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Miscibility gap

A miscibility gap is a region in the phase diagram of a binary or multicomponent mixture where the components exhibit limited solubility, leading to phase separation into two or more distinct phases across a specific range of compositions and temperatures. This separation occurs because the Gibbs free energy of the homogeneous mixture exceeds that of the coexisting phases, rendering mixing thermodynamically unfavorable.^[1] The thermodynamic foundation of a miscibility gap is rooted in the free energy of mixing, often modeled using the regular solution approximation, which accounts for non-ideal enthalpy contributions while assuming ideal entropy of mixing. In this model, the interaction parameter Ω quantifies the energetic penalty for unlike-pair interactions; when Ω is sufficiently positive and temperature-dependent, the free energy curve develops a double-well shape, with common tangent constructions defining the phase boundaries.^[1] The gap typically narrows or closes at higher temperatures near a critical point, where thermal entropy overcomes enthalpic repulsion, allowing complete miscibility.^[1] Miscibility gaps are prevalent in diverse systems, including metallic alloys such as Pb-Sn and Ag-Cu, where they manifest as two-phase regions (e.g., α and β solids) below the liquidus, influencing solidification and mechanical properties.^[1] In liquid systems like aluminosilicate melts, gaps appear in compositions with low alumina content (e.g., <2 wt% Al₂O₃ in Na₂O-SiO₂), driven by polymerization differences and cation associations, and can be suppressed by additives or pressure.^[2] Within the gap, metastable regions enable spinodal decomposition, a diffusion-driven mechanism forming modulated microstructures without nucleation barriers, which is critical for applications in semiconductors and glasses.^[3]

Fundamentals

Definition

A miscibility gap is a region in the phase diagram of a mixture where two or more components exhibit immiscibility, resulting in phase separation into distinct phases, such as two coexisting liquid phases or two solid phases.^[4] This occurs when the mixture's composition and conditions, like temperature, fall within boundaries where the components cannot form a single homogeneous phase, leading to spontaneous demixing.^[1] In mixtures, complete miscibility implies that components can dissolve in each other across all proportions under given conditions, forming a single phase, whereas partial miscibility allows solubility only up to certain limits, beyond which a miscibility gap emerges. The gap specifically denotes the concentration and temperature range where these solubility limits are exceeded, causing the system to split into multiple phases with compositions at the gap's boundaries.^[4] For instance, in binary mixtures, this gap appears as a lens-shaped area in temperature-composition diagrams, separating regions of single-phase stability from two-phase coexistence.^[1] The concept of miscibility gaps was first described in the context of binary mixtures during the 19th century, with observations of phase separation in liquid systems, and was formalized through J. Willard Gibbs' phase rule in the 1870s, which provided the thermodynamic framework for understanding equilibrium in multi-phase systems. Gibbs' work integrated composition variables into phase equilibria, enabling precise prediction of conditions for immiscibility.^[5] Basic prerequisites for a miscibility gap include differences in intermolecular forces between unlike components compared to like components, which contribute to a positive enthalpy of mixing that can outweigh the stabilizing entropy of mixing. This imbalance in interaction energies leads to thermodynamic instability in certain composition ranges, promoting phase separation as the system minimizes its free energy.^[1]

Thermodynamic Principles

The formation of a miscibility gap in binary mixtures is governed by the Gibbs free energy of mixing, \Delta G_{\text{mix}}, which determines the thermodynamic stability of homogeneous phases. For an ideal solution, \Delta G_{\text{mix}} = \Delta H_{\text{mix}} - T \Delta S_{\text{mix}}, where \Delta H_{\text{mix}} is the enthalpy of mixing, T is the temperature, and \Delta S_{\text{mix}} is the entropy of mixing.^[6] In non-ideal systems, such as those exhibiting limited solubility, \Delta G_{\text{mix}} often features a double-well shape or a positive maximum as a function of composition, indicating instability and a tendency for phase separation into two coexisting phases with lower overall free energy.^[6] This instability arises when the second derivative \partial^2 \Delta G_{\text{mix}} / \partial x^2 < 0 over a composition range x, defining the spinodal region within the broader miscibility gap.^[7] At equilibrium, the compositions of the coexisting phases are identified using the common tangent construction on the \Delta G_{\text{mix}} versus composition curve. This graphical method draws a tangent line that touches the free energy curve at the compositions of the two phases, ensuring equal chemical potentials and minimizing the total free energy of the system.^[6] The relative amounts of each phase follow the lever rule, where the fraction of one phase is proportional to the distance from the overall composition to the tangent points. The driving force for immiscibility primarily stems from the enthalpy term: positive \Delta H_{\text{mix}} reflects unfavorable intermolecular interactions between unlike components, such as in regular solution models where \Delta H_{\text{mix}} = \Omega x_A x_B and \Omega > 0.^[6] In contrast, the entropic contribution favors mixing, given by the ideal entropy of mixing \Delta S_{\text{mix}} = -R \sum_i x_i \ln x_i (per mole), which is always positive for $0 < x_i < 1 and promotes homogeneity through increased configurational disorder.^[8] The competition between these terms results in a miscibility gap that typically widens at lower temperatures, where the -T \Delta S_{\text{mix}} term diminishes relative to \Delta H_{\text{mix}}. The boundaries of the miscibility gap are delimited by critical solution temperatures, known as the upper critical solution temperature (UCST) or lower critical solution temperature (LCST), where the gap closes and complete miscibility is achieved across all compositions.^[9] Below the UCST (common in systems with positive \Delta H_{\text{mix}}), or above the LCST (seen in hydrogen-bonding systems with negative \Delta H_{\text{mix}}), the two-phase region exists due to the curvature of \Delta G_{\text{mix}} at the critical point, where both the first and second derivatives with respect to composition vanish.^[9] For polymeric systems, the Flory-Huggins theory provides a lattice-based model for \Delta G_{\text{mix}}, incorporating the interaction parameter \chi to quantify enthalpic interactions. For polymer solutions (solvent with N=1, polymer with large N), it approximates \Delta G_{\text{mix}} / RT = (1-\phi) \ln(1-\phi) + \phi \ln \phi + \chi \phi (1-\phi), where \phi is the volume fraction of polymer, with immiscibility when \chi > 0.5.^[10] For symmetric polymer blends (both components polymers of equal degree of polymerization N), the entropy terms are reduced: \Delta G_{\text{mix}} / RT = (\phi / N) \ln \phi + ((1-\phi)/N) \ln (1-\phi) + \chi \phi (1-\phi), leading to phase separation when \chi > 2/N, a much smaller threshold for large N due to diminished entropic stabilization from chain connectivity.^[7] This mean-field approximation highlights how polymeric architecture promotes immiscibility compared to small-molecule mixtures.

Representation in Phase Diagrams

Binary Systems

In binary systems, miscibility gaps are represented in isobaric temperature-composition (T-x) phase diagrams at constant pressure, where the gap manifests as a lens-shaped two-phase region bounded by solvus lines that define the solubility limits of each component in the coexisting phases.^[11] These diagrams illustrate how, within the gap, mixtures separate into two distinct phases with differing compositions, while outside the gap, the system remains fully miscible as a single phase.^[1] The solvus lines converge at a critical point, marking the boundary beyond which complete miscibility is achieved. Miscibility gaps in binary systems can exhibit either upper critical solution temperature (UCST) or lower critical solution temperature (LCST) behavior. In UCST systems, the gap exists below the critical temperature, narrowing as temperature increases until the solvus lines meet at the UCST, above which the phases become fully miscible; a representative example is the methyl acetate-carbon disulfide mixture, where the UCST occurs at 39°C.^[11] Conversely, LCST systems display the gap above the critical temperature, with immiscibility increasing as temperature rises and the solvus lines converging at the LCST from below; poly(N-isopropylacrylamide)-water is a classic example, exhibiting an LCST near 32°C due to polymer coil collapse.^[12] Within the miscibility gap, tie lines are horizontal constructs in T-x diagrams that connect the compositions of the two coexisting phases at a fixed temperature, allowing determination of phase equilibria.^[11] The relative proportions of these phases for an overall composition falling in the gap are calculated using the lever rule: the fraction of the phase with composition x_\alpha is (x - x_\beta)/(x_\alpha - x_\beta), where x is the overall composition and x_\alpha, x_\beta are the endpoint compositions along the tie line, analogous to balancing a lever.^[13] In isothermal pressure-composition (P-x) diagrams, the miscibility gap's extent depends on pressure, often narrowing or closing with increasing pressure due to enhanced molecular interactions that favor mixing.^[14] This pressure sensitivity highlights how compressive forces alter phase boundaries in binary mixtures.

Multicomponent Systems

In multicomponent systems with three or more components, miscibility gaps extend beyond the simplicity of binary representations, introducing additional degrees of freedom that result in more complex phase behaviors. Ternary phase diagrams, which depict systems with three components, are typically projected onto equilateral triangular composition plots, often combined with temperature as a vertical axis to form triangular T-x-y diagrams. In these diagrams, miscibility gaps manifest as polyhedral regions bounded by surfaces where phase separation occurs, such as lens-shaped or irregular volumes isolating immiscible liquid or solid phases.^[15]^[16] Liquidus surfaces in ternary diagrams represent the boundary above which a single liquid phase exists, sloping downward from the melting points of pure components and often forming valleys or ridges separated by invariant lines like eutectic or peritectic reactions. Solvus surfaces, analogous to those in binaries, delineate the limits of solid solution stability, enclosing regions where solid phases separate into multiple compositions due to limited solubility. These surfaces in multicomponent diagrams can intersect to create multifaceted polyhedra, complicating the visualization of phase equilibria compared to two-dimensional binary plots.^[15]^[16] Isothermal sections of ternary phase diagrams, sliced at constant temperature, provide planar views of phase assemblages across the composition triangle. Within these sections, miscibility gaps appear as areas separated by tie lines connecting coexisting two-phase regions, while three-phase coexistence is indicated by tie triangles—enclosed areas where the vertices represent the compositions of the three equilibrium phases. Such tie triangles highlight invariant equilibria under the Gibbs phase rule for ternary systems at fixed temperature and pressure, enabling the determination of phase fractions via the lever rule extended to triangular geometry.^[15] Mapping miscibility gaps in multicomponent systems poses significant challenges due to the high dimensionality, requiring extensive experimental data for validation and often leading to incomplete diagrams for quaternary or higher-order systems. Computational tools like the CALPHAD (Calculation of Phase Diagrams) method address these by minimizing the Gibbs free energy across phases using thermodynamic models extrapolated from lower-order subsystems, accurately predicting gap boundaries without initial composition guesses. This approach has been refined through algorithms that ensure convergence for arbitrary component numbers, facilitating reliable predictions of polyhedral miscibility regions.^[17]^[18]

Phase Separation Mechanisms

Binodal and Spinodal Decomposition

The binodal curve defines the boundary of the miscibility gap in a phase diagram, marking the compositions at which two phases coexist in equilibrium. It is determined by the common tangent construction applied to the Gibbs free energy of mixing as a function of composition, where the tangent lines connect points of equal chemical potential between the coexisting phases, ensuring the overall free energy is minimized. Within the miscibility gap, the spinodal curve delineates the boundary between the metastable and unstable regions, specifically where the second derivative of the free energy of mixing with respect to composition, \partial^2 \Delta G_{\text{mix}} / \partial c^2, equals zero. This condition signifies the onset of diffusive instability, as small composition fluctuations become amplified rather than damped, leading to spontaneous phase separation without an energy barrier. Spinodal decomposition occurs in the unstable region inside the spinodal curve, where infinitesimal composition fluctuations grow exponentially through diffusion, resulting in the formation of interconnected, modulated domains. This process is mathematically described by the Cahn-Hilliard equation,

\frac{\partial c}{\partial t} = \nabla \cdot \left( M \nabla \frac{\delta F}{\delta c} \right),

where c is the composition, M is the mobility, and F is the free energy functional incorporating both bulk and gradient contributions. Unlike nucleation and growth, which requires overcoming a free energy barrier to form distinct droplets, spinodal decomposition is barrierless and initially faster, driven solely by thermodynamic instability. Early stages of spinodal decomposition are experimentally observed using small-angle X-ray scattering (SAXS), which detects the characteristic scattering peaks corresponding to the wavelength of composition modulations as they evolve over time. SAXS profiles typically show an initial peak shift to higher wavevectors followed by growth in intensity, confirming the diffusive amplification predicted by theory.

Nucleation and Growth

In the metastable region of a miscibility gap, located between the binodal and spinodal curves, phase separation proceeds via nucleation and growth mechanisms, where an energy barrier must be overcome to form stable domains of the minority phase.^[19] This contrasts with the barrierless spinodal decomposition in the unstable region inside the spinodal. Nucleation involves the formation of small, critical-sized clusters that serve as precursors to the separated phases, driven by the competition between the bulk free energy gain and the interfacial energy penalty. Classical nucleation theory describes this process by modeling the free energy change for forming a spherical nucleus of radius r as \Delta G(r) = \frac{4}{3} \pi r^3 \Delta G_v + 4 \pi r^2 \sigma, where \Delta G_v is the volumetric free energy difference between the parent and nucleating phases (negative in the metastable region), and \sigma is the interfacial energy. The critical nucleus size r^* occurs at the maximum of this function, r^* = -\frac{2\sigma}{\Delta G_v}, yielding a free energy barrier \Delta G^* = \frac{16\pi \sigma^3}{3 (\Delta G_v)^2}.^[20] The nucleation rate is then I = I_0 \exp\left( -\frac{\Delta G^*}{k_B T} \right), where I_0 is a kinetic prefactor, k_B is Boltzmann's constant, and T is temperature; this barrier height decreases with increasing undercooling or deviation from the binodal, facilitating nucleation.^[20] Nucleation can be homogeneous, occurring uniformly within the bulk without preferential sites, or heterogeneous, catalyzed by impurities, container walls, or existing phases that lower the effective \Delta [G](/page/G)^* by reducing the interfacial energy term. In immiscible alloys like undercooled Cu-Co, homogeneous nucleation dominates for the Co-rich phase when the Cu-rich liquid envelops potential heterogeneous sites, suppressing surface-catalyzed events and leading to a higher activation energy of approximately 67 k_B T.^[19] Heterogeneous nucleation prevails closer to the binodal, where the driving force is weaker but sites are more effective.^[19] Following nucleation, the growth stage involves diffusion-limited coarsening of the domains, where smaller particles dissolve and larger ones grow to minimize total interfacial energy, as described by Lifshitz-Slyozov-Wagner (LSW) theory. In this regime, the average domain radius R scales as R \sim t^{1/3}, with the constant of proportionality increasing with the volume fraction of the minority phase; for dilute systems, \bar{R}^3(t) = \bar{R}^3(0) + Kt, where K depends on diffusivity and supersaturation.^[21] This t^{1/3} kinetics arises from the balance of solute diffusion fields around particles, assuming no elastic interactions or coalescence. Several factors influence the nucleation and growth in the metastable region, including undercooling, which amplifies |\Delta G_v| and reduces \Delta G^*; composition deviations from the binodal, which modulate supersaturation; and additives or impurities that act as heterogeneous sites or alter interfacial tension \sigma. For instance, in ternary III-V alloys like InGaAs, higher group V concentrations narrow the miscibility gap and suppress nucleation barriers by up to 64°C in critical temperature, while surface energy differences between phases can fully eliminate the gap during growth.^[22] In electrochemical systems, additives like sodium sulfate reduce solubility and promote nucleation by narrowing the metastable zone width.^[23]

Examples

Metallic Alloys

Miscibility gaps are prevalent in substitutional metallic alloys, such as the Cu-Ni system, where they manifest as regions of phase immiscibility in the solid state due to thermodynamic instabilities that drive atomic ordering and subsequent phase separation. In Cu-Ni alloys, the miscibility gap appears below approximately 600 K, with phase boundaries at around 34 at.% Cu and 74 at.% Cu at 573 K, leading to spinodal decomposition or nucleation-driven separation that results in nanoscale compositional modulations. Similarly, in Alnico permanent magnet alloys (e.g., Fe-Ni-Al-Co systems), the miscibility gap in the Fe-Ni-Al subsystem exhibits an asymmetric form, with the α and α′ phases separating below the Curie temperature, influencing magnetic domain structures through controlled phase partitioning.^[24]^[25]^[26] These miscibility gaps play a critical role in age-hardening processes within metallic alloys, where supersaturated solid solutions are formed at high temperatures and then quenched to trap solutes, followed by controlled aging to induce precipitation within the gap region. This precipitation exploits the thermodynamic drive for phase separation, forming coherent or semi-coherent precipitates that impede dislocation motion and enhance strength, as seen in aluminum alloys where Guinier-Preston zones emerge within the metastable miscibility gap during early aging stages. In noble metal systems like Au-Ni, the gap enables similar hardening by limiting solute solubility at lower temperatures, resulting in ordered phases that increase hardness without significant loss of ductility.^[27]^[28] Recent advancements leverage these gaps for microstructural engineering in additively manufactured alloys. A 2025 study on laser-processed Alnico-8H demonstrated that low-temperature annealing (e.g., 500–600°C) exploits the solid-state miscibility gap to refine nanoscale α₁ and α₂ phases, achieving enhanced coercivity (up to 1.5 kOe) and remanence while maintaining high-temperature stability, thus improving hard magnetic performance over traditional cast Alnico. In ternary systems, such as Ag-Cu-Se, liquid miscibility gaps identified in 2025 phase diagram analyses reveal two extensive immiscible regions, promoting the formation of core-shell microstructures during solidification, where Se-rich cores are encapsulated by Ag-Cu shells, enabling tailored nanoparticle morphologies for electronic applications.^[29]^[30] The presence of miscibility gaps profoundly affects mechanical properties in metallic alloys, often providing strengthening through fine-scale phase separation but risking embrittlement if uncontrolled. Precipitation within the gap, as in age-hardened alloys, can increase yield strength by 50–200% via obstacle formation to dislocations, yet excessive separation in systems like Fe-Cr leads to the 475°C embrittlement, where α′ ferrite formation depletes Cr from the matrix, reducing toughness by up to 80% and promoting intergranular fracture. Alloying elements like Al or Co can modulate the gap width to balance these effects, narrowing it to favor strengthening over brittleness in duplex stainless steels.^[31]^[32]^[33]

Mineral and Geological Systems

In mineral and geological systems, miscibility gaps are prominent in the plagioclase feldspar solid solution series, where they manifest as regions of compositional instability leading to exsolution textures during cooling. The Huttenlocher gap occurs between approximately An₅₅ and An₉₅ (where An denotes the anorthite mole fraction), resulting in high-temperature exsolution of sodic and calcic phases in intermediate to calcic plagioclases.^[34] Similarly, the Bøggild gap spans An₃₉-An₄₈ and An₅₃-An₆₃, producing lamellar intergrowths of andesine and labradorite compositions that exhibit iridescence due to optical interference.^[35] The peristerite gap, found around An₅-An₁₅, involves fine-scale exsolution between albite-rich and oligoclase phases, often observed in low-grade metamorphic or slowly cooled igneous rocks.^[36] These miscibility gaps have significant geological implications, particularly in igneous rocks where exsolution textures form diagnostic features for thermometry and cooling history reconstruction. Lamellae spacing in peristerite or Bøggild intergrowths, for instance, records cooling rates from hundreds to thousands of degrees per million years, providing insights into plutonic emplacement and thermal evolution. Such textures arise via slow cooling through the solvus surface, promoting diffusional unmixing and resulting in perthitic intergrowths that enhance mineral stability under subsolidus conditions.^[37]

Liquid and Polymeric Mixtures

Miscibility gaps in liquid mixtures manifest as regions where two fluids do not fully mix, leading to phase separation under certain conditions. A classic example is the oil-water system, where immiscibility arises due to the low solubility of non-polar oils in polar water, resulting in distinct phases. This phenomenon is particularly evident in crystallization processes, where "oiling out" occurs as a liquid-liquid phase separation (LLPS) driven by a miscibility gap in the solute-solvent system. During cooling or antisolvent addition, the solute-rich phase forms an oily droplet dispersion instead of solid crystals, complicating product isolation and purity control.^[38]^[39]^[40] In some aqueous alcohol systems, such as ethanol-water mixtures, temperature-dependent behavior can influence effective miscibility, particularly when combined with solutes exhibiting lower critical solution temperature (LCST) transitions. LCST denotes the temperature above which phase separation occurs in otherwise miscible mixtures, often due to entropy-driven changes in hydrogen bonding and hydrophobic interactions. For instance, adding ethanol to water-based solutions of thermoresponsive polymers lowers the LCST, enhancing phase separation for applications like controlled release, though pure ethanol-water remains fully miscible across typical ranges.^[41]^[42] Polymeric mixtures often display pronounced miscibility gaps due to the entropic penalties of mixing long chains and unfavorable enthalpic interactions. In blends like polystyrene (PS) and polybutadiene (PB), the Flory-Huggins interaction parameter χ exceeds the critical value of approximately 2 (scaled by degree of polymerization), promoting immiscibility and microphase separation into domains. This leads to morphologies such as lamellae or cylinders, which influence mechanical properties like toughness in rubber-toughened plastics. The χ parameter, quantifying pairwise interactions, highlights how polar differences between PS and PB drive domain formation on the nanoscale.^[43]^[44] Spinodal decomposition in liquid mixtures occurs rapidly within the unstable region of a miscibility gap, as seen in partially miscible fluids like binary metallic alloys in the melt state. Upon quenching into the spinodal, composition fluctuations amplify spontaneously, forming interconnected bicontinuous structures without nucleation barriers. This diffusion-driven process contrasts with nucleation in metastable regions and is modeled via Cahn-Hilliard equations, yielding characteristic length scales on the order of micrometers in fluids with moderate viscosities.^[45]^[46] Recent advancements in sustainable chemistry have emphasized miscibility data for green solvents to optimize eco-friendly processes. A 2025 study compiled miscibility tables for 28 green solvents, including bio-based options like ethyl lactate and cyrene, revealing patterns such as full miscibility among polar aprotic alternatives but gaps with non-polar hydrocarbons. These tables guide solvent selection in extraction and reaction media, reducing environmental impact by favoring recyclable, low-toxicity pairs over volatile organic compounds.^[47]^[48] Miscibility gaps in fluids also induce hydrodynamic instabilities, notably Rayleigh-Taylor and Kelvin-Helmholtz types, as explored in 2025 investigations. The Rayleigh-Taylor instability arises when a denser fluid overlays a less dense one under gravity, accelerated by phase separation in binary mixtures with temperature-sensitive gaps, leading to fingering patterns. Similarly, Kelvin-Helmholtz instability develops at shear interfaces in miscible-to-immiscible transitions, promoting vortex formation and enhanced mixing in flows. Phase-field simulations of these phenomena in partially miscible binary fluids demonstrate how gap width influences instability growth rates, with applications in microfluidics and emulsion stability.^[49]^[50]^[51]

Applications and Developments

Thermal Energy Storage

Miscibility gap alloys (MGAs) serve as innovative phase change materials (PCMs) in thermal energy storage systems, leveraging the latent heat of fusion in binary metal systems exhibiting a miscibility gap. These alloys, such as Ga-In or Bi-Sn, feature inverse microstructures where a low-melting fusible phase (e.g., liquid In or Sn) is encapsulated within a solid skeletal matrix of the higher-melting component (e.g., solid Ga or Bi), enabling operation through the miscibility gap during melting and solidification. This design provides high latent heat capacities, typically ranging from 180 to 200 kJ/kg for systems like Fe-Cu or Bi-Sn, surpassing many conventional organic or salt-based PCMs while maintaining structural integrity.^[52]^[53]^[54] The primary advantages of MGAs in thermal storage include exceptional shape stability, as the solid matrix prevents volume expansion or leakage during phase transitions, high thermal conductivity (often 50-200 times greater than salt hydrates or paraffins due to their metallic nature, typically 20-100 W/m·K), and compatibility with electro-thermal energy storage (ETES) systems for efficient heat transfer. These properties allow MGAs to address key limitations of traditional PCMs, such as low conductivity and container corrosion, making them suitable for applications requiring reliable, long-duration storage without encapsulation needs. For instance, in concentrated solar power (CSP) systems, conceptual designs integrate MGAs for high-temperature storage (up to 500°C), with numerical analyses demonstrating reduced heat exchanger sizes and improved efficiency through enhanced heat transfer rates.^[52]^[55]^[56] Recent advancements highlight MGAs' practical deployment, including the 2025 reboot and commissioning of a 5 MWh pilot plant by MGA Thermal for green steam and industrial thermal storage, enabling continuous renewable steam production at costs competitive with fossil fuels. Additionally, a 2025 thesis from the University of Newcastle explored novel MGA compositions for latent heat storage, focusing on high-temperature variants (e.g., Al-Si or Fe-based systems) to meet demands in CSP and industrial processes, with prototypes showing over 1,000 cycles at 400-600°C. These developments underscore MGAs' potential for scalable ETES, such as modular blocks stackable up to multi-MWh capacities.^[57]^[58]^[59] Despite these benefits, MGAs face challenges including high material costs due to rare metals like gallium and indium (estimated at $10-50/kWh for systems), which can limit commercialization, and concerns over long-term cycling stability, where repeated thermal exposure may degrade the microstructure after 500-1,000 cycles in some alloys. Ongoing research addresses these through alloy optimization and cost modeling to enhance economic viability for widespread adoption in renewable energy integration.^[60]^[61]^[52]

Battery and Electrochemical Materials

In lithium-ion battery cathodes, miscibility gaps play a critical role in phase stability and performance degradation, particularly in high-voltage spinel materials like LiNi_0.5Mn_1.5O₄ (LNMO). The ordered spinel structure of LNMO exhibits a room-temperature miscibility gap during lithium extraction, leading to two-phase coexistence between Li-rich and Li-poor phases, which induces volume changes and mechanical stress that accelerate capacity fade over cycling.^[62] Recent advancements involve multi-element doping with Si, Ti, and Ge to tailor this miscibility gap, suppressing phase separation by stabilizing the solid solution phase and enhancing charge/discharge reversibility, resulting in improved cycling stability up to 1000 cycles at 4.75 V.^[63] Cation mixing further influences miscibility gaps in these cathodes, where Ni/Mn disorder narrows the gap under high current densities, promoting a more continuous solid solution reaction over abrupt two-phase transitions. Studies from 2022 demonstrate that increasing current density from 0.1C to 5C reduces the miscibility gap width in LNMO variants, enhancing rate capability but risking incomplete phase reversion and long-term instability if not managed.^[64] This narrowing effect stabilizes the structure during fast charging, crucial for electric vehicle applications, though excessive mixing can lead to irreversible capacity loss.^[65] In battery electrolytes, miscibility gaps in binary fluid mixtures enable stimuli-responsive behaviors, such as temperature-triggered phase separation for enhanced safety. For instance, poly(ethylene oxide)/ionic liquid systems exhibit lower critical solution temperature (LCST) behavior, where heating above ~60°C induces phase separation into polymer-rich and ionic liquid-rich phases, rapidly increasing resistance to shut down ion transport and prevent thermal runaway in lithium-ion batteries.^[66] This reversible separation maintains electrochemical performance at ambient temperatures while providing overcharge protection, with prototypes showing negligible capacity loss after multiple thermal cycles.^[67] The implications of miscibility gaps in these materials include accelerated capacity fade due to phase decomposition and associated side reactions, such as manganese dissolution in LNMO cathodes, which reduces active material utilization by up to 20% after 500 cycles.^[62] Strategies like post-synthesis annealing at 700–900°C control cation ordering and narrow the gap, minimizing decomposition by promoting homogeneous solid solutions and extending cycle life.^[64] In emerging applications, overcoming the miscibility gap in GaN/InN systems via plasma-assisted molecular beam epitaxy (PAMBE) enables cubic In_xGa_1-xN alloys across the full composition range, supporting high-efficiency semiconductors for power electronics in next-generation batteries with reduced polarization losses.

Nanomaterials and Emerging Uses

Miscibility gaps play a pivotal role in the design of multicomponent alloy nanoparticles, enabling the synthesis of complex nanostructures such as core-shell particles by predicting immiscible boundaries in temperature-composition space. A 2022 review highlights how thermodynamic modeling of these gaps guides precursor ratios to achieve stable, phase-separated architectures in high-entropy alloys, expanding the compositional space beyond traditional binary systems.^[68] This approach facilitates tailored properties like enhanced catalytic activity and magnetic responsiveness at the nanoscale. In binary fluids exhibiting temperature-sensitive miscibility gaps, hydrodynamic instabilities offer innovative pathways for nanoscale applications. The Rayleigh-Taylor instability, where a denser fluid overlies a lighter one under acceleration, has been modeled using phase-field methods to capture transitions from immiscible to miscible states, revealing distinct growth regimes influenced by interfacial tension and diffusion. Such dynamics are leveraged for targeted drug delivery, where stimuli-responsive phase separation enables precise release mechanisms in biological environments. Similarly, the Kelvin-Helmholtz instability, driven by velocity shear across interfaces, promotes mixing in partially miscible fluids, with simulations showing suppressed wave growth as miscibility increases, which is critical for microfluidic devices in lab-on-a-chip technologies.^[69] Advancements in semiconductor nanomaterials exploit miscibility gaps to extend alloy compositions. In molecular beam epitaxy (MBE) growth of cubic (In,Ga)N films, strain management overcomes the GaN/InN miscibility gap, achieving indium contents up to 40% without phase separation, as demonstrated on GaN/AlN templates. This enables polarization-free optoelectronic devices with tunable bandgaps for UV-visible applications. Machine learning has emerged as a tool for predicting miscibility gaps in complex systems, particularly body-centered cubic (BCC) alloys. Neural network models trained on ab initio data accurately forecast phase diagrams, identifying stable regions and gaps with errors below 5% for binary and ternary BCC compositions, accelerating materials discovery for high-temperature applications.^[70] Ab initio calculations combined with Bayesian learning have clarified discrepancies in the Ti-V phase diagram, attributing the observed miscibility gap in the β-phase to oxygen impurities that stabilize clustering at concentrations as low as 1 at.%.^[71] These insights refine alloy design for aerospace components, confirming no intrinsic gap in oxygen-free systems. In green chemistry, updated miscibility tables for 28 bio-based and sustainable solvents address gaps in traditional datasets, evaluating pairwise compatibilities to minimize hazardous mixtures in organic synthesis.^[72] This resource supports scalable, eco-friendly processes by predicting phase behavior for solvent selection in pharmaceutical and fine chemical production.

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In this way, a self-consistent thermodynamic database was developed for the binary phase diagram and its miscibility gap under any pressure. 6. Results and ...
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[PDF] Calculation of ternary phase diagrams - eCommons
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Modelling of Ternary Alloy Systems Using Liquidus, Solidus, Solvus ...
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Thermodynamic Modeling of Multicomponent Phase Equilibria
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An algorithm for calculating multicomponent miscibility gaps
A general and very simple algorithm for calculating multicomponent miscibility gaps is described. Given one single expression for the free energy of a ...
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Liquid immiscibility and core-shell morphology formation in ternary Al–Bi–Sn alloys
### Summary of Findings on Liquid Immiscibility in Ternary Al-Bi-Sn Alloys Leading to Core-Shell Microstructures
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Core-shell microstructure formed in the ternary Fe-Co-Cu peritectic ...
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[PDF] Theory of nucleation and growth during phase separation
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[PDF] Review Progress in Ostwald ripening theories and their applications ...
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Surface energy driven miscibility gap suppression during nucleation ...
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Determination of the Metastable Zone Width and Nucleation ... - MDPI
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Atom Probe Study of the Miscibility Gap in CuNi Thin Films and ...
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Microstructure of Alnico Alloys - AIP Publishing
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In these systems complete miscibility occurs at high temperatures, but at lower temperatures there is a miscibility gap.
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Sep 17, 2025 · This study delves into the miscibility gap present in the phase diagram to tune nanoscale microstructure through controlled annealing for ...
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Phase diagrams and microstructures related to the miscibility gap of ...
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Review Effect of 475 °C embrittlement on the mechanical properties ...
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Three plagioclases in the composition range An66–70 from the different geological environments were selected for investigation of the Huttenlocher ...
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Revisiting the Bøggild Intergrowth in Iridescent Labradorite Feldspars
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Molecular dynamics simulation of Al/Si-ordered plagioclase feldspar
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Oiling Out in Crystallization - Mettler Toledo
A LLPS due to a miscibility gap is a thermodynamic phenomenon (depending on system temperature, concentration and miscibility capability) and phase separation ...
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Liquid–liquid phase separation in pharmaceutical crystallization
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Oiling Out - LinkedIn
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Adjusting the low critical solution temperature of poly(N-isopropyl ...
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Spinodal Decomposition - an overview | ScienceDirect Topics
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Oct 7, 2025 · Green solvents play a central role in the design of more sustainable chemical processes. Among properties influencing solvent selection, ...
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Kelvin-Helmholtz instability in binary fluids with miscibility gap
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(PDF) Miscibility Gap Alloys: A New Thermal Energy Storage Solution
Miscibility gap alloys (MGAs) are a new thermal storage technology that utilises the latent heat of fusion of metals. MGAs encapsulate the liquid phase while ...
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Miscibility gap alloys with inverse microstructures and high thermal ...
New high energy-density thermal storage materials are proposed which use miscibility gap binary alloy systems to operate through the latent heat of fusion ...
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[PDF] Thermal capacitors made from Miscibility Gap Alloys (MGAs)
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The miscibility gap alloys are thermal storage materials which address many of the current thermal storage issues primarily through the use of metallic ...
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Conceptual design and numerical analysis of a miscibility gap alloy ...
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Energy Storage Demonstration Unit - MGA Thermal
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Further developments of the miscibility gap alloy: applications and ...
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(PDF) Price estimation for miscibility gap alloy thermal storage systems
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[PDF] Extended Thermal Cycling of Miscibility Gap Alloy High Temperature
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Tailoring the room-temperature miscibility gap in ordered spinel LiNi ...
Jun 25, 2025 · The results demonstrate that multi-element doping enhances structural stability, tailored charge/discharge reaction mechanisms, and improves ...
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Tailoring the room-temperature miscibility gap in ordered spinel LiNi ...
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Mind the miscibility gap: Cation mixing and current density driven ...
Nov 13, 2022 · Cathode materials that exhibit phase transitions with large structural rearrangements during electrochemical cycling are generally seen as disadvantageous.
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[PDF] Mind the miscibility gap: Cation mixing and current density driven ...
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Functional Electrolytes: Game Changers for Smart Electrochemical ...
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Thermally responsive polymers for overcoming thermal runaway in ...
Feb 17, 2023 · Several strategies based on thermoresponsive polymers have been explored to prevent or inhibit the thermal runaway of ESDs due to rapid, ...
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Pushing the Boundaries of Multicomponent Alloy Nanostructures
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Kelvin-Helmholtz instability in binary fluids with miscibility gap - arXiv
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https://www.tandfonline.com/doi/full/10.1080/14786435.2025.2558154
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Clarifying the Ti-V Phase Diagram Using First-Principles ... - arXiv
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miscibility and potential applications of green solvents
Sep 2, 2025 · Solvent miscibility is an important criterion in the selection of solvents for a process. While miscibility tables have been developed to guide ...