Codetermination of crystal structures at high pressure: Combined application of theory and experiment to the intermetallic compound AuGa${}_2$

A combination of x-ray diffraction at high pressures and first-principles calculations reveals the sequence of crystal-structural phase transitions in AuGa${}_2$ from cubic ($Fm\overline{3}m$) to orthorhombic (Pnma) at 10 (±4) GPa and then to monoclinic ($P$2${}_1$/$n$) at 33 (±6) GPa. Neither theory nor experiment would have been adequate, on their own, in documenting this sequence of phases, but together they confirm a sequence differing from the $Fm\overline{3}m\to Pnma\to P{6}_3/mmc$ transitions predicted for CaF${}_2$ and Pnma → $P$112${}_1$/$a$ transition reported for PbCl${}_2$ and SnCl${}_2$. The combined results from theory and experiment also allow us to constrain the equations of state of the three phases of AuGa${}_2$. Calculations on the analog PbCl${}_2$ predict a transition to the $P$2${}_1$/$n$ phase seen in AuGa${}_2$ that could, therefore, be a common high-pressure phase for PbCl${}_2$-structured compounds.

Figure 1

Calculated enthalpies of all phases studied, relative to that of the cubic ($Fm\overline{3}m$) structure. The computed enthalpies suggest a transition from the cubic ($Fm\overline{3}m$) to orthorhombic (Pnma) phase at about 14 GPa and from the latter to the monoclinic ($P$2${}_1$/$n$) phase at about 32 GPa.

Figure 2

Comparison of observed and calculated diffraction patterns for the (a) cubic ($Fm\overline{3}m$) at 13 GPa, (b) orthorhombic (Pnma) at 16 GPa, and (c) monoclinic ($P$2${}_1$/$n$) phases at 36 GPa. The pattern for fully decompressed sample (top panel) reveals that AuGa${}_2$ transforms back to its ambient $Fm\overline{3}m$ phase. The Rietveld refinement of experimental data was performed using atomic coordinates from the theoretical calculations. The weak peaks indicated by * in (a) are due to orthorhombic phase.

Figure 3

Experimental unit-cell volumes determined for AuGa${}_2$ under static compression. The data show three separate regions: a low-pressure region (≤15 GPa) corresponding to the cubic ($Fm\overline{3}m$) phase, an intermediate-pressure region (8 GPa ≤ $P$ ≤ 35 GPa) corresponding to the orthorhombic (Pnma) phase, and a high-pressure region (>35 GPa) corresponding to the monoclinic ($P$2${}_1$/$n$) phase. The filled and open symbols represent compression and decompression, respectively. The dashed and solid lines are the P-V compression curves from theory with and without pressure correction, respectively.

Figure 4

Calculated enthalpies of all phases of PbCl${}_2$ studied, relative to that of the cubic ($Fm\overline{3}m$) structure. The calculations suggest a displacive transition from the ambient orthorhombic structure (Pnma) to the Co${}_2$Si-type structure (Pnma) at low pressure and then to the monoclinic ($P$2${}_1$/$n$) phase at about 1600 GPa. Metallization begins at about 100 GPa.