Nonequilibrium melting and crystallization of a model Lennard-Jones system

Nonequilibrium melting and crystallization of a model Lennard-Jones system were investigated with molecular dynamics simulations to quantify the maximum superheating/supercooling at fixed pressure, and over-pressurization/over-depressurization at fixed temperature. The temperature and pressure hystereses were found to be equivalent with regard to the Gibbs free energy barrier for nucleation of liquid or solid. These results place upper bounds on hysteretic effects of solidification and melting in high heating- and strain-rate experiments such as shock wave loading and release. The authors also demonstrate that the equilibrium melting temperature at a given pressure can be obtained directly from temperatures at the maximum superheating and supercooling on the temperature hysteresis; this approach, called the hysteresis method, is a conceptually simple and computationally inexpensive alternative to solid-liquid coexistence simulation and thermodynamic integration methods, and should be regarded as a general method. We also found that the extent of maximum superheating/supercooling is weakly pressure dependent, and the solid-liquid interfacial energy increases with pressure. The Lindemann fractional root-mean-squared displacement of solid and liquid at equilibrium and extreme metastable states is quantified, and is predicted to remain constant (0.14) at high pressures for solid at the equilibrium melting temperature.     

Ab initio melting curve of molybdenum by the phase coexistence method

Ab initio calculations of the melting curve of molybdenum for the pressure range 0-400 GPa are reported. The calculations employ density functional theory (DFT) with the Perdew-Burke-Ernzerhof exchange-correlation functional in the projector augmented wave (PAW) implementation. Tests are presented showing that these techniques accurately reproduce experimental data on low-temperature body-centered cubic (bcc) Mo, and that PAW agrees closely with results from the full-potential linearized augmented plane-wave implementation. The work attempts to overcome the uncertainties inherent in earlier DFT calculations of the melting curve of Mo, by using the "reference coexistence" technique to determine the melting curve. In this technique, an empirical reference model (here, the embedded-atom model) is accurately fitted to DFT molecular dynamics data on the liquid and the high-temperature solid, the melting curve of the reference model is determined by simulations of coexisting solid and liquid, and the ab initio melting curve is obtained by applying free-energy corrections. The calculated melting curve agrees well with experiment at ambient pressure and is consistent with shock data at high pressure, but does not agree with the high-pressure melting curve deduced from static compression experiments. Calculated results for the radial distribution function show that the short-range atomic order of the liquid is very similar to that of the high-T solid, with a slight decrease of coordination number on passing from solid to liquid. The electronic densities of states in the two phases show only small differences. The results do not support a recent theory according to which very low dT(m)dP values are expected for bcc transition metals because of electron redistribution between s-p and d states.     

Interpretation of boundaries in the pressure–temperature diagram for liquid tellurium and their relationship to the melting-curve maximum

Research on liquid tellurium is reviewed and interpreted in an effort to obtain a consistent picture of the effect of pressure and temperature on the structure and properties of tellurium in the liquid state. Electrical resistance experiments on liquid tellurium support the existence of reaction boundaries in the p–T diagram. The boundaries are believed to identify stages in the reaction whereby the 2-coordinate covalent chain structure transforms to a 3-coordinate covalent network structure which eventually dissociates with pressure and temperature into a metallic system. The increasing liquid density associated with the molecular reaction is given as the cause of the maximum on the P–T melting curve. The melting curve maximum in tellurium is shown to be related to maxima in selenium and sulfur. Quenching tellurium from different liquid fields, delineated by reaction boundaries, resulted in materials with different x-ray spectra.     

Liquid-liquid phase transformations and the shape of the melting curve

The phase diagram of elemental liquids has been found to be surprisingly rich, including variations in the melting curve and transitions in the liquid phase. The effect of these transitions in the liquid state on the shape of the melting curve is analyzed. First-order phase transitions intersecting the melting curve imply piecewise continuous melting curves, with solid-solid transitions generating upward kinks or minima and liquid-liquid transitions generating downward kinks or maxima. For liquid-liquid phase transitions proposed for carbon, phosphorous selenium, and possibly nitrogen, we find that the melting curve exhibits a kink. Continuous transitions imply smooth extrema in the melting curve, the curvature of which is described by an exact thermodynamic relation. This expression indicates that a minimum in the melting curve requires the solid compressibility to be greater than that of the liquid, a very unusual situation. This relation is employed to predict the loci of smooth maxima at negative pressures for liquids with anomalous melting curves. The relation between the location of the melting curve maximum and the two-state model of continuous liquid-liquid transitions is discussed and illustrated by the case of tellurium.     

Two-phase simulation of the crystalline silicon melting line at pressures from -1 to 3 GPa

Results of a numerical investigation of crystalline silicon melting line within the range of pressures from -1 to 3 GPa are presented. A two-phase molecular dynamics method is applied to obtain temperature, pressure, and densities of solid and liquid phases on the melting line. Using a special procedure we ensure the strict control of the two-phase equilibrium in the simulation cell. To describe the interaction between the atoms four classic potentials have been chosen: the Stillinger-Weber one and three modified variants of the Tersoff potential. For the Stillinger-Weber and Tersoff potentials in the modification by Kumagai-Izumi-Hara-Sakai a good coincidence with experimental data on crystalline Si melting temperature is obtained within the range of pressure from 0 to 3 GPa. Calculations of the solid and liquid phase densities on the silicon melting line for the Stillinger-Weber potential are also in close agreement with experiments.     

Liquid-solid transition in fully ionized hydrogen at ultra-high pressures

We study the phase diagram of an effective ion model of fully ionized hydrogen at ultra-high pressure. We assume that the protons interact with a screened Coulomb potential derived from a static linear response theory. This model accurately reproduces the physical properties of hydrogen for densities greater than g/ρ(m)=10 cm(3) corresponding to the range of the coupling parameter r(s) ? 0.6. The pressure range, P ? 20 TPa, is well beyond present experimental limitations. Assuming classical protons, we find that the zero temperature enthalpy of the perfect bcc crystal is slightly lower than for other structures at g/ρ(m)=12.47 cm(3) while the fcc structure gains stability at higher density. Using Monte Carlo calculations, we compute the free energy of various phases and locate the melting transition versus density. We find that on melting, bcc is energetically favored with respect to fcc over the entire range investigated. In the solid phase the system undergoes a structural transition from bcc at higher temperature to fcc at lower temperature. The free energy difference between these two structures is very small so that obtaining a quantitative estimate of this second transition line requires accuracy beyond that provided by our method. We estimate the effect of proton zero point motion on the bcc melting line for hydrogen, deuterium, and tritium by a path integral Monte Carlo method. Although zero point effects on hydrogen are large, since the two competing phases (bcc and liquid) have locally similar environments, the effect on the melting line is small; the melting temperature for hydrogen is lowered by about 10% with respect to the classical value.     

Path integral calculation of free energies: quantum effects on the melting temperature of neon

The path integral formulation has been combined with several methods to determine free energies of quantum many-body systems, such as adiabatic switching and reversible scaling. These techniques are alternatives to the standard thermodynamic integration method. A quantum Einstein crystal is used as a model to demonstrate the accuracy and reliability of these free energy methods in quantum simulations. Our main interest focuses on the calculation of the melting temperature of Ne at ambient pressure, taking into account quantum effects in the atomic dynamics. The free energy of the solid was calculated by considering a quantum Einstein crystal as reference state, while for the liquid, the reference state was defined by the classical limit of the fluid. Our findings indicate that, while quantum effects in the melting temperature of this system are small, they still amount to about 6% of the melting temperature, and are therefore not negligible. The particle density as well as the melting enthalpy and entropy of the solid and liquid phases at coexistence is compared to results obtained in the classical limit and also to available experimental data.     

Molar volume calculated at various pressures and the Pippard relations close to the melting point in benzene

The molar volume of solid and liquid benzene was calculated at various pressures (at constant temperatures), and the Pippard relations were examined close to the melting point in this organic molecule.

The molar volume calculated is in good agreement with the observed data, which decreases as the pressure increases up to about 150 MPa. The Pippard relations are also valid within this pressure range at constant temperatures studied here for the solid and liquid phases of benzene.     

Exploring the Free Energy and Conformational Landscape of tRNA at High Temperature and Pressure

A combined temperature‐ and pressure‐dependent study was employed to reveal the conformational and free‐energy landscape of phenylalanine transfer RNA (tRNA^Phe), a known model for RNA function, to elucidate the features that are essential in determining its stability. These studies also help explore its structural properties under extreme environmental conditions, such as low/high temperatures and high pressures. To this end, fluorescence and FTIR spectroscopies, calorimetric and small‐angle scattering measurements were carried out at different ion concentrations over a wide range of temperatures and pressures up to several hundred MPa. Compared with the pronounced temperature effect, the pressure‐dependent structural changes of tRNA^Phe are small. A maximum of only 15 % unpaired bases is observed upon pressurization up to 1 GPa. RNA unfolding differs not only from protein unfolding, but also from DNA melting. Its pressure stability seems to be similar to that of noncanonical DNA structures.     

Solid-liquid transitions of sodium chloride at high pressures

We investigate solid-liquid transitions in NaCl at high pressures using molecular dynamics simulations, including the melting curve and superheating/supercooling as well as solid-solid and liquid-liquid transitions. The first-order B1-B2 (NaCl-CsCl type) transition in solid is observed at high pressures besides continuous liquid structure transitions, which are largely analogous to the B1-B2 transition in solid. The equilibrium melting temperatures (T(m)) up to megabar pressure are obtained from the solid-liquid coexistence technique and the superheating-supercooling hysteresis method. Lindemann's vibrational and Born's mechanical instabilities are found upon melting. The Lindemann frequency is calculated from the vibrational density of states. The Lindemann parameter (fractional root-mean-squared displacement) increases with pressure and approaches a constant asymptotically, similar to the Lennard-Jones system. However, the Lindemann melting relation holds for both B1 and B2 phases to high accuracy as for the Lennard-Jonesium. The B1 and B2 NaCl solids can be superheated by 0.18T(m) and 0.24T(m), and the NaCl liquid, supercooled by 0.22T(m) and 0.32T(m), respectively, at heating or cooling rates of 1 K/s and 1 K/ps. The amount of maximum superheating or supercooling and its weak pressure dependence observed for NaCl are in accord with experiments on alkali halides and with simulations on the Lennard-Jones system and Al.     

一种支氏液晶共聚酯的合成

在聚对苯二甲酸乙二醇酯与对羟基苯甲酸 (HBA)形成的共聚酯 (PET HBA)分子链中 ,引入具有分形结构的单体———三羟基苯 (TOP) ,以降低其熔点 ,改善加工性能 .考察乙酰化时间、缩聚时间、压力、TOP和HBA加入量对新型分形共聚酯的对数比浓粘度的影响规律 ,以及TOP和HBA加入量对新型分形共聚酯的熔点和液晶清亮点的影响 .TOP的加入能使PET HBA共聚酯的熔点下降 10℃以上 ,而液晶清亮点没有变化 ,拓宽了液晶区域     

Aspects of the melting of metallic elements

Melting is a most familiar phenomenon: closely similar patterns of solid/liquid transformation occur on heating innumerable and diverse crystalline substances. While some behaviual trends have been characterized, no melting theory of general applicability has yet found widespread acceptance. The present comparative survey is concerned with the melting of metallic elements, to determine quantitatively the enthalpy and density changes that accompany these solid/liquid transitions. The relationship of melting with other physicochemical processes is considered. Metals were selected as apparently the simplest systems for this analysis, many crystal structures involve the close packing of (at least approximately) spherical atoms. Appropriate physical data are available for a large number of different elements, some 70 are considered here, representing a wide range of melting points, T _m. Aspects of the kinetics and mechanisms of melting are discussed. These data comparisons show that melting enthalpies for metals are relatively small. The averages found represent only about 26% of the energy required to heat these solids from 0 K to completion of melting at T_m and only about 5% of the volatilization enthalpy. The density changes on fusion are also relatively small, on average -4.7%. To account for these observations, a representational model of fusion has been formulated. It is suggested that, on melting, the bonding and of local structural dispositions between neighbouring atoms in the liquid and in the solid condensed phases undergo changes that are only limited in extent. T_hus, the regular ordered structures, characteristic of crystalline phases, are extensively maintained in the melt at Tm. Melting is ascribed to destabilization of the crystal through excess vibrational energy, resulting in replacement of the overall extended and constant rigid structure of the solid by a dynamic equilibrium between small, locally regular domains in the liquid. Each such structurally ordered domain is a region of one or other of the alternative possible, crystal-type structures of comparable stability. In the liquid, constant transfer of the components between these regular arrays, stabilised by the enthalpy of fusion, within the compact assemblage of domains accounts for the fluidity of the liquid, its inability to withstand a shearing force and the absence of long-range order. Melting is, therefore, identified with relaxation, at T _m, of the constraint that only a single lattice form is present (as in a crystal) and the liquid is composed of all the structures that are sufficiently stable to participate in the constant flux of interconverting domains. This model of melting may have wider applicability. The small modifications both of enthalpy and of density on fusion make the formulation of a quantitative model, capable of predicting T _m, difficult because minor or secondary controls may be significant in determining the temperature of this physical phase change and the structural changes that occur.     

TRANSITION IN THE MELT OF FEP COPOLYMER

The nature of the transition in molten FEP copolymer was examined in relation to the enthalpy change, mechanical damping and melt viscosity. For a pre-heat-treated FEP copolymer sample a small endothermic peak appeared at 309—312 ℃in DSC trace with enthalpy change 0.03—0.05 cal/g. A peak was also detected in damping versus temperature curve at the same temperature range. The theological property of FEP copolymer melt was similar to that of liquid crystal, but no birefrigence was viewed in the melt. Therefore the transition was explained as the melting of small crystallites which persist in typical copolymer beyond its melting temperature. These crystallites can act as nuclei for crystallization upon cooling.     

Characterization of the TIP4P-Ew water model: vapor pressure and boiling point

The liquid-vapor-phase equilibrium properties of the previously developed TIP4P-Ew water model have been studied using thermodynamic integration free-energy simulation techniques in the temperature range of 274-400 K. We stress that free-energy results from simulations need to be corrected in order to be compared to the experiment. This is due to the fact that the thermodynamic end states accessible through simulations correspond to fictitious substances (classical rigid liquids and classical rigid ideal gases) while experiments operate on real substances (liquids and real gases, with quantum effects). After applying analytical corrections the vapor pressure curve obtained from simulated free-energy changes is in excellent agreement with the experimental vapor pressure curve. The boiling point of TIP4P-Ew water under ambient pressure is found to be at 370.3+/-1.9 K, about 7 K higher than the boiling point of TIP4P water (363.7+/-5.1 K; from simulations that employ finite range treatment of electrostatic and Lennard-Jones interactions). This is in contrast to the approximately +15 K by which the temperature of the density maximum and the melting temperature of TIP4P-Ew are shifted relative to TIP4P, indicating that the temperature range over which the liquid phase of TIP4P-Ew is stable is narrower than that of TIP4P and resembles more that of real water. The quality of the vapor pressure results highlights the success of TIP4P-Ew in describing the energetic and entropic aspects of intermolecular interactions in liquid water.     

Prediction of macroscopic properties of protic ionic liquids by ab initio calculations

We have systematically investigated combinations of anions and cations in a number of protic ionic liquids based on alkylamines and used ab initio methods to gain insight into the parameters determining their liquid range and their conductivity. A simple, almost linear, relation of the experimentally determined melting temperature with the calculated volume of the anion forming the ionic liquid is found, whereas the dependence of the melting temperature with increasing cation volume goes through a minimum for relatively short side chain length. On the basis of the present results, we propose a strategy to predict the nature of protic ionic liquids in terms of low vapor pressure and conductivity. Comparisons with previously reported strategies for prediction of melting temperatures for aprotic ionic liquids are also made.     

Ab initio melting curve of copper by the phase coexistence approach

Ab initio calculations of the melting properties of copper in the pressure range 0-100 GPa are reported. The ab initio total energies and ionic forces of systems representing solid and liquid copper are calculated using the projector augmented wave implementation of density functional theory with the generalized gradient approximation for exchange-correlation energy. An initial approximation to the melting curve is obtained using an empirical reference system based on the embedded-atom model, points on the curve being determined by simulations in which solid and liquid coexist. The approximate melting curve so obtained is corrected using calculated free energy differences between the reference and ab initio system. It is shown that for system-size errors to be rendered negligible in this scheme, careful tuning of the reference system to reproduce ab initio energies is essential. The final melting curve is in satisfactory agreement with extrapolated experimental data available up to 20 GPa, and supports the validity of previous calculations of the melting curve up to 100 GPa.     

Melting points and thermal expansivities of proton-disordered hexagonal ice with several model potentials

A method of free energy calculation is proposed, which enables to cover a wide range of pressure and temperature. The free energies of proton-disordered hexagonal ice (ice Ih) and liquid water are calculated for the TIP4P [J. Chem. Phys. 79, 926 (1983)] model and the TIP5P [J. Chem. Phys. 112, 8910 (2000)] model. From the calculated free energy curves, we determine the melting point of the proton-disordered hexagonal ice at 0.1 MPa (atmospheric pressure), 50 MPa, 100 MPa, and 200 MPa. The melting temperatures at atmospheric pressure for the TIP4P ice and the TIP5P ice are found to be about T(m)=229 K and T(m)=268 K, respectively. The melting temperatures decrease as the pressure is increased, a feature consistent with the pressure dependence of the melting point for realistic proton-disordered hexagonal ice. We also calculate the thermal expansivity of the model ices. Negative thermal expansivity is observed at the low temperature region for the TIP4P ice, but not for the TIP5P ice at the ambient pressure.     

Pressure‐induced amorphization and disordering on cooling in semi‐crystalline polymers: calorimetric evidence for inverse melting in one component system

We report some unusual phase behaviour, of general implication for condensed matter, on the polymer poly‐4‐methyl pentene‐1 (P4MP1) induced by changes in pressure (P) and temperature (T), as observed by in‐situ X‐ray diffraction and high pressure DSC. Upon increasing pressure beyond a threshold value, the polymer, crystalline at ambient conditions, looses its crystalline order isothermally. The process is reversible. This behaviour is observed in two widely separated temperature regions, one below the glass transition temperature (< 50°C) and one close to the melting temperature (250°C), thus showing solid state amorphization and inversion in the melting temperature with increasing pressure. This further suggests inverse melting, i.e. re‐entrant of the two widely separated liquid and amorphous phases along the T‐axis at fixed P. This is confirmed experimentally as disordering in the crystalline structure on cooling. The inverse melting in P4MP1 raises the possibility of exothermic melting and endothermic crystallization as anticipated by Tammann (1903), see reference 1. The anticipated exothermic melting and endothermic crystallization is confirmed experimentally in the one component system P4MP1. We are observing similar features in a range of polymers.     

Critical temperature measurements of liquids by means of differential thermal analysis

When studying crytalline substances and liquids in sealed off glass ampoules by differential thermal analysis the melting ranges but not the heat of evaporation of the liquids and fused substances are found, because inside the glass ampoule, there will always be the vapour pressure equillibrium which corresponds to the temperature. With liquids undergoing decomposition, it is possible to measure the range and heat of decomposition. Given a suitable quantity inside the ampoule the critical temperature, e.g., of water of ethanol can be measured for non-decomposing liquids. The measuring effect is based on the pronounced change of the liquid's specific heat at the critical temperature.Fundamental studies of the measurement of critical temperatures of liquids were carried out by the turn of the century. One the methods reported is the meniscus method, optimal measurement of the critical temperature, which comprises a liquid being filled into a glass tube which is then sealed by melting. The glass tube is heated while observing the meniscus. Its rise means that the critical volume has been exceeded, while a drop means that it has not yet been reached. The conditions are only met when that volume of liquid has been filled into the tube at which the meniscus neither rises nor falls on heating but rather remains, e.g. at mid level of the tube until it disappears. The tube contains the critical volume at the critical density when the critical temperature is reached. The critical pressure is then present. These conditions are obtained when the meniscus disappears and the liquid completely goes over into the vapour phase.The melting range (and the latent heat of fusion) are found when investigating a crystalline material under normal pressure by differential thermal analysis. Given a suitable arrangement the boiling temperature and, in rough approximation, the heat of evaporation are also found (Fig.1). The latent heat of fusion is found again when carrying out the same measurement in a closed system (glass tube sealed by melting). The heat of evaporation can no longer be measured since the vapour pressure equilibrium coresponding to the given temperature is present in the glass tube.     

Stability of smectic phases in the Gay-Berne model

We present a detailed computer simulation study of the phase behavior of the Gay-Berne liquid crystal model with molecular anisotropy parameter kappa=4.4. According to previous investigations: (i) this model exhibits isotropic (I), smectic-A (Sm-A), and smectic-B (Sm-B) phases at low pressures, with an additional nematic (N) phase between the I and Sm-A phases at sufficiently high pressures; (ii) the range of stability of the Sm-A phase turns out to be essentially constant when varying the pressure, whereas other investigations seem to suggest a pressure-dependent Sm-A range; and (iii) the range of stability of the Sm-B phase remains unknown, as its stability with respect to the crystal phase has not been previously considered. The results reported here do show that the Sm-A phase is stable over a limited pressure range, and so it does not extend to arbitrarily low or high pressures. This is in keeping with previous investigations of the effect of molecular elongation on the phase behavior of Gay-Berne models. A detailed study of the melting transition at various pressures shows that the low-temperature crystalline phase melts into an isotropic liquid at very low pressures, and into a nematic liquid at very high pressures. At intermediate pressures, the crystal melts into a Sm-A liquid and no intermediate Sm-B phase is observed. On the basis of this and previous investigations, the reported Sm-B phase for Gay-Berne models appears to be a molecular solid rather than a smectic liquid phase.