High-pressure behavior of structural, optical, and electronic transport properties of the golden Th${}_2$S${}_3$-type Ti${}_2$O${}_3$

Recently, a golden colored, dense polymorph of titanium sesquioxide, Ti${}_2$O${}_3$ with a Th${}_2$S${}_3$-type structure, has been synthesized at high-pressure high-temperature conditions. In this paper, we present results of investigations of structural, optical, and electronic transport properties of this unusual golden polymorph of Ti${}_2$O${}_3$ under high pressure. Several experimental techniques were used, including x-ray diffraction studies using synchrotron radiation, Raman spectroscopy, electrical resistivity, and thermoelectric power. The structural studies showed that the Th${}_2$S${}_3$-type lattice is conserved under pressure, while it is subjected to an isostructural phase transition with a ∼0.7$\%$ volume drop at 38.5 GPa. We speculated that this transition could be driven by the $s\to d$ electron transfer in the Ti atoms. For the Th${}_2$S${}_3$-type Ti${}_2$O${}_3$, we have established a bulk modulus value, $B_0$ $=$ 258.3 GPa at $B_0^{\prime }$ $=$ 4.1. A full profile analysis of the diffraction patterns allowed us to discover anomalies in the compression behavior of the Th${}_2$S${}_3$-type structure. The bond valence sums method suggested that at ambient conditions the Ti cations have predominantly Ti${}^{3+}$ oxidation state, but applied pressure stimulates a partial charge disproportionation between the Ti1 and Ti2 sites achieving the maximal effect—reduction of the Ti1 cations to ∼Ti${}^{2.5+}$ and oxidation of the Ti2 ones to ∼Ti${}^{3.5+}$ near 14 GPa. Pressure evolution of Raman spectra across the above crossovers showed distinct changes corroborating the above findings. The high-pressure electronic transport studies confirmed that the Th${}_2$S${}_3$-type Ti${}_2$O${}_3$ remains semiconducting up to 21 GPa at ambient and low temperatures down to 4.2 K. These studies found additional features, e.g., in the activation energy curve near 7 GPa, that is accompanied by inversion of the dominant conductivity type from electron to hole. The intriguing high-pressure behavior of Ti${}_2$O${}_3$ with the Th${}_2$S${}_3$-type structure can contribute to better understanding of high-pressure properties of transition-metal sesquioxides.

Figure 1

X-ray diffraction patterns of the golden Th${}_2$S${}_3$-type Ti${}_2$O${}_3$ at ambient temperature under high pressure. (a) Pressure evolution of the XRD patterns with subtracted background. Pressure values are given near the curves. (b) Examples of Rietveld refinement of the XRD patterns collected at 2.6 and 56.4 GPa in the Th${}_2$S${}_3$-type lattice (Pnma space group). Points are experimental data, solid lines are calculated profiles, dashes denote expected reflex positions for the Th${}_2$S${}_3$-type lattice, and the lowermost curves are the difference between the experimental and the calculated profiles. The asterisks (*) mark the residual broad peak from the diamond anvils and the cross (+) in the XRD pattern (a) marks some artifact peak. Insets show the corresponding 2D diffraction images. The diffractions’ rings are reflections from the sample, and huge spots are from the diamond anvils.

Figure 2

Pressure dependencies of the unit cell parameters of the golden Th${}_2$S${}_3$-type Ti${}_2$O${}_3$ at ambient temperature. Large yellow arrows indicate the features. (a) Pressure dependencies of the lattice parameters. Inset shows relative changes of the lattice parameters with pressure. (b) Pressure dependencies of the lattice parameter ratios, $c$/$a$ (main plot), $a$/$b$ and $c$/$b$ (inset). (c) Pressure dependence of the unit cell volume per formula unit ($V_0$/$Z$). Points are the experimental data; solid and dashed lines are fittings and theoretical prediction. The error bars are smaller than the symbols. Photograph of the golden polymorph of Ti${}_2$O${}_3$ and its crystal structure in the form of a 2×2×2 supercell are shown as lower and upper insets, respectively.

Figure 3

Pressure dependencies of the bond lengths, polyhedra volumes and distortion indexes, and bond valence sums of the Ti ions in the Th${}_2$S${}_3$-type Ti${}_2$O${}_3$ at ambient temperature. (a) Relative changes in the bond lengths with pressure. Labels 1$\times$ and 2$\times$ denote the multiplicity of the bond lengths. Some of the curves correspond not to the individual bond lengths but to their combinations if these bonds demonstrate rather similar behavior under pressure [e.g., Ti1-O2 (1$\times$ and 2$\times$) is a combination of three Ti1-O2 bonds, two of which are identical (Table )]. The pressure behavior of all the bonds demonstrates a number of features. (b) Pressure dependencies of the average bond lengths, $\langle \mathrm{Ti}1-\mathrm{O}\rangle$ and $\langle \mathrm{Ti}2-\mathrm{O}\rangle$. Inset shows the coordination spheres of the Ti1 and Ti2 ions in the Th${}_2$S${}_3$-type structure. (c) Shrinkage in the coordination polyhedra volumes of the Ti1 and T2 ions with pressure. (d) Distortion indexes of the coordination polyhedra of the Ti1 and Ti2 ions calculated using Eq. (2). Inset shows a network of the Ti2 coordination polyhedra. (e) Pressure dependencies of the bond valence sums of the Ti1 and Ti2 ions calculated using Eq. (3). Thick lines in (a) and dashed lines in (b)–(e) are guides for the eye.

Figure 4

Pressure evolution of Raman spectra of the golden Th${}_2$S${}_3$-type Ti${}_2$O${}_3$ at ambient temperature. Pressure values are given near the curves. Moderate changes in these Raman spectra are highlighted by dotted rectangles. (a) Raman spectra collected on pressurization run across the smooth crossover near 15 GPa and the isostructural transition near 38.5 GPa found in the XRD studies (Figs. 2 and 3). The phonon peaks in the spectrum gathered at ambient conditions are labeled by letters $A$, $B$, …$U$. The asterisk marks an unclear peak. (b) Raman spectra collected on decompression run across the isostructural phase transition near 38.5 GPa (Fig. 2).

Figure 5

Pressure dependencies of phonon frequencies of the golden Th${}_2$S${}_3$-type Ti${}_2$O${}_3$ at ambient temperature (summary of three sets of experiments, shown by different symbols). The phonon labels $A$, $B$, …$U$ correspond to those in Fig. 4a. (a) General view. (b) In range of wave numbers between 200 and 440 cm${}^{-1}$. The crossover near 38 GPa is shown by the vertical gray line.

Figure 6

Pressure dependencies of electrical resistance of bulk sample $A$ of the golden Th${}_2$S${}_3$-type Ti${}_2$O${}_3$ at ambient temperature. These curves were obtained in high-pressure cells with conventional flat anvils. Labels #1 and #2 mark two different samples cut from the same bulk sample $A$. Arrows show directions of pressure variation. Left inset shows temperature dependencies of electrical resistivity for samples $A$ and $B$ at ambient pressure. Right inset presents evidence of activation character of electrical resistivity near room temperature and down to ∼150 K and reports the activation energies values, $E_a$.

Figure 7

Pressure dependencies of thermoelectric power (Seebeck effect) of samples $A$ (a) and $B$ (b) of the golden Th${}_2$S${}_3$-type Ti${}_2$O${}_3$ at ambient temperature. Labels #1 and #2 mark two different samples cut from the same bulk samples $A$ and $B$. Arrows show directions of pressure variation. (a) These thermopower curves were measured in a high-pressure cell with both semispherically concave (#1) and conventional flat anvils (#2; Ref. 52). Sign inversion of the thermopower from negative to positive above 6–8 GPa unambiguously suggests the dominant conductivity-type inversion from $n$ to $p$ type. Inset shows examples of thermopower determination from linear slopes of dependencies of thermoelectric voltage on temperature difference, Δ$T$ along the sample thickness. (b) These thermopower curves were measured in a high-pressure cell with conventional flat anvils. Sample $B$ has been established earlier to have regions of dominant $n$- and $p$-type conductivity (Ref. 1). Thus, plot (b) presents pressure dependencies of thermopower of $n$- and $p$-type samples (#1 and #2, respectively). Sample #1 with original $n$-type conductivity behaves similarly to both samples $A$ (a).

Figure 8

Parametric electrical resistivity vs thermopower dependencies for samples #1 and #2 cut from the same bulk sample $B$ of the golden Th${}_2$S${}_3$-type Ti${}_2$O${}_3$. These curves were calculated for the second/third pressurization cycles for sample #2 and for the fourth/fifth pressurization cycles for sample #1. The ${\sigma }_n$/${\sigma }_p$ ratio (parameter $b$) may be found from the linear slopes [see Eq. (4) and the following discussion].

Figure 9

Temperature dependencies of electrical resistance of the golden Th${}_2$S${}_3$-type Ti${}_2$O${}_3$ for different applied pressures up to 21 GPa. The pressure values are shown at the plots. These temperature dependencies are shown in three representations: (a) in conventional coordinates and (b) in logarithmic electrical resistance vs $1/T$ (left and top axes) and vs $1/T^{0.25}$ (right and bottom axes).

Figure 10

Pressure dependencies of the activation energy $T_0$ (left axis) of hopping conductance and $T_{\mathrm{kink}}$ (a) and of electrical resistance at 280 K (b) of the golden Th${}_2$S${}_3$-type Ti${}_2$O${}_3$. Dashed lines represent linear fits of the data in different regions. Inset in (a) shows pressure dependence of the band gap, $E_g$, estimated from the activation energies. Ambient value of $E_g$ for sample $B$ was taken from Fig. 6. The vertical lines at about 7 and 17 GPa separate different pressure regions on the curves.

Figure 11

Temperature dependencies of the derivative of the electrical resistance (i.e., $\omega =d\ln \rho /d\ln T$) curves from Fig. 9a of the golden Th${}_2$S${}_3$-type Ti${}_2$O${}_3$ for different applied pressures up to 21 GPa.