Gibbs Thomson Coefficient Research Articles

Solid–liquid interfacial energy of solid succinonitrile in equilibrium with succinonitrile-1,4-diiodobenzene eutectic liquid

The grain boundary groove shapes for equilibrated solid SCN in equilibrium with the SCN-0.5 mol% DIB eutectic liquid have been directly observed by using a horizontal linear temperature gradient apparatus. The ratio of thermal conductivity of equilibrated liquid to thermal conductivity of solid SCN has also been determined to be 0.90. From the observed grain boundary groove shapes and measured thermal conductivity ratio, the Gibbs–Thomson coefficient (Г) of solid SCN has been determined to be (5.46 ± 0.55) × 10−8 K m. The solid–liquid interfacial energy (σ SL) and the grain boundary energy of solid SCN have also been determined to be (8.25 ± 1.24) × 10−3 J m−2 and (15.84 ± 2.53) × 10−3 J m−2, respectively.

The solid–liquid interfacial energy for solid Zn solution at the eutectic Zn–Sn–Mg ternary alloy

Abstract The Gibbs–Thomson coefficient, Γ , the effective entropy change, Δ S f , the solid–liquid interfacial energy, σ SL , and the grain boundary energy, σ GB , for solid Zn solution at the eutectic Zn–Sn–Mg ternary alloy have been calculated using the grain boundary groove method with Bridgman-type directional solidification apparatus.

A Method to Estimate Interfacial Energy between Eutectic Solid Phases from the Results of Eutectic Solidification Experiments

In solidification experiments of binary eutectic alloys, the eutectic spacing and undercooling are measured as function of the solidification rate. A new theoretical relationship is derived herewith between the Gibbs-Thomson coefficient and the above mentioned values for both lamellar and rod type eutectics. This new equation allows the estimation of the interfacial energy between eutectic solid phases. For the Sn/Pb eutectics the value of about 0.15 N/m is found in this paper using experimental literature data on eutectic solidification experiments. This is consistent with an earlier value obtained by a more complex experimental method of Gündüz and Hunt.

Experimentally-aided Simulation of Directional Solidification of Steel

Dendritic microstructures are most dominant patterns in solidified alloys. The microstructural features of these structures control the segregation profiles of solute elements in the interdendritic regions, thus determining the mechanical properties of cast structures. In this study, a 2D model of solid/liquid interface instability in a low carbon steel was introduced, using the multi-phase-field software code MICRESS® combined with an in-situ study of solidification in a laser-scanning confocal microscope. The use of a moving-frame boundary condition and a linear temperature gradient within the simulation allows further optimization of the solidification studies in the laser-scanning confocal microscope. By analysing the shape of the delta-ferrite grain boundary at the solid/liquid interface, in-situ and at temperature, it was possible to experimentally determine the Gibbs-Thomson coefficient and the solid/liquid interfacial energy of the alloy. The interface mobility of the solid/liquid interface was calibrated in the model so as to reproduce the experimentally measured interface velocity at the onset of interface instability. The proposed model was used to describe the morphological transitions from planar to cellular to dendritic modes during solidification and solute segregation under a variety of processing conditions such as cooling rate and temperature gradient. The importance of this approach is that the verified model has been used to extend the prediction of microstructural development to cooling rates well beyond what can be achieved experimentally and into the regime pertinent to high-speed continuous casting. Significant microstructural differences that arise as a result of varying processing conditions are discussed.

The Experimental Determination of Interfacial Energies for Solid Cd in Equilibrium with Sn-Cd-Sb Liquid

The equilibrated grain boundary groove shapes of solid Cd in equilibrium with Sn-Cd-Sb liquid were observed from a quenched sample by using a radial heat flow apparatus. The Gibbs–Thomson coefficient, solid–liquid interfacial energy, and grain boundary energy of the solid Cd were determined from the observed grain boundary groove shapes. The thermal conductivity of the eutectic solid phase for Sn-35.80 at. pct Cd-6.71 at. pct Sb alloy and the thermal conductivity ratio of the liquid phase to the solid phase for Sn-35.80 at. pct Cd-6.71 at. pct Sb alloy at eutectic temperature were also measured with a radial heat flow apparatus and a Bridgman-type growth apparatus, respectively.

Lamellar coupled growth in the neopentylglycol-(D)camphor eutectic

Lamellar eutectic growth was investigated in the transparent organic alloy neopentylglycol-(D)camphor of eutectic composition (NPG-45.3wt% DC) using bulk (3D) and thin (2D) samples. Two types of eutectic grains were observed in the polycrystalline samples, either with lamellae well aligned to the direction of solidification or inclined at an angle of 21.5±1.5°. The well aligned grains were used for determining lamellar spacing as function of growth velocity V and temperature gradient G. Based on these data the Jackson–Hunt constant was evaluated to be KJH=1.60±0.15μm3s−1. For low growth velocity experiments the contact angles for (DC) and (NPG) lamellae at eutectic triple junctions were also evaluated, being θ(DC)=50.9±4.1° and θ(NPG)=41.8±4.7°, respectively. Using these values, as well as phase diagram data and the Gibbs–Thomson coefficients, the chemical coefficient of diffusion of (D)camphor in the eutectic liquid at eutectic temperature 53°C was estimated to be DL=97±15µm2s−1.

Solid–liquid interfacial energy of solid succinonitrile solution in equilibrium with succinonitrile–neopentylglycol eutectic liquid

The grain boundary groove shapes for solid succinonitrile solution (SCN–5mole% NPG) in equilibrium with the succinonitrile (SCN)–neopentylglycol (NPG) eutectic liquid (SCN–9.55mole% NPG) have been directly observed by using a horizontal linear temperature gradient apparatus at 317.1K equilibrium temperature. From the observed grain boundary groove shapes, the Gibbs–Thomson coefficient (Г) and solid-liquid interfacial energy (σSL) of solid SCN solution have been determined to be (5.43±0.50)×10−8Km and (8.09±1.21)×10−3Jm−2, respectively. The grain boundary energy of solid SCN solution has been determined to be (14.22±2.28)×10−3Jm−2 from the observed grain boundary groove shapes. The thermal conductivity for SCN–9.55mole% NPG eutectic solid phase and the thermal conductivity ratio of eutectic liquid phase to eutectic solid phase at the melting temperature have also been measured with a radial heat flow apparatus and Bridgman type growth apparatus, respectively.

Solid–Liquid Interfacial Energy of Solid Neopentylglycol Solution in Equilibrium with Neopentylglycol–Aminomethylpropanediol Eutectic Liquid

The grain boundary groove shapes for solid neopentylglycol solution (NPG-40 mol pct AMPD) in equilibrium with the neopentylglycol (NPG)–aminomethylpropanediol (AMPD) eutectic liquid (NPG-42.2 mol pct AMPD) have been directly observed using a horizontal linear temperature gradient apparatus. From the observed grain boundary groove shapes, the Gibbs–Thomson coefficient (Г) and solid–liquid interfacial energy (σSL) of solid NPG solution have been determined to be (7.4 ± 0.7) × 10−8 K m and (6.4 ± 1.0) × 10−3 J m−2, respectively. The grain boundary energy of solid NPG solution has been determined to be (12.5 ± 1.0) × 10−3 J m−2 from the observed grain boundary groove shapes. The ratio of thermal conductivity of equilibrated eutectic liquid to thermal conductivity of solid NPG solution has also been determined to be 0.48.

Interface energy of solid cadmium (Cd) phase in the Cd-Pb (Cadmium-Lead) binary alloy

The grain boundary groove shapes for the Cadmium (Cd) phase in equilibrium with the Lead (Pb)-Cd eutectic liquid were obtained with radial heat flow apparatus. From the obtained grain boundary groove shapes, the Gibbs-Thomson coefficient, solid-liquid and grain boundary energy for the Cd phase in equilibrium with the Pb-Cd eutectic liquid were determined to be (8.35 ± 0.41) x 10-8 Km, (128.00 ± 12.8) × 10-3 Jm-2 and (239.33 ± 26.32) × 10−3 Jm-2, respectively. The thermal conductivities of the solid and liquid phases at the eutectic composition and temperature were also measured by using radial heat flow and Bridgman-type directional growth apparatus, respectively. Key words: Crystal growth, phase equilibria, thermal conductivity, Gibbs-Thomson coefficient, grain boundary energy.

The measurement of interfacial energies for solid Sn solution in equilibrium with the Sn–Bi–Ag liquid

The equilibrated grain boundary groove shapes of solid Sn solution in equilibrium with Sn–Bi–Ag liquid were observed from a quenched sample by using a radial heat flow apparatus. The Gibbs–Thomson coefficient, solid–liquid interfacial energy, and grain boundary energy of the solid Sn solution were determined from the observed grain boundary groove shapes. The thermal conductivity of the solid phase for Sn-10 at.%Bi-2 at.%Ag alloy and the thermal conductivity ratio of the liquid phase to the solid phase for Sn-10 at.%Bi-2 at.%Ag alloy at the melting temperature were also measured with a radial heat flow apparatus and a Bridgman-type growth apparatus, respectively. A comparison of present results for solid Sn solution in the Sn–10 at.%Bi–2 at.%Ag alloy with the results obtained in previous works for similar solid Sn in equilibrium with different binary or ternary liquid was made. From the comparison, it can be concluded that for solid Sn solution in equilibrium with different liquid, the Gibbs–Thomson coefficient seems to be constant and does not depend on the composition of liquid but solid–liquid interfacial energy changes little bit with composition of liquid at a constant temperature.

Solid–liquid interfacial energy of solid aminomethylpropanediol solution in equilibrium with aminomethylpropanediol–neopentylglycol–D camphor liquid

The grain boundary groove shapes for equilibrated solid aminomethylpropanediol solution, BCC (AMPD–42.8mol% NPG–3mol% DC) in equilibrium with the liquid (AMPD–7mol% NPG-3mol% DC) have been directly observed by using a horizontal linear temperature gradient apparatus. From the observed grain boundary groove shapes, the Gibbs–Thomson coefficient (Г), solid–liquid interfacial energy (σSL) of solid AMPD solution have been determined to be (5.20±0.52)×10−8Km and (8.89±1.33)×10−3Jm−2, respectively. The grain boundary energy of solid AMPD solution has been determined to be (17.12±2.73)×10−3Jm−2 from the observed grain boundary groove shapes. The ratio of thermal conductivity of equilibrated liquid to thermal conductivity of solid AMPD solution has also been determined to be 0.35.

Calculation of crystal-melt interfacial free energy of Cu by molecular dynamics simulation

The growing and melting of crystal nuclei in liquid Cu are investigated by molecular dynamics simulation. The critical undercooling is proportional to the reciprocle of the nanoparticle radius. The Gibbs-Thomson coefficient of Cu is 1.12× 10-7 K·m. Then the crystal-melt interfacial free energy of Cu is 0.146 J/m2 estimated from the Gibbs-Thomson coefficient, and the Turnbull coefficient of Cu is 0.416. All the values by simulation are consistent with the experimental results of Turnbull.

Calculation of crystal-melt interfacial free energies of fcc metals

Crystal-melt interfacial free energies of fcc metals were calculated by molecular dynamics simulation. Spherical crystal nucleus was embedded in the undercooled melt to create an ideal model of homogeneous nucleation. Growth and melting behaviors of the nucleus were examined. There was a critical temperature dividing growth and melting of the nucleus. The critical undercooling, as the difference between the critical temperature and the bulk melting point, was proportional to the inverse of the nucleus radius, which is regarded as the Gibbs–Thomson effect. The Gibbs–Thomson coefficient was determined from the relation between the critical undercooling and the nucleus radius. The crystal-melt interfacial free energies, which were estimated from the Gibbs–Thomson coefficients, were consistent with the experimental results of Turnbull.

Solid–liquid interfacial energy of neopentylglycol solid solution in equilibrium with succinonitrile-neopentylglycol-aminomethylpropanediol liquid

The grain boundary groove shapes for equilibrated solid neopentylglycol (NPG) solution (NPG–26mol% AMPD–4 mol% SCN) in equilibrium with the succinonitrile (SCN)–neopentylglycol (NPG)–aminomethylpropanediol (AMPD) liquid (NPG–45mol% SCN–2 .9mol% AMPD) have been directly observed by using a horizontal linear temperature gradient apparatus. From the observed grain boundary groove shapes, the Gibbs–Thomson coefficient (Γ) and solid–liquid interfacial energy (σSL) of solid NPG solution have been determined to be (7.8±0.8)×10−8Km and (8.1±1.2)×10−3Jm−2, respectively. The grain boundary energy of solid NPG solution has been determined to be (15.8±2.5)×10−3Jm−2 from the observed grain boundary groove shapes. The ratio of thermal conductivity of equilibrated liquid to thermal conductivity of solid NPG solution has also been determined to be 0.42.

The Application of Computational Thermodynamics for the Determination of Surface Tension and Gibbs-Thomson Coefficient of Aluminum Ternary Alloys

Casting simulation requires high quality information about the thermophysical properties of the alloy, but the number of alloys for which such information is available is limited. In this paper, a solution of Butler’s formulation for surface tension is presented for Al-Cu-Si ternary alloys and consequently, permitting the Gibbs-Thomson coefficient to be determined. The importance of the Gibbs-Thomson coefficient is related to the reliability of predictions furnished by predictive microstructure growth models and of numerical computations of solidification thermal variables, which will be strongly dependent on the values of the thermophysical properties adopted in the calculations. The Gibbs-Thomson coefficient for ternary alloys is seldom reported in the literature. A numerical model based on Powell hybrid algorithm and on a finite difference Jacobian approximation was coupled with a ThermoCalc TCAPI interface to assess the excess Gibbs energy of the liquid phase, permitting the surface tension and Gibbs-Thomson coefficient for Al-Cu-Si hypoeutectic alloys to be calculated. The computed results are presented as a function of the alloy composition.

Experimental determination of interfacial energy for solid Zn solution in the Sn-Zn eutectic system

The grain boundary groove shapes for Zn solid solution in equilibrium with Sn-Zn eutectic liquid were observed with a radial heat flow apparatus. From the observed grain boundary groove shapes, the Gibbs-Thomson coefficient, the solid-liquid and the grain boundary energy for the Zn solid solution in equilibrium with Sn-Zn eutectic liquid were determined to be (2.32 ± 0.13)×10−8 Km, (120.87 ± 13.29)×10−3 J.m−2 and (194.76 ± 23.37)×10−3 J.m−2, respectively. The termal conductivity of the eutectic Sn-9 wt% Zn solid solution, κS, was obtained as 74.74 W/Km by using a radial heat flow apparatus. The thermal conductivity ratio of the eutectic liquid to the eutectic solid, R = κL/κS was found to be 0.58 with a Bridgman-type directional growth apparatus. Thus, the value of the thermal conductivity of eutectic Sn-9 wt% Zn liquid solution, κL, was obtained as 43.82 W/Km.

Solid–liquid interfacial energy of neopentylglycol solid solution in equilibrium with neopentylglycol–(D) camphor eutectic liquid

The grain boundary groove shapes for equilibrated solid neopentylglycol (NPG) solution (NPG–3 mol% D-camphor) in equilibrium with the NPG–DC eutectic liquid (NPG–36.1 mol% D-camphor) have been directly observed using a horizontal linear temperature gradient apparatus. From the observed grain boundary groove shapes, the Gibbs–Thomson coefficient ( Г), solid–liquid interfacial energy ( σ SL) of NPG solid solution have been determined to be (7.5±0.7)×10 −8 K m and (8.1±1.2)×10 −3 J m −2, respectively. The Gibbs–Thomson coefficient versus T m Ω 1/3, where Ω is the volume per atom was also plotted by linear regression for some organic transparent materials and the average value of coefficient ( τ) for nonmetallic materials was obtained to be 0.32 from graph of the Gibbs–Thomson coefficient versus T m Ω 1/3. The grain boundary energy of solid NPG solution phase has been determined to be (14.6±2.3)×10 −3 J m −2 from the observed grain boundary groove shapes. The ratio of thermal conductivity of equilibrated eutectic liquid to thermal conductivity of solid NPG solution was also measured to be 0.80.

The application of computational thermodynamics and a numerical model for the determination of surface tension and Gibbs–Thomson coefficient of aluminum based alloys

In this paper, a solution for Butler's formulation is presented permitting the surface tension and the Gibbs–Thomson coefficient of Al-based binary alloys to be determined. The importance of Gibbs–Thomson coefficient for binary alloys is related to the reliability of predictions furnished by predictive cellular and dendritic growth models and of numerical computations of solidification thermal variables, which will be strongly dependent on the thermophysical properties assumed for the calculations. A numerical model based on Powell hybrid algorithm and a finite difference Jacobian approximation was coupled to a specific interface of a computational thermodynamics software in order to assess the excess Gibbs energy of the liquid phase, permitting the surface tension and Gibbs–Thomson coefficient for Al–Fe, Al–Ni, Al–Cu and Al–Si hypoeutectic alloys to be calculated. The computed results are presented as a function of the alloy composition.

Thermal conductivity and interfacial energies of solid Sn 3Sb 2 in the Sn–Sb peritectic system

The equilibrated grain boundary groove shapes of solid Sn 3Sb 2 in equilibrium with the Sn–Sb peritectic liquid have been observed from quenched sample with a radial heat flow apparatus. The Gibbs–Thomson coefficient, solid–liquid interfacial energy and grain boundary energy of solid Sn 3Sb 2 have been determined from the observed grain boundary groove shapes. The variation of thermal conductivity with temperature for solid Sn 3Sb 2 and peritectic solid has been measured up to five degree below the meting temperature with a radial heat flow apparatus. The ratio of thermal conductivity of liquid phase to solid phase for Sn–7.8 at.%Sb alloy at the melting temperature has also been measured with a Bridgman type growth apparatus.

Experimental determination of solid–liquid interfacial energy for solid Sn in the Sn–Mg system

The equilibrated grain boundary groove shapes for solid Sn in equilibrium with the Sn–9 at.% Mg eutectic liquid were directly observed annealing a sample at the eutectic temperature for about 5 days with a radial heat flow apparatus. The thermal conductivities of the solid phase, κ S, and the liquid phase, κ L, for the groove shapes were measured. From the observed grain boundary groove shapes, the Gibbs–Thomson coefficient, the solid–liquid interfacial energy and grain boundary energy for solid Sn in equilibrium with the Sn–9 at.% Mg eutectic liquid have been determined to be (7.35 ± 0.36) × 10 −8 Km, (136.41 ± 13.64) × 10 −3 J m −2 and (230.95 ± 25.40) × 10 −3 J m −2, respectively.