moderate influence on the structural properties. We find that despite localized electronic states near the Fermi level, the quantum nature of the nuclear motion leads to a renormalization of the electronic gap surprisingly similar to that found in crystalline diamond. We also discuss the notable influence of nuclear quantum effects on band-like and variable-hopping mechanisms contributing to electrical conduction. Our calculations indicate that methods often used to evaluate electron–phonon coupling in ordered solids are inaccurate to study the electronic and transport properties of amorphous semiconductors composed of light atoms.

Effect of Cooling Rate on the Crystal Quality and Crystallization Rate of SiC during Rapid Solidification Based on the Solid–Liquid Model

The silicon carbide (SiC) that can achieve better electron concentration and motion control is more suitable for the production of high temperature, high frequency, radiation resistance, and high-power electronic devices. However, the fabrication of the high purity single crystal is challenging, and it is hard to observe the structural details during crystallization. Here, we demonstrate a study of the crystallization of single-crystal SiC by the molecular dynamic simulations. Based on several structure analysis methods, the transition of the solid–liquid SiC interface from a liquid to a zinc-blende structure is theoretically investigated. The results indicate that most of the atoms in the solid–liquid interface begin to crystallize with rapid solidification at low cooling rates, while crystallization does not occur in the system at high cooling rates. As the quenching progresses, the number of system defects decreases, and the distribution is more concentrated in the solid–liquid interface. A maximum crystallization rate is observed for a cooling rate of 1010 K/s. Moreover, when a stronger crystallization effect is observed, the energy is lower, and the system is more stable.

Extended Defects in Graphene and Their Contribution to the Excess Specific Heat at High Temperatures

The recent experiments on fast (microsecond) pulse heating of graphite suggest the existence of sharp maximum (6500 K at 1-2 GPa) on its melting curve. To check the validity of these findings, we propose to investigate the accumulation of extended in-plane defects in graphene. Such defects would contribute to thermodynamic properties of graphene and impose the upper limit on its melting temperature. We propose a type of extended defect of graphene, consisting of pentagonal and heptagonal rings with record low formation energy, whose accumulation leads to the loss of shear rigidity of graphene at temperatures above 6400 K, thus setting the upper limit on its melting temperature. We found that this model satisfactorily explains the increase of specific heat observed in the premelting region of graphite in slow (millisecond) pulse heating experiments. However, in fast (microsecond) pulse heating experiments such an increase of specific heat was not observed, which is a strong indication of overheating that takes place in these experiments.

Atomic and Electronic Structure of Solid-Density Liquid Carbon

A liquid carbon (l-C) sample is generated through constant volume heating exposing an amorphous carbon foil to an intense ultrashort laser pulse. Time-resolved x-ray absorption spectroscopy at the C K edge is used to monitor the dynamics of the melting process revealing a subpicosecond rearrangement of the electronic structure associated with a sudden change of the C bonding hybridization. The obtained l-C sample, resulting from a nonthermal melting mechanism, reaches a transient equilibrium condition with a temperature of about 14 200 K and pressure in the order of 0.5 Mbar in about 0.3 ps, prior to hydrodynamic expansion. A detailed analysis of the atomic and electronic structure in solid-density l-C based on time-resolved x-ray absorption spectroscopy and theoretical simulations is presented. The method can be fruitfully used for extending the experimental investigation of the C phase diagram in a vast unexplored region covering the 10^{3}-10^{4}  K temperature range with pressures up to 1 Mbar.

Characterization of three phases of liquid carbon by tight-binding molecular dynamics simulations

We have performed tight-binding molecular dynamics simulations to study the structures and properties of liquid carbon with the density ranging from 1.4 to 3.5 g cm⁻³, and identified three liquid carbon phases at different density regime.

Melting Line of Graphite

A thin plate of highly oriented pyrolytic graphite (HOPG) with the hexagonal axis (c axis) perpendicular to its surface was sandwiched between two plates of the window material and heated by an electric current pulse. The quasistatic heating process has been affected, in which the graphite sample undergoes thermal expansion only along the c axis and is melted at a pressure of 0.3-2 GPa. The set of thermodynamic quantities characterizing completely the thermodynamic states of the sample in such a process (specific volume, enthalpy, temperature, and pressure) as well as the electrical resistivity, were measured with an uncertainty <5%. It has been found that under the above pressures the HOPG melts at the temperatures of 6.3 to 6.7 kK, which are substantially higher than the literature values derived from indirect measurements. The jumps in the volume, resistivity and enthalpy of carbon on melting have been determined as well as values of the isochoric heat capacity and the sound velocity of the graphite and liquid carbon. The heat capacities in the vicinity of the melting line turned out to be close to the Dulong-Petit value while the sound velocity of liquid carbon clearly demonstrates an increase with volume indicating a change from the planar sp^{2} to tetrahedral sp^{3} covalent bonding.

Atomistic simulations of the equation of state and hybridization of liquid carbon at a temperature of 6000 K in the pressure range of 1-25 GPa

The equation of state and the structure of liquid carbon are studied by molecular simulation. Both classical and quantum molecular dynamics (QMD) are used to calculate the equation of state and the distribution of chemical bonds at 6000 K in the pressure range 1-25 GPa. Our calculations and results of other authors show that liquid carbon has a fairly low density on the order of 1.2-1.35 g/cm³ at pressures about 1 GPa. Owing to the coordination number analysis, this fact can be attributed to the high content of sp¹-bonded atoms (more than 50% according to our ab initio computations). Six empirical potentials have been tested in order to describe the density dependence of pressure and structure at 6000 K. As a result, only one potential, ReaxFF/lg, was able to reproduce the QMD simulations for both the equation of state and the fraction of sp¹, sp², sp³-bonded atoms.

Experimental study of liquid carbon

Direct measurements of the functional dependencies of the electric resistivity and the molar volume on enthalpy and pressure have been performed for graphite and liquid carbon. It has been found that for graphite at the pressures P  ⩽  1 GPa the isochoric temperature coefficient of resistance is positive, while for liquid carbon it is negative over the entire pressure range investigated where P  =  0.5-3.5 GPa. These observations probably indicate that graphite is a metal whereas liquid carbon is not a metal, so that the melting of graphite under such pressures coincides with a metal-to-nonmetal transition.

The work done by an external electromagnetic field

Ehrenfest's theorem is used to derive the rate of change of kinetic energy induced by an external field. The expression for the power is valid for any electromagnetic field in arbitrary gauge. We discuss the applicable conditions for the Mott-Davis and Moseley-Lukes form of the Kubo-Greenwood formula (KGF) for the electrical conductivity which has been implemented in ab initio codes. We show that the conventional KGF does not satisfy gauge invariance, and is suitable only for computing the ac conductivity at sufficiently high frequency and when the gradient of the carrier density is small.

Real-world predictions from ab initio molecular dynamics simulations

In this review we present the techniques of ab initio molecular dynamics simulation improved to its current stage where the analysis of existing processes and the prediction of further chemical features and real-world processes are feasible. For this reason we describe the relevant developments in ab initio molecular dynamics leading to this stage. Among them, parallel implementations, different basis set functions, density functionals, and van der Waals corrections are reported. The chemical features accessible through AIMD are discussed. These are IR, NMR, as well as EXAFS spectra, sampling methods like metadynamics and others, Wannier functions, dipole moments of molecules in condensed phase, and many other properties. Electrochemical reactions investigated by ab initio molecular dynamics methods in solution, on surfaces as well as complex interfaces, are also presented.

Electrical conductivity of high-pressure liquid hydrogen by quantum Monte Carlo methods

We compute the electrical conductivity for liquid hydrogen at high pressure using Monte Carlo techniques. The method uses coupled electron-ion Monte Carlo simulations to generate configurations of liquid hydrogen. For each configuration, correlated sampling of electrons is performed in order to calculate a set of lowest many-body eigenstates and current-current correlation functions of the system, which are summed over in the many-body Kubo formula to give ac electrical conductivity. The extrapolated dc conductivity at 3000 K for several densities shows a liquid semiconductor to liquid-metal transition at high pressure. Our results are in good agreement with shock-wave data.

Carbon phase diagram from ab initio molecular dynamics

We compute the free energy of solid and liquid diamond from first-principles electronic structure theory using efficient thermodynamic integration techniques. Our calculated melting curve is in excellent agreement with the experimental estimate of the graphite-diamond-liquid triple point and is consistent with shock wave experiments. We predict the phase diagram of diamond at pressures and temperatures that are difficult to access experimentally. We confirm early speculations on the presence of a reentrant point in the diamond melting line but find no evidence for a first order liquid-liquid phase transition near the reentrant point.

Prediction of new phases of nitrogen at high pressure from first-principles simulations

A rich variety of competing phases is predicted for nitrogen at accessible pressures, including a new metallic chainlike phase very close in energy to the previously predicted cubic gauche phase, and other phases at slightly higher energies, e.g., one with N2 and N6 units. Large energy barriers between structures can account for recent observations of metastability, and we identify a low barrier transition path from the known epsilon phase to the chainlike metallic phase. In analogy to MgB2, the metal is anisotropic with multiple Fermi surfaces formed from pi and sigma states.