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

Abstract

This letter predicts unprecedented order-to-disorder transition behaviors in multicomponent MXenes using an integrated and improved first-principles Monte Carlo (MC) framework. The improvements include (i) structural relaxation and (ii) selective atom swapping during MC iterations for more accurate and efficient predictions. Using (TiMo)-based double transition metal (DTM) carbide MXenes as a model system, ab initio MC simulations reveal that surface termination and coordination environments play critical roles in governing chemical ordering in MXenes. Specifically, the formation of out-of-plane MXene (o-MXenes) with Mo segregation to outermost metallic layers (M') is only driven by the oxygen (O) termination at prismatic sites. In contrast, O termination at octahedral sites and fluorine (F) termination at both prismatic and octahedral sites always promote the formation of o-MXenes with Ti-segregated to M' layers. Furthermore, changing the F/O ratio at prismatic termination sites or alternating the atomic coordination within the MXene lattices can induce an order-to-disorder transition in DTM MXenes.

Figures (4)

• Figure 1: Integrated density functional theory (DFT) and Monte Carlo (MC) simulation framework to predict the minimum energy configurations (MECs) of multicomponent MXenes. (a) Workflow of the DFT/MC framework with new functionalities include ($i$) structural relaxation and ($ii$) selective atom swapping during the MC steps at certain interval. (b) Schematic diagrams showing the atomic configurations of multicomponent MXenes at different MC stages.
• Figure 2: Chemical ordering of (TiMo)-based DTM MXenes with different surface termination elements and coordination environments. (a-b) Schematics of octahedral and prismatic coordination in rocksalt and WC-hexagonal transition metal carbides (MC). DFT/MC-identified MECs of (Ti$_{0.5}$Mo$_{0.5}$)$_4$C$_3$F$_2$ with (c) octahedral and (d) prismatic coordination of M' sites. DFT/MC-identified MECs of Ti$_{0.5}$Mo$_{0.5}$)$_4$C$_3$O$_2$ with (e) octahedral and (f) prismatic coordination of M' sites. For each panel, the interlayer distance ($d$) between M layers are determined based on DFT/MC-searched and fully relaxed structures. The energy profile $vs.$ MC iterations for each (TiMo)-based DTM MXene is shown in Fig. S1.
• Figure 3: Chemical ordering of (TiMo)-based DTM MXenes with varying O/F surface termination ratios. DFT/MC-identified MECs of ($\mathrm{Ti}_{0.5}\mathrm{Mo}_{0.5})_{4}\mathrm{C}_{3}$(O$_x$F$_{1-x}$)$_2$ MXenes with increasing O content: (a) $x$ = 0.25, (b) $x$ = 0.50, (c) $x$ = 0.75, and (d) $x$ = 0.89. The compositional profiles $\rho_M$ for both Ti and Mo atoms across the four M layers are shown for each case. (e) Ordering analysis based on degree of ordering parameter, $\alpha$, as a function of O concentration on surface, $x_\textrm{O}$, for both Ti and Mo atoms. The energy profiles $vs.$ MC iterations are provided in Fig. S2.
• Figure 4: Effects of atomic coordination in bare (TiMo)-based DTM MXenes on local chemical ordering. Schematic of M$_4$C$_3$ MXenes with (a) OOOOO, (b) OOPOO, (c) PPOPP, and (d) PPPPP coordination and their DFT/MC-simulated MECs of three (TiMo)-based DTM MXenes, (Ti$_x$Mo$_{1-x}$)$_4$C$_3$, with $x$ = 0.25, 0.5, and 0.75. The compositional profiles $\rho_M$ for both Ti and Mo atoms across the four M layers are shown for each case. Degree of ordering parameter, $\alpha$, of both Ti and Mo atoms are plotted as a function of Ti content ($x_\textrm{Ti}$) for each coordination system. The energy profiles $vs.$ MC iterations are provided in Fig. S3.