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1.
A method recently developed to rigorously determine solid-liquid equilibrium using a free-energy-based analysis has been extended to analyze multiatom molecular systems. This method is based on using a pseudosupercritical transformation path to reversibly transform between solid and liquid phases. Integration along this path yields the free energy difference at a single state point, which can then be used to determine the free energy difference as a function of temperature and therefore locate the coexistence temperature at a fixed pressure. The primary extension reported here is the introduction of an external potential field capable of inducing center of mass order along with secondary orientational order for molecules. The method is used to calculate the melting point of 1-H-1,2,4-triazole and benzene. Despite the fact that the triazole model gives accurate bulk densities for the liquid and crystal phases, it is found to do a poor job of reproducing the experimental crystal structure and heat of fusion. Consequently, it yields a melting point that is 100 K lower than the experimental value. On the other hand, the benzene model has been parametrized extensively to match a wide range of properties and yields a melting point that is only 20 K lower than the experimental value. Previous work in which a simple "direct heating" method was used actually found that the melting point of the benzene model was 50 K higher than the experimental value. This demonstrates the importance of using proper free energy methods to compute phase behavior. It also shows that the melting point is a very sensitive measure of force field quality that should be considered in parametrization efforts. The method described here provides a relatively simple approach for computing melting points of molecular systems.  相似文献   

2.
3.
In the second part of our paper, we address crystal nucleation in the metastable liquid miscibility region of eutectic systems that is always present, though experimentally often inaccessible. While this situation resembles the one seen in single component crystal nucleation in the presence of a metastable vapor-liquid critical point addressed in previous works, it is more complex because of the fact that here two crystal phases of significantly different compositions may nucleate. Accordingly, at a fixed temperature below the critical point, six different types of nuclei may form: two liquid-liquid nuclei: two solid-liquid nuclei; and two types of composite nuclei, in which the crystalline core has a liquid "skirt," whose composition falls in between the compositions of the solid and the initial liquid phases, in addition to nuclei with concentric alternating composition shells of prohibitively high free energy. We discuss crystalline phase selection via exploring/identifying the possible pathways for crystal nucleation.  相似文献   

4.
Cloud-point curves, critical points, and coexistence curves with feed concentrations close to the critical concentration were measured in three systems involving cyclohexane + different polydisperse polystyrenes. The shape of the coexistence curves is analyzed by using a scaling expression. In two systems the critical exponent β possesses values somewhat larger than in actual binary systems (where β ≈ 1/3), whereas in the third system a somewhat smaller value is found. By using a three-parameter Gibbs free energy relation, cloud-point curves and coexistence curves are calculated from the critical point data and from the slope of the cloud-point curve at this point. To account for polydispersity, the method of continuous thermodynamics is applied. The cloud-point curves are well described, but the prediction of the coexistence curves is bad due to the mean-field character of the Gibbs free energy relation resulting in β = 1/2. Hence, the often used practice of fitting the parameters of a mean-field Gibbs free energy relation to the critical point and to some cloud points and then to calculate the coexistence data is to be considered with great care.  相似文献   

5.
We use numerical simulation to examine the possibility of a reversible liquid-liquid transition in supercooled water and related systems. In particular, for two atomistic models of water, we have computed free energies as functions of multiple order parameters, where one is density and another distinguishes crystal from liquid. For a range of temperatures and pressures, separate free energy basins for liquid and crystal are found, conditions of phase coexistence between these phases are demonstrated, and time scales for equilibration are determined. We find that at no range of temperatures and pressures is there more than a single liquid basin, even at conditions where amorphous behavior is unstable with respect to the crystal. We find a similar result for a related model of silicon. This result excludes the possibility of the proposed liquid-liquid critical point for the models we have studied. Further, we argue that behaviors others have attributed to a liquid-liquid transition in water and related systems are in fact reflections of transitions between liquid and crystal.  相似文献   

6.
Molecular dynamics simulations are used to examine static and dynamic coexistence between solid and liquid phases in nanoscale silver, copper, and nickel clusters. We find static coexistence in the 561-atom copper icosahedron, the 561-atom silver icosahedron, and the 923-atom nickel icosahedron, and in cluster sizes above these thresholds, but not in smaller clusters. Nonetheless, in smaller clusters we typically observe either dynamic coexistence between fully solid and liquid states or transient coexistence which is essentially dynamic coexistence between a fully solid state and a solid-liquid state.  相似文献   

7.
Nonequilibrium melting and crystallization of a model Lennard-Jones system   总被引:3,自引:0,他引:3  
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.  相似文献   

8.
Molecular simulation results for the solid-liquid coexistence properties of untruncated, truncated, truncated and shifted, and truncated and shifted-force 12-6 Lennard-Jones potentials are reported. It is found that solid-liquid coexistence properties vary systematically with potential truncations, shifts, and cut-off values. Potential truncations and shifts have important consequences at low temperatures, particularly in the vicinity of the triple point. The main influence is on the coexistence pressure whereas both liquid and solid densities are less sensitive to the truncations and shifts. The data reported in this work indicate that the cut-off radius mainly affects the properties of the liquid phase whereas its influence on the solid phase is almost negligible. The data suggest a monotonic variation of the melting temperature as a function of cut-off radius, which contradicts the oscillatory behavior of the melting temperature reported elsewhere.  相似文献   

9.
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.  相似文献   

10.
We present a new thermodynamic integration method that directly connects the vapor and solid phases by a reversible path. The thermodynamic integration in the isothermal-isobaric ensemble yields the Gibbs free energy difference between the two phases, from which the sublimation temperature can be easily calculated. The method extends to the binary mixture without any modification to the integration path simply by employing the isothermal-isobaric semigrand ensemble. The thermodynamic integration, in this case, yields the chemical potential difference between the solid and vapor phases for one of the components, from which the binary sublimation temperature can be calculated. The coexistence temperatures predicted by our method agree well with those in the literature for single component and binary Lennard-Jones systems.  相似文献   

11.
The solid-fluid coexistence properties of the n - 6 Lennard-Jones system, n from 7 to 12, are reported. The procedure relies on determining Helmholtz free energy curves as a function of volume for each phase independently, from several NVT simulations, and then connecting it to points of known absolute free energy. For n = 12 this requires connecting the simulated points to states of very low densities on the liquid phase, and to a harmonic crystal for the solid phase, which involves many extra simulations for each temperature. For the reference points of the remaining systems, however, the free energy at a given density and temperature can be calculated relative to the n = 12 system. The method presented here involves a generalization of the multiple histogram method to combine simulations performed with different potentials, provided they visit overlapping regions of the phase space, and allows for a precise calculation of relative free energies. The densities, free energies, average potential energies, pressure, and chemical potential at coexistence are presented for up to T? = 5.0 and new estimations of the triple points are given for the n - 6 Lennard-Jones system.  相似文献   

12.
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.  相似文献   

13.
Molecular dynamics simulations in conjunction with MEAM potential models have been used to study the melting and freezing behavior and structural properties of both supported and unsupported Au nanoclusters within a size range of 2 to 5 nm. In contrast to results from previous simulations regarding the melting of free Au nanoclusters, we observed a structural transformation from the initial FCC configuration to an icosahedral structure at elevated temperatures followed by a transition to a quasimolten state in the vicinity of the melting point. During the freezing of Au liquid clusters, the quasimolten state reappeared in the vicinity of the freezing point, playing the role of a transitional region between the liquid and solid phases. In essence, the melting and freezing processes involved the same structural changes which may suggest that the formation of icosahedral structures at high temperatures is intrinsic to the thermodynamics of the clusters, rather than reflecting a kinetic phenomenon. When Au nanoclusters were deposited on a silica surface, they transformed into icosahedral structures at high temperatures, slightly deformed due to stress arising from the Au-silica interface. Unlike free Au nanoclusters, an icosahedral solid-liquid coexistence state was found in the vicinity of the melting point, where the cluster consisted of coexisting solid and liquid fractions but retained an icosahedral shape at all times. These results demonstrated that the structural stability in the structures of small Au nanoclusters can be enhanced through interaction with the substrate. Supported Au nanoclusters demonstrated a structural transformation from decahedral to icosahedral motifs during Au island growth, in contrast to the predictions of the minimum-energy growth sequence: icosahedral structures appear first at very small cluster sizes, followed by decahedral structures, and finally FCC structures recovered at very large cluster sizes. The simulations also showed that island shapes are strongly influenced by the substrate, more specifically, the structural characteristic of a Au island is not only a function of size, but also depends on the contact area with the surface, which is controlled by the wetting of the cluster to the substrate.  相似文献   

14.
We present a new thermodynamic integration method that directly connects the liquid and the solid phases of a binary mixture by a reversible path. The states along the path are simulated in the isothermal-isobaric semigrand canonical ensemble, in which temperature, pressure, the total number of particles, and the fugacity fractions of the components are held fixed. The thermodynamic integration yields the chemical-potential difference between the two phases for one of the components and this information is then used to locate the solid-liquid coexistence points. The melting temperatures predicted by our method agree well with those predicted by the Gibbs-Duhem integration for a truncated and shifted Lennard-Jones system with a cutoff radius of 2.5sigma.  相似文献   

15.
This series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the NVT ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. 131, 234504 (2009)] showed that strongly correlating liquids have "isomorphs," which are curves in the phase diagram along which structure, dynamics, and some thermodynamic properties are invariant in reduced units. In the present paper, using the fact that reduced-unit radial distribution functions are isomorph invariant, we derive an expression for the shapes of isomorphs in the WU phase diagram of generalized Lennard-Jones systems of one or more types of particles. The isomorph shape depends only on the Lennard-Jones exponents; thus all isomorphs of standard Lennard-Jones systems (with exponents 12 and 6) can be scaled onto a single curve. Two applications are given. One tests the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. 131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence curve, whereas the agreement is less convincing on the solid side. A second application is the derivation of an approximate equation of state for generalized Lennard-Jones systems by combining the isomorph theory with the Rosenfeld-Tarazona expression for the temperature dependence of the potential energy on isochores. It is shown that the new equation of state agrees well with simulations.  相似文献   

16.
A novel lambda-integration path is proposed for calculating the Gibbs free energy difference between any arbitrary solid and liquid state needed for the location of melting lines. This technique involves reversibly forcing a liquid state to a solid state across the phase transition along a nonphysical path, thermodynamically coupling the two states directly. The process eliminates the need for coupling to idealized reference states as is presently performed and hence simplifies the location of phase transitions for computer simulation systems. More specifically the path involves a three stage process, whereby, initially a liquid state is transformed to a weakly attractive fluid using linear lambda-integration scaling of the intermolecular potential. In the second stage, the resulting fluid is then constrained to the required solid configurational phase space via the insertion of a periodic lattice of 3D Gaussian wells. The final stage involves reversing to full strength the main intermolecular potential while gradually turning off the constraining 3D Gaussian lattice finally resulting in a stable (or metastable) solid state. Each stage was found to be completely reversible and the resulting change in free energy was thermodynamically integrable. The methodology is demonstrated and validated by calculating solid-liquid coexistence points using the new technique and comparing to those in present literature for the truncated and shifted Lennard-Jones system. The results are found to be in good agreement. The new method is not limited to melting phase transitions and is readily applicable to any simulation methodology, simulation cell size and/or intermolecular potential including ab initio methods.  相似文献   

17.
Molecular dynamics simulations are performed to determine the melting points of aluminum nanoparticles of 55-1000 atoms with the Streitz-Mintmire [Phys. Rev. B 1994, 50, 11996] variable-charge electrostatic plus potential. The melting of the nanoparticles is characterized by studying the temperature dependence of the potential energy and Lindemann index. Nanoparticles with less than 850 atoms show bistability between the solid and liquid phases over temperature ranges below the point of complete melting. The potential energy of a nanoparticle in the bistable region alternates between values corresponding to the solid and liquid phases. This bistability is characteristic of dynamic coexistence melting. At higher temperatures, only the liquid state is stable. Nanoparticles with more than 850 atoms undergo a sharp solid-liquid-phase transition characteristic of the bulk solid phase. The variation of the melting point with the effective nanoparticle radius is also determined.  相似文献   

18.
The phase-switch Monte Carlo method of Wilding and Bruce [Phys. Rev. Lett. 85, 5138 (2000)] is extended to enable calculation of solid-liquid phase coexistence for soft potentials. The method directly accesses coexistence information about a system while avoiding simulation of the interfacial region. Order parameters are introduced that allow one to define a path that connects liquid and crystalline phases. Transition matrix methods are employed to bias the sampling such that both phases are sampled in a rapid and efficient manner. Coexistence properties are determined through an analysis of specific volume probability distributions, which are generated naturally during a biased simulation. The approach is demonstrated with the Lennard-Jones system. Finite-size effects are examined and compared to those for the hard sphere system. In addition, two techniques are considered for accounting for long-range interactions. The methodology presented here is general and therefore provides a basis for its application to other soft systems.  相似文献   

19.
In this work we present an implementation for the calculation of the melting point of ice I(h) from direct coexistence of the solid-liquid interface. We use molecular dynamics simulations of boxes containing liquid water and ice in contact. The implementation is based on the analysis of the evolution of the total energy along NpT simulations at different temperatures. We report the calculation of the melting point of ice I(h) at 1 bar for seven water models: SPC/E, TIP4P, TIP4P-Ew, TIP4P/ice, TIP4P/2005, TIP5P, and TIP5P-E. The results for the melting temperature from the direct coexistence simulations of this work are in agreement (within the statistical uncertainty) with those obtained previously by us from free energy calculations. By taking into account the results of this work and those of our free energy calculations, recommended values of the melting point of ice I(h) at 1 bar for the above mentioned water models are provided.  相似文献   

20.
We consider the computation of the coexistence pressure of the liquid-solid transition of a system of hard spheres from direct simulation of the inhomogeneous system formed from liquid and solid phases separated by an interface. Monte Carlo simulations of the interfacial system are performed in three different ensembles. In a first approach, a series of simulations is carried out in the isothermal-isobaric ensemble, where the solid is allowed to relax to its equilibrium crystalline structure, thus avoiding the appearance of artificial stress in the system. Here, the total volume of the system fluctuates due to changes in the three dimensions of the simulation box. In a second approach, we consider simulations of the inhomogeneous system in an isothermal-isobaric ensemble where the normal pressure, as well as the area of the (planar) fluid-solid interface, are kept constant. Now, the total volume of the system fluctuates due to changes in the longitudinal dimension of the simulation box. In both approaches, the coexistence pressure is estimated by monitoring the evolution of the density along several simulations carried out at different pressures. Both routes are seen to provide consistent values of the fluid-solid coexistence pressure, p=11.54(4)k(B)T/sigma(3), which indicates that the error introduced by the use of the standard constant-pressure ensemble for this particular problem is small, provided the systems are sufficiently large. An additional simulation of the interfacial system is conducted in a canonical ensemble where the dimensions of the simulation box are allowed to change subject to the constraint that the total volume is kept fixed. In this approach, the coexistence pressure corresponds to the normal component of the pressure tensor, which can be computed as an appropriate ensemble average in a single simulation. This route yields a value of p=11.54(4)k(B)T/sigma(3). We conclude that the results obtained for the coexistence pressure from direct simulations of the liquid and solid phases in coexistence using different ensembles are mutually consistent and are in excellent agreement with the values obtained from free energy calculations.  相似文献   

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