Ab initio exploration of post-PPV transitions in low-pressure analogs of ${\mathrm{MgSiO}}_3$

Here, we present an ab initio investigation of the pressure-induced behavior of ${\mathrm{MgGeO}}_3$ and ${\mathrm{NaMgF}}_3$ perovskite (PV), traditional low-pressure analogs (LPAs) of ${\mathrm{MgSiO}}_3$ PV. The latter is an exceedingly important system in planetary sciences displaying novel phases and phase reactions under pressure that are impractically high and still challenging to experiments. Specifically, we investigate the possibility of ${\mathrm{MgGeO}}_3$ and ${\mathrm{NaMgF}}_3$ to display at lower pressures the novel phases, $I\overline{4}2d$-type ${\mathrm{A}}_2\mathrm{B}{X}_4$, $P{2}_1/c$-type ${\mathrm{AB}}_2{X}_5$, and dissociation/recombination transitions displayed by ${\mathrm{MgSiO}}_3$ above $\sim 500\mathrm{GPa}$, alone or in the presence of its binary compounds, MgO and ${\mathrm{SiO}}_2$. We find that, although neither ${\mathrm{MgGeO}}_3$ nor ${\mathrm{NaMgF}}_3$ are perfect LPAs of ${\mathrm{MgSiO}}_3$, they are useful for several reasons: (i) both display the post-PV transition observed in ${\mathrm{MgSiO}}_3$ PV; (ii) starting at $\sim 20\mathrm{GPa}$, the Na-Mg-F system produces a novel $P{2}_1/c$-type ${\mathrm{NaMg}}_2{\mathrm{F}}_5$ phase by dissociation of ${\mathrm{NaMgF}}_3$ or by its compression with ${\mathrm{MgF}}_2$. Instead, the Mg-Ge-O system produces a $I\overline{4}2d$-type ${\mathrm{Mg}}_2{\mathrm{GeO}}_4$ by dissociation of ${\mathrm{MgGeO}}_3$ or by its compression with MgO starting at $\sim 200\mathrm{GPa}$. Such pressures are routinely accessible in laser-heated diamond-anvil cells today; (iii) like ${\mathrm{MgSiO}}_3$, both systems ultimately dissociate into the binary AX and $\mathrm{B}{X}_2$ compounds, confirming this trend in ternary systems first predicted in ${\mathrm{MgSiO}}_3$. We also predict potential metastable phase transitions into a ${\mathrm{Gd}}_2{\mathrm{S}}_3$-type structure in ${\mathrm{MgGeO}}_3$ and into a ${\mathrm{U}}_2{\mathrm{S}}_3$-type structure in ${\mathrm{NaMgF}}_3$. Metastable polymorphic transitions may occur more easily than dissociation/recombination reactions under insufficiently heated compression.

Figure 1

Crystal structures investigated in the present paper. Yellow and blue spheres or polyhedra denote $A$ and $B$ cations and coordinations. Red small spheres denote anions $X$. The numerals indicates coordination numbers of cations $A$ and $B$. In the $\mathrm{AB}{X}_3$ PV and PPV structures, $A$ and $B$ ions are located in approximately bicapped triangular prisms and octahedra. In ${\mathrm{Gd}}_2{\mathrm{S}}_3$-type and ${\mathrm{U}}_2{\mathrm{S}}_3$-type $\mathrm{AB}{X}_3$, both $A$ and $B$ ions are located in bicapped triangular prisms. For $\mathrm{B}{X}_2$, the structural unit is octahedra in the pyrite-type phase and a tricapped triangular prism. In $P{2}_1/c{\mathrm{AB}}_2{X}_5$, the $A$ cations are at the center of tricapped triangular prisms. There are two kinds of $B$ cations; they are at the center of capped triangular prisms and tricapped triangular prisms.

Figure 2

Pressure-induced post-PPV phase transitions predicted in the Mg-Si-O system as indicated in (a) reactions 1–4, (b) reaction 5, and (c) reaction 6 [1, 2, 3, 8, 27, 28]. The indicated transition pressures were obtained using the static LDA and ultrasoft pseudopotentials especially generated for these high-pressure calculations [25]. LDA is known to underestimate transition pressures by $\sim 5–10\mathrm{GPa}$ in the Mg-Si-O system [3, 25].

Figure 3

Relative static enthalpies of (a) aggregation of possible dissociation products of ${\mathrm{MgGeO}}_3$ and other polymorphs (${\mathrm{U}}_2{\mathrm{S}}_3$-type and ${\mathrm{Gd}}_2{\mathrm{S}}_3$-type) of ${\mathrm{MgGeO}}_3$ with respect to ${\mathrm{MgGeO}}_3$ PPV, (b) aggregation of possible dissociation products of ${\mathrm{Mg}}_2{\mathrm{GeO}}_4$ with respect to $I\overline{4}2d$-type ${\mathrm{Mg}}_2{\mathrm{GeO}}_4$, and (c) aggregation of possible dissociation products of ${\mathrm{MgGe}}_2{\mathrm{O}}_5$ with respect to $P{2}_1/c$-type ${\mathrm{MgGe}}_2{\mathrm{O}}_5$.

Figure 4

Phase boundaries of pressure-induced phase transitions in (a) ${\mathrm{MgGeO}}_3$, (b) ${\mathrm{MgGeO}}_3$ and MgO, and (c) ${\mathrm{MgGeO}}_3$ and ${\mathrm{GeO}}_2$, both cases with the molar ratio of 1:1. In (a), the red dashed line denotes the metastable phase boundary between PPV and ${\mathrm{Gd}}_2{\mathrm{S}}_3$ type.

Figure 5

Relative static enthalpies of (a) aggregation of possible dissociation products of ${\mathrm{NaMgF}}_3$ and other polymorphs (${\mathrm{U}}_2{\mathrm{S}}_3$ type and ${\mathrm{Gd}}_2{\mathrm{S}}_3$ type) of ${\mathrm{NaMgF}}_3$ with respect to ${\mathrm{NaMgF}}_3$ PPV, (b) aggregation of possible dissociation products of ${\mathrm{Na}}_2{\mathrm{MgF}}_4$ with respect to $I\overline{4}2d$-type ${\mathrm{Na}}_2{\mathrm{MgF}}_4$, and (c) aggregation of possible dissociation products of ${\mathrm{NaMg}}_2{\mathrm{F}}_5$ with respect to $P{2}_1/c$-type ${\mathrm{NaMg}}_2{\mathrm{F}}_5$.

Figure 6

Phase boundaries of pressure-induced phase transitions in (a) ${\mathrm{NaMgF}}_3$, (b) ${\mathrm{NaMgF}}_3$ and NaF and (c) ${\mathrm{NaMgF}}_3$ and ${\mathrm{MgF}}_2$, both with the molar ratio of 1:1. Below 1000 K, panel (a) is identical to that reported by Ref. [67]. In (a), the red dashed line denotes the metastable phase boundary between the PPV and the ${\mathrm{U}}_2{\mathrm{S}}_3$-type phase. For the sake of simplicity, we omit low-pressure phases of ${\mathrm{MgF}}_2$ below pyrite type and an experimental phase boundary of ${\mathrm{NaMgF}}_3$ perovskite between orthorhombic and cubic phases [66].