Amorphous Solidification Research Articles

Liquid state properties and amorphous solidification kinetics of multicomponent Fe_{50-x}Co_{x}Cr_{14}Mo_{14}C_{9}B_{8}Tm_{5} alloys investigated under containerless processing conditions.

The liquid state thermophysical properties and amorphous solidification kinetics of Fe_{50-x}Co_{x}Cr_{14}Mo_{14}C_{9}B_{8}Tm_{5} (x=10, 15, 20, and 25) alloys were explored by electromagnetic and electrostatic levitation techniques. It was found that the surface tension of liquid alloys with Fe contents below 30 at.% had a strong temperature dependence. The high surface tension led to a sharp increase in the interfacial free-energy penalty. A high nucleation barrier was formed inside the melt, which greatly inhibited the nucleation rate. The liquid viscosity revealed the strong liquid feature of this alloy series, which became the dominant kinetic factor determining their solidification mechanisms. The high viscosity hindered atomic diffusion and delayed nucleation. The long crystallizing incubation time of Fe_{30}Co_{20}Cr_{14}Mo_{14}C_{9}B_{8}Tm_{5} ensured a strong glass-forming ability and a low critical cooling rate of 2.11×10^{3}Ks^{-1}. As a result, a bulk metallic glass rod with an 8-mm diameter was successfully prepared by a convenient casting procedure. This rod could remain in a glassy state at a higher temperature and over a wider temperature range due to its high glass-transition temperature and large undercooled liquid region. The apparent activation energy for nucleation was derived as 463.8 kJmol^{-1} according to the nonisothermal crystallization kinetics, indicating that the bulk metallic glass had to absorb a large amount of energy to overcome the potential barriers before nucleation and thus exhibited excellent thermal stability.

Amorphous solidification mechanism of multicomponent Ti-Cu based alloy investigated by molecular dynamics simulation and drop tube experiments

Amorphous solidification mechanism of multicomponent Ti-Cu based alloy investigated by molecular dynamics simulation and drop tube experiments

Direct measurement of the structural change associated with amorphous solidification using static scattering of coherent radiation.

In this paper, we demonstrate that the weak temperature dependence of the structure factor of supercooled liquids, a defining feature of the glass transition, is a consequence of the averaging of the scattering intensity due to angular averaging. We show that the speckle at individual wavevectors, calculated from a simulated glass former, exhibits a Debye-Waller factor with a sufficiently large temperature dependence to represent a structural order parameter capable of distinguishing liquid from glass. We also extract from the speckle intensities a quantity proportional to the variance of the local restraint, i.e., a direct experimental measure of the amplitude of structural heterogeneity.

Dynamic Gardner cross-over in a simple glass.

The criticality of the jamming transition responsible for amorphous solidification has been theoretically linked to the marginal stability of a thermodynamic Gardner phase. While the critical exponents of jamming appear independent of the preparation history, the pertinence of Gardner physics far from equilibrium is an open question. To fill this gap, we numerically study the nonequilibrium dynamics of hard disks compressed toward the jamming transition using a broad variety of protocols. We show that dynamic signatures of Gardner physics can be disentangled from the aging relaxation dynamics. We thus define a generic dynamic Gardner cross-over regardless of the history. Our results show that the jamming transition is always accessed by exploring increasingly complex landscape, resulting in anomalous microscopic relaxation dynamics that remains to be understood theoretically.

Amorphous solidification of a supercooled liquid in the limit of rapid cooling.

We monitor the transformation of a liquid into an amorphous solid in simulations of a glass forming liquid by measuring the variation of a structural order parameter with either changing temperature or potential energy to establish the influence of the cooling rate on amorphous solidification. We show that the latter representation, unlike the former, exhibits no significant dependence on the cooling rate. This independence extends to the limit of instantaneous quenches, which we find can accurately reproduce the solidification observed during slow cooling. We conclude that amorphous solidification is an expression of the topography of the energy landscape and present the relevant topographic measures.

Non-equilibrium view of the amorphous solidification of liquids with competing interactions.

The interplay between short-range attractions and long-range repulsions (SALR) characterizes the so-called liquids with competing interactions, which are known to exhibit a variety of equilibrium and non-equilibrium phases. The theoretical description of the phenomenology associated with glassy or gel states in these systems has to take into account both the presence of thermodynamic instabilities (such as those defining the spinodal line and the so called λ line) and the limited capability to describe genuine non-equilibrium processes from first principles. Here, we report the first application of the non-equilibrium self-consistent generalized Langevin equation theory to the description of the dynamical arrest processes that occur in SALR systems after being instantaneously quenched into a state point in the regions of thermodynamic instability. The physical scenario predicted by this theory reveals an amazing interplay between the thermodynamically driven instabilities, favoring equilibrium macro- and micro-phase separation, and the kinetic arrest mechanisms, favoring non-equilibrium amorphous solidification of the liquid into an unexpected variety of glass and gel states.

Microscopic structure evolution and amorphous solidification mechanism of liquid quinary Zr<sub>57</sub>Cu<sub>20</sub>Al<sub>10</sub>Ni<sub>8</sub>Ti<sub>5</sub> alloy

The substantial undercooling and rapid solidification of liquid quinary Zr<sub>57</sub>Cu<sub>20</sub>Al<sub>10</sub>Ni<sub>8</sub>Ti<sub>5</sub> alloy are achieved by electromagnetic levitation (EML) technique. The amorphous solidification mechanism is revealed with molecular dynamics (MD) simulation. It is observed in EML experiment that the containerlessly solidified alloy is characterized by a core-shell structure, with mainly amorphous phase becoming the core and crystalline ZrCu, Zr<sub>2</sub>Cu and Zr<sub>8</sub>Cu<sub>5</sub> phases forming the shell. The volume fraction of amorphous core structure increases with undercooling and attains a value up to 81.3% at the maximum experimental undercooling of 300 K, which indicates that the critical undercooling required for complete amorphous solidification is 334 K. TEM analyses show that the alloy microstructure is mainly composed of Zr<sub>8</sub>Cu<sub>5</sub> phase, whereas the ZrCu phase and Zr<sub>2</sub>Cu phase are suppressed when liquid undercooling approaches this threshold. Once the critical undercooling is reached, amorphous solidification prevails over the crystallization of Zr<sub>8</sub>Cu<sub>5</sub> phase. In addition, a small quantity of amorphous phases are found in the crystalline shell and a little trace of Zr<sub>8</sub>Cu<sub>5</sub> nano-cluster is detected among the amorphous core. It is further verified by MD simulation that the formation of amorphous phase in the shell is caused by the microsegregation-induced solutal undercooling when liquid alloy attains the critical undercooling, while the nano-clusters within the core is mainly ascribed to the micro-thermal fluctuation effect inside highly undercooled liquid phase.

A general structural order parameter for the amorphous solidification of a supercooled liquid.

The persistent problem posed by the glass transition is to develop a general atomic level description of amorphous solidification. The answer proposed in this paper is to measure a configuration's capacity to restrain the motion of the constituent atoms. Here, we show that the instantaneous normal modes can be used to define a measure of atomic restraint that accounts for the difference between fragile and strong liquids and the collective length scale of the supercooled liquid. These results represent a significant simplification of the description of amorphous solidification and provide a powerful systematic treatment of the influence of microscopic factors on the formation of an amorphous solid.

A kinetic transition from peritectic crystallization to amorphous solidification of rapidly quenched refractory Nb-Ni alloy

In this study, the kinetic transition of solidification modes for refractory peritectic Nb54Ni46 alloy was revealed using melting spinning experiments combined with molecular dynamics (MD) simulation and classical nucleation theory. This begins with a shift from the usual peritectic solidification to the direct precipitation of the peritectic Nb7Ni6 phase when the roller speed reaches 10 m/s. Once the roller speed exceeds 20 m/s, the nucleation of the Nb7Ni6 phase is suppressed and the amorphous phase forms. The high-resolution transmission electron microscopy images indicate that the stacking fault and twining model of the peritectic Nb7Ni6 phase are {101¯2}/<1¯011> with a misorientation angle of 35.65°. The results of an individual local crystallization zone in amorphous matrix imply that the chemically disordered crystalline structure is more likely to form during the early stages of nucleation and growth, whereas the chemically ordered crystalline structure may evolve during the growth of the complex intermetallic compound Nb7Ni6 phase. Furthermore, the MD simulation of the glass transition temperature agrees well with the experiment, and the Voronoi polyhedron analysis suggests that the Ni-centered 〈0,0,12,0〉, 〈0,2,8,2〉 as well as Nb-centered 〈0,1,10,4〉 icosahedron-like clusters and their medium-range ordered structures play an important role in the formation of amorphous Nb54Ni46 alloy. In addition, the predictions made using classical nucleation theory and the time-temperature-transformation diagram propose that the phase selection rules are consistent with the experimental results as the undercooling and cooling rate increase, with the critical cooling rate for the formation of amorphous phase determined to be 1.71 × 107 K/s.

Effect of Calcium Oxide on the Structure and the Thermal Properties of Granulated High-Iron Slags

The effect of calcium oxide (3.5–11.1%) on the microstructure, the elemental composition, and the microhardness of the phases that form during the water granulation of the molten slags having formed in autogenous smelting of copper–zinc concentrates is studied by metallography, X-ray diffraction, and electron-probe microanalysis. The slag granulation leads to the formation of an amorphous component, the amount of which decreases with increasing calcium oxide content. Copper, lead, and arsenic in the slags are mainly in the form of sulfide inclusions, and zinc is present in both sulfides and oxides. The introduction of calcium oxide in the slags (up to 11.1%) promotes coarsening of sulfide inclusions and an increase in the microhardness of the silicate phases. Differential scanning calorimetry is used to determine the thermal properties of the slags, namely, the temperatures and heats of devitrification, “cold crystallization” of amorphous phases, melting, and solidification. The results obtained can be used to choose slag cooling conditions and to prepare slags for the extraction of valuable metals by beneficiation methods.

Design rules for glass formation from model molecules designed by a neural-network-biased genetic algorithm.

The glass transition - an apparent amorphous solidification process - is a central feature of the physical properties of soft materials such as polymers and colloids. A key element of this phenomenon is the observation of a broad spectrum of deviations from an Arrhenius temperature of dynamics in glass-forming liquids, with the extent of deviation quantified by the "fragility" of glass formation. The underlying origin of "fragile" glass formation and its dependence on molecular structure remain major open questions in condensed matter physics and soft materials science. Here we employ molecular dynamics simulations, together with a neural-network-biased genetic algorithm, to design and study model rigid molecules spanning a broad range of fragilities of glass formation. Results indicate that fragility of glass formation can be controlled by tuning molecular asphericity, with extended molecules tending to exhibit low fragilities and compact molecules tending toward higher fragilities. The glass transition temperature itself, on the other hand, correlates well with high-temperature activation behavior and with density. These results point the way towards rational design of glass-forming liquids spanning a range of dynamical behavior, both via these physical insights and via future extensions of this evolutionary design strategy to real chemistries. Finally, we show that results compare well with predictions of the nonlinear Langevin theory of liquid dynamics, which is a precursor of the more recently developed elastically collective nonlinear Langevin equation theory of Mirigian and Schweizer, identifying this framework as a promising basis for molecular design of the glass transition.

Weak and Strong Gels and the Emergence of the Amorphous Solid State.

Gels are amorphous solids whose macroscopic viscoelastic response derives from constraints in the material that serve to localize the constituent molecules or particles about their average positions in space. These constraints may either be local in nature, as in chemical cross-linking and direct physical associations, or non-local, as in case of topological “entanglement” interactions between highly extended fiber or sheet structures in the fluid. Either of these interactions, or both combined, can lead to “gelation” or “amorphous solidification”. While gels are often considered to be inherently non-equilibrium materials, and correspondingly termed “soft glassy matter”, this is not generally the case. For example, the formation of vulcanized rubbers by cross-linking macromolecules can be exactly described as a second order phase transition from an equilibrium fluid to an equilibrium solid state, and amorphous solidification also arises in diverse physical gels in which molecular and particle localization occurs predominantly through transient molecular associations, or even topological interactions. As equilibrium, or near equilibrium systems, such gels can be expected to exhibit universal linear and non-linear viscoelastic properties, especially near the “critical” conditions at which the gel state first emerges. In particular, a power-law viscoelastic response is frequently observed in gel materials near their “gelation” or “amorphous solidification” transition. Another basic property of physical gels of both theoretical and practical interest is their response to large stresses at constant shear rate or under a fixed macroscopic strain. In particular, these materials are often quite sensitive to applied stresses that can cause the self-assembled structure to progressively break down under flow or deformation. This disintegration of gel structure can lead to “yield” of the gel material, i.e., a fluidization transition, followed by shear thinning of the resulting heterogeneous “jelly-like” fluid. When the stress is removed, however, the material can relax back to its former equilibrium gel state, i.e., gel rejuvenation. In contrast, a non-equilibrium material will simply change its form and properties in a way that depends on processing history. Physical gels are thus unique self-healing materials in which the existence of equilibrium ensures their eventual recovery. The existence of equilibrium also has implications for the nature of both the linear and non-linear rheological response of gel materials, and the present paper explores this phenomenon based on simple scaling arguments of the kind frequently used in describing phase transitions and the properties of polymer solutions.

Compression Freezing Kinetics of Water to Ice VII.

Time-resolved x-ray diffraction (XRD) of compressed liquid water shows transformation to ice VII in 6nsec, revealing crystallization rather than amorphous solidification during compression freezing. Application of classical nucleation theory indicates heterogeneous nucleation and one-dimensional (e.g., needlelike) growth. These first XRD data demonstrate rapid growth kinetics of ice VII with implications for fundamental physics of diffusion-mediated crystallization and thermodynamic modeling of collision or impact events on ice-rich planetary bodies.

Physics of active jamming during collective cellular motion in a monolayer

Although collective cell motion plays an important role, for example during wound healing, embryogenesis, or cancer progression, the fundamental rules governing this motion are still not well understood, in particular at high cell density. We study here the motion of human bronchial epithelial cells within a monolayer, over long times. We observe that, as the monolayer ages, the cells slow down monotonously, while the velocity correlation length first increases as the cells slow down but eventually decreases at the slowest motions. By comparing experiments, analytic model, and detailed particle-based simulations, we shed light on this biological amorphous solidification process, demonstrating that the observed dynamics can be explained as a consequence of the combined maturation and strengthening of cell-cell and cell-substrate adhesions. Surprisingly, the increase of cell surface density due to proliferation is only secondary in this process. This analysis is confirmed with two other cell types. The very general relations between the mean cell velocity and velocity correlation lengths, which apply for aggregates of self-propelled particles, as well as motile cells, can possibly be used to discriminate between various parameter changes in vivo, from noninvasive microscopy data.

22. Avoiding the problems of ice in tissues via vitrification

Cryopreservation involving freezing in the presence of protective agents such as dimethyl sulfoxide is a well-established method for storing cells and small tissues. While successful techniques for cryopreservation have been developed over the past seven decades, they are generally related to small specimens, in the scale-range of cell suspensions and clusters to small-organized tissues ( μ m to mm range), with blood cells, stem cells, embryos and pancreatic islets as examples. Cryopreservation of larger-size specimens (cm and above) has been accomplished only in cases where the mechanical functionality has a higher priority need than the recovery of biological functionality, as with heart valves. There is evidence that ice formation within the extracellular matrix of multicellular tissues is the principal event that limits the survival of cryopreserved tissues using conventional freezing techniques. This mode of injury can be circumvented by using an ice-free cryopreservation approach, known as vitreous cryopreservation. Vitrification, the amorphous solidification of a supercooled liquid, can be achieved by adjusting the solute composition and thermal processing rates such that nucleation and growth of ice crystals are essentially prevented. Avoidance of ice by vitrification can be generally achieved with one of two approaches or a combination of both. The first approach employs cooling highly concentrated solutions (typically > 50% w/w) that become sufficiently viscous at low temperatures to suppress crystallization rates. Typically, a vitrified material is considered solid when the viscosity reaches 10 15 poise. Vitrification can also be achieved by selecting sufficiently high cooling rates to prevent ice crystallization in relatively dilute solutions ( 50% w/w). This second approach generally produces a metastable state that is at risk of devitrification and/or recrystallization during warming. Ice formation during warming is just as potentially injurious as during cooling. Applications of the vitrification approach to the cryopreservation of viable tissues such as blood vessels and cartilage has been demonstrated to result in a dramatic improvement in post-rewarm functionality from a meagre 20% after classical freezing to a respectable > 80% after ice-free cryopreservation. These achievements provide confidence and enthusiasm that this approach holds great promise for future cryobanking of complex bulky tissues and organs, with an isolated case of kidney cryopreservation having been reported. Nevertheless there are well recognized challenges that remain to be investigated and resolved. While vitrification is a well-understood phenomenon, its application to biological systems comes with potentially harmful effects of toxicity of the cryoprotectants and structural damage due to thermo-mechanical stresses. In fact, these effects represent competing needs important for selecting cryoprotectants and their concentrations, and represent a significant barrier to the development of cryopreservation technology. New approaches to alleviate this couple molecules that modulate ice nucleation and growth with the cryoprotectant cocktail. Both natural and synthetic compounds are being explored as a new class of additives that are anticipated to be essential for ice-free cryopreservation of bulky tissues and organs. In addition, new innovative technologies are conceived to address the challenges associated with the needed for uniform heating of vitrified tissues to avoid the problems of devitrification and recrystallization during warming.

Cationic gel crystals and amorphous solids of lightly cross-linked poly(2-vinylpyridine) spheres in the deionized aqueous suspension

Colloidal crystallization and amorphous solidification of deionized suspensions of the polydispersed cationic gel spheres of lightly cross-linked poly(2-vinylpyridine), CAIBA-P2VP (107∼113 nm in diameter, ±19∼22 nm in dispersity), have been studied from the reflection spectroscopy, morphology, phase diagram, and elastic property. Crystallization takes place even for the polydispersed cationic gel spheres by the significant contribution of the extended electrical double layers formed around the spheres. Critical concentrations of melting coexisted with ion exchange resins were around 0.02 in volume fraction and high compared with those of other cationic and anionic gel crystals examined hitherto. The densities (ρ) of CAIBA-P2VP in suspension state, i.e., weight percent of the gel spheres divided by the corresponding volume percent, was around 0.3. The ρ values decreased sharply with decreasing size of P2VP gel spheres, which supports the small gel spheres containing much water inside and being softer than the large ones. The closest intersphere distances of the crystals and/or amorphous solids were much longer than the hydrodynamic diameters of the gel spheres especially at low sphere concentrations. Fluctuation parameters (b) evaluated from the rigidities of CAIBA-P2VP (0.15∼0.28) were large compared with those of gel crystals of large-sized P2VP-based cationic gel spheres, anionic thermosensitive gel spheres of poly(N-isopropylacrylamide) (0.05∼0.09) and further much larger than those of typical colloidal hard spheres (around 0.03). The dispersity in sphere size played an important role for distinguishing crystal and amorphous solid. Importance of the extended electrical double layers around the cationic gel spheres is supported in addition to the excluded volume effect of the sphere themselves on the crystallization and/or solidification.

Nucleation kinetics of continuously cooling Fe–17 at.%B droplets produced by controlled capillary jet breakup

A new method for the investigation of the nucleation kinetics of traveling droplets was applied to mono-size droplets of an Fe–17 at.%B alloy generated by a controlled capillary jet breakup process. The developed method determines the in-flight nucleation kinetics of droplets from metallographic data and simulated droplet-cooling schedules. An iterative procedure is used to cross-validate the metallographic data and the model predictions. With the cross-validated data and simulation models, nucleation temperatures of Fe–17 at.%B droplets were calculated for various diameters and cooling conditions and shown in the form of continuous-cooling transformation (CCT) diagrams. The critical cooling rate for the amorphous solidification of Fe–17 at.%B droplets was predicted as a function of droplet diameter and verified metallographically.

Cryoreservation of alginate–fibrin beads involving bone marrow derived mesenchymal stromal cells by vitrification

Application of cell-–biomaterial systems in regenerative medicine can be facilitated by their successful low temperature preservation. Vitrification, which avoids ice crystal formation by amorphous solidification, is an emerging approach to cryopreservation. Developing vitrification strategy, effective cryopreservation of alginate–fibrin beads with porcine mesenchymal stromal cells has been achieved in this study. The cell–biomaterial constructs were pre-cultured for 20 days before cryopreservation, allowing for cell proliferation and construct stabilization. Ethylene glycol (EG) was employed as the basic cryoprotectant for two equilibration solutions. Successful cryopreservation of the constructs was achieved using vitrification solution composed of penetrating (EG MW 62 Da) and non-penetrating (sucrose MW 342 Da) cryoprotectants. Stepwise procedure of introduction to and removal of cryoprotectants was brief; direct plunging into liquid nitrogen was applied. Cell viability, evaluated by combining live/death staining and confocal laser microscopy, was similar for both control and vitrified cells in the beads. No detectable damage of microstructure of cryopreserved beads was found as shown by scanning electron microscopy. Both osteogenically induced control and vitrified cells in the constructs were equally capable of mineral production and deposition. There was no statistically significant difference in metabolic activity and proliferation between both groups during the entire culture period. Our study leads to the conclusion that the developed cryopreservation protocol allowed to maintain the integrity of the beads while preserving the ability of the pig bone marrow derived mesenchymal stromal cells to proliferate and subsequently differentiate; demonstrating that vitrification is a promising approach for cryopreser-vation of “ready-to-use” cell–biomaterial constructs.

The effect of rapidly solidified microstructures on martensitic transformation behaviours in Ti 50Ni 30Cu 20 alloys

Ti 50Ni 30Cu 20 (at.%) alloy ribbons have been fabricated by melt spinning and then their microstructures and shape memory characteristics were investigated by means of X-ray diffraction optical and transmission electron microscopies and differential scanning calorimetry. In these experiments particular attention has been paid to change the velocity of cooling wheel from 33 m/s to 55 m/s to control the thickness of ribbons. Microstructural analysis of melt-spun ribbons showed that the proportion of amorphous solidification at the chilled side of the ribbon increased with wheel. The perfect amorphous ribbon was produced in Ti 50Ni 30Cu 20 alloy when the ribbon was fabricated at the wheel velocity of 55 m/s and the melt spinning temperature of 1500 °C. After annealing the amorphous ribbons at 440 °C for 10 min, they were crystallized with fine grains of B19 phase. The effect of these microstructural changes on martensitic transformation behaviours is discussed.

Thermodynamics of Liquid Alloys and Metastable Phase Transformations in the Copper - Titanium System

We have used solution calorimetry at temperatures of 1573 K and 1873 K over broad concentration ranges to study the mixing enthalpy of Cu - Ti liquid alloys. The molar mixing enthalpies of the system are significant negative values. We have established the temperature dependence of the molar mixing enthalpies of the system: there is an increase in their exothermicity as the temperature is lowered. The significant negative mixing enthalpies of the system allow us to conclude that the chemical bonds are localized in the studied melts and consequently associates form. We tested this conclusion within ideal associated solution theory, which describes well the results obtained with a set of CuTi and CuTi2 associates. Using the model obtained, we have calculated the excess thermodynamic functions of mixing (enthalpy, Gibbs free energy, heat capacity) for the liquid alloys. We estimated the Gibbs energies of fcc, bcc, and hcp solutions in the system by the CALPHAD method, using data from the initial sections of the phase diagrams and from the corresponding thermodynamic data. We have calculated the metastable phase equilibria between the limiting solid solutions and the liquid or supercooled liquid phase. It was shown that for the supercooled liquid and the amorphous phase, a broad concentration range of relative thermodynamic stability can be obtained. The concentration range of amorphization of Cu - Ti melts corresponds to the position of the metastable liquidus line and the T0 line at temperatures close to the temperature range of amorphous solidification.