Background

Mixed aluminates-titanates with perovskite structure formed in the RAlO3–ATiO3 pseudo-binary systems (R = rare earths, A = Sr, Ca) are prospective functional materials. In conjunction with alkaline-earth titanates, rare earth aluminates reveal excellent temperature-stable high-Q microwave dielectric properties and are widely used as radio-frequency ceramics in modern electronic devices ([1–6] and references herein). The highest Q-values among RAlO3- and ATiO3-based microwave ceramics were reported for LaAlO3–SrTiO3 system, which exhibits solid solubility across the entire compositional range. It was shown that dielectric properties of mixed aluminates-titanates ceramics do not significantly depend on the nature of the rare earth and the value of resonant frequency (t f) can be tuned by changing the concentration of solid solution. Thus potentially useful ceramics with temperature-stable relative permittivity can be obtained in other RAlO3–ATiO3 perovskite series.

The interest to the RAlO3–SrTiO3 systems has been increased considerably during the last decade after discovering of the intrigue phenomena of two-dimensional electron gas at the interface between two insulators LaAlO3 and SrTiO3 [7]. The interface effects occurred in the RAlO3–SrTiO3 perovskite systems are in the focus of active research in the field of tunable metal-insulator transition, 2D superconductivity, coexistence of superconductivity and ferromagnetism, etc. [8–11].

The aim of the present work is the study of the phase and structural behaviour of the mixed aluminates-titanates formed in the NdAlO3–SrTiO3 pseudo-binary system. At room temperature, the end members of the system—NdAlO3 and SrTiO3—adopt different variants of the perovskite structure: rhombohedral R \( \overline{3} \) c and cubic Pm \( \overline{3} \) m, respectively. Rhombohedral NdAlO3 transforms into the cubic perovskite structure near 2100 K ([6] and references herein), whereas strontium titanate SrTiO3 undergoes a low-temperature (LT) phase transition from the cubic to tetragonal I4/mcm perovskite structure below 105 K [12, 13]. Owing to the abovementioned peculiarities of NdAlO3 and SrTiO3 crystal structures, complex phase and structural behaviour is expected in the mixed neodymium-strontium aluminate-titanate system.

Methods

Mixed aluminates-titanates of nominal compositions Nd1−x Sr x Al1−x Ti x O3 (x = 0.3, 0.5, 0.7, 0.8, 0.9) were prepared by solid-state reaction technique. Stoichiometric amounts of the constituent oxides Nd2O3, Al2O3, TiO2 and strontium carbonate SrCO3 were ball-milled in ethanol for 5 h, dried, pressed into pellets and annealed in air at 1673 K for 9 h. After cooling the product, it was regrinded and repeatedly annealed at 1773 K for 9 h. X-ray powder diffraction technique (Huber imaging plate Guinier camera G670, Cu Kα1 radiation, λ = 1.54056 Å) was used for the phase and structural characterization of the samples at room temperature. All crystallographic calculations including full-profile Rietveld refinement were performed by using WinCSD program package [14].

Results and Discussion

Analysis of X-ray diffraction (XRD) data collected at room temperature (RT) showed that all samples synthesized adopt pure perovskite structure. No traces of foreign phases were detected (Fig. 1). Close examination of diffraction maxima revealed detectable rhombohedral deformation of the Nd1−x Sr x Al1−x Ti x O3 samples with x = 0.3 and 0.5, whereas no visible reflections splitting or deformation was observed for the specimens with higher x values (Fig. 1, inset). However, a presence of minor superstructure (113) reflection, which is indicative for rhombohedral distortion of perovskite structure, testifies that the rhombohedral structure in Nd1−x Sr x Al1−x Ti x O3 series persists at least up to x = 0.8.

Fig. 1
figure 1

Experimental XRD patterns of the Nd1-xSrxAl1-xTixO3 series. Stars indicate a superstructure (113) reflection. Inset shows enlarger part of patterns

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Full-profile Rietveld refinement of Nd1-x Sr x Al1-x Ti x O3 structures, performed in space groups R \( \overline{3} \) c and Pm \( \overline{3} \) m for the samples with x ≤ 0.8 and x = 0.9, respectively, entirely confirms suggested crystal structures of the specimens. Examples of graphical results of Rietveld refinement, showing excellent fits between experimental and calculated profiles of rhombohedral Nd0.5Sr0.5Al0.5Ti0.5O3 and cubic Nd0.1Sr0.9Al0.1Ti0.9O3 structures are presented on Fig. 2. Refined structural parameters of all synthesized Nd1-x Sr x Al1-x Ti x O3 samples and corresponding residuals are presented in Table 1.

Fig. 2
figure 2

Graphical results of Rietveld refinement of Nd0.1Sr0.9Al0.1Ti0.9O3 and Nd0.5Sr0.5Al0.5Ti0.5O3 structures. The experimental X-ray powder diffraction patterns (dots) are shown in comparison with the calculated patterns (blue lines). The difference curves between measured and calculated profiles are shown below the diagrams. Inset shows the view of the cubic and rhombohedral structures as corner-shared Al/TiO6 octahedra with Nd/Sr species located between them

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Table 1 Unit cell parameters, coordinates and isotropic displacement parameters of atoms in Nd1−x Sr x Al1−x Ti x O3 structures at RT
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Concentration dependencies of the obtained lattice parameters and unit cell volumes of Nd1-x Sr x Al1-x Ti x O3 series in comparison with the literature data for NdAlO3 [6] and SrTiO3 [12] (Fig. 3) prove a formation of two kinds of solid solutions in the NdAlO3–SrTiO3 pseudo-binary system. Simultaneous aliovalent substitution of Sr2+ and Ti4+ species for Nd3+ and Al3+ sites reduces rhombohedral deformation in Nd1-x Sr x Al1-x Ti x O3 series and led to morphotropic phase transition to the cubic perovskite structure at x = 0.84 (Fig. 3). In the related systems LaAlO3–SrTiO3 and PrAlO3–SrTiO3, the phase boundary between two perovskite structures takes place above x = 0.8 and at x = 0.88, respectively [15, 16].

Fig. 3
figure 3

Unit cell dimensions of Nd1-xSrxAl1-xTixO3 series. The rhombohedral lattice parameters are normalized to the perovskite cell as follow: a p   = a r /√2,c p   = c r /√12,V p   = V r /6. The dotted line marks the phase boundary between the Rh and the C phases

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A decreasing structural deformation in Nd1−x Sr x Al1−x Ti x O3 series as a consequence of increasing Goldschmidt tolerance factor with increasing x should significantly effect on the temperature of structural phase transition R \( \overline{3} \) c − Pm \( \overline{3} \) m, which occurs in NdAlO3 at about 2100 K [6]. According to structural phase diagram of the related LaAlO3–SrTiO3 system [15], the temperature of rhombohedra-to-cubic transition decreases almost linearly from 850 K in “pure” LaAlO3 to 350 K in the sample with nominal composition La0.2Sr0.8Al0.2Ti0.8O3. Our recent in situ X-ray synchrotron powder diffraction investigations of the PrAlO3–SrTiO3 series [16] showed that the R \( \overline{3} \) c − Pm \( \overline{3} \) m transition temperature decreases gradually from 1770 K in PrAlO3 to 930 K in Pr0.5Sr0.5Al0.5Ti0.5O3 sample. Similar structure and phase behaviour at the elevated temperatures are also expected in the studied NdAlO3–SrTiO3 system, tentative phase diagram of which is shown on Fig. 4. However, extrapolation of the cubic phase boundary from high-temperature region to the higher SrTiO3 concentrations would be speculative because of the different low-temperature structures of the parent compounds NdAlO3 and SrTiO3 (R \( \overline{3} \) c and I4/mcm, respectively). Evidently, phase boundary between the R \( \overline{3} \) c and I4/mcm structural modifications of Nd1-x Sr x Al1-x Ti x O3 solid solution has to be present in the SrTiO3-rich part of the phase diagram at low temperatures (Fig. 4). In addition, appearance of intermediate orthorhombic phase between rhombohedral R \( \overline{3} \) c and tetragonal I4/mcm phase fields, as it occurs in the related PrAlO3–SrTiO3 [16] and NdAlO3–CeAlO3 [17] systems, could not be neglected.

Fig. 4
figure 4

Tentative phase diagram of the PrAlO3–SrTiO3 pseudo-binary system. The letters L, C, Rh and Te designate liquid, cubic, rhombohedral and tetragonal phase fields, respectively. The solid symbols designate the rhombohedral (triangles) and cubic (squares) perovskite structures experimentally observed in Nd1-xSrxAl1-xTixO3 series at RT

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Comprehensive analysis of A/B-cation substitution on the antiferrodistortive phase transition Pm \( \overline{3} \) m − I4/mcm in SrTiO3 recently performed in [18] revealed that transition temperature increases in nonlinear manner with decreasing tolerance factor, depending on substituent concentration. Based on this observation, one can predict that SrTiO3-richest samples in the NdAlO3–SrTiO3 system will transform to the tetragonal I4/mcm structure at the temperatures higher than the pure SrTiO3 (105 K). To shad light on the low-temperature phase behaviour in the NdAlO3–SrTiO3 system, thorough structural, calorimetric and spectroscopic investigations are required.

Conclusions

Continuous solid solution Nd1-xSrxAl1-xTixO3 with perovskite structure is formed in the NdAlO3–SrTiO3 pseudo-binary system at 1773 K. Comparison of the obtained structural parameters with corresponding data for the parent compounds NdAlO3 and SrTiO3 proves a decrease of perovskite structure deformation as a consequence of increasing Goldschmidt tolerance factor with increasing x in Nd1-xSrxAl1-xTixO3 series. As a result, concentration-induced phase transition from a rhombohedral R \( \overline{3} \) c to the cubic perovskite structure occurs in the Nd1-xSrxAl1-xTixO3 system at x = 0.84. Experimental X-ray powder diffraction patterns and crystal structure parameters of rhombohedral Nd0.7Sr0.3Al0.7Ti0.3O3 and cubic Nd0.1Sr0.9Al0.1Ti0.9O3 phases are published by the International Centre of Diffraction Data (ICDD) in the last release of the Powder Diffraction Files (PDF cards NN 00-066-0395 and 00-066-0396, respectively) [19].