Crystal structure of ${\mathrm{LaTiO}}_{3.41}$ under pressure

The crystal structure of the layered, perovskite-related ${\mathrm{LaTiO}}_{3.41}$ $\left({\mathrm{La}}_5{\mathrm{Ti}}_5{\mathrm{O}}_{17+\delta }\right)$ has been studied by synchrotron powder x-ray diffraction under hydrostatic pressure up to $27\mathrm{GPa}$ $(T=295\mathrm{K})$. The ambient-pressure phase was found to remain stable up to $18\mathrm{GPa}$. A sluggish, but reversible phase transition occurs in the range $18–24\mathrm{GPa}$. The structural changes of the low-pressure phase are characterized by a pronounced anisotropy in the axis compressibilities, which are at a ratio of approximately $1:2:3$ for the $a$, $b$, and $c$ axes. The possible effects of pressure on the electronic properties of ${\mathrm{LaTiO}}_{3.41}$ are discussed.

Figure 1

The monoclinic crystal structure (Ref. 1) of ${\mathrm{LaTiO}}_{3.41}$ at ambient conditions (space group $P{2}_1∕c$, $Z=4$) can be represented by slabs of corner-sharing ${\mathrm{TiO}}_6$ octahedra. Within the slabs of thickness $d_1$, the octahedra are connected and tilted cooperatively in the same fashion as in the more familiar ${\mathrm{GeFeO}}_3$-type distorted perovskites such as ${\mathrm{LaTiO}}_3$. La ions are located in the voids between the octahedra.

Figure 2

(a) Diffraction diagrams of ${\mathrm{LaTiO}}_{3.41}$ at high pressures $(\lambda =0.4176\mathrm{\AA })$. The diffractogram of the high-pressure phase at $24\mathrm{GPa}$ shows a line at $1.65°$ (inset), corresponding to the $\left(002\right)$ reflection of the ambient-pressure phase. (b) X-ray powder diffraction diagram $\left(I_{\mathrm{obs}}\right)$ of ${\mathrm{LaTiO}}_{3.41}$ at $10.0\mathrm{GPa}$ and difference curve $(I_{\mathrm{obs}}-I_{\mathrm{calc}})$ for a partial Rietveld refinement ($\mathrm{La}$ and $\mathrm{Ti}$ positions only). Markers show the calculated peak positions.

Figure 3

Structural parameters of ${\mathrm{LaTiO}}_{3.41}$ as a function of pressure. (a) Lattice parameters $a,b,c$, as well as estimates of the slab thickness $d_1$ and interlayer separation $d_2$, normalized to their respective zero-pressure values. The zero-pressure values of $d_1$ and $d_2$ amount to $d_{10}\approx 11.14\mathrm{\AA }$ and $d_{20}\approx 4.50\mathrm{\AA }$, respectively. See text for details. (b) The experimental pressure-volume data can be represented by a Murnaghan equation of state (solid line). The inset shows the variation of the monoclinic angle with pressure. Solid symbols represent angles determined from the lattice parameters $a$ and $c$; open symbols refer to the results of the refinements.

Figure 4

Evolution of the $\mathrm{Ti}\left(5\right)$ and $\mathrm{Ti}\left(6\right)$ $z$ coordinates as a function of pressure. Open squares and diamonds represent the $\mathrm{Ti}\left(5\right)$ and $\mathrm{Ti}\left(6\right)$ data, respectively, as determined in the Rietveld refinements. These data scatter in a correlated fashion. The circles show the averaged $z$ coordinates of $\mathrm{Ti}\left(5\right)$ and $\mathrm{Ti}\left(6\right)$. The solid line represents a linear fit to the data $\left[z\right(P)\approx 0.1781+0.00029P∕\mathrm{GPa}]$, with the outlier at $14\mathrm{GPa}$ (open circle) not being taken into account. The error bars mark three times the uncertainties reported by the refinement program GSAS.

Figure 5

Evolution of the $\mathrm{La}\left(4\right)$ and $\mathrm{La}\left(5\right)$ atomic coordinates $y$ and $z$ as a function of pressure. Closed (open) symbols refer to refinement results, where preferred orientation effects were (were not) taken into account. The error bars mark three times the uncertainties of the $\mathrm{La}$-$y$ coordinates reported by the refinement program GSAS. For clarity, they are shown only for one data set. In the case of the $\mathrm{La}$-$z$ coordinates, the uncertainties are similar to the symbol size. Lines are guides to the eye.

Figure 6

Octahedral tilt angles $\phi$ vs pressure derived from the lattice parameters $a$ and $b$ and the slab thickness $d_1$, according to Eqs. (1, 2).