Gibbs Thomson Coefficient Research Articles

Assessment of Thermodynamic variables affecting phase nucleation

Complete understanding of any natural phenomenon can only be achieved by explicitly expressing it in terms of primitive variables. The laws of thermodynamics have been extensively studied for centuries, accelerating societal progress through developments across several branches of science and technology. Phase nucleation can be observed in the melting and freezing of rocks and ice caps, abundant shapes of snow flocks, rain regimes, snowfall, casting, and metal forming, among other applications. The most challenging aspect of nucleation is the equilibrium shift controlled by the gradients in temperatures, species, work, and other variables, in accordance with the first law of thermodynamics, which defines the thermal field. In this study, the thermal field and thermal field tensor were defined in terms of equilibrium dislocations to assess their primitive variables. Theoretical simulations for the Gibbs–Thomson coefficients were applied to predict the experimental microstructure evolution.

Experimental determination of solid-liquid interface energy for para- and diamagnetic solid solution in equilibrium with eutectic liquid under a high magnetic field

The solid-liquid interface energy (SLIE) of the Al-Cu and Bi-Cd systems under a high magnetic field (HMF) has been experimentally determined by a Bridgeman-type directional solidification furnace. The equilibrated grain boundary groove shapes for the paramagnetic solid α-Al solution and the diamagnetic solid Bi solution in equilibrium with the eutectic liquid under various HMFs were observed in Al-15.3at%Cu alloy and Bi-50at%Cd alloy. It can be found that the profiles of grain boundary grooves changed significantly under the action of the HMF. The Gibbs-Thomson coefficient and the SLIE for the solid α-Al and solid Bi solution in equilibrium with the eutectic liquid under various HMFs were obtained from obtained grain boundary groove shapes. The results show that the SLIE of the Al-Cu and Bi-Cd alloys increase and decrease under an HMF, respectively. The interaction theory of magnetic dipoles induced by an HMF can be responsible for the above experimental phenomena. Additionally, the results of the differential thermal analysis (DTA) and theoretical analysis indicate that the undercooling of the Al-15.3at%Cu and Bi-50at%Cd alloys increase and decrease under the influence of an HMF, respectively, which is ascribed to the existence of HMF-induced interface energy.

Determination of solid-liquid interfacial energy of solid Mg2Si intermetallic phase in equilibrium with liquid AlSiMg eutectic solution in AlSiMg energy storage alloy

The grain boundary groove method has been successfully used to measure Gibbs-Thomson coefficient, Γ, solid-liquid interfacial energies, σSL, experimentally for transparent materials, binary eutectic, peritectic, monotectic systems, colloidal system, any alloy system, multi-component systems as well as pure materials. It has been shown that the grain boundary groove shapes could be obtained for any system provided that the prepared sample could be held at the evaluated temperature long enough with a very stable temperature gradient. Equilibrated grain boundary groove shapes for binary solid Mg2Si intermetallic phase in equilibrium with liquid AlSiMg ternary eutectic solution have been directly observed with a radial heat flow apparatus. The Gibbs-Thomson coefficient, Γ, was determined with a numerical method using observed groove shapes. The measured thermal conductivities of the solid and liquid AlSiMg solutions at the eutectic temperature and the temperature gradient in the solid Mg2Si phase were used for the calculation of Γ. Then σSL was determined using the Gibbs-Thomson equation. The grain boundary energy, σgb, for the same system was also obtained from the observed groove shapes. The results of the work were compared with the results of the related experimental works.

The application of numerical and analytical approaches for the determination of thermophysical properties of Al–Si–Cu–Mg alloys

Thermophysical properties are very important to simulate the behavior of materials. Computer simulations are low cost as compared to what is needed for physical simulations, as far as it normally requires only a computer, a model and a computer language. However, the accuracy of numerical simulations depends on the quality of the thermophysical properties used in the prediction of physical phenomena, such as fluid flow, heat transfer, alloy solidification and solid-state phase transformations. The thermophysical properties for pure metals are widely available in the literature; nevertheless, for multicomponent metallic alloys, this is not the case. In this paper, a novel definition of non-equilibrium Gibbs–Thomson coefficient is presented, and thermodynamics calculations are carried out based on analytical and numerical approaches for the prediction of: liquidus and eutectic temperatures, equilibrium and non-equilibrium latent heats of fusion, solid–liquid surface tensions, solid and liquid densities, equilibrium and non-equilibrium Gibbs–Thomson coefficients, viscosity and surface tension as a function of temperature of quaternary Al–Si–Cu–Mg alloys.

Experimental determination of interfacial energy for solid Al in the Al-Sn-Mg eutectic system with Bridgman-type apparatus

The equilibrated grain boundary groove shape of solid Al in equilibrium with Al-Sn-Mg eutectic liquid was observed by using a Bridgman type directional solidification apparatus. The ratio of the thermal conductivity of the equilibrated liquid to the thermal conductivity of solid Al has been obtained as 0.91. In addition, the average Gibbs-Thomson coefficient, Γ‾=(4.20±0.35)×10−8Km, the solid-liquid interfacial energy, σSL=180.68±23.48mJ/m2 and the grain boundary energy, σGB=309.30±29.47mJ/m2, in the Al/Al-Sn-Mg system have been calculated from the measured grain boundary shapes.

Solid-liquid interfacial energy of Al-Zn solid-solutions in equilibrium with Al-Zn liquid

The grain boundary groove method has been successfully used to measure solid-liquid interfacial energies, σSL, experimentally for binary eutectic and peritectic systems, multi-component systems as well as pure materials and for opaque materials as well as transparent materials. It was shown that the grain boundary groove method can be use to obtain σSL for any alloy system provided that the prepared alloy sample can be held at the evaluated temperature for a long enough time with a very stable temperature gradient. In order to show the applicability of the groove method to any system, a part of the Al-Zn phase diagram was chosen. Equilibrated grain boundary groove shapes for solid Alα solution (Al-30wt%Zn) in equilibrium with AlZn liquid (Al-60wt%Zn) have been directly observed with a radial heat flow apparatus. The Gibbs-Thomson coefficient, Γ, was determined with a numerical method using observed groove shapes. The measured thermal conductivities of the solid Alα solution and AlZn liquid phases and the temperature gradient in the solid phase at the solid-liquid interface were used for the calculation of Γ and then σSL was determined using the Gibbs-Thomson equation. The grain boundary energy for the same system was also obtained from the observed groove shapes. The results of the work were compared with the results of the related experimental works.

Uncertainty analysis of microsegregation during laser powder bed fusion

Quality control in additive manufacturing can be achieved through variation control of the quantity of interest (QoI). We choose in this work the microstructural microsegregation to be our QoI. Microsegregation results from the spatial redistribution of a solute element across the solid–liquid interface that forms during solidification of an alloy melt pool during the laser powder bed fusion process. Since the process as well as the alloy parameters contribute to the statistical variation in microstructural features, uncertainty analysis of the QoI is essential. High-throughput phase-field simulations estimate the solid–liquid interfaces that grow for the melt pool solidification conditions that were estimated from finite element simulations. Microsegregation was determined from the simulated interfaces for different process and alloy parameters. Correlation, regression, and surrogate model analyses were used to quantify the contribution of different sources of uncertainty to the QoI variability. We found negligible contributions of thermal gradient and Gibbs–Thomson coefficient and considerable contributions of solidification velocity, liquid diffusivity, and segregation coefficient on the QoI. Cumulative distribution functions and probability density functions were used to analyze the distribution of the QoI during solidification. Our approach, for the first time, identifies the uncertainty sources and frequency densities of the QoI in the solidification regime relevant to additive manufacturing.

Determination of solid–liquid interfacial energy of Ni3Sn2 phase by grain boundary groove method in a temperature gradient

The Ni3Sn2 phase plays an important role in numerous fields including solder alloys and lithium storage. However, the precise measurements of many parameters which are essential in describing the physical properties of this phase, such the Gibbs-Thomson coefficient, solid–liquid interfacial energy, grain boundary energy and entropy of fusion per unit volume have not been carried out yet. In this work, the equilibrated grain boundary groove (GBG) shapes for a solid Ni3Sn2 phase in equilibrium with the liquid were observed from Sn-36 at.%Ni peritectic alloy in a linear temperature gradient by using a Bridgman type directional solidification apparatus after experiencing a thermal stabilization time of 8 h. The time required to obtain the GBG shapes in this alloy with a large freezing range was analyzed through the temperature gradient zone melting (TGZM) theory. The Gibbs-Thomson coefficient, solid-liquid interfacial energy and grain boundary energy for the solid Ni3Sn2 phase in equilibrium with liquid were determined in this work, which will help the growth and property control of the fields mentioned above.

On an expression for the growth of secondary dendrite arm spacing during non-equilibrium solidification of multicomponent alloys: Validation against ternary aluminum-based alloys

The technological importance of the microstructure length scale is directly related to the influence exerted on solute redistribution and microporosity formation and on mechanical properties, such as, toughness, ductility, ultimate and yield tensile strengths. There is a huge lack of literature concerning theoretical predictive dendritic growth models for unsteady-state solidification of multicomponent alloys. Most of the existing models have been proposed for steady-state solidification and for binary alloys. One of these models, initially restricted to binary alloys, has been extended for multicomponent alloys; however, it was shown to be valid only for low growth rates and small dendrite tip undercooling, that is, conditions that are very close to those of equilibrium cooling from the melt. In this paper, an extended approach is proposed, encompassing the back diffusion parameter β to allow back diffusion treatment to be included in the analysis. A technique based on Butler’s formulation and on thermodynamic databases is used to permit necessary thermophysical parameters, such as the surface energy and the Gibbs-Thomson coefficient to be calculated for Al-Cu-(Si;Mg) alloys. Directional solidification apparatuses are used to provide a wide range of experimental solidification cooling rates and growth rates along the length of the directionally solidified castings. The model predictions are validated against the experimental scatters of secondary dendrite arm spacings of Al-Cu-Si; Mg) alloys castings solidified under transient upward and horizontal heat flow conditions. It is shown that the predictions fit quite well the experimental results.

The use of computational thermodynamics for the determination of surface tension and Gibbs–Thomson coefficient of multicomponent alloys

The simulation of casting processes demands accurate information on the thermophysical properties of the alloy; however, such information is scarce in the literature for multicomponent alloys. Generally, metallic alloys applied in industry have more than three solute components. In the present study, a general solution of Butler’s formulation for surface tension is presented for multicomponent alloys and is applied in quaternary Al–Cu–Si–Fe alloys, thus permitting the Gibbs–Thomson coefficient to be determined. Such coefficient is a determining factor to the reliability of predictions furnished by microstructure growth models and by numerical computations of solidification thermal parameters, which will depend on the thermophysical properties assumed in the calculations. The Gibbs–Thomson coefficient for ternary and quaternary alloys is seldom reported in the literature. A numerical model based on Powell’s hybrid algorithm and a finite difference Jacobian approximation has been coupled to a Thermo-Calc TCAPI interface to assess the excess Gibbs energy of the liquid phase, permitting liquidus temperature, latent heat, alloy density, surface tension and Gibbs–Thomson coefficient for Al–Cu–Si–Fe hypoeutectic alloys to be calculated, as an example of calculation capabilities for multicomponent alloys of the proposed method. The computed results are compared with thermophysical properties of binary Al–Cu and ternary Al–Cu–Si alloys found in the literature and presented as a function of the Cu solute composition.

Thermophysical properties of NPG solid solution in the NPG–SCN organic system

AbstractA horizontal linear heat flow apparatus connected to an optical microscope was used to directly observe the grain boundary groove shapes of solid neopentylglycol solution equilibrated with neopentylglycol-succinonitrile eutectic liquid at a constant temperature gradient. The thermal conductivity variations with temperaure for solid neopentylglycol solution and neopentylglycol-succinonitrile eutectic solid were measured with a radial heat flow apparatus. By using the observed grain boundary groove shapes and measured values of temperature gradients and thermal conductivity of solid phase and liquid phase, the values of the Gibbs–Thomson coefficient, solid–liquid interfacial energy and grain boundary energy were determined for the solid neopentylglycol solution equilibrated with the neopentylglycol-succinonitrile eutectic liquid.

Application of Computational Thermodynamics to the Evolution of Surface Tension and Gibbs-Thomson Coefficient during Multicomponent Aluminum Alloy Solidification

Numerical simulation of multicomponent alloy solidification demands accuracy of thermophysical properties in order to obtain a numerical representation as close as possible to the physical reality. Some alloy properties are only seldom found in the literature. In this paper, a solution of Butler’s formulation for surface tension is presented for Al-Cu-Si ternary alloys, allowing the Gibbs-Thomson coefficient to be calculated as a function of Cu and Si contents. 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 that will be strongly dependent on the values of the thermophysical properties adopted in the calculations. A numerical model based on Powell hybrid algorithm and 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 measurements of some thermophysical properties of solid CdSb intermetallic in the Sn–Cd–Sb ternary alloy

The equilibrated grain boundary groove shapes of solid CdSb in equilibrium with Sn–Cd–Sb eutectic 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 CdSb intermetallic were determined from the observed grain boundary groove shapes. The thermal conductivity of the eutectic solid and the thermal conductivity ratio of eutectic liquid to the eutectic solid in the Sn–35.8 at.%Cd–6.71 at.%Sb eutectic alloy at its eutectic melting temperature were also measured with a radial heat flow apparatus and a Bridgman-type growth apparatus, respectively.

The experimental determination of thermophysical properties of intermetallic CuAl2 phase in equilibrium with (Al + Cu + Si) liquid

The equilibrated grain boundary groove shapes of solid CuAl2 in equilibrium with (Al+Cu+Si) eutectic 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 CuAl2 were determined from these observed shapes. The thermal conductivity of the eutectic solid and the thermal conductivity ratio of eutectic liquid to the eutectic solid in the (Al+26.82wt.% Cu+5.27wt.% Si) eutectic alloy at its eutectic melting temperature were also measured with a radial heat flow apparatus and a Bridgman-type growth apparatus, respectively. The three phases of (Al+Cu+Si) alloy have detected as Al solution, Si and θ (CuAl2) phases with EDX composition analysis and the microstructure of these phases were photographed by SEM.

Determination of thermodynamic properties of aluminum based binary and ternary alloys

In the present work, the Gibbs–Thomson coefficient, solid–liquid and solid–solid interfacial energies and grain boundary energy of a solid Al solution in the Al–Cu–Si eutectic system were determined from the observed grain boundary groove shapes by measuring the thermal conductivity of the solid and liquid phases and temperature gradient. Some thermodynamic properties such as the enthalpy of fusion, entropy of fusion, the change of specific heat from liquid to solid and the electrical conductivity of solid phases at their melting temperature were also evaluated by using the measured values of relevant data for Al–Cu, Al–Si, Al–Mg, Al–Ni, Al–Ti, Al–Cu–Ag, Al–Cu–Si binary and ternary alloys.

The Experimental Determination of Interfacial Energies for Solid Zn in Equilibrium with Zn-Al-Sb Liquid

The equilibrated grain boundary groove shapes of solid Zn in equilibrium with Zn-Al-Sb liquid were observed from a quenched sample using a radial heat flow apparatus. The Gibbs–Thomson coefficient, solid–liquid interfacial energy, and grain boundary energy of the solid Zn were determined from the observed grain boundary groove shapes. The thermal conductivity of the eutectic solid phase for Zn-0.4 at. pct Al-0.4 at. pct Sb alloy and the thermal conductivity ratio of the liquid phase to the solid phase for Zn-0.4 at. pct Al-0.4 at. pct Sb alloy at eutectic temperature were also measured with a radial heat flow apparatus and a Bridgman-type growth apparatus, respectively.

Effects of physical parameters on the cell-to-dendrite transition in directional solidification**Project supported by the National Natural Science Foundation of China (Grant Nos. 51271213 and 51323008), the National Basic Research Program of China (Grant No. 2011CB610402), the National High Technology Research and Development Program of China (Grant No. 2013AA031103), the Specialized Research Fund for the Doctoral Program of Higher Education of

A quantitative cellular automaton model is used to study the cell-to-dendrite transition (CDT) in directional solidification. We give a detailed description of the CDT by carefully examining the influence of the physical parameters, including: the Gibbs–Thomson coefficient Γ, the solute diffusivity Dl, the solute partition coefficient k0, and the liquidus slope ml. It is found that most of the parameters agree with the Kurz and Fisher (KF) criterion, except for k0. The intrinsic relations among the critical velocity Vcd, the cellular primary spacing λc,max, and the critical spacing λcd are investigated.

Thermal conductivity and interfacial energy of solid Bi in the Bi–Ag eutectic system

The equilibrated grain boundary groove shapes for solid Bi (Bi–2.87 at.%Ag) in equilibrium with Bi–Ag eutectic 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 Bi have been determined from the observed grain boundary groove shapes. The variation of thermal conductivity with temperature for eutectic solid phase (Bi–4.7 at.%Ag) has been measured. The ratio of thermal conductivity of equilibrated eutectic liquid phase to eutectic solid phase has also been measured with a Bridgman-type growth apparatus at the melting temperature. The Gibbs–Thomson coefficient, solid–liquid interfacial energy and grain boundary energy of solid Bi in equilibrium with Bi–Ag eutectic liquid were determined to be (9.2 ± 0.6) × 10–8 K m, (52.7 ± 6.3) × 10–3 J m–2 and (102.4 ± 13.3) × 10–3 J m–2, respectively, from observed grain boundary groove shapes.

Experimental determination of interfacial energies for solid Sn in equilibrium with Sn-Mg-Zn liquid

The equilibrated grain boundary groove shapes of solid Sn in equilibrium with Sn-Mg-Zn 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 solid Sn were determined from the observed grain boundary groove shapes. The thermal conductivity of the eutectic solid phase for Sn-8.12 at% Mg-4.97 at% Zn alloy and the thermal conductivity ratio of the liquid phase to the solid phase for Sn-8.12 at% Mg-4.97 at% Zn alloy at eutectic temperature were also measured with a radial heat flow apparatus and a Bridgman-type growth apparatus, respectively. The Gibbs-Thomson coefficient, solid-liquid interfacial energy and grain boundary energy of solid Sn in equilibrium with Sn-Mg-Zn liquid were determined to be (8.3 ± 0.6)×10-8 Km, (118.5 ± 14.2)×10-3 Jm-2 and (225.1 ± 29.3)×10-3 J m-2 respectively from observed grain boundary groove shapes. A comparison of present results for solid Sn in the Sn-8.12 at% Mg-4.97 at% Zn alloy with the results obtained in previous works for similar solid Sn in equilibrium with different binary or ternary liquid was made.

Nicotinamide–Indole Binary Drug System: Thermodynamic and Interfacial Studies

Crystal engineering, which can potentially be applied to a wide range of crystalline materials, offer an alternative and potentially fruitful method for improving pharmaceutical properties of drugs. The molecular mobility inherent to amorphous/crystalline phases can lead to molecular associations between different components, such that a single crystalline phase of multiple components is formed. The present investigation measures the solid–liquid equilibria (SLE) of nicotinamide (NA)-indole (IN) binary drug system. The solid–liquid equilibrium phase diagram of NA-IN system was determined by the thaw-melt method in the form of a temperature-composition curve. It shows the formation of a simple eutectic at a 0.953 mole fraction of indole, at 48°C. The excess thermodynamic quantities (gE, hE, and sE) have been estimated by computing heat of fusion data and activity coefficient of the component in a binary mix. These values highlight the ordering, stability, and structure of eutectic and non-eutectic alloys. The thermodynamic mixing functions provide information about the nature of mixing of the components during alloying. The negative value of the integral mixing function, ΔGM for eutectic and some non-eutectic alloys indicates spontaneous mixing. The driving force of nucleation during solidification (ΔGv) and the critical free energy of nucleation (ΔG*) obtained at different undercoolings have also been highlighted. The values of radius of critical nucleus (r*) of alloys lies within the nm scale, which suggests new dimensions of solidification processes for nano solid drug dispersions. The solid–liquid interfacial energy (σ), the grain boundary energy (σgb), and the Gibbs–Thomson coefficient (τ) of the drug alloys have been discussed. Interface morphology of the alloys follows the Jackson's surface roughness (α) theory and predicts that faceted growth (α > 2) proceeds in all cases.Supplemental data for this article can be accessed at www.tandfonline.com/gmcl