Thermodynamic Phase Stability Research Articles

From Simple to Complex: Design of Inorganic Crystal Structures with a Topologically Extended Zintl–Klemm Concept

We present a novel approach to the generation of new crystalline phases, which is based on a combination of the topological description of crystal structures as a periodic net and the extended Zintl-Klemm concept, which establishes the structural relations between chemically and structurally simpler and more complex inorganic compounds. With this approach, we have explored the structural similarities between all known binary sulfides, selenides, and the corresponding simple sulfates and selenates and have theoretically revealed seven new high-pressure phases in the last two groups of compounds. Using density functional theory methods, we have studied the thermodynamic and mechanical stability of the new phases, have adjusted the transition pathways in the sulfate and selenate systems, and have revealed new structural correlations of the baric polymorphism in these systems. The advantages of the topological approach compared to conventional methods of modeling crystal structures are discussed and illustrated.

Effect of carbon shell on stabilization of single-phase lanthanum and praseodymium hexaaluminates prepared by a modified Pechini method

A modified Pechini method involving the formation of carbon shell was proposed and used for the synthesis of the unsubstituted lanthanum and praseodymium hexaaluminates with the magnetoplumbite structure. The peculiarities of the LaAlO3 and LaAl11O18 phases' formation were studied in a wide temperature range starting from their appearance at 700 °C and finishing at 1300 °C when the complete phase formation occurs. It was found that the size of the formed hexaaluminate's crystallites is a crucial factor affecting the phase purity of the final product. The critical size of the thermodynamic stability of the LaAlO3 phase is supposed to be 10 nm, which corresponds to the specific surface area of 90 m2/g. The use of a carbon template approach leading to the formation of a core-shell structure during the synthesis procedure allows stabilizing the oxide particles in size and preventing their agglomeration at high temperatures. Depending on the carbon template nature, the carbon content in the samples was found to be 13 wt% (low-carbon-shelled samples) and 40 wt% (high-carbon-shelled samples). In the case of high carbon content, the resulting LaAl11O18 and PrAl11O18 hexaaluminates possess the surface areas as high as 160 m2/g.

Effect of temperature on the hot deformation behavior of AZ80 magnesium alloy

The present research studies the hot forgeability of a cast AZ80 alloy by means of uniaxial compression tests using a Gleeble® 3500 thermal-mechanical simulator. Compression tests were conducted for temperatures ranging from 300 °C to 450 °C, and constant true strain rates ranging from 0.001 s−1 to 1 s−1, while the characterization of deformed samples for microstructure and texture was performed only for the samples deformed within 300 °C–400 °C, at a strain rate of 0.001 s−1. The samples were deformed to true strains of 0.05, 0.15, 0.4 and 1.0, to study the microstructure and texture evolution with deformation strain, while the characterization was performed using optical microscopy, SEM-EDX, and EBSD. Analysis of the flow stress data suggested a transition in the rate controlling deformation mechanism from dislocation cross-slip at 300 °C to dislocation climb at 400 °C, with a corresponding transition in the dominant DRX mechanism from continuous dynamic recrystallization (CDRX) to discontinuous dynamic recrystallization (DDRX). The thermodynamic stability of the Mg17Al12 phase (which is the dominant secondary phase in the AZ80 alloy) varied over the test temperature range, and significantly impacted the microstructure and texture evolution at different test temperatures. At 300 °C, multiple morphologies of the Mg17Al12 precipitates were present in the microstructure during deformation, and affected the DRX behavior of the material differently. At 400 °C, the precipitates rapidly dissolved in the α-Mg matrix, while the DRX took place by the grain boundary bulging mechanism, with the newly formed DRXed grains preserving the deformation texture. The study shows that the effect of temperature on the hot deformation behavior of the AZ80 alloy is especially pronounced due to a changing amount of the Mg17Al12 phase in the microstructure.

Structural, mechanical, electronic properties of refractory Hf–Al intermetallics from SCAN meta-GGA density functional calculations

Hf–Al intermetallics are novel promising high-temperature structural materials, which exhibit excellent mechanical properties. In this work, the structural parameters, elastic constants, and mechanical anisotropies of Hf–Al intermetallics are investigated by applying the latest meta-GGA functional SCAN as well as several other widely used density functionals such as LDA, PBE and PBEsol. It is found that HfAl2 is the most thermodynamically stable stoichiometric compound among all Hf–Al binary intermetallics. The elastic moduli like B, G, E, ductility index (B/G ratio) and Poisson's ratio (σ) of Hf–Al intermetallics are predicted based on Voigt–Reuss–Hill approximation, indicating most Hf–Al binary intermetallics are brittle except Hf5Al3 and Hf2Al. Besides, the three-dimensional (3D) contour plots of mechanical moduli are provided to characterize the elastic anisotropy in Hf–Al intermetallics. HfAl shows obvious anisotropy in both Young's and bulk moduli along different crystallographic directions, while very weak anisotropy is revealed for both HfAl2 and Hf4Al3 phases since the 3-D surface contours of mechanical moduli show little deviations from isotropic spherical shapes. The calculated electronic properties indicate that relatively high thermodynamic stability of HfAl2 phase is mainly ascribed to the formation of a pseudo-gap in the electron density of states originating mainly from the Al-2p and Hf-5d states at the Fermi level.

First-principles study on predicting the crystal structures, mechanical properties and electronic structures of HfCxN1-x

The crystal structures, mechanical properties and electronic structures of HfCxN1-x have been predicted by using evolutionary structure search followed by the first-principles calculations in this study. The crystal structures predicted indicate that there are 10 thermodynamic stable phases for HfCxN1-x, of which 8 are newly discovered crystal structures and 2 are already known. We investigated the mechanical properties, including the bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio and Vickers hardness, of all 10 stable phases, and further established the relationship between such properties and the ratio of nitrogen to carbon content. Besides, the Fermi energy level and electronic density of states of these 10 stable phases are calculated as well, and the results reveal the fundamental reason why the mechanical properties change with the ratio of nitrogen to carbon. The predictions of this study agree well with both the experimental data and the previous theoretical evaluations.

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Two‐dimensional (2D) transition metal dichalcogenides (TMDs) usually have poly‐phases, such as 2H, 3R and 1T. Controlling the structure phase of 2D TMDs is the key for engineering the physical and chemical properties of the materials and hence is vital to the applications. Many approaches, including doping/intercalation, alloying, defects, strain, electric field and so on, have been developed to tune the thermodynamic stability of the different phases of TMDs and then phase selective synthesis or controlled phase conversion has been achieved. More details are discussed in the article by Xie et al. on page 753–760.image

Thermodynamic Modeling of Phase Equilibria in the FeO-MgO-Al<sub>2</sub>O<sub>3</sub> System

Thermodynamic modeling of coordinates of phase diagrams’ liquidus lines of the FeO–MgO, FeO–Al2O3, MgO–Al2O3 systems and coordinates of phase diagram’s liquidus surface of the FeO–MgO–Al2O3 system has been carried out. In the course of work, a thermodynamic model which describes activity of oxide melt had been selected for each of the systems; energy parameters of the model have been determined. Regions of thermodynamic stability of solid phases which are at equilibrium with the oxide melt have been determined. Results of the modeling have been compared with experimental data existing in the literature. Modeling technique has also allowed evaluating enthalpies and entropies of FeAl2O4 and MgAl2O4 compounds’ formation out of components of the oxide melt. The obtained results are of interest for steelmaking industry processes when determining the melt temperature of a slag containing oxides of iron, magnesium and aluminum.

Redox effects in Cu, Co or Fe in oxides nanocrystals with high catalytic activity for the acetonitrile combustion

The cobalt, copper and iron oxides were investigated in selective catalytic combustion (SCC) of acetonitrile toward N2 in gas phase. Catalysts were characterized by physical–chemical technics like XRD, H2-TPR, DRS UV–Vis, whose confirmed crystalline phases of CuO, Co3O4 and Fe2O3. Thermodynamic stability of crystalline phase from metal oxides ruled important contributions in redox properties and become able to compare clearly the catalytic activity of the three catalyst. Relationship between H2-TPR analysis and catalytic results obtained showed great relevance to understand how metal oxide works on reaction, who were related to easy redox process involved. SCC studies were carried out with range of 100–600 °C and Co3O4 showed best activity (100% conversion at 570 °C) and high selectivities to N2 and CO2 starting in lower temperature. Byproducts from nitrogen-compounds were observed in low quantities for all catalysts.

Stratifying Polymer Solutions in Microsized Pores: Phase Transitions Induced by Deformation of a Porous Material

Based on the thermodynamic approach, the influence of pore morphology on the phase equilibria in stratifying liquid solutions entrapped in a porous matrix is analyzed. As illustrated by an example of a solution of oligomeric fractions of polybutadiene and polystyrene, the matrix deformation determining the geometric characteristics of pores makes it possible to control the mutual solubilities of components and the volumes and thermodynamic stability of phases coexisting at equilibrium. The change in the geometric characteristics of pores in the general case is simulated by introducing a parameter that corresponds to the degree of deviation of the interface shape from the spherical one. Moreover, the behavior of the component solubilities as a function of pore volume is different in pores of different shapes, which is explained by various mechanisms of reducing the free energy of the system. With significant matrix deformations, the phase separation in microsized pores is suppressed and any solution compositions up to equimolar ones become.

First-principles study of phase stability and temperature-dependent mechanical properties of (Cr, M)23C6 (M = Fe, Mo) phases

Although Cr-rich (Cr, M)23C6 (M = Fe, Mo) carbides as ineluctable precipitates dramatically affect the mechanical performances of advanced materials such as refractory steels and superalloys, their high-temperature material properties are difficult to be determined in experiments. In the present work, the first-principles method is applied to comprehensively investigate the phase stability and thermodynamic and temperature-dependent mechanical properties of Cr23-xMxC6 (M = Fe, Mo; x = 0–23). The results indicate that Cr23-xFexC6 presents thermodynamic phase stability under a broad occupying concentration of Fe (i.e., x = 1, 3, 9, 12, 13, 14, 15). Amongst which, the Cr8Fe15C6 with 4a, 8c and 48 h sites co-occupied by Fe is the most stable. Whereas Cr21Mo2C6 is the only stable phase among Cr23-xMoxC6. The mechanical properties of (Cr, M)23C6 are found to exhibit a strong doping composition-position dependence and a negative temperature dependence. Doping a low concentration of M leads to an increase of the elasticity of Cr23C6. The occupation of 4a or 8c sites alone plays an effective role in enhancing mechanical properties. The present work provides necessary information for understanding the heterogeneous deformation process and the fatigue crack initiation mechanism for alloys with the precipitate of M23C6 inclusions.

Models of phase stability in Jackiw-Teitelboim gravity

We construct solutions within Jackiw-Teitelboim (JT) gravity in the presence of nontrivial couplings between the dilaton and the Abelian $1$-form where we analyse the asymptotic structure as well as the phase stability corresponding to charged black hole solutions in $1+1$ D. We consider the Almheiri-Polchinski (AP) model as a specific example within $1+1$ D JT gravity which plays a pivotal role in the study of Sachdev-Ye-Kitaev (SYK)/anti-de Sitter (AdS) duality. The corresponding vacuum solutions exhibit a rather different asymptotic structure than their uncharged counterpart. We find interpolating vacuum solutions with AdS$_2$ in the IR and Lifshitz$_2$ in the UV with dynamical exponent $z_{\text{dyn}}=3/2$. Interestingly, the presence of charge also modifies the black hole geometry from asymptotically AdS to asymptotically Lifshitz with same value of the dynamical exponent. We consider specific examples, where we compute the corresponding free-energy and explore the thermodynamic phase stability associated with charged black hole solutions in $1+1$ D. Our analysis reveals the existence of a universal thermodynamic feature that is expected to reveal its immediate consequences on the dual SYK physics at finite density and strong coupling.

High-Pressure Phase Transitions in Densely Packed Nanocrystallites of TiO2-II

Phase behaviors of nanocrystalline TiO2-II have not been well studied due to the difficulty in its preparations at ambient pressure. In this work, we prepared nanocrystallites of TiO2-II with average sizes of ∼10–20 nm via high-pressure processing of anatase particles in a large volume press. X-ray diffraction (XRD) and electron microscopy examinations show that the TiO2-II nanocrystallites formed from cracking and phase transformation of large anatase particles under compression. The high-pressure phase behaviors of the TiO2-II nanocrystallites were investigated using in situ synchrotron XRD and Raman spectroscopy. Results show that, under compression up to ∼35–40 GPa, the phase transitions in nano TiO2-II proceed via two parallel routes of TiO2-II (∼9–15 GPa) → baddeleyite (∼25 GPa) → TiO2-OI and TiO2-II (∼19 GPa) → TiO2-OI. At different TiO2-II sizes, the TiO2-II-to-baddeleyite transition occurs at pressures from ∼9 to 15 GPa, while the TiO2-II-to-TiO2-OI transition occurs at ∼19 GPa. This difference originates from the different interfacial energies of the involved titania phases, which control their relative thermodynamic phase stabilities at nano sizes. This work enriches our understanding of the complex phase behaviors of titania and provides fundamental knowledge for developing applications of the less-explored titania nanophase of TiO2-II.

Solid solution formation in Mg2(Si,Sn) and shape of the miscibility gap

Investigation of the thermochemical stability of Mg2(Si,Sn) thermoelectric materials is crucial for further development of thermoelectric modules. There is a miscibility gap reported for the quasibinary Mg2Si–Mg2Sn series, though the exact compositions of its limits are disputed. Gaining a better understanding of intersolubility limits in Mg2(Si,Sn) is important for further optimization of material performance by exploiting the gap-induced phase segregation. For a better understanding on the boundaries of the miscibility gap below 700 °C, two approaches were taken to provide evidence of thermodynamic stable phases and, hereby, monitor the borders of the miscibility gap. The approaches cover the homogenization of Mg2SixSn1-x at 700 °C and diffusion couple experiments at 600 °C, 525 °C, and 450 °C. For 600 °C we find two ranges where Mg2Si and Mg2Sn are not miscible, namely x = 0.35 ± 0.05 and x = 0.75 ± 0.05 for miscibility gap I and 0.85 ± 0.05 < x < 0.95 ± 0.05 for the second gap. The deduced complex temperature dependence of the mixing / demixing behavior helps to understand the previously observed, apparently contradicting experimental results. We also show that there is no demixing for the compositions with the best thermoelectric properties at temperatures above 700 °C.

Thermomechanical, electronic and thermodynamic properties of ZnS cubic polymorphs: an ab initio investigation on the zinc-blende-rock-salt phase transition.

In the present work, an extensive and detailed theoretical investigation is reported on the thermomechanical, electronic and thermodynamic properties of zinc-blende (sphalerite, zb-ZnS) and rock-salt zinc sulfide (rs-ZnS) over a wide range of pressure, by means of ab initio Density Functional Theory, Gaussian type orbitals and the well known B3LYP functional. For the first time, vibrational frequencies, phonon dispersion relations, elasto-piezo-dielectric tensor, thermodynamic and thermomechanical properties of rs-ZnS were calculated with a consistent approach that allows a direct comparison with the low-pressure polymorph. Special attention was paid to the evaluation of the thermodynamic pressure-temperature stability of the mineral phases between 0-25 GPa and 0-800 K. The static (T = 0 K) bulk moduli of sphalerite and rock-salt ZnS were 72.63 (3) GPa and 84.39 (5) GPa, respectively. The phase transition in static conditions calculated from the equation of state was about 15.5 GPa, whereas the elastic constants data resulted in Ptrans = 14.6 GPa. At room temperature (300 K), the zb-rs transition occurs at 14.70 GPa and a negative Clapeyron slope (dP)/(dT) = 0.0023 was observed up to 800 K. The electronic band structure showed a direct band gap for zb-ZnS (Eg = 4.830 eV at equilibrium geometry), which became an indirect one by increasing pressure above 11 GPa. The results were found to be in good agreement with the available experimental and theoretical data, further extending the knowledge of important properties of zinc sulfide, in particular the thermomechanical ones of the rock-salt polymorph here extensively explored for the first time.

Role of phonons on phase stabilization of RE2Si2O7 over wide temperature range (RE = Yb, Gd)

Thermodynamic phase stabilities of α, β, γ and δ polymorphs of RE2Si2O7 (RE = Yb, Gd), promising candidates for environmental barrier coating systems of gas turbine engines in next generations, were investigated using harmonic and quasi-harmonic lattice dynamics in conjunction with ab initio calculations. By quantifying their Gibbs free energies with dynamics of atoms taken into account, we showed the phase stability of β-Yb2Si2O7 up to melting temperature under an ideal condition, and also under thermal stresses, ensuring the reliability of β-Yb2Si2O7 in environmental barrier coating systems. It was also found that the difference of anharmonic phonons in these polymorphs, which was measured as mode Grüneisen parameters, significantly changed their phonon free energies and invoked the formation of δ-Gd2Si2O7 at high temperature. These results enable a quantitative comprehension of the phase transformation of RE2Si2O7 and future discussions of other factors which may affect the phase stability such as lattice defects.

Thermodynamic modeling of isotherms of oxygen solubility in liquid metal of Fe – Mg – Al – O system

Studying the interaction between oxygen and magnesium and aluminum dissolved in liquid iron is an important task in order to choose optimal parameters for refining and casting of steels. Relevance of this research is caused by determining the possibility and conditions for formation of unfavorable refractory particles of magnesium oxideand magnesian spinel in a metal melt. In the course of this research, thermodynamic modeling of phase equilibria implemented in liquid metal of such systems as Fe – Mg – O, Fe – Al – O and Fe – Mg – Al – O within the temperature range of 1550 – 1650 °С was carried out. Calculation was made using the technique of constructing the solubility surfaces for the metal components which connects quantitative changes in composition of a liquid metal with qualitative changes in composition of products obtained as a result of interaction of a metallic melt’s components. The modeling method was based not only on usin­g equilibrium constants of reactions occurring between components of the systems under research in the selected temperature range, but also on taking into account the values of interaction parameters of the first order (according to Wagner) of elements in liquid iron. In order to simulate activities of the oxide melt conjugated with the metallic one, approximation of the theory of subregular ionic solutions was used. To model activities of oxides solid solution, approximation of the theory of regular ionic solutions was used. And the theory of ideal ionic solutions was used for the solid solution of spinels. In the course of the work, isotherms of oxygen’s solubility in liquid metal of systems Fe – Mg – O, Fe – Al – O and Fe – Mg – Al – O have been constructed, and regions of thermodynamic stability of oxide phases conjugated with the metallic melt have been determined. In particular, compositions area of a liquid metal which is going to be in equilibrium with the solid solution of spinels | FeAl 2 O 4 , MgAl 2 O 4 | solid solution has been determined for Fe – Mg – Al – O system. Results obtained in the course of thermodynamic modeling have been compared to experimental data.

Uncertainty Quantification for Parameter Estimation and Response Prediction

Integrated Computational Materials Engineering (ICME) is an engineering approach where the materials, manufacturing process, and component designs are optimized concurrently before an actual physical component is realized. This requires the integration of models across vast length and timescales. A key benefit of ICME is the ability to reduce the bulk of expensive and lengthy experiments via tailored simulation. However, ICME introduces new challenges and limitations as the statistical confidence in the final design and manufacturing process must be established from simulation rather than experimental observation and testing. The computational materials science community has not formally adopted tools for verification and validation or UQ for materials simulations. In this study, a Bayesian hierarchical model is considered which accounts for parameter uncertainty, the inherent variability in the properties of material samples tested, and measurement noise. The Bayesian inferential framework is used to calibrate model parameters given calibration data and also to make forward predictions with a confidence level established through the highest posterior density intervals. The generality of the framework is demonstrated through two case studies: (1) parameter estimation for a crystal plasticity model which provides key microstructural and grain-level deformation information to use within the ICME chain; (2) the estimation in uncertainty in thermodynamic phase stability from multiple databases for phase stability.

Phase behavior of empirical potentials of titanium dioxide

In recent years, several relatively similar empirical models of titanium dioxide have been proposed as reparameterizations of the potential of Matsui and Akaogi, with the Buckingham interaction replaced by a Lennard-Jones interaction. However, because of the steepness of the repulsive region of the Lennard-Jones potential, such reparameterized models result in rather different mechanical and thermodynamic properties compared to the original potential. Here, we use free-energy calculations based on the Einstein crystal method to compute the phase diagram of both the Matsui–Akaogi potential and one of its Lennard-Jones-based reparameterizations. Both potentials are able to support a large number of distinct crystalline polymorphs of titanium dioxide that have been observed in experiment, but the regions of thermodynamic stability of the individual phases are significantly different from one another. Moreover, neither potential results in phase behavior that is fully consistent with the available experimental evidence.

Thermodynamic Modeling of Isotherms of Oxygen Solubility in Liquid Metal of the Fe–Mg–Al–O System

In this paper, we studied the interaction of magnesium and aluminum dissolved in liquid iron with oxygen, which is an important problem for choosing the optimal parameters of steel refining and casting. The relevance of the study is determined by the possibility and conditions for the formation of adverse refractory particles of magnesium oxide and magnesian spinel in the melt. We performed the thermodynamic modeling of phase equilibria realized in the liquid metal of the Fe–Mg–O, Fe–Al–O, and Fe–Mg–Al–O systems in the temperature range of 1550–1650°C. The calculation was carried out using a technique for constructing the surface of the component solubility in a metal, which associates quantitative changes in the liquid metal composition with changes in the composition of the interaction products of molten metal components. The modeling method was based both on the use of equilibrium constants of reactions occurring between the components of the studied systems in the selected temperature range and on the account of the values ​​of the first-order interaction parameters (according to Wagner) of elements in liquid iron. To simulate the activities of an oxide melt conjugated with a metal melt, the approximation of the theory of subregular ionic solutions was used. The approximation of the theory of regular ionic solutions was used to model the activity of a solid solution of oxides while the theory of perfect ionic solutions was used to model the activity of a solid solution of spinels. The isotherms of oxygen solubility in the liquid metal of the Fe–Mg–O, Fe–Al–O, and Fe–Mg–Al–O systems were plotted, and the regions of thermodynamic stability of oxide phases conjugated with the metal melt were determined. In particular, for the Fe–Mg–Al–O system, the region of liquid metal compositions, in equilibrium with which there will be a solid solution of spinels |FeAl2O4, MgAl2O4|ss, was determined. The obtained results of thermodynamic modeling are compared with experimental data.

Modeling the Origin of the Interface Resistance in Solid-State Batteries

The major bottleneck for the all-solid-state batteries lies at the high interfacial resistance, which is due to two main factors, physical contact and chemical effect, both will be evaluated via modeling in this talk. First, we devise a model, incorporating atomic electrochemical potentials, thermodynamic stability of bulk electrolyte phases, and point defect formation energies to yield quantitative profiles of the electrostatic potential, lithium chemical potential, and electronic energy levels. This model complements direct microscopic and macroscopic simulations by rigorously and simultaneously determining the potential drop, electrostatic dipole, and space-charge layer at the interface. The application of this model to the Li/LiPON/LixCoO2 system leads to the important discovery that the space-charge layer varies with the state of charge (i.e. Li concentration in LixCoO2). This new physics insight unifies the seemingly contradictory experimental observations and leads to new device design rules to promote interfacial ion transport in future SSBs. Secondly, we combined contact mechanics with 1D Newman battery model to capture the effect of imperfect electrode/electrolyte interfacial contacts, which can be formed during cell fabrication and worsened due to cycling. Constant current discharging processes at different rates and contact areas were simulated to correlate the capacity drop with the contact area loss. Furthermore, the model suggested how much pressures should be applied to recover the capacity drop due to contact area loss.