Crystal structure solution of a high-pressure polymorph of scintillating ${\mathrm{MgMoO}}_4$ and its electronic structure

The structure of the potentially scintillating high-pressure phase of $\beta \text{−}{\mathrm{MgMoO}}_4$ ($\gamma \text{−}{\mathrm{MgMoO}}_4$) has been solved by means of high-pressure single-crystal x-ray diffraction. The phase transition occurs above 1.5 GPa and involves an increase of the Mo coordination from fourfold to sixfold accommodated by a rotation of the polyhedra and a concommitant bond stretching resulting in an enlargement of the $c$ axis. A previous high-pressure Raman study had proposed such changes with a symmetry change to space group $P2/c$. Here it has been found that the phase transition is isosymmetrical ($C2/m⟶C2/m$). The bulk moduli and the compressibilities of the crystal axes of both the low- and the high-pressure phase, have been obtained from equation of state fits to the pressure evolution of the unit-cell parameters which were obtained from powder x-ray diffraction up to 12 GPa. The compaction of the crystal structure at the phase transition involves a doubling of the bulk modulus $B_0$ changing from 60.3(1) to 123.7(8) GPa and a change of the most compressible crystal axis from the (0, $b$, 0) direction in $\beta \text{−}{\mathrm{MgMoO}}_4$ to the ($0.9a$, 0, $0.5a$) direction in $\gamma \text{−}{\mathrm{MgMoO}}_4$. The lattice dynamical calculations performed here on $\gamma \text{−}{\mathrm{MgMoO}}_4$ served to explain the Raman spectra observed for the high-pressure phase of $\beta \text{−}{\mathrm{MgMoO}}_4$ in a previous work demonstrating that the use of internal modes arguments in which the ${\mathrm{MoO}}_n$ polyhedra are considered as separate vibrational units fails at least in this molybdate. The electronic structure of $\gamma \text{−}{\mathrm{MgMoO}}_4$ was also calculated and compared with the electronic structures of $\beta \text{−}{\mathrm{MgMoO}}_4$ and ${\mathrm{MgWO}}_4$ shedding some light on why ${\mathrm{MgWO}}_4$ is a much better scintillator than any of the phases of ${\mathrm{MgMoO}}_4$. These calculations yielded for $\gamma \text{−}{\mathrm{MgMoO}}_4$ a $Y_2\mathrm{\Gamma }⟶\mathrm{\Gamma }$ indirect band gap of 3.01 eV in contrast to the direct bandgaps of $\beta \text{−}{\mathrm{MgMoO}}_4$ (3.58 eV at $\mathrm{\Gamma }$) and ${\mathrm{MgWO}}_4$ (3.32 eV at $Z$).

Figure 1

Crystal structures of (left) $\beta \text{−}{\mathrm{MgMoO}}_4$ at 0.87(4) GPa and (right) its high-pressure polymorph, $\gamma \text{−}{\mathrm{MgMoO}}_4$ at 1.95(10) GPa, projected along the $b$ axis. Top: ball-and-stick drawing; Mg, Mo, and O atoms are represented by gray, black, and red color, respectively. At the bottom, polyhedra drawing representing the coordination of Mg and Mo atoms by oxygen atoms.

Figure 2

Sections of the reciprocal space of $\gamma \text{−}{\mathrm{MgMoO}}_4$ at 1.95(10) GPa in the (a) ($hk0$), (b) ($hk1$), and (c) ($h0l$) planes showing the reflection condition, i.e., $h+k=2n$ for all reflections $hkl$, for the $C$-face centered Bravais lattice. (d) Powder XRD patterns of $\beta \text{−}{\mathrm{MgMoO}}_4$ at 1 atm and of $\gamma \text{−}{\mathrm{MgMoO}}_4$ at 5 GPa after the completion of the phase transition. Dots represent the experimental data while the red continuous lines are the Rietveld refinements. The $2\theta$ location of the reflections and the residuals of the fit are also shown as vertical markers and continuous green lines, respectively.

Figure 3

(a) Experimental [9] ${\omega }_{exp}$ vs calculated ${\omega }_{calc}$ Raman frequencies of $\gamma \text{−}{\mathrm{MgMoO}}_4$ show their excellent agreement. (b) Experimental [9] (open circles) and calculated (red dots) pressure coefficients of the same Raman active modes as a function of their frequencies.

Figure 4

(a) Pressure dependence of the lattice parameters of ${\mathrm{MgMoO}}_4$. The arrows indicate the contraction of $a$ and $b$ as well as the expansion of $c$. (b) Pressure dependence of the monoclinic $\beta$ angle. (c) Pressure dependence of the unit-cell volume of both phases. The full dots are data from the low-pressure $\beta \text{−}{\mathrm{MgMoO}}_4$ phase while the empty dots are data from the high-pressure $\gamma \text{−}{\mathrm{MgMoO}}_4$ phase. The straight lines are the fits to second-order Birch-Murnaghan equations of state.

Figure 5

Electronic structure of (a) $\beta \text{−}{\mathrm{MgMoO}}_4$, (b) $\gamma \text{−}{\mathrm{MgMoO}}_4$, and (c) ${\mathrm{MgWO}}_4$. The last one was previously calculated [30]. The straight blue lines indicate the Fermi level.

Figure 6

Total (black) and partial (colors) density of states of the valence and conduction bands around the band gap showing the contribution of the different atomic orbitals in (a) $\beta \text{−}{\mathrm{MgMoO}}_4$, (b) $\gamma \text{−}{\mathrm{MgMoO}}_4$, and (c) ${\mathrm{MgWO}}_4$.