Site preference of chalcogen atoms in 1T$^\prime$ $MX_{2(1-x)}Y_{2x}$ ($M=$ Mo and W; $X, Y=$ S, Se, and Te)

TL;DR

The paper investigates how chalcogen site occupancy in $MX_{2(1-x)}Y_{2x}$ monolayers (M = Mo, W; X,Y ∈ {S, Se, Te}) in the 1T′ phase governs the phase stability and an emergent insulator-metal transition. A first-principles enumeration of $2\times 1$ supercell configurations quantifies formation energies $\Delta E_\gamma(x)$ and decomposes them into phase-transition $\Delta E_{PT}$ and relaxation $\Delta E_{relax}$ contributions, revealing a universal link between $\Delta E$ and the Peierls-like distortion amplitude $\Delta y/b$. The results show that Te occupancy in the elongated region drives the linear in-plane elastic constants via a linear relation $c_{ij} = A (\Delta y/b) + B$, and that certain compositions (notably $x \ge 0.5$ for WS$_{2(1-x)}$Te$_{2x}$ and WSe$_{2(1-x)}$Te$_{2x}$) stabilize the 1T′ phase, with SOC further lowering energies in WSe$_{2(1-x)}$Te$_{2x}$. Across the linear regime, this work establishes a direct structure-property map linking site occupancy, distortion amplitude, and elastic response; in the nonlinear regime, elasticity is more anisotropic and less sensitive to site preference. Overall, the study provides fundamental insight into phase engineering of 2D MX$_2$ alloys by controlling chalcogen site distribution.

Abstract

The insulator-metal transition, accompanying the structural phase transition from 2H to 1T$^\prime$ structure, has been reported in two-dimensional W-S-Te and W-Se-Te systems. It is also reported that Te atoms tend to occupy a specific site of the 1T$^\prime$ structure. Here, we study the site preference of chalcogen atoms in $MX_{2(1-x)}Y_{2x}$ ($M=$ Mo and W; $X, Y=$ S, Se, and Te; $0\le x \le 1$) using first-principles approach. We demonstrate that the site preference of chalcogen atoms explains the universal correlation between the formation energy and the Peierls-like distortion amplitude in the 1T$^\prime$ phase. The impact of the site preference on the linear elastic properties is strong, whereas its impact is weak in the non-linear regime. This establishes the structure-property relationships in $MX_{2(1-x)}Y_{2x}$ systems.

Figures (5)

• Figure 1: Top and side views of (a) 2H and (b) 1T$^\prime$$MX_2$ in a $2\times 1$ supercell. The metal atom $M$ shifts to $-y$ direction (a Peierls-like distortion) in the 1T$^\prime$ phase, which separates into the compressed and elongated (shaded) region. Top view of (c) the lowest and (d) the second lowest energy structure of 2H $M$SSe [$M=$ Mo and Te (purple)]. The chalcogen atoms in the bottom side have different atomic species of the upper side [i.e., S $\leftrightarrow$ Se (yellow and green)]. (e) The lowest energy structure of 1T$^\prime$ Mo$X_{2(1-x)}$Te$_{{2x}}$ and W$X_{2(1-x)}$Te$_{{2x}}$ at $x=0.5$. Te atoms are located in the elongated region [i.e., the shaded area in (b)]. (f) Schematic illustration of the Peierls-like distortion, where $M$ atom in the center exhibits a displacement of $\Delta y$.
• Figure 2: (a) $\Delta E_\gamma$ for $MX_{2(1-x)}Y_{2x}$ alloys with 2H and 1T$^\prime$ structures. $M$S$_{2(1-x)}$Se$_{2x}$ alloys ($M=$ Mo and W) in the 1T$^\prime$ structure has $\Delta E > 0.1$ eV/atom that is outside of the energy window. $\Delta E$ including the SOC is also plotted for 1T$^\prime$ WSe$_{2(1-x)}$Te$_{2x}$. (b) $\Delta E_{\rm PT}$ and $\Delta E_{\rm relax}$ for 1T$^\prime$ structure.
• Figure 3: (a) $\Delta E$ as a function of the $M$ atom displacement in the 1T$^\prime$ structure relative to the 1T structure. The dashed line is a linear fit to the data ($\Delta E = -3.418\Delta y/b + 0.516$). (b) $\Delta E$ versus $\Delta y/b$ for each $M$-$X$-$Y$. The data of $(\Delta y/b, \Delta E)$ is classed into five groups indicated as $m \ (=0, 1, 2, 3, 4)$.
• Figure 4: (a) Distribution of elastic constants $c_{ij}$ in W$X_{2(1-x)}$Te$_{2x}$ ($X=$ S and Se). $c_{ij}$ of 2H and 1T$^\prime$ is plotted for $x < 0.5$ and $x\ge 0.5$, respectively. (b) The $\Delta y/b$-dependence of $c_{ij}$ in the 1T$^\prime$ phase with $x\ge 0.5$. The dashed line is a linear fit to the data.
• Figure 5: Stress-strain curve for (a) WS$_{2(1-x)}$Te$_{2x}$ and (b) WS$_{2(1-x)}$Te$_{2x}$ with respect to the tensile strain along $x$ and $y$ directions. 2H (blue) and 1T$^\prime$ (black) phases were assumed for $x<0.5$ and $x\ge 0.5$, respectively. The curves become partially transparent as $x$ approaches 0.5. The curves for WTe$_2$ (i.e., $x=1$) are colored red. (c) The distribution of the maximum stress $\sigma_{i}^{\rm max}$, the maximum strain $\varepsilon_{i}^{\rm max}$, and the normalized displacement $\Delta y/b$ for WS$_{2(1-x)}$Te$_{2x}$ and WSe$_{2(1-x)}$Te$_{2x}$ in the 1T$^\prime$ phase. The dashed line is a linear fit to the data.