Solid-liquid Phase Boundaries Research Articles

Thermal Properties of Metastable Ices IV and XII: Comparison, Isotope Effects and Relative Stabilities.

Pure samples of H2O (D2O) ice IV and of H2O (D2O) ice XII were prepared by isobaric heating of high-density amorphous ice at a rate of ≈0.5 K min−1 up to ≈175 K and a pressure of 0.81 GPa for ice IV, and at a heating rate of ≈12 K min−1 and a pressure of 1.21 GPa for ice XII. The crystalline phases recovered at 77 K and 1 bar were characterized by X-ray diffraction and differential scanning calorimetry (DSC). X-Ray diffractograms of D2O ice IV show that it transforms directly into cubic ice, and not via some amorphous phase as intermediate. The DSC scans of all four types of crystalline phases recorded on heating revealed three thermal features in this order: a reversible endothermic step, an intense exotherm from the phase transition to cubic ice, and a weak exotherm from the cubic → hexagonal ice phase transition. For H2O (D2O) ice IV the onset and end temperature of the endothermic step (Tonset and Tend) are at 139.8 ± 0.3 and 147.1 ± 0.2 K (at 146.2 ± 0.8 and 150.2 ± 0.8 K) on heating at 30 K min−1, and the increase in heat capacity (ΔCp) is 1.2 ± 0.2 (0.5 ± 0.1) J K−1 mol−1. On heating at 5 K min−1, the extrapolated peak onset and peak minimum temperature (Te and Tmin) of the phase transition to cubic ice is at 148.7 ± 0.3 and 151.1 ± 0.1 K (at 152.7 ± 0.1 and 155.3 ± 0.2 K), and the enthalpy of the phase transition to cubic ice is −938 ± 14 (−986 ± 14) J mol−1. The corresponding values for H2O (D2O) ice XII are for the endothermic step on heating at 30 K min−1: Tonset and Tend at 131.4 ± 0.8 and 139.5 ± 0.7 K (at 138.1 ± 0.4 and 145.0 ± 0.5 K), and ΔCp is 1.5 ± 0.2 (1.4 ± 0.2) J K−1 mol−1. On heating at 5 K min−1, Te and Tmin of the phase transition to cubic ice is at 149.9 ± 0.3 and 153.0 ± 0.2 K (at 154.0 ± 1.2 and 156.9 ± 0.9 K), and the enthalpy of the phase transition to cubic ice is −1233 ± 23 (−1408 ± 8) J mol−1. Therefore, ΔH for the H2O (D2O) ice XII to H2O (D2O) ice IV phase transition is −295 (−422) J mol−1, and ice XII is more metastable than ice IV at ≈150 K and 1 bar. For H2O (D2O) ice XII the endothermic step is separated by a plateau region from the beginning of crystallization, whereas for H2O (D2O) ice IV these two thermal effects overlap because its Tonset is higher by ≈8 K. Tonset and Te are separated by 4.9 K for D2O ice IV and 7.3 K for H2O ice IV. Thus overlap is more pronounced for the former, the endothermic step being cut off by the beginning of crystallization, which is consistent with the lower ΔCp value for D2O ice IV. The endothermic DSC features are interpreted as before for H2O ice XII by Salzmann et al. (Phys. Chem. Chem. Phys., 2003, 5, 3507), in terms of relaxation of the frozen-in proton order–disorder toward equilibrium via proton order → disorder transition. When H2O (D2O) cubic ice is obtained on heating ice IV, its phase transition to hexagonal ice has a ΔH value of −20 ± 7 (−15 ± 5) J mol−1 which is lower than most of the values reported in the literature. We further present new low-frequency Raman spectra of ice XII and show that a peak at 127 cm−1 has its counterpart in the Raman spectra of Chou et al.'s new “High-Pressure Phase of H2O Ice” (Science, 1998, 281, 809). This supports our previous conclusion (J. Phys. Chem. B, 2002, 106, 1) that the Chou phase is in fact ice XII. We then conjecture on the solid–liquid phase boundaries of both ice IV and ice XII, and on a metastable triple point where ice IV, ice XII and liquid water are in metastable equilibrium.

Thermal properties of metastable ices IV and XII: comparison, isotope effects and relative stabilities

Pure samples of H2O (D2O) ice IV and of H2O (D2O) ice XII were prepared by isobaric heating of high-density amorphous ice at a rate of ≈0.5 K min−1 up to ≈175 K and a pressure of 0.81 GPa for ice IV, and at a heating rate of ≈12 K min−1 and a pressure of 1.21 GPa for ice XII. The crystalline phases recovered at 77 K and 1 bar were characterized by X-ray diffraction and differential scanning calorimetry (DSC). X-Ray diffractograms of D2O ice IV show that it transforms directly into cubic ice, and not via some amorphous phase as intermediate. The DSC scans of all four types of crystalline phases recorded on heating revealed three thermal features in this order: a reversible endothermic step, an intense exotherm from the phase transition to cubic ice, and a weak exotherm from the cubic → hexagonal ice phase transition. For H2O (D2O) ice IV the onset and end temperature of the endothermic step (Tonset and Tend) are at 139.8 ± 0.3 and 147.1 ± 0.2 K (at 146.2 ± 0.8 and 150.2 ± 0.8 K) on heating at 30 K min−1, and the increase in heat capacity (ΔCp) is 1.2 ± 0.2 (0.5 ± 0.1) J K−1 mol−1. On heating at 5 K min−1, the extrapolated peak onset and peak minimum temperature (Te and Tmin) of the phase transition to cubic ice is at 148.7 ± 0.3 and 151.1 ± 0.1 K (at 152.7 ± 0.1 and 155.3 ± 0.2 K), and the enthalpy of the phase transition to cubic ice is −938 ± 14 (−986 ± 14) J mol−1. The corresponding values for H2O (D2O) ice XII are for the endothermic step on heating at 30 K min−1: Tonset and Tend at 131.4 ± 0.8 and 139.5 ± 0.7 K (at 138.1 ± 0.4 and 145.0 ± 0.5 K), and ΔCp is 1.5 ± 0.2 (1.4 ± 0.2) J K−1 mol−1. On heating at 5 K min−1, Te and Tmin of the phase transition to cubic ice is at 149.9 ± 0.3 and 153.0 ± 0.2 K (at 154.0 ± 1.2 and 156.9 ± 0.9 K), and the enthalpy of the phase transition to cubic ice is −1233 ± 23 (−1408 ± 8) J mol−1. Therefore, ΔH for the H2O (D2O) ice XII to H2O (D2O) ice IV phase transition is −295 (−422) J mol−1, and ice XII is more metastable than ice IV at ≈150 K and 1 bar. For H2O (D2O) ice XII the endothermic step is separated by a plateau region from the beginning of crystallization, whereas for H2O (D2O) ice IV these two thermal effects overlap because its Tonset is higher by ≈8 K. Tonset and Te are separated by 4.9 K for D2O ice IV and 7.3 K for H2O ice IV. Thus overlap is more pronounced for the former, the endothermic step being cut off by the beginning of crystallization, which is consistent with the lower ΔCp value for D2O ice IV. The endothermic DSC features are interpreted as before for H2O ice XII by Salzmann et al. (Phys. Chem. Chem. Phys., 2003, 5, 3507), in terms of relaxation of the frozen-in proton order–disorder toward equilibrium via proton order → disorder transition. When H2O (D2O) cubic ice is obtained on heating ice IV, its phase transition to hexagonal ice has a ΔH value of −20 ± 7 (−15 ± 5) J mol−1 which is lower than most of the values reported in the literature. We further present new low-frequency Raman spectra of ice XII and show that a peak at 127 cm−1 has its counterpart in the Raman spectra of Chou et al.'s new “High-Pressure Phase of H2O Ice” (Science, 1998, 281, 809). This supports our previous conclusion (J. Phys. Chem. B, 2002, 106, 1) that the Chou phase is in fact ice XII. We then conjecture on the solid–liquid phase boundaries of both ice IV and ice XII, and on a metastable triple point where ice IV, ice XII and liquid water are in metastable equilibrium.

Effect of Size Polydispersity on Melting of Charged ColloidalSystems

We introduce simple prescriptions of the Yukawa potential to describethe effect of size polydispersity and macroion shielding effect incharged colloidal systems. The solid-liquid phase boundaries werepresented with the Lindemann criterion based on molecular dynamicssimulations. Compared with the Robbins-Kremer-Grest simulation results,a deviation of melting line is observed at small λ, which meanslarge macroion screening length. This deviation of phase boundary isqualitatively consistent with the simulation result of the nonlinearPoisson-Boltzmann equation with full many-body interactions. It is foundthat this deviation of the solid-liquid phase behaviour is sensitive tothe screening parameter.

The Anisotropic Free Energy of the Solid-Liquid Phase Boundary in Al

We have performed large-scale molecular dynamics simulations of solid-liquid interfaces in aluminum, in order to calculate their interfacial stiffness and free energy. The anisotropy of these properties, though small, is key for determining the steady-state solutions for solidification in three dimensions. We find that the interfacial free energy, γ(θ), can be well represented by the form γ(θ) = γ0(1 + e cos 4θ, where θ measures the angle relative to the [100] interface, rotating about a [001] direction. We find values of γ0 = 120 ± 6 mJ/m2 and e = 1.3 ± 0.4%, in agreement with previous estimates and current experimental results.

Silicon ingot casting: process development by numerical simulations

Multicrystalline silicon from ingot casting processes has reached a high market share in photovoltaic industry. One reason for this is the increase of the quality of multicrystalline wafers which leads to higher solar cell efficiency. This progress was supported by numerical simulations, namely for the SOLPIN ingot casting process which is used by the Deutsche Solar GmbH for the production of high-quality multicrystalline wafers. In this paper, we give some examples of numerical simulation results, showing the temperature distribution in furnaces and silicon ingots for various process conditions. The influence of lateral and vertical heat flux due to the shape of the liquid–solid phase boundary and the solidification velocity is demonstrated in numerical case studies. As an example for the potential of our process simulations we report about the reduction of the dislocation density in a multicrystalline ingot, which was predicted by simulations and verified by experimental results.

Colloidal dispersions confined in voids of polymer gel matrix

Dispersions of ionic polymer latex (diameter=600nm) consisted of 10 to 1000 particles were confined in spherical voids having diameters of several tens pm formed in a hydrogel (agarose) matrix. The system was constructed first by confining the latex dispersions in giant liposomes, immobilizing the liposomes by using the hydrogel matrix, and then removing the liposome membranes from the matrix. The latex particles inside the voids showed an extensive Brownian motion. This system, as a whole, could be regarded as a model system of one superfine particle. The solid-liquid phase transition was examined both for bulk and the confined colloids, by applying confocal laser scanning microscopy and phase contrast microscopy. The salt concentration was 2μM. In bulk, the solid-liquid phase boundary laid at particle concentration, Cp=1.0-1.5vol%. On the other hand, the confined dispersion took a liquid state even at Cp=2.5vol%. The present observation might correspond to a size effect for the melting point of a superfine particle system.

Investigation of thermosolutally caused convection during Bridgman-growth of BiSbTe 3-mixed crystals at normal and reduced gravity

BiSbTe 3-mixed crystals have been grown at normal and reduced gravity (during the MIR'97-mission) using a Bridgman-configuration of the TITUS facility. The distribution of the components in the melt, and so the homogeneity of the growing crystal, is strongly influenced by the flow in the melt even in the case of weak convection. The flow configuration in the melt especially in front of the solid-liquid phase boundary can be investigated by means of a segregation analysis of the system components and an additional Pb-dopant. The BiSbTe 3-system is because of its hydro-dynamic properties a typical representative of semiconductor melts (low Prandtl number, high Schmidt number) but there are also some special properties relating to the segregationally caused enrichment of the lighter tellurium at the phase boundary and the resulting solutal destabilities. Experimental experiences from segregation analysis have shown that the mass transport in the melt at normal gravity is mainly influenced by convective mixing determined by thermally and solutally caused buoyancy forces. Numerical simulations have been performed for the real experimentally used configurations. These simulations have shown that a strong coupling of thermal and solutal effects exists and have given axial as well as radial segregation profiles being in excellent agreement with the experimental results for the vertical normal gravity grown crystals. For micro gravity conditions a reduction of the flow velocity of more than two orders of magnitude (depending on the micro gravity level and the direction of the residual acceleration) resulting in diffusion controlled component segregation has been predicted. The results of the two micro gravity grown crystals, especially the axial and radial segregation profiles as a sensitive indicator for the flow configuration in front of the phase boundary will be given and discussed in the paper. They will be compared with the results of numerical simulations of the melt flow for the real processing parameters measured during the TITUS growth processes and with experimental as well as numerical results for vertical normal gravity grown reference Samples.

Computer simulation of grain growth by grain boundary migration during liquid phase sintering

From many experiments with mixtures of small and large particles, it can be concluded that during liquid phase sintering, smaller particles partially dissolve and a solid phase precipitates on the larger particles. Therefore, the number of smaller particles decreases due to coarsening. The growth rate can be controlled either by the solid-liquid phase boundary reaction or by diffusion through the liquid phase. This dissolution-reprecipitation process leads to further densification by rearrangement of smaller and larger particles. The microstructure may change either by larger particles growing during the Ostwald ripening process or by shape accommodation. In this study, two-dimensional simulation of grain growth by grain boundary migration based on such a physical and corresponding numerical modeling of liquid phase sintering was considered. The simulation method developed is based on the defined submodels for model system definition, for solution-precipitation, and for grain coarsening process.

Tethered networks in two dimensions: A low-temperature view

Perturbation theory and Monte Carlo simulation are applied to the study of low-temperature properties of a triangular phantom network of harmonic springs with nonzero resting length. We determine the equation of state and elastic moduli in the solid (ordered) phase, as well as the location of the solid-liquid phase boundary. A simple explanation is given for negative thermal expansivity. Agreement between two-loop perturbative results and simulation is fairly good, the largest discrepancies being in the location of the phase boundary. An expansion in inverse area, useful for the ordered phase, is also given.

Phase Behavior of Binary Mixture of Heptaethylene Glycol Decyl Ether and Water: Formation of Phase Compound in Solid Phase

Differential scanning calorimetry (DSC) and Fourier transform infrared spectroscopy (FT-IR) were used to construct and characterize the phase diagram for a binary mixture of heptaethylene glycol decyl ether (C10E7) and water in the temperature range from −60 to 80°C. Plots of the endothermic peak temperatures obtained by DSC measurements against compositions provided eutectic solid–liquid phase boundaries with a eutectic composition of 34 wt% of H2O. On the other hand, heat of fusion per unit weight of the mixture changed discretely at the composition corresponding to the “eutectic” composition. Furthermore, the IR spectra obtained for the mixture in the solid phase were well reproduced as a superposition of those for the mixture of 34 wt% H2O and pure components but were not reproduced by superimposing the spectra obtained for the solid surfactant and ice. These observations indicate that a solid phase compound is formed between C10E7and water with a stoichiometry of 1:14 and that the compound and pure components exist as separate phases, rather than the phases separating into surfactant and ice, which would be expected if the C10E7/water mixture formed a true eutectic mixture system. It is estimated from the composition corresponding to the phase compounds that two molecules of water per oxyethylene unit are bound to hydrophilic polyoxyethylene chain of C10E7to form a hydrated compound.

Metastable liquid-liquid and solid-liquid phase boundaries in polymer-solvent-nonsolvent systems

In general liquid-liquid demixing processes are responsible for the porous morphology of membranes obtained by immersion precipitation. For rapidly crystallizing polymers, solid-liquid demixing processes also generate porous morphologies. In this study, the interference of both phase transitions has been analyzed theoretically using the Flory-Huggins theory for ternary polymer solutions. It is demonstrated that four main thermodynamic and kinetic parameters are important for the structure formation in solution: the thermodynamic driving force for crystallization, the ratio of the molar volumes of the solvent and the nonsolvent, the polymer-solvent interaction parameter, and the rate of crystallization of the polymer compared to the rate of solvent-nonsolvent exchange. An analysis of the relevance of each of these parameters for the membrane morphology is presented.

Inverse-Based reconstruction of internal solid-liquid phase boundaries and associated solid phase temperature fields

This paper describes an inverse technique for imaging multi-dimensional optically opaque phase change boundaries and associated near-melt solid phase temperature fields. The algorithm confines calculations to the solid region immediately surrounding the melt interface, uses a coarse, spatially limited finite element mesh, and is capable of determining phase boundaries in nonlinear, heterogeneous, anisotropic materials. Upwind differencing is introduced to circumvent instabilities associated with large grid Peclet numbers while first order regularization is used to enhance solution stability. Since all a priori unknown boundary heat fluxes are determined by the inverse procedure and ad hoc assumptions are eliminated, the technique is non-problem-specific and portable. Algorithm performance is examined using a simple analog welding experiment. In cases where the fusion boundary is known and fixed in the inverse code, and for initial heat flux guesses that differ by up to four orders of magnitude from the ch...

Pressure effect on phase behavior of binary mixtures of cis-unsaturated fatty acids

The solid-to-liquid phase transition of binary mixtures of cis-monounsaturated fatty acids was investigated as a function of their composition under various pressures up to about 200 MPa by means of a high pressure differential thermal analysis. Two mixture systems were examined; one is the mixture composed of oleic acid (OA; cis-9-octadecenoic acid) and palmitoleic acid (POA; cis-9-hexadecenoic acid), and the other is that composed of asclepic acid (APA; cis-11-octadecenoic acid) and POA. The components in the former mixture differ in the length of ω-chain (the aliphatic chain segment between the double bond and methyl end group) by two methylene units, whereas those in the latter mixture differ in the length of Δ-chain (the chain segment between double bond and carboxyl group) by two methylene units. In both mixtures, the temperature of solid-liquid phase boundary, i.e. solidus and liquidus lines, was drastically increased by the increase in pressure. On the other hand, the shape of the phase boundary remained almost unaltered regardless of the pressure. The characteristic features in solid phase of these fatty acid mixtures, i.e. the molecular compound formation for OA/POA mixture and the highly restricted mutual miscibility for APA/POA mixture, are retained even under high pressure. This indicates that the intermolecular interaction of cis-monounsaturated fatty acids responsible for determining the phase behavior of binary mixture systems is rather insensitive to pressure, at least in the range up to 200 MPa.

Inverse finite element reduced mesh method for predicting multi-dimensional phase change boundaries and nonlinear solid phase heat transfer

An inverse finite element method is developed for simultaneous solution of multi-dimensional solid-liquid phase boundaries and associated three-dimensional solid phase temperature fields. The technique, applicable to quasisteady phase change problems, fixes element nodes at known temperature locations and uses a coarse, spatially limited mesh. This approach is designed to: (1) reduce direct and overall solution costs, (2) eliminate iterative direct solutions associated with temperature dependent thermophysical properties, (3) limit calculations to the heat affected zone and (4) eliminate ad hoc assumptions concerning the boundary heat flux distribution. The inverse algorithm couples a nonlinear solid phase conduction solver with conjugate gradient minimization. First-order regularization and upwind differencing are implemented to improve solution smoothness and stability and an analog welding experiment is used to investigate the technique's capabilities.

Finite computational cell-size effects and the nature of the melting transition of Kr adlayers deposited on graphite.

The recently developed histogram Monte Carlo (MC) method is employed in conjunction with a (N,\ensuremath{\rho},T) MC ensemble with periodic boundary conditions to study monolayer and submonolayer melting transitions of a krypton adlayer physisorbed on a graphite substrate. The simulation results are found to depend on the size of the model system. The number of atoms in the MC cell are 900, 400, 324, 289, and 100. The calculated coverage-temperature (\ensuremath{\rho},T) phase diagram exhibits three distinct regions: an upper section (0.7\ensuremath{\lesssim}\ensuremath{\rho}\ensuremath{\le}1) in which the melting temperature ${\mathit{T}}_{\mathit{m}}$ is very sensitive to \ensuremath{\rho}, a steep intermediate region (0.25\ensuremath{\lesssim}\ensuremath{\rho}\ensuremath{\lesssim}0.7) where ${\mathit{T}}_{\mathit{m}}$\ensuremath{\approxeq}85 K and is relatively insensitive to \ensuremath{\rho}, and a lower part (0\ensuremath{\lesssim}0.25) in which sensitivity to the density resumes. The N=400 solid-fluid boundary agrees well with the experimental phase diagram, and investigations at N=900 confirm that the N\ensuremath{\gtrsim}=400 results are closely approaching those of the thermodynamic limit; the N=400 simulation is taken to be a reasonable model of the krypton-graphite system in the \ensuremath{\rho}\ensuremath{\le}1 regime. Departures from such large-N behavior with decreasing N are understood by applying artificial stabilization arguments in the upper and intermediate regimes of the solid-liquid phase boundary, and using finite-patch size-effect arguments in the lower regime. Examination of a series of atomic configurations shows that the three separate parts of the phase boundary correspond to different types of melting: vacancy-mediated melting in the upper wing, the melting of a connected atomic network in the intermediate section, and individual patch melting on the lower portion where sensitivity of ${\mathit{T}}_{\mathit{m}}$ with \ensuremath{\rho} resumes.

Ab initio molecular dynamics study of first-order phase transitions: melting of silicon.

We present a scheme to compute the thermodynamic properties and the phase stability of materials based on parameter-free microscopic quantum theory. Taking silicon as an example we show that properties like the specific entropy, the specific volume, or the heat capacity of a solid and a liquid can be calculated accurately. In particular, we can locate the solid-liquid phase boundary and compute how thermodynamic properties change upon melting. This greatly extends the range of first-principles predictions of materials properties.

Solid-Liquid Equilibria for Binary Mixtures Containing Cresols, Ethylenediamine, and Anisole

Solid-liquid equilibrium phase boundaries were determined with a solid-disappearance method for binary systems composed of m-cresol, p-cresol, ethylenediamine, and anisole. Among these mixtures, intermolecular complexes formed in ethylenediamine + m-cresol and ethylenediamine + p-cresol and a single eutectic point was exhibited on the liquidus line of anisole + m-cresol and anisole + p-cresol, respectively. To correlate the solid-liquid equilibrium data with theoretical models, the heat of fusion and liquid molar volume were also measured for each constituent. The phase-equilibrium calculations showed that the Wilson model could reproduce the liquidus lines for the systems without forming congruently melting compounds, and the ideal-chemical model satisfactorily correlated the equilibrium data for the systems having aggregate formation.

Simulation of weld pool flow and capillary interface shapes associated with the plasma arc welding process

A three-dimensional finite element model of the plasma arc welding process is presented. The model allows calculation of the weld pool's approximate capillary and solid-liquid phase boundaries, the weld pool's three-dimensional flow and temperature fields, and the solid phase temperature distribution. Taking into account thermocapillary, jet shear, and buoyancy forces within the pool, it is found that under moderate Reynolds number conditions pool flow is driven primarily by thermocapillary and jet shear forces.

Simulations of shear-induced melting and ordering.

We describe the effect of shear on the solid-liquid phase boundary of particles that interact via a screened Coulomb potential. Both fcc and bcc phases shear through layer-over-layer sliding. As the shear rate γ increases from zero, the degree of disorder in the layers increases and the stacking sequence changes. A first-order shear-melting transition occurs if the temperature is greater than about half of the equilibrium melting temperature T m eq . Near T m eq the transition rate is proportional to T m eq -T. As γ increases further, shear becomes an ordering influence and a reentrant solid phase is observed

Three-dimensional simulation of the plasma arc welding process

A finite element-based simulation of the plasma arc welding process is presented. The simulation determines the weld pool's three-dimensional capillary surface shape, the approximate solid-liquid phase boundary, and calculates the pool's three-dimensional flow and temperature fields. The simulation is first used to examine the effect of ambient temperature and plate speed on pool shape. Pool flow is then studied. The flow's qualitative features are primarily determined by jet shear and thermocapillarity while buoyancy is of secondary importance.