Ab initio Monte Carlo prediction of order-to-disorder transitions in multicomponent MXenes

1. Problem Statement

Multicomponent MXenes (2D transition metal carbides/nitrides with the formula $M_{n+1}X_nT_x$) offer vast compositional spaces and tunable properties, particularly when incorporating multiple transition metals (e.g., Double Transition Metal or DTM MXenes, and High-Entropy MXenes). A critical challenge in designing these materials is understanding the driving forces behind chemical ordering (the arrangement of different metal atoms in specific layers) versus disordering (random solid-solution-like arrangements).

While configurational entropy is widely recognized as a driver for order-to-disorder transitions, the specific roles of surface terminations (e.g., F, O) and local coordination environments (octahedral vs. prismatic sites) remain poorly understood. Existing computational methods often lack the ability to efficiently capture these local chemical orderings and structural relaxations simultaneously, hindering the rational design of novel MXenes.

2. Methodology

The authors developed an integrated and improved first-principles Density Functional Theory (DFT) and Monte Carlo (MC) framework to predict Minimum Energy Configurations (MECs) of multicomponent MXenes.

• Improved DFT/MC Workflow:
  • Structural Relaxation: Unlike previous static approaches, this framework performs structural relaxation at specific intervals (every 30 iterations) during the MC loop. This accounts for lattice distortions caused by element substitution.
  • Selective Atom Swapping: The MC algorithm allows for selective swapping of atoms at specific sites (M, X, and T sites). In this study, swapping was restricted to M (metal) and T (termination) sites to investigate order-to-disorder transitions.
  • Metropolis Criterion: New configurations are accepted or rejected based on energy differences calculated via DFT, guiding the system toward energetically favorable states.
• Computational Details:
  • Software: Vienna Ab initio Simulation Package (VASP).
  • Functionals: Generalized Gradient Approximation (GGA-PBE) with Projector Augmented-Wave (PAW) method.
  • Corrections: Van der Waals corrections (PBE-D2) were included to accurately model interlayer interactions.
  • Parameters: 500 eV cutoff energy, $\Gamma$-centered $4 \times 4 \times 1$ k-point mesh. Spin polarization was omitted for (TiMo) systems due to negligible magnetization.
• Model System: Equimolar (TiMo)-based DTM carbide MXenes, specifically $(Ti_{0.5}Mo_{0.5})_4C_3T_2$, were used as the primary model to explore various termination ratios and coordination environments.

3. Key Contributions

1. Methodological Advancement: Introduction of a robust DFT/MC workflow that couples structural relaxation with selective atom swapping, significantly improving the accuracy and efficiency of predicting local chemical ordering in complex multicomponent systems.
2. Discovery of Termination-Driven Ordering: Identification that surface termination type (F vs. O) and coordination site (octahedral vs. prismatic) are critical determinants of chemical ordering, capable of inducing order-to-disorder transitions even in low-entropy DTM systems.
3. Coordination-Dependent Reversal: Demonstration that the local atomic coordination (octahedral vs. prismatic) can completely reverse the chemical ordering preference (i.e., which metal segregates to the outer layers).

4. Key Results

A. Influence of Surface Termination and Coordination

• Fluorine (F) Termination: Whether F occupies octahedral or prismatic sites, it consistently promotes the formation of out-of-plane (o-MXenes) where Ti segregates to the outermost ($M'$) layers and Mo remains in the inner ($M''$) layers. F atoms energetically prefer octahedral sites.
• Oxygen (O) Termination:
  • At octahedral sites: Similar to F, it drives Ti to the outer $M'$ layers.
  • At prismatic sites: This is the unique case where Mo segregates to the outer $M'$ layers and Ti remains in the inner $M''$ layers. This specific configuration matches experimental observations of Mo-rich outer layers in (TiMo) MXenes, suggesting that in experiments, O likely terminates at prismatic sites.
• Structural Impact: The chemical ordering directly influences interlayer distances. Ti-rich outer layers result in larger distances between inner layers compared to Mo-rich outer layers.

B. Order-to-Disorder Transitions via F/O Ratio

By varying the ratio of O to F on prismatic sites in $(Ti_{0.5}Mo_{0.5})_4C_3(O_xF_{1-x})_2$:

• Low O content ($x_O \le 0.50$): The system exhibits a disordered state with no clear layer segregation.
• Intermediate O content ($x_O = 0.75$): A partially ordered state emerges.
• High O content ($x_O \approx 0.89$): A fully ordered o-MXene forms with Mo-rich outer layers and Ti-rich inner layers.
• Conclusion: Increasing the O/F ratio drives a transition from an ordered Ti-outer phase $\to$ disordered phase $\to$ ordered Mo-outer phase.

C. Influence of Atomic Coordination (Octahedral vs. Prismatic)

The study analyzed bare MXenes with varying coordination sequences (OOOOO, OOPOO, PPOPP, PPPPP):

• Purely Octahedral (OOOOO): Always forms ordered structures with Ti in inner layers and Mo in outer layers, regardless of Ti concentration.
• Twinned (OOPOO): Shows a transition from ordered (low Ti) to disordered (equimolar) back to ordered (high Ti). The equimolar case is highly disordered, unlike the purely octahedral case.
• Prismatic Dominance (PPOPP, PPPPP):
  • In fully prismatic (PPPPP) coordination, the equimolar case forms an o-MXene with reversed ordering compared to the octahedral case: Ti segregates to the outer layers, and Mo to the inner layers.
  • This reversal is attributed to the energetically favorable Mo-C bonding in prismatic sites, which stabilizes Mo in the inner layers.
  • Complex asymmetric ordering patterns were observed in mixed coordination systems (e.g., PPOPP).

5. Significance

• Design Strategy: The findings provide a clear design strategy for tuning the chemical ordering of multicomponent MXenes. By controlling surface termination (F/O ratio) and synthesis conditions that dictate coordination environments, researchers can deliberately engineer specific ordered or disordered states.
• Beyond High-Entropy: The study proves that order-to-disorder transitions are not exclusive to high-entropy systems but occur in low-entropy DTM MXenes, driven by local chemical environments.
• Generalizability: The improved DFT/MC framework is versatile and can be extended to other multicomponent systems to study short-range ordering, interfacial segregation, and other complex phenomena.
• Future Outlook: The authors note that while spin polarization was neglected here, it may be crucial for magnetic MXenes (e.g., Cr-based). Additionally, future work should explore temperature effects, as metastable phases at elevated temperatures could further influence ordering transitions.

The paper concludes that the interplay between surface chemistry and local lattice geometry is the fundamental driver for chemical ordering in MXenes, offering a powerful tool for the rational design of next-generation 2D materials.