Role of rare earth sites and vacancies in the anomalous compression of modulated scheelite tungstates ${RE}_2$(${\mathrm{WO}}_4{)}_3$

X-ray powder diffraction experiments at high pressures combining conventional sources and synchrotron radiation, together with theoretical simulations have allowed us to study the anomalous compression of the entire α-${RE}_2$(${\mathrm{WO}}_4{)}_3$ ($\mathit{RE}$ = La-Ho) family with modulated scheelite structure (α phase). The investigated class of materials is of great interest due to their peculiar structural behavior with temperature and pressure, which is highly sought after for specialized high-tech applications. Experimental data were analyzed using full-profile refinements and were complemented with computational methods based on density functional theory (DFT) total energy calculations for a subset of the samples investigated. An unusual change in the compression curves of the lattice parameters $a, c$, and β was observed in both the experiments and theoretical simulations. In particular, in all the studied compounds the lattice parameter $a$ decreased with pressure to a minimum value and then increased upon further compression. Pressure evolution of the experimental x-ray diffraction (XRD) patterns and cell parameters is correlated with the ionic radius of the rare earth element: (1) the lighter La-Nd tungstates underwent two phase transitions, and both transition pressures decreased as the rare earth's ionic radius increased. The XRD patterns of the first high pressure phase could be indexed with propagation vectors parallel to the $a$ axis (tripling the unit cell). At higher pressures, the lattice parameters for the second phase (referred to as the preamorphous phase) showed little variation with pressure. (2) The heavier tungstates, from Sm to Dy, undergo a transition to the preamorphous phase without any intermediate phase. The reversibility of both phase transitions was investigated. DFT calculations support this unusual response of the crystal structures under pressure and shed light on the structural mechanism of negative linear compressibility (NLC) and the resulting softening. The pressure dependence of the structural modifications is related to tilting, along with small elongation and alignment, of the ${\mathrm{WO}}_4^{2-}$ tetrahedrons. These changes correlate with those in the alternating RE…RE…RE chains and blocks of cationic vacancies arranged along the $a$ axis. Possible stacking defects, which emerge between them, helped to explain this anomalous compression and the pressure induced amorphization. Such mechanisms were compared with other ferroelastic families of molybdates, niobates, vanadates, and other compounds with similar structural motifs classified as having “hinge frames.”

Figure 1

A $b$ axis view of the α-${\mathrm{Eu}}_2$(${\mathrm{WO}}_4{)}_3$ structure. Orange and green lines show the parent scheelite and the α-phase unit cell, respectively. Tungsten and europium atoms and their corresponding tetrahedra and polyhedra are colored in orange and green, respectively. Vacancies are colored in gray. Black dashed lines draw the unconventional c' parameter.

Figure 2

Volume dependence of the experimental lattice parameters of ${RE}_2$(${\mathrm{WO}}_4{)}_3$ compounds ($\mathit{RE}$ = La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Tb, and Ho) at room temperature (in black) and the theoretical ones for $\mathit{RE}$ = La (red), Nd (yellow), Gd (blue), and Dy (violet). Open symbols indicate the c′ and β′ parameters.

Figure 3

Left: Diffraction patterns of selected ${RE}_2$(${\mathrm{WO}}_4{)}_3$ compounds ($\mathit{RE}$ = La, Nd, Gd, and Dy) at different pressures measured in GPa, given as a label by the corresponding diffractogram. In the patterns refined at selected pressures (right), the experimental results (red lines) are shown together with the calculated patterns (black lines). The blue sticks indicate the positions of Bragg reflections for the α phase. Satellite peaks are marked with red sticks. Patterns with the label R correspond to released pressures.

Figure 4

Theoretical and experimental volume dependence of different $d_{hkl}$ interplanar distances for ${RE}_2$(${\mathrm{WO}}_4{)}_3$ cell ($\mathit{RE}$ = La, Nd, Gd, and Dy). In all cases the filled circles correspond to theoretical values whereas the empty circles are experimental results, and lines are just a guide for the eye.

Figure 5

Pressure dependence lattice parameters a, b, c, and β for ${\mathrm{La}}_2$(${\mathrm{WO}}_4{)}_3$ (red), ${\mathrm{Ce}}_2$(${\mathrm{WO}}_4{)}_3$ (orange), ${\mathrm{Pr}}_2$(${\mathrm{WO}}_4{)}_3$ (pale orange), ${\mathrm{Nd}}_2$(${\mathrm{WO}}_4{)}_3$ (yellow), ${\mathrm{Sm}}_2$(${\mathrm{WO}}_4{)}_3$ (olive), ${\mathrm{Eu}}_2$(${\mathrm{WO}}_4{)}_3$ (green), ${\mathrm{Gd}}_2$(${\mathrm{WO}}_4{)}_3$ (pale blue), ${\mathrm{Tb}}_2$(${\mathrm{WO}}_4{)}_3$ (blue), ${\mathrm{Dy}}_2$(${\mathrm{WO}}_4{)}_3$ (violet), and ${\mathrm{Ho}}_2$(${\mathrm{WO}}_4{)}_3$ (magenta).

Figure 6

P(V) curve for ${\mathrm{La}}_2$(${\mathrm{WO}}_4{)}_3$ (red), ${\mathrm{Ce}}_2$(${\mathrm{WO}}_4{)}_3$ (orange), ${\mathrm{Pr}}_2$(${\mathrm{WO}}_4{)}_3$ (pale orange), ${\mathrm{Nd}}_2$(${\mathrm{WO}}_4{)}_3$ (yellow), ${\mathrm{Sm}}_2$(${\mathrm{WO}}_4{)}_3$ (olive), ${\mathrm{Eu}}_2$(${\mathrm{WO}}_4{)}_3$ (green), ${\mathrm{Gd}}_2$(${\mathrm{WO}}_4{)}_3$ (pale blue), ${\mathrm{Tb}}_2$(${\mathrm{WO}}_4{)}_3$ (blue), ${\mathrm{Dy}}_2$(${\mathrm{WO}}_4{)}_3$ (violet), and ${\mathrm{Ho}}_2$(${\mathrm{WO}}_4{)}_3$ (magenta).

Figure 7

Phase diagram representing the phase transitions and other anomalies obtained by compressing the α-$R{E}_2{\left(\mathrm{WO}\right)}_{43}$ family. Open (experimental) and filled (theoretical) black circles indicate the pressures in which the $a$ parameter is minimum. Pressures of the expected transition to the reversible superlattice phase are shown by brown squares. The pressures of the expected transition to the preamorphous phase are shown by dark red triangles. Also, the range of the measured pressures are marked with a dashed blue line.

Figure 8

The theoretical structure of ${\mathrm{Dy}}_2$(${\mathrm{WO}}_4{)}_3$ from the DFT simulations, viewed along the $b$ axis (top) and through the plane (−1, 0, 2) (bottom) at the three selected pressures of 4.5 GPa (left), 8.9 GPa (center), and 16.8 GPa (right). The Dy atoms are purple and the W atoms are orange. The shortest Dy…Dy contacts are indicated as dashed purple lines. Polyhedral Dy…O contacts are drawn in order to follow the more important movements: (1) Rotation of less symmetric tetrahedra until reaching the minimum of the $a$ parameter and the $\mathit{RE}$…$\mathit{RE}$…$\mathit{RE}$ angle. (2) Elongation of the more symmetric tetrahedra improving their alignment along the $a$ axis and leading to the opening of the $\mathit{RE}$…$\mathit{RE}$…$\mathit{RE}$ angle.

Figure 9

Calculated pressure dependence of the $\mathit{RE}$..$\mathit{RE}$ contact length and the $\mathit{RE}$…$\mathit{RE}$…$\mathit{RE}$ angle for ${\mathrm{La}}_2$(${\mathrm{WO}}_4{)}_3$ (red) ${\mathrm{Nd}}_2$(${\mathrm{WO}}_4{)}_3$ (yellow), ${\mathrm{Gd}}_2$(${\mathrm{WO}}_4{)}_3$ (blue), and ${\mathrm{Dy}}_2$(${\mathrm{WO}}_4{)}_3$ (violet).

Figure 10

Different orderings of the rare earth atoms (in purple) and vacancies (shown within orange rectangles that show the ${\mathrm{WO}}_4^{2-}$ tetrahedra), which are observed in α-${RE}_2$(${\mathrm{MoO}}_4{)}_3$ (left); and simulated with the metric: (0.63)a* + (0.68)b* (middle) and with the metric: (0.5)a* + (0.8)b* (right).