Gibbs free energies for phases in the system Al2O3-SiO2-H2O have been calculated from reversed experiments in order to correct earlier values and to calculate a phase diagram consistent with more recent experiments. An internally consistent diagram could not be calculated that agreed with all published experiments, and choices of preferred data were made. The following Gibbs free energies, relative to the elements at STP (298.15 K, 1 bar), have been derived

The above values were calculated assuming literature values for corundum, quartz, and H2O (v).

Examination of available thermodynamic, experimental, and observational data on the aluminum hydroxides gibbsite, boehmite, bayerite, and nordstrandite suggests that these minerals are metastable with respect to diaspore + water at STP and at higher temperatures. Similarly, halloysite and dickite are metastable with respect to kaolinite at these conditions. The occurrence of these minerals in soils must therefore be ascribed to nonequilibrium processes, and the use of equilibrium phase diagrams to explain their occurrence is inappropriate.

The development of a consistent framework for Calphad model sensitivity is necessary for the rational reduction of uncertainty via new models and experiments. In the present work, a sensitivity theory for Calphad was developed, and a closed-form expression for the log-likelihood gradient and Hessian of a multi-phase equilibrium measurement was presented. The inherent locality of the defined sensitivity metric was mitigated through the use of Monte Carlo averaging. A case study of the Cr–Ni system was used to demonstrate visualizations and analyses enabled by the developed theory. Criteria based on the classical Cramér–Rao bound were shown to be a useful diagnostic in assessing the accuracy of parameter covariance estimates from Markov Chain Monte Carlo. The developed sensitivity framework was applied to estimate the statistical value of phase equilibria measurements in comparison with thermochemical measurements, with implications for Calphad model uncertainty reduction.

The BaNd2O4 compound and the BaO–Nd2O3 system are of interest for electroceramics. In this work, we synthesized BaNd2O4 by solid-state reaction, measured its heat capacity from 573 to 1273 K by differential scanning calorimetry, and determined its enthalpy of formation from component oxides at 298 K by high-temperature oxide melt solution calorimetry to be −43.75 ± 4.68 kJ/mol. Our newly determined values and available literature data were employed to assess the phase equilibria in the BaO–Nd2O3 system using CALPHAD methodology. A self-consistent thermodynamic database and the calculated phase diagram of the BaO–Nd2O3 system are provided. The optimized thermodynamic parameters are in good agreement with available experimental data. BaNd2O4 is calculated to melt incongruently at 2177 K. This thermodynamic analysis is essential for the optimization of synthesis conditions for materials and for the evaluation of their stability under appropriate technological operating conditions.

While rhenium has proven to be an ideal material in fast-cycling high-temperature applications such as rocket nozzles, its prohibitive cost limits its continued use and motivates a search for viable cost-effective substitutes. We show that a simple design principle that trades off average valence electron count and cost considerations proves helpful in identifying a promising pool of candidate substitute alloys: The Mo–Ru–Ta–W quaternary system. We demonstrate how this picture can be combined with a computational thermodynamic model of phase stability, based on high-throughput ab initio calculations, to further narrow down the search and deliver alloys that maintain rhenium’s desirable hcp crystal structure. This thermodynamic model is validated with comparisons to known binary phase diagram sections and corroborated by experimental synthesis and structural characterization demonstrating multiprinciple-element hcp solid-solution samples selected from a promising composition range.

The discovery, design, and development of new alloys have long been critical elements of advanced engineering systems. Challenged by their chemical and structural complexity, this design process is, however, often too slow. This article highlights progress in theory, computation, data, and advanced experimental techniques that are advancing our capabilities for rapid discovery and design of new multicomponent alloys. Applied across the length scales, these new capabilities support exploration across broad composition spaces; examples of new materials and associated advances in the understanding of underlying thermochemical and thermomechanical phenomena are presented. We highlight current challenges, gaps, and specific areas that, if further developed, could have future high payoff.

Modern approaches to alloy design increasingly exploit the framework of computational thermodynamics and kinetics to guide the selection of alloy compositions and processing strategies, to achieve desired microstructures, and yield tailored properties. In this context, phase diagrams play a critical role and their assessment can represent a bottleneck in the design of new multicomponent systems. In recent years, it has become possible to accelerate this process through the coupling of the CALculation of PHAse Diagram (CALPHAD) computational thermodynamics framework with high-throughput quantum mechanical calculations. This article reviews recent developments and applications in this area, and discusses future opportunities for high-throughput calculations in the context of modeling kinetics, highlighting the important role of interfacial processes and atomic mobilities.

Traditional approaches to materials synthesis have largely relied on uniform, equilibrated phases leading to static “condensed-matter” structures (e.g., monolithic single crystals). Departures from these modes of materials design are pervasive in biology. From the folding of proteins to the reorganization of self-regulating cytoskeletal networks, biological materials reflect a major shift in emphasis from equilibrium thermodynamic regimes to out-of-equilibrium regimes. Here, equilibrium structures, determined by global free-energy minima, are replaced by highly structured dynamical states that are out of equilibrium, calling into question the utility of global thermodynamic energy minimization as a first-principles approach. Thus, the creation of new materials capable of performing life-like functions such as complex and cooperative processes, self-replication, and self-repair, will ultimately rely upon incorporating biological principles of spatiotemporal modes of self-assembly. Elucidating fundamental principles for the design of such out-of-equilibrium dynamic self-assembling materials systems is the focus of this issue of MRS Bulletin.

Design approaches and achievements for the development of wrought TiAl alloys to be used for LPT and HPC blades are constructed. In case of Ti-Al-M1-M2 quaternary systems, conventional equivalency concept does not work for the alloy design, and a new thermodynamic database for phase diagram calculations in multi-component systems of the alloys is built by introducing the interaction parameters among four phases of β−Ti, α2−Ti3Al, α−Ti and γ−TiAl phases in the systems, in order to reproduce the experimentally determined phase diagrams. Based on the phase diagram calculations, the composition range of a unique phase transformation pathway of β+α→α→β+γ in the multi-component system can be identified, and thus model alloys with excellent hot workability even at higher strain rate and mechanical properties can be successfully proposed. It can be concluded that an introduction of bcc β phase and the morphology control through the phase transformation pathway make it possible to improve the room temperature ductility, creep and fatigue crack propagation resistance.

Effects of Cr addition to TiAl alloy on the phase equilibria among β/α/α2/γ Phases and phase transformation pathways within the temperature range of 1523 K∼1073 K were investigated using several alloys in the composition of interest. In between 1473 K and 1373 K, The slope of β/α tie-line in the three-phase coexisting region of β+α+γ remains basically unchanged. However, this slope drastically rotates in a clockwise direction, in between 1373 K and 1273 K and below the eutectoid reaction temperature in the binary system (1400 K). This is a strong indication that α-phase exists even below the 1400 K, i.e. addition of Cr stabilizes α against α2 and the three-phase coexisting region of β+α2+γ at lower temperatures is formed through a ternary eutectoid reaction (α → β+α2+γ) with decreasing temperature. This three-phase tie-triangle moves towards lower Al content in phase diagram. This suggests that Cr addition results in increase of the volume fraction of γ-phase with decreasing temperature even in alloys with low Al content.

A new class of high-temperature materials based on refractory elements was investigated with an aim to improve the energy efficiency of thermal power plants. Alloys based on Nb and Mo composed of BCC solid solution (BCCss) (Nb-Mo) and T2-silicide (Nb,Mo)5(Si,B)3 are promising candidates as high-temperature materials. Further investigation on the alloy phase equilibria of this system is required to improve the mechanical properties and oxidation resistance through optimization of the phase compositions. Cr is one candidate to modify the properties of the alloy because Cr is expected to stabilize the T2 compound phase along with B. Here, the phase equilibria among BCCss and the T2 compound are widely investigated in the Cr-Mo-Nb-Si-B system, and a BCCss-T2 two-phase microstructure is found in Mo-rich alloys. The B/Si ratio in the T2 phase increases with the Cr content, while almost no B solubility was found in BCCss. As the Si content increases in alloys, the A15 silicide phase ((Cr, Mo, Nb)3Si) and/or Laves phase appear.

Nanoindentation tests were conducted to investigate the mechanical properties of the BCCss phase of the alloys in the Cr-Mo-Nb-Si-B system. The nanohardness and reduced elastic modulus of these alloys tended to be higher with an increase in Cr.

Solid-state electrolytes can offer improved lithium-ion battery safety while potentially increasing the energy density by enabling alkali metal anodes. There have been significant research efforts to improve the ionic conductivity of solid-state electrolytes and the electrochemical performance of all-solid-state batteries; however, the root causes of their poor performance—interfacial reaction and subsequent impedance growth—are poorly understood. This is due to the dearth of effective characterization techniques for probing these buried interfaces. In situ and operando methodologies are currently under development for solid-state interfaces, and they offer the potential to describe the dynamic interfacial processes that serve as performance bottlenecks. This article highlights state-of-the-art solid–solid interface probing methodologies, describes practical limitations, and describes a future for dynamic interfacial characterization.

High-entropy and multiprincipal element alloys present exciting opportunities and challenges for computational modeling of their structure and phase stability. Recent interest has catalyzed rapid development of techniques and equally rapid growth of new results. This review surveys the essential concepts of thermodynamics and total energy calculation, and the bridge between them provided by statistical mechanics. Specifically, we review the electronic density functional theory of alloy total energy as applied to supercells and special quasirandom structures. We contrast these with the coherent potential approximation and semi-empirical approximations. Statistical mechanical approaches include cluster expansions, hybrid Monte Carlo/molecular dynamics simulations, and extraction of entropy from correlation functions. We also compare first-principles approaches with Calculation of Phase Diagrams (CALPHAD) and highlight the need to augment experimental databases with first-principles derived data. Numerous example applications are given highlighting recent progress utilizing the concepts and methods that are introduced.

Refractory high-entropy alloys (RHEAs) have recently attracted much attention, primarily due to their mechanical properties at elevated temperatures. However, the equilibrium phase-stability of these alloy systems is not well established. The present investigation focuses on the phase stability of Al0.5NbTa0.8Ti1.5V0.2Zr RHEA at temperatures ranging from 600 to 1200 °C. The detailed phase characterization involves coupling of scanning electron microscopy, transmission electron microscopy, and atom probe tomography. The stable phases present at these temperatures are (i) 1200 °C—body-centered cubic (BCC) matrix with nano-B2 precipitates; (ii) 1000 °C and 800 °C—a BCC matrix phase with Al–Zr rich hexagonal closed packed intermetallic precipitates and, (iii) 600 °C—a BCC + B2 microstructure, comprising a continuous BCC matrix with discrete B2 precipitates. These results highlight the substantial changes in phase stability as a function of temperature in RHEAs, and high-entropy alloys in general, and also the importance of accounting for these changes especially while designing alloys for high temperature applications.

Published electron microprobe analyses of mattheddleite, a lead sulpho-silicate apatite from Leadhills, Scotland, have 9–13% IV site deficiencies. However, galena was used as a standard for S, which suggested that low S resulted from a shift in the S-Kα peak. Wavelength scans with a PET crystal show that the S-Kα peak is shifted down by 0.0026 Å for sulphates relative to sulphides. Quantitative analyses show a ∼30% increase of S in mattheddleite using a celestite standard, which fills the IV site, but with Si > S, on average Pb5S1.2Si1.8O11.7Cl0.6(OH)0.4. Direct analysis of oxygen with the electron microprobe implies that the charge imbalance engendered from the inequality of Si and S is compensated with substitution of a vacancy (□), as in Pb5S1.2Si1.8[O11.7□0.3] [Cl0.6(OH)0.4] or Pb5S1.2Si1.8[O11.7(Cl, OH)0.73]. [Cl,OH)0.7 □0.3]. Calculation of OH as l–C1 suggests the presence of both OH- and Cl-dominant mattheddleite at Leadhills, but direct analysis of H is needed to confirm the dominance of OH in the channel site. Wavelength-dispersive analyses of S in apatite and other sulphates must be undertaken with sulphate standards: use of sulphide standards yields a negative error on the order of 10–20% in the resultant S concentration. Reactions of mattheddleite with other Pb minerals at Leadhills show that their stability depends on fluid composition as well as pressure and temperature. An X-ray map of Cl shows complex zoning between Cl-poor and Cl-rich mattheddleite, recording rapid changes in the fluid chemistry during late-stage hydrothermal processes at Leadhills.

Potassium-rich mafic dykes and lavas from the Highwood Mountains Igneous Province, USA were studied by electron-microprobe and bulk-rock analysis. For the mafic phonolites, compositional trends for olivine and augite phenocrysts and groundmass biotite, alkali feldspar and titanomagnetites are presented and substitution mechanisms discussed. Phenocrysts of biotite and augite in the minettes are also characterized, together with groundmass alkali feldspar and titanomagnetite. The alkali feldspars and biotites are commonly enriched in Ba. Olivine, clinopyroxene and biotite phenocrysts are generally quite magnesium-rich, which is consistent with the primitive natures of the least evolved rocks.

Bulk-rock major-element compositions are combined with modal and microprobe data for the principal phenocrysts to calculate model residual liquid compositions for mafic phonolites, minettes and a syenitic rock. On the basis of phase-equilibria, it is suggested that the main controls of differentiation are polybaric involving crystallization during transport of primary magmas from the mantle for the minettes, and low-pressure differentiation for the mafic phonolites. Whereas magma mixing might have contributed to petrogenesis, many of the disequilibrium features exhibited by clinopyroxene and biotite phenocrysts can also be attributed to pre-existing phenocrysts undergoing decompression melting during magma uprise from its mantle source, followed by rapid crystal growth and episodic volatile loss in sub-volcanic magma chambers.

The rare mineral otavite CdCO3 was found at the abandoned Pb-Zn mine of Montevecchio (SW Sardinia, Italy). Otavite occurs in the oxidised gossan, in association with aurichalcite. SEM imaging shows that otavite is composed of lenticular hollow structures containing aggregates of tiny rhombohedral crystals. Oxidation of primary Cd-bearing sulphides (sphalerite and greenockite) releases up to 24 ppm of Cd to drainage waters of the Montevecchio area. These waters are generally saturated with respect to otavite. Therefore, this mineral might play an important role in controlling Cd mobility in the environment.

Talc was identified as an equilibrium associate of omphacite, kyanite, zoisite, and garnet in some coesitebearing eclogites and as a retrograde phase in associated garnet peridotite from the Bixiling mafic-ultramafic complex in the Dabie ultrahigh-P metamorphic terrane, central China. Observed talc- and tremolite-bearing assemblages within the coexisting mafic and ultramafic rocks together with established phase relations for the simple system CaO-MgO-Al2O3-SiO2-H2O constrain the P-T path for retrograde metamorphism. This, together with reported talc occurrences from the Dora Maira massif, leads to the conclusion that UHP talc assemblages are confined to mafic and pelitic rocks of unusual chemistry, and are not stable at ultrahigh pressures in ultramafic rocks. Thus, talc cannot be an important H2O-bearing phase in deep mantle ultramafic rocks.

CALPHAD databases have traditionally been developed for investigation of single-principal component alloys. With the advent of batch processing capability, engineering teams have proposed using these models to systematically explore compositional space for multiprincipal element systems. However, the uncertainty of phase equilibria predictions outside of traditional compositional bounds has yet to be evaluated. This study assesses the current capabilities of commercially available CALPHAD databases to predict phase equilibria within ternary phase space as a function of the number of full binary system descriptions contained within the thermodynamic databases, the spatial location in compositional space relative to subsystem descriptions, and the specific database used. A strong correlation was observed between the fraction of subsystem descriptions available for the free energy calculation and the accuracy of phase predictions in undefined ternary space. The accuracy of equilibria predictions degraded with increased compositional extrapolation from defined subsystems.

The Nb-Ru system is of interest because the ∼NbRu phase has potential for high temperature shape memory alloys. Previous workers have identified the phase transformation variously as involving twinning, of cubic-to-tetragonal and tetragonal–to-orthorhombic (or monoclinic) transformations. As well as the terminal (Nb) and (Ru) solid solutions, two intermetallic phases have been identified: ∼NbRu and ∼NbRu3 / ∼Nb3Ru5 / ∼NbRu2, but the boundaries between the different phases are still not fully established. This investigation looked at six as-cast alloys of different compositions across the Nb-Ru system, which were made from 99.95 % purity Nb and Ru. The samples were made by arc-melting under an argon atmosphere, using titanium as an oxygen-getter. These samples were sectioned and prepared metallographically for optical microscopy, SEM and XRD analyses, the latter using an X’pert database. The phases found were (Nb), (Ru), ∼NbRu and “∼NbRu3”, as expected. Although the samples were mainly homogeneous, there was porosity in the (Ru) phase between the “∼NbRu3” dendrites in the Nb28.5:Ru71.5 at.% sample. The Nb14.2:Ru85.8 at.% sample was mainly single-phase (Ru).