Thermoelectric and structural correlations in $\left(\mathrm{S}{\mathrm{r}}_{1-x-y}\mathrm{C}{\mathrm{a}}_x\mathrm{N}{\mathrm{d}}_y\right)\mathrm{Ti}{\mathrm{O}}_3$ perovskites

Structural and thermoelectric properties are reported for a specially designed class of $A$-site substituted perovskite titanates, $\left(\mathrm{S}{\mathrm{r}}_{1-x-y}\mathrm{C}{\mathrm{a}}_x\mathrm{N}{\mathrm{d}}_y\right)\mathrm{Ti}{\mathrm{O}}_3$. Two series synthesized with various $A$-site Sr-rich or Ca-rich (Sr-poor) concentrations were investigated using high-resolution neutron powder diffraction as a function of temperature and Nd doping. Each series was designed to have a nominally constant tolerance factor at room temperature. We determine the room temperature structures as tetragonal $I4/mcm$ and orthorhombic $Pbnm$ for the Sr-rich and Ca-rich series, respectively. Three low-temperature orthorhombic structures, $Pbnm, Ibmm$, and $Pbcm$ were also observed for the Sr-rich series, whereas the symmetry of the Ca-rich series remains unchanged throughout the full measured temperature range. Thermoelectric properties of $\left(\mathrm{S}{\mathrm{r}}_{1-x-y}\mathrm{C}{\mathrm{a}}_x\mathrm{N}{\mathrm{d}}_y\right)\mathrm{Ti}{\mathrm{O}}_3$ were investigated and correlated with the structural variables. We succeeded in achieving a relatively high figure of merit $ZT=0.07$ at $\sim 400\mathrm{K}$ in the Sr-rich $\mathrm{S}{\mathrm{r}}_{0.76}\mathrm{C}{\mathrm{a}}_{0.16}\mathrm{N}{\mathrm{d}}_{0.08}\mathrm{Ti}{\mathrm{O}}_3$ composition which is comparable to that of the best $n$-type TE $\mathrm{SrT}{\mathrm{i}}_{0.80}\mathrm{N}{\mathrm{b}}_{0.20}{\mathrm{O}}_3$ oxide material reported to date. For a fixed tolerance factor, the Nd doping enhances the carrier density and effective mass at the expense of the Seebeck coefficient. Thermal conductivity greatly reduces upon Nd doping in the Ca-rich series. With an enhanced Seebeck coefficient at elevated temperatures and reduced thermal conductivity, we predict that $\mathrm{S}{\mathrm{r}}_{0.76}\mathrm{C}{\mathrm{a}}_{0.16}\mathrm{N}{\mathrm{d}}_{0.08}\mathrm{Ti}{\mathrm{O}}_3$ and similar compositions have the potential to become some of the best materials in their class of thermoelectric oxides.

Figure 1

Room-temperature diffraction data for SCT50 in a narrow $d$ spacing range. Superlattice reflections marked by arrows indicate the orthorhombic $Pbnm \left(a^{-}{a}^{-}{c}^{+}\right)$ symmetry. Tick marks represent symmetry allowed reflections. The [612 162] reflections of the (odd odd even) OOE type (labeling of reflections is with respect to the parent cubic subcell) are due to in-phase tilting, whereas the [533 353 515 155] index set as EEO are due to $A$-cation displacements in both the $x$ and $y$ directions. Marked peaks have no corresponding reflections in the $I4/mcm$ tilt system. Strong peaks of the EEE type correspond to the elementary unit cell. Peaks of the OOO type are associated with antiphase tilting.

Figure 2

Extracts from room-temperature neutron-diffraction patterns for $\mathrm{S}{\mathrm{r}}_{0.73}\mathrm{C}{\mathrm{a}}_{0.27}\mathrm{Ti}{\mathrm{O}}_3$. Superlattice reflections of the OOO type with respect to the parent cubic subcell are indicated by arrows in (a) and (b). The tetragonal structure is demonstrated by the splitting of the primitive cubic ${\left(200\right)}_p$ peak into a [220/004] doublet ($I4/mcm$ symmetry).

Figure 3

Neutron-diffraction patterns showing superlattice reflections for $\mathrm{S}{\mathrm{r}}_{0.73}\mathrm{C}{\mathrm{a}}_{0.26}\mathrm{N}{\mathrm{d}}_{0.01}\mathrm{Ti}{\mathrm{O}}_3$ at select temperatures. Weak peaks arise due to distortions from the 300-K tetragonal structures. Strong peaks appear truncated in the figure to emphasize the weak reflections.

Figure 4

Temperature evolution of the tetragonal reflections ${(440/008)}_{I4/mcm}$ in SCT27 showing evidence of a mixed phase region between 150 and 200 K.

Figure 5

Plots of reduced $c(c_p=c/2)$ and $b_p(=b/\surd 2)$ lattice constants and the bond lenghts [$A$-O] and [Ti-O] as a function of temperature.

Figure 6

Unit-cell volume behavior as a function of temperature for all of our Sr-rich and Ca-rich samples together with those of the parent $\mathrm{CaTi}{\mathrm{O}}_3$ and $\mathrm{SrTi}{\mathrm{O}}_3$ materials as extracted from multiple literature references. The inset shows the zoomed in data for both series.

Figure 7

Top: $T$ variations of the average $\langle \text{Ti-O-Ti}\rangle$ bond angle for Sr-rich materials. The abrupt drops correlate with first-order phase transitions to lower symmetries. The bond angles level off at low temperatures while at higher temperature they tend to converge to a common value for all the samples in this series. The inset shows the $\langle \text{Ti-O-Ti}\rangle$ bond angle behavior at room temperature as a function of Nd substitutions which is nearly constant for each series in agreement with the designed t-constant requirement. Bottom: temperature-dependent $\langle \text{Ti-O-Ti}\rangle$ bond angle in the Ca-rich series. The $\mathrm{Ti}{\mathrm{O}}_6$ octahedral distortion is gradually suppressed as a function of increasing temperature. The inset shows the linear relationship between tolerance factor ($t$) and the squared cosine of the bond angle.

Figure 8

Tolerance factor vs temperature for the full $\mathrm{S}{\mathrm{r}}_{(1-x-y)}\mathrm{C}{\mathrm{a}}_{\left(x\right)}\mathrm{N}{\mathrm{d}}_{\left(y\right)}\mathrm{Ti}{\mathrm{O}}_3$ system. Literature data are used for the parent $\mathrm{SrTi}{\mathrm{O}}_3$ [61] and $\mathrm{CaTi}{\mathrm{O}}_3$ [13, 28] materials. For $\mathrm{SrTi}{\mathrm{O}}_3$, low-temperature data [61] in the 1.5- to 50-K range were extrapolated to $t=1$ using the same power law employed with the other materials from which we obtained a transition temperature, $T_S$, to the cubic symmetry at $\sim 110\mathrm{K}$ in excellent agreement with the literature [68]. Solid lines correspond to the fitting of the NPD data (10–300 K) to elevated temperatures. Open symbols shown on the critical cubic and tetragonal transition lines are data obtained experimentally from the APS 11BMB x-ray beamline for comparison. See Table 4 for a full summary of the transition temperatures. Inset shows the thermal variation of tolerance factor for the Sr-rich series where various low-$T$ crystal structures were observed.

Figure 9

Representative x-ray contour maps collected at the APS showing the structural transition temperatures for the Ca-rich samples with Nd content $y$ of 0 and $3\%$. The bottom panel displays the orthorhombic to tetragonal and tetragonal to cubic phase-transition temperatures for the same samples extracted by fitting the tolerance factor curves as a function of temperature $\mathit{t}\left(T\right)$ to a power law of the form $\mathit{t}\left(T\right)=t_0\left(T=0\mathrm{K}\right)+A{T}^n$ with $n=2$.

Figure 10

Left panel: Sr-rich thermoelectric measurements in the temperature range $13-400\mathrm{K}$. Right panel: Similar measurements for the Ca-rich compositions.

Figure 11

(a),(d) Variation of the TE power factor $\left(S^2\sigma \right)$ with the tolerance factor. Strong correlation is observed between the two parameters for all the samples. Panels (b) and (d) show the effect of Nd substitution (increases the electron concentration of the system) on the Seebeck coefficient $S$ and the carrier effective mass $m^{*}$. The measured negative $S$ values indicate the nature of doping. The value of $y$ where the two curves intersect represents the optimal Nd content $y_o\sim 0.06$ in the Sr-rich series which is quite close to the Sr-rich Nd $8\%$ concentration observed to exhibit the best $ZT$ value among all the compositions investigated in this work.