Metastable Phase Diagram Research Articles

Geochemical Exploration Techniques with Deep Penetration: Implications for the Exploration of Concealed Potash Deposits in the Covered Area on the Southern Margin of the Kuqa Basin

In recent years, deep–penetrating geochemical exploration techniques have played a crucial role in the detection of concealed minerals. These methods effectively detect deep−seated anomalies and have been tested in various landscape–covered areas, yielding remarkable results. This study focuses on the covered areas of the southern margin of the Kuqa Basin, utilizing deep–penetrating geochemical methods for systematic sampling to explore concealed potassium salt. This study examines the chemical composition of several underground brine samples, revealing salinity levels ranging from 9.41 to 26.16 g/L and potassium concentrations of between 0.04 and 0.22 g/L. The hydrochemical coefficients indicate a high nNa+/nCl− value, with low K+ × 103/Cl− values. The average nNa+/nCl− ratio is approximately 0.97, and the Br− × 103/C1− value is about 0.07. The brine samples fall within the halite phase region of the Quaternary system Na+, K+, Mg2+//C1−–H2O at 25 °C, concentrated at the high Na terminal, suggesting halite dissolution. In the metastable phase diagram of the Na+, K+, Mg2+//C1−, SO42−–H2O five−element water system, all the brine samples were cast in the glauberite phase area, which may indicate that the shallow underground brine is still in the initial stage of potassium salt deposition. The underground brine mainly dissolved and filtered the stone salt in the formation during the process of runoff underground and then was squeezed by the strong active structure and discharged to the surface along the formation fault or fissure channel. The deep–penetration geochemical survey of the fracture reveals that certain profile points show significantly higher potassium and other salt contents than others, indicating a potassium anomaly. This suggests the potential ascent and migration of potassium–rich brine along deep fracture segments, providing preliminary evidence of potassium richness in the Kuqa Basin’s depths and offering significant guidance for key exploration areas in potassium salt prospecting.

A metastable temperature-strain phase diagram of HfxZr1−xO2 thin films based on synchrotron-based in situ 2D GIXRD investigation

The in-plane strain in the ferroelectric HfxZr1−xO2 (HZO) thin films has been considered to be the global factor behind many process parameters affecting the concentration of metastable polar-orthorhombic phase (O-phase Pca21) formed in the transformation pathway from tetragonal to monoclinic phase. However, the strain is generally effective in crystal phase nucleation and transition with the thermal budget and itself also changes with the thermal budget. The issue of how the O-phase is formed and changed in real time with effect of both thermal budget and in-plane strain has not been clarified, which is critical for engineering the O-phase concentration. Focusing on this issue, this work demonstrates the co-effect of strain and temperature on phase formation and transition in HZO by employing the synchrotron-based in situ two-dimensional (2D) grazing incidence x-ray diffraction (GIXRD) investigation. HZO thin films with different process parameters exhibit four types of phase transition processes during heating and cooling. Meanwhile, the in-plane strain magnitude and each phase concentration in the films during annealing are extracted. Based on both, the study established a universal temperature-strain phase diagram of HZO films and proposed a kinetic model for optimizing the ferroelectric O-phase formation. The study provides deep insights into O-phase engineering and ferroelectricity optimization in HZO thin films.

Third-Generation CALPHAD Modeling of Elemental Nb and Zr and Partial Re-Assessment of Their Binary Phase Diagram.

Liquid metals and metallic alloys often exist as metastable phases or can be undercooled below their equilibrium melting point. The Traditional CALPHAD (CALculation of PHAse Diagrams) approach struggles to accurately model these metastable conditions, which are important in rapid quenching techniques like additive manufacturing, and to understand glass formation or oxidation phenomena occurring in the liquid phase during nuclear and high-temperature aerospace applications. On the contrary, the third-generation CALPHAD models have the potential to accurately describe metastable phase diagrams to provide better predictions of molten phase behavior under non-equilibrium conditions. The latter approach is utilized in this study to achieve a more accurate description of the thermodynamic properties of elemental Nb and Zr, with a particular focus on their liquid phases. By incorporating available first-principles data, the representation of the liquid state is improved for both elements, capturing the peculiar behavior of the heat capacity in a wide temperature range. These improvements enable a more reliable prediction of phase stability and liquidus boundaries in the Nb-Zr system. A partial re-assessment of the Nb-Zr binary phase diagram is also conducted with refined predictions of liquidus boundaries that align well with experimental data.

Phase behavior of metastable water from large-scale simulations of a quantitatively accurate model near ambient conditions: The liquid-liquid critical point.

The molecular mechanisms of water's unique anomalies are still debated upon. Experimental challenges have led to simulations suggesting a liquid-liquid (LL) phase transition, culminating in the supercooled region's LL critical point (LLCP). Computational expense, small system sizes, and the reliability of water models often limit these simulations. We adopt the CVF model, which is reliable, transferable, scalable, and efficient across a wide range of temperatures and pressures around ambient conditions. By leveraging the timescale separation between fast hydrogen bonds and slow molecular coordinates, the model allows a thorough exploration of the metastable phase diagram of liquid water. Using advanced numerical techniques to bypass dynamical slowing down, we perform finite-size scaling on larger systems than those used in previous analyses. Our study extrapolates thermodynamic behavior in the infinite-system limit, demonstrating the existence of the LLCP in the 3D Ising universality class in the low-temperature, low-pressure side of the line of temperatures of maximum density, specifically at TC = 186 ± 4 K and PC = 174 ± 14 MPa, at the end of a liquid-liquid phase separation stretching up to ∼200 MPa. These predictions align with recent experimental data and sophisticated models, highlighting that hydrogen bond cooperativity governs the LLCP and the origin of water anomalies. We also observe substantial cooperative fluctuations in the hydrogen bond network at scales larger than 10nm, even at temperatures relevant to biopreservation. These findings have significant implications for nanotechnology and biophysics, providing new insights into water's behavior under varied conditions.

Eutectic Solidification Morphologies in Rapidly Solidified Hypereutectic Sn–Ag Solder Alloy

The effect of rapid solidification upon hypereutectic Sn–Ag solder alloy has been investigated using a 6.5 m drop tube. Powder sizes ranging from > 850 to < 38 μm were produced, with equivalent cooling rates of 250 to 14,800 K s−1 for 850 and 38 μm droplets, respectively. At all cooling rates investigated, dendritic β-Sn was observed as the primary solidification phase, not proeutectic Ag3Sn as predicted by the phase diagram. The volume fraction of interdendritic eutectic was observed to decrease with increasing cooling rate, with the Ag concentration in the residual interdendritic liquid estimated at 12.5–15 wt pct Ag, far in excess of the eutectic concentration of 3.8 wt pct. Much of the Ag3Sn observed within the eutectic had a blocky, divorced eutectic appearance. A model is proposed which can explain these observations in terms of sluggish nucleation of the Ag3Sn intermetallic, coupled with a metastable phase diagram that permits significant supersaturation of Ag at modest undercooling.

Metastable defect phase diagrams as roadmap to tailor chemically driven defect formation

Thermodynamic bulk phase diagrams have become the roadmap used by researchers to identify alloy compositions and process conditions that result in novel materials with tailored properties. Recent experimental studies show that changes in the alloy composition can drive not only transitions in the bulk phases present in a material, but also in the concentration and type of defects they contain. Defect phase diagrams in combination with density functional theory provide a natural route to study these chemically driven defects. Our results reveal, however, that direct application of equilibrium bulk thermodynamics can fail to reproduce experimentally observed defect formation. Therefore, we extend the concept to metastable defect phase diagrams to account for kinetic limitations that prevent the system from reaching equilibrium. We apply this concept to successfully explain the formation of large concentrations of planar defects in supersaturated Fe-Nb solid solutions. We then utilize it to design suitable conditions for synthesis, which we subsequently realized experimentally, successfully validating the formation of the predicted defects in Mg-Al-Ca alloys. The concept offers new avenues for the design of materials performance by tailoring defect structures.

Oiling-Out: Insights from Gibbsian Surface Thermodynamics by Stability Analysis.

The crystallization process is a significant stage in the pharmaceutical industry. During the process of crystallization with cooling, it is possible for a secondary liquid phase to appear before the formation of crystals. This phenomenon is called "oiling out" or liquid-liquid phase separation (LLPS). In this article, we explore the oiling-out phenomenon in a binary system of water and vanillin using stability analysis based on Gibbsian surface thermodynamics. To obtain the full picture of oiling out, we investigated three cases: droplet-solute-lean liquid equilibrium (DLE), crystal-solute-rich liquid equilibrium (CL'E), and crystal-solute-lean liquid equilibrium (CLE). The phase diagram of the system is plotted using the NRTL model for activity coefficients, along with considering the effect of the interfacial curvature on the phase diagram. From the phase boundaries and free-energy diagram of each case, we showed that the occurrence of the oiling-out phenomenon is justified based on the lower energy barrier of the droplet formation compared to that of the crystal formation. However, the energy level of a stable crystal is significantly lower and hence more stable than that of a stable droplet. Finally, we have determined different regions for droplet and crystal formation in the metastable phase diagram based on their supersaturation and provide insight for the oiling-out phenomenon.

Learning the stable and metastable phase diagram to accelerate the discovery of metastable phases of boron

Boron, an element of captivating chemical intricacy, has been surrounded by controversies ever since its discovery in 1808. The complexities of boron stem from its unique position between metals and insulators in the Periodic Table. Recent computational studies have shed light on some of the stable boron allotropes. However, the demand for multifunctionality necessitates the need to go beyond the stable phases into the realm of metastability and explore the potentially vast but elusive metastable phases of boron. Traditional search for stable phases of materials has focused on identifying materials with the lowest enthalpy. Here, we introduce a workflow that uses reinforcement learning coupled with decision trees, such as Monte Carlo tree search, to search for stable and metastable boron phases, with enthalpy as the objective. We discover new boron metastable phases and construct a phase diagram that locates their phase space (T, P) at different levels of metastability (ΔG) from the ground state and provides useful information on the domains of relative stability of the various stable and metastable boron phases.

Exploring secondary phases in the Sm–Fe–V system beneficial for coercivity

Magnetic isolation of hard magnetic grains with an intergranular phase is a key factor in obtaining high coercivity, which has been established in the microstructure of Nd-Fe-B magnets owing to the phase equilibrium of hard magnetic Nd2Fe14B with a low melting point phase. In this work, we investigated the phase equilibrium in the Sm-Fe-V system to establish an optimum composition range to develop high coercivity SmFe12-based permanent magnets. In addition to the solid 1:12/liquid Sm-rich phase equilibrium, an additional V-rich phase is found for the first time in the Sm-Fe-V phase diagram for V contents between 19 and 35 at.% at 1500 K. The equilibrium between the 1:12 phase and the two phases with low melting points is computationally modeled for Sm-Fe-V metastable phase diagram. This is experimentally confirmed by analyzing the microstructure of the Sm8Fe72V20 thin film, where anisotropic columnar 1:12 grains are enveloped with predominantly V-rich phases along with some Sm-rich intergranular phases resulting in a coercivity (µ0Hc) of 0.9 T. Although this large V content in Sm(Fe,V)12-based alloy is not beneficial for achieving a large magnetization, the finding of a new V-rich intergranular phase can benefit the development of anisotropic sintered magnets via two alloy powder methods; one alloy powder with large V-content for forming intergranular phase and the other with V-lean content to maintain a large magnetizations. To further improve the coercivity to its highest limit μ0Hc ≈0.2–0.3Ha ≈2–3 T, decreasing the ferromagnetic elements in the intergranular phase is essential.

The relation between the glass forming ability and nucleation kinetics of metastable quasicrystals in Mg–Zn–Yb liquid

Bulk metallic glass (BMG), metastable quasicrystals (QCs) and two types of approximant phases concurrently form from the melt during cooling at different rates in a Mg–Zn–Yb model alloy. Such an enriched phase competition between various metastable and stable crystals has also been found during the heating of Mg–Zn–Yb metallic glass between the glass transition and liquidus temperatures. Metastable QC acts as a transient phase that nucleates first from the melt and subsequently transforms into an equilibrium approximant phase. During heating, a metastable approximant phase transforms into the Mg-QC phase mixture which then transforms into the Mg and equilibrium approximant eutectic microstructure. Nucleation kinetics of QCs is critical to analyze for further understanding the relation between QC formation and glass forming ability of the alloy. For this purpose, a metastable phase diagram for QCs has been determined using a novel experimental strategy via fast differential scanning calorimetry (FDSC). Along compositional line binding Mg to Zn17Yb3, one stable eutectic point, i.e. Mg68.6Zn26.7Yb4.7 at 390°C, and one metastable eutectic composition, i.e. Mg64.6Zn30.1Yb5.3 at 350°C, were determined during interrupted heating experiments. We have demonstrated that the glass forming ability of Mg–Zn–Yb alloys strongly depends on the metastable phase diagram of QCs and their nucleation kinetics. Nucleation of metastable QCs limits the metallic glass formation, therefore the bulk metallic glass forming compositional region was found to be below metastable hypoeutectic compositions.

Two-step nucleation in a binary mixture of patchy particles.

Nucleation in systems with a metastable liquid-gas critical point is the prototypical example of a two-step nucleation process in which the appearance of the critical nucleus is preceded by the formation of a liquid-like density fluctuation. So far, the majority of studies on colloidal and protein crystallization have focused on one-component systems, and we are lacking a clear description of two-step nucleation processes in multicomponent systems, where critical fluctuations involve coupled density and concentration inhomogeneities. Here, we examine the nucleation process of a binary mixture of patchy particles designed to nucleate into a diamond lattice. By combining Gibbs-ensemble simulations and direct nucleation simulations over a wide range of thermodynamic conditions, we are able to pin down the role of the liquid-gas metastable phase diagram on the nucleation process. In particular, we show that the strongest enhancement of crystallization occurs at an azeotropic point with the same stoichiometric composition of the crystal.

Surface amorphization of bulk NiTi induced by laser radiation

The surface of medical grade Ni (50.8 at.%)Ti is treated with pulsed femtosecond laser radiation causing the formation of an amorphous layer < 200 nm thick. The chemical composition matches that of the original material. The formation of the amorphous layer on NiTi is briefly discussed considering both the thermodynamic and the kinetic perspective including calculated stable and metastable phase diagrams as well as theory for rapid solidification of undercooled melts. Solidification kinetics of NiTi alloy exhibit a tendency for transition to the amorphous state by complete solute and disorder trapping. The observed phenomenon has potential to enhance the properties governed by the surface. Specifically, the homogeneity of the amorphous region may enhance corrosion resistance and/or the resistance against crack initiation. The alloy's pseudoelastic and shape memory bulk properties are expected to remain unaffected by such thin layers, because the original bulk microstructure is conserved.

Predicting and accessing metastable phases

Metastable phase formation of Ln2O3 phases was explained and successfully predicted using calculated metastable phase diagrams. Irradiation experiments of Lu2O3 show formation of 3 phases, confirming the prediction, showing a unique behavior.

Thermodynamical and topological properties of metastable Fe3Sn

The Fe–Sn-based kagome compounds attract intensive attention due to its attractive topological transport and rich magnetic properties. Combining experimental data, first-principles calculations, and Calphad assessment, thermodynamic and topological transport properties of the Fe–Sn system were investigated. Density functional theory (DFT) calculations were performed to evaluate the intermetallics’ finite-temperature heat capacity (Cp). A consistent thermodynamic assessment of the Fe–Sn phase diagram was achieved by using the experimental and DFT results, together with all available data from previous publications. Here, we report that the metastable phase Fe3Sn was introduced into the current metastable phase diagram, and corrected phase locations of Fe5Sn3 and Fe3Sn2 under the newly measured corrected temperature ranges. Furthermore, the anomalous Hall conductivity and anomalous Nernst conductivity of Fe3Sn were calculated, with magnetization directions and doping considered as perturbations to tune such transport properties. It was observed that the enhanced anomalous Hall and Nernst conductivities originate from the combination of nodal lines and small gap areas that can be tuned by doping Mn at Fe sites and varying magnetization direction.

Stable, metastable and unstable states of the mixed spin (1, 3/2) Ising model in the absence and presence of constant magnetic fields

Stable, metastable and unstable states of the mixed spin (1, 3/2) Ising system in the absence and presence of constant external magnetic fields (CEMFs) were investigated both by the cluster variation method (CVM) and the path probability method (PPM). First, we examine the thermal behavior of the magnetizations by using the CVM and search the metastable and unstable branches of magnetizations in addition to the stable branches. We present the metastable phase diagrams besides to equilibrium phase diagrams in the absence of the CEMFs. We also constructed only the metastable phase diagram under the presence of CEMFs. Since the metastability is a stable state of a dynamical system, we used the PPM on the model and found the dynamic equations. Dynamic equations were solved by means of the flow diagrams (FDs). The FDs clearly display the stable, metastable and unstable states in which also obtained within the CVM. The FDs display the role of the metastable, unstable states and initial conditions as well as how the system trapped into the metastable state. Some properties of the metastable states were observed from the FDs. These studies were made both for the ferrimagnetic and antiferrimagnetic cases.PACS: 05.50. + q, 05.70.Fh, 05.70.Ln, 64.60.Cn, 64.60. My, 75.10.Hk

Effects of order-disorder transition on phase relationship, elastic strength, and mechanical anisotropy of Al-Li alloys

In this work, the effects of order-disorder transition on phase relationship, elastic strength, and mechanical anisotropy of Al-Li system are investigated by first-principles calculations with the help of cluster expansion, Monte Carlo simulation and quasi-harmonic Debye model. The results show that at higher temperature disordered FCC is energetical favorable at xLi < 0.59, while BCC becomes stable at xLi ≥ 0.59. The order-disorder transition at low temperature, deduced from metastable phase diagram at Al-rich side (0.00 ≤ xLi ≤ 0.54), promotes the transformation of disordered α FCC to ordered δ’ L12 Al3Li and δ B32 AlLi structures. The elastic strength indicates the precipitate hardening of Li addition originates from the α – δ’ ordering, while softening is found after the α – δ ordering or δ’ – δ phase transition. The change of FCC, either ordered or disordered, to BCC structures incurs strong mechanical anisotropy, as a result of centrosymmetry breaking and angular electronic bonding. The newly identified long-range ordering of AlLi4 tetrahedron pairs and corresponding bonding electron morphology play the key role in the order-disorder transition and mechanical anisotropy. Our findings not only provide clues for the rational design of Al-Li alloys with higher Li concentration, but also shed lights on the complex experimental phenomena of Al-Li alloys.

Machine learning the metastable phase diagram of covalently bonded carbon

Conventional phase diagram generation involves experimentation to provide an initial estimate of the set of thermodynamically accessible phases and their boundaries, followed by use of phenomenological models to interpolate between the available experimental data points and extrapolate to experimentally inaccessible regions. Such an approach, combined with high throughput first-principles calculations and data-mining techniques, has led to exhaustive thermodynamic databases (e.g. compatible with the CALPHAD method), albeit focused on the reduced set of phases observed at distinct thermodynamic equilibria. In contrast, materials during their synthesis, operation, or processing, may not reach their thermodynamic equilibrium state but, instead, remain trapped in a local (metastable) free energy minimum, which may exhibit desirable properties. Here, we introduce an automated workflow that integrates first-principles physics and atomistic simulations with machine learning (ML), and high-performance computing to allow rapid exploration of the metastable phases to construct “metastable” phase diagrams for materials far-from-equilibrium. Using carbon as a prototypical system, we demonstrate automated metastable phase diagram construction to map hundreds of metastable states ranging from near equilibrium to far-from-equilibrium (400 meV/atom). We incorporate the free energy calculations into a neural-network-based learning of the equations of state that allows for efficient construction of metastable phase diagrams. We use the metastable phase diagram and identify domains of relative stability and synthesizability of metastable materials. High temperature high pressure experiments using a diamond anvil cell on graphite sample coupled with high-resolution transmission electron microscopy (HRTEM) confirm our metastable phase predictions. In particular, we identify the previously ambiguous structure of n-diamond as a cubic-analog of diaphite-like lonsdaelite phase.

Metastable phase diagram of the Gd2O3–SrO–CoO x ternary system

Abstract The metastable phase diagram of the Gd2O3–SrO–CoO x system in air was established based on the powder X-ray diffraction results of the 1100 °C-synthesized and then furnace-cooled or slowly-cooled (1 K min−1) samples. It consists of two solid solutions, Gd1−x Sr x CoO3−δ (0.6 ≤ x ≤ 0.9) with a tetragonal I4/mmm superstructure and Gd x Sr2−x CoO4−δ (0.5 ≤ x ≤ 1.2) with a layered tetragonal I4/mmm K2NiF4-type structure, and one ternary compound Gd2SrCo2O7 with a tetragonal P42/mnm structure. The existence of six binary oxide compounds Gd2SrO4, GdCoO3, Sr2Co2O5 (R), Sr6Co5O15, Sr5Co4O12 and Sr14Co11O33 was confirmed. This metastable phase diagram is of technological interest in the controlled preparation of single-phase complex oxides. New phases Gd0.375Sr2.625Co2O7−δ and τ4 with an orthorhombic Immm structure were found in the quenched samples. Differences between the present metastable phase diagram and the reported 1100 °C equilibrium one are discussed.

Computational Thermodynamics and Microstructure Simulations to Understand the Role of Grain Boundary Phase in Nd-Fe-B Hard Magnets

To control the coercivity of Nd hard magnets efficiently, the thermal stability of constituent phases and the microstructure changes observed in hard magnets during thermal processes should be understood. Recently, the CALPHAD method and phase-field method have been recognized as promising approaches to realize phase stability and microstructure developments in engineering materials. Thus, we applied these methods to understand the thermodynamic feature of grain boundary phase and the microstructural developments in Nd-Fe-B hard magnets. The results are as follows. 1) The liquid phase is a promising phase for covering the Nd2Fe14B grains uniformly. 2) The metastable phase diagram of the Fe-Nd-B ternary system suggests that the tie line end of the liquid phase changes drastically depending on the average composition of Nd. 3) The Nd concentration in the grain boundary phase can reach 100 at% if the volume fraction of the grain boundary phase is constrained. 4) The effect of Cu addition to the Nd-Fe-B system on the microstructural morphology is reasonably modeled based on the phase-field method. 5) The morphology of the liquid phase can be controlled using phase separation in the liquid phase and the grain size of Nd2Fe14B phase.

Thermodynamic analysis of structural transformations induced by annealing of amorphous Si–C–N ceramics derived from polymer precursors

Abstract Thermodynamic modeling has been used to explain structural transformations induced by heat treatment of amorphous Si –C–N ceramics derived from polymers. Nanocrystalline silicon carbide and nanocrystalline silicon nitride identified in the ceramic microstructure have been regarded as metastable NASIC and NASIN phases in the Si–C–N system. The Gibbs energies G(NASIC) and G(NASIN) have been derived and used together with the previously modeled Gibbs energy of the amorphous am-SICN to compute metastable phase diagrams. Computational results allow explanation of the crystallization process of amorphous Si –C–N ceramics. According to this model, the temperature of invariant reaction between carbon and silicon nitride changes with the growth of nanocrystallites, which explains the dependence of the thermal stability on the ceramic microstructure.