Gibbs-Thomson Effect Research Articles

Multi-phase-field modeling of the dissolution behavior of stoichiometric particles on experimentally relevant length scales

The dissolution of stoichiometric particles within a melt plays a crucial role in various material processes. This study presents a comprehensive phase-field model to analyze the dissolution behavior of these stoichiometric particles under experimental conditions. Our approach addresses the classical phase-field challenges related to modeling stoichiometric compounds and scaling to experimentally relevant lengths in a multi-phase, multi-component context. To overcome the difficulties posed by stoichiometric compounds, we rederive the classical phase-field evolution equations for a multi-phase system, adopting a composition-independent free energy expression for the stoichiometric compound. Additionally, we extend Feyen’s high driving force model [Feyen and Moelans, Acta Materialia, 256 (2023)] to multi-component systems, allowing us to perform quantitative simulations for technologically relevant material systems at experimental length scales within a reasonable computing time. The model’s precision in capturing diffusion-controlled transformations, including dissolution, growth, and the Gibbs–Thomson effect, is validated against analytical solutions for a hypothetical system. The quantitative nature of the model is validated by applying it to the dissolution of Al2O3 particles in CaO–Al2O3–SiO2 slags. We break new ground by conducting three-dimensional simulations for a system size of 875μm×875μm×875μm, directly comparable to confocal scanning laser microscopy experiments, where previous models were limited to two-dimensional simulations and a system size of 2μm×2μm. This validation underscores the model’s proficiency to quantitatively describe the diffusion-controlled dissolution of Al2O3 at the experimentally relevant length scales.

Large-Scale Synthesis of High-Loading Single Metallic Atom Catalysts by a Metal Coordination Route.

Single atom catalyst (SAC) is one of the most efficient and versatile catalysts with well-defined active sites. However, its facile and large-scale preparation, the prerequisite of industrial applications, has been very challenging. This dilemma originatesfrom the Gibbs-Thomson effect, which renders it rather difficult to achieve high single atom loading (< 3 mol%). Further, most synthesizing procedures are quitecomplex, resulting in significant mass loss and thus low yields. Herein, a novel metal coordination route is developed to address these issues simultaneously, which is realized owing to the rapid complexation between ligands (e.g., biuret) and metal ions in aqueous solutions and subsequent in situ polymerization of the formed complexes to yield SACs. The whole preparation process involves only one heating step operated in air without any special protecting atmospheres, showing general applicability for diverse transition metals. Take Cu SAC for an example, a record yield of up to 3.565kg in one pot and an ultrahigh metal loading 16.03 mol% on carbon nitride (Cu/CN) are approached. The as-prepared SACs are demonstrated to possess high activity, outstanding selectivity, and robust cyclicity for CO2 photoreduction to HCOOH. This research explores a robust route toward cost-effective, massive production of SACs for potential industrial applications.

Direct CALPHAD coupling phase-field model: Closed-form expression for interface composition satisfying equal diffusion potential condition.

We formulated two phase-field models to compute interfacial compositions, characterized by their high computational accuracy and efficiency. The inaugural model utilizes convergence calculations to fulfill the equal diffusion potential condition, while the subsequent model obviates the need for such calculations. Despite this, its computational outcomes strongly agree with those of the preceding model. Notably, in these models, the alteration in composition attributable to interfacial curvatures aligns with the Gibbs-Thomson effect within the equilibrium system. In this study, the solidification processes of Ni-Al-Cr and Ag-Cu-Sn alloys serve as case studies to underscore the computational precision and swiftness of the proposed models.

Water–ice phase transition in frozen soils: a mesoscopic numerical study based on lattice Boltzmann method

ABSTRACT The phenomenon of water–ice phase transition in frozen soils is the key to explaining the mechanism of frost heaving and thawing settlement disaster. However, numerical analysis of water–ice phase transitions in frozen soils at mesoscale is rarely reported. This study combines the modified Gibbs-Thomson equation and the enthalpy-based lattice Boltzmann model, and develops a mesoscale numerical method to simulate the water–ice phase transition in the local pores of saturated frozen soil during freezing and thawing process. In order to accurately simulate this process, a new η coefficient is proposed to modify the Gibbs-Thomson equation, which is unrelated to the type of soil sample and gradation characteristics. According to the particle size distribution curve, the two-dimensional random circle generation method is used to reconstruct the soil pore structure. The freezing and thawing processes are verified with the experimental data. A larger non-uniformity coefficient C u and curvature coefficient C c of the grain size distribution result in a lower degree of subcooling and lower residual water content of the soil during the freezing process. The new model provides an effective means to understand the water–ice phase transition in frozen soil at a mesoscopic scale.

Estimation of unfrozen water content of saturated sandstones using nuclear magnetic resonance, mercury intrusion porosimetry, and ultrasonic tests

The unfrozen water content (UWC) is a crucial parameter that affects the strength and thermal properties of rocks in relation to engineering construction and geological disasters in cold regions. In this study, three different methods were employed to test and estimate the UWC of saturated sandstones, including nuclear magnetic resonance (NMR), mercury intrusion porosimetry (MIP), and ultrasonic methods. The NMR method enabled the direct measurement of the UWC of sandstones using the free induction decay (FID). The MIP method was used to analyze the pore structures of sandstones, with the UWC subsequently calculated based on pore ice crystallization. Therefore, the MIP test constituted an indirect measurement method. Furthermore, a correlation was established between the P-wave velocity and the UWC of these sandstones based on the mixture theory, which could be employed to estimate the UWC as an empirical method. All methods demonstrated that the UWC initially exhibited a rapid decrease from 0 °C to −5 °C and then generally became constant beyond −20 °C. However, these test methods had different characteristics. The NMR method was used to directly and accurately calculate the UWC in the laboratory. However, the cost and complexity of NMR equipment have precluded its use in the field. The UWC can be effectively estimated by the MIP test, but the estimation accuracy is influenced by the ice crystallization process and the pore size distribution. The P-wave velocity has been demonstrated to be a straightforward and practical empirical parameter and was utilized to estimate the UWC based on the mixture theory. This method may be more suitable in the field. All methods confirmed the existence of a hysteresis phenomenon in the freezing-thawing process. The average hysteresis coefficient was approximately 0.538, thus validating the Gibbs–Thomson equation. This study not only presents alternative methodologies for estimating the UWC of saturated sandstones but also contribute to our understanding of the freezing-thawing process of pore water.

On Evaluation of the Gibbs–Thomson Effect and Selection of Nucleus Size for the Kampmann–Wagner Numerical Model

On Evaluation of the Gibbs–Thomson Effect and Selection of Nucleus Size for the Kampmann–Wagner Numerical Model

Self-Assembled Monolayer and Nanoparticles Coenhanced Fragmented Silver Nanowire Network Memristor.

Silver nanowire (AgNW) networks with self-assembled structures and synaptic connectivity have been recently reported for constructing neuromorphic memristors. However, resistive switching at the cross-point junctions of the network is unstable due to locally enhanced Joule heating and the Gibbs-Thomson effect, which poses an obstacle to the integration of threshold switching and memory function in the same AgNW memristor. Here, fragmented AgNW networks combined with Ag nanoparticles (AgNPs) and mercapto self-assembled monolayers (SAMs) are devised to construct memristors with stable threshold switching and memory behavior. In the above design, the planar gaps between NW segments are for resistive switching, the AgNPs act as metal islands in the gaps to reduce threshold voltage (Vth) and holding voltage (Vhold), and the SAMs suppress surface atom diffusion to avoid Oswald ripening of the AgNPs, which improves switching stability. The fragmented NW-NP/SAM memristors not only circumvent the side effects of conventional NW-stacked junctions to provide durable threshold switching at >Vth but also exhibit synaptic characteristics such as long-term potentiation at ultralow voltage (≪Vth). The combination of NW segments, nanoparticles, and SAMs blazes a new trail for integrating artificial neurons and synapses in AgNW network memristors.

The crystal orientation of THF clathrates in nano-confinement by in situ polarized Raman spectroscopy.

Gas hydrates form at high pressure and low temperatures in marine sediments and permafrost regions of the earth. Despite forming in nanoporous structures, gas hydrates have been extensively studied only in bulk. Understanding nucleation and growth of gas hydrates in nonporous confinement can help create ways for storage and utilization as a future energy source. Herein, we introduce a new method for studying crystal orientation/tilt during tetrahydrofuran (THF) hydrate crystallization under the influence of nano-confinement using polarized Raman spectroscopy. Uniform cylindrical nanometer size pores of anodic aluminum oxide (AAO) are used as a model nano-confinement, and hydrate experiments are performed in a glass microsystem for control of the flash hydrate nucleation kinetics and analysis via in situ polarized Raman spectroscopy. The average THF hydrate crystal tilt of 56 ± 1° and 30.5 ± 0.5° were observed for the 20 nm and 40 nm diameter pores, respectively. Crystal tilt observed in 20 and 40-nanometer-size pores was proportional to the pore diameter, resulting in lower tilt relative to the axis of the confinement at larger diameter pores. The results indicate that the hydrates nucleation and growth mechanism can depend on the nanoconfinement size. A 1.6 ± 0.01 °C to 1.8 ± 0.01 °C depression in melting point compared to the bulk is predicted using the Gibbs-Thomson equation as a direct effect of nucleation in confinement on the hydrate properties.

Phase stability and nucleation kinetics of salts in confinement

Of fundamental importance to energy storage, electrochemistry and separation processes, ionic liquids in confinement exhibit unexpected thermodynamic behaviors. Such complex behaviors highlight the need for multi-scale descriptions of the thermodynamics and dynamics of nanoconfined ionic liquids. Here, we probe the impacts of confinement on the freezing point and nucleation kinetics of a simple molten salt which shares important features with ionic liquids. Using molecular modeling techniques, the melting temperature of salt in confinement is found to be larger than its bulk counterpart. Relying on conventional thermodynamic models (Clapeyron and Gibbs-Thomson equations), we capture the crystal/liquid coexistence in bulk and confinement with simple parameters derived from molecular simulations. Then, by considering different nucleation mechanisms – bulk, surface, and confined nucleation, the metastability barrier upon salt formation is shown to decrease upon confinement, therefore providing theoretical insight into the larger nucleation rate constants observed in experiments on nanoconfined ionic liquids. We also discuss the effects of wettability on capillary freezing of ionic liquids at various confining surfaces through varying the contact angle. These findings provide a practical means to predict the melting point, wettability, and freezing kinetics of ionic liquids at various surface conditions from simple thermodynamic data.

Growth and characterization of germanium telluride nanowires via vapor–liquid–solid mechanism

Phase-change materials (PCMs), which can transition reversibly between crystalline and amorphous phases, have shown great promise for next-generation memory devices due to their nonvolatility, rapid switching periods, and random-access capability. Several groups have investigated phase-change nanowires for memory applications in recent years. The ability to regulate the scale of nanostructures remains one of the most significant obstacles in nanoscience. Herein, we describe the growth and characterization of germanium telluride (GeTe) nanowires, which are essential for phase-change memory devices. GeTe nanowires were produced by combining thermal evaporation and vapor–liquid–solid (VLS) techniques, using 8 nm Au nanoparticles as the metal catalyst. The influence of various growth parameters, including inert gas flow rate, working pressure, growth temperature, growth duration, and growth substrate, was examined. Ar gas flow rate of 30 sccm and working pressure of 75 Torr produced the narrowest GeTe nanowires horizontally grown on a Si substrate. Using scanning electron microscopy, the dimensions, and morphology of GeTe nanowires were analyzed. Transmission electron microscopy and energy-dispersive x-ray spectroscopy were utilized to conduct structural and chemical analyses. Using a SiO2/Si substrate produced GeTe nanowires that were thicker and lengthier. The current–voltage characteristics of GeTe nanowires were investigated, confirming the amorphous nature of GeTe nanowires using conductive atomic force microscopy. In addition, the effects of the VLS mechanism and the Gibbs–Thomson effect were analyzed, which enables the optimization of nanowires for numerous applications, such as memory and reservoir computing.

Crystal dissolution by particle detachment

Crystal dissolution, which is a fundamental process in both natural and technological settings, has been predominately viewed as a process of ion-by-ion detachment into a surrounding solvent. Here we report a mechanism of dissolution by particle detachment (DPD) that dominates in mesocrystals formed via crystallization by particle attachment (CPA). Using liquid phase electron microscopy to directly observe dissolution of hematite crystals — both compact rhombohedra and mesocrystals of coaligned nanoparticles — we find that the mesocrystals evolve into branched structures, which disintegrate as individual sub-particles detach. The resulting dissolution rates far exceed those for equivalent masses of compact single crystals. Applying a numerical generalization of the Gibbs-Thomson effect, we show that the physical drivers of DPD are curvature and strain inherently tied to the original CPA process. Based on the generality of the model, we anticipate that DPD is widespread for both natural minerals and synthetic crystals formed via CPA.

Scaling of inter-pore spacing of lotus-type pores

Abstract The present study is to scale the inter-pore spacing and bubble radius required for controlling the porosity of the lotus-type pores in the solid during a unidirectional solidification. The porosity in solid degrade properties of material in welding, casting and additive manufacturing, etc. On the other hand, the ordered cylindrical pores in the material are often used to improve the functional properties, such as the tensile and compression stresses, the impact and acoustic energy absorption, the permeability, and the thermal and electrical conductivity, etc. Different from the traditional minimum undercooling criterion to estimate the porosity and size of lotus-type pores, this study relevantly combines the Gibbs-Thomson equation, the Young-Laplace equation, the nucleation theory, and the Henry’s law or Sieverts’ law to scale the inter-pore spacing and the critical radius of the lotus-type pores, which are considered as the same order of the wavelength and the amplitude of the morphological instability of the solidification front, respectively. This work revises the minimum undercooling criterion which ignores the nucleating bubble on the solidification front, and conducts irrelevant evaluation of the curvature of the solidification front. The present work finds the revised scaling results and available experimental data to be in good agreement. The sizes of the pores and the porosity in the solid can be successfully controlled in advance.

Engulfment Avalanches and Thermal Hysteresis for Antifreeze Proteins on Supercooled Ice.

Antifreeze proteins (AFPs) bind to the ice-water surface and prevent ice growth at temperatures below 0 °C through a Gibbs-Thomson effect. Each adsorbed AFP creates a metastable depression on the surface that locally resists ice growth, until ice engulfs the AFP. We recently predicted the susceptibility to engulfment as a function of AFP size, distance between AFPs, and supercooling [ J. Chem. Phys. 2023, 158, 094501]. For an ensemble of AFPs adsorbed on the ice surface, the most isolated AFPs are the most susceptible, and when an isolated AFP gets engulfed, its former neighbors become more isolated and more susceptible to engulfment. Thus, an initial engulfment event can trigger an avalanche of subsequent engulfment events, leading to a sudden surge of unrestrained ice growth. This work develops a model to predict the supercooling at which the first engulfment event will occur for an ensemble of randomly distributed AFP pinning sites on an ice surface. Specifically, we formulate an inhomogeneous survival probability that accounts for the AFP coverage, the distribution of AFP neighbor distances, the resulting ensemble of engulfment rates, the ice surface area, and the cooling rate. We use the model to predict thermal hysteresis trends and compare with experimental data.

Melting Point of a Confined Fluid within Nanopores: The Composition Effect on the Gibbs-Thomson Equation.

The Gibbs-Thomson (GT) equation finds that the shift in the freezing/melting temperature under confinement with respect to its bulk counterpart is inversely proportional to the pore size. This century old relation successfully elaborates the freezing experiments of many fluids (e.g., water, molten salt), while it fails in quantitatively predicting the phase stability of the nonstoichoimetric crystals (e.g., gas hydrates). Based only on the crystal/liquid coexistence, we here revisit the GT equation to treat the multicomponent compounds within a slit confined geometry. In addition to the interfacial energy contribution, the extended GT equation accounts for the excess free energies associated with the composition variations upon the freezing/melting transition. Using the direct coexisting method (DCM), we first probe the melting temperatures of a face-centered cubic (fcc) crystal confined in slit pores as well as its bulk counterpart. The melting temperature under confinement is shown to be depressed compared to the bulk. We then turn to estimate the parameters entering the GT equation using several independent molecular simulations. The melting temperature depression observed in the DCM simulations is found to be well described by the GT equation if used with accurate estimates of the pore/crystal and pore/liquid interfacial tensions. Finally, using the above molecular modeling strategies, we show that the GT equation with the composition correction successfully predicts the shifted melting temperature of methane hydrate confined in porous solids. For such nonstoichoimetric compounds under confinement, accounting for the composition effects is of utmost importance as it exhibits a non-negligible contribution to the GT description. The extended GT equation can be expected to investigate the capillary freezing of the nonstoichoimetric compound in nanopores and to provide a better understanding of the pore body.

Homogenizing Zn Deposition in Hierarchical Nanoporous Cu for a High-Current, High Areal-Capacity Zn Flow Battery.

A Zn anode can offset the low energy density of a flow battery for a balanced approach toward electricity storage. Yet, when targeting inexpensive, long-duration storage, the battery demands a thick Zn deposit in a porous framework, whose heterogeneity triggers frequent dendrite formation and jeopardizes the stability of the battery. Here, Cu foam is transferred into a hierarchical nanoporous electrode to homogenize the deposition. It begins with alloying the foam with Zn to form Cu5 Zn8 , whose depth is controlled to retain the large pores for a hydraulic permeability ≈10-11 m2 . Dealloying follows to create nanoscale pores and abundant fine pits below 10nm, where Zn can nucleate preferentially due to the Gibbs-Thomson effect, as supported by a density functional theory simulation. Morphological evolution monitored by in situ microscopy confirms uniform Zn deposition. The electrode delivers 200h of stable cycles in a Zn-I2 flow battery at 60mAhcm-2 and 60mAcm-2 , performance that meets practical demands.

Nickel Nanoparticle/Carbon Films as an Interlayer To Improve the Stability of Solder Joints

The growth of brittle intermetallic compounds (IMCs) generated between a solder and a substrate is crucial for the reliability of solder joints. Therefore, it is necessary to control the growth of IMCs at the interface. Herein, we propose a strategy with the nickel nanoparticle/carbon (Ni&C) films as an interlayer to improve the stability of the solder joint. After adding the interface with the Ni&C film and reflowing for 450 s, the growth of IMCs decreased by 41.05%. After reflowing for 450 and 2100 s, the grain size in the 300 s-Ni&C/Cu substrate decreased by 14.34 and 20.50%, respectively, compared with the pure Cu substrate. Furthermore, the Ni&C film changes the microstructure of the interface and the diffusion pattern of elements, thus reducing the number of Kirkendall voids. As the reflow time increases, the scalloped IMCs are transformed to be prismatic, which can be well explained by the Gibbs–Thomson effect. The synergistic effect between Ni and carbon in Ni&C can jointly control the interface reaction and the growth of IMCs, with the Ni&C film acting as an inert barrier to inhibit the growth of IMCs.

Using PCL oligomers to study the differences in melting behavior between polymers and small molecules crystals

Polymer crystals usually show a completely different melting behavior than small molecules. Instead of starting from the crystal growth front, the lamellar crystals within polymer spherulites always experience a successive thickening process upon heating before they simultaneously melt. However, a systematic comparative study of the different melting behavior of crystals formed by small and large polymer chains is still scarce. In this work, two PCL oligomers with similar molecular weight are selected to study their crystallization and melting behavior. The defect-free oligomer (PCL2.4) exhibits a similar melting behavior as polymeric crystals (where spherulites melt simultaneously). In contrast, the other oligomer (PCL2.0) with a mid-chain defect shows prominent surface melting starting at the spherulite growth front. SAXS, SSA thermal fractionation, and flash DSC results confirm that an extended chain-like crystal structure could form at relatively high crystallization temperatures. According to the Gibbs-Thomson equation, the melting temperature of PCL2.0 crystals at the spherulite growth front is relatively lower than in the inner part due to different surface free energies. On the other hand, the thermal stability of PCL2.4 is enhanced due to melting and recrystallization during heating, and the spherulites show identical melting points and lamellar thicknesses at their growth front centers.

Generalization of Young-Laplace, Kelvin, and Gibbs-Thomson equations for arbitrarily curved surfaces

The Young-Laplace, Kelvin, and Gibbs-Thomson equations form a cornerstone of colloidal and surface sciences and have found successful applications in many subfields of physics, chemistry, and biology. The Gibbs-Thomson effect, for example, predicts that small crystals are in equilibrium with their liquid melt at a lower temperature than large crystals and the positive interfacial energy increases the energy required to form small particles with a high curvature interface. In cases of liquids contained within porous media (confined geometry), the effect indicates decreasing the freezing/melting temperatures and the increment of the temperature is inversely proportional to the pore size. These phenomena can be reformulated for Gaussian maps of macromolecules and can be asked the following question: can one use the equations for predicting the melting temperature and shape of polymer chains in confined geometries? The answer is no, mainly because macromolecules form highly curved surfaces (Gaussian maps), and the equations hold only for simple geometries (sphere, plane, or cylinder). Here, we present general Young-Laplace, Kelvin, and Gibbs-Thomson equations for arbitrarily curved surfaces and apply them to predict temperature distribution on a few protein surfaces. Also, after increased interest toward liquid/liquid phase separation in biology, we derive generic Ostwald ripening and show that for shape-changing condensates, instead of a monotonic growing mechanism, a variety of processes are possible. Due to the generality of equations, we clarify that at appropriate internal/external pressure conditions systems, bounded by surfaces, may adopt any shape and thermal stability is strongly influenced by the geometries of confined spaces.

Optimization of the Surface Structure of the SiC Substrate for SiC-Ni Melt-bonding Using Simulation by Phase-Field Method

When SiC is melt-bonded with Ni electrode, a regrowth layer containing C is formed due to the dissolution of C into the molten NiSi, which deteriorates the electrical properties. We found that the regrowth layer can be suppressed by giving the surface of the SiC substrate wavy shape. The wavy-shape substrate with appropriate periodic length and amplitude lead to the suppression of regrowth layer at the bottom of the groove. The mechanism of the suppression of the regrowth layer is that the condensation of NiSi in the grooves of the substrate causes the decrease of undercooling by decreasing the equilibrium melting point. Thinner the groove is, higher the condensation of NiSi becomes, however, further thinning of the groove reduces the curvature at the bottom of the groove and increases the melting point due to the Gibbs-Thomson effect. This effect cancels the lowering of the melting point due to the NiSi condensation, making it difficult to suppress the regrowth layer. There is an optimum range of periodic length and amplitude of the substrate surface for suppressing regrowth layer. The substrate shape with a periodic length of 9.4 μm and an amplitude of 0.92 μm was most effective to suppress the regrowth layer.

Melting temperature, critical nucleus size, and interfacial free energy in single FCC metals — A Molecular Dynamics study of liquid–solid phase equilibria

Molecular dynamics simulations in the isobaric–isenthalpic ensemble are used to derive various important parameters related to nucleation from the melt. In particular, by using results from liquid–solid phase equilibria, we present a simple, yet reliable, approach to extract melting temperature, critical nucleus size, and liquid–solid interfacial free energy for six different embedded atom FCC systems. Our approach is based on the fundamental thermodynamic relation given by the Gibbs–Thomson equation that uses the heat released during solidification to drive growth of the solid phase until thermodynamic equilibrium is achieved. Equilibrium between the liquid and solid phases is identified by a steady-state evolution in the temperature of the two-phase system.