Undercooling Conditions Research Articles

Corner and finger formation in Hele-Shaw flow with kinetic undercooling regularisation

We examine the effect of a kinetic undercooling condition on the evolution of a free boundary in Hele-Shaw flow, in both bubble and channel geometries. We present analytical and numerical evidence that the bubble boundary is unstable and may develop one or more corners in finite time, for both expansion and contraction cases. This loss of regularity is interesting because it occurs regardless of whether the less viscous fluid is displacing the more viscous fluid, or vice versa. We show that small contracting bubbles are described to leading order by a well-studied geometric flow rule. Exact solutions to this asymptotic problem continue past the corner formation until the bubble contracts to a point as a slit in the limit. Lastly, we consider the evolving boundary with kinetic undercooling in a Saffman-Taylor channel geometry. The boundary may either form corners in finite time, or evolve to a single long finger travelling at constant speed, depending on the strength of kinetic undercooling. We demonstrate these two different behaviours numerically. For the travelling finger, we present results of a numerical solution method similar to that used to demonstrate the selection of discrete fingers by surface tension. With kinetic undercooling, a continuum of corner-free travelling fingers exists for any finger width above a critical value, which goes to zero as the kinetic undercooling vanishes. We have not been able to compute the discrete family of analytic solutions, predicted by previous asymptotic analysis, because the numerical scheme cannot distinguish between solutions characterised by analytic fingers and those which are corner-free but non-analytic.

Unusual coordination structure in undercooled eutectic Ga-In alloy melt

The local structures in the normal and undercooled liquid eutectic Ga-In alloy are investigated by using X-ray absorption spectroscope (XAS), X-ray diffractometer (XRD) and the ab initio molecular dynamics (AIMD) simulations. The results from these three techniques all indicate that the nearest-neighbor coordination number decreases with decreasing temperature in the liquid eutectic Ga-In alloy. Moreover, the nearest-neighbor interatomic distance increases and the local atomic packing density decreases with decreasing temperature. The X-ray absorption near edge structure (XANES) measurement shows that the atomic rearrangement at the undercooled temperature results in the formation of low-coordinated polyhedron clusters with high symmetries. This finding provides a new perspective for understanding the liquid-solid transition in undercooled conditions.

Solidified morphology and mechanism of bulk nanocrystalline Fe80P13C7 alloy at isothermal undercooling

The molten Fe80P13C7 alloys can achieve a large undercooling up to 320 K by fluxing technique. With the help of fluxing technique, the molten Fe80P13C7 alloys can be solidified at different undercooling (ΔT) through isothermal undercooling experiment. It is indicated that the microstructure of the solidified Fe80P13C7 alloy specimens is refined significantly with the increasing undercooling and the grain size is about 20 μm, 10 μm, 200 nm and 70 nm for ΔT=50 K, 150 K, 250 K and 320 K, respectively. The solidification morphologies of the solidified Fe80P13C7 alloy specimens under different undercooling are quite different. When ΔT=50 K, it presents a traditional solidification microstructure under a undercooling condition, composed of the primary dendrite and anomalous eutectic within the dendrites. When ΔT=150 K, a cell-like solidification morphology can be found, which can be proposed to be formed based on the nucleation and growth of spinodal decomposition mechanism. When ΔT=250 K, there is a strong direction of the solidification under an optical micrograph, two zones can be divided, and the microstructure of each zone presents a network which results from a liquid spinodal decomposition. When ΔT=320 K, the microstructure presents a random network completely. Microhardness test shows that the hardness of the solidified specimens increases with the undercooling.

Non-Equilibrium Processing of Ni-Si Alloys at High Undercooling and High Cooling Rates

Melt encasement (fluxing) and drop-tube techniques have been used to solidify a Ni-25 at.% Si alloy under conditions of high undercooling and high cooling rates respectively. During undercooling experiments a eutectic structure was observed, comprising alternating lamellae of single phase γ (Ni31Si12) and Ni-rich lamellae containing of a fine (200-400 nm) dispersion of β1-Ni3Si and α-Ni. This is contrary to the equilibrium phase diagram from which direct solidification to β-Ni3Si would be expected for undercoolings in excess of 53 K. Conversely, during drop-tube experiments a fine (50 nm) lamellar structure comprising alternating lamellae of the metastable phase Ni25Si9 and β1-Ni3Si is observed. This is also thought to be the result of primary eutectic solidification. Both observations would be consistent with the formation of the high temperature form of the β-phase (β2/β3) being suppressed from the melt.

A comparative study of dendritic growth within undercooled liquid pure Fe and Fe50Cu50 alloy

The dendritic growth characteristics within undercooled liquid pure Fe and binary Fe50Cu50 alloy were investigated by glass fluxing and electromagnetic levitation methods. The growth velocity of pure Fe dendrite increases with undercooling, which reaches 69ms−1 at the maximum undercooling of 280K (0.15Tm). The microstructure appears as well-defined dendrites under slight undercooling, while it is characterized by a network of grain boundaries without discernible dendrites under substantial undercooling. A glass fluxing method was used to study the dendritic growth within the undercooled liquid Fe50Cu50 alloy. The maximum undercooling achieved was 261K (0.15TL), and the corresponding growth velocity was 15ms−1. A critical undercooling for metastable liquid phase separation of 7K was determined. At larger undercoolings, the sample separates into an Fe-rich zone and a Cu-rich zone. The microstructure of the Fe-rich zone displays well-branched dendrites in the condition of slight undercooling, whereas it transforms into monotectic solidification structures in the highly undercooled regime. Slender dendrites and spheres are characteristics of the structural morphology of the Cu-rich zone at all of the undercoolings. Energy-dispersive spectroscopy analysis shows that the average compositions of phase-separated zones have a large deviation from the original alloy composition, and conspicuous solute trapping has taken place.

HOLZ Rings in EBSD Patterns of the UFeB4 Compound: Association with a Random Distribution of Planar Defects

The UFeB₄ phase present in different alloys of the B-Fe-U system was studied by powder X-ray diffraction (PXRD) and scanning electron microscopy complemented with energy-dispersive spectroscopy and electron backscattered diffraction (EBSD). The PXRD data showed that the ternary compound crystallized adopting essentially the YCrB₄-type structure. However, microstructural observations revealed that under high undercooling conditions the UFeB₄ phase exhibits a random distribution of defects parallel to, which are consistently associated with intense higher-order Laue zone rings in EBSD patterns. Indexation of the EBSD patterns showed that the defective structure is compatible with an intergrowth of YCrB₄- and ThMoB₄-type layers according to the (010)(YCrB₄)//(110)(ThMoB₄) and [001]YCrB₄//[001](ThMoB₄) orientation relation previously reported for an analogous compound. Magnetic studies indicated that the annealed UFeB₄ compound has a paramagnetic behavior in the 2-300 K temperature range.

Investigating the Influence of Morphology in the Dynamical Behavior of Semicrystalline Triton X-100: Insights in the Detection/Nondetection of the α′-Process

The paper investigates the influence of the crystalline structure in the dynamical behavior of semicrystalline Triton X-100 allowing enlightening the reason for the detection/nondetection of the α'-process. The work was preceded by the study of the full amorphous material for which dielectric relaxation spectroscopy (DRS) identified multiple relaxations: the α-process associated with the dynamical glass transition and two secondary relaxations (β- and γ- processes). To evaluate how crystallinity affects the detected relaxation processes, different crystallizations were induced under high and low undercooling conditions. While the secondary relaxations are unaffected by crystallization, the mobility of the cooperative bulk α-process is sensitive to the distinct morphologies. The distinct semicrystalline states were structurally characterized by X-ray diffraction and polarized optical microscopy (POM). Differential scanning calorimetry (DSC) was used as a complementary tool. Depending on the extension of undercooling, large and well-defined shperulites or grainy-like structure emerge, respectively, for low and high undercooling degrees, as monitored by POM. In the two crystalline structures, X-ray diffraction patterns detected the amorphous halo meaning that both are semicrystalline. However, no differences between the amorphous regions are indentified by this technique; the distinction was done by means of dielectric measurements probing different mobilities in each of those regions. When the large spherulites evolve, the bulk-like α-process never goes to extinction and slightly shifts to low frequencies increasing the associated glass transition by 2-3 K, as confirmed by DSC; the slight change is an indication that the dimensions of the persisting amorphous regions become comparable to the length scale inherent to the cooperative motion that determines the glass transition in the full amorphous material. For the grainy-like structure, the α-process becomes extinct and an α'-process evolves as revealed by isochronal plots of dielectric measurements, with the features of a glass transition as confirmed by temperature modulated differential scanning calorimetry; both techniques indicate a 10-12 K displacement of the associated hindered glass transition toward higher temperatures relative to the amorphous glass transition. It is concluded that the detection of the α'-process in Triton X-100 is greatly determined by the high degree of constraining of the amorphous regions imposed by the grainy crystalline structure disabling the occurrence of a bulk-like α-process. Triton X-100 can be taken as a model for understanding low molecular weight materials crystallization, allowing correlating the observed dynamical behavior with the achieved crystalline morphology.

Field and petrographical insight into the formation of orbicular granitoids from the Bonney Pluton, southern Victoria Land, Antarctica

AbstractThe diversity of orbicule types exposed within granitoids of the Bonney Pluton in southern Victoria Land attests to the dynamic and complex interplay of magmatic processes that were responsible for their formation. Orbicules formed in small pockets of H2O-rich silicate melt that was extracted from the crystallizing and fractionating Bonney Pluton magma and concentrated along the pluton margins. These pockets of melt experienced a superheating event that destroyed almost all pre-existing nuclei and a subsequent delay in crystallization, which led to undercooling conditions that promoted rapid dendritic crystal growth. Superheating was induced by the injection of hot mafic magmas, evidenced by elevated plagioclase XAn, and Mg-Al-Ti-contents in hornblende that point to a higher temperature and a more mafic composition in the melt that the orbicule shells crystallized from. Variation in the type and structure of orbicules (hornblende-rich versus plagioclase-rich shells) were likely due to repeated changes in the composition, H2O-content, temperature and PH2O at the crystallizing orbicule boundary layer in response to pulses in the movement of magma, competition between crystallizing phases, episodic vesiculation, degassing and/or second boiling which dictated the composition, texture and size of individual orbicule shells. Brittle fragmentation of orbicules occurred in response to vesiculation and fragmented orbicules are often found as cores within intact orbicules, indicating that multiple phases of orbicule formation were common. The alignment and compaction of orbicules in ‘pods’ indicates movement of orbicules within the melt-rich pockets occurred, prior to resumption of near-equilibrium crystallization in the host granite.

Direct nucleation and growth of peritectic phase induced by substantial undercooling condition

Peritectic phase forms through peritectic transformation in most cases. Here we predicted theoretically a growth mechanism transition from peritectic transformation to the direct nucleation and growth of peritectic phase during rapid solidification. To demonstrate this experimentally, liquid Cu–Sn alloy was undercooled by up to 268K (0.31TL). Once the undercooling exceeds a critical value of about 220K, peritectic η phase forms directly from the metastable liquid phase by suppressing the nucleation of primary ε phase and peritectic transformation. As undercooling increases in the range below 201K, the primary ε phase is refined and peritectic transformation is promoted.

Solidification behavior and microstructural evolution of the Cr‐Nb eutectic alloy

A series of microstructures including fully coupled eutectic, both α‐Cr and β‐Cr2Nb primary dendrites embedded in eutectic and only β‐Cr2Nb primary dendrites plus eutectic were observed in the arc‐melted Cr‐Cr2Nb eutectic alloy. By employing EPMA analysis performed at the eutectic regions, the eutectic composition of the Cr‐Cr2Nb system was indicated to contain less than 18 at.%Nb. Based on the solidification phase selection involving phase competitive nucleation and growth, the α‐Cr phase was predicted to be the primary nucleating phase and the β‐Cr2Nb the primary growing phase. Under large undercooling conditions, the solidification process was controlled by nucleation, which led to the formation of α‐Cr primary particles. With the decrease in undercooling, the solidification process developed into growth controlling, which caused the occurrence of β‐Cr2Nb primary phase since the actual solidification path of the alloy lay within the hypereutectic region. The explanation was confirmed by the experimental composition analysis.

Isothermal crystallization behavior of PP and PP-g-GMA copolymer at high undercooling

The study involves synthesis of polypropylene grafted with glycidyl methacrylate (PP-g-GMA) using three different initiators, benzoyl peroxide, dicumyl peroxide and tertiary butyl cumyl peroxide (TBSP). Among the peroxides used, dicumyl peroxide resulted in considerable reduction of molecular weight of the resulting graft copolymer. The melting/crystallization behavior and isothermal crystallization kinetics of PP homopolymer and PP-g-GMA copolymers were studied with differential scanning calorimetry (DSC) at high undercooling (44–60°C). The results showed that the degree of crystallinity and overall crystallization rate of copolymers is greater than that of virgin PP. Among the three initiators used, TBCP exhibited lowest half crystallization time. The isothermal crystallization kinetics of the PP and copolymers was described with the Avrami equation and Sestak-Berggren (SB) equation. The Avrami exponent n of the PP and copolymers were found to be in the range 1.03 to 1.41 at high undercooling conditions employed in this study. The agreement between the values of n calculated from SB kinetics and Avrami equation is satisfactory with few exceptions. The crystallization rate of PP-g-GMA copolymer was found to be more sensitive to temperature. The isothermally crystallized samples showed a single melting peak for PP while a double peak at lower temperature was recorded for PP-g-GMA copolymer samples. The equilibrium melting point was deduced according to Hoffman-Weeks theory. The decrease of recorded for the PP modified with GMA suggests that the thermodynamic stability of the PP crystals is influenced by the chemical interactions.

The effects of undercooling and deformation rates on the crystallization kinetics of Stromboli and Etna basalts

We have investigated the effect of undercooling and deformation on the evolution of the texture and the crystallization kinetics of remelted basaltic material from Stromboli (pumice from the March 15, 2007 paroxysmal eruption) and Etna (1992 lava flow). Isothermal crystallization experiments were conducted at different degrees of undercooling and different applied strain rate (T = 1,157–1,187 °C and $$ \dot{\gamma }_{i} $$ = 4.26 s−1 for Stromboli; T = 1,131–1,182 °C and $$ \dot{\gamma }_{i} $$ = 0.53 s−1 for Etna). Melt viscosity increased due to the decrease in temperature and the increase in crystal content. The mineralogical assemblage comprises Sp + Plg (dominant) ± Cpx with an overall crystal fraction (ϕ) between 0.06 and 0.27, increasing with undercooling and flow conditions. Both degree of undercooling and deformation rate deeply affect the kinetics of the crystallization process. Plagioclase nucleation incubation time strongly decreases with increasing ΔT and flow, while slow diffusion-limited growth characterizes low ΔT—low deformation rate experiments. Both Stromboli (high strain rate) and Etna (low strain rate) plagioclase growth rates (G) display relative small variations with Stromboli showing higher values (4.8 ± 1.9 × 10−9 m s−1) compared to Etna (2.1 ± 1.6 × 10−9 m s−1). Plagioclase average nucleation rates J continuously increase with undercooling from 1.4 × 106 to 6.7 × 106 m−3 s−1 for Stromboli and from 3.6 × 104 to 4.0 × 106 m−3 s−1 for Etna. The extremely low value of 3.6 × 104 m−3 s−1 recorded at the lowest undercooling experiment for Etna (ΔT = 20 °C) indicates that the crystallization process is growth-dominated and that possible effects of textural coarsening occur. G values obtained in this paper are generally one or two orders of magnitude higher compared to those obtained in the literature for equivalent undercooling conditions. Stirring of the melt, simulating magma flow or convective conditions, facilitates nucleation and growth of crystals via mechanical transportation of matter, resulting in the higher J and G observed. Any modeling pertaining to magma dynamics in the conduit (e.g., ascent rate) and lava flow emplacement (e.g., flow rate, pāhoehoe–‘a‘ā transition) should therefore take the effects of dynamic crystallization into account.

Textural and micro-petrological variations in the eruptive products of the 2006 dome-forming eruption of Merapi volcano, Indonesia: Implications for sub-surface processes

The interplay between magma ascent, degassing and changing magmatic properties are widely recognized as critical factors controlling the style of silicic volcanic eruptions. Microlite textures in samples from the prolonged dome-forming eruption of Merapi in 2006 provide a record of changing magmatic ascent conditions and shallow conduit processes throughout the eruption. Analysis of microlite textural parameters, including measurements of areal number density (NA), mean microlite size, crystal aspect ratio and groundmass crystallinity (φ), combined with the monitoring record and field observations, indicate that magma ascent paths change between continuous ascent at varying rates from a deeper magma storage region, to ascent being temporarily stalled at shallow depths in the latter stages of the eruption, supporting the idea of an ephemeral shallow magma storage region at Merapi. Plagioclase microlite compositions show evidence of decompression-induced degassing, often displaying rims of anorthoclase and more K-rich alkali feldspar (sanidine). Anorthite contents also support the textural data of later erupted magma being temporarily stalled at shallow depths. Crystal size distributions (CSDs) are interpreted to show that both growth-dominated and nucleation-dominated crystallisation regimes existed during the 2006 eruption, resulting from changing conditions of undercooling (ΔT) during variable magma ascent paths. By contrast, microlite textural analysis and feldspar microlite compositions of samples from the fast-growing lava dome of the second phase of the 2010 eruption prior to the cataclysmic events on 5 November indicate faster ascent rates, a crystallisation regime more strongly dominated by nucleation due to high ΔT and interaction of the 2010 magma with more hotter magma from depth.

Correlated process of phase separation and microstructure evolution of ternary Co-Cu-Pb alloy

The phase separation and rapid solidification of liquid ternary Co45Cu42Pb13 immiscible alloy have been investigated under both bulk undercooling and containerless processing conditions. The undercooled bulk alloy is solidified as a vertical two-layer structure, whereas the containerlessly solidified alloy droplet is characterized by core-shell structures. The dendritic growth velocity of primary α(Co) phase shows a power-law relation to undercooling and achieves a maximum of 1.52 m/s at the undercooling of 112 K. The Pb content is always enriched in Cu-rich zone and depleted in Co-rich zone. Numerical analyses indicate that the Stokes motion, solutal Marangoni convection, thermal Marangoni convection, and interfacial energy play the main roles in the correlated process of macrosegregation evolution and microstructure formation.

Development of Phase Field Simulation for the Growth of Dendrite Structure of Al-Si Cast Alloy

Micro to nano scale study of dendrite structure is important in order to have better properties control of casting product. The present study concerns on the morphological study of dendrite structure by phase-field simulation, in order to obtain the morphological growth of this structure that close its real morphology. Focus was given on the morphological growth of dendrite structure of Al-Si cast alloys, therefore thermodynamic data were taken for this type of materials. Anisotropy noise, strength of anisotropy and different undercooled conditions were applied as the variable parameters in the present works. It was observed that by introducing higher anisotropy noise, higher degree fragmentation of dendrite structure was obtained. Similar condition was obtained by introducing higher strength of anisotropy value, that higher degree of fragmentation was obtained. Both of these phenomena was also supported by the heat flux rate features of these variations that higher heat flux rate to almost all direction was obtained with the higher value of anisotropy noise and strength of anisotropy. In addition it was also observed that higher degree fragmentation of dendrite only possible to occur if sufficient undercooled condition established.

Effects of experimental reheating of natural basaltic ash at different temperatures and redox conditions

A set of experiments have been performed on volcanic materials from Etna, Stromboli and Vesuvius in order to evaluate how the exposure to thermal and redox conditions close to that of active craters affects the texture and composition of juvenile pyroclasts. Selected samples were placed within a quartz tube, in presence of air or under vacuum, and kept at T between 700 and 1,130 °C, for variable time (40 min to 12 h). Results show that reheating reactivates the melt, which, through processes of chemical and thermal diffusion, reaches new equilibrium conditions. In all the experiments performed at T = 700–750 °C, a large number of crystal nuclei and spherulites grows in the groundmass, suggesting conditions of high undercooling. This process creates textural heterogeneities at the scale of few microns but only limited changes of groundmass composition, which remains clustered around that of the natural glasses. Reheating at T = 1,000–1,050 °C promotes massive groundmass crystallization, with a different mineral assemblage as a function of the redox conditions. Morphological modifications of clasts, from softening to sintering as temperature increases, occur under these conditions, accompanied by progressive smoothing of external surfaces, and a reduction in size and abundance of vesicles, until the complete obliteration of the pre-existing vesicularity. The transition from sintering to welding, characteristic of high temperature, is influenced by redox conditions. Experiments at T = 1,100–1,130 °C and under vacuum produce groundmass textures and glass compositions similar to that of the respective starting material. Collapse and welding of the clasts cause significant densification of the whole charge. At the same temperature, but in presence of air, experimental products at least result sintered and show holocrystalline groundmass. In all experiments, sublimates grow on the external surfaces of the clasts or form a lining on the bubble walls. Their shape and composition is a function of temperature and fO2 and the abundance of sublimates shows a peak at 1,000 °C. The identification of the features recorded by pyroclasts during complex heating–cooling cycles allows reconstructing the complete clasts history before their final emplacement, during weakly explosive volcanic activity. This has a strong implication on the characterization of primary juvenile material and on the interpretation of eruption dynamics.

Precise Measurements of Dendrite Growth of Ice Crystals in Microgravity

An ice crystal growth experiment was performed on board the International Space Station. The experiment was repeated 134 times with various undercooling conditions. Dendrite crystal growth velocity and tip radius were precisely measured by using a newly developed software. The results are compared with those obtained previously on the ground as well as with those reported by Glicksman et al. for Succinonitrile (SCN). The plot of the dimensionless velocity V as a function of the dimensionless undercooling Δ under microgravity revealed values that were consistently lower than those obtained under 1-G which indicates that thermal convection was suppressed. The plot of the dimensionless radius R0 as a function of Δ showed a less scattered value. The stability factor σ* became close to that of SCN when it was calculated using the geometrical mean radius.

Theory of rod eutectic growth under far-from-equilibrium conditions: Nanoscale spacing and transition to glass

The growth of eutectic under large undercooling conditions is important in obtaining nanoscale composite microstructures. Many glass-forming eutectic systems also exhibit a fine rod eutectic microstructure and often show a direct transition from eutectic to glass with increasing undercooling at the interface. A theoretical model of rod eutectic growth is developed in this paper, which quantitatively evaluates the system and growth parameters that will give rise to large undercooling at the interface. In addition to the diffusion and capillary undercooling, the model incorporates the effects of a sharp decrease in the diffusion coefficient that is exhibited by fragile glass-forming systems, the presence of highly nonlinear liquidus lines at large undercooling, and the effects of non-equilibrium at the interface. The results of the model are then discussed to obtain an insight into the system and growth parameters that are critical for obtaining a large undercooling at the eutectic interface, which is important in the design of nanoscale composite materials and in the selection of potential glass-forming systems.

Temperature dependence of surface tension of molten iron under reducing gas atmosphere

Surface tension of molten iron was measured under Ar-He-5vol.%H2 gas by oscillating droplet method using electromagnetic levitation furnace in consideration of the temperature dependence of oxygen partial pressure, Po2, of the gas. For comparison, the measurement was carried under Ar-He atmosphere to fix the Po2 of the inlet gas at 10−2Pa. The surface tension was successfully measured over a wide temperature range of about 780K including undercooling condition. When Po2 is fixed at 10−2 Pa, the surface tension increased and then decreased with increasing temperature like a boomerang shape. When the measurement was carried out under the H2-containing gas atmosphere, the temperature dependence of the surface tension shows unique kink at around 1810K instead of liner relationship due to competition between the temperature dependence of the Po2 and that of the equilibrium constant of oxygen adsorption reaction. The relationship between the calculated lnKad with respect to inverse temperature using Szyszkowski model was different between the atmospheric gases.

Interfacial Free Energy: An Entropy Portent to Energy Changes

Interfacial free energy is a critical quantity governing the behavior in processes such as crystal nucleation and growth, and there have been extensive efforts to measure or calculate this quantity for a variety of systems. Here, we show that profiles for the changes in energy and entropy across a solid/liquid interface can be extracted from molecular simulations. These smooth molecular level profiles can then be employed to estimate the free energy profile across a two-phase system. A distinctive feature of this profile is the presence of a peak in the free energy at the interface arising from the displacement of the change in entropy in advance of that of the energy. This concept is explicitly examined for the basal and prism interfaces of ice/water systems at the melting point and at undercooled conditions. The values obtained from this analysis for the interfacial free energy and thickness are in accord with previous estimates. The success of this approach demonstrates that microscopic details, captured in molecular level profiles, can be effectively linked to key thermodynamic quantities such as the interfacial free energy.