Search

This article proposes an analytical model to understand the rod growth of eutectic in the bulk undercooled melt. Based on the previous derivations of the lamellar eutectic growth models, relaxing the assumptions of small Péclet numbers, the model is derived by considering melt kinetic and thermal undercoolings. The intent of this model is to predict the transitions in eutectic pattern for conditions of the low and high growth velocities. In addition to investigation of the transition between lamellar and rod eutectic patterns, mathematical simplifications of solving Bessel function are presented as well, which is the most important priority to model calculation. © 2021 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd. Deutsche Forschungsgemeinschaft, DFG: GA 1142/11-1; Natural Science Foundation of Shaanxi Provincial Department of Education: 18JS050; Key Science and Technology Program of Shaanxi Province: 2016KJXX-87 This work was supported by the Key Science and Technology Program of Shaanxi Province (No. 2016KJXX-87) and the Natural Science Foundation of Shaanxi Provincial Department of Education (No. 18JS050). P. K. G. acknowledges financial support of the German Research Foundation (Deutsche Forschungsgemeinschaft [DFG]) under Project GA 1142/11-1. The authors thank J. T. Cao and A. L. Bao for their help in this work. Open Access funding enabled and organized by Projekt DEAL.

The distinctions of dendritic morphology and sidebranching behavior when solidified under atmosphere pressure, constant pressure which is higher than atmosphere pressure (hereinafter referred to as constant pressure) and periodic pressure were investigated using 3-D phase field method. When growing at atmosphere pressure, side branches (secondary dendritic arms) are irregular. When solidified under constant pressure with a relatively high value, side branches are much more luxuriant, with more developed high-order side branches. When applied with periodic pressure, resonant sidebranching happens, leading to many more regular side branches and the smallest secondary dendritic arm spacing (SDAS) in the three cases. The significant difference in dendritic morphology is associated with tip velocity modulated by total undercooling including pressure and temperature undercooling. In the case of constant pressure, tip velocity increases linearly with total undercooling, and it varies periodically in periodic pressure case. The different variation trend in tip velocity is the reason for the distinct dendrite growth behavior in different cases. Unlike the phenomenon in constant pressure case where the dendrite grows faster with higher pressure, the dendrite grows slower under periodic pressure with higher amplitude, resulting in less developed primary dendrite and side branches. This is influenced by tip remelting due to low undercooling or even negative undercooling. It is revealed that the accelerated velocity of tip remelting increases with the decline of undercooling. The greater the amplitude of periodic pressure, the faster the tip remelting velocity during one period. This is the reason why the average tip velocity decreases with the rise of amplitude of periodic pressure.

The effects of high-density electric current pulse (ECP) treatment on the solidification of Cu–37.4 wt% Pb monotectic alloy melt were investigated. Compared to the method of molten glass purification combined with cyclic superheating, ECP treatment created finer microstructures of Cu–Pb alloys, with more homogeneous distribution of the Pb phase in the matrix. This phenomenon can be explained by the cluster theory for liquid metals and the non-equilibrium diffusion theory. First, ECP treatment could cause the fission of larger atomic clusters to increase the undercooling that enabled a large number of smaller clusters to grow and reach the critical nucleation radius. Second, ECP treatment could reduce the diffusion energy barrier to enhance the non-equilibrium diffusion of solute atoms and suppress the segregation of Pb.

The leading phase of eutectic materials has an effect on the solidification behavior and further influences on their properties. Many studies have been carried out on the leading phase of metal/metal and nonmetal/metal eutectic alloys. Nevertheless, few studies were focused on no‐metal/no‐metal eutectic materials. In the present work, the leading phase in the Al2O3/Y3Al5O12 eutectic crystal during solidification was investigated by electron back‐scattered diffraction and discussed according to the classical solidification theory. It is observed that the Y3Al5O12 was the leading phase. The leading phase was determined by the wetting angle and the undercooling. At a given wetting angle, the Y3Al5O12 would be the leading phase when the undercooling exceeds the critical value.

The formation of twinned dendrites was investigated in orthorhombic CrB-structured NiGd. A NiGd droplet embedded in borosilicate glass-flux was processed by differential scanning calorimetry. A small undercooling of ≈ 20 °C was reached and a cross-section of the solidified sample was analyzed with EBSD. A twinned dendrite is found, that exhibits a twin boundary in its center, both parts sharing a direction and a misorientation angle of 40° between its two parts. The present findings are in agreement with model predictions for CrB-structured alloy solidification based on the investigation of deeply undercooled and homogeneously nucleating NiZr. The present investigation on NiGd serves as a first important step to validate the model’s predictions. Due to the observation of twinned dendrites at small undercoolings, the present study may further serve as a first-step to extend the model to heterogeneous growth regimes.

High-strength aluminium alloy powders modified with different nanoparticles by ball milling (7075/TiC, 2024/CaB6, 6061/YSZ) have been investigated in-situ during rapid solidification by differential fast scanning calorimetry (DFSC). Solidification undercooling has been evaluated and was found to decrease with an increasing number of nanoparticles, as the particles act as nuclei for solidification. Lower solidification undercooling of individual powder particles correlates with less hot cracking and smaller grains in the material produced by powder bed fusion of metals by a laser beam (PBF-LB/M). Quantitatively, solidification undercooling less than about 10–15 K correlates with almost crack-free PBF-LB/M components and grain sizes less than about 3 µm. This correlation shall be used for future purposeful powder material design on small quantities before performing extensive PBF-LB/M studies.

This study introduces the application of infrared (IR) thermography for the determination of melting and solidification temperatures of Sn-Ag-Cu based solder materials commonly used for interconnects in electronic components and devices. The presented setup allows a fast and simultaneous analysis with heating and cooling rates of approx. 0.93 K/s and 0.74 K/s respectively. In order to prove feasibility, measurements were carried out on free standing solder spheres with a diameter of 270 µm which is a typical size for solder interconnects in electronic devices. Four Sn-Ag-Cu alloys (Sn-2.0Ag-0.5Cu, Sn-3.0Ag-0.25Cu, Sn-3.0Ag-0.7Cu, Sn-3.0Ag-0.5Cu) with 19 samples per alloy were investigated per experimental run, resulting in a total of 76 samples per measurement. The reproducible extraction of the respective onset temperatures for melting and solidification is demonstrated by the analysis of representative heating and cooling graphs. The onset temperature of melting, which represents the eutectic temperature of these alloys, was measured between 215.1 °C and 218.1 °C. This is less accurate but in good agreement with additionally conducted Differential Scanning Calorimetry (DSC) measurements (217.2 °C to 218.0 °C), as well as the eutectic temperature from the phase diagram (217.2 °C). The solidification temperature of these samples was statistically evaluated by four subsequent experimental runs (generating up to 76 values per alloy). The measured temperature range combined for all four alloys was between 127.2 °C and 196.4 °C. The DSC results (nine values per alloy; three samples; three runs) are comparable but yield a smaller range from 142.2 °C to 185.2 °C. Furthermore, the melting and solidification temperatures of small Sn-Ag FlipChip solder bumps (approx. ∅ 87 µm) were reproducibly analyzed by the IR thermography method and range from 220.3 °C to 220.5 °C and 176.3 °C to 196.7 °C respectively. The presented IR thermography method has proven a valuable alternative, especially for a statistical analysis of undercooling distributions in small samples, such as Sn-Ag-Cu solder joints.

The Dakalasu No.1 pegmatitic rare-element deposit is a representative of Be-Nb-Ta pegmatites in Altai, Xinjiang, China. Beryl is the most important beryllium-carrying mineral in Dakalasu No.1 pegmatite. To constrain the concentration mechanism of Be, we conducted a study of the textural relationships and chemical compositions (major and trace elements) of beryl, along with microthermometry and Raman spectroscopy on beryl-hosted fluid inclusions. Two generations of beryl were recognized. The early beryl I was formed in the magmatic stage, whereas the late beryl IIa and IIb were formed in the magmatic-hydrothermal stage. Lithium and Cs contents increased from beryl I, beryl IIa, to beryl IIb, whereas Mg and Rb contents decreased. Scandium, V, and Ga contents of beryl IIa are similar to beryl IIb, but different in beryl I. Titanium is enriched in beryl IIa. The high FeO contents and Na/Cs ratios of beryl (I, IIa, and IIb) reveal the low degree of differentiation evolution of the Dakalasu No.1 pegmatite. Two types of melt inclusions and four types of fluid inclusions were identified in beryl IIa, IIb, and associated quartz. The microthermometry results indicated that beryl II is formed at 500 °C–700 °C, and 200 MPa–300 MPa. The Dakalasu No.1 pegmatite melt is enriched in volatiles, such as B, F, and CO2, evidenced by a large amount of tourmaline in the wall zone, the occurrence of a variety of tiny cryolite (Na3AlF6) inclusions, and CO2-rich fluid inclusions in beryl IIa. The enrichment mechanism of Be may be related to the crystallization of beryl at highly undercooled states of melt, and melt–melt–fluid immiscibility during the evolution and differentiation of the melt.

The crystal growth velocity is one thermodynamic parameter of solidification experiments of undercooled melts under non-equilibrium conditions, which is directly accessible to observation. We applied the electrostatic levitation technique in order to study the crystal growth velocity $v$ as a function of the undercooling $\Delta T$ for the intermetallic, congruently melting binary alloy NiTi and the glass forming alloy Cu--Zr, as well as for the Zr-based ternary alloys (Cu$_{\mathrm{x}}$Ni$_{\mathrm{1-x}}$)Zr ($x= 0.7, 0.6$) and the Ni-based ternary alloy Ni(Zr$_{\mathrm{x}}$Ti$_{\mathrm{1-x}}) (x= 0.5)$. All investigated systems within this work, except the eutectics $Cu_{56}Zr_{44}$ and $Cu_{46}Zr_{54}$, exceeded the hypercooling limit $\Delta T_{\mathrm{hyp}}$ and, remarkably, every $v(\Delta T)$ relation changed significantly at $\Delta T_{\mathrm{hyp}}$. Our results for glass forming CuZr indicate that the influence of the diffusion coefficient $D(T)$ on $v(\Delta T)$ at high undercoolings, as claimed in literature, cannot be the sole reason for the existence of a maximum in the $v(\Delta T)$ behaviour. These observations could make a valuable contribution concerning an extension of growth theories to undercooling temperatures $\Delta T > \Delta T_{\mathrm{hyp}}$. Nevertheless, our finding has direct consequences to various disciplines, as our earth and all living beings are examples for non-equilibrium systems. The scatter of our velocity data is at least two orders of magnitude smaller than measurements performed by former works due to our experimental setup, which allowed precise contactless triggering at a specific undercooling, and our analysis method, which considered the respective solidification morphologies., Comment: 7 pages, 7 figures, 1 table

Olivine is an important mineral phase in naturally cooled basaltic rocks. The texture and composition of olivine are strictly related to the interplay between the degree of magma undercooling and crystal growth rate. Crystals formed at low undercoolings and growth rates generally show polyhedral-hopper textures and quite homogeneous compositions, while skeletal-dendritic textures and evident crystal zonations occur at high undercoolings and growth rates. In this context, we have performed equilibrium and disequilibrium (i.e., cooling rate) experiments to better understand, by a comparatively approach, the effects of crystallization kinetics on the incorporation of major and trace cations in olivine lattice. The experiments were carried out in a 1 atm vertical tube CO-CO2 gas-mixing furnace to perform experiment at atmospheric pressure and oxygen fugacity of QFM-2 using a basaltic glass (i.e., OIB) as starting materials. The equilibrium experiment was performed at 1175 °C. These target temperatures were kept constant for 240 h and then quenched. Conversely, the disequilibrium experiments were performed at the superliquidus temperature of 1250, and 1300 °C, which was kept constant for 2 h before cooling. The final target temperatures of 1150 (undercooling -ΔT = 50 °C), and 1175 °C (-ΔT = 25 °C) were attained by applying cooling rates of 2 °C/h, 20 °C/h, and 60 °C/h. Then the experimental charges were quenched. Results show that the olivine texture shifts from euhedral (i.e., equilibrium) to anhedral (i.e., disequilibrium) under the effect of cooling rate and rapid crystal growth. In equilibrium experiments, the composition of olivine is homogeneous and non chemical gradients are found in the melt next to the crystal surface. In contrast, a diffusive boundary layer develops in the melt surrounding the olivine crystals growing rapidly under the effect of cooling rate and degree of undercooling. The compositional gradient in the melt increases with increasing cooling rate and undercooling, causing the diffusive boundary layer to expand towards the far field melt. Because of the effects of crystallization kinetics, skeletal-dendritic olivines incorporates higher proportions of major and trace elements that are generally incompatible within their crystal lattice under equilibrium conditions.

The effect of the hypercooling limit on the crystal growth velocity v as a function of the undercooling temperature Δ T for intermetallic binary and ternary alloys remains unexplained yet. In combination with the electrostatic levitation technique, we performed in-situ high energy synchrotron X-ray diffraction measurements at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France, to investigate the phase formation of the binary alloy NiTi , the Zr -based ternary alloys (NixCu1−x)Zr ( x = 0.3 , 0.4 ) and the Ni -based ternary alloy Ni ( Zr 0.5 Ti 0.5 ) for solidification events at undercooling temperatures Δ T Δ T hyp and Δ T > Δ T hyp , whereas Δ T hyp are the corresponding hypercooling limits of the systems. Our results indicate that the cubic B2-type ( CsCl -type, space group Pm3 m # 221 ) phase is always the primary solidifying phase for all investigated alloys. This holds for all undercoolings obtained. Thus, the deceleration effect observed in the crystal growth velocity for all investigated alloys at their hypercooling limits seems to be caused by something different than the formation of different phases.

A novel solution approach is proposed for the numerical simulation of the solidification process of binary Al-Si hypoeutectic alloys during upward and downward solidification modes. Undercooling is always observed during solidification, but the phenomenon could not be considered in the present-day numerical solution. In this approach, the temperature distribution in the mushy zone was used to define the fraction of solid, which enabled the evaluation of the effect of dendrite tip undercooling on the characteristics of the binary alloy solidification. The present numerical algorithm was found to significantly reduce the computation time. Transient temperature distribution and solidification time from the numerical analysis, with consideration of natural convection due to temperature and concentration gradients, have been successfully simulated and validated with experiment results. Numerical results with consideration of dendrite tip undercooling have better agreement with experimental results. The effect of dendrite tip undercooling on the fluid flow (velocity profile), G, R and λ1 for both upward and downward solidification modes of Al-Si alloys have been investigated and discussed. Consideration of undercooling was found to increase G and reduce R in both solidification modes. During downward solidification, considering undercooling significantly increased flow velocity and decreased λ1. The primary dendrite arm spacing could be validated with results from uni-directional solidification experiments only when dendrite tip undercooling was considered.

Growth restriction refers to the phenomenon of reduced growth velocity due to the solute enrichment/depletion at the solid/liquid interface during alloy solidification. Although significant progress has been made to understand this phenomenon, so far there has been no effective parameter to quantify growth restriction. In this paper, we have derived a new parameter, β, to quantify the growth restriction in multicomponent systems effectively, and which incorporates the nature of solutes, solute concentrations and solidification conditions holistically. Theoretical analysis and phase field simulations have confirmed that growth velocity is a unique function of β regardless of the nature of solutes, solute concentrations and solidification conditions, but it is not a unique function of the widely used growth restriction factor, Q. Our analysis suggests that the overall β for a multicomponent alloy system can be either calculated accurately by the ratio of the liquid fraction to the solid fraction (β = fL/fS) or approximated with great confidence by a linear addition of the β values of the constituent binary systems. In addition, we have shown theoretically that for a given alloy system solidifying under a given undercooling, there is a critical solute concentration, below which solidification becomes partitionless and therefore there is no growth restriction during solidification. Furthermore, our analysis has shown that the physical origin of growth restriction is the blockage of the supply of the critical elements for crystal growth, i.e., solvent atoms in the case of eutectic-forming.

Glass formation of a liquid undercooled below its melting temperature requires the complete avoidance of crystal nucleation and subsequent crystal growth. Even though they are not part of the glass formation process, a detailed knowledge of both processes involved in crystallization is mandatory to determine the glass-forming ability of metals and metallic alloys. In the present work, methods of containerless processing of drops by electrostatic and electromagnetic levitation are applied to undercool metallic melts prior to solidification. Heterogeneous nucleation on crucible walls is completely avoided giving access to large undercoolings. A freely suspended drop offers the additional benefit of showing the rapid crystallization process of an undercooled melt in situ by proper diagnostic means. As a reference, crystal nucleation and dendrite growth in the undercooled melt of pure Zr are experimentally investigated. Equivalently, binary Zr-Cu, Zr-Ni and Zr-Pd and ternary Zr-Ni-Cu alloys are studied, whose glass-forming abilities differ. The experimental results are analyzed within classical nucleation theory and models of dendrite growth. The findings give detailed knowledge about the nucleation-undercooling statistics and the growth kinetics over a large range of undercooling.

Boundary conditions for the solid-liquid interface of the solidifying pure melt have been derived. In the derivation the model of Gibbs interface is used. The boundary conditions include both the state quantities of bulk phases are taken at the interface and the quantities characterizing interfacial surface such as the surface temperature and the surface heat flux. Introduction of the surface temperature as an independent variable allows us to describe the scattering energy at the interface. For the steady-state motion of the planar interface the expression for the temperature discontinuity across the phase boundary has been obtained. Effect of Kapitza resistance on the interface velocity is considered. It is shown that heat resistance leads to non-linearity in solidification kinetics, namely, in "velocity-undercooling" relationship. The conditions of the steady--state motion of the planar interface has been found., 26 pages, regular article submitted to Physica A

The solid-phase pattern in the form of a dendrite is one of the frequently met structures produced from undercooled liquids. In the last decades, an analytical approach describing the steady-state crystal growth in the presence of conductive heat and mass transport has been constructed. However, experimental works show that crystal patterns frequently grow in the presence of convection. In this paper, a theoretical description based on convective heat and solute concentration transport near the solid/liquid phase interface is developed. The stable regime of crystallization in the presence of vigorous convection near the steady-state crystal vertex is studied. The stability analysis, determining the stable growth mode, and the undercooling balance law have been applied to deduce the stable values for the growth rate and tip diameter. Our analytical predictions (with convective transport) well describe experimental data for a small melt undercooling. Moreover, we compare both convective and conductive mechanisms in the vicinity of the crystal vertex. Our theory shows that convective fluxes substantially change the steady-state growth of crystals. © 2021 Institute of Physics Publishing. All rights reserved. The present work comprises different parts of research studies, including (i) the model formulation, stability and solvability analyses, derivation of the selection criterion, and (ii) numerical simulations and comparison with experimental data. Different parts of this study were supported by different grants and programs. With this in mind, the authors are grateful to the following foundations, programs, and grants. The first theoretical part (i) was supported by the Russian Science Foundation (grant no. 21-19-00279). The second part (ii) was made possible due to the financial support from the Ministry of Science and Higher Education of the Russian Federation (FEUZ-2020-0057).

In order to elucidate the kinetic partitioning of cations between olivine and basalt, we performed undercooling (−ΔT) and cooling rate (CR) experiments at atmospheric pressure and QFM-2 buffer. Starting from the superliquidus temperature of 1250 °C, a Hawaiian tholeiitic basalt was cooled at the rates of 4 (CR4), 20 (CR20), and 60 (CR60) °C/h to the final target temperatures of 1175 °C (−ΔT = 35 °C; −ΔT35) and 1125 °C (−ΔT = 85 °C; −ΔT85). Results show that polyhedral olivine morphologies are obtained at -ΔT35, whereas strong disequilibrium skeletal and/or dendritic textures form at -ΔT85. The amount of forsterite in olivine decreases from to 85% to 78% with increasing both -ΔT and CR. A diffusive boundary layer also develops in the melt next to the olivine surface and its composition becomes progressively enriched in Ca, owing to its incompatible behavior with the lattice site. Residual melts are progressively depleted in silica and enriched in alkali from CR4 to CR60, but silica-rich melts are observed with increasing -ΔT. In terms of Fe2+-Mg exchange, olivines obtained at -ΔT35 are always in equilibrium with the diffusive boundary layer, comprising both the interface melt next to the olivine surface and the far-field melt where all chemical gradients cease. At -ΔT85, however, the Fe2+-Mg exchange indicates two distinct equilibration stages between olivine core and far-field melt, and between olivine rim and interface melt. Partition coefficients (Kd) of Mg, Fe, Mn, Ca, and Cr calculated at the olivine-melt interface preferentially change as a function of -ΔT rather than CR. From -ΔT35 to -ΔT85, KdMg, KdFe, KdMn, and KdCr remarkably increase, whereas the opposite applies to KdCa. Through the application of equilibrium partitioning models, we found that Mg, Fe, Mn, and Ca are incorporated into the olivine lattice site at near-equilibrium proportions. This generally good agreement with modeling data demonstrates that diffusive mass transport of cations in our experiments occurred under the conditions of local equilibrium at the olivine surface. In contrast, marked deviations from the expected equilibrium are found for KCr in response to the major influence of crystal field stabilization energy on cation incorporation.

A second melting temperature occurs at a temperature Tn+ higher than Tm in glass-forming melts after heating them from their glassy state. The melting entropy is reduced or increased depending on the thermal history and on the presence of antibonds or bonds up to Tn+. Recent MD simulations show full melting at Tn+ = 1.119Tm for Zr, 1.126Tm for Ag, 1.219Tm for Fe and 1.354Tm for Cu. The non-classical homogeneous nucleation model applied to liquid elements is based on the increase of the Lindemann coefficient with the heating rate. The glass transition at Tg and the nucleation temperatures TnG of glacial phases are successfully predicted below and above Tm. The glass transition temperature Tg increases with the heating rate up to Tn+. Melting and crystallization of glacial phases occur with entropy and enthalpy reductions. A universal law relating Tn+ and TnG around Tm shows that TnG cannot be higher than 1.293Tm for Tn+= 1.47Tm. The enthalpies and entropies of glacial phases have singular values, corresponding to the increase of percolation thresholds with Tg and TnG above the Scher and Zallen invariant at various heating and cooling rates. The G-phases are metastable up to Tn+ because the antibonds are broken by homogeneous nucleation of bonds.

In contrast to the classical eutectic growth models, according to which the eutectic spacing decreases invariably with undercooling, an anomalous transition from fine to coarse lamellar eutectics was found in the undercooled Ni-29.8 at. pct Si eutectic alloy. In this study, the growth kinetics, recalescence processes, and grain orientations were analyzed. A sharp increase of the growth velocity at an undercooling of about 100 K was found. The recalescence front transited in sequence from a diffuse one with tips, to a diffuse one without tips and then to a sharp one. The microstructures changed from a mixture of directional rod-shaped γ-Ni31Si12 grains and fine lamellar eutectics to solely coarse lamellar eutectics. Coarse lamellar eutectics were found to be formed by rapid solidification of primary directional rod-shaped Ni31Si12 intermetallic compound and subsequent epitaxial growth of secondary Ni2Si intermetallic compound, being consistent with the predictions of eutectic–dendritic and dendritic growth models. Coarse anomalous eutectics at low undercooling were formed by fragmentation of fine lamellar eutectics and their subsequent coarsening. At high undercooling, they were formed by decoupled-eutectic growth.

Mantle-derived, hydrous mafic magmas are often invoked as a mechanism to transfer heat, mass and volatiles to felsic plutons in the Earth’s crust. Field observations suggest that mafic, water-rich magmas often intrude viscous felsic crystal-rich mushes. This scenario can advect water from the crystallising mafic magma to the felsic magma, leading to an increase in melt fraction in the felsic mush and subsequent mobilisation, at the same time as the mafic magma becomes quenched through a combination of cooling and water loss. To investigate such a scenario, we conducted experiments on a water-undersaturated (4 wt% H2O in the interstitial melt) dacitic crystal mush (50–80 vol% quartz crystals) subject to volatile supply from a water-saturated (≥6 wt% H2O) andesite magma at 950 °C and 4 kbar. Our experimental run products show unidirectional solidification textures (i.e. comb layering) as crystals nucleate at the mafic–felsic interface and grow into the mafic end-member. This process is driven by isothermal and isobaric undercooling resulting from a change in liquidus temperature as water migrates from the mafic to the felsic magma. We refer to this process as “chemical quenching” and suggest that some textures associated with natural mafic–felsic interactions are not simply cooling-driven in origin, but can be caused by exsolution of volatiles adjacent to an interface, whether a water-undersaturated felsic magma (as in our experiments) or a fracture.

Glass-forming Ni50Zr50 intermetallic compound is containerless undercooled and solidified using electrostatic levitation. Large undercoolings up to ∆T = 300 K are achieved. The dendrite growth velocity of the congruently melting alloy is measured as a function of undercooling using a high-speed camera technique. The experimental data is analysed within a sharp interface theory. It is found that the driving force of crystallisation is controlling the growth kinetics at ∆T

The process of ice formation and propagation during cryopreservation impacts on the post-thaw outcome for a sample. Two processes, either network solidification or progressive solidification, can dominate the water–ice phase transition with network solidification typically present in small sample cryo-straws or cryo-vials. Progressive solidification is more often observed in larger volumes or environmental freezing. These different ice phase progressions could have a significant impact on cryopreservation in scale-up and larger volume cryo-banking protocols necessitating their study when considering cell therapy applications. This study determines the impact of these different processes on alginate encapsulated liver spheroids (ELS) as a model system during cryopreservation, and develops a method to replicate these differences in an economical manner. It was found in the current studies that progressive solidification resulted in fewer, but proportionally more viable cells 24 h post-thaw compared with network solidification. The differences between the groups diminished at later time points post-thaw as cells recovered the ability to undertake cell division, with no statistically significant differences seen by either 48 h or 72 h in recovery cultures. Thus progressive solidification itself should not prove a significant hurdle in the search for successful cryopreservation in large volumes. However, some small but significant differences were noted in total viable cell recoveries and functional assessments between samples cooled with either progressive or network solidification, and these require further investigation.

The kinetics of triple-junctions (TJs) in eutectic solidification is modeled by the thermodynamic extremum principle (TEP). It consists of two parts. First, TJs as the interaction of interfaces follow the interface kinetics according to which the temperature and concentration at the TJs are determined. This interface part of TJ kinetics is closely related to the eutectic point in the kinetic phase diagram. Second, TJs have their specific kinetics according to which their morphology (e.g., the contact angles in two dimensions) is determined. Using a new solution of solute diffusion in liquid, the TJ kinetics is incorporated into the current lamellar eutectic growth model. The model is applicable to the concentrated alloy systems and can be extended to any kind of eutectics. Simulation results of the rapid solidification of a lamellar Ni5Si2–Ni2Si (γ–δ) eutectic show that both parts of TJ kinetics can play important roles in eutectic solidification and need to be considered to improve the current eutectic theory.

The authors gratefully acknowledge the financial support of the Slovak Grant Agency under the contract VEGA 2/0111/11 and the Slovak Research and Development Agency under the contract APVV-0647-10, APVV-0413-06, APVV-0492-11 and by CEX FUN-MAT. V.S. gratefully acknowledges the fellowship of the Slovak Academic Information Agency. The work is partially supported by RFBR, project N 13-03-00598-a. The influence of small additions of gallium and antimony on magnetic susceptibility of the bulk glass forming Co47Fe20.9B21.2Si4.6Nb6.3 alloy was studied in a wide temperature range up to 1830K by the Faraday's method. The undercooling for all the samples was measured experimentally. Both Ga and Sb additions were found to increase liquidus and solidification temperatures. However, gallium atoms strengthen interatomic interaction in the melts, whereas antimony atoms reduce it (C) 2013 Elsevier B.V. All rights reserved.

Kinetics of crystal growth in undercooled melts is analyzed by methods of theoretical modeling. Special attention is paid to rapid growth regimes occurring at deep undercoolings at which non-linearity in crystal velocity appears. A traveling wave solution of the phase field model (PFM) derived from the fast transitions theory is used for a quantitative description of the crystal growth kinetics. The “velocity – undercooling” relationship predicted by the traveling wave solution is compared with the data of molecular dynamics simulation (MDS) which were obtained for the crystal-liquid interfaces growing in the 〈 100〉-direction in the Ni50Al50 alloy melt.

The solid–liquid interface of metallic systems of small entropy of fusion is characterized by a rough interface and dendritic morphology. In contrast, systems of high entropy of fusion like semimetals and semiconductors show smooth interfaces and facetted interfaces. The present work demonstrates that, in an undercooled melt of a metal–metalloid alloy Ni2B of intermediate entropy of fusion, a transition from a rough to a smooth interface is induced by forced convection of the melt. Electrostatic levitation is used to container-less undercool droplets in a quiescent state with no convection while electromagnetic levitation (EML) is used to undercool droplets with forced convection. The growth velocity of the solid phase is monitored as a function of undercooling by a high-speed video camera. The data are analysed within dendrite growth theory. In the case of EML, a transition from a rough to a smooth interface is indicated during dendrite growth in the undercooled melt. This is confirmed by facetted micros...

International audience; The hypoeutectic composition Co-61.8 at.% Si was undercooled and solidified using electromagnetic levitation, electromagnetic levitation under a static magnetic field, electrostatic levitation and glass-fluxing. The samples generally showed two thermal events, either separated or continuous depending on undercooling. In situ monitoring of the two thermal events with a high-speed camera revealed a sudden decrease of dendritic growth velocities of primary phases at a critical undercooling of 88 K. Scanning electron microscopy studies of the solidified samples showed that the CoSi compound and the CoSi2 compound nucleate as the primary phase for low and high undercoolings, respectively. The microstructure of the samples depends not only on undercooling, but also on the onset temperature or delay time of the second thermal event. Melt convection has no effect on the primary phase selection in undercooled melts, but it has a significant effect on the delay time and therefore on microstructure formation of the samples for high undercoolings

Undercooled Fe 75 Ni 25 melts were phase-seeded by a high purity iron. It was found that above a critical undercooling, Δ T c =135 K, a metastable δ phase (b.c.c) solidifies from the iron-seeded melts instead of a thermodynamically stable γ phase (f.c.c). While undercooling of the melt (Δ T ) is below Δ T c , solidification of the γ phase prevails in the iron-seeded melts. For the undercooled melts subjected to spontaneous nucleation, the γ phase always solidifies. After solidification, the as-solidified γ phase transforms completely to martensite; whereas the as-solidified metastable δ phase partially transforms to the γ phase, and then to martensite. The untransformed δ phase retains as α -ferrite particles in the microstructures. Based on the classical nucleation theory, catalytic nucleation of the metastable δ phase in the phase-seeded undercooled Fe 75 Ni 25 melts was analyzed. It was quantitatively demonstrated that when Δ T >Δ T c , the formation of the δ phase can be ascribed to a better catalytic effect of the iron on its nucleation than that on the nucleation of the γ phase.

Microstructure and properties of bulk samples of Ni50Co 23Fe2Ga25 Heusler alloy undercooled and solidified in an electromagnetic levitation facility have been studied. Microstructure characterization showed the samples to consist of a mixture of fcc phase and non-modulated tetragonal martensite phase at low undercoolings and a single phase microstructure containing only martensite at high undercooling. The fcc phase content increases with undercooling up to 170 K and then disappears at undercooling above 200 K. Hardness and magnetization correlate differently with the phase content of the sample. � 2011 Elsevier Ltd. All rights reserved.

Rapid solidification processes of glass-fluxed Ni 81.3 Sn 18.7 eutectic alloys at various undercoolings were observed in situ using a high-speed camera. The microstructure of the samples was characterized using optical microscopy, scanning electron microscopy and electron back-scattering diffraction analysis. It was found that the recalescence front sweeps the sample surface from one side to the other, which coincides with the formation of a directional solidification microstructure. Such a finding suggests that it is feasible to measure crystal growth velocities in the undercooled liquid by tracking the loci of the recalescence front. The measured data show sudden acceleration of crystal growth kinetics at a medium undercooling, giving evidence for a transition from coupled growth to uncoupled growth. Microscopic studies revealed that the sample with an undercooling of 202 K comprises two types of anomalous eutectic, which are distinguished by the size and orientations of Ni-rich grains. The results verify a recent hypothesis that anomalous eutectic in undercooled Ni–Sn alloys has a dual origin: it results from eutectic dendrites growing at low undercoolings and from single-phase Ni-rich dendrites growing at high undercoolings.

WOS: 000288232500004, Ni-10 at.% Si alloys (Ni and Si of purity of 99.99%) were prepared by arc melting method under argon atmosphere in a water-cooled copper hearth with a non-consumable tungsten electrode and titanium getter. Spherical-shaped Ni-10 at.% Si alloy melts are undercooled in a containerless electromagnetic levitation apparatus. The effects of undercooling (Delta T) on the microstructure, electrical resistivity (rho) and microhardness (HV) were investigated. The experimental results reveal that with the increase of the undercooling of the melts from 16 to 110 K, the microstructures undergo transition from coarse dendritic morphology to ultra fine dendritic morphology. The measurements of microhardness of the samples were performed by using a microhardness test device. The dependence of microhardness on undercooling was analyzed and it has been found that with increasing the undercooling the HV increases. Variations of electrical resistivity of the Ni10 at.% Si alloy with the temperature in the range of 300-800 K were also determined by using a standard d.c. four-point probe technique. The resistivity of samples increases with increasing temperature and undercooling. (C) 2010 Elsevier By. All rights reserved., Scientific and Technical Research Council of Turkey (TUBITAK) [2219], This research was supported financially by the Scientific and Technical Research Council of Turkey (TUBITAK) under 2219 postdoctoral research fellowship program. The author thanks Professor Dieter M. Herlach and Dr. Evgeny Davydov, for their continuous support and laboratory facilities.

In order to solve undercooling and phase separation of sodium acetate trihydrate (SAT), experimental screening method was used to select nucleating agents and thickeners that are suitable for SAT, and the optimal ratio was identified. Through screening experiments of nucleating agents, it is found that disodium hydrogen phosphate can be used as an effective nucleating agent for SAT. When the weight content of disodium hydrogen phosphate in SAT is 2%, the degree of undercooling was reduced to approximately 2 K. The addition of 1&ndash, 1.5% (weight) of xanthan gum (XG) to SAT can effectively inhibit the phase separation. Since the properties of SAT changes after the modification, the corresponding comparison analysis was performed. The results showed that XG has a significant influence on the SAT performance of SAT. With the addition of 1.5 wt % of XG in pure SAT, the latent heat of fusion and solid/liquid volume expansion reduce by 5.2% and 5.4% respectively, and the thermal conductivity and solid/liquid density also decreases accordingly.

Difficult nucleation of β-Sn during solidification of tin and tin-based lead-free solder alloys can result in high degrees of undercooling of the liquid prior to solidification. The undercooling can produce solder joints with large grains, anisotropic behavior, and undesirable mechanical properties. This paper describes our examination of the amount of undercooling of tin on both graphite (non-wetting) and copper (wetting) surfaces using in situ x-ray diffraction. The microstructure was further characterized by optical microscopy, scanning electron microscopy, and electron backscattering diffraction imaging microscopy. Undercoolings as high as 61°C were observed for Sn solidified on graphite, while lower undercoolings, up to 30°C, were observed for Sn solidified on copper. The microstructure of the high purity Sn sample solidified on graphite showed very few grains in the cross-section, while the commercially pure Sn sample solidified with only one grain and was twinned. Tin solidified on copper contained significant amounts of copper in the tin, intermetallic phase formation at the interface, and a eutectic microstructure.

A new model has been proposed to estimate the solid-liquid interfacial energy on the basis of classical nucleation theory. The present model does not need any experimental data on nucleation kinetics, as is the case with the earlier models. The solid-liquid interfacial energy for both pure metals and glass forming liquids has been estimated using the present model. The estimated interfacial energy values have been used to calculate the critical cooling rates required for the formation of glass. � 2006 Elsevier B.V. All rights reserved.

The Fe 83 B 17 eutectic alloy was undercooled by an electromagnetic levitator ranging up to an undercooling 217 K and the recalescence fronts were in-situ recorded by a high-speed camera. The measured growth velocity as a function of undercooling was well predicted by the current eutectic dendrite model for concentrated alloys with a non-linear phase-diagram but not the previous models for dilute alloys with a linear phase-diagram.

Electromagnetic and electrostatic levitation are applied to containerless undercool and solidify metallic melts. A large undercooling range becomes accessible with the extra benefit that the freely suspended drop is accessible directly for in situ observation. The short-range order in undercooled melts is investigated by combining levitation with elastic neutron scattering and X-ray scattering using synchrotron radiation. Muon Spin Rotation (µSR) experiments show magnetic ordering in deeply undercooled Co80Pd20 alloys. The onset of magnetic ordering stimulates nucleation. Results on nucleation undercooling of zirconium are presented showing the limit of maximum undercoolability set by the onset of homogeneous nucleation. Metastable phase diagrams are determined by applying energy-dispersive X-ray diffraction of Ni-V alloys with varying concentration. Nucleation is followed by crystal growth. Rapid dendrite growth velocity is measured on levitation-processed samples as a function of undercooling ∆T by using high-speed video camera technique. Solute trapping in dilute solid solutions and disorder trapping in intermetallic compounds are experimentally verified. Measurements of glass-forming Cu-Zr alloy show a maximum in the V(∆T) relation that is indicative for diffusion-controlled growth. The influence of convection on dendrite growth of Al50Ni50 is shown by comparative measurements of dendrite growth velocity on Earth and in reduced gravity. Eventually, faceting of a rough interface by convection is presented as observed on Ni2B alloys.

The solidification process of Pb-Sn and Bi-Sn alloy melts is discussed to obtain a basic understanding of the essential phenomena of solidification with undercooling. First, from macroscopic observations, it is shown that the solidification process consists of the following three stages: (1) free growth with recalescence dissipation of thermal undercooling, (2) expansion of crystals with the relaxation of constitutional undercooling or with the recovering process of interrupted quasi-steady heat conduction, and (3) equilibrium solidification. The specific features of free growth under non-uniform undercooling are also shown by comparison with the Lipton, Glicksman, and Kurz model. Next, from microscopic observations, the distribution of the solute concentration and the change of crystal morphology in the solidified materials were investigated quantitatively using scanning electron microscopy and energy-dispersive spectroscopy. Finally, the solidification path during the above three fundamental processes is dynamically represented on phase diagrams. © 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Accepted: 2006-10-16, 資料番号: SA1005122000

Accepted: 2002-02-13, 資料番号: SA1002363000