Stability, Metastability, and Exfoliability of MAX Phases and Their 2D MXene Derivatives: Insights from Electronic Structure Calculations

Descriptors capable of predicting thermodynamic metastability of materials remain scarce because quantifying kinetic effects is challenging. Yet many technologically important materials—such as diamond at ambient conditions or graphite in an oxidizing atmosphere—owe their practical existence to kinetic barriers that trap them in local minima of the free energy. Identifying a descriptor for such metastable materials is therefore essential for guiding their synthesis and discovering new members of this class. To date, however, only heuristics that probe the depth of local minima (e.g., the energy above the convex hull) have been accessible, and these often diverge from experimental observations because they rely on arbitrary thresholds. Here, we present a simple, thermodynamic descriptor that discriminates between metastability and instability. We develop and validate it for two-dimensional (2D) metal carbides and nitrides, referred to as MXenes, which are synthesized by selectively etching the A layer from their MAX phase precursors using an etchant, e.g., hydrofluoric acid (HF). So far, descriptors for the etching remain inadequate, and their predictions often conflict with experimental observations. This is chiefly because the etching process, also known as exfoliation, is dynamic and the resulting MXenes are metastable. Using the Gibbs free energy change ΔᵣG of MXenes compared to that of the competing phases (CPs) in HF, we find that all MXenes are intrinsically metastable independent of their synthesizability, i.e., ΔᵣG^(MXene) > ΔᵣG^(CPs). Consequently, ΔᵣG alone fails to distinguish MXenes that have been realized from compositions that cannot be synthesized. Instead, we show that the vacancy formation energy ΔE_f of M and X can be used for identifying metastability. We find that ΔE_f correlates with metastability and the exfoliability (the ease of removing the A layer) of the precursors. Experimentally realized MXenes exhibit positive ΔE_f for both M and X elements, whereas non-synthesizable candidates exhibit at least one negative value. Conversely, MAX phases that are exfoliable possess a negative ΔE_f^A for the A element, while non-exfoliable MAX phases show positive values. Therefore, successful exfoliation occurs when a MAX/MXene pair satisfies (i) ΔE_f^M > 0 and ΔE_f^X > 0 in the MXene and (ii) ΔE_f^A < 0 in the corresponding MAX phases. Using this criterion, we screen all plausible MXenes, which are naturally limited by the availability of their precursors. Therefore, to predict new stable candidates, we first begin with the stability predictions of MAX phases. We systematically screen all MAX (Mₙ₊₁AXₙ) compositions with M = Sc–Au (except Tc), A = groups IIIA–IVA, X = C or N, and n = 1, 2, 3. Stability is predicted from the formation enthalpy ΔᵣH relative to all possible competing phases, calculated through density functional theory (DFT) combined with thermodynamic analysis. Accordingly, we predict 129 so far unreported MAX phases—58 carbides and 71 nitrides—five of which are predicted to be magnetic. Among empirical atom-attribute based descriptors proposed previously—valence electron concentration (VEC), electronegativity difference Δχ, and atomic radii difference ΔRₐₜ—only VEC and Δχ partially correlate with stability (ΔᵣH); each stable phase satisfies VEC < 5.5 and Δχ > 1.5. The converse, however, does not hold: not every phase satisfying these conditions is necessarily stable, rendering these criteria only necessary but not sufficient. We further analyze unconventional MAX phases formed by substitution or etching of the A element that include Ti₂AuN, Mo₂Ga₂C, Mo₂GaC (from Mo₂Ga₂C by etching), and Mo₂Ga₁₋ₓCuₓC. Although such unconventional compositions do not yield any new plausible MXene composition, thermodynamic characterization of their formation has so far been lacking. We therefore evaluate their reaction enthalpies ΔᵣH and find that Au, Ga, and Cu substitution as well as Ga etching in Mo₂Ga₂C are thermodynamically favored by negative ΔᵣH. The driving force (ΔᵣH < 0) is the reduced chemical potential of the expelled A element in the surrounding environment. For instance, by forming a solid solution or intermetallic phase with Au, Al expels from the MAX phase, thereby permitting substitution by Au. This reactivity (or dissolution) between expelled and substituting elements can guide their selection for future studies. Finally, we apply the vacancy-formation energy descriptor to screen the metastability of new MXene compositions and the exfoliability of their precursors. Our dataset contains 24 MXenes in total that uniquely correspond to the predicted and synthesized MAX phases. Of these, we predict seven hitherto unreported MXenes that are both metastable and have an exfoliable precursor under conventional HF etching conditions (pH = 2, T = 25 °C). At higher pH values, we identify additional MXenes as metastable and exfoliable; however, these conditions are not practically attainable using HF. This motivates the exploration of alkaline or alternative etchants. The descriptor introduced here is transferable to other metastable 2D materials formed by exfoliation, such as MBenes, and to other chemical etchants, including alkalis and molten salts.