Two-dimensional (2D) metal carbides and nitrides, known as MXenes, are synthesized through the chemical exfoliation of three-dimensional layered materials called MAX phases. The process involves selectively removing the A element from the Mn+1AX structure using etching agents like HF. While this method has yielded various MXenes, the underlying principles determining which MAX phases are amenable to this process remain unclear. This lack of understanding hinders computational screening for new 2D materials. Previous theoretical studies calculated exfoliation energies but overlooked the crucial role of electroneutrality and the chemical environment during etching. These studies often used elemental bulk phases as references for the removed A element, failing to accurately represent the dissolution process. Some studies explored thermodynamic stability using Pourbaix diagrams, showing that MXenes are stable under certain pH and potential conditions. However, these conditions are not always consistent with experimental synthesis, and MXenes degrade in water over time, indicating that thermodynamic stability against solvation may not be the primary predictor of synthesizability. This paper addresses these limitations by computationally studying the etching of 23 MAX phases in HF, considering the entire exfoliation process and competing reactions during the initial steps while explicitly incorporating electroneutrality and the chemical potentials of species in solution. The study compares computational results with experimental data, including previously unpublished data on unsuccessful etching attempts, to build a comprehensive understanding of MXene synthesis.

Several theoretical studies have attempted to predict the exfoliability of MAX phases into MXenes. Khazaei et al. and Khaledialidusti et al. calculated exfoliation energies, suggesting weaker M-A bonds compared to M-X bonds. However, both studies used elemental bulk phases as references for the A elements, resulting in positive formation energies, failing to explain the driving force for MXene formation from a thermodynamic perspective. Ashton et al. utilized Pourbaix diagrams to study the electrochemical synthesis of MXenes, demonstrating thermodynamic stability under certain pH and potential conditions. However, their results and high pH values contradict conventional experimental conditions. This study builds upon these prior works by explicitly including the solution chemistry and the constraint of electroneutrality in the thermodynamic modeling of the etching process, thus addressing the gaps in the existing literature.

This research employs density functional theory (DFT) calculations using the VASP code with the projector-augmented wave (PAW) method and the Perdew-Burke-Ernzerhof (PBE) functional. A plane-wave basis set with a kinetic energy cutoff of 520 eV was used. K-point sampling ensured a distance between k-points less than 0.2 Å⁻¹. Spin-polarized calculations were performed for ferromagnetic and two antiferromagnetic configurations. A p(2 x 2) unit cell was used for defect-free MAX phases and MXenes, with at least 15 Å of vacuum to minimize interactions between periodic images. MXenes were modeled with and without surface terminations (oxygen and fluorine). For studying stepwise etching, a p(4 x 4) unit cell with two MXene units and two A layers was employed to minimize vacant site interactions. Chemical potentials were calculated by considering all relevant ions and molecules involving the element under electroneutrality constraints. Tabulated formation free energies for molecules and ions in solution were used, along with the calculated formation free energies of solids. The chemical potentials of H+ and F were expressed as a function of pH. The exfoliation free energy (ΔGexf) was defined using a chemical equation representing the etching reaction. Solvation free energy (ΔGsolv) and vacancy formation free energy (ΔG_A/M) were also calculated to analyze the complete and initial steps of the etching, respectively. Two sets of calculations were performed, one without any restrictions and one with the constraint that oxygen-containing species are not formed during etching, reflecting the acidic HF environment. The experimental part involved etching powders and thin films of several MAX phases in HF solutions with varying concentrations, etching times, and temperatures, analyzing the resulting products using X-ray diffraction to identify successful and unsuccessful etching attempts.

The study revealed that the complete exfoliation free energy (ΔGexf) alone is insufficient to predict exfoliability. While negative ΔGexf values were observed for all considered MAX phases when surface terminations were included, many with negative values did not exfoliate experimentally. Instead, analyzing the initial etching step, where either an A or M element is removed from the MAX phase, provided crucial insight. It was found that successful exfoliation correlates with a negative free energy change (ΔG_A) for A element removal and a positive free energy change (ΔG_M) for M element removal, under the constraint that oxygen-containing species are not formed in the acidic HF environment. This constraint reflects the reality of the experimental etching conditions. The exception is Mo₂ScAlC₂, where both A and M element removal are favorable, however, experimental observation confirms partial Sc etching. Mo₂Ga₂C, which has a double Ga layer, is exfoliable while Mo₂GaC is not. Stepwise etching calculations revealed that the exfoliation of Mo₂GaC becomes exergonic only after ~30% of the etching is complete. Analyzing the solvation free energies of A and M elements in their elemental reference states provides a broader perspective. Al exhibits the most favorable solvation among A elements, while Mo, Nb, and Ta show less tendency to dissolve among the M elements, explaining their common presence in successful MXene syntheses. Conversely, Sc, Zr, and Hf are readily dissolved, explaining why MXenes containing them are less often synthesized.

The findings demonstrate that predicting chemical exfoliation requires a more nuanced understanding than simply considering the overall thermodynamic favorability of the complete transformation. The initial steps of the etching process and the specific chemical environment play a crucial role. The constraint of excluding oxygen-containing species during etching is particularly significant, and accurately reflects experimental conditions in HF. By combining DFT calculations with experimental data and considering solution chemistry, this study provides a more accurate and predictive model for chemical exfoliation. This approach can be applied to computational screening of novel materials, potentially accelerating the discovery of new 2D materials.

This study offers a refined approach to predicting the chemical exfoliation of MAX phases into MXenes. The key finding is that focusing on the initial etching steps, under the condition of excluding oxygen-containing species in the acidic HF environment and considering electroneutrality, provides a much more accurate prediction than simply considering the overall thermodynamic favorability. This approach enhances our understanding of MXene synthesis and facilitates the computational design of novel 2D materials. Future research could explore different etching environments and investigate the role of grain boundaries in the etching process.

The study relies on DFT calculations, which have inherent limitations in accurately describing complex chemical processes. While the inclusion of solution chemistry and electroneutrality improves the model's accuracy, approximations were made to simplify the calculations, such as assuming the etching starts from the inside of the MAX phase. The experimental data, while including previously unpublished results, may not encompass the full range of possible MAX phase compositions. Further experimental validation of predictions for MAX phases not yet synthesized could refine the model's predictive power.