Solid-liquid Phase Coexistence Research Articles

Transition of a 2D crystal to a non-equilibrium two-phase coexistence state

In this paper, we present experimental observation of the transition of a 2D dust crystal to a non-equilibrium solid–liquid phase coexistence state. The experiments have been carried out in an L-shaped dusty plasma experimental device in a DC glow discharge argon plasma environment. Initially, a monolayer crystalline structure is formed, which is later transformed to a two-phase coexistence state using the background neutral pressure as a control parameter. Self-excited horizontal oscillations are found in the center of the monolayer prior to the appearance of the coexistence state. It is observed that a molten center coexists with a solid periphery. Various structural, thermodynamic, and dynamical quantities are used to characterize the phase state. The surface tension at the solid–liquid circular interface is also determined. A detailed parametric study is made to delineate the existence region of such a state. It is found that melting caused at the core is due to the onset of a localized Schweigert instability in the presence of a few stray particles beneath the top layer in that region.

Rigid Procedure to Calculate the Melting Point of Metal Using the Solid-Liquid Phase (Coexistence) Method

Melting point, particularly metal, is one of the important data for many applications. For developing new materials, adequate theories for melting point are very crucial. The determination of melting point using the popular phase-change curve method is very easy but usually overestimate. In current work, we determine the melting point of a pure metal (iron) using the method of solid-liquid phase coexistence. For this goal, molecular dynamics simulation was applied to obtain data of trajectories of atoms. Simulation (LAMMPS) and data analysis (OVITO) procedures are strictly applied to obtain the accurate melting point of iron based on the obtained trajectories data. For initial structure design of simulation, we used the ATOMSK program. The melting point of iron obtained using the phase change curve (PCC) method is about 2750 K < TPCC < 3250 K and using the coexistence phase (CP) method is TCP = 2325 K. A more accurate calculation needs to include defects factor in the simulated material and calculation. In this research we use the Morse potential to represent all of the atomic interaction among atoms of Fe material.

Crystal structure and grain formation mechanism of bismuth–indium particles generated by ultrasonic irradiation

The miniaturization and high functionalization of electronic devices are driving the micronization of electronic components. In order to effectively microjoin electronic components, it is necessary to micronize the particles used in the soldering paste. In this study, we utilized an ultrasonic irradiation method to produce fine metal particles, and examined the influence of ultrasonic irradiation on the solidification process of the soldering materials. Bismuth–indium (Bi–45wt.%In) solder melted in a high-boiling-point solvent was exposed to ultrasonic irradiation to form droplets. By irradiating these droplets with ultrasonic waves during solidification, the amount of BiIn2 in the solid solder composition increased, while that of Bi3In5 decreased. In addition, submicron-sized agglomerations consisting of numerous small particles (~ 30 nm in diameter) were detected in the solvent; the In content of these clusters was ≥ 70 wt.%. It is thought that the amount of Bi3In5 generated decreased due to cavitation during solid–liquid phase coexistence, which caused the liquid-phase components with high In concentrations to separate from the droplets.

Thermodynamic relationships for homogeneous crystalline and liquid phases in the phase-field crystal model

We present thermodynamic relationships between the free energy density of the phase-field crystal (PFC) model and thermodynamic state variables that correspond to the model input parameters: temperature, lattice spacing, and an average value of the PFC order parameter, n¯. These relationships, derived for homogeneous phases under hydrostatic and nonhydrostatic stresses, are based on the thermodynamic formalism for crystalline solids of Larché and Cahn (1973). These relationships provide clear thermodynamic descriptions of the physical processes that are associated with changing PFC input parameters, and demonstrate that a crystalline phase from the PFC model can be considered a network of lattices occupied by atoms and vacancies, as described by Larché and Cahn. The equilibrium conditions between a crystalline phase and a liquid phase are imposed on the thermodynamic relationships for the PFC model to obtain a procedure for determining solid-liquid phase coexistence. The resulting procedure is found to be in agreement with the method commonly used in the PFC community. Finally, we apply the procedure to an eighth-order-fit (EOF) PFC model that has been parameterized to body-centered-cubic (bcc) iron (Jaatinen et al., 2009) to verify the applicability of the procedure. We demonstrate that the EOF-PFC model parameterization does not predict stable bcc structures with positive vacancy densities. This result suggests an alternative parameterization of the PFC model which requires the primary peak position of the two-body direct correlation function to shift as a function of n¯.

Slow Relaxation of Shape and Orientational Texture in Membrane Gel Domains.

Gel domains in lipid bilayers are structurally more complex than fluid domains. Growth dynamics can lead to noncircular domains with a heterogeneous orientational texture. Most model membrane studies involving gel domain morphology and lateral organization assume the domains to be static. Here we show that rosette shaped gel domains, with heterogeneous orientational texture and a central topological defect, after early stage growth, undergo slow relaxation. On a time scale of days to weeks domains converge to circular shapes and approach uniform texture. 1,2-Dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) enriched gel domains are grown by cooling 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC):DPPC bilayers into the solid-liquid phase coexistence region and are visualized with fluorescence microscopy. The relaxation of individual domains is quantified through image analysis of time-lapse image series. We find a shape relaxation mechanism which is inconsistent with Ostwald ripening and coalescence as observed in membrane systems with coexisting liquid phases. Moreover, domain texture changes in parallel with the changes in domain shape, and selective melting and growth of particular subdomains cause the texture to become more uniform. We propose a relaxation mechanism based on relocation of lipids from high-energy lattice positions, through evaporation-condensation and edge diffusion, to low-energy positions. The relaxation process is modified significantly by binding Shiga toxin, a bacterial toxin from Shigella dysenteriae, to the membrane surface. Binding alters the equilibrium shape of the gel domains from circular to eroded rosettes with disjointed subdomains. This observation may be explained by edge diffusion while evaporation-condensation is restricted, and it provides further support for the proposed overall relaxation mechanism.

Quantitative NMR investigation on the low-temperature dissolution mechanism of chitin in NaOH/urea aqueous solution

The low-temperature dissolution mechanism of chitin in NaOH/urea aqueous solution has not been well established yet, especially at a temperature that lowers the crystallization temperature of both NaOH and urea. Using multiple nuclei (H-1, N-15 and Na-23) nuclear magnetic resonance (NMR) methods, we find that the ternary NaOH/urea/D2O system, different from the fully frozen binary NaOH-D2O system, exhibits solid-liquid phase coexistence below -40 degrees C, and the residual liquid phase consists of certain concentrations of NaOH (10 wt%), urea (13 wt%) and D2O at -40 degrees C. Our NMR results further demonstrate that chitin dissolves in the residual liquid phase (containing 5-10 wt% NaOH and 8-12 wt% urea) at low temperatures (-40 and -70 degrees C). An important role of urea is enhancing the low-temperature stability of NaOH aqueous solutions and then increasing the dissolution temperature range of chitin, thus providing an essential low-temperature liquid environment for chitin dissolution.

An empirical extension for a generalized cubic equation of state, applied to a pure substance with small molecules

An equation of state to describe the complete phase diagram of a pure substance is developed. The equation of state is constructed by using a generic cubic equation plus the term −fT/(v−e)10. This term (where f>0 and e are adjustable parameters) is the attractive contribution of the solid phase. It has a volume short-range contribution, and extends the traditional use of a cubic equation, incorporating the thermodynamics description of the solid phase, which allows to represent the experimental triple point, the solid–liquid, and the solid–vapor phase transitions, together with the traditional description of the liquid–vapor transition. For the solid–liquid phase coexistence at any temperature, molar volume predictions of the solid phase define a curve which never connects to its corresponding liquid phase curve. This feature is in agreement with experimental evidences that seem to not accept the existence of a solid–liquid critical point. Finally, calculations for the complete phase diagram for carbon dioxide and argon were carried out in order to show the capabilities and features of the equation of state, and these results were also compared with other predictions from the literature.

Pressure dependence of confined liquid behavior subjected to boundary-driven shear

Non-equilibrium molecular dynamics simulations of boundary-driven sheared Lennard-Jones liquids at variable pressure up to 5 GPa (for argon) reveal a rich out-of-equilibrium phase behavior with a strong degree of shear localization. At the lowest apparent shear rate considered (wall speed ~1 m s(-1)) the confined region is an homogeneously sheared solid (S) with no slip at the walls. This transforms at higher shear rates to a non-flowing plug with slip at the walls, referred to as the plug slip (PS) state. At higher shear rate a central localized (CL) state formed in which the shear gradient was localized in the center of the film, with the rest of the confined sample in a crystalline state commensurate with the wall lattice. The central zone liquidlike region increased in width with shear rate. A continuous rounded temperature profile across the whole system reflects strong dynamical coupling between the wall and confined region. The temperature rise in the confined film is consistent with the Brinkman number. The transition from the PS to CL states typically occurred at a wall speed near where the shear stress approached a critical value of ~3% of the shear modulus, and also near the peak in the traction coefficient, μ. The peak traction coefficient values computed, ~0.12-0.14 at 1000 MPa agree with those found for traction fluids and occur when the confined liquid is in the PS and CL states. At low wall speeds slip can occur at one wall and stick at the other. Poorly wetting liquids manifest long-lived asymmetries in the confined liquid properties across the system, and a shift in solid-liquid phase co-existence to higher shear rates. A non-equilibrium phase diagram based on these results is proposed. The good agreement of the tribological response of the Lennard-Jones fluid with that of more complicated molecular systems suggests that a corresponding states scaling of the tribological behavior could apply.

Effect of potential truncations and shifts on the solid-liquid phase coexistence of Lennard-Jones fluids

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.

Superheating in metal nanoparticles with non-melting surfaces

We construct microcanonical caloric curves for aluminium nanoparticles with non-melting surface facets and diameters of up to 11 nm using molecular dynamics simulations. We find that fcc aluminium particles can be superheated above the bulk melting temperature, but only for a finite range of particle sizes i.e. diameters between 5–9 nm. We also observe a critical particle size where solid-liquid phase coexistence becomes stable, and a second larger critical size where premelted (100) facets can coexist with solid (111) facets. Ultimately, it is the premelting of the (100) facets that appears to limit the superheating effect in these particles.

Superheating and Solid-Liquid Phase Coexistence in Nanoparticles with Nonmelting Surfaces

We present a phenomenological model of melting in nanoparticles with facets that are only partially wet by their liquid phase. We show that in this model, as the solid nanoparticle seeks to avoid coexistence with the liquid, the microcanonical melting temperature can exceed the bulk melting point and that the onset of coexistence is a first-order transition. We show that these results are consistent with molecular dynamics simulations of aluminum nanoparticles which remain solid above the bulk melting temperature.

Solid-liquid phase coexistence and structural transitions in palladium clusters

We use molecular dynamics with an embedded atom potential to study the behavior of palladium nanoclusters near the melting point in the microcanonical ensemble. We see transitions from both fcc and decahedral ground-state structures to icosahedral structures prior to melting over a range of cluster sizes. In all cases this transition occurs during solid-liquid phase coexistence and the mechanism for the transition appears to be fluctuations in the molten fraction of the cluster and subsequent recrystallization into the icosahedral structure.

Transition from Icosahedral to Decahedral Structure in a Coexisting Solid-Liquid Nickel Cluster

We have used molecular dynamics simulations to construct a microcanonical caloric curve for a 1415 atom Ni icosahedron. Prior to melting, the Ni cluster exhibits static solid-liquid phase coexistence. Initially, a partial icosahedral structure coexists with a partially wetting melt. However, at energies very close to the melting point the icosahedral structure is replaced by a truncated decahedral structure that is almost fully wet by the melt. This structure remains until the cluster fully melts. The transition appears to be driven by a preference for the melt to wet the decahedral structure.

Time autocorrelation function analysis of master equation and its application to atomic clusters

We derive the energy fluctuation Delta(2)E, and the time autocorrelation kappa(tau) and its Fourier transformation--the fluctuation spectra S(omega)--of the master-equation transition matrix. The contribution from each eigenmode of the transition matrix to these fluctuation quantities reveals the relevant importance of the individual mode in the relaxation processes. The time scales associated with these relaxation processes are determined by the corresponding eigenvalues. Unlike traditional time evolution analysis, the autocorrelation function and fluctuation spectra analysis does not involve an arbitrary initial population. It is also more suitable for analyzing the underlying dynamic, kinetic behavior near the equilibrium and the behavior of the long-time-scale rare events. We utilize our technique to analyze the solid-liquid phase coexistence of the 13-atom Morse cluster and the fcc-to-icosahedral structure transition of the 38-atom Lennard-Jones cluster. For the processes studied, the fluctuation spectra from the master equation simplify the analysis of the transition matrix, and the important relaxation modes are easily extracted.

Solid-liquid phase coexistence of the Lennard-Jones system through phase-switch Monte Carlo simulation.

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.

Equilibrium and nonequilibrium molecular dynamics methods for determining solid–liquid phase coexistence at equilibrium

The solid–liquid equilibrium phase transition of a one-component Lennard-Jones system is determined by equilibrium and nonequilibrium molecular dynamics simulation methods. One method uses the observation that the scaling exponent of the pressure or energy of a shearing Lennard-Jones liquid is approximately 1 at the solid phase. This enables us to locate the density of the coexisting solid phase. The coexisting liquid phase density is then obtained by constructing a tie line between the coexisting solid phase point and the liquid phase curve. Alternatively, the coexisting liquid phase density can be efficiently obtained by observing the change in pressure as a function of strain rate and density. The coexisting solid phase density can be then obtained from a tie line from the liquid curve to the solid curve. These calculations are the first reported use of combined equilibrium and nonequilibrium molecular dynamics methods for phase coexistence at equilibrium. Our results are in very good agreement with those obtained by alternative simulation methods for phase equilibria.

Melting of 55-atom Morse clusters

Canonical ensemble Monte Carlo simulations of 55-atom Morse clusters are used to study the effect of the range of the pair interaction on the cluster melting transition. Several different structural indicators are employed to monitor the solid–liquid transition and to locate the melting and freezing temperatures. The behavior of Landau free energy curves in the solid–liquid phase coexistence regime is correlated with the distribution of inherent minima sampled by the system. The melting transition temperatures, the width of the phase coexistence regime, and the internal energy change on melting are shown to increase with decreasing range of the pair interaction, which parallels the behavior seen in bulk Morse systems. Unlike in the case of bulk melting, cluster melting falls into three distinct categories based on the range of the pair interaction: (i) a rigidity transition in long-range systems with a low density of metastable states, (ii) the cluster analogue of bulk melting where the system transits from the basin of an ordered global minima into a set of metastable, amorphous packing minima, and (iii) transition from a set of defected solid-like minima into a set of amorphous packing minima.