Prediction of $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type $\mathrm{TiT}{\mathrm{e}}_2$ under pressure

$\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type dioxides are significant both for geoscience and condensed-matter physics. For example, $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type $\mathrm{Si}{\mathrm{O}}_2$ has been proposed to be one of the dominant components in the mantles of super-Earths and $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type $\mathrm{Ti}{\mathrm{O}}_2$ has been shown to have a large visible absorbance. Here we report the discovery of an $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type phase in a typical transition-metal dichalcogenide (TMD), $\mathrm{TiT}{\mathrm{e}}_2$, using crystal structure prediction and first-principles calculations. Ambient layered $\mathrm{TiT}{\mathrm{e}}_2$ will first transform to a monoclinic $C2/m$ phase and then finally to the hexagonal $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type phase above 33 GPa. $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type $\mathrm{TiT}{\mathrm{e}}_2$ is predicted to be metallic, contrasting with the semiconductivity of $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type $\mathrm{Ti}{\mathrm{O}}_2$. The same high-pressure phase ($\mathrm{F}{\mathrm{e}}_2\mathrm{P}$ type) appears both in transition-metal dioxides and TMDs, indicating that the stacking patterns of anions and cations play an increasingly important role in determining the high-pressure phase.

Figure 1

Crystal structures for (a) the ambient trigonal (space group $P\text{−}3m1$, $Z=1$) phase, (b) the high-pressure monoclinic (space group $C2/m$, $Z=6$) phase, and (c) the high-pressure hexagonal $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type structure (space group $P\text{−}62m$, $Z=3$) of $\mathrm{TiT}{\mathrm{e}}_2$. The coordination polyhedra of the three phases are shown for (d) the $P\text{−}3m1$ phase, (e) the $C2/m$ phase (marked with Ti1 and Ti2 for $2d$ and $4i$ positions, respectively), and (f) the $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type structure (marked with Ti1 and Ti3 for $2d$ and $1a$ positions, respectively). The cyan and golden-brown balls separately represent Ti and Te atoms.

Figure 2

Enthalpy and volume curves as a function of pressure for $\mathrm{TiT}{\mathrm{e}}_2$ from 0 to 100 GPa. (a) The relative enthalpy up to 100 GPa with the ambient $P\text{−}3m1$ phase as a reference. (b) The volume variation with pressure for the $P\text{−}3m1$, $C2/m$, and $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type phases. At the transition pressures of 12 and 33 GPa, the $C2/m$ phase and the $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type phase show 6 and 2% volume decrements, respectively.

Figure 3

Simulated synchrotron XRD patterns ($\lambda =0.6199\AA$) of the $P\text{−}3m1$ phase at 0 GPa (black line), the $C2/m$ phase at 20 GPa (blue line), and the $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type structure at 50 GPa (red line). The Miller indices (h k l) for the diffraction peaks of the $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type $\mathrm{TiT}{\mathrm{e}}_2$ are marked.

Figure 4

Calculated phonon band structures of (a) the $P\text{−}3m1$ phase at 0 GPa, (b) the $C2/m$ phase at 20 GPa, and (c) the $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type structure at 50 GPa.

Figure 5

(a) Energy barrier between the initial $C2/m$ and final $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type structure at 33 GPa. The $C2/m$ phase was chosen as a reference for enthalpy. (b) Phase transition pathway for $C2/m$ to $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type structure. To illustrate clearly, here we gave the primitive cell of $C2/m$ phase.

Figure 6

Electronic properties of $\mathrm{TiT}{\mathrm{e}}_2$ using PBE (black line) and hybrid functional HSE06 (red line) within the spin-orbit coupling effect: electronic band structure for (a) $P\text{−}3m1$ phase at 0 GPa, (b) $C2/m$ phase at 20 GPa, and (c) $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type structure at 50 GPa. (d)–(f) Corresponding DOS of HSE06.

Figure 7

The 2D ELF $\mathrm{TiT}{\mathrm{e}}_2$ for (a) $P\text{−}3m1$ phase in (1 0 0) plane, (b) $C2/m$ phase in (0 1 0) plane, and (c) $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type structure in (0 0 1) plane.

Figure 8

The Madelung energy with pressure for the $P\text{−}3m1$, $C2/m$, and $\mathrm{F}{\mathrm{e}}_2\mathrm{P}$-type phases.