Metastable extensions of phase equilibrium lines and singular points of simple substance

The thermodynamic properties of crystal, liquid, and gas in the stable and metastable states have been determined by molecular dynamics simulation of a system of 2048 Lennard-Jones particles. The spinodals of a superheated crystal, a superheated liquid, and a supersaturated vapor have been approximated; the spinodal for a supercooled liquid turns out to be nonexistent. The liquid-vapor, liquid-crystal, and crystal-vapor equilibrium curves and their extensions beyond the triple point have been calculated. It has been shown that, as distinct from the metastable extension of the saturation curve, which terminates at the zero isotherm, the metastable melting and sublimation curves terminate at, respectively, the stretched liquid and superheated crystal spinodals. The properties of the critical end points of metastable equilibrium of extended phases are considered.     

Melting line, spinodal and the endpoint of the melting line in the system with a modified Lennard—Jones potential

A molecular dynamics method was used to calculate the pressure p* and the internal energy e* of a liquid and a crystal in stable and metastable states in a system of 2048 particles, which interaction is described by a modified Lennard—Jones potential. For the liquid phase, calculations were performed along 13 isotherms from the range of reduced temperature T* = 0.35–3.0, and for the crystal phase, along 16 isotherms from the range T* =0.1–3.0. The thermal p* = p*(ρ*,T*) and caloric e* = e*(ρ*,T*) equations of state for liquids and crystals have been constructed. The parameters of crystal-liquid phase equilibrium have been determined from the conditions of phases coexistence at positive pressures and in the region of negative pressures, where the coexistent phases are metastable. The spinodal of a stretched liquid has been approximated. It has been found that with a temperature decrease the metastable extension of the melting line meets the spinodal of the liquid phase. The point of their meeting, the endpoint of the melting curve, is the point of termination of crystal-liquid phase equilibrium without the onset of identity of the phases.     

Anomalous Scenario for Termination of Metastable Melting in Simplified Coulomb Models in the Zero‐Temperature Limit

Two non‐standard scenarios of melting termination in deep metastable states are studied in the zero‐temperature limit on the base of two variants of modified one‐component Coulomb models. These additional scenarios supplement the previously studied standard case of “spinodal decomposition” (Iosilevskiy and Chigvintsev, arXiv:0609059) when liquid binodal of metastable freezing (liquidus) is terminated in intersection with gas‐liquid spinodal. In the first new scenario hypothetical unique crystal‐fluid global phase coexistence is realized as smooth superposition of melting and sublimation transitions (without gas‐liquid transition and corresponding critical point). The second new type of “spinodal decomposition” scenario is related to the situation when solid binodal of metastable melting (solidus) intersects spinodal of metastable isostructural crystal‐crystal phase transition. Modified one‐component Coulomb models allow one to investigate in details all features of such “spinodal decomposition” scenarios (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Metastable states and coexistence of phases in scaling theory

The methods of scaling theory are used to investigate the physical properties of matter in a large neighborhood of the stability boundary (spinodal), including metastable states and lines of phase equilibrium. Expressions are obtained for the pressure isotherms in metastable gas and liquid phases, a phase equilibrium equation, and an expression for the width of the metastable region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 73–77, March, 1981.We thank V. M. Sysoev and Yu. I. Shimanskii for valuable comments and for discussing the results.     

Phase equilibria,metastable states,and critical points in a simple one-component system

Stability of metastable phase states against infinitesimal perturbations in a simple one-component system is considered. The method of molecular dynamics simulation was used to determine the boundaries of essential instability of supersaturated vapor, a superheated liquid, and a superheated crystal. The absence of a spinodal from a supercooled liquid and the dependence of the boundary of essential instability of a superheated crystal on the character of deformation were established. It is shown that each of the three lines of phase equilibria in a one-component system has an endpoint of termination of phase coexistence. As distinct from the liquid–gas critical point, which is the point of phase identity and is located in the region of stable states, the endpoints of melting and sublimation lines are located in the region ofmetastable states. At these points, a critical (spinodal) state is achieved only for one of the coexisting phases.     

Surface free energy of the crystal-liquid interface on the metastable extension of the melting curve

The surface free energy γ, excess surface energy e, and excess surface stress τ at the crystal-liquid interface of a Lennard-Jones system have been determined by molecular dynamics simulation. The calculations have been performed for temperatures both above and below the triple-point temperature for the region where each of the coexisting phases is metastable and is at a negative pressure. The asymptotic behavior of γ, e, and τ has been analyzed near the endpoint of the melting curve, which is a point of the contact of the metastable extension of the melting curve and the spinodal of the stretched liquid [V.G. Baidakov and S.P. Protsenko, Phys. Rev. Lett. 95, 015701 (2005)]. It has been found that γ, e, and τ at this point are finite and the excess surface entropy is zero.     

The equation of state of metastable liquid xenon near the critical point

This paper presents the results of measurements of xenon density near the critical liquid-vapour point in stable and metastable states. The spinodal has been approximated. The equation of state of metastable liquid is discussed.     

On the theory of explosive boiling of a transparent liquid on a laser-heated target

The possible manifestations of thermodynamical instability (explosive vaporisation) are discussed for different regimes of laser heating of the metal/transparent liquid system. The present calculations show that the explosive vaporisation in the metastable region may occur if the nucleation rate is high enough. This condition is achievable if the surface tension of the superheated liquid tends to zero near the spinodal. It is also shown that the dependence of the phase explosion time on laser intensity markedly changes its behaviour when the water temperature reaches the spinodal.     

Metastable phase equilibria in a Lennard-Jones system

A method of molecular dynamics is used to calculate the pressure, internal energy, and isochoric heat capacity in a system of 2048 Lennard-Jones particles in the range of reduced temperatures from 0.1 to 2.0 and the range of densities from 0.001 to 1.15. Local equations of state for the gas, liquid, and crystalline phases are derived. The spinodals of a superheated (extended) liquid, supersaturated vapor, and superheated (extended) crystal are determined. It is shown that the spinodal of a supercooled liquid is nonexistent. An algorithm to calculate the lines of phase equilibria is constructed. The lines of liquid-gas, liquid-crystal, crystal-gas phase equilibria, and their metastable extensions are determined. It is shown that the metastable extensions of the melting and sublimation lines terminate at the spinodals of the liquid and crystal, respectively. The properties of final critical points in the lines of melting and sublimation are considered.     

Estimation of the Possibility of Using the Classical Theory of Nucleation in the Calculation of the Limiting Superheat for a Metastable Liquid in the Region of Onset of Nucleate Boiling

Experimental data obtained at VTI for the onset of nucleate boiling of water in a uniformly heated pipe with a diameter of 5.77 and 6.34 mm at a mass flow rate Wj = 1400–5000 kg/(m2 s) and at a pressure of P = 9.81, 14.7, 19.62 MPa are presented in comparison with a theoretical calculation on the homogeneous nucleation mechanism in a metastable liquid for the liquid superheating limits obtained using the classical Gibbs formula [1]. It is assumed that the thermodynamic instability of the process in the area under the spinodal affects the breakage of metastable liquid films with the formation of holes through the entire thickness thereof, which ultimately leads to the formation of unwettable dry spots (spinodal dewetting) and causes a spontaneous transition to the film boiling mode.     

Crystal-liquid phase relations in silicon at negative pressure

The stable and metastable melting relations for silicon in the diamond and Si136 clathrate-II structures at positive and negative pressures are calculated by molecular dynamics computer simulation. The simulated liquid and crystalline clathrates undergo cavitation at approximately -3 and -12 GPa. Between these limits a stretched crystal would transform directly to gas in response to a mechanical instability. Most importantly, the clathrate-II crystal becomes thermodynamically stable over the diamond at negative pressure below -1 GPa at the melting point. Si136 should then crystallize from a slightly stretched liquid, which would have the same volume as a diamond-structure crystal.     

亚稳相的高压暴露

 很久以前,便有人指出,气态冷凝成固态时,要连续经历液相及各种高温相,才达到平衡结晶相。但是,液态及高温相往往需靠很大的冷却速度才能冻结下来,这在当时对绝大多数合金,是不可能的。近些年,随着超急冷等技术的进步,关于非晶等亚稳相得研究十分活跃。当超过一定临界冷却速度时,液态合金可固化为非晶态。虽然,亚稳结晶相较非晶应更容易冻结,但是,由于产生各种亚稳相所需的过冷条件各不相同,以及对冷却速度的选择不能是任意的,因此有时它们较非晶还难于形成。与液相凝固过程相似,非晶合金的晶化也服从构型最小重排原理,即在晶化完成之前,存在某些亚稳相变态阶段。但是,限于热力学上的不稳定性及动力学因素,在常压下这些亚稳相同样是难以发现的。作者根据对多种合金系的研究,提出高压暴露亚稳相的设想,并利用非晶等亚稳相的高压变态过程,将进行液态急冷时的速度控制方式,改为便于掌握的高压退火方式,来获得新亚稳相。本文对压力暴露亚稳相的原理和实践,加以论述。     

Liquid limits: glass transition and liquid-gas spinodal boundaries of metastable liquids

The liquid-gas spinodal and the glass transition define ultimate boundaries beyond which substances cannot exist as (stable or metastable) liquids. The relation between these limits is analyzed via computer simulations of a model liquid. The results obtained indicate that the liquid-gas spinodal and the glass transition lines intersect at a finite temperature, implying a glass-gas mechanical instability locus at low temperatures. The glass transition lines obtained by thermodynamic and dynamic criteria agree very well with each other.     

复相系平衡条件及平衡稳定性条件的分析

复相系平衡条件及平衡稳定性条件的分析曾丹苓（重庆大学热力工程系重庆６３００４４）关键词复相系，平衡条件，平衡稳定性条件１引言汽液相变是工程上常见的现象，它是一个复杂的物理过程，涉及到传热传质、相转变、表面现象、流体流动及工质热物性等领域，但从热力学的...     

Phase diagram of trivalent and pentavalent patchy particles

We compute the equilibrium phase diagram of two simple models for patchy particles with three and five patches in a very broad range of pressure and temperature. The phase diagram presents low-density crystal structures which compete with the fluid phase. The phase diagram of the five-patch model shows re-entrant melting, in analogy with the previously studied four-patch case, a metastable gas-liquid critical point and a stable, high-density liquid. The three-patch model shows a stable gas-liquid critical point and, in the region of temperatures where equilibration is numerically feasible, a stable liquid phase, suggesting the possibility that in this small valence model the liquid retains its thermodynamic stability down to the vanishing range limit.     

On the theory of spinodal decomposition in solid and liquid binary mixtures

The kinetics of phase separation is discussed with emphasis on the transition between spinodal decomposition and nucleation. A reanalysis of the theory of Langer, Baron and Miller shows that it exhibits a spinodal line somewhat closer to the coexistence curve than the meanfield spinodal. There the same (as we think unphysical) critical singularities occur as in Cahn-Hilliard theory. The precise location of this spinodal line depends on the cell size of the coarse graining. For concentrations less than the spinodal one the structure factorS(k, t) converges then towards the structure factor of the metastable onephase state, implying an infinite lifetime of the latter.In order to include the effects of nucleation and growth we hence present an alternative treatment, extending our previous work on cluster dynamics. From a simple approximation for the radial concentration distribution function of clustersS(k, t) is computed numerically. Even at rather low concentrations the time evolution ofS(k, t) is then similar to what Langer et al. find at high concentrations, implying a very gradual transition from nucleation and growth to spinodal decomposition, at least for parameter values appropriate to the Ising model. This treatment, which is consistent with Lifshitz-Slyozov's coarsening law at late times, is extended to the early stages of phase separation in liquid mixtures.     

Dynamics of freezing and liquid instability

A theoretical analysis of the dynamic stability of a supercooled simple liquid to finite amplitude periodic density waves is presented. The theory predicts absence of a classical spinodal point for a simple one component liquid. A dynamical constraint on the formation of the bcc phase is revealed.     

Metastability and Spinodal Points for a Random Walker on a Triangle

We investigate time-dependent properties of a single-particle model in which a random walker moves on a triangle and is subjected to nonfocal boundary conditions. This model exhibits spontaneous breaking of a Z ₂ symmetry. The reduced size of the configuration space (compared to related many-particle models that also show spontaneous symmetry breaking) allows us to study the spectrum of the time evolution operator. We break the symmetry explicitly and find a stable phase, and a metastable phase which vanishes at a spinodal point. At this point, the spectrum of the time evolution operator has a gapless and universal band of excitations with a dynamical critical exponent z=1. Surprisingly, the imaginary parts of the eigenvalues E _j(L) are equally spaced, following the rule . Away from the spinodal point, we find two time scales in the spectrum. These results are related to scaling functions for the mean path of the random walker and to first passage times. For the spinodal point, we find universal scaling behavior. A simplified version of the model which can be handled analytically is also presented.     

Phase diagrams and kinetics of phase transitions in protein solutions

The phase behavior of proteins is of interest for fundamental and practical reasons. The nucleation of new phases is one of the last major unresolved problems of nature. The formation of protein condensed phases (crystals, polymers, and other solid aggregates, as well as dense liquids and gels) underlies pathological conditions, plays a crucial role in the biological function of the respective protein, or is an essential part of laboratory and industrial processes. In this review, we focus on phase transitions of proteins in their properly folded state. We first summarize the recently acquired understanding of physical processes underlying the phase diagrams of the protein solutions and the thermodynamics of protein phase transitions. Then we review recent findings on the kinetics of nucleation of dense liquid droplets and crystals. We explore the transition from nucleation to spinodal decomposition for liquid-liquid separation and introduce the new concept of solution-to-crystal spinodal. We review the two-step mechanism of protein crystal nucleation, in which mesoscopic metastable protein clusters serve as precursors to the ordered crystal nuclei. The concepts and mechanisms reviewed here provide powerful tools for control of the nucleation process by varying the solution thermodynamic parameters.