Building and Breaking Bonds by Homogenous Nucleation in Glass-Forming Melts Leading to Transitions in Three Liquid States

The thermal history of melts leads to three liquid states above the melting temperatures T_m containing clusters—bound colloids with two opposite values of enthalpy +Δε_lg × ΔH_m and −Δε_lg × ΔH_m and zero. All colloid bonds disconnect at T_n+ > T_m and give rise in congruent materials, through a first-order transition at T_LL = T_n+, forming a homogeneous liquid, containing tiny superatoms, built by short-range order. In non-congruent materials, (T_n+) and (T_LL) are separated, T_n+ being the temperature of a second order and T_LL the temperature of a first-order phase transition. (T_n+) and (T_LL) are predicted from the knowledge of solidus and liquidus temperatures using non-classical homogenous nucleation. The first-order transition at T_LL gives rise by cooling to a new liquid state containing colloids. Each colloid is a superatom, melted by homogeneous disintegration of nuclei instead of surface melting, and with a Gibbs free energy equal to that of a liquid droplet containing the same magic atom number. Internal and external bond number of colloids increases at T_n+ or from T_n+ to T_g. These liquid enthalpies reveal the natural presence of colloid–colloid bonding and antibonding in glass-forming melts. The Mpemba effect and its inverse exist in all melts and is due to the presence of these three liquid states.     

Non-Isothermal Kinetic Analysis of the Crystallization of Metallic Glasses Using the Master Curve Method

The non-isothermal transformation rate curves of metallic glasses are analyzed with the Master Curve method grounded in the Kolmogorov-Johnson-Mehl-Avrami theory. The method is applied to the study of two different metallic glasses determining the activation energy of the transformation and the experimental kinetic function that is analyzed using Avrami kinetics. The analysis of the crystallization of Cu₄₇Ti₃₃Zr₁₁Ni₈Si₁ metallic glassy powders gives E_a = 3.8 eV, in good agreement with the calculation by other methods, and a transformation initiated by an accelerating nucleation and diffusion-controlled growth. The other studied alloy is a Nanoperm-type Fe₇₇Nb₇B₁₅Cu₁ metallic glass with a primary crystallization of bcc-Fe. An activation energy of E_a = 5.7 eV is obtained from the Master Curve analysis. It is shown that the use of Avrami kinetics is not able to explain the crystallization mechanisms in this alloy giving an Avrami exponent of n = 1.     

Calorimetric glass transition in a mean-field theory approach

The study of the properties of glass-forming liquids is difficult for many reasons. Analytic solutions of mean-field models are usually available only for systems embedded in a space with an unphysically high number of spatial dimensions; on the experimental and numerical side, the study of the properties of metastable glassy states requires thermalizing the system in the supercooled liquid phase, where the thermalization time may be extremely large. We consider here a hard-sphere mean-field model that is solvable in any number of spatial dimensions; moreover, we easily obtain thermalized configurations even in the glass phase. We study the 3D version of this model and we perform Monte Carlo simulations that mimic heating and cooling experiments performed on ultrastable glasses. The numerical findings are in good agreement with the analytical results and qualitatively capture the features of ultrastable glasses observed in experiments.The theoretical interpretation of the properties of glasses is highly debated. There are two extreme viewpoints:

• • One approach, the random first-order transition (RFOT) theory (1), which uses mostly the replica method (2) as its central tool, assumes that the dynamical properties of glasses do reflect the properties of the appropriate static quantities [such as the Franz–Parisi potential (3); for a review see refs. 2 and 4].
• • The other approach, kinetically constrained models (KCMs), assumes that the glass transition is a purely dynamical phenomenon without any counterpart in static quantities (5–7).

The mean-field version of the RFOT approach predicts the presence of a dynamical transition [identified with the mode-coupling transition (8)] at a nonzero temperature T_d, whereupon the configuration space of the glass former splits into a collection of metastable states. Below T_d the system will remain trapped inside a metastable state. Beyond mean-field theory the dynamical transition T_d becomes a cross-over point: At T_d the correlation time and the dynamical correlation length become very large, but finite. Below T_d, the relaxation time increases rapidly and becomes comparable with human timescales, leading to the phenomenological glass transition. In the KCM approach this slowdown is a phenomenon originated only by constraints on the dynamics, whereas the RFOT picture views the off-equilibrium states as metastable, thermodynamic states, that can be identified with the minima of a suitable equilibrium free-energy functional and then studied using a modified equilibrium formalism, generally built on the replica method.According to replica formalism, the system explores the whole collection of possible states, with lower and lower free energy, as the temperature is lowered from T_d to another temperature T_K (the Kauzmann temperature), where the states with the lowest free energy are reached. Most RFOT models (but actually not all, because T_K = 0 for some models) predict then an equilibrium phase transition at T_K, with a real divergence of the relaxation time.To test this scenario, it would be necessary to perform experiments and simulations at various temperatures in this range, but then one must face the problem of equilibrating the glass former at temperatures T ≈ T_K ? T_g (where T_g is the phenomenological glass transition temperature), where it is by definition impossible to do so. Indeed, a simple estimate shows that the increase of the equilibration time below T_d is so sharp that one cannot get nearer to T_K than ΔT ≈ ?T_K without falling out of equilibrium, making it impossible for us to get a good look at the lowest states: Only the high free-energy states near T_d can be probed experimentally.Some progress in this direction has been made recently both in experiments (9) and numerical simulations (10), with the introduction of the so-called vapor deposition technique, which allows one to obtain extraordinarily stable glasses [usually referred to as ultrastable glasses (10–13)] in a relatively short time, even for temperatures much lower than T_d. First numerical simulations on an ultrastable glass of binary Lennard-Jones mixture seem to support the existence of a thermodynamic phase transition (10). On the theoretical side, the intrinsic out-of-equilibrium nature of glass poses another challenge, because the methods of equilibrium statistical mechanics cannot be used in the usual way, requiring, in principle, to resort to dynamical tools. This strategy is actually viable and was used, for example, by Keys et al. (14), where a suitably tuned East model has been shown to reproduce well the experimental behavior observed in DSC (differential scanning calorimetry) experiments on different glass-former materials, for example glycerol (15) and boron oxide (16). This approach, however, has the drawback of being phenomenological in nature.The recent introduction (17) of a semirealistic soluble model for glasses, the Mari–Kurchan (MK) model, gives us the possibility of addressing both the equilibration and the theoretical problem. It allows us to obtain equilibrated configurations also beyond the dynamical transition and deep into the glass phase, using the so-called planting method (18). Moreover, it is in principle solvable in the replica method, allowing us to study the metastable glassy states with a static formalism, without having to solve the dynamics.Our aim is to use this model to simulate slow annealing experiments usually performed on glasses and ultrastable glasses, to compare the numerical outcomes with experimental results and theoretical predictions in the replica method.     

Analysis of the Crystallization Kinetics and Thermal Stability of the Amorphous Mg72Zn24Ca4 Alloy

The aim of this study was to analyze the crystallization of the Mg₇₂Zn₂₄Ca₄ metallic glass alloy. The crystallization process of metallic glass Mg₇₂Zn₂₄Ca₄ was investigated by means of the differential scanning calorimetry. The glass-forming ability and crystallization are both strongly dependent on the heating rate. The crystallization kinetics, during the isothermal annealing, were modelled by the Johnson–Mehl–Avrami equation. Avrami exponents were from 2.7 to 3.51, which indicates diffusion-controlled grain growth. Local exponents of the Johnson–Mehl–Avrami equation were also calculated. In addition, the Mg phase—being the isothermal crystallization product—was found, and the diagram of the time–temperature phase transformation was developed. This diagram enables the reading of the start and end times of the crystallization process, occurring in amorphous ribbons of the Mg₇₂Zn₂₄Ca₄ alloy on the isothermal annealing temperature. The research showed high stability of the amorphous structure of Mg₇₂Zn₂₄Ca₄ alloy at human body temperature.     

Delocalization of Electrons in Strong Insulators at High Dynamic Pressures

Systematics of material responses to shock flows at high dynamic pressures are discussed. Dissipation in shock flows drives structural and electronic transitions or crossovers, such as used to synthesize metallic liquid hydrogen and most probably Al₂O₃ metallic glass. The term “metal” here means electrical conduction in a degenerate system, which occurs by band overlap in degenerate condensed matter, rather than by thermal ionization in a non-degenerate plasma. Since H₂ and probably disordered Al₂O₃ become poor metals with minimum metallic conductivity (MMC) virtually all insulators with intermediate strengths do so as well under dynamic compression. That is, the magnitude of strength determines the split between thermal energy and disorder, which determines material response. These crossovers occur via a transition from insulators with electrons localized in chemical bonds to poor metals with electron energy bands. For example, radial extents of outermost electrons of Al and O atoms are 7 a₀ and 4 a₀, respectively, much greater than 1.7 a₀ needed for onset of hybridization at 300 GPa. All such insulators are Mott insulators, provided the term “correlated electrons” includes chemical bonds.     

Physical vapor deposition as a route to hidden amorphous states

Stable glasses of indomethacin (IMC) were prepared by using physical vapor deposition. Wide-angle X-ray scattering measurements were performed to characterize the average local structure. IMC glasses prepared at a substrate temperature of 0.84 T_g (where T_g is the glass transition temperature) and a deposition rate of 0.2 nm/s show a broad, high-intensity peak at low q values that is not present in the supercooled liquid or melt-quenched glasses. When annealed slightly above T_g, the new WAXS pattern transforms into the melt-quenched glass pattern, but only after very long annealing times. For a series of samples prepared at the lowest deposition rate, the new local packing arrangement is present only for deposition temperatures below T_g −20 K, suggesting an underlying first-order liquid-to-liquid phase transition.     

Solid-State Polymerization as a Vitrimerization Tool Starting from Available Thermoplastics: The Effect of Reaction Temperature

In the current work, solid-state polymerization (SSP) was studied for the synthesis of poly(butylene terephthalate), PBT-based vitrimers. A two-step process was followed; the first step involved alcoholysis reactions and the incorporation of glycerol in the polymer chains. The second step comprised transesterification reactions in the solid state (SSP) in the presence of zinc(II) catalyst resulting in the formation of a dynamic crosslinked network with glycerol moieties serving as the crosslinkers. The optimum SSP conditions were found to be 3 h at 180 °C under N₂ flow (0.5 L/min) to reach high vitrimer insolubility (up to 75%) and melt strength (2.1 times reduction in the melt flow rate) while increasing the crosslinker concentration (from 3.5 to 7 wt.%) improved further the properties. Glass transition temperature (T_g) was almost tripled in vitrimers compared to initial thermoplastic, reaching a maximum of 97 °C, whereas the melting point (T_m) was slightly decreased, due to loss of symmetry perfection under the influence of the crosslinks. Moreover, the effect of the dynamic crosslinked structure on PBT crystallization behavior was investigated in detail by studying the kinetics of non-isothermal crystallization. The calculated effective activation energy using the Kissinger model and the nucleating activity revealed that the higher crosslinker content impeded and slowed down vitrimers melt crystallization, also inducing an alteration in the crystallization mechanism towards sporadic heterogeneous growth.     

Magnetic and Magneto-Caloric Properties of the Amorphous Fe92−xZr8Bx Ribbons

Magnetic and magnetocaloric properties of the amorphous Fe_92−xZr₈B_x ribbons were studied in this work. Fully amorphous Fe₈₉Zr₈B₃, Fe₈₈Zr₈B₄, and Fe₈₇Zr₈B₅ ribbons were fabricated. The Curie temperature (T_c), saturation magnetization (M_s), and the maximum entropy change with the variation of a magnetic field (−ΔS_m^peak) of the glassy ribbons were significantly improved by the boron addition. The mechanism for the enhanced T_c and −ΔS_m^peak by boron addition was studied.     

On Structural Rearrangements Near the Glass Transition Temperature in Amorphous Silica

The formation of clusters was analyzed in a topologically disordered network of bonds of amorphous silica (SiO₂) based on the Angell model of broken bonds termed configurons. It was shown that a fractal-dimensional configuron phase was formed in the amorphous silica above the glass transition temperature T_g. The glass transition was described in terms of the concepts of configuron percolation theory (CPT) using the Kantor-Webman theorem, which states that the rigidity threshold of an elastic percolating network is identical to the percolation threshold. The account of configuron phase formation above T_g showed that (i) the glass transition was similar in nature to the second-order phase transformations within the Ehrenfest classification and that (ii) although being reversible, it occurred differently when heating through the glass–liquid transition to that when cooling down in the liquid phase via vitrification. In contrast to typical second-order transformations, such as the formation of ferromagnetic or superconducting phases when the more ordered phase is located below the transition threshold, the configuron phase was located above it.     

Influence of Cr,Mn, Co and Ni Addition on Crystallization Behavior of Al13Fe4 Phase in Al-5Fe Alloys Based on ThermoDynamic Calculations

Alloying is an effective method to refine coarse grains of an Al₁₃Fe₄ phase and strengthen Al-Fe alloys. However, the grain refinement mechanism remains unclear in terms of the thermodynamics. Herein, the influence of M-element, i.e., Cr, Mn, Co and Ni, addition on the activity of Al and Fe atoms, Gibbs free energy of the Al₁₃Fe₄ nucleus in Al-Fe melt and the formation enthalpy of an Al₁₃Fe₄ phase in Al-Fe alloys is systematically investigated using the extended Miedema model, Wilson equation, and first-principle calculations, respectively. The results reveal that the addition of different M elements increases the activity of Fe atoms and reduces the Gibbs free energy of the Al₁₃Fe₄ nucleus in Al-Fe melt, where the incorporation of Ni renders the most obvious effect, followed by Mn, Co, and Cr. Additionally, the formation enthalpy decreases in the following order: Al₇₈(Fe₂₃Cr) > Al₇₈(Fe₂₃Mn) > Al₁₃Fe₄ > Al₇₈(Fe₂₃Ni) > Al₇₈(Fe₂₃Co), where the formation enthalpy of Al₇₈(Fe₂₃Ni) is close to Al₇₈(Fe₂₃Co). Moreover, the presence of Ni promotes the nucleation of the Al₁₃Fe₄ phase in Al-Fe alloys, which reveals the mechanism of grain refinement from a thermodynamics viewpoint.     

Thermal Evolutions to Glass-Ceramics Bearing Calcium Tungstate Crystals in Borate Glasses Doped with Photoluminescent Eu3+ Ions

Thermal evolutions of calcium-tungstate-borate glasses were investigated for the development of luminescent glass-ceramics by using Eu³⁺ dopant in a borate glass matrix with calcium tungstate, which was expected to have a combined character of glass and ceramics. This study revealed that single-phase precipitation of CaWO₄ crystals in borate glass matrix was possible by heat-treatment at a temperature higher than glass transition temperature T_g for (100−x) (33CaO-67B₂O₃)−xCa₃WO₆ (x = 8−15 mol%). Additionally, the crystallization of CaWO₄ was found by Raman spectroscopy due to the formation of W=O double bondings of WO₄ tetrahedra in the pristine glass despite starting with the higher calcium content of Ca₃WO₆. Eu³⁺ ions were excluded from the CaWO₄ crystals and positioned in the borate glass phase as a stable site for them, which provided local environments in higher symmetry around Eu³⁺ ions.     

Vortex Flow on the Surface Generated by the Onset of a Buoyancy-Induced Non-Boussinesq Convection in the Bulk of a Normal Liquid Helium

The onset of the Rayleigh–Benard convection (RBC) in a heated from above normal He-I layer in a cylindrical vessel in the temperature range T_λ < T ≤ T_m (RBC in non-Oberbeck–Boussinesq approximation) is attended by the emergence of a number of vortices on the free liquid surface. Here, T_λ = 2.1768 K is the temperature of the superfluid He-II–normal He-I phase transition, and the liquid density passes through a well-pronounced maximum at T_m ≈ T_λ + 6 mK. The inner vessel diameter was D = 12.4 cm, and the helium layer thickness was h ≈ 2.5 cm. The mutual interaction of the vortices between each other and their interaction with turbulent structures appeared in the layer volume during the RBC development gave rise to the formation of a vortex dipole (two large-scale vortices) on the surface. Characteristic sizes of the vortices were limited by the vessel diameter. The formation of large-scale vortices with characteristic sizes twice larger than the layer thickness can be attributed to the arising an inverse vortex cascade on the two-dimensional layer surface. Moreover, when the layer temperature exceeds T_m, convective flows in the volume decay. In the absence of the energy pumping from the bulk, the total energy of the vortex system on the surface decreases with time according to a power law.     

ESR evidence for 2 coexisting liquid phases in deeply supercooled bulk water

Using electron spin resonance spectroscopy (ESR), we measure the rotational mobility of probe molecules highly diluted in deeply supercooled bulk water and negligibly constrained by the possible ice fraction. The mobility increases above the putative glass transition temperature of water, T_g = 136 K, and smoothly connects to the thermodynamically stable region by traversing the so called “no man''s land” (the range 150–235 K), where it is believed that the homogeneous nucleation of ice suppresses the liquid water. Two coexisting fractions of the probe molecules are evidenced. The 2 fractions exhibit different mobility and fragility; the slower one is thermally activated (low fragility) and is larger at low temperatures below a fragile-to-strong dynamic cross-over at ≈225 K. The reorientation of the probe molecules decouples from the viscosity below ≈225 K. The translational diffusion of water exhibits a corresponding decoupling at the same temperature [Chen S-H, et al. (2006) The violation of the Stokes–Einstein relation in supercooled water. Proc Natl Acad Sci USA 103:12974–12978]. The present findings are consistent with key issues concerning both the statics and the dynamics of supercooled water, namely the large structural fluctuations [Poole PH, Sciortino F, Essmann U, Stanley HE (1992) Phase behavior of metastable water. Nature 360:324–328] and the fragile-to-strong dynamic cross-over at ≈228 K [Ito K, Moynihan CT, Angell CA (1999) Thermodynamic determination of fragility in liquids and a fragile-to-strong liquid transition in water. Nature 398:492–494].     

Liquid–liquid transition in supercooled water suggested by microsecond simulations

The putative liquid–liquid phase transition in supercooled water has been used to explain many anomalous behaviors of water. However, no direct experimental verification of such a phase transition has been accomplished, and theoretical studies from different simulations contradict each other. We investigated the putative liquid–liquid phase transition using the Water potential from Adaptive Force Matching for Ice and Liquid (WAIL). The simulation reveals a first-order phase transition in the supercooled regime with the critical point at ∼207 K and 50 MPa. Normal water is high-density liquid (HDL). Low-density liquid (LDL) emerges at lower temperatures. The LDL phase has a density only slightly larger than that of the ice-Ih and shows more long-range order than HDL. However, the transformation from LDL to HDL is spontaneous across the first-order phase transition line, suggesting the LDL configuration is not poorly formed nanocrystalline ice. It has been demonstrated in the past that the WAIL potential provides reliable predictions of water properties such as melting temperature and temperature of maximum density. Compared with other simple water potentials, WAIL is not biased by fitting to experimental properties, and simulation with this potential reflects the prediction of a high-quality first-principle potential energy surface.Many substances possess a phase transition between a gas and a liquid. The possibility of a second fluid–fluid phase transition between two liquids is less known. Experimental evidences have revealed several examples of liquid–liquid phase transitions (LLPTs), such as a pressure-induced phase transition between two forms of liquid phosphorus (1) and a similar phase transition in molten carbon (2). Sulfur is believed to have two LLPTs, the λ transition at low pressure (3) and a metal to nonmetal transition at high pressure (4). For these substances, the LLPTs occur above the melting temperature, T_m. For silicon, an amorphous–amorphous transition occurs below the glass transition temperature T_g, between two metastable phases. Although this transition has characteristics of a LLPT, it can also be argued that this is a transition between two metastable forms of the same phase. LLPTs have also been reported in other pure liquids or mixtures (5).One of the most intriguing and controversial LLPTs is the putative LLPT in water (6). The critical point of this phase transition is believed to be above the T_g but below the T_m. Experiments performed below T_g support a first-order phase transition between two amorphous forms of supercooled water (7–9). Investigating the transition experimentally above T_g is very challenging; ultrafast experiments have to be performed to compete with homogenous nucleation to gain insight into this regime of the phase space (6). Although experimental studies do support LLPT in confined water (10, 11), some evidences have indicated strong influence of water properties as a result of confinements (12).Mixed conclusions have been made from theoretical studies of the putative LLPT in water. A two-state thermodynamic model (13) and several simulations using atomistic water models, such as TIP4P/2005 (14), TIP5P (15), and ST2 (16, 17), support the existence of a LLPT; on the other hand, other models such as the coarse-grained mW potential do not support a LLPT (18). The conclusion from any atomistic simulation depends on the underlying model potential. These potentials, also referred to as force fields, were typically created by training to reproduce certain experimental properties. By training to experimental properties, it is hard to determine if cancelations of errors are responsible for reproducing the properties being fit. The predicting power for such models can be problematic. In addition, none of the atomistic models used previously correctly predict the phase diagram around the ice-Ih melting temperature. TIP4P/2005 gives a T_m too low by 20 K (19), ST2 overestimates T_m by almost 30 K (20), and TIP5P predicts ice-Ih to be metastable (21). It has been argued that simultaneous prediction of good T_m and liquid state properties is impossible with a simple point charge model (19).Rather than fitting to experimental properties, the Water potential from Adaptive Force Matching (22) for Ice and Liquid (WAIL) was created by fitting to a coupled-cluster quality potential energy surface (PES) of water (23) obtained through quantum mechanics and molecular mechanics (QM/MM) calculations. Both the parameters (24) and the energy expressions (25) of this model were optimized to best reproduce the first principle PES. At the same time, the WAIL potential only uses pair-wise point-charge–based energy expressions; this allows very long simulations to be performed on modern computers.The WAIL potential predicts the T_m of ice-Ih to be 270 K and a temperature of maximum density of 9 °C (24). When quantum nuclear effect is accounted for with path-integral simulations (26), the WAIL model also predicts the radial distribution functions (RDFs) and the heat of vaporization for both ice and liquid in good agreement with experiments. Not only is the performance of the WAIL potential significantly better than any other existing water models for simulation of ice–liquid mixtures, the WAIL model is not biased by fitting to experimental data; thus, simulation results from the WAIL model can be regarded as a true prediction based on the underlying electronic structure PES.     

Enhancement of Gamma-ray Shielding Properties in Cobalt-Doped Heavy Metal Borate Glasses: The Role of Lanthanum Oxide Reinforcement

The direct influence of La³⁺ ions on the gamma-ray shielding properties of cobalt-doped heavy metal borate glasses with the chemical formula 0.3CoO-(80-x)B₂O₃-19.7PbO-xLa₂O₃: x = 0, 0.5, 1, 1.5, and 2 mol% was examined herein. Several significant radiation shielding parameters were evaluated. The glass density was increased from 3.11 to 3.36 g/cm³ with increasing La³⁺ ion content from 0 to 2 mol%. The S5 glass sample, which contained the highest concentration of La³⁺ ions (2 mol%), had the maximum linear (μ) and mass (μ_m) attenuation coefficients for all photon energies entering, while the S1 glass sample free of La³⁺ ions possessed the minimum values of μ and μ_m. Both the half value layer (T_1/2) and tenth value layer (TVL) of all investigated glasses showed a similar trend of (T_1/2, TVL)_S1 > (T_1/2, TVL)_S2 > (T_1/2, TVL)_S3 > (T_1/2, TVL)_S4 > (T_1/2, TVL)_S5. Our results revealed that the S5 sample had the highest effective atomic number (Z_eff) values over the whole range of gamma-ray energy. S5 had the lowest exposure (EBF) and energy absorption (EABF) build-up factor values across the whole photon energy and penetration depth range. Our findings give a strong indication of the S5 sample’s superior gamma-ray shielding characteristics due to the highest contribution of lanthanum oxide.     

Features of the Structure and Electrophysical Properties of Solid Solutions of the System (1-x-y) NaNbO3-xKNbO3-yCd0.5NbO3

Ferroelectric ceramic materials based on the (1-x-y) NaNbO₃-xKNbO₃-yCd_0.5NbO₃ system (x = 0.05–0.65, y = 0.025–0.30, Δx = 0.05) were obtained by a two-stage solid-phase synthesis followed by sintering using conventional ceramic technology. It was found that the region of pure solid solutions extends to x = 0.70 at y = 0.05 and, with increasing y, it narrows down to x ≤ 0.10 at y = 0.25. Going out beyond the specified concentrations leads to the formation of a heterogeneous region. It is shown that the grain landscape of all studied ceramics is formed during recrystallization sintering in the presence of a liquid phase, the source of which is unreacted components (Na₂CO₃ with T_melt. = 1126 K, K₂CO₃ with T_melt. = 1164 K, KOH with T_melt. = 677 K) and low-melting eutectics in niobate mixtures (NaNbO₃, T_melt. = 1260 K, KNbO₃, T_melt. = 1118 K). A study of the electrophysical properties at room temperature showed the nonmonotonic behavior of all dependences with extrema near symmetry transitions, which corresponds to the logic of changes in the electrophysical parameters in systems with morphotropic phase boundaries. An analysis of the evolution of dielectric spectra made it possible to distinguish three groups of solid solutions: classical ferroelectrics (y = 0.05–0.10), ferroelectrics with a diffuse phase transition (y = 0.30), and ferroelectrics relaxors (y = 0.15–0.25). A conclusion about the expediency of using the obtained data in the development of materials and devices based on such materials has been made.     

Tunable molecular orientation and elevated thermal stability of vapor-deposited organic semiconductors

Physical vapor deposition is commonly used to prepare organic glasses that serve as the active layers in light-emitting diodes, photovoltaics, and other devices. Recent work has shown that orienting the molecules in such organic semiconductors can significantly enhance device performance. We apply a high-throughput characterization scheme to investigate the effect of the substrate temperature (T_substrate) on glasses of three organic molecules used as semiconductors. The optical and material properties are evaluated with spectroscopic ellipsometry. We find that molecular orientation in these glasses is continuously tunable and controlled by T_substrate/T_g, where T_g is the glass transition temperature. All three molecules can produce highly anisotropic glasses; the dependence of molecular orientation upon substrate temperature is remarkably similar and nearly independent of molecular length. All three compounds form “stable glasses” with high density and thermal stability, and have properties similar to stable glasses prepared from model glass formers. Simulations reproduce the experimental trends and explain molecular orientation in the deposited glasses in terms of the surface properties of the equilibrium liquid. By showing that organic semiconductors form stable glasses, these results provide an avenue for systematic performance optimization of active layers in organic electronics.Glasses (or amorphous solids) of low molecular weight organic compounds exhibit desirable properties for organic electronics. Because these materials are made from organic molecules, properties that depend on chemical identity such as optical absorptions, bandgap, and glass transition temperature can be tuned via chemical synthesis. These glasses have solid-like mechanical properties similar to those of crystalline materials, but offer morphological homogeneity, greater ease of processing, and nearly unlimited compositional tunability. An underappreciated feature of these materials, a result of their nonequilibrium nature, is that many different glasses can be prepared with the same chemical composition.There has been considerable recent interest in controlling molecular orientation in organic semiconducting glasses (1–7). Whereas one might expect all glasses to be isotropic because of their structural disorder, Yokoyama et al. and other groups have shown that molecular orientation in vapor-deposited glasses can be quite anisotropic (3, 4, 8, 9) and depend upon deposition conditions (3). It has recently been suggested that orientation resulting from deposition could be used as a figure of merit to identify promising compounds for these applications (10). Oriented materials can increase light outcoupling by a factor of 1.5 by directing emission out of the plane of the device (10–14). It has also been shown that oriented layers can improve device lifetime (15) and charge mobility (16–18). Given the potential utility of controlling molecular orientation in device layers (4, 5, 7), it is desirable to understand the extent to which molecular orientation can be tuned in glasses made from a particular compound and the mechanistic origins of this effect. Anisotropic glassy solids are also of interest for applications in optics and optoelectronics (19).Concurrently, other investigators have shown that vapor-deposited glasses can have desirable physical properties unobtainable by any other means, when the substrate temperature during deposition (T_substrate) is held somewhat below the glass transition temperature (T_g). Discovered using model glass formers and labeled “stable glasses,” these glasses have lower enthalpies (20), higher densities (21), and resist structural reorganization to higher temperatures than is possible with any other preparation route (22–24). The properties of stable glasses are explained by the high mobility of the free surface during the vapor deposition process (20, 25). Because of lowered constraints to motion (26), molecules near the free surface can adopt near-equilibrium packing arrangements during deposition even at temperatures where the bulk structural relaxation time is thousands of years (21, 27). Subsequent deposition traps this efficient packing into the bulk solid. Like organic semiconductors, stable glasses can be birefringent (21) and also anisotropic in wide-angle X-ray scattering (28, 29).Here we show that organic semiconductors form stable glasses, and that surface mobility during vapor deposition governs bulk molecular orientation in these materials. Using a high-throughput experimental scheme, we are able to efficiently characterize the effect of T_substrate on three organic compounds used in semiconducting devices: TPD, NPB, and DSA-Ph [Fig. 1E; N,N’-Bis(3-methylphenyl)-N,N’-diphenylbenzidine, N,N’-Di(1-napthyl)-N,N’-diphenyl-(1,1’-biphenyl)-4,4’-diamine, and 1–4-Di-[4-(N,N-diphenyl)amino]styryl-benzene, respectively]. We find that these compounds form stable glasses, and we show that the orientation of the vapor-deposited molecules is controlled by T_substrate/T_g and is nearly independent of the molecular aspect ratio. Using simulations, we show that anisotropic molecular orientation in the glass can be understood in terms of molecular orientation and mobility near the free surface of the equilibrium liquid. By connecting two apparently disparate bodies of work, we develop avenues for research on organic devices and the physics of glasses, and further the development of “designer” anisotropic solids.Open in a separate windowFig. 1.Schematic illustration of the experimental procedure. (A) Organic molecules are vapor-deposited in a vacuum chamber. A silicon substrate with a controlled range of temperatures allows simultaneous deposition of many glasses with different properties but identical chemical composition. (B) After vapor deposition, each glass is independently interrogated using spectroscopic ellipsometry with a focused beam. (C) Example optical constants for TPD at T_substrate = 215 K. The optical constants for light polarized normal to (z) and in the plane of the substrate (xy) can be independently determined (49). (D) Using the optical constants, the orientation order parameter, S_z, can be computed at each T_substrate. θ_z is the angle of the long molecular axis relative to the substrate normal and P₂ is the second Legendre polynomial. (E) Structures and glass transition temperatures for the three compounds studied.     

Magnetic Properties of the Ferromagnetic Shape Memory Alloys Ni50+xMn27?xGa23 in Magnetic Fields

Thermal strain, permeability, and magnetization measurements of the ferromagnetic shape memory alloys Ni_50+xMn_27−xGa₂₃ (x = 2.0, 2.5, 2.7) were performed. For x = 2.7, in which the martensite transition and the ferromagnetic transition occur at the same temperature, the martensite transition starting temperature T_Ms shift in magnetic fields around a zero magnetic field was estimated to be dT_Ms/dB = 1.1 ± 0.2 K/T, thus indicating that magnetic fields influences martensite transition. We discussed the itinerant electron magnetism of x = 2.0 and 2.5. As for x = 2.5, the M⁴ vs. B/M plot crosses the origin of the coordinate axis at the Curie temperature, and the plot indicates a good linear relation behavior around the Curie temperature. The result is in agreement with the theory by Takahashi, concerning itinerant electron ferromagnets.     

The Use of Thermal Techniques in the Characterization of Bio-Sourced Polymers

The public pressure about the problems derived from the environmental issues increasingly pushes the research areas, of both industrial and academic sectors, to design material architectures with more and more foundations and reinforcements derived from renewable sources. In these efforts, researchers make extensive and profound use of thermal analysis. Among the different techniques available, thermal analysis offers, in addition to high accuracy in the measurement, smartness of execution, allowing to obtain with a very limited quantity of material precious information regarding the property–structure correlation, essential not only in the production process, but overall, in the design one. Thus, techniques such as differential scanning calorimetry (DSC), differential thermal analysis (DTA), dynamic mechanical analysis (DMA) and thermogravimetric analysis (TGA) were, are, and will be used in this transition from fossil feedstock to renewable ones, and in the development on new manufacturing processes such as those of additive manufacturing (AM). In this review, we report the state of the art of the last two years, as regards the use of thermal techniques in biopolymer design, polymer recycling, and the preparation of recyclable polymers as well as potential tools for biopolymer design in AM. For each study, we highlight how the most known thermal parameters, namely glass transition temperature (T_g), melting temperature (T_f), crystallization temperature (T_c) and percentage (%c), initial decomposition temperature (T_i), temperature at maximum mass loss rate (T_m), and tan δ, helped the researchers in understanding the characteristics of the investigated materials and the right way to the best design and preparation.     

Compositional landscape for glass formation in metal alloys

A high-resolution compositional map of glass-forming ability (GFA) in the Ni–Cr–Nb–P–B system is experimentally determined along various compositional planes. GFA is shown to be a piecewise continuous function formed by intersecting compositional subsurfaces, each associated with a nucleation pathway for a specific crystalline phase. Within each subsurface, GFA varies exponentially with composition, wheres exponential cusps in GFA are observed when crossing from one crystallization pathway to another. The overall GFA is shown to peak at multiple exponential hypercusps that are interconnected by ridges. At these compositions, quenching from the high-temperature melt yields glassy rods with diameters exceeding 1 cm, whereas for compositions far from these cusps the critical rod diameter drops precipitously and levels off to 1 to 2 mm. The compositional landscape of GFA is shown to arise primarily from an interplay between the thermodynamics and kinetics of crystal nucleation, or more precisely, from a competition between driving force for crystallization and liquid fragility.The glass-forming ability, or GFA, of a liquid metal alloy is not an intrinsic material attribute, but rather defined by the absence of a viable crystallization pathway as the liquid is undercooled below its thermodynamic melting temperature (1, 2). Crystallization is typically triggered by nucleation of a particular crystalline phase, followed by other competing phases, often catalyzed by the presence of the first phase. Crystal nucleation rates depend not only on temperature, pressure, and alloy composition, but also on extrinsic factors such as the presence of chemical impurities, trace crystalline debris (e.g., oxide inclusions), container wall effects, or shear flow conditions in the liquid, to name a few (3–7). Variations in these extrinsic factors often lead to inconsistent and nonreproducible GFA.The classical nucleation theory of crystals in undercooled liquids was originally developed by Turnbull (1) to account for the substantial undercooling observed in elemental liquid metals. He later extended his theory to explain metallic glass formation in rapidly cooled low melting eutectic Au–Si and Au–Ge–Si alloys (8, 9). Below the liquidus temperature T_L, the liquid viscosity, η(T), rises steeply with falling temperature. A liquid ultimately freezes at a glass transition temperature T_g, where the viscosity reaches a solid-like value of ∼10¹² Pa⋅s. Turnbull considered the “reduced glass transition temperature” t_rg = T_g/T_L as a characteristic material parameter. He argued that crystal nucleation rates should fall precipitously as t_rg increases, becoming immeasurably small for t_rg ≈ 2/3. This is widely referred to as Turnbull’s criteria for bulk glass formation; it has been proven to be a valuable, albeit rough, guide in the development of bulk metallic glasses (10–12).In the present work, a systematic experimental approach is developed to quantify the intrinsic dependence of GFA on composition for near-eutectic multicomponent metal alloys. The optimization of GFA for quinary Ni–Cr–Nb–P–B alloys is presented as a case study wherein bulk glasses of centimeter thickness are achieved. This quinary system is based on the low melting binary Ni₈₁P₁₉ eutectic alloy with small additions of Cr and Nb as substitutes for Ni, and B as a substitute for P.Binary Ni–P and ternary Ni–Cr–P alloys have long been known to form glassy ribbons of 20 to 40-μm thickness on quenching from the melt at cooling rates of 10⁵ to 10⁶ K/s using rapid melt quenching approaches such as planar flow casting (13, 14). Following the discovery of bulk metallic glasses, Hashimoto and coworkers (15) as well as Inoue and coworkers (16) investigated bulk glass formation in quinary Ni–Cr–Nb–P–B alloys and identified specific alloy compositions capable of forming metallic glass rods with diameters of 1 to 2 mm. In the current investigation, by using an efficient and reproducible GFA assessment and optimization strategy, we report that maximum attainable metallic glass rod diameters in the same Ni–Cr–Nb–P–B system are an order of magnitude larger (1–2 cm) than reported in prior work.To accurately quantify the intrinsic composition dependence of GFA requires (i) precisely controlling alloy composition and impurity content, (ii) quantitatively and reproducibly determining GFA at a specific composition by controlling the sample cooling history, and (iii) minimizing the influence of extrinsic factors such as heterogeneous nucleation sites (foreign oxide inclusions, the container wall, etc.) and melt flow conditions during cooling. In this work, alloys with precisely controlled composition were produced from high-purity starting elements. GFA was determined by melting the alloys in silica tubes and subsequently water quenching to form metallic glass rods. The silica tubes exhibit no detectable reaction with the present alloys. Moreover, being a glass, the silica tube is not expected to induce heterogeneous nucleation at the inner wall. Finally, the melt being confined inside the tube during quenching does not undergo significant shear flow. As such, the cooling history of the sample is governed almost solely by conduction without any significant convection, and is therefore expected to be reproducible. GFA is characterized by a critical rod diameter, d_cr, defined as the largest diameter rod that can be quenched into a fully glassy structure without detectable crystallinity, as verified by X-ray diffraction. Additional details on the alloy preparation, cooling history, and determination of GFA are presented in Materials and Methods.The quinary Ni–Cr–Nb–P–B system has a 4D composition space with independent variables, w, x, y, and z, where composition is expressed as Ni_{100−w−x−y−z}Cr_wNb_xP_yB_z. The variables are in atomic percentages. In Fig. 1A, we present a detailed 2D GFA contour map associated with composition variation along 2 degrees of freedom, w and x, while keeping y and z constant at 16.5 and 3, respectively. This high-resolution contour map is based on the measured d_cr for 42 alloys. Two distinct local maxima with d_cr ≥ 10 mm are clearly evident in the contour map. More specifically, along the compositional line x = 4.0625−0.125w (where y and z are held constant at 16.5 and 3), a ridge interconnecting the two peaks is observed in the GFA landscape. The compositional dependence of GFA along this compositional line is presented in Fig. 1B. Along this ridge and within 4.5 < w < 10.5 (which corresponds to 2.75 < x < 3.5), d_cr is found to vary between 8 and 10 mm, whereas a precipitous dip in the GFA is observed for w < 4.5 and w > 10.5. At w = 5.6 and 8.5 (corresponding to x = 3.4 and 3), the compositions Ni_71.5Cr_5.6Nb_3.4P_16.5B₃ and Ni₆₉Cr_8.5Nb₃P_16.5B₃ are seen to exhibit local maxima with d_cr ≥ 10 mm.Open in a separate windowFig. 1.(A) Two-dimensional GFA contour map for Ni_80.5−w−xCr_wNb_xP_16.5B₃ alloys plotting the critical rod diameter d_cr against the Cr and Nb atomic concentrations w and x, while keeping the P and B atomic concentrations y and z constant at 16.5% and 3%, respectively. (B) One-dimensional GFA plot for Ni_{77.4375−0.875w}Cr_wNb_{4.0625−0.125w}P_16.5B₃ alloys plotting the critical rod diameter d_cr against the Cr atomic concentration w along the compositional line x = 4.0625 − 0.125w associated with the GFA ridge in the w–x domain shown in A. The dotted line is a trend line through the experimental data (open circles).In Fig. 2A we present a second 2D GFA contour map associated with composition variation in the x–z plane. This map was generated from GFA data on 58 separate alloy compositions. Another ridge in the GFA landscape is identified in this compositional plane along the compositional line x = z where the sum of transition metals (w + x) and metalloids (y + z) are held constant at 11.5 and 19.5, respectively. The GFA compositional dependence along this line is presented in Fig. 2B. Along this ridge with 3< (x, z) < 4, d_cr varies between 9 and 10 mm, whereas it gradually degrades outside this range. A ridge in GFA along x = z suggests that the GFA dependence on Nb and B contents is strongly correlated. This suggests Nb and B atoms tend to occupy associated sites in the short-range configurational order of the glass structure. It is also worth noting that another shallower peak is identified in this 2D plane, isolated from the x = z ridge near x = 2 and z = 5, where d_cr ≈ 7 mm.Open in a separate windowFig. 2.(A) Two-dimensional GFA contour map for Ni₆₉Cr_11.5−xNb_xP_19.5−zB_z alloys plotting the critical rod diameter d_cr against the Nb and B atomic concentrations x and z, while keeping the sum of Cr and Nb and the sum of P and B atomic concentrations (w + x) and (y + z) constant at 11.5% and 19.5%, respectively. (B) One-dimensional GFA plot for Ni₆₉Cr_11.5−zNb_zP_19.5−zB_z alloys plotting the critical rod diameter d_cr against the B atomic concentration z along the compositional line x = z associated with the GFA ridge in the x–z domain shown in A. The dotted line is a trend line through the experimental data (open circles).None of the local maxima identified in the compositional planes of Figs. 1 and ​and22 necessarily represent a global maximum for the overall GFA. Other higher maxima, including an absolute global maximum, may exist in the 4D composition space along different planes; however such maxima are not expected to be far from the common peaks appearing in the planes of Figs. 1A and ​and2A.2A. If a global GFA maximum exists in the current compositional neighborhood it would be hard to predict it given the steepness of the GFA composition maps. In the present work, alloys with an even higher GFA have in fact been discovered for compositions in the neighborhood surrounding Ni₆₉Cr_8.5Nb₃P_16.5B₃. For example, a six-component alloy Ni_68.6Cr_8.7Nb₃P₁₆B_3.2Si_0.5, which includes a minority addition of Si in its metalloid moiety, demonstrates d_cr ≈ 20 mm when processed by a high-temperature fluxing process (Materials and Methods). A fully amorphous 17-mm-diameter rod of Ni_68.6Cr_8.7Nb₃P₁₆B_3.2Si_0.5, along with an X-ray diffraction pattern and a calorimetric scan verifying its amorphous structure, are shown in Fig. 3.Open in a separate windowFig. 3.(A) A sectioned 17-mm fully amorphous Ni_68.6Cr_8.7Nb₃P₁₆B_3.2Si_0.5 rod (section shown next to a dime for comparison). (B) X-ray diffractogram taken along the rod cross-section verifying the amorphous structure of the rod. (C) Differential calorimetry scan taken at 20 K/min scan rate. Arrows from left to right designate the glass transition, crystallization onset, solidus, and liquidus temperatures of 678 K, 722 K, 1119 K, and 1157 K, respectively.To map the detailed compositional dependence of GFA in the neighborhood of a peak, we evaluated the GFA along a family of straight lines in the composition space that intersect the peak, where each line is referred to as an “alloy series.” The detailed compositional dependence of GFA for four alloy series (labeled I–IV) intersecting the common composition Ni₆₉Cr_8.5Nb₃P_16.5B₃ is presented in Fig. 4. Series I–IV respectively correspond to varying w, x, z, and (y + z) around the composition Ni₆₉Cr_8.5Nb₃P_16.5B₃, which corresponds to a local maximum in GFA in the 4D compositional space. For series I–IV one observes a steeply rising GFA followed by a rapidly decaying GFA as the peak at d_cr is traversed. These GFA functions along the composition lines generally consist of piecewise continuous curves, or branches. The curves meet at cusps. It was observed that the individual branches of the GFA map have a roughly exponential dependence on composition (see SI Materials and Methods for a list of the exponential fitting parameters.). We argue below that the atomic rearrangement and formation of a critical nucleus within a liquid are both thermally activated processes with associated barrier heights that should depend linearly, to leading order, on composition. As such, an exponential dependence of GFA on composition ensues.Open in a separate windowFig. 4.Compositional dependence of GFA along four series intersecting a GFA peak at composition Ni₆₉Cr_8.5Nb₃P_16.5B₃. Solid lines are exponential fits to the experimental data (open circles) on each side of the peak. (A) Critical rod diameter d_cr plotted against the Cr atomic concentration as a substitute for Ni according to Ni_77.5−wCr_wNb₃P_16.5B₃. (B) Critical rod diameter d_cr plotted against the Nb atomic concentration as a substitute for Cr according to Ni₆₉Cr_11.5−xNb_xP_16.5B₃. (C) Critical rod diameter d_cr plotted against the B atomic concentration as a substitute for P according to Ni₆₉Cr_8.5Nb₃P_19.5−zB_z. (D) Critical rod diameter d_cr plotted against the atomic concentration of metalloids substituting for metals according to (Ni_0.8541Cr_0.1085Nb_0.0374)_100−(y+z)(P_0.8376B_0.1624)_(y+z).From transition state theory, the nucleation of a phase α (α refers to one of the competing crystalline phases) is expected to be an activated process involving the crossing of a temperature and composition dependent nucleation barrier, ΔG_α(T, c) (5, 6, 8, 9). The rate at which atomic configurations are sampled in an undercooled liquid is taken to be proportional to the liquid fluidity, or inverse viscosity η^?1. Viscous flow is taken to be an activated process that may be characterized by a temperature and composition dependent barrier, W(T, c) (17, 18). The characteristic time for the nucleation of an α-crystal takes the general formτ_α = ν^?1?exp[{W(T, c) + ΔG_α(T, c)}/kT], [1]where ν is an attempt frequency taken to be a characteristic atomic vibrational frequency in the liquid. For a fixed c, a plot of ln?τ_α vs. T produces the well-known C-shaped time-temperature-transformation (TTT) diagram for the α-crystal nucleation. Below the α-liquidus temperature where the crystal becomes thermodynamically stable, competition between a rising W vs. a falling ΔG_α determines the TTT diagram. The TTT diagram exhibits a minimum crystallization time scale, τα∗, at an associated “nose” temperature, Tα∗, for which the nucleation time is minimized. One obtains τα∗ and Tα∗ by requiring dτ_α/dT = 0 at fixed c. Assuming τα∗ to be a well-behaved function of c and expanding τα∗ vs. c in a Taylor series around an initial composition c_o, one obtains the compositional dependence of τα∗ for a small composition change, c − c_o, to leading order asτα∗(c)−τα∗(co)≈exp[λα⋅(c−co)],[2]where λα=∇(ln⁡τα∗(c))=∇[{W(T∗,c)+ΔGα(T∗,c)}/kT∗] is formally the gradient vector with respect to composition of ln⁡τα∗(c) evaluated at a fixed composition, c_o, and at the nose temperature T^?. Eq. 2 predicts that for the α-crystallization pathway, ln⁡τα∗ should vary exponentially with c for small compositional displacements, c − c_o. The exponential composition dependence is a consequence of crystal nucleation being a thermally activated process. The minimum crystallization time, τα∗, is a fundamental measure of GFA. According to the Fourier heat flow equation, one expects the time scale for cooling a molten sample to scale with the square of the lateral dimension of the sample, i.e., τα∗≈dcr2. Accordingly, a GFA composition map that reflects the composition variation of τα∗ can be constructed by mapping dcr2 as a function of composition. This map would reflect the composition variation of τα∗ for the α-crystallization event where such event has the shortest (i.e., the limiting) crystallization time. Collectively considering the set of all competing crystallization pathways for the various crystalline phases (e.g., α, β, γ, etc.), a global GFA composition map is constructed determined at each composition by the competing phase which has the shortest crystallization time. The overall GFA map will consist of piecewise continuous exponential subsurfaces, indexed by α, β, γ, etc., which intersect to form exponential cusps at compositions associated with the cross-over in the nucleation pathway (e.g., from α to β, etc.).According to Eq. 1, GFA is determined by the competition of two thermally activated processes: that of forming the critical nucleus of the crystalline phase and that of configurationally rearranging the liquid, having respective activation barriers W(T^?, c) and ΔG_α(T^?, c). In our analysis, we only assume that these barriers are smooth functions of temperature and composition. The rising η with increasing undercooling can be well described by the liquid fragility parameter m, defined as m = [d(log?η)/d(T_g/T)]_Tg together with the value of T_g (19). To lowest order, the driving force for crystallization with increasing liquid undercooling scales with 1 ? T/T_L, so that ΔG_α scales according to (1?T/T_L)^?2 for modest undercooling (2). So at the Kauzmann temperature T_K where the entropy of the liquid is assumed to match the entropy of the crystal (also referred to as the ideal or thermodynamic glass transition) (20), the leading term in ΔG_α would be of order (1?T_K/T_L)^?2. Here we assume that the calorimetric glass transition temperature T_g, which is readily accessible experimentally, adequately approximates T_K. As such, the leading term in ΔG_α is taken here to be of order (1?t_rg)^?2. Both t_rg and m are experimentally accessible material properties that provide a quantitative measure of the respective activation barriers along with their variation with composition. One can describe mathematically the dependence of the crystallization time scale τα∗ on the independent parameters t_rg and m by examining the dependence of the activation barriers W(T, c) and ΔG_α(T, c) on these parameters (see SI Materials and Methods for a more detailed discussion). Below we argue that the observed compositional dependence of GFA in the present work is attributable almost entirely to the combined effects of varying t_rg and m with composition.To clarify the origin of the composition dependence of GFA, we performed detailed calorimetric and rheometric measurements to evaluate both t_rg and m as functions of composition along the representative alloy series III (Fig. 4C), Ni₆₉Cr_8.5Nb₃P_19.5−zB_z (see Materials and Methods for details on measurements of m and t_rg, and SI Materials and Methods for calorimetry and viscosity plots). A similar analysis can be applied to the other composition series. The GFA composition data along this series are plotted in terms of dcr2 vs. z in Fig. 5A; the data were fitted by two exponential functions of composition for the two branches of the GFA curve. For a local GFA maximum at composition c_o, like the one at 3 atomic percent B (i.e., at z_o = 3), the τα∗ values for two different competing crystallization pathways cross over and are mutually equal at z_o. We arbitrarily refer to the two crystal branches (low z and high z) of the GFA curve using crystal labels “α” and “β ”. Firstly, within the error of our calorimetry data, we observe that c_o is located quite precisely at a eutectic composition for which the alloy liquidus is minimum (see SI Materials and Methods for melting data). This is actually true for all of the alloy series I–IV (Fig. 4). GFA is therefore optimized very close to a quinary eutectic composition. The d_cr data for series I–IV, therefore, describe GFA along lines in composition space that all pass through this eutectic composition. From the calorimetric liquidus measurements along series III, the α region z < z_o is a hypoeutectic (with a falling liquidus curve as z increases) region whereas the β region z_o > z_o is hypereutectic (with a rising liquidus curve as z increases). Because t_rg depends inversely on the liquidus temperature, its composition dependence demonstrates a cusp-like maximum with discontinuous slope at z_o. The plot of t_rg along series III shown in Fig. 5B reveals this sharp discontinuity. Specifically, t_rg is highest at the eutectic composition and drops precipitously for z > z_o. In contrast, t_rg increases very slightly as z approaches z_o in the hypoeutectic region. On the other hand, the experimental liquid fragility, m, being a property of the liquid phase alone and independent of the crystal/liquid phase equilibria, is shown in Fig. 5C to be a continuous and monotonically decreasing function of c. Specifically, m drops steeply as z increases with an approximately exponentially decaying trend. A decreasing m corresponds to a higher viscosity throughout the undercooled liquid region, i.e., from T_g to T_L, thereby implying a greater viscosity at the nucleation temperature, Tα∗. One therefore expects GFA to increase with falling m.Open in a separate windowFig. 5.(A) Compositional dependence of GFA plotted in terms of dcr2 against the B atomic concentration as a substitute for P according to Ni₆₉Cr_8.5Nb₃P_19.5-zB_z. Solid lines are exponential fits to the experimental data (open circles) on each side of the peak (at 3 at. % B). (B) Reduced glass transition temperature t_rg plotted against the B atomic concentration as a substitute for P according to Ni₆₉Cr_8.5Nb₃P_19.5-zB_z. Solid lines are polynomial fits to the experimental data (open circles) on each side of the cusp (at 3 at.% B). (C) Liquid fragility m plotted against the B atomic concentration as a substitute for P according to Ni₆₉Cr_8.5Nb₃P_19.5-zB_z. The solid line is an exponential fit to the experimental data (open circles).By qualitatively analyzing the plots of Fig. 5 B and C, one can gain critical insight into the origin of the piecewise continuous form of the GFA function (Fig. 5A). The drop in t_rg for z > z_o is steep and should lead to rapid exponential decay of GFA. This drop in t_rg in the hypereutectic β-region arises from a steep rise in T_L (SI Materials and Methods). In turn, this increases the crystallization driving force and steeply reduces ΔG_β such that GFA decays rapidly. For z < z_o, one has nearly constant or slightly rising t_rg as z increases. This slight rise in t_rg cannot explain the sharply rising GFA. Rather, the sharp GFA rise in the hypoeutectic α-region can be plausibly explained by the rapidly falling fragility, m. As the liquid structure becomes stronger (decreasing m with increasing B content), the rate at which atomic configurations are sampled at Tα∗ slows, increasing the time to achieve a critical crystal nucleus, τα∗. The hypo- and hypereutectic branches of the GFA map are apparently the result of an interplay of the t_rg and m variations with composition.To quantify the analysis above, consider Eq. 2 and the exponential decay parameters λ_α and λ_β obtained from the exponential fits to the GFA data for the respective hypo- and hypereutectic branches of the GFA curve. According to Eq. 2, the discontinuity in the slope of ln⁡dcr2 vs. z at the GFA cusp is simply given by the difference λ_β ? λ_α. Without loss of generality, one can show that λ_α and λ_β can be separated into contributions arising from variations in t_rg and m, and potentially any other relevant material parameters that enter the expression for ln⁡τα∗(c) (the mathematical details of this separation are presented in SI Materials and Methods). Using the chain rule to evaluate λα=∇(ln⁡τα∗(c)), one obtainsλ_α = λ_m ? λ_trg,α[3a]λ_β = λ_m ? λ_trg,β.[3b]Here λ_m being a property of the liquid phase only, is identical for both branches; its composition dependence given by λm={[d(ln⁡dcr2)/dm](dm/dc)}trg. The λ_trg parameters depend on the nucleating crystal and are different for α and β; they are given by λtrg={[d(ln⁡dcr2)/dtrg](dtrg/dc)}m. The λ_trg jumps discontinuously with varying c on going from the α- to the β-branch of the curve due to the change in the slope dt_rg/dc (as seen in Fig. 5B). It was already pointed out that the composition c_o of the GFA cusp coincides precisely with the eutectic composition (at which the α- and β-liquidus curves cross). From this, one can conclude that any other parameter that influences GFA (e.g., the melt–crystal interfacial energy for the α- and β-crystalline phases) must be nearly equal for both branches of the GFA curve. Were this not the case, the GFA cusp would be shifted off the eutectic composition, c_o. The above facts suggest that λ_α and λ_β in Eqs. 3a and 3b are determined mainly by the measured composition dependences of t_rg and m. In this case, Eqs. 3a and 3b become a pair of linear equations with two unknowns, λ_m and d(ln⁡dcr2)/dtrg. At the cusp composition, experimental fitting yields λ_α = 1.43, λ_β = ?0.693, dt_rg,α/dc = 0.00211, and dt_rg,β/dc = ?0.0213 (where c is in units of z, i.e., in atomic percentages of B, and d_cr is in millimeters; Fig. 5 A and B and SI Materials and Methods). Solving for the two unknowns one obtains λ_m = 1.24 and d(ln⁡dcr2)/dtrg=90.6, which give λ_trg,α = 0.191 and λ_trg,β = ?1.93. One finds that λ_α consists of a fragility contribution λ_m/λ_α = 87%, and a contribution from Turnbull’s parameter λ_trg,α/λ_α = 13%. In the hypoeutectic α-region, therefore, the decreasing liquid fragility parameter (i.e., the increasing liquid viscosity at the nucleation nose) dominates the exponential rise in GFA. By contrast, the negative λ_β consists of an overwhelming negative contribution from Turnbull’s parameter λ_trg,β/λ_β = 278%, and a positive contribution from fragility λ_m/λ_β = ?178%. Hence, the exponential GFA decay in the hypereutectic β-region would have been significantly greater (by a factor of 2.78) had the fragility of the liquid not been decreasing with increasing c.As follows from the analysis above, the Turnbull parameter and fragility alone give a plausible and self-consistent account of the composition variations of GFA. Specifically, the large variation in fragility over a fairly narrow compositional change has a dramatic effect on the compositional dependence of GFA; it steepens the GFA rise in the hypoeutectic region and offsets the GFA drop in the hypereutectic region. Finally, we note that from our fit for m(z) in Fig. 5C, we have dm/dc = ?5.4 as evaluated at z_o. Using our value of λ_m, one obtains the intrinsic dependence of GFA on m, i.e., d(ln⁡dcr2)/dm=−0.23. For a fixed t_rg, this value implies that a decrease in the fragility parameter m of about 4.5 is associated with a remarkable 65% increase in d_cr. Clearly, the liquid fragility m plays a very important role in determining glass formation. Mukherjee et al. (21) directly measured the TTT diagrams for a series of compositionally distinct Zr-based glasses all having nearly the same t_rg but varying liquid fragility. The measured τα∗, which was found to vary by more than 1 order of magnitude among these alloys, was shown to be directly proportional to the liquid viscosity at the nose temperature Tα∗. It was argued that the GFA variation among these Zr-based glasses arises mainly from the variation in fragility m. In a separate work, Na et al. (22) studied the fragility of compositionally distinct Fe-based metallic glasses, and showed that their GFA and fragility obey a fairly tight correlation that extended over nearly 2 orders of magnitude in τα∗. These studies are consistent with the key findings of the present work. One is naturally led to consider the numerous parameters and criteria proposed in the literature to guide the discovery of bulk metallic glasses (3, 6, 10–12, 21). Based on the present work, it is clear that the successful prediction of GFA requires, at a minimum, properly describing the roles of Turnbull’s parameter and liquid fragility.