Temperature-composition Space Research Articles

Coherent Phase Change in Interstitial Solutions: A Hierarchy of Instabilities.

Metal hydrides or lithium ion battery electrodes can take the form of interstitial solid solutions with a miscibility gap. This work discusses theory approaches for locating, in temperature-composition space, coherent phase transformations during the charging/discharging of such systems and for identifying the associated transformation mechanisms. The focus is on the simplest scenario, where instabilities derive from the thermodynamics of the bulk phase alone, considering strain energy as the foremost consequence of coherency and admitting for stress relaxation at free surfaces. The extension of the approach to include capillarity is demonstrated by an example. The analysis rests on constrained equilibrium phase diagrams that are informed by geometry- and dimensionality-specific mechanical boundary conditions and on elastic instabilities-again geometry-specific-as implied by the theory of open-system elasticity. It is demonstrated that some scenarios afford the analysis of chemical stability to be based entirely on a linear stability analysis of the mechanical equilibrium, which provides closed-form solutions in a straightforward manner. Attention is on the impact of the system geometry (infinitely extended or of finite size) and on the chemical (closed or open system) and mechanical (incoherent or coherent) boundary conditions. Transformation mechanism maps are suggested for documenting the findings. The maps reveal a hierarchy of instabilities, which depend strongly on each of the above characteristics. Specifically, realistic, finite-sized systems differ qualitatively from idealized systems of infinite extension. Among the transformation mechanisms exposed by the analysis are a uniform switchover to the other phase when the open system reaches its chemical spinodal, practical coherent nucleation, as well as chemo-elastically coupled spontaneous buckling modes, which may take the form of either, single-phase or dual-phasestates.

Electrochemical Performances of Nickel-Rich Single-Crystal LiNi0.83 Co0.12 Mn0.05 O2 Cathode Material for Lithium-Ion Batteries Synthesized by Tuning Li+ /Ni2+ Mixing.

Single-crystal nickel-rich materials are promising alternatives to polycrystalline cathodes owing to their excellent structure stability and cycle performance while the cathode material usually appears high cation mixing, which may have a negative effect on its electrochemical performance. The study presents the structural evolution of single-crystal LiNi0.83 Co0.12 Mn0.05 O2 in the temperature-composition space using temperature-resolved in situ XRD and the cation mixing is tuned to improve electrochemical performances. The as-synthesized single-crystal sample shows high initial discharge specific capacity (195.5 mAh g-1 at 1 C), and excellent capacity retention (80.1 % after 400 cycles at 1 C), taking account of lower structure disorder (Ni2+ occupying Li sites is 1.56 %) and integrated grains with an average of 2-3 μm. In addition, the single-crystal material also displays a superior rate capability of 159.1 mAh g-1 at the rate of 5 C. This excellent performance is attributed to the rapid Li+ transportation within the crystal structure with fewer Ni2+ cations in Li layer as well as intactly single grains. In sum, the regulation of Li+ /Ni2+ mixing provides a feasible strategy for boosting single-crystal nickel-rich cathode material.

Short-range ordering heredity in eutectic high entropy alloys: A new model based on pseudo-ternary eutectics

Eutectic high entropy alloys (EHEAs) have garnered wide attention in the metal community due to their excellent castability and unique microstructures. However, the formation mechanisms of these eutectic microstructures and their compositional design remain puzzling. In this paper, we have developed a simple yet unified pseudo-ternary model to unravel the puzzle of multiple eutectics in Ni-Al-containing high entropy alloys (HEAs) deploying a combination of the chemical similarity/dissimilarity coefficient concept, CALPHAD technique and first principle molecular dynamics simulation. Using the chemical similarity/dissimilarity parameters derived from CALPHAD model parameters and the eutectic valleys of Ni-Al-Cr, we reproduce the multiple eutectic patterns in the Ni-Al-containing HEAs and present a general approach for pinpointing the composition of eutectic HEA (EHEA) in the vast temperature-composition space. Aided by the first principle molecular dynamics calculation, we have shown that although the eutectic structures of Ni-Al containing EHEAs are different, the formation mechanism of the eutectic structure is similar, which stems from the short-range-ordering (SRO) heredity of EHEA liquid from the eutectic valleys of the pseudo Ni-Al-Cr ternary. Two EHEAs, EHEA 1 (Al16.95Cr16.95Fe19.1Ni47) with L12+B2 eutectic structures and EHEA 2 (Al33.5Cr33Co4Ni29.5) with BCC+B2 eutectic structures were designed using the model and experimentally verified. This unified Ni-Al-Cr ternary model, validated by experimental data in both literature and our fabricated EHEAs, presents a compelling solution to the long-debated grouping strategy in EHEA design and offers a new paradigm to map the complicated but intriguing eutectic microstructures in EHEAs and conventional alloys.

Pushing the Boundaries of Multicomponent Alloy Nanostructures: Hybrid Approach of Liquid Phase Separation and Selective Leaching Processes.

ConspectusAlloying, or mixing of multiple metallic elements, is the classical way of novel materials development since the Bronze age. Increased numbers of principal elements expand the compositional space for alloy design vastly, leading to nearly endless possibilities of unexpected and unique materials properties. In contrast to bulk alloying processes represented by casting of molten metal mixtures, the fabrication of multicomponent alloy (MCA) nanostructures such as nanoparticles and nanofoams with more than three elements is often challenging, and a few methodologies for directly synthesizing alloy nanostructures up to denary systems have been suggested recently. However, forming alloy nanoparticles inside another metal matrix, instead of inside aqueous media in wet-chemical synthesis, is a fairly well understood strategy in terms of physical metallurgy. Extracting those alloy nanophases from the matrix could provide an alternative way to fabricate novel MCA nanostructures.In this Account, we describe a hybrid approach of metallurgical bottom-up and chemical top-down processes for fabricating MCA nanostructures including nanoparticles and nanofoams. The former utilizes a liquid-state phase separation process that resembles "oil and water" but occurs at the nanoscale due to thermodynamic mixing relations among alloying elements and a rapid quenching process. Thermodynamic prediction of the immiscible boundary in a temperature-composition space (miscibility gap) plays a key role in designing precursor alloys for MCA nanostructures. Selective leaching, the chemical top-down process for extracting the alloy nanostructures from the precursors, uses the chemical reactivity difference between the embedded nanostructures and the matrix phase against a certain chemical solution. We discuss here that the precise control of alloy composition and cooling rate based on thermodynamic assessments enables researchers to prepare phase-separating precursor alloys for fabricating both nanoparticles and nanofoams with a broad size range from a few nanometers to a few hundred nanometers. Depending on the alloy systems, the atomic structure of alloy nanostructures could be controlled from fully amorphous to nanocrystalline and even to quasicrystalline structure. We demonstrate how the different sizes of alloy nanostructures fabricated by a single hybrid procedure can be effectively exploited for investigating size-dependent physical properties. The future and potential research directions for this hybrid approach are also briefly discussed. This unique approach for fabricating nanosized alloys provides an extended methodology to discover novel metallic nanomaterials with promising properties in diverse compositional spaces of MCA systems.

Explore the full temperature-composition space of 20 quinary CCAs for FCC and BCC single-phases by an iterative machine learning + CALPHAD method

The search for desired complex concentrated alloys (CCAs) remains a daunting task because of the vast temperature/chemical composition space. While CALPHAD is a reliable technique, it requires intensive computations. In contrast, machine-learning (ML) methods can be fast and efficient but rely on a large and high-quality dataset. In this work, we combine these two techniques by implementing a reinforcement learning strategy to accelerate the exploration of CCAs. Starting from an initial small dataset from Thermo-Calc calculations with TCHEA3 database, the reinforcement learning is performed iteratively with the XGBoost ML training/testing and CALPHAD verification to progressively augment the dataset. This strategy allows for the identification of all single-phase FCC and BCC structures in the temperature-composition space of 20 Al-containing quinary alloy families formed by Al, Co, Cr, Cu, Fe, Mn, Ni and Ti, and achieves testing accuracies of above 97% and 92% on Thermo-Calc and on experimental data, respectively. The data analyses show that these 20 families exhibit a large disparity in their single-phase formation ability with AlCoCrFeNi and AlCrFeMnNi having the highest formation ability for FCC and BCC, respectively. Remarkably, this large disparity can be well explained by refined phase selection rules and structural inheritance from binary and ternary systems. Our extensive analysis also reveals the rarity of single-phase CCAs at room temperature. The method proposed and the findings revealed present new dimensions for the design and engineering of CCAs.

Revealing high-fidelity phase selection rules for high entropy alloys: A combined CALPHAD and machine learning study

We reveal high-fidelity new phase selection rules for high entropy alloys (HEAs) by combining CALPHAD calculations and the machine learning (ML) method. Employing Thermo-Calc and TCHEA3 database, we first generate more than 300,000 equilibrium phase data from 20 quinary families formed by the 8 elements of Al Co, Cr, Cu, Fe, Mn, Ni, and Ti, and choose initially 15 materials/physical descriptors. The eXtreme Gradient Boosting (XGBoost) method is then used to identify 5 most important descriptors that best delineate the single and mixed phases in the complex temperature-composition space of HEAs. The ML model trained by the 5 features is validated by 155 annealing experimental data points from 15 publications and then used to predict 213 new single-phase alloys with BCC and FCC structures of the alloy families of AlCrNiFeMn and AlCrCoNiFeTi. We also highlight the importance of equilibrium temperature and offer in-depth insights into the paradigm of composition-feature-phase of HEAs. On the basis of the 5 important features, we establish new phase selection rules for single FCC and BCC phases with a success rate above 90%, significantly outperforming all existing phase selection rules and providing a powerful tool for mapping single-phase in the complex temperature-composition space of HEAs.

A comparison between the stability fields of a Cl-rich scapolite and the end-member marialite

AbstractScapolites are pervasive rock-forming aluminosilicates that are found in metamorphic, igneous, and hydrothermal environments; nonetheless, the stability field of Cl-rich scapolite is not well constrained. This experimental study investigated two reactions involving Cl-rich scapolite. First, the anhydrous reaction 1 of plagioclase + halite + calcite to form scapolite [modeled as: 3 plagioclase (Ab80An20) + 0.8 NaCl + 0.2 CaCO3 = scapolite (Ma80Me20)] was investigated to determine the effect of the Ca-rich meionite (Me = Ca4Al6Si6O24CO3) component on the Na end-member marialite (Ma = Na4Al3Si9O24Cl). Second, the effect of water on this reaction was investigated using the hydrothermally equivalent reaction 2, H2O + scapolite (Ma80Me20) = 3 plagioclase (Ab80An20) + CaCO3 + liquid, where the liquid is assumed to be a saline-rich hydrous-silicate melt. Experiments were conducted with synthetic phases over the range of 500–1030 °C and 0.4–2.0 GPa. For reaction 1, intermediate composition scapolite shows a wide thermal stability and is stable relative to plagioclase + halite + calcite at temperatures above 750 °C at 0.4 GPa and 760 °C at 2.0 GPa. For reaction 2, intermediate scapolite appears to be quite tolerant of water; it forms at a minimum bulk salinity [XNaCl = molar ratio of NaCl/(NaCl+H2O)] of the brine of approximately 0.2 XNaCl at 830 and 680 °C at pressures of 2.0 and 1.5 GPa, respectively. Based on the study done by Almeida and Jenkins (2017), pure marialite is very intolerant of water when compared to intermediate composition scapolite. Compositional changes in the scapolite and plagioclase were characterized by X-ray diffraction and electron microprobe analysis and found to shift from the nominal bulk compositions to the observed compositions of Ma85Me15 for scapolite and to Ab91An09 for plagioclase. These results were used to model the phase equilibria along the marialitemeionite join in temperature-composition space. This study demonstrates that a small change in the scapolite composition from end-member marialite to Ma85Me15 expands the stability field of marialite significantly, presumably due to the high entropy of mixing in scapolite, as well as increases its tolerance to water. This supports the much more common presence of intermediate scapolites in hydrothermal settings than either end-member meionite or marialite as is widely reported in the literature.

Experimental measurements and thermodynamic modeling of the Ce–Co–Fe ternary system

The experimental determinations of the isothermal section at 823 K and the supplementary measurements of the liquidus projection of the Ce-Co-Fe ternary system were presented in the present study. In the Ce-Co-Fe ternary system, in consideration of the temperature dependent solubilities of the linear phases such as Ce2(Co,Fe)17 and Ce(Co,Fe)2, as well as the specific locations of the univariant lines between each two primary solidification surfaces, it is necessary to study more than one isothermal section and some particular as-cast alloys to construct the phase equilibria in the temperature-composition space of the Ce-Co-Fe system. The samples for determining the liquidus projection were prepared by arc-melting method under high purity argon atmosphere in a water-cooled copper hearth, and then those for measuring the isothermal section at 823 K were isothermally treated and quenched in ice water. The microstructures and the phase compositions of samples were measured by means of scanning electron microscopy (SEM), X-ray diffraction (XRD) and electron probe micro-analyzer (EPMA). Some primary solidification regions and univariant lines of the Ce-Co-Fe ternary system were complementally determined, and the reasonability of the liquidus projection reported in previous literature was further confirmed. The phase equilibrium relations at 823 K were determined, including two-phase and three-phase equilibria. No ternary compounds were discovered in the present study. Based on the experimental results of both the previous literature reports (the reported liquidus projection and isothermal sections at 723 and 1173 K) and the present experimental study, the Ce-Co-Fe ternary system was thermodynamically assessed using the CALPHAD method. The isothermal sections, the vertical sections and the liquidus projection were calculated using the present optimized thermodynamic parameters, and a reasonable agreement between the calculated results and the experimental data was obtained.

Reconstructing phase diagrams from local measurements via Gaussian processes: mapping the temperature-composition space to confidence

We show the ability to map the phase diagram of a relaxor-ferroelectric system as a function of temperature and composition through local hysteresis curve acquisition, with the voltage spectroscopy data being used as a proxy for the (unknown) microscopic state or thermodynamic parameters of materials. Given the discrete nature of the measurement points, we use Gaussian processes to reconstruct hysteresis loops in temperature and voltage space, and compare the results with the raw data and bulk dielectric spectroscopy measurements. The results indicate that the surface transition temperature is similar for all but one composition with respect to the bulk. Through clustering algorithms, we recreate the main features of the bulk diagram, and provide statistical confidence estimates for the reconstructed phase transition temperatures. We validate the method by using Gaussian processes to predict hysteresis loops for a given temperature for a composition unseen by the algorithm, and compare with measurements. These techniques can be used to map phase diagrams from functional materials in an automated fashion, and provide a method for uncertainty quantification and model selection.

Evaporation maps for non-ideal ternary mixtures

Evaporation maps are a convenient way of representing the dynamic composition of evaporating liquid mixtures. Specifically, these maps represent the residual composition of evaporating ternary non-ideal mixtures over the full range of composition, and are analogous to the commonly used residue curve maps of simple distillation processes. The evaporation process considered here involves gas-phase limited evaporation from a liquid or wetted-solid surface, over which a gas flows at known conditions. Evaporation may occur into a pure inert gas, or into one pre-loaded with a known fraction of one or more of the ternary components. The model developed here uses an exact solution to the Maxwell–Stefan equations for mass transfer in the gas film, with a lumped approach applied to the liquid phase. Solutions to the evaporation model take the form of trajectories in temperature–composition space, which are then projected onto a ternary diagram to form the map. Efficient Newton-based methods are used to calculate the composition and temperature of pseudo-azeotropes in the mixture, and to calculate the wet-bulb temperature at a given composition. A numerical continuation method is used for tracking the bifurcations which occur in the evaporation maps, where the composition of one component of the pre-loaded gas is the bifurcation parameter. The bifurcation diagrams can in principle be used to determine the required gas composition to produce a specific terminal pseudo-azeotrope composition. Provided the gas-phase limited assumption applies, such analysis is applicable to applications such as drying of solvent-based coatings and tray-drying of granulated pharmaceutical products.

Three dimensional (temperature–tension–composition) phase map of mixed DOPC–DPPC vesicles: Two solid phases and a fluid phase coexist on three intersecting planes

Mapping the phase behavior of multicomponent phospholipid membranes has been an ongoing pursuit, motivated by interest in both fundamental physics and cell function. Prior investigations addressed temperature-composition space and the features of the associated domains. The current study additionally considers membrane tension, analogous to pressure in bulk materials. Focusing on model mixed 1,2-dioleoyl-sn-glycero-3-phosphocholine and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DOPC and DPPC respectively) membranes, we examine the thermodynamic impact of tension on fluid-solid coexistence and the nature of phase-separated domains. Reported here is the 3 dimensional composition-temperature-tension phase map containing three intersecting curved surfaces. Depending on the system’s position in this 3D space, giant unilamellar vesicles containing DOPC and DPPC may exhibit, in addition to a 2-component fluid Lα phase, two different types of solid DPPC-rich domains: tracer-excluding hexagonal patches or tracer-selective stripes. The fluid phase occurs at high temperatures. At cool temperatures striped solid DPPC-rich domains coexist with the fluid at elevated tensions. These stripes occur independent of tension, at the coolest temperatures. At low tensions and intermediate temperatures, patchy solid DPPC-rich domains coexist with the Lα fluid and may persist, if kinetically trapped, at lower temperatures. We associate the striped DPPC domains with a tilt-gel (Lβ’) morphology and the hexagonal DPPC patches with a dense corrugated ripple phase (Pβ’). These assignments, based on the reported areal densities of the corrugated and tilt solids, enabled first principles estimates of the coexistence boundaries that match the experiments well, including the tension sensitivity of coexistence curves and triple-point-like features for fixed composition.

Structure-phase states in the Cu-Pd-Pt system

A three-dimensional diagram of the structural states in the Cu-Pd-Pt system is formulated using literature data, by geometric construction of multicomponent phase diagrams on the basis of topological principles. Regions of relatively unstable (pretransition) long-period structural-phase states containing nanostructural elements are present in the resulting diagram, in temperature-composition space. The prediction of promising nanostructural functional materials is considered.

Exact phase boundary of an amphiphile-rich phase in a ternary solution on a Bethe lattice

A model ternary solution is considered in which the bonds of a three-coordinate Bethe lattice are covered by rodlike molecules of types AA, BB, and AB, the AB-type molecule representing an amphiphile. The phase boundary in temperature-composition space of an ordered amphiphile-rich phase is calculated exactly.

Rapid constructing magnetic phase diagrams by magneto-optical imaging of composition spread films

In this paper we present a new method of the rapid construction of magnetic phase diagrams in a temperature-composition space, using magneto-optic imaging with an indicator film technique (MOIF). The method is applied for mapping the diagram for the La1–xCaxMnO3 colossal magneto-resistive oxide, using the spread films deposited on a SrTiO3 substrate. The constructed magnetic diagram is in a good agreement with data on uniform films and bulk crystals of this system. The MOIF study of transitions under cooling and heating has revealed the formation of a non-magnetic phase in the area of temperatures from 5 K to 57 K and compositions from x = 0 to x = 0.5.

Amphiphile-rich phase in a model ternary solution on the honeycomb lattice

A model three-component system is considered in which the bonds of a honeycomb lattice are covered by bifunctional molecules of types AA, BB, and AB. The AB type molecule represents an amphiphile. An accurate approximation to the boundary in temperature-composition space of an ordered amphiphile-rich phase is calculated by transforming an accurate closed-form approximation of the critical frontier of an antiferromagnetic phase in an equivalent Ising model. This Ising model has coupling constants and a magnetic field that are temperature dependent.

An exactly solvable model ternary solution with strong three-body interactions

We consider a three-component model of rodlike molecules AA, BB, and AB, confined to the bonds of the honeycomb or three-coordinated Bethe lattice, and with three-body interactions between the molecular ends near a common lattice site. The model is equivalent to an Ising model on an associated lattice and has been previously transformed first to an Ising model on an intermediate lattice then to a standard Ising model on the original honeycomb or Bethe lattice. The exact coexistence curves for phase separation have been previously calculated for weak three-body interactions. In the present paper the same transformations are used for the case of strong three-body interactions, the difference being that in this case the Ising parameters on the intermediate lattice are complex. Exact, closed-form expressions are obtained for the two-phase coexistence surface in temperature-composition space. The exact coexistence curves are drawn for various values of a reduced three-body coupling constant and the reduced temperature. It is proved there is no phase separation in the model on these lattices if the reduced three-body coupling constant is sufficiently large.

The transition of three types of three-phase behavior in a temperature-composition space of water/C 12 EO 6 /propanol/heptane system

The change of three-phase behavior of a water/hexaethylene-glycol dodecyl ether (C12EO6)/propanol/heptane system was studied with increasing temperature (30.0–48.9 °C). A cone-like three-phase body consisting of aqueous (W), surfactant (Dp), and oil (O) phases is formed in the composition tetrahedron at lower temperatures. The body is expanded with increasing temperature, and touches the water–C12EO6–heptane triangle (the base) at 44.8 °C. At about 45.6 °C the loci of the Dp and O phases meet and cut off at a critical double end point and the three-phase body separates into two bodies: one has a chiral shape and the other is unclosed. The unclosed body is transformed with the change of shape of the tie triangle on the base as temperature increases and leaves from the base at 48.9 °C. A closed-loop miscibility gap between middle surfactant (D′p) and O phases or a cone-like three-phase body is formed inside the composition tetrahedron at higher temperatures. The roles of C12EO6 and propanol are also discussed.

Dependence of the electro-optical properties of polymer dispersed liquid crystals on the photopolymerization process

We have studied the dependence of the electro-optical properties of polymer dispersed liquid crystals (PDLC) on the ultraviolet (UV) cure of the solution of monomer and liquid crystal. The kinetics of UV polymerization and its effect on the morphology of the phase separated droplets of liquid crystal determine the switching voltage, response time, and luminance of the PDLC. Using a series of statistically designed experiments, we have mapped the dependence of these responses on the weight fraction of liquid crystal, the temperature of the cell during cure, and light intensity. Temperature and composition are strongly coupled parameters that influence switching voltage, luminance, and response times. Switching voltages are minimized at 4–5 V for an 8 μm cell gap over a large region of temperature-composition space. An abrupt transition line occurs through that space. On one side of the transition line, voltage increases linearly either as temperature increases or composition decreases, and on the other side of the line, voltage is constant. Analyses of decay times, the slower response time of the PDLC, show that the times peak along a line of points in temperature-composition space that is close to the transition line for increasing switching voltages. We present these results as contours on the same graphs and relate them to our understanding of the phase separation process in the PDLC mixture.

A lattice-statistical model for ternary polymer mixtures: exact phase diagrams

We consider a model for ternary polymer mixtures with bi- and tri-functional monomers and solvent molecules embedded on a honeycomb lattice. We first show that the grand partition function of the model polymer mixture is equivalent to the partition function of an eight-vertex model on the same lattice. This equivalence transforms the model into an Ising model in a non-zero external magnetic field. Using the known results for the Ising model, an exact analysis of the phase diagrams for the phase separation transition in the ternary system is carried out. Particularly, we determine the exact two-phase coexistence surface in the temperature-composition space and study the connectivity properties of the model. It is noteworthy that the theory incorporates cyclicity (polymer rings) as well as excluded volume effects.

The Temperature-Composition Phase Diagram and Mesophase Structure Characterization of the Monoolein/Water System

The temperature-composition phase diagram of monoolein in water was constructed using X-ray diffraction in the range of $0~^\circ{\rm C}$ to $104~^\circ{\rm C}$ and 0% (w/w) to 47% (w/w) water in the heating direction. The phases identified in this system include the lamellar crystalline (Lc) phase, the lamellar liquid crystalline (Lα) phase, the fluid isotropic (FI) phase, two inverted cubic phases (Q230, Ia3d; Q224, Pn3m), and the inverted hexagonal (HII) phase. The overall features of the monoolein/water phase diagram reported herein match those of existing phase diagrams for this system. There are some important differences, however. Accordingly, every effort has been taken to ensure that the current phase diagram represents equilibrium behavior and that the assorted phase boundaries have been determined accurately. The interpreted phase diagram is based on close to 400 discrete measurements in temperature-composition space recorded as a function of temperature in $5~^\circ{\rm C}$ increments ($3~^\circ{\rm C}$ in the HII phase) and of composition in 2% (w/w) water increments on average. The various mesophases have been characterized structurally as a function of temperature and hydration, and the corresponding thermal and composition expansion coefficients are reported. These and related data show that the average radius of water channels in the fully hydrated bicontinuous cubic Pn3m phase is remarkably sensitive to temperature and to monoacylglycerol chain identity.