Structures of the cation-deficient perovskite Nd_0.7Ti_0.9Al_0.1O₃ from high-resolution neutron powder diffraction in combination with group-theoretical analysis

The crystal structures of Nd_0.7Ti_0.9Al_0.1O₃, taken to represent the ideal Nd_2/3TiO₃, have been elucidated from 4 to 1273 K using high-resolution neutron powder diffraction in combination with group-theoretical analysis. The room-temperature structure is monoclinic in C2/m, on a cell with a = 7.6764 (1), b = 7.6430 (1), c = 7.7114 (1) Å, β = 90.042 (2)°. Pertinent features are the layered ordering of the A-site Nd cations/vacancies along the z axis and out-of-phase tilting of the (Ti/Al)O₆ octahedra around both the x and z axes. From about 750 to 1273 K, the octahedra are tilted around just one axis (x axis) perpendicular to the direction of the cation ordering, giving rise to an orthorhombic structure with space-group symmetry Cmmm.

1. Introduction

The crystal structures and cation/vacancy ordering in perovskite systems with A-site vacancies, A_x□_{(1 − x)}BO₃, are of interest for potentially attractive properties of ionic conductivity, dielectric behaviour and magnetic response. Mitchell (2002) surveyed the published structural data for this class of materials and concluded that further studies are required as many of the reported structures are probably incorrect. Nd_2/3TiO₃ is such a compound with one third of the A sites vacant. The crystal structure of Nd_2/3TiO₃ was first reported by Yoshii (2000) as orthorhombic in the space group Pmmm on a 1 × 1 × 2 cell (referred to the edge of the cubic aristotype). It was suggested by Howard & Zhang (2004a,b) that Nd_2/3TiO₃ would be isostructural with La_2/3TiO₃, which has an ortho­rhombic structure in Cmmm on a 2 × 2 × 2 cell. More recently, Sefat et al. (2005) refined the powder neutron data of Nd_0.7TiO₃ in both Cmmm (on a 2 × 2 × 2 cell) and Pban (on a 2^1/2 × 2^1/2 × 2 cell) and found the Cmmm model to be superior. It is generally accepted that Nd_2/3TiO₃ is unstable in its pure form. However, the structure can be stabilized at a slight oxygen deficiency (Yoshii, 2000) or by low-level doping with NdTiO₃ (Sefat et al., 2005) or NdAlO₃ (Lee et al., 2004). Lee et al. (2004) studied the microstructure of the (1 − x)Nd_2/3TiO₃–xNdAlO₃ system using transmission electron microscopy (TEM). They recorded superlattice reflections indicative of cell doubling in one direction for x = 0.1–0.7 and attributed this to different ionic populations on successive layers of the perovskite A-site. They also proposed for Nd_0.7Ti_0.9Al_0.1O₃ (x = 0.1) both out-of-phase and in-phase tilting of the oxygen octahedra along with A-site cation displacement, based on the observation of superlattice reflections indexing, when referred to the cell of the aristotype, at ½(odd odd odd), ½(odd odd even) and ½(odd even even). However, no space-group symmetry was assigned to their structures.

In this paper, we report a new monoclinic structure for the composition Nd_0.7Ti_0.9Al_0.1O₃. The structure has been deduced through a combination of high-resolution neutron powder diffraction and group-theoretical analysis. The structure, in the space group C2/m on a 2 × 2 × 2 cell, is characterized by a layered ordering of the A-site cations/vacancies, and (Ti/Al)O₆ octahedral tilting independently around two axes. Temperature studies of the transition to the ortho­rhombic structure Cmmm are also reported.

2. Symmetry considerations

Among the room-temperature structures considered for Nd_2/3TiO₃ (Yoshii, 2000; Howard & Zhang, 2004a,b), Nd_0.7TiO₃ (Sefat et al., 2005) and Nd_0.7Ti_0.9Al_0.1O₃ (Lee et al., 2004), there is a consensus on cell doubling in at least one direction, arising from a layered ordering of Nd such that one layer is rich in the cations, and the next is poorer in cations since it contains a greater number of vacancies. It is also agreed that the room-temperature structure is orthorhombic, however, the detailed driving mechanism for the orthorhombic distortion has been a matter for conjecture. Based on our previous experience, we believe that the room-temperature structure arises from a layered ordering of A-site cations/vacancies in combination with the tilting of corner-linked BX₆ octahedral units relative to one another (Howard & Zhang, 2003, 2004a,b). Again a group-theoretical approach was used to enumerate the possible structures. The methodology has been described at greater length in two recent publications by Howard & Stokes (2004, 2005).

The layered ordering of cations (or vacancies) on the perovskite A-site was recognized as transforming according to the irreducible representation X₃^- (k = 0,0,½) of the aristotype space group and giving rise to a structure in the space group P4/mmm on a 1 × 1 × 2 cell. The octahedral tilting was represented through the irreducible representations (irreps) R₄⁺ (k = ½,½,½) corresponding to modes with out-of-phase tilting of octahedra in successive layers and M₃⁺ (k = ½,½,0) associated with in-phase octahedral tilting. The different possible structures were obtained using the computer program ISOTROPY,¹ with results as summarized here in Fig. 1. For each structure, that figure shows the space group with the tilt system indicated, described using Glazer's notation (Glazer, 1972, 1975) – briefly, the symbol a^#b^#c^# is used to indicate no tilt, in-phase octahedral tilting or out-of-phase octahedral tilting around the 〈001〉 axes of the parent perovskite by showing the superscript # as 0, + or −, respectively. The figure also includes the approximate dimensions of the unit cell in terms of the cell edge of the aristotype. The group–subgroup relationships are also shown in Fig. 1; a dashed line joining a group to its subgroup indicates that the corresponding phase transition is required by Landau theory to be first order.

Figure 1 A schematic diagram showing the different possible structures generated by the layered ordering of cations on the perovskite A site, followed by the tilting of the corner-linked BX6 octahedra. The tilting pattern is indicated using Glazer's notation, as explained in the text. The space group is shown, along with the approximate cell dimensions in terms of the cell edge of the parent – angles not required to be 90° are approximately 90°. The lines on the schematic indicate group–subgroup relationships among the 19 space groups shown – a dashed line indicates that, according to Landau theory, the corresponding phase transition cannot be continuous. This figure has been reproduced from Howard & Stokes (2004).

It is interesting to re-examine the literature in light of this analysis. The proposed orthorhombic structures at room temperature in Pmmm on a 1 × 1 × 2 cell (Yoshii, 2000) and in Pban on a 2^1/2 × 2^1/2 × 2 cell (Sefat et al., 2005) do not appear as possibilities in Fig. 1. The other proposal is that Nd_2/3TiO₃ is isostructural with La_2/3TiO₃ (Howard & Zhang, 2004a,b; Sefat et al., 2005) in the space group Cmmm on a 2 × 2 × 2 cell, a structure that has been shown already (Howard & Zhang, 2004a,b) to be consistent with the symmetry analysis above. This orthorhombic structure (a⁻b⁰c⁰ using Glazer's notation) is characterized by A-site cation/vacancy ordering along the z axis and out-of-phase TiO₆ octahedral tilting around an axis (x axis) perpendicular to the ordering direction. However, because of the slightly smaller ionic radius of Nd³⁺ (Shannon, 1976), hence the lower perovskite tolerance factor {t = (R_A + R_O)/ [2^1/2(R_B + R_O)], where R_A, R_B and R_O are the ionic radii of the A- and B-site ions and the O ion, respectively (Goldschmidt, 1926; Roth, 1957)}, Nd_2/3TiO₃ is expected to show greater octahedral tilting than La_2/3TiO₃ and possibly lower symmetry due to tilting around more than one axis (Reaney et al., 1994). In fact, our experiments did indicate that the orthorhombic structure in Cmmm was only observed at high temperatures for Nd_0.7Ti_0.9Al_0.1O₃, following a continuous phase transition at around 750 K (see §4). Therefore, as can be seen from Fig. 1, the only possibilities for the room-temperature structure are the structures in C2/m (a⁻b⁰c⁻ on a 2 × 2 × 2 cell), Pmma (a⁺b⁻c⁰ on a 2 × 2 × 2 cell), Amm2 (a⁻b⁰c⁺ on a 2 × 2 × 2 cell) or P2/m (a⁻b⁻c⁰ on 2^1/2 × 2 × 2^1/2 cell) – these are the only subgroups allowing a single, possibly continuous transition to the structure in Cmmm.

3. Experimental

Nd_0.7Ti_0.9Al_0.1O₃ samples were produced by our standard alkoxide/nitrate route (Ringwood et al., 1988). This method involved the mixing of correct molar quantities of titanium isopropoxide and aluminium sec-butoxide in ethanol with aqueous solutions of neodymium nitrate, while continuously stirring. After thorough mixing and stir drying, the materials were calcined in air at 1023 K for 1 h to remove nitrates and alcohol, followed by wet milling for 16 h using zirconia balls. The slurry was then dried at 383 K overnight and the dried clumps were crushed in a mortar and pestle into fine powder. The powder was pelletized and sintered in air at 1723 K for 48 h, then furnace cooled. A polished surface was carbon-coated and characterized by scanning electron microscopy (SEM), using a Jeol 6400 instrument fitted with a Tracor Northern energy-dispersive spectrometer (EDS) operated at 15 kV. A comprehensive set of standards was used for the quantitative work, giving a high degree of accuracy. This verified the sample composition and showed the sample to be homogeneous with a very small amount of Nd₂Ti₂O₇ (the amount of impurity phase was below the detection limit by X-ray powder diffraction using a Philips X'Pert Pro Diffractometer with Cu Kα radiation).

Time-of-flight neutron powder diffraction data were recorded using the high-resolution powder diffractometer, HRPD, at the ISIS neutron facility, Rutherford Appleton Laboratories, UK (Ibberson et al., 1992). The temperature range of interest, from 4.2 to 1273 K, necessitated the use of both cryostat and furnace. For measurements in the cryostat at 4.2, 100 and 200 K, the powdered sample was lightly packed into an aluminium can of slab geometry, area 20 × 20 mm, 15 mm thick, with thin neutron-transparent windows front and back. Heat was supplied to the sample through a 100 W cartridge heater inserted in the side wall of the sample can and temperature was monitored using a Rh/Fe sensor located in the opposite wall. A gadolinium, neutron-absorbing mask was attached to the side of the can facing the incident and back-scattering detectors to reduce contaminant Bragg peaks arising from either the body of the sample can, including sensor or heater, or the stainless steel frames supporting the vanadium windows. The assembly was attached to a centre-stick and mounted in an AS Scientific, 50 mm diameter, `Orange' helium cryostat, located at the 1 m position of the diffractometer. The exchange gas was He at 30 mbar. For measurements at room temperature and above, the sample was loaded into an 11 mm diameter vanadium can, which was then either suspended from the standard ISIS candlestick for room-temperature measurements or mounted in the RAL vacuum furnace for temperature runs from 373 to 1273 K in 100 K steps. The furnace has vanadium heating elements and the thermometry is based on type-K thermocouples positioned in contact with the sample can at about 20 mm above the beam centre. The sample temperature was controlled to ± 0.2 K. Diffraction patterns from the sample, whether in cryostat or furnace, were recorded over the time-of-flight range 30–130 ms in both back-scattering and 90° detector banks, corresponding to d-spacings from 0.6 to 2.6 Å (at a resolution of Δd/d ≃ 4 × 10⁻⁴) and from 0.9 to 3.7 Å (Δd/d ≃ 2 × 10⁻³), respectively. The patterns were normalized to the incident-beam spectrum as recorded in the upstream monitor and corrected for detector efficiency according to prior calibration with a vanadium scan. Patterns were recorded to a total incident proton beam of ca 75 µA h at room temperature and above, and 100 µA h below room temperature, corresponding to approximately 2.3 and 3.1 h of data collection, respectively, to allow good structure determinations.

4. Results and discussion

An extract from the neutron diffraction pattern, 1.8 < d < 2.4 Å, recorded from Nd_0.7Ti_0.9Al_0.1O₃ at room temperature is shown in Fig. 2. The peaks in the figure are identified by indices based on the 2 × 2 × 2 cell. Peaks with all-even indices correspond to peaks from the ideal cubic aristotype. The superlattice peaks are also indexed on the basis of the 2 × 2 × 2 cell and are marked as the X point (two even, one odd indices), R point (all odd indices) or M point (one even, two odd indices). Intensities at the X points arise from A-site cation/vacancy ordering and those at the R points from out-of-phase (−) octahedral tilting. Intensities at the M points could arise from in-phase (+) octahedral tilting; alternatively, very weak intensities (as observed) could appear at these points due to X- and R-point distortions acting in concert.

Figure 2 Extract (1.8 < d < 2.4 Å) from the diffraction pattern recorded in the back-scattering detectors from Nd0.7Ti0.9Al0.1O3 at room temperature. The peaks are indexed on a cell of dimensions (referred to the edge of the cubic aristotype) 2 × 2 × 2. Crosses represent the observed data. The continuous lines are fits obtained by the Rietveld method using the proposed structure in C2/m, the vertical marks show the peak positions expected in this structure and the line beneath the pattern records the difference between the observed pattern and that calculated in the Rietveld analysis. The inset shows details of the 131/311/113 reflections (boxed region). The solid line through the data points is the envelope of the Voigt/sharp-edged exponential three-peak fit and the vertical lines indicate the individual peak intensities and positions (with error bars).

The inset of Fig. 2 shows the details of the 131/311/113 R-point reflections. In order to separate the individual components, this region was fitted with three peaks each comprising a Voigt function convolved with a sharp-edged exponential, on a linear background – assuming all peaks have the same widths and shapes.² The heights of the three vertical lines indicate the individual peak intensities, showing that the intensities are in the order of 131 reflection > 113 reflection > 311 reflection. According to Glazer (1975), a⁻ (out-of-phase tilting around the x axis) produces reflections of approximately equal intensities at odd–odd–odd with k ≠ l (here 131 and 113), b⁻ reflections with h ≠ l (113 and 311) and c⁻ reflections with h ≠ k (131 and 311). Applying the above results from Glazer, we can now rule out three of the possible structures enumerated from group-theoretical analysis (Fig. 1): structures in Amm2 (a⁻b⁰c⁺), Pmma (a⁺b⁻c⁰) and P2/m (a⁻b⁻c⁰). The structures in Amm2 (a⁻b⁰c⁺) and Pmma (a⁺b⁻c⁰) would not have produced any intensity at the observed 311 and 131 reflections, respectively, while the structure in P2/m (a⁻b⁻c⁰) would have resulted in the 113 peak being the strongest (not the 131 reflection as observed). This leaves the structure in C2/m (a⁻b⁰c⁻) as the only possibility. Indeed, such a structure, according to Glazer (1975), does produce the relative intensities as observed [I(131) > I(113) > I(311)]. The elimination of structures in Amm2 (a⁻b⁰c⁺) and Pmma (a⁺b⁻c⁰), both involving in-phase (+) octahedral tilting, is supported by the fact that the observed intensities of all the M-point reflections are either very weak or negligible, consistent with the origin of these superlattice peaks as the combination of A-site cation/vacancy ordering (X point) and out-of-phase (−) octahedral tilting (R point), rather than in-phase (+) octahedral tilting. Based on the above arguments, we propose the structure in C2/m, tilt system a⁻b⁰c⁻, as the room-temperature structure for Nd_0.7Ti_0.9Al_0.1O₃.

The diffraction pattern has been fitted, and both lattice parameters and atomic coordinates were determined using the Rietveld method as implemented in the GSAS computer program (Larson & von Dreele, 2000; Toby, 2001). Patterns from both the back-scattering and the 90° detector banks were fitted simultaneously, the diffractometer constant for the 90° bank being released to ensure that the lattice parameters were determined in every case by the higher-resolution back-scattering bank. Internal coordinates were refined along with displacement parameters and oxygen displacement parameters were taken to be anisotropic (however, in refinements of the very slightly distorted monoclinic structure, the oxygen displacement parameters were constrained to correspond to orthorhombic Cmmm sym­metry). The isotropic displacement parameters for the two B-site cations, Ti⁴⁺ and Al³⁺, were constrained to be equal. The distribution of the Nd³⁺ ions over the two crystallographically distinct A sites was allowed to vary, with the total occupancy constrained to 1.4. The details of the structure, as refined by the Rietveld method, are included in Table 1. This monoclinic structure, along with the structure of the high-temperature orthorhombic phase, is depicted in Fig. 3. Note that a refinement from the room-temperature data was also carried out assuming the Cmmm model; the goodness-of-fit (χ² = 5.0) was, as expected, worse than for the C2/m model.

Table 1
Details of the room-temperature monoclinic and high-temperature orthorhombic structures of Nd_0.7Ti_0.9Al_0.1O₃

The Wyckoff symbol for each site is shown. The number in parentheses beside each entry indicates the s.u. referred to the last digit shown. The Nd site at z ≃ 0 is essentially fully occupied; the occupancy of the site at z ≃ 1/2 is close to 40%.

Atom	Site	x	y	z	Occupancy	U
Room temperature (296 K), space group C2/m, a = 7.6764 (1), b = 7.6430 (1), c = 7.7114 (1) Å, β = 90.042 (2)°
Nd1	4(i)	0.2522 (6)	0	0.0022 (8)	0.970 (5)	0.91 (9)
Nd2	4(i)	0.2493 (14)	0	0.5096 (17)	0.430 (5)	0.97 (18)
Ti,Al	8(j)	0.0046 (11)	0.2474 (9)	0.2606 (5)	0.9, 0.1	0.53 (6)
O1	4(g)	0	0.2827 (6)	0	1	1.45 (27)
O2	4(h)	0	0.2231 (8)	0.5	1	3.44 (31)
O3	4(i)	0.0135 (7)	0	0.2092 (5)	1	1.15 (24)
O4	4(i)	−0.0297 (8)	0.5	0.2683 (5)	1	1.56 (27)
O5	8(j)	0.2536 (8)	0.2730 (7)	0.2338 (4)	1	2.49 (20)
						Measure of fit: χ^2 = 4.2
T = 873 K, space group Cmmm, a = 7.7102 (1), b = 7.6943 (1), c = 7.7476 (1) Å
Nd1	4(g)	0.2503 (8)	0	0	0.989 (5)	2.28 (11)
Nd2	4(h)	0.2535 (18)	0	0.5	0.411 (5)	2.25 (21)
Ti,Al	8(n)	0	0.2477 (14)	0.2623 (4)	0.9, 0.1	1.64 (7)
O1	4(i)	0	0.2805 (8)	0	1	3.37 (31)
O2	4(j)	0	0.2254 (10)	0.5	1	4.28 (34)
O3	4(k)	0	0	0.2111 (6)	1	2.53 (32)
O4	4(l)	0	0.5	0.2649 (7)	1	4.46 (41)
O5	8(m)	0.25	0.25	0.2354 (7)	1	4.54 (23)
						Measure of fit: χ^2 = 2.3

Figure 3 Representations of (a), (b) room-temperature monoclinic, and (c), (d) high-temperature orthorhombic structures of Nd0.7Ti0.9Al0.1O3. The (Ti/Al)O6 groups are shown as octahedra, the Ti/Al ion being visible within them; the darker and lighter spheres outside these octahedra represent Nd in the fully and partly occupied layers, respectively. The unit cell is outlined in each case. The figures shown are perspective views along the x and z axis. The movements of O^2− and Ti^4+/Al^3+ ions respectively towards and away from the fully occupied Nd layers result in an offset of the Ti/Al atom discernible in (a) and (c). The octahedral tilting in (a), (b) and (c) is also clearly visible. These figures were prepared using the computer program ATOMS (Dowty, 1999).

As shown in Table 1,³ the room-temperature refinement confirms the cation ordering to the extent that the A sites at z ≃ 0 are essentially fully occupied by Nd³⁺ ions (97% occupancy), while the A sites at z ≃ 1/2 contain nearly all the vacancies (43% occupancy). It can be seen, from the values of z tabulated, that the Ti⁴⁺/Al³⁺ ions move away from the fully occupied layer and the O²⁻ ions move (on average) towards it, as might be expected given the additional positive charge on these layers. Not only do these movements make sense, but also they may well account for the stability of the layered ordering that is observed (Thomas et al., 2006). The distinctive feature of the present model is the movement of O atoms associated with octahedral tilting around both the x and z axes. The angles of tilt can be estimated from the oxygen coordinates as the angle made by the line joining O3 with O4 to the y axis. This tilt angle around the x axis is given by tan⁻¹{[z(O4) − z(O3)]c/(b/2)} and is ∼ 6.8°. Similarly the tilt angle around the z axis is given by tan⁻¹{[x(O3) − x(O4)]a/(b/2)} and is ∼ 5.0°. These angles are bigger than the tilt angle of ∼ 4.7° (around the x axis only) reported for La_0.6Sr_0.1TiO₃ at room temperature (having an orthorhombic structure in Cmmm; Howard & Zhang, 2003), consistent with (see §2) the slightly smaller ionic size of Nd³⁺ compared with La³⁺.

Diffraction patterns obtained at high temperatures were inspected closely to look for phase transition(s). In fact, this was done before the room-temperature structure was solved, since that relied upon the correct identification of the high-temperature structure and a consideration of structures derived from it (see §2). As in the case of La_0.6Sr_0.1TiO₃, layered ordering of cations/vacancies is expected to remain in the temperature range of this study (up to 1273 K) due to the low cation mobility (Howard & Zhang, 2003). However, phase transitions due to the disappearance of octahedral tilting are expected upon heating. Again the details of the superlattice peaks proved to be pivotal. Fig. 4(a) shows details of the 131/311/113 reflections observed at various temperatures. The same peak-fitting procedure, as that applied to the room-temperature data, was carried out for all the temperature runs. The results at T = 100, 673 and 773 K are shown in Figs. 4(b)–(d), respectively; the vertical lines indicate the intensity of each individual peak. For temperatures up to 673 K, three peaks are necessary to fit the 131/311/113 region satisfactorily. For temperatures ranging from 773 to 1273 K, however, the intensity of the middle 311 peak becomes negligible, i.e. only two peaks are required to fit this region. According to Glazer (1975), the appearance of intensity in R-point reflections with k ≠ l (i.e. 131 and 113), together with the absence of intensity at the corresponding k = l reflection (i.e. 311), implies that only around the x axis does the (out-of-phase) octahedral tilt occur. This is similar to the diffraction pattern obtained at room temperature from La_0.6Sr_0.1TiO₃, which was successfully refined using a structure model in Cmmm, tilt system a⁻b⁰c⁰ (Howard & Zhang, 2003). Therefore, we propose the same orthorhombic structure for the high-temperature phase of Nd_0.7Ti_0.9Al_0.1O₃.

Figure 4 (a) Details of the 131/311/113 reflections (2.28 < d < 2.36 Å) at temperatures ranging from 4.2 to 1073 K, (b)–(d) curve-fitting results of the same region at 100, 673 and 773 K, respectively. Note the abscissae in (b)–(d) are time-of-flight, related to d-spacing by t (ms) = 48.235d (Å). The solid line through the data points in (b)–(d) is the envelope of the Voigt/sharp-edged exponential peak fits and the vertical lines indicate the individual peak intensities and positions (with error bars).

Diffraction patterns were also recorded below room temperature at 4.2, 100 and 200 K, to check for a possible low-temperature phase. The details of the 131/311/113 reflections at 4.2, 100 and 200 K are shown in Figs. 4(a) and (b); the presence of the middle 311 peak is more evident at lower temperatures due to the slightly wider spacing between peaks. The diffraction patterns are, however, exceedingly well fitted assuming the same C2/m structure as occurs at room temperature, suggesting that there is no additional phase occurring below room temperature.

Structure refinements were carried out for all the temperature runs, from 4.2 to 1273 K, using the same protocol as described earlier. The results of the refinement from the patterns recorded at 873 K, a temperature at which the orthorhombic structure is well established, are also shown in Table 1. The refinements confirm the cations are still ordered in the high-temperature orthorhombic phase, such that one layer is essentially fully occupied by Nd³⁺ ions and the next contains nearly all the vacancies. As noted in the monoclinic structure at room temperature, the values of z tabulated for the orthorhombic structure at 873 K also reveal that the Ti⁴⁺/Al³⁺ ions move away from the fully occupied layer, and the O²⁻ ions move (on average) towards it. The driving force for the phase transition to orthorhombic is the disappearance of the octahedral tilting around the z axis, leaving only the tilting around the x axis. Again this angle is given by tan⁻¹{[z(O4) − z(O3)]c/(b/2)} and is ∼ 6.2° at 873 K, slightly smaller than that at room temperature.

Lattice parameters obtained from the refinements are recorded in Fig. 5. The cell edges show saturation effects at lower temperatures, and accordingly have been fitted with functions of the form l = l₀ + l₁θ_s coth(θ_s/T) (Salje et al., 1991) with saturation temperature θ_s at 350 K. At 1273 K, the highest temperature studied, the structure is still clearly orthorhombic. Extrapolating on parameters a and b suggests that a transition to a tetragonal structure might occur at around 1480 K. This would be the structure, space group P4/mmm, formed by perovskites with layered cation/vacancy ordering on the A sites in the absence of octahedral tilting and adopted, for example, by La_0.6Sr_0.1TiO₃ at elevated temperatures (Howard & Zhang, 2003). However, the possibility of other effects, such as the onset of disorder on the A site due to increased cation mobility at high temperatures, cannot be excluded.

Figure 5 Lattice parameters for Nd0.7Ti0.9Al0.1O3 as a function of temperature. The dashed curves fitted to the cell edges are of the form l = l0 + l1θscoth(θs/T), with θs = 350 K, to describe the saturation effects at lower temperatures. Extrapolation on a and b suggests the structure would become tetragonal at around 1480 K. The curve fitted to the monoclinic angle is of the form β − 90° ∝ (Tc − T)^1/4, consistent with a tricritical transition occurring at Tc ≃ 690 K.

The monoclinic β angle is fitted reasonably well with a function of the form β – 90° ∝ (T_c – T)^1/4, with T_c = 690 K, consistent with a continuous but tricritical phase transition from the monoclinic to the orthorhombic phase (Salje, 1990). The continuous nature of this phase transition is confirmed by directly comparing the diffraction patterns from the monoclinic phase with those from the orthorhombic phase – there are no discernible differences aside from the subtle ones in R-point reflections already discussed. The transition temperature from monoclinic to orthorhombic cannot be determined very accurately due to the coarse (100 K) temperature steps used as well as the difficulty (see β in Fig. 5) in obtaining precise estimates of the small monoclinic distortion. Based on our observations of the R-point reflections (Fig. 4), we believe the transition occurs between 673 and 773 K, so tentatively suggest 750 K for the temperature of this transition.

Finally, it should be mentioned that our model for the room-temperature structure in C2/m was used successfully to generate the selected-area electron diffraction (SAED) patterns recorded by Lee et al. (2004) in their TEM study of Nd_0.7Ti_0.9Al_0.1O₃. Calculated patterns were obtained using the program EMS On Line (Electron Microscopy Image Simulation⁴), which includes multiple scattering effects. In addition, a multiple domain effect was taken into consideration as the SAED patterns recorded by Lee et al. (2004) were from at least two different domains due to the small domain size in their sample. It is clear that the superlattice reflections indexed at ½(odd odd odd), ½(odd even even) and ½(odd odd even) in their paper (referred to the 1 × 1 × 1 cubic cell of the aristotype) can be accounted for by the out-of-phase octahedral tilting, the layered ordering of the Nd³⁺ ions and a combination of the two, respectively. The manner in which `concert' reflections can be produced by combinations of distortions is highlighted in recent simulations by Woodward & Reaney (2005). It is not necessary in the present case to invoke in-phase tilting or any particular A-site cation displacement as Lee et al. (2004) proposed.

5. Summary and conclusions

The room-temperature structure of Nd_0.7Ti_0.9Al_0.1O₃, which we take to represent the structure of Nd_2/3TiO₃, has been successfully determined. Symmetry arguments were used to limit the possibilities, then the structure solution completed from a high-resolution neutron powder diffraction study revealed details of the weak superlattice reflections that arise from octahedral tilting. The structure, monoclinic in C2/m, has been successfully refined by the Rietveld method. It is characterized by a layered ordering of the A-site cations/vacancies along the z axis (alternately occupied and partly occupied layers of Nd cations), and out-of-phase tilting of the (Ti/Al)O₆ octahedra independently around two axes (∼ 6.8 and 5.0° around the x and z axes, respectively).

The phase transition to orthorhombic in Cmmm has also been examined, with the transition temperature roughly estimated at around 750 K. The driving force for this phase transition is the disappearance of the octahedral tilting around the z axis (parallel to the direction of the cation ordering). Upon further heating (beyond the temperature range of this experiment), the octahedral tilting around the x axis (perpendicular to the direction of the cation ordering) is also expected to disappear, leading to a tetragonal structure in P4/mmm, as observed for La_0.6Sr_0.1TiO₃ (Howard & Zhang, 2003).

Supporting information

Computing details

Figures

(ND0.7AL0.1TI0.9O3_RT_overall)

Crystal data

?	β = ?°
Mr = ?	γ = ?°
?, ?	V = ? Å^3
a = ? Å	Z = ?
b = ? Å	? radiation, λ = ? Å
c = ? Å	?, ? × ? × ? mm
α = ?°

Data collection

Refinement

Least-squares matrix: full	? data points
Rp = 0.053	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 1084.6 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 12.72 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0; TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 2262.7 #6 (sig-2) = 243.9 #7 (gam-0) = 0.00 #8 (gam-1) = 12.79 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rwp = 0.057	62 parameters
Rexp = 0.045; 0.017	0 restraints
R(F^2) = 0.12475; 0.13144	(Δ/σ)max = 0.02
χ^2 = 4.162	Background function: GSAS Background function number 1 with 6 terms. Shifted Chebyshev function of 1st kind 1: 0.239911 2: -3.948660E-02 3: 1.313250E-02 4: -6.363930E-03 5: -4.017170E-03 6: -4.553510E-03; GSAS Background function number 1 with 4 terms. Shifted Chebyshev function of 1st kind 1: 0.264321 2: -7.504890E-02 3: 1.714960E-02 4: -3.143980E-02

(ND0.7AL0.1TI0.9O3_RT)

Crystal data

Al0.1Nd0.7O3Ti0.9	β = 90.042 (2)°
Mr = 194.76	V = 452.43 (2) Å^3
Monoclinic, C2/m	Z = 8
a = 7.67637 (12) Å	? radiation, λ = ? Å
b = 7.64297 (12) Å	?, ? × ? × ? mm
c = 7.71137 (12) Å

Data collection

Refinement

Least-squares matrix: full	? data points
Rp = 0.053	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 1084.6 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 12.72 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rwp = 0.057	62 parameters
Rexp = 0.045	0 restraints
R(F^2) = 0.12475	(Δ/σ)max = 0.02
χ^2 = 4.162	Background function: GSAS Background function number 1 with 6 terms. Shifted Chebyshev function of 1st kind 1: 0.239911 2: -3.948660E-02 3: 1.313250E-02 4: -6.363930E-03 5: -4.017170E-03 6: -4.553510E-03

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Nd1	0.2522 (6)	0.0	0.0021 (8)	0.0091 (9)*	0.970 (5)
Nd2	0.2493 (14)	0.0	0.5096 (17)	0.0097 (18)*	0.430 (5)
Ti	0.0046 (11)	0.2474 (9)	0.2606 (5)	0.0053 (6)*	0.9
O1	0.0	0.2827 (6)	0.0	0.01449
O2	0.0	0.2231 (8)	0.5	0.0344
O3	0.0135 (7)	0.0	0.2092 (5)	0.01148
O4	−0.0297 (8)	0.5	0.2683 (5)	0.01557
O5	0.2536 (8)	0.2730 (7)	0.2338 (4)	0.02488
Al	0.0046 (11)	0.2474 (9)	0.2606 (5)	0.0053 (6)*	0.1

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.030 (3)	0.006 (3)	0.0080 (17)	0.0	0.0	0.0
O2	0.059 (4)	0.042 (4)	0.0023 (18)	0.0	0.0	0.0
O3	0.011 (3)	0.015 (2)	0.008 (2)	0.0	0.0	0.0
O4	0.026 (3)	0.005 (2)	0.016 (2)	0.0	0.0	0.0
O5	0.0008 (10)	0.030 (3)	0.044 (2)	−0.005 (2)	0.0	0.0

(ND0.7AL0.1TI0.9O3_RT_p_01)

Crystal data

?	β = ?°
Mr = ?	γ = ?°
?, ?	V = ? Å^3
a = ? Å	Z = ?
b = ? Å	? radiation, λ = ? Å
c = ? Å	?, ? × ? × ? mm
α = ?°

Data collection

Refinement

Rp = 0.064	? data points
Rwp = 0.072	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 1084.6 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 12.72 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rexp = 0.045
R(F^2) = 0.12475	Background function: GSAS Background function number 1 with 6 terms. Shifted Chebyshev function of 1st kind 1: 0.239911 2: -3.948660E-02 3: 1.313250E-02 4: -6.363930E-03 5: -4.017170E-03 6: -4.553510E-03
χ^2 = NOT FOUND

(ND0.7AL0.1TI0.9O3_RT_p_02)

Crystal data

?	β = ?°
Mr = ?	γ = ?°
?, ?	V = ? Å^3
a = ? Å	Z = ?
b = ? Å	? radiation, λ = ? Å
c = ? Å	?, ? × ? × ? mm
α = ?°

Data collection

Refinement

Rp = 0.041	? data points
Rwp = 0.050	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 2262.7 #6 (sig-2) = 243.9 #7 (gam-0) = 0.00 #8 (gam-1) = 12.79 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rexp = 0.017
R(F^2) = 0.13144	Background function: GSAS Background function number 1 with 4 terms. Shifted Chebyshev function of 1st kind 1: 0.264321 2: -7.504890E-02 3: 1.714960E-02 4: -3.143980E-02
χ^2 = NOT FOUND

(ND0.7AL0.1TI0.9O3_600C_overall)

Crystal data

?	β = ?°
Mr = ?	γ = ?°
?, ?	V = ? Å^3
a = ? Å	Z = ?
b = ? Å	? radiation, λ = ? Å
c = ? Å	?, ? × ? × ? mm
α = ?°

Data collection

Refinement

Least-squares matrix: full	1632 data points
Rp = 0.037	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 509.3 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 11.74 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0; TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 1822.8 #6 (sig-2) = 248.4 #7 (gam-0) = 0.00 #8 (gam-1) = 12.55 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rwp = 0.041	54 parameters
Rexp = 0.039; 0.018	0 restraints
R(F^2) = 0.27973; 0.06728	(Δ/σ)max = 0.03
χ^2 = 2.310	Background function: GSAS Background function number 1 with 6 terms. Shifted Chebyshev function of 1st kind 1: 0.497571 2: 6.126860E-02 3: 2.448550E-02 4: -1.455740E-02 5: -9.745710E-03 6: -1.060520E-02; GSAS Background function number 4 with 4 terms. Power series in Q**2n/n! 1: 0.500328 2: -1.113600E-02 3: 5.555480E-04 4: 1.833090E-05

(ND0.7AL0.1TI0.9O3_600C)

Crystal data

Al0.1Nd0.7O3Ti0.9	c = 7.74755 (10) Å
Mr = 194.76	V = 459.62 (2) Å^3
Orthorhombic, Cmmm	Z = 8
a = 7.71021 (11) Å	? radiation, λ = ? Å
b = 7.69428 (11) Å	?, ? × ? × ? mm

Data collection

Refinement

Least-squares matrix: full	1632 data points
Rp = 0.037	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 509.3 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 11.74 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rwp = 0.041	54 parameters
Rexp = 0.039	0 restraints
R(F^2) = 0.27973	(Δ/σ)max = 0.03
χ^2 = 2.310	Background function: GSAS Background function number 1 with 6 terms. Shifted Chebyshev function of 1st kind 1: 0.497571 2: 6.126860E-02 3: 2.448550E-02 4: -1.455740E-02 5: -9.745710E-03 6: -1.060520E-02

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Nd1	0.2503 (8)	0.0	0.0	0.0228 (11)*	0.989 (5)
Nd2	0.2535 (18)	0.0	0.5	0.023 (2)*	0.411 (5)
Ti	0.0	0.2477 (14)	0.2623 (4)	0.0164 (7)*	0.9
O1	0.0	0.2805 (8)	0.0	0.03371
O2	0.0	0.2254 (10)	0.5	0.0428
O3	0.0	0.0	0.2111 (6)	0.02528
O4	0.0	0.5	0.2649 (7)	0.04457
O5	0.25	0.25	0.2354 (7)	0.04537
Al	0.0	0.2477 (14)	0.2623 (4)	0.0164 (7)*	0.1

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.063 (4)	0.019 (3)	0.020 (2)	0.0	0.0	0.0
O2	0.073 (4)	0.044 (4)	0.011 (2)	0.0	0.0	0.0
O3	0.029 (4)	0.021 (3)	0.026 (3)	0.0	0.0	0.0
O4	0.091 (6)	0.007 (3)	0.035 (3)	0.0	0.0	0.0
O5	0.0179 (14)	0.054 (2)	0.064 (3)	0.002 (4)	0.0	0.0

(ND0.7AL0.1TI0.9O3_600C_p_01)

Crystal data

?	β = ?°
Mr = ?	γ = ?°
?, ?	V = ? Å^3
a = ? Å	Z = ?
b = ? Å	? radiation, λ = ? Å
c = ? Å	?, ? × ? × ? mm
α = ?°

Data collection

Refinement

Rp = 0.047	? data points
Rwp = 0.054	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 509.3 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 11.74 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rexp = 0.039
R(F^2) = 0.27973	Background function: GSAS Background function number 1 with 6 terms. Shifted Chebyshev function of 1st kind 1: 0.497571 2: 6.126860E-02 3: 2.448550E-02 4: -1.455740E-02 5: -9.745710E-03 6: -1.060520E-02
χ^2 = NOT FOUND

(ND0.7AL0.1TI0.9O3_600C_p_02)

Crystal data

?	β = ?°
Mr = ?	γ = ?°
?, ?	V = ? Å^3
a = ? Å	Z = ?
b = ? Å	? radiation, λ = ? Å
c = ? Å	?, ? × ? × ? mm
α = ?°

Data collection

Refinement

Rp = 0.025	1632 data points
Rwp = 0.032	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 1822.8 #6 (sig-2) = 248.4 #7 (gam-0) = 0.00 #8 (gam-1) = 12.55 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rexp = 0.018
R(F^2) = 0.06728	Background function: GSAS Background function number 4 with 4 terms. Power series in Q**2n/n! 1: 0.500328 2: -1.113600E-02 3: 5.555480E-04 4: 1.833090E-05
χ^2 = NOT FOUND

 

Footnotes

¹ISOTROPY is a software package developed by Stokes and Hatch at Brigham Young University. ISOTROPY is available at https://www.physics.byu.edu/~stokesh/isotropy.html .

²Peak-fitting program due to Devinder Sivia, ISIS Facility.

³Supplementary data for this paper are available from the IUCr electronic archives (Reference: BK5024 ). Services for accessing these data are described at the back of the journal.

⁴EMS On Line is an internet version of the commercial software package developed by Pierre Stadelmann at the Centre Interdépartemental de Microscopie Electronique (CIME) of the Ecole Polytechnique Fédérale de Lausanne (EPFL) in Switzerland. The interface for this version (https://cimesg1.epfl.ch/CIOL/ems.html ) was developed by Pierre-Henri Jouneau.