Structural, magnetic, transport, and thermoelectric properties of the pseudobrookite ${\mathrm{AlTi}}_2{\mathrm{O}}_5\text{−}{\mathrm{Ti}}_3{\mathrm{O}}_5$ system

We investigated the structural, magnetic, transport, and high-temperature thermoelectric properties of single crystals of the pseudobrookite ${\mathrm{Al}}_{1-x}{\mathrm{Ti}}_{2+x}{\mathrm{O}}_5$ for $0\le x\le 1$ grown using a floating zone. We found a correlation of spin-singlet ${\mathrm{Ti}}^{3+}\text{−}{\mathrm{Ti}}^{3+}$ dimers coupled with the lattice even in the conductive $\alpha$ and $\lambda$ phases which develops with increasing $x$. This developing dimer correlation reduces the number of unpaired ${\mathrm{Ti}}^{3+}$ ions, which makes the compound more conductive owing to the suppression of disorder for $x$ up to about 0.75. The dimer fluctuation causes a critical enhancement of the magnetic susceptibility at around 150 K in the $\lambda$ phase near the boundary ($x\sim 0.9$) between the $\lambda$ and the $\beta$ phases. Such a correlation of the spin-singlet ${\mathrm{Ti}}^{3+}\text{−}{\mathrm{Ti}}^{3+}$ dimers may produce a high Seebeck coefficient in the conductive $\alpha$ and $\lambda$ phases leading to a large thermoelectric power factor at high temperatures.

Figure 1

Crystal structures at RT for (a) ${\mathrm{AlTi}}_2{\mathrm{O}}_5(x=0)$ ($\alpha$ phase), (b) ${\mathrm{Al}}_{0.25}{\mathrm{Ti}}_{2.75}{\mathrm{O}}_5(x=0.75)$ ($\lambda$ phase), and (c) ${\mathrm{Ti}}_3{\mathrm{O}}_5(x=1)$ ($\beta$ phase). In the left figure of (a), the octahedra with dark and light colors are at the $x$ coordinates 0 and 1/4, respectively. The right figure of (a) extracts the structure at the $x$-coordinate 0 to make it easy to see. Similarly, the octahedra with dark and light colors in the left figures of (b) and (c) are at the $y$-coordinates 0 and 1/4, respectively, and the right figures of (b) and (c) extract the structures at the $y$-coordinate 0. The difference in color intensity at the same $y$ coordinate of (c) shows the difference in valences of Ti ions in the center of a ${\mathrm{TiO}}_6$ octahedron, which was deduced from the bond-valence sum. The valences of Ti ions of dark-color octahedra (Ti1 and Ti3) are close to 3, and those of light-color octahedra (Ti2) are close to 4. The dotted lines in the right figures of (a)–(c) represent the short Ti-Ti bonds.

Figure 2

Powder x-ray diffraction profiles of ${\mathrm{Al}}_{1-x}{\mathrm{Ti}}_{2+x}{\mathrm{O}}_5$ for (a) $x=0({\mathrm{AlTi}}_2{\mathrm{O}}_5$), (b) $x=0.75$, (c) $x=0.85$, and (d) $x=1\left({\mathrm{Ti}}_3{\mathrm{O}}_5\right)$. Filled circles and solid lines show the observed profiles and profiles calculated via Rietveld analysis, respectively, whereas the bars and the line under the observed and calculated profiles show the expected Bragg peak positions and the difference between the observed and the calculated data, respectively. The obtained crystal parameters are summarized in Fig. 3 and Tables S.I– S.VI of the Supplemental Material [17].

Figure 3

Crystal parameters at RT obtained via Rietveld analysis. (a)–(c) show $x$ dependences of lattice constants of ${\mathrm{Al}}_{1-x}{\mathrm{Ti}}_{2+x}{\mathrm{O}}_5$ along the (a) $a$ axis in the $\alpha$ phase ($0\le x\le 0.5$) and $b$ axis in the $\lambda$ and $\beta$ phases ($0.5<x\le 1$), (b) $b$ axis in the $\alpha$ phase and $a$ axis in the $\lambda$ and $\beta$ phases, and (c) $c$ axis. (d)–(f) show the (d) angle between the $a$ axis and the $c$ axis ($\beta$ angle), (e) unit-cell volume $V$, and (f) volume fractions of $\lambda$ and $\beta$ phases near the phase boundary ($x\sim 0.9$). The solid and thick solid lines are guides for the eyes. The vertical dashed line at $x=0.5$ shows the boundary between the $\alpha$ and the $\lambda$ phases at RT, whereas the vertical dotted line at $x=0.9$ shows the boundary between the $\lambda$ and the $\beta$ phases at RT.

Figure 4

Phase diagram of ${\mathrm{Al}}_{1-x}{\mathrm{Ti}}_{2+x}{\mathrm{O}}_5$ determined by the measurements of powder XRD, $M$, and $S$. The filled circles show the kink temperatures in the $T$ dependences of $S$, and the filled triangles and filled squares show the transition temperatures deduced from the measurements of $M$ on heating and on cooling, respectively. The filled diamond at $x=1$ (${\mathrm{Ti}}_3{\mathrm{O}}_5$) shows the temperature of the structural transition between the high-$T\alpha$ phase and the middle $\lambda$ phase determined by the kink in the $\chi \text{−}T$ curve (not shown). The open diamonds, circles, triangles, and squares show the measurement temperatures of the powder XRD, revealing the $\alpha$ phase, $\lambda$ phase, $\lambda \text{−}\beta$ coexistent phase, and $\beta$ phase, respectively.

Figure 5

$\chi \text{−}T$ curves of ${\mathrm{Al}}_{1-x}{\mathrm{Ti}}_{2+x}{\mathrm{O}}_5$ for $0\le x\le 1$ at $H=0.5\mathrm{T}$. The inset shows the magnifications of $\chi \text{−}T$ curves for $x=0$, 0.75, 0.88, 0.99, and 1. (b) $\chi \text{−}T$ and ${\chi }^{-1}\text{−}T$ curves for $x=0$ and 0.5 with the results of fitting to the Curie-Weiss relation $\chi =M/H=C/(T-{\theta }_{\mathrm{CW}})+{\chi }_0$, where ${\theta }_{\mathrm{CW}}$ is the Curie-Weiss temperature and ${\chi }_0$ is a constant. The solid lines show the fitting results for both compounds and the deduced ${\theta }_{\mathrm{CW}}$ and ${\chi }_0$ are summarized in Table 1.

Figure 6

$M\text{−}H$ curves of ${\mathrm{Al}}_{1-x}{\mathrm{Ti}}_{2+x}{\mathrm{O}}_5$ for $x=0$, 0.25, 0.5, 0.75, 0.88, 0.9, and 1 at 5 K. The solid lines are the calculated curves. The inset shows the magnification of the result for $x=1\left({\mathrm{Ti}}_3{\mathrm{O}}_5\right)$. The solid line in the inset is also the calculated curve. By manually varying $n({\mathrm{Ti}}^{3+}$) in these analyses, we adjust the calculated line to the observed data (open circles).

Figure 7

Number of ${\mathrm{Ti}}^{3+}$ ions per Ti atom $\left[n\left({\mathrm{Ti}}^{3+}\right)\right]$ deduced from the $\chi \text{−}T$ and $M\text{−}H$ curves against this number calculated from the formal valence of Ti ions $[n_0\left({\mathrm{Ti}}^{3+}\right)=(1+x)/(2+x)]$. Filled squares are the ratios deduced from the Curie-Weiss constant determined by fitting the $\chi \text{−}T$ curves, and filled circles and filled triangles are those deduced from the $M\text{−}H$ curves without and with the $H$-linear contributions to $M$, respectively.

Figure 8

$\rho \text{−}T$ curves of ${\mathrm{AlTi}}_2{\mathrm{O}}_5(x=0)$ at ambient pressure (0 GPa) below 1050 K and at 20 GPa below RT. The inset shows the local activation energy ($E_{\mathrm{a}}=d\ln \rho /d{T}^{-1}$) deduced from the $\rho \text{−}T$ curves. The closed circles show $E_{\mathrm{a}}$ for $x=0$ without and with applying pressures, and the line shows that for $x=0.75$.

Figure 9

$\rho \text{−}T$ curves of ${\mathrm{Al}}_{1-x}{\mathrm{Ti}}_{2+x}{\mathrm{O}}_5$ for $0\le x\le 1$. The inset shows the $x$ dependence of $E_{\mathrm{a}}$ at 1000 K.

Figure 10

$x$ dependences of $\rho$ of ${\mathrm{Al}}_{1-x}{\mathrm{Ti}}_{2+x}{\mathrm{O}}_5$ at 290 and 1000 K. The closed circles and closed diamonds show ρ at 290 and 1000 K, respectively. The closed triangles show ρ of ${\mathrm{AlTi}}_2{\mathrm{O}}_5$ at 290 K at 12, 15, and 20 GPa. The solid lines are guides for the eyes. The vertical dashed line at $x=0.5$ shows the boundary between the $\alpha$ and the $\lambda$ phases at RT, whereas the vertical dotted line at $x=0.9$ shows the boundary between the $\lambda$ and the $\beta$ phases at RT.

Figure 11

$T$ dependences of (a) $S$ and (b) PF of ${\mathrm{Al}}_{1-x}{\mathrm{Ti}}_{2+x}{\mathrm{O}}_5$ for $0\le x\le 1$. The arrows show the kink temperatures indicating the structural phase transitions between the $\alpha$ and the $\lambda$ phases. The open circles in (a) show the result for another ${\mathrm{AlTi}}_2{\mathrm{O}}_5$ crystal.

Figure 12

$x$ dependences of $S,S_0$, and PF at 1000 K for ${\mathrm{Al}}_{1-x}{\mathrm{Ti}}_{2+x}{\mathrm{O}}_5$.