Metastable Melt Research Articles

Exploring surface properties and premelting in crystals.

Crystal surfaces play a pivotal role in governing various significant processes, such as adsorption, nucleation, wetting, friction, and wear. A fundamental property that influences these processes is the surface free energy, γ. We have directly calculated γ(T) for low-index faces of Lennard-Jones (LJ), germanium, and silicon crystals along their sublimation lines using the computational cleavage technique. Our calculations agree well with experimental values for Si(111) and Ge(111), highlighting the accuracy of the method and models used. For LJ crystals, we identified a premelting onset at Tpm = 0.75Tm, marked by a sharp increase in atom mobility within the second outermost surface layer. Notably, Tpm closely aligned with the endpoint of the LJ melting line at negative pressures, Tend = 0.76Tm. We hypothesize that the emergence and coexistence of a liquid film atop the LJ crystal at Tpm < T < Tm correspond to the metastable melting line under negative pressures experienced by stretched crystal surfaces. Furthermore, our study of thin LJ crystal slabs reveals that premelting-induced failure leads to recrystallization below the homogeneous freezing limit, offering a promising avenue to explore crystal nucleation and growth at extremely deep supercoolings. Finally, no evidence of premelting was detected in the model crystals of Ge and Si, which is consistent with the experimental observations. Overall, our findings offer valuable insights into crystal surface phenomena at the atomic scale.

Thermal properties and thermodynamic model of lithium doped 45S5 bioglass

AbstractShakhmatkin and Vedishcheva thermodynamic model (SV TDM) of the 45S5 Bioglass® doped with three different amounts of Li2O (4.1, 9.9, and 12.3 mol%) was evaluated at T = 800 K. The 55 components of SV TDM were considered, among them 12 lithium containing compounds. Different number of components with not negligible equilibrium molar amount was found for different glass compositions (9 or 10). In all glass compositions containing nonzero amount of Li2O, the four lithium compounds with not negligible equilibrium amount were identified, i.e., Li2O·SiO2, 3Li2O·P2O5, Li2O·2CaO·2SiO2, and 2Li2O·SiO2. In the 45S5 glass composition four phosphate compounds with not negligible abundance were identified: 9Na2O·6SiO2·2P2O5, Na2O·2CaO·P2O5, 5Na2O·4SiO2·P2O5, and Na2O·CaO·P2O5. In all other glasses the 3Li2O.P2O5 was found with not negligible abundance. Moreover, in the glass with 4.1 mol% Li2O the Na2O·2CaO·P2O5 and 3Li2O·P2O5 compounds were found with not negligible abundance. For each studied glass the glass transition temperature, coefficient of thermal expansion of glass and metastable melt were measured by thermodilatometry. The low temperature viscosity was measured by thermomechanical analysis. The viscous flow activation energy was evaluated from the viscosity temperature dependence. The compositional dependence of measured thermal properties was analyzed by correlation analysis with the Q-distribution of silicate and phosphate units.

Shock-induced melting and crystallization in titanium irradiated by ultrashort laser pulse

Modification of titanium microstructure after propagation of a melting shock wave (SW) generated by a femtosecond laser pulse is investigated experimentally and analyzed using hydrodynamic and atomistic simulations. Scanning and transmission electron microscopy with analysis of microdiffraction is used to determine the microstructure of modified subsurface layers of titanium. We found that two layers are modified beneath the surface. A top surface polycrystalline layer of nanoscale grains is formed from shock-molten material via rapid crystallization. In a deeper subsurface layer, where the shock-induced melting changes into plastic deformation due to attenuation of SW, the grain structure of solid is considerably affected, which results in a grain size distribution differing from that in the intact titanium. Molecular dynamics simulation of single-crystal titanium reveals that the SW front continues to melt even after its temperature drops below the melting curve Tm(P). The enormous shear stress of ∼12 GPa generated in a narrow SW front leads to free slip of atomic planes, collapse of the crystal lattice, and formation of a supercooled metastable melt. Such melt crystallizes in an unloading tail of SW. The mechanical melting ceases after drop in the shear stress giving rise to the shock-induced plastic deformation. The last process triggers a long-term rearrangement of atomic structures in solid. The overall depth of modified layers is limited by SW attenuation to the Hugoniot elastic limit and can reach several micrometers. The obtained results reveal the basic physical mechanisms of surface hardening of metals by ultrashort laser pulses.

Quenching of basaltic melts by volatile exsolution

Normally, volatiles in silicate melts are ephemeral components that escape as gases when the melt reaches fluid saturation. When fluid saturation occurs at elevated pressure, magmatic fluids may have large amounts of oxide solute dissolved, are less volatile, and may resemble viscous gels. In Cyprus we have the rare case that solutes of a magmatic fluid coexist with H2O saturated basaltic to boninitic glasses. Quenching of the melts and fluid solutes was induced by fluid segregation. When the fluids exsolved, the liquidus temperature was raised and the melts were left supercooled, while the system temperature remained ± constant. Quenching rates deduced from the morphologies and compositions of quench crystals were high. We analyzed coexisting glasses and fluid solutes for major and trace elements. The fluid mobile trace elements (Rb, K, Pb, Sr) are enriched in both the glasses and fluid solutes. Both endmembers (melt and fluid) have a common parentage and originated within a hydrous mantle source. The glasses have 2.5 ± 0.25 wt.% H2O and record residual H2O contents left after fluid exsolution was completed. Water contents in glasses correspond to an H2O partial pressure (pH2O) of 65 ± 10 MPa and an emplacement depth on the seafloor of 6500 ± 1000 m, provided equilibrium was reached between the pH2O imposed by the melts and the seawater column. Following fluid exsolution, the degree of supercooling ∆T of the melts relative to the dry MgO-in-melt liquidus temperature was – 65 ± 10 °C. The cooling rate ∆T/t at the time of crystallization of dendritic clinopyroxene crystals can be semi-quantified from the distribution of Al2O3 between metastable clinopyroxene dendrites and melt, to at least – 50 °C h−1. Toward the end of the article we speculate if other cases exist where quenching was triggered by fluid exsolution. A possible example are spinifex textures deep inside komatiite flows where quenching rates by conductive cooling did not exceed 0.3 to 1 °C h−1. Our proposition assumes that many spinifex-textured komatiites were hydrous, that they contained H2O in quantities sufficient to reach fluid saturation at emplacement pressure, and that spinifex textures formed as a result of supersaturation by fluid loss.

Mathematical Modeling of Nucleation and Growth Processes of Ellipsoidal Crystals in Binary Melts

The transient behavior of an ensemble of ellipsoidal particles in a supercooled binary melt is considered. The model laws, based on the Fokker-Planck type kinetic equation for the particle-volume distribution function, the thermal and mass integral balances for the binary melt temperature and solute concentration, as well as the corresponding boundary and initial conditions, are formulated and solved analytically. We show that the temperature and concentration increase with time due to the effects of impurity displacement and latent heat emission by the growing ellipsoidal particles. These effects are also responsible for metastability reduction. As this takes place, increasing the initial solute concentration in a metastable binary melt increases the intensity of its desupercooling. The theory is developed for arbitrary nucleation frequency with special consideration of two important nucleation kinetics according to the Meirs and Weber-Volmer-Frenkel Zel’dovich mechanisms. An analytical solution to the integrodifferential model equations is found in a parametric form. The theory contains all limiting transitions to previously developed analytical approaches. Namely, it contains the growth of spherical crystals in binary melts and ellipsoidal crystals in single-component melts.

On the Mechanism of Cocrystal Mechanochemical Reaction via Low Melting Eutectic: A Time-Resolved In Situ Monitoring Investigation

Mechanochemistry has become a sustainable and attractive cost-effective synthetic technique, largely used within the frame of crystal engineering. Cocrystals, namely, crystalline compounds made of different chemical entities within the same crystal structure, are typically synthesized in bulk via mechanochemistry; however, whereas the macroscopic aspects of grinding are becoming clear, the fundamental principles that underlie mechanochemical cocrystallization at the microscopic level remain poorly understood. Time-resolved in situ (TRIS) monitoring approaches have opened the door to exceptional detail regarding mechanochemical reactions. We here report a clear example of cocrystallization between two solid coformers that proceeds through the formation of a metastable low melting binary eutectic phase. The overall cocrystallization process has been monitored by time-resolved in situ (TRIS) synchrotron X-ray powder diffraction with a customized ball milling setup, currently available at μSpot beamline at BESSY-II, Helmholtz-Zentrum Berlin. The binary system and the low melting eutectic phase were further characterized via DSC, HSM, and VT-XRPD.

Variational theory of crystal growth and its application for analysis of forming processes for metastable phases in overcooled metallic melts with eutectic composition

The new crystallization theory for overcooled metastable melt is developed; it is based on variational mechanical principles and takes into account regularities of forming and diffusion growth of equilibrium crystals as well as diffusion-free growth of metastable crystals. Calculations for the melt Fe83B17 were conducted on the model; they displayed that simultaneous nucleation and growth of Fe and Fe2B with metastable phase Fe3B are observed in overcooled melt, and growth speed of near-critical dimensional crystals of Fe3B exceeds crystal growth speed of Fe and Fe2B. The effect of diffusion-free growth is observed for Fe3B crystals, when quickly growing Fe3B crystal surface catches boron atoms. Quasi-equilibrium phase diagram for overcooled Fe-B melt was built on the base of the developed theory; it takes into account both equilibrium crystal growth and metastable phase growth. The obtained diagram allows to predict the values of components concentration near the surface of growing crystals both for Fe and Fe2B crystals meeting the requirements of local equi-librium condition on their surface and for Fe3B metastable crystals which are characterized by diffusion-free growth stipulated by high motion speed of crystal surface.

Nucleation and growth dynamics of ellipsoidal crystals in metastable liquids.

When describing the growth of crystal ensembles from metastable solutions or melts, a significant deviation from a spherical shape is often observed. Experimental data show that the shape of growing crystals can often be considered ellipsoidal. The new theoretical models describing the transient nucleation of ellipsoidal particles and their growth with and without fluctuating rates at the intermediate stage of bulk phase transitions in metastable systems are considered. The nonlinear transport (diffusivity) of ellipsoidal crystals in the space of their volumes is taken into account in the Fokker-Planck equation allowing for fluctuating growth rates. The complete analytical solutions of integro-differential models of kinetic and balance equations are found and analysed. Our solutions show that the desupercooling dynamics is several times faster for ellipsoidal crystals as compared to spherical particles. In addition, the crystal-volume distribution function is lower and shifted to larger particle volumes when considering the growth of ellipsoidal crystals. What is more, this function is monotonically increasing to the maximum crystal size in the absence of fluctuations and is a bell-shaped curve when such fluctuations are taken into account. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Electron beam wire cladding of nickel alloys and stainless steel on a reactor pressure vessel steel

Claddings made of nickel-base alloys or stainless steel are frequently used in the oil, chemical, and power generation industries to protect low-alloy steels from corrosion. Arc weld overlays, which are commonly deposited, often exhibit microstructures near the fusion line that are susceptible to cracking. Due to its very localized and controlled heat input, electron beam welding has the potential to produce claddings with a more resistant microstructure. In this study, multi-layer nickel-base alloy and stainless steel claddings were fabricated by wire-feed electron beam additive manufacturing. Dilution was high because of the specific wire melting technique. It was found that the degree of dilution had a considerable influence on the precipitation of secondary phases, which, however, did not impair the integrity of the claddings. The influence of dilution on the formation of precipitates could be rationalized with thermodynamic calculations. In the nickel-base alloy claddings, the fusion line was sharp without any interfacial martensite. Only a few potentially detrimental type-II grain boundaries were found. Instead, epitaxial solidification was prevalent. This was attributed to metastable melting that was caused by high heating rates. Thus, electron beam-based manufacturing could produce claddings that are more resistant to disbonding than standard arc weld overlays.

Теория метастабильной кристаллизации переохла-жденного эвтектического расплава

A new theory of crystallization of a supercooled metastable melt, based on the variational principles of mechanics, was developed. The theory takes into account the regularities of the dif-fusion growth of equilibrium crystals, as well as the regularities the diffusionless growth of meta-stable crystals. Mathematical modeling showed that in the supercooled melt Fe83B17 there is sim-ultaneous nucleation and growth of the stable Fe and Fe2B phases with the metastable Fe3B phase. The growth rate of crystals of near-critical sizes of the Fe3B phase exceeds the growth rate of the Fe and Fe2B crystals. For the Fe3B crystals the effect of diffusionless growth has been ob-served; in this case, the rapidly growing surface of the Fe3B crystal captures the boron atoms. On the basis of the developed theory, a quasi-equilibrium phase diagram for a supercooled Fe-B melt was constructed. The phase diagram takes into account both the equilibrium crystal growth and the growth of the metastable phase. The resulting diagram makes it possible to pre-dict the values of the concentration of components at the surface of growing crystals for the Fe and Fe2B crystals, for which the condition of local equilibrium is observed on their surface, and for the metastable Fe3B crystals, whose diffusionless growth is due to the high speed of the crys-tal surface movement. The performed mathematical modeling of the nucleation and growth of crystals in the over-cooled eutectic melt Fe83B17 showed that in a supercooled melt there is simultaneous nucleation and growth of the stable Fe and Fe2B phases with the metastable Fe3B phase. The regularities of nucleation and growth of the metastable Fe3B phase have been studied. The growth mechanism of the Fe3B nuclei differs from the growth of the Fe and Fe2B nuclei due to diffusionless capture of the boron atoms by the growing surface of the Fe3B crystals.

Structuring in Metastable Melt

The dendritic parameter is estimated on the assumption that three-dimensional structure of the solid phase is formed in metastable supercooled melt. The solidification of such melt is considered in the quasi-chemical approximation, on the assumption that the transient state corresponds to an ideal solution. The dimensions of the structural cell are found to depend on the relation between the diffusion rate within the cell and the rate of heat loss. The theoretical estimate of the structural parameter agrees with experimental results.

Mathematical modeling of the growth of ellipsoidal crystals in metastable melts and solutions

The evolution of individual crystals of ellipsoidal shape in supercooled one‐component and binary melts as well as in supersaturated solutions is studied theoretically. The crystal volume growth rate is derived using the prolate ellipsoidal coordinates. We show that this rate is a function of the current crystal volume and supercooling/supersaturation of the ambient liquid. Also, we demonstrate that the particle growth rate increases with increasing the volume of ellipsoidal crystals and supercooling.

How the shift in the phase transition temperature influences the evolution of crystals during the intermediate stage of phase transformations

The influence of the phase transition temperature shift on the growth dynamics of a polydisperse ensemble of spherical crystals in metastable melts and solutions is studied. This shift is connected with the Gibbs–Thomson effect and the attachment kinetics of atoms at the phase transition interfaces of evolving crystals. The nonlinear model of kinetic and balance equations with allowance for the particle “diffusion” term is solved analytically. The obtained solution is compared with the case when this temperature shift is not taken into account. It is shown that the Gibbs–Thomson and attachment kinetics effects slightly accelerate the system desupercooling for a single-component titanium melt. This shifts the particle-size distribution function and changes the shape of its tail, which is responsible for the concluding stage of Ostwald ripening.

Mechanism of structure formation in a metastable melt and estimation of its spatial scale

An estimate of the dendritic parameter based on the assumption of the formation of the spatial structure of the solid phase in a metastable supercooled melt (MSM) is proposed. The solidification of MSM is considered in the quasichemical approximation, which assumes a transition state corresponding to the ideal solution system. It is shown, that the dimensions of the structural cell depend on the ratio of the diffusion rate within the cell and the rate of heat removal. The theoretical estimate of the structure parameter is consistent with the experimental dependence. Keywords: metastable melt, dendritic parameter, cooling rate, segregation zone, diffusion. chirkov@bmstu.ru

Calorimetric (DSC) and dielectric (TSDC) investigation on the thermal behavior and molecular mobility in the supercooled liquid and glassy states of bifonazole and lamotrigine

The thermal behavior of the two glass-forming drugs bifonazole and lamotrigine was studied by differential scanning calorimetry (DSC); we reported a bifonazole polymorph not yet described in the literature, as well as weak evidence for lamotrigine polymorphism; still by DSC we investigated the glass-forming ability, the tendency for crystallization from the glass (glass stability) from the metastable and equilibrium melt, for the two glass-formers under analysis. Finally, this technique was used to characterize the glass transition of the two active pharmaceutical ingredients by determining the activation energy of the structural relaxation, the dynamic fragility and the heat capacity jump associated with the glass transformation. Using thermally stimulated depolarization currents (TSDC) and, on the other hand, different aspects of the molecular mobility of these glass-formers were analyzed; the glass transition relaxation and the dynamic fragility, as well as the secondary mobility of the two glass-forming systems, were characterized by this dielectric technique. The absence of other dynamic studies on these glass-formers does not allow the comparison of our results with those of other techniques, namely with dielectric spectroscopy; however, despite this, attention was drawn to the general need to understand in their mutual relationship the TSDC and DRS results on the secondary relaxations.

Thermal behavior and molecular mobility studies in the supercooled liquid and glassy states of carvedilol and loratadine.

The thermal behavior of carvedilol and loratadine was studied by differential scanning calorimetry (DSC). The glass-forming ability, as well as the the tendency for crystallization from the glass (glass stability) and from the metastable and equilibrium melt were also investigated by DSC. In addition this technique was also used to characterize the glass transition of carvedilol and loratadine by determining the activation energy of the structural relaxation, the dynamic fragility, and the heat capacity jump associated with the glass transformation. Different aspects of the molecular mobility in carvedilol and loratadine were analyzed by Thermally Stimulated Depolarization Currents (TSDC), while in carvedilol the Dielectric Relaxation Spectroscopy (DRS) technique was also used. Carvedilol stands out for its high values of specific heat jump and dynamic fragility, which has been attributed to the particular mobility of this glass-former in the glass transformation region, a consequence of specific characteristics of its molecular structure. These molecular features are also at the origin of a relaxation above Tg that has been detected and characterized by TSDC; the DRS investigation allowed to better understand the molecular dynamics in carvedilol in the amorphous solid, in the metastable liquid state and in the glass transformation region. Finally, the secondary relaxations in loratadine were studied by TSDC, while those in carvedilol were studied by the two dielectric techniques and the results were compared and discussed.

Property Decoupling across the Embryonic Nucleus-Melt Interface during Polymer Crystal Nucleation.

Spatial distributions are presented that quantitatively capture how polymer properties (e.g., segment alignment, density, and potential energy) vary with distance from nascent polymer crystals (nuclei) in prototypical polyethylene melts. It is revealed that the spatial extent of nuclei and their interfaces is metric-dependent as is the extent to which nucleus interiors are solid-like. As distance from a nucleus increases, some properties, such as density, decay to melt-like behavior more rapidly than polymer segment alignment, indicating that a polymer nucleus resides in a nematic-like droplet. This nematic-like droplet region coincides with enhanced formation of ordered polymer segments that are not part of the nucleus. It is more favorable to find nonconstituent ordered polymer segments near a nucleus than in the surrounding metastable melt, pointing to the possibility of one nucleus inducing the formation of other nuclei. In this vein, there is also a second region of enhanced ordering that lies along the nematic director of a nucleus, but beyond its nematic droplet and fold regions. These results indicate that crystal stacking, a key characteristic of lamellae in semicrystalline polymeric materials, begins to emerge during the earliest stages of polymer crystallization (i.e., crystal nucleation). More generally, the findings of this study provide a conceptual bridge between polymer crystal nucleation under nonflow and flow conditions and are used to rationalize previous results.

On the theory of phase transformation process in a binary supercooled melt

The processes of bulk crystallization of a supercooled binary melt where the nucleation and growth of solid particles occur are considered with allowance for different mechanisms of nucleation kinetics. A nonlinear set of integro-differential equations is analytically solved by means of the saddle-point technique. The crystal-radius distribution function, temperature, solute concentration, and supercooling of a binary liquid are found taking into account the nonlinear growth rates of spherical crystals. The supercooling represents a decreasing function of time while the distribution function increases up to a maximum size of crystals in a metastable melt.

Simulation of crystal growth in multicomponent metastable alloys

A method for predicting the regularities of crystal growth from metastable melts has been developed. The process of crystal growth from a multicomponent melt is described by the methods of nonequilibrium thermodynamics, taking into account the mutual influence of thermal and diffusion processes. The application of a new variational approach to the constructed system of equations made it possible to obtain expressions of the crystal growth rate from a multicomponent melt convenient for practical calculations. The obtained technique allowed us to analyze the features of crystal growth at high rate of crystallization front, which leads to “impurity capture” effect – deviation from equilibrium conditions at the phase interface. The developed mathematical model makes it possible to calculate the growth rate of new phase particles and to estimate the effect of metastable effects on deviation of the components’ concentration at surface of the growing crystal from equilibrium values. Thus, using the obtained method, a “metastable” phase diagram of the system under study can be constructed. The developed approach is applied to the calculation of growth of α-Fe(Si) nanocrystals during annealing of amorphous alloy Fe73,5 Cu1 Nb3 Si13,5B9. The calculation results were compared with the results of the experiment on the alloy primary crystallization. It is shown that the concentration of Fe at the surface of the growing crystal does not significantly deviate from the equilibrium values. On the other hand, silicon atoms are captured by the crystallization front, silicon concentration at the surface of the growing nanocrystal deviates significantly from equilibrium values. The calculation has shown that after the initial crystallization of the amorphous phase, occurring at a temperature of 400 – 450 °C, the deviation of silicon concentration from equilibrium value is about 2 %, while this equilibrium value is about 13.3 %.

Thermodynamic Regularities of Nuclei Growth during Crystallization of Metastable Alloys

The process of crystal growth in a metastable multicomponent melt has a high speed of the solidification front, which captures atoms of some other components. As a result of such a growth, at the surface of the growing crystal the effect of “impurity capture” is observed, and the concentrations of components significantly deviate from the local equilibrium. Under such conditions, the conventional physico-chemical methods for description of processes at the interfacial surface become inapplicable. Therefore, a new variational approach was applied for an integrated description of diffusion and thermal processes at the phase interface. The growth rate of crystal nucleus in a metastable melt was obtained, using the methods of non-equilibrium thermodynamics. The developed approach allows estimation of the degree of metastable effects influence on a crystal growth rate.