Embedded atom model for liquid metals: Liquid iron

A method for calculating the embedded atom model potential suggested earlier for liquid Ga and Bi uses data on the structure and thermodynamic properties of metals close to their melting points. This method was applied to liquid iron at temperatures and pressures up to 5000 K and 360 GPa. Several iron models with the potential of the embedded atom model were constructed by the method of molecular dynamics at temperatures from 1820 to 5000 K and densities from 8.00 to 12.50 g/cm³. The thermodynamic, structural, diffusion, and viscosity properties of iron were calculated. The self-diffusion coefficients decreased almost linearly as the volume of the system became smaller. The conclusion is drawn that iron in the external region of the Earth’s core behaves as a liquid with self-diffusion coefficients of about ～10^-5 cm²/s and viscosity ～10^-3?10^-2 Pa s. At the boundary between the external and inner core regions, at densities of 11–12 g/cm³, iron has the properties of an amorphous phase and its self-diffusion coefficient becomes too low to be estimated by the method of molecular dynamics. Under the Earth’s inner core conditions, the embedded atom model of iron spontaneously crystallizes.     

The embedded atom model of liquid cesium

The embedded atom potential was calculated for cesium over the temperature range 323–1923 K at pressures up to 9.8 GPa from the diffraction data on the structure of the metal close to the temperature of fusion (T _f). The parameters of the embedded atom potential were adjusted using the data on the thermodynamic properties and structure of liquid cesium. The embedded atom potential well predicts the structural and thermodynamic characteristics of the liquid metal as the temperature increases along the liquid-vapor equilibrium line and under strong compression. The calculated potential energy and structure of liquid cesium closely agree with the experimental data at temperatures up to 1373 K. The calculated bulk compression modulus is close to its experimental values at all temperatures except 323 K. The self-diffusion coefficients increase as the temperature grows by a power law with an exponent close to 2 and satisfy the Stokes-Einstein equation. Deviations from experimental data at temperatures above 1400 K are explained by the metal-nonmetal transition that occurs as the density decreases.     

The use of the embedded atom model for liquid metals: Liquid potassium

The method for calculations the embedded atom potential for liquid metals based on the diffraction data on the structure close to the melting temperature was applied to potassium. The embedded atom potential parameters were adjusted using the data on the structure of potassium at 343, 473, and 723 K and the thermodynamic properties of potassium at temperatures up to 37240 K. The use of the molecular dynamics method and the embedded atom potential gave close agreement with the experimental data on the structure, density, and potential energy of liquid metal along the p ? 0 isobar at temperatures up to 2200 K and along the shock adiabat up to a pressure of ～85 GPa and 37240 K. The calculated bulk compression modulus at 343 K was close to its actual value, and the self-diffusion coefficients increased under isobaric heating conditions following a power law with an exponent of 1.6478. The melting temperature of body-centered potassium with the embedded atom potential was (319 ± 1) K, which was close to the actual melting temperature. The potential obtained incorrectly described crystalline potassium.     

The embedded atom model of molten lead

The method for calculating the embedded atom potential for liquid metals from the diffraction structural data close to the melting point was applied to lead at temperatures from 613 to 20000 K. The embedded atom potential parameters were adjusted using the data on the lead structure at 613–1173 K, the thermodynamic properties of lead over the temperature range 613–2000 K, and the results of shock wave experiments. The embedded atom potential and molecular dynamics method allowed the structural characteristics of the liquid metal to be successfully predicted up to 1173 K. The calculated bulk compression modulus at 613 K was close to its actual value. The self-diffusion coefficients along the liquid-vapor equilibrium line increased as the temperature rose following the power law with the exponent close to 2.03. The properties of lead under extremal conditions were calculated up to the temperature 20000 K and density 20.721 g/cm³. At 1000 K and a density of 18.156 g/cm³, close agreement with the experimental pressure (101.5 GPa) was obtained. The potential found fairly well described the properties of crystalline lead. At the same time, the embedded atom potential adjusted to describe the properties of the crystalline phase only poorly described the properties of liquid lead at increased densities.     

Modeling the molecular dynamics of liquid metals at high pressures: Liquid potassium

A way of building potassium models by molecular dynamics using the embedded atom model (EAM) is developed. The contribution from pairwise interaction is presented as power series at an interpartial distance. Embedded potential parameters are determined by the experimental dependence of pressure on volume for a static compression of potassium at 300 K to a pressure of 53 GPa (potential A). By using potential A to describe shock compression and choosing the appropriate temperature at given degree of compression (up to 40000 K at compression to 0.29 of initial volume) it is shown that the model pressure can be made equal to the pressure indicated by the Rankine-Hugoniot relations. The model energy is lower than the actual energy determined by the relations, and the difference in energies increases with temperature almost linearly; such growth corresponds to an excess average heat capacity of about 11.6 J/(mol K), compared to the model heat capacity. It is established that the reasons for this divergence are the inability of the EAM potential to describe the temperature dependency of metal properties precisely, and the appearance of an energy contribution upon heating that is dependent on temperature but not on atom coordinates. Adding another summand to the potential energy (which is dependent on temperature only) allows us to match the heat capacities of real potassium and the models. The dependence of potassium’s melting temperature on pressure is calculated. The calculated melting temperature at 41.2 GPa is 1231 K. Additional data (e.g., the actual temperature on the Rankine-Hugoniot curve and precise quantum mechanics calculations of heat capacity at extreme conditions) is required to eliminate potential ambiguity.     

The embedded atom model for liquid metals: Liquid gallium and bismuth

A method for calculating embedded atom potentials in liquid metals is suggested. The method uses diffraction structural data, density, bulk compression modulus, and thermal expansion coefficient close to the melting point. The method was applied to liquid gallium and bismuth at temperatures from their melting to critical points. The critical temperatures of these metals were estimated at 4940 and 4225 K. The other critical parameters were also determined. The self-diffusion coefficients were found to increase almost linearly as the temperature grew. The model allows changes in the structural characteristics of the metals when the temperature increases by several hundred kelvin units to be correctly described.     

Nonisothermal effects in the process of soot formation in ethylene pyrolysis behind shock waves

The nonisothermal nature of hydrocarbon pyrolysis explains the differences in the critical temperatures of soot formation in the experimental studies of these processes. When reaction heats are taken into account, the critical temperatures become close to 1600 K for all the systems studied. The estimated standard enthalpy of carbon atom formation in the composition of soot particles is δH_{f, z}. ≈ 11 ±6 kJ/mol. A kinetic model is proposed for soot formation in ethylene pyrolysis that describes the experimental data. The calculated temperature of soot particles may differ substantially depending on the choice of a model for energy exchange in collisions.     

Pressure effect and crystal structure reinvestigations on the spin crossover system: [Fe(bt)2(NCS)2] (bt = 2,2'-bithiazoline) polymorphs A and B

The crystal structure of [Fe(bt)2(NCS)2] (A) was determined by X-ray diffraction at 293 and at 150 K in order to analyze the structural changes associated with the spin transition. The space group is P1 with Z = 2 at both temperatures. Lattice constants are as follows: a = 8.5240(4), b = 11.0730(6), c = 12.5300(8) at 293 K and a = 8.1490(4), b = 11.4390(5), c = 12.1270(6) at 150 K. The iron(II) atom lies at the center of a distorted [FeN6] defined by two bt ligands arranged in a cis conformation. The two remaining coordination positions are occupied by two isothiocyanate anions. The average bond lengths of 2.159(4) A (293 K) and 1.951(2) A (150 K) clearly indicate the change in spin configuration. The trigonal distortion parameter phi has a value of 9.6 degrees and 5.5 degrees at 293 and 150 K, respectively. For A, DeltaV = DeltaV(SCO) = 28 A(3) per formula unit and is accompanied by a hysteresis of 10 K. chi(M)T vs T curves at atmospheric pressure for A show an abrupt spin transition with Tc downward arrow = 176 K and Tc upward arrow = 187 K. The thermodynamic parameters associated with the spin transition are DeltaH = 8.4 +/- 0.4 kJ mol(-1) and DeltaS = 46.5 +/- 3 J K mol(-1). The thermal dependence of the magnetic susceptibility at different pressures, 0.1-0.91 GPa, points out an unusual behavior, which can only be understood in terms of a crystallographic phase transition or a change in the bulk modulus of the complex. Polymorph B crystallizes in the C2/c space group with an average Fe-N bond length of 2.168(2) A and phi = 14.7 degrees at 293 K. B remains in the HS configuration even at pressures of 1.06 GPa.     

Plastic deformation of glassy polymethylene: Computer-aided molecular-dynamic simulation

Molecular-dynamic simulation of low-temperature plastic deformation (T _def = 50 K, T _def/T _g ≤ 0.3) is studied for glassy polymethylene under the regime of active uniaxial compression and tension for a cell composed of 64 chains containing 100 -CH₂ groups in each (as united atoms) and with periodic boundary conditions. Thirty-two such cells are created, and, in each cell, polymethylene chains in the statistical coil conformation are independently constructed. The cells are subjected to isothermal uniaxial compression at T _def = 50 K by ɛ = 30% and by ɛ = 70% under uniaxial tension. In the course of loading, a σ-ɛ diagram is recorded, while the mechanical work spent on deformation, the changes in the overall potential energy of the system, and the contributions from various potential interactions (noncovalent van der Waals bonds, chemical links, valence and torsional angles) are estimated. The results are averaged over all 32 cells. The relaxation of stored potential energy and residual strain after complete unloading of the deformed sample is studied. The relaxation of stored energy and residual strain is shown to be incomplete. Most of this energy and strain is stored in the sample at the deformation temperature for long period. The conformational composition of chains and the average density of polymer glass during loading are analyzed. Simulation results show that inelastic deformations commence not with the conformational unfolding of coils but with the nucleation of strain-bearing defects of a nonconformational nature. The main contribution to the energy of these defects is provided by van der Waals interactions. Strain-bearing defects are nucleated in a polymer glass during tension and compression primarily as short-scale positive volume fluctuations in the sample. During tension, the average density of the glass decreases; during compression, this parameter slightly increases to ɛ ≈ 8% and then decreases. An initial increase in the density indicates that, during compression and at ɛ < 8%, coils undergo compactization via an increase in chain packing. During compression, the concentration of trans conformers remains unchanged below ɛ ≈ 8% and then decreases. During compression, it means that in a glass, coils do not increase their sizes at strains below ɛ ≈ 8%. During tensile drawing, coils remain unfolded below ɛ ≈ 35%; at higher strains, coils become enriched with trans conformers or unfold. At this stage, the concentration of trans conformers linearly increases. The development of a strain-induced excess volume (strain-bearing defects) entails an increase in the potential energy of the sample. Under the given conditions of deformation, nucleation of strain-bearing defects and an increase in their concentration are found to be the only processes occurring at the initial stage of loading of glassy polymethylene. The results of computer-aided simulation are compared with the experimental data reported in the literature.     

The phase diagram of fullerene C60 at high temperatures and pressures

Experimental and literature data were used to calculate the Gibbs energies of polymerized C₆₀ phases and construct the equilibrium T-p phase diagram of fullerene C₆₀ at temperatures from 0 to 1000 K and pressures from 0 to 8 GPa. The diagram contains stability regions of the orthorhombic, tetragonal, and rhombohedral polymerized C₆₀ phases and primitive cubic (PC) and face-centered cubic (FCC) nonpolymerized C₆₀ phases. The orthorhombic phase (linear polymer) is an equilibrium phase at 298 K and 1 bar and in the adjacent region. The equilibrium line observed experimentally (FCC C₆₀—orthorhombic phase) is well described by the phase diagram. The optimum temperatures and pressures of the synthesis of polymerized phases are determined by kinetic rather than thermodynamic parameters.     

Diffusion in polymers dependence on crosslink density

Kinetics of N-methyl pyrrolidone evaporation from swollen photo-crosslinked polyacrylate was monitored thermogravimetrically at temperatures ranging from 323 to 398 K. Crosslink density dependence of evaporation kinetics was investigated in photo-crosslinked polyacrylates with crosslinked density ranging from ≈1.2 × 10² to ≈1.7 × 10⁴ mol m⁻³ and number of main chain atoms between crosslinks ranging from ≈70 atoms to ≈6 atoms, respectively. As was shown, evaporation kinetics was controlled by the solvent diffusion in polymer. Activation energies of evaporation (diffusion) were deduced from the rate measurements at different temperatures. Apparent activation energy of evaporation decreased from 48.7 to 31.1 kJ mol⁻¹ with crosslink density increase. Activation energy of pure N-methyl pyrrolidone evaporation was 50.6 kJ mol⁻¹. Decrease of the rate of solvent diffusion and unexpected decrease of diffusion activation energy with increase of crosslink density of swollen polymer matrix was explained by decrease in polymer chain segments mobility, as indicated by Eyring’s approach to diffusion in polymers.     

Thermodynamic properties of some polymeric forms of fullerite C<Subscript>60</Subscript> at temperatures ranging from 0 to 320 K

The temperature dependences of the heat capacityC ⁰ _p of fullerites C₆₀ were studied at temperatures ranging from 5 to 320 K in an adiabatic vacuum calorimeter with an accuracy of 0.4–0.2%. The fullerite C₆₀ samples were prepared by treating the starting fullerite C₆₀ under 8 GPa at 920 and 1270 K and “quenched” by a sharp decrease in pressure to −10⁵ Pa and in temperature to ∼300 K. Fullerite C₆₀(8 GPa, 920 K), a crystalline polymer with layered structure formed by polymerized fullerene C₆₀ molecules, was obtained at 920 K and 8 GPa. Fullerite C₆₀(8 GPa, 1270 K), a three-dimensional polymer with a graphite-like structure formed by fragments of decomposed C₆₀ molecules and containing many C(sp³)−C(sp³) bonds, was obtained at 1270 K and 8 GPa. Both polymers are metastable polymeric phases. The anomalous character of the temperature dependence of the heat capacity was revealed in the 49–66 K range for the polymer formed at 1270 K. The thermodynamic functions of the substances under study were calculated for the 0–320 K region along with entropies of their formation from graphite. The entropies of transformation of the starting fullerite C₆₀ into metastable phases and that of intertransformation of phases were estimated. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 277–281, February, 2000.     

Molecular dynamics simulation of cavitation in a lead melt at negative pressures

The molecular dynamics method was used to simulate cavitation in a metastable lead melt and determine the stability limits. States at temperatures below critical (T < 0.5T _c) and large negative pressures were considered. Interatomic interactions were described by the realistic embedded atom potential. The kinetic boundary of liquid phase stability was shown to be different from the spinodal. The kinetics and dynamics of cavitation were studied. The pressure dependences of cavitation frequencies were obtained over the temperature range 700–2700 K. The results of molecular dynamics calculations were compared with estimates based on classical nucleation theory.     

Molecular dynamics simulation of the thermodynamic properties of mercury at pressures below 2.5 GPa and temperatures below 10000 K

Models of mercury were constructed by molecular dynamics using the interparticle potential of the embedded atom model (EAM) at temperatures below 10 000 K and pressures below 2.5 GPa. The thermodynamic properties of the models were presented on the isobars of 0.5, 1.0, 1.5, 2.0, and 2.5 GPa. The compressibility factors Z = pV/(RT) were calculated; the coordinates of the inversion points of the Joule–Thomson coefficient below 5600 K were found from the positions of minima on the Z(p, T) isobars. At densities above 8–9 g/cm³, the results of simulation agreed well with experiment; at lower densities there were discrepancies associated with a loss of metal properties by real mercury. The behavior of the models was analyzed in the region of the van der Waals loop. The calculated critical temperature of mercury was found to be significantly overestimated relative to the experiment. Modeling the “meta-mercury” with the EAM potential with excluded embedded potential contribution gave better agreement with the equation of state of mercury at lower densities. The states with Z = 1 can be observed below 1.0 GPa. The calculated temperature of the inversion of the Joule–Thomson coefficient increased monotonically to 5600 K as the pressure increased to 2.5 GPa.     

Structure and speciation in hydrous silica melts. 2. Pressure effects

The effect of pressure on structure and water speciation in hydrated liquid silica is examined over a range of temperatures and compositions. The Feuston-Garofalini (FG) potential is used in isobaric-isothermal Monte Carlo simulations carried out at four pressures (0.25, 1.0, 2.5, and 10 GPa) for seven temperatures (2000 < or = T < or= 9000 K) and five compositions (0.0 < or = x_w < or = 0.4). The FG potential yields a stable melt phase for p > or = 1.0 GPa and/or x_w < or = 0.1 for all temperatures. The volume minimum seen in previous simulations of pure and hydrated liquid silica using the FG potential persists up to 2.5 GPa but is no longer evident at 10 GPa. This is correlated with gradual structural changes of the liquid up to 2.5 GPa and with more significant changes at 10 GPa. Even at high overall concentrations of water (x_w = 0.4), only about 2% of oxygen atoms are present as molecular water species at the lowest temperature. This percentage decreases with increasing pressure and temperature.     

Structural transitions in liquid cesium

Two series of models of liquid cesium at temperatures of 493 and 623 K and pressures lower than 18 GPa are constructed by means of molecular dynamics using the potential of the embedded atom model. The thermodynamic properties of the models, pair correlation functions, pair radial distribution functions, structure factors, coordination numbers, and distributions of the Voronoi polyhedra and Delaunay simplexes are analyzed. No indications of structural transitions in liquid cesium of the first-order phase transition type are observed near a pressure of 3.9 GPa. Divergences from the results of some X-ray diffraction studies could be due to incorrect determination of the coordination numbers via the standard method because of the strong asymmetry of the first peaks of the pair radial distribution functions.     

High P-T transformations of nitrogen to 170 GPa

X-ray diffraction and optical spectroscopy techniques are used to characterize stable and metastable transformations of nitrogen compressed up to 170 GPa and heated above 2500 K. X-ray diffraction data show that varepsilon-N2 undergoes two successive structural changes to complex molecular phases zeta at 62 GPa and a newly discovered kappa at 110 GPa. The latter becomes an amorphous narrow gap semiconductor on further compression and if subjected to very high temperatures (approximately 2000 K) crystallizes to the crystalline cubic-gauche-N structure (cg-N) above 150 GPa. The diffraction data show that the transition to cg-N is accompanied by 15% volume reduction.     

Coupling effects of high temperature and pressure on the decomposition mechanisms of 1,1-diamino-2,2-dinitroehethe crystal: Ab initio molecular dynamics simulations

Recently, Dreger et al. experimentally investigated the phase diagram and decomposition of 1,1-diamino-2,2-dinitroethene (FOX-7) single crystal compressed hydrostatically up to 10 GPa and heated over a range of 293–750 K (J. Phys. Chem. C 2016 , 120, 11092–11098). As a continuation, we performed ab initio molecular dynamic simulations to study the initiation mechanisms and subsequent decomposition of FOX-7 at a temperature of 504 K (initial decomposition temperature) coupled with a pressure of 1–5 GPa, 604 K at 5GPa, and 704 K at 5 GPa. However, our two compressing ways are different: the former is static hydrostatical compression, while our way is dynamic compression. Our results indicate that the initial decomposition mechanism was dependent on the temperature but independent of the pressure. The initial decomposition step is the bimolecular intermolecular hydrogen transfer. The subsequent decomposition of FOX-7 is sensitive to both the temperature and pressure. At 504 K, the decomposition of FOX-7 was accelerated from 1 to 2 GPa and from 3 to 5 GPa but decelerated from 2 to 3 GPa. The temperature exhibits a positive effect on the decomposition. Overall, the temperature and pressure have great cooperative effects on the decomposition of FOX-7. Our study may provide new insight into understanding the initial mechanisms and decomposition reactions of energetic materials at relatively low temperatures coupled with different pressures in atomic detail.     

An Unusual but Consistent View on Flow Induced Crystallization of Polymers

Summary.  There is a considerable difference of more than 40 degrees centigrade between the equilibrium melting point of the α-crystal modification of i-PP and the lower temperature, where the α-spherulites of this polymer melt. The equilibrium melting point represents the temperature, where ideal crystals melt. In these crystals the macromolecules are in a stretched conformation. In contrast, in the spherulites the molecules are contained in lamellae of finite thickness. As a consequence it seems that in the interval between these two characteristic temperatures the nucleation kinetics is very different from the kinetics observed at temperatures below the melting temperature of the spherulites. This observation is of importance because almost all measurements on flow induced crystallization have been carried out below the melting temperature of the spherulites. It can be shown that at these lower temperatures the kinetics of crystallization (including flow induced crystallization) has nothing to do with the classical ideas about sporadic nucleation.