Neutron and electron diffraction studies of La(Zn_1/2Ti_1/2)O₃ perovskite

The crystallography and microwave dielectric properties of La(Zn_1/2Ti_1/2)O₃ (LZT) ceramics prepared via the mixed-oxide route were investigated in this study. While samples were largely single phase, small amounts of ZnO impurity were detected in sintered pellets. Observed reflections in electron and neutron diffraction patterns indicate that the symmetry of LZT is P2₁/n. The B site is ordered on {110} or pseudocubic {111}, but the presence of the pseudocubic (111) reflection is in itself insufficient to indicate the existence of such order. Rietveld refinements of the neutron diffraction data yield an excellent fit for such a model. The structure is highly twinned, with variants related through common {211} composition planes and 90° rotations about 〈011〉. The microwave dielectric properties measured were ∊_r = 34, Qf = 36 090 and τ_f = −70 MK⁻¹.

1. Introduction

Microwave resonators are used extensively in telecommunications equipment, including cellular telephones and satellite links, and are at the heart of a multi-billion dollar market. Oxide ceramics are critical elements in these devices, and three properties are important in determining their usefulness as dielectric resonators. First, the material must have a high dielectric constant (∊_r) to enable size reduction. Second, a high quality factor, Q (1/tanδ), means fine frequency tunability and better filters. Third, these ceramics compensate for frequency drift because of their low-temperature coefficient of resonant frequency (τ_f).

Perovskite is a term used to describe an ABO₃ arrangement of cations and O anions that is isomorphous with CaTiO₃, that is, corner-shared anion octahedra enclosing a single cation. This structure has been illustrated, for example, in the review by Ubic et al. (1998). The basic principles for tuning τ_f in complex perovskites have already been established. Colla et al. (1992, 1993) and Reaney et al. (1994) have shown that temperature stability in Ba- and Sr-based complex perovskites is fundamentally related to the onset and degree of octahedral tilting. Moreover, τ_f can be tuned through ±300 MK⁻¹ without significantly altering Q or ∊_r by manipulating the perovskite tolerance factor, t, from 1.01 to 0.93. Reducing t results in the onset of octahedral tilt transitions. The tolerance factor was first suggested by Megaw (1946) to determine the stability of the perovskite phase for a given set of ions. In general, the perovskite phase is stable when the value of t is close to unity, which is true for SrTiO₃, for which t = 1.00. Reducing t results in the onset of octahedral tilt transitions and the lowering of symmetry.

The family of rare-earth zinc/magnesium titanates is of interest as possible microwave resonator materials chiefly because of their negative τ_f values, although La(Mg_1/2Ti_1/2)O₃ has also been considered a candidate substrate material for the growth of high-T_c superconducting films (Harshé et al., 1994; Cho et al., 1999), where the requirement is for low ∊_r and high Q. The negative τ_f of these materials, combined with the typical ease with which perovskites accept dopants, means that solid solutions can be formulated with materials with positive values for τ_f (e.g. CaTiO₃, SrTiO₃ etc.), to yield ceramics with τ_f ≃ 0.

The structure of La(Mg_1/2Ti_1/2)O₃ (LMT) was first described (Macke & Blasse, 1976; Macke, 1977) as `probably orthorhombic' and at least partly disordered on the B site. LMT was later reported (German & Kovba, 1983) as a cubic phase with a lattice constant of a = 7.868 Å. Several years later, Negas et al. (1991) found LMT to be orthorhombic, but Harshé et al. (1994) failed to find any orthorhombic peak splitting and again suggested a cubic unit cell, but with a lattice constant of a = 3.9195 Å. LMT's average perovskite tolerance factor is 0.952, which, according to the work of Reaney et al. (1994), suggests the presence of both in-phase and anti-phase tilting of oxygen octahedra. Accordingly, Meden & Čeh (1998) refined the structure in the orthorhombic space group Pbnm, which forbids B-site ordering. More recently, LMT has been reported (Lee et al., 2000; Avdeev et al. 2002a,b; Seabra, Salak et al., 2003; Seabra et al., 2004; Vanderah et al., 2004) as an ordered perovskite in the monoclinic space group P2₁/n; however, LMT becomes disordered and orthorhombic when doped with very small amounts of either CaTiO₃ (Seabra, Avdeev et al., 2003), SrTiO₃ (Lee et al., 2000; Avdeev et al., 2002b) or BaTiO₃ (Avdeev et al., 2002a; Seabra et al., 2004). Most recently (Vanderah et al., 2004), pure La(Mg_1/2Ti_1/2)O₃ has been ascribed lattice constants of a = 5.5608, b = 5.5749, c = 7.8610 Å, β = 90.034° in P2₁/n, and the structural model published by Avdeev et al. (2002a) shows the B site to be mostly ordered but with about 4% disorder.

The microwave dielectric properties of LMT have been measured by various groups. Cho et al. (1999) suggested that they were the first to measure such values (∊_r = 29, Qf = 75 500 at 10 GHz and τ_f = −65 MK⁻¹), but they were in fact beaten by both a Kyocera Corporation (Kyoto, Japan) patent (Kyocera Corporation, 1987), which reported ∊_r = 32 and τ_f = −88.3 MK⁻¹, and Negas et al. (1991), who published values (∊_r = 33, Qf = 40 000 at 5 GHz and τ_f = −100 MK⁻¹) 8 years earlier. As dense samples have sometimes been difficult to prepare [e.g. the pellets in the work of Vanderah et al. (2004) were only 90% dense], there has been some variability in the measured properties. The relative permittivity varies from 27 (Salak et al., 2003) to 33 (Negas et al., 1991), and Qf values range from 40 000 (Negas et al., 1991) to ∼60 000 (Lee et al., 2000; Vanderah et al., 2004) to 75 500 (Cho et al., 1999) all the way up to 114 300 (Seabra, Avdeev et al., 2003; Seabra, Salak et al., 2003). Similarly, τ_f measurements seem to vary between groups, with values typically approximately −81 MK⁻¹ (Lee et al., 2000; Seabra, Avdeev et al., 2003; Seabra, Salak et al., 2003; Vanderah et al., 2004; Kyocera Corporation, 1987; Salak et al., 2003), although values of −65 MK⁻¹ (Cho et al., 1999) and −100 MK⁻¹ (Negas et al., 1991) have also been reported. Commercially promising compositions were found by doping with either CaTiO₃ (0.44LMT–0.56CT: ∊_r = 47, Qf = 28 120 at 3.8 GHz and τ_f = 0; Negas et al., 1991) or BaTiO₃ (0.5LMT–0.5BT: ∊_r ≃ 60, Qf ≃ 9600 and τ_f = −2 MK⁻¹; Seabra et al., 2004). Kyocera Corporation (1987) holds a patent on compositions in the system (1 − x)La(Mg_1/2Ti_1/2)O₃–xCaTiO₃ (0 ≤ x ≤ 0.7), including the temperature-stable composition x = 0.55, for which they disclose ∊_r = 47.6, tan δ = 0.00028 and τ_f = 0.6 MK⁻¹.

Cell constants for La(Zn_1/2Ti_1/2)O₃ (LZT) were published by Kucheiko et al. (1996) (orthorhombic; a = 5.6077, b = 7.8986, c = 5.5641 Å), but no atomistic model has yet been proposed. The microwave properties they measured were ∊_r = 28.69, Qf = 59 892 and τ_f = −71 MK⁻¹, but the density of their samples was only about 90% of the theoretical density (ρ_th). These properties were later remeasured by Cho et al. (1997) on samples which were about 97% ρ_th. They reported ∊_r = 34, Qf = 59 000 and τ_f = −52 MK⁻¹. Like LMT, LZT is reportedly ordered but becomes disordered upon the addition of small amounts of either CaTiO₃ (Cho et al., 2001) or SrTiO₃ (Cho et al., 1998, 2001) dopants, although evidence of short-range order was still found by FT–IR at higher doping levels (Cho et al., 2001). In the case of xSrTiO₃–(1 − x)LZT, long-range order at the B site is lost at x ≥ 0.4 (Cho et al., 1998, 2001). A-site cation displacements and in-phase octahedral tilting are lost at x ≥ 0.6 (Cho et al., 1998), and finally antiphase tilts disappear at x ≥ 0.9 (Cho et al., 1998). As for LMT, commercially promising compositions are all doped to about the 50% level. Indeed, Yeo et al. (1996) reported that 0.5LZT–0.5CaTiO₃ had ∊_r = 50, Qf = 38 000 and τ_f = 0, while Cho et al. (1998) found that 0.5LZT–0.5SrTiO₃ had ∊_r = 55, Qf ≃ 60 000 and τ_f = 0. Kyocera Corporation (2000) have also recently developed ceramics in the system CaTiO₃–La(Zn_1−xM_x)O₃ (M = W, Ni, Co, Zr, Sn, Mn and Cu).

The average tolerance factor of LZT is t = 0.947, which, like LMT, suggests the presence of both in-phase and anti-phase tilting of oxygen octahedra. The effects of this tilting have been observed (Cho et al., 2001) by X-ray diffraction (XRD) in the form of (311) and (310) superlattice reflections corresponding to anti-phase and in-phase tilting, respectively. Systematic cation displacement was also detected by the appearance of (210) reflections, and (111) reflections were observed and ascribed to the doubling of the unit cell caused by the B-site cation ordering. Based on this crystallographic evidence, three possible orthorhombic space groups can be derived for the structure (Pmmn, Pnma, Cmcm), none of which can also account for the B-site ordering. Single-microcrystal XRD measurements or transmission electron microscopy combined with neutron diffraction would be required to establish the structure unambiguously, and the results of such work are described here.

2. Experimental procedure

LZT samples were prepared by conventional mixed-oxide powder processing. Starting materials included La₂O₃ (99.9% Meldform Rare Earths, UK), TiO₂ (99.9% Alfa Aesar, UK) and ZnO (99.9% Elementis Specialties, UK). As described in detail elsewhere (Ubic et al., 2005), La₂O₃ powder was first hydrated by mixing it with a surplus of distilled water and leaving it to dry overnight at 353 K. Stoichiometric amounts of all the powders were then milled together in a nylon millpot partly filled with ZrO₂ media and distilled water for 4 h. A small amount (1 wt%) of Dispex A40 (Allied Colloids, Bradford, UK) was added as a deflocculant. The slurries were then dried overnight at 353 K. Dried powders were subsequently granulated with a mortar and pestle and sieved to under 250 µm. The powders were then heated to 873 K for 2 h in an open alumina crucible and allowed to cool. The powders were then mixed by hand, covered with a lid and re-heated to 1473 K for 2 h. After calcination, the powder was re-milled for a further 4 h with 2 wt% PEG 1500 (Whyte Chemicals, London) being added in aqueous solution 5–10 min before completion. These slurries were then dried at 353 K and subsequently pressed (125 MPa) into cylindrical pellets, 10 mm in diameter and 3 mm thick. These pellets were sintered in closed alumina boats for 2 h at 1773 K.

Some samples underwent thinning by ion milling (model 600, Gatan, California, USA) for observation in the transmission electron microscope (JEM 2010, Jeol, Tokyo). High-resolution neutron diffraction data were acquired on the HRPD instrument at the Rutherford Appleton Laboratory's ISIS facility (experiment number RB 14933). Data from the backscattering detector bank was analysed in the d-spacing range 0.70–3.94 Å with the General Structure Analysis System (GSAS; Larson & Von Dreele, 1987) Rietveld refinement program. Measurements of ∊_r, Q and τ_f were obtained at Filtronic Comtek (Wolverhampton, UK) on a vector network analyser (model 8753E, Hewlett Packard, USA).¹

3. Structure of La(Zn_1/2Ti_1/2)O₃

It is very difficult to determine the symmetry of tilted perovskites such as LZT from powder XRD alone. Peaks associated with oxygen octahedral tilting, as well as those arising from cation ordering, are very weak in XRD – hence the confusion in the early literature (Harshé et al., 1994; Macke & Blasse, 1976; Macke, 1977; German & Kovba, 1983; Negas et al., 1991) on the structure of LMT already described. Electron diffraction of single crystals within a ceramic has some advantages, although the interpretation of patterns can be complicated by the presence of double diffraction and twinning.

The selected-area diffraction patterns (SADPs) in Fig. 1, obtained from several grains, have been indexed self-consistently according to the simple pseudocubic perovskite unit cell (a = 3.9449 Å). Evidence of in-phase octahedral tilting can be found by examining the 〈100〉 pseudocubic SADPs (Figs. 1a–1c). Each pattern can reveal such tilting about a single axis by allowing, according to the Weiss zone law, a unique set of {even, odd, odd}-type γ reflections to appear. As can clearly be seen, only Fig. 1(a) contains γ reflections, indicating the presence of in-phase tilting about a single pseudocubic axis. The most efficient way of characterizing the structure for in-phase tilts is instead to examine a 〈111〉 pseudocubic SADP, as shown in Fig. 1(d). Such a pattern would simultaneously allow every type of γ reflection to appear and so show all in-phase tilt axes present. In agreement with Figs. 1(a)–(c), only a single γ reflection is observed in Fig. 1(d), again indicating the presence of in-phase tilting about a single axis. The presence of {odd, even, even}-type β reflections in Figs. 1(b) and (c) indicates a lanthanum relative displacement with components parallel to one or two pseudocubic axes. Antiphase tilting can be revealed by studying, instead, the 〈110〉 pseudocubic SADPs, each one allowing a single set of {odd, odd, odd}-type α reflections corresponding to antiphase tilting about two possible axes. Such patterns are shown in Figs. 1(e)–(g), each of which shows the presence of superlattice α reflections. If the first of these patterns is labelled as [110], then the α reflections marked correspond to (odd, odd, odd), where h ≠ l and k ≠ l, e.g. (). Such reflections can be evidence of antiphase tilting about either a or b; however, as it has already been proved (Figs. 1a–d) that octahedra are rotated in-phase about a, the correct interpretation of Fig. 1(e) must be that of antiphase tilting about b. Similarly, if Fig. 1(f) is interpreted as the [101] SADP then the α reflections marked correspond to (odd, odd, odd), where h ≠ k and k ≠ l, e.g. . Such reflections can be evidence of antiphase tilting about either a or c; however, again antiphase tilting about a can be discounted and the SADP interpreted as showing antiphase tilting about c. Finally, Fig. 1(g) shows the [011] SADP, the α reflections of which correspond to (odd, odd, odd) where h ≠ k and h ≠ l, e.g. , again demonstrating antiphase tilting about b and/or c. Thus, from the collection of superlattice reflections observed, it seems clear that LZT can be described as a perovskite with octahedra tilted in antiphase about two axes and in-phase about the third. What is left unquantified is the relative magnitude of each of these distortions.

Figure 1 SADPs of LZT indexed according to the simple pseudocubic perovskite unit cell (a = 3.9449 Å) corresponding to (a) [100], (b) [010], (c) [001], (d) [111], (e) [110], (f) [101] and (g) [011].

The possible tilt systems, according to Glazer's (1972, 1975) notation, are a⁺b⁻c⁻, a⁺a⁻c⁻, a⁺b⁻b⁻ and a⁺a⁻a⁻. Howard et al. (2003) showed by a group theoretical approach that, in fact, the a⁺b⁻c⁻, a⁺a⁻c⁻ and a⁺a⁻a⁻ tilt systems cannot be produced by octahedral tilting or cation ordering, leaving just a⁺b⁻b⁻, corresponding to Pmnb symmetry (Glazer, 1975) or P2₁/c (Howard et al., 2003). In either case, the basic perovskite unit is doubled in the a, b, and c directions. A new unit cell can be obtained by inscribing within the doubled pseudocubic cell a smaller one with a = 2a_c, b = c = 2^1/2a_c (the subscript c indicates the undoubled pseudocubic lattice constant). In the case of LZT, a ≃ 7.8898, b ≃ 5.5789, c ≃ 5.5789 Å. This orientation of the unit cell corresponds to Glazer's (1972, 1975) work, although Kucheiko et al. (1996) turned it around such that the long axis corresponded to b, presumably to agree with the usual description of CaTiO₃ in the standard Pnma setting (strangely, LMT models are typically turned such that c is the long axis).

The neutron diffraction pattern in Fig. 2 reveals much of the fine structure of LZT. The peak at 4.56 Å is a superlattice reflection which corresponds to {111} of the pseudocube or {101} and/or {110} of the orthorhombic/monoclinic unit cell described above. The geometrical relationship is (101) || (111)_c and (110) || _c (the subscript c again indicates indices relative to the pseudocubic axes). The appearance of such a peak in XRD is usually associated (Lee et al., 2000; Avdeev et al., 2002a,b; Seabra, Avdeev et al., 2003; Seabra, Salak et al., 2003; Seabra et al., 2004; Cho et al., 1998; Kim & Yoon, 2003; Anderson et al., 1993) with cation ordering on pseudocubic {111}, although this interpretation is slightly ambiguous, as the (101) reflection is allowed in Pmnb, which forbids such cation order. The supposition that the existence of a peak corresponding to {111} always implies the existence of cation order is generally incorrect and has no basis in the work of Glazer (1972, 1975) so often cited. For example, it is quite possible to create a disordered model of LZT in space group Pmnb, which shows, in calculated diffraction patterns, intensity at d = 4.56 Å. Such a peak corresponds to the allowed (101) reflection, equivalent to the pseudocubic (111). Such a model was developed for LMT by Meden & Čeh (1998); although not commented upon at the time, this model clearly shows intensity in this region despite the fact that Mg²⁺ and Ti⁴⁺ cations randomly share the 4b positions. This finding has important implications for the study of order in complex perovskites by diffraction, the effect of order on properties, and for Raman and IR studies of order which have used diffraction experiments to calibrate the spectroscopic results.

Figure 2 Neutron diffraction data from (a) the backscattered detector and (b) the 90° detector for LZT and the results of a Rietveld refinement in space group P21/n. The inset in (b) shows peak splitting indicative of a symmetry lower than tetragonal.

The correct space group must instead be determined from convergent-beam electron diffraction patterns, from single-crystal XRD or by sequential Rietveld refinements. Towards this end, a first attempt at refinement was made in space group Pmnb. A reasonable fit (wRp = 0.1512, Rp = 0.1432, χ² = 5.349) was obtained for this model over 556 reflections when all 14 structural variables were refined. During the process, small peaks corresponding to ZnO were noticed, and the fit improved (wRp = 0.1395, Rp = 0.1358, χ² = 4.554) when about 2.06 wt% ZnO was included in the calculations. As Pmnb forbids B-site ordering on pseudocubic {111}, one must look to subgroups for ordered models. Examining the centrosymmetric nonisomorphic subgroups of Pmnb, it is readily apparent that P2₁/n or are the only possible candidates. Space group would correspond to a tilt system of a⁻b⁻c⁻, antiphase tilting about all three pseudocubic axes, whereas the octahedra in LZT are clearly tilted in-phase about one of these axes (Figs. 1a and d). By this process of elimination, the only symmetry left is P2₁/n, which implies a tilt system of a⁺b⁻b⁻. Again, what is left to quantify is the relative magnitude of the antiphase tilts with respect to the in-phase tilt. Refinements of a fully ordered LZT model in P2₁/n yielded the best fit of all attempted models, with wRp = 0.0776, Rp = 0.0783, χ² = 1.408 and R_F ²= 0.0642 over 1031 LZT reflections and accommodating 2.15 wt% ZnO. The lattice parameters found were a = 7.89497 (5), b = 5.59640 (3), c = 5.58089 (3) Å, β = 90.034 (1)°. Attempting to partially disorder the structure resulted in a reasonable fit for a narrow range of neutron times of flight (34–90 ms) corresponding to d-spacings of 0.70–1.86 Å. The results showed that the degree of order was about 90%, in general agreement with previous work (Macke & Blasse, 1976; Macke, 1977; Avdeev et al., 2002a; Howard et al., 2003) on similar materials; however, extending the refinement up to 190 ms (d = 3.94 Å) showed the degree of order to be greater than 99%. For this reason, the Rietveld refinement of neutron diffraction data shown in Fig. 2 is based on the fully ordered model in P2₁/n symmetry. The fit has been extended to 5.8 Å in Fig. 2(b) with data from the 90° detector bank. The inset in Fig. 2(b) shows the broad peak at 4.56 Å split into (101), (01) and (110) peaks, indicating that, although b ≃ c and β ≃ 90°, the symmetry cannot be tetragonal.

Clearly, the unit cell is distorted only very slightly from the ideal tetragonal case (a = 7.8898, b = c = 5.5789 Å, β = 90°). Table 1 shows the calculated atomic positions, occupancies and isotropic displacement parameters for this model of LZT, and the structure is illustrated in Fig. 3. As suggested by Fig. 1, the La³⁺ positions are indeed shifted in an antiparallel fashion by 0.1050 and 0.1570 Å along [010]_c and [001]_c, respectively. The predicted in-phase tilting of octahedra about [100] is also present, with entire chains of octahedra along [100]_c tilted by ∼8.3° either clockwise or anticlockwise. The antiphase tilting in the octahedral chains along [010] and [001] is a smaller effect, with octahedra in the chains tilted alternately clockwise and anticlockwise by only ∼2.4°. The presence of the ZnO impurity phase is either the result of weighing errors or indicative of a nonstoichiometry in LZT, and work is currently underway to explain this impurity.

Table 1
Refined atomic parameters for La(Zn_1/2Ti_1/2)O₃

Standard uncertainties are given in parentheses.

Atom	Wycoff	x	y	z	Uiso
La	4(e)	0.250 (2)	0.0330 (9)	0.9933 (2)	0.0168 (2)
Zn	2(c)	0	0.5	0	0.0232 (3)
Ti	2(b)	0	0	0.5	0.0160 (4)
O1	4(e)	0.9605 (3)	0.2059 (3)	0.2234 (3)	0.0155 (4)
O2	4(e)	0.9593 (3)	0.7211 (3)	0.2971 (3)	0.0200 (5)
O3	4(e)	0.2415 (3)	0.9837 (1)	0.4224 (2)	0.0144 (3)

Figure 3 Diagram of the proposed crystal structure of La(Zn1/2Ti1/2)O3, viewed along a direction near [010] or [01]c.

The Ti—O bond lengths range from 1.9513 to 1.9576 Å, giving an overall Ti bond-valence sum of 4.1149 (3). Similarly, the Zn—O bond lengths range from 2.0880 to 2.0938 Å, resulting in an overall bond-valence sum for Zn of 2.1135 (3). There is greater variability in the La—O bond lengths, which range from 2.4116 (La—O3) to 3.3459 Å (La—O2), yielding a La bond-valence sum of 2.92757 (8). These values are all near the ideal valencies and match well those calculated from structural models of LMT. The O—Zn—O and O—Ti—O bond angles have values of either 88.28 (7) to 91.72 (7)° and 89.56 (7) to 90.74 (7)°, respectively, and are consistent with slightly distorted octahedra.

It is important to note that the relative strength of the peak at d = 4.56 Å in the P2₁/n space group does in fact imply some degree of cation ordering, in general agreement with work by Howard et al. (2003); however, such ordering cannot be inferred by the mere presence of this peak. Indeed, this reflection does not vanish when the B site is randomized. Curiously, the calculated structure factors (|F|) for the overlapping (110) and (101) reflections decrease by 56 and 78%, respectively, when the unit cell is disordered, but the structure factor for () is increased by 265%, creating an overall reduction of intensity for this peak of only 71%. Clearly, the existence of this peak cannot be used in itself to demonstrate cation order. Even for a perfectly ordered LZT structure with or without octahedral tilting, the peak would have a relative intensity in XRD of only about 1%, making it difficult to justify the adjective strong or distinguish it from a weaker version indicative of less order. Even in SADPs (Fig. 1), such spots can easily be explained in either Pmnb or P2₁/n by double diffraction, and some are actually allowed.

The SADPs of Fig. 1 can now be reinterpreted according to the calculated P2₁/n unit cell, and the resulting indexing is shown schematically in Fig. 4.

Figure 4 Schematic indexing, according to the proposed P21/n structure, of the SADPs in Fig. 1. Solid circles represent allowed reflections, while open circles represent reflections present via double diffraction. (a) [100], (b) [011], (c) [], (d) [102], (e) [111], (f) [] and (g) [001].

The finding of complete order in LZT contrasts with previous work on LMT (Macke & Blasse, 1976; Macke, 1977; Avdeev et al., 2002a) and its Nd analogue, Nd(Mg_1/2Ti_1/2)O₃ (Groen et al., 1986). Groen et al. (1986) suggest that a possible cause for the disorder may be twinning; however, LZT samples in this study also showed a high degree of twinning.

Owing to the almost exact coincidence of reflections in electron diffraction patterns, it was not possible to detect twins related by a 180° rotation about 〈010〉_c, which might be expected to occur; however, Fig. 5 shows evidence of twins related by a 90° rotation about 〈011〉 or 〈010〉_c. A direct comparison can be made with Fig. 1(b). The variants can be indexed as [011] and [], in which case the twin plane is either () or (), or [] and [], making the twin plane either (211) or (). In any case, the twin axis is 〈111〉 or 〈101〉_c. Such twins have been observed previously in simple perovskites (White et al., 1985). A sketch of the geometrical relationship between matrix and twin is shown in Fig. 6, with the common () and () or (211) and () indicated. The twins are related to the parent LZT (four unit cells of which are shown in the figure) according to the following matrix transformations:

corresponding to either Fig. 5(a) (rotation about [011]) or 5b (rotation about []). The SADPs in Figs. 5, 7 and 8 can all be indexed with reference to Fig. 6. Fig. 7(a) can be indexed as the matrix [011] SADP plus the twin-related [100] SADP. The twin plane in this case is (211), and the result is effectively an amalgam of Figs. 1(a) and 1(b). Fig. 7(b) shows the same two twin variants plus an additional one, oriented parallel to [], related to the matrix and the first twin by () and () twin planes, respectively. Fig. 8(a) can be indexed as a combination of two twin variants oriented along [120] and [], with a twin plane of (), or [] and [] with a twin plane of (). In either case, it can easily be shown that the 60° angle between matrix and twin {001} agrees exactly with the diagram in Fig. 6. Fig. 8(b) shows the same two variants plus a third related to the others by an additional {211} twin plane.

Figure 5 SADP from two overlapping twin variants related by a 90° rotation about 〈011〉 or pseudocubic 〈010〉. Horizontal ovals represent reflections from variant A, while vertical ovals are from variant B. Reflections left unmarked are common to both variants. The two variants can be indexed as [011] and [] or [] and [], making the twin plane {211} type, with a 〈111〉 twin axis. This geometry corresponds to a pseudocubic {110} twin plane and 〈110〉 twin axis.

Figure 6 Diagrammatic representation of the geometrical relationship between twin variants. The twin is related to the parent by a 90° rotation about [011] and a shared () or () twin plane in (a) or a 90° rotation about [] and a shared (211) or () twin plane in (b).

Figure 7 (a) SADP from two overlapping twin variants related by a {211} twin plane and a 90° rotation about 〈011〉. Horizontal ovals represent reflections from variant A oriented along 〈011〉, while vertical ovals are from variant B oriented along [100]. Reflections left unmarked are common to both variants. (b) SADP from three overlapping twin variants related by {211} twin planes. Horizontal ovals represent reflections from variant A oriented along 〈011〉; vertical ovals are from variant B oriented along [100]; and reflections marked with a circle arise from the third variant oriented opposite to variant A along 〈011〉. Reflections left unmarked are common to all three variants.

Figure 8 (a) SADP from two overlapping twin variants related by a {211} twin plane and a 90° rotation about 〈011〉. Horizontal and vertical ovals represent variants oriented oppositely along 〈120〉. Reflections left unmarked are common to both variants. (b) SADP from three overlapping twin variants related by {211} twin planes. Horizontal and vertical ovals have the same meaning as in (a), and circled reflections arise from a third variant related by another {211} twin plane and oriented similarly along 〈120〉. Reflections left unmarked are common to all three variants.

The microwave properties of dense (96% ρ_th) LZT samples agree well in some respects with previous literature on these materials; however, disparities were noted. At 4.25 GHz, the relative permittivity was measured as ∊_r = 34. This value agrees well with most reports on LZT (Cho et al., 1997, 1998, 2001); however, there is less agreement on the other properties. The best value of Qf found was 36 090 (4.25 GHz), significantly lower than the value given in most other reports. Similarly, although the measured value of τ_f, −70 MK⁻¹, agrees well with the previous work of Kucheiko et al. (1996), it is much lower than that reported by most other groups. As complete order was found in LZT samples in this study, it is difficult to ascribe these discrepancies, especially in Q, to the degree of order achieved. Other explanations may involve twinning or the ZnO impurity phase detected in the samples. Further investigation is warranted.

4. Conclusions

The structure of LZT has been determined by a combination of electron diffraction and Rietveld refinement of neutron diffraction data. It has monoclinic P2₁/n symmetry, with lattice constants a = 7.8950, b = 5.5964, c = 5.5809 Å, β = 90.034°. The B sites are completely ordered on {110}, although the presence of (111) superlattice reflections is insufficient to unambiguously establish this fact. Numerous {211}-type twins were also observed. The microwave dielectric properties measured were ∊_r = 34, Qf = 36 090 and τ_f = −70 MK⁻¹.

Supporting information

Computing details

Figures

(LZT)

Crystal data

?	V = 246.58 Å^3
Mr = ?	Z = ?
Monoclinic, P21/n	Dx = 6.560 Mg m^−3
a = 7.8950 Å	Cu Kα1 radiation, λ = 1.54056 Å
b = 5.5964 Å	µ = 1491.34 mm^−1
c = 5.5809 Å	× × mm
β = 90.034°

Data collection

h = ?→?	l = ?→?
k = ?→?

Refinement

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

	x	y	z	Uiso*/Ueq
La	0.25	0.03308	0.9933	0.05*
Zn	0	0.5	0	0.05*
Ti	0	0	0.5	0.05*
O1	0.9605	0.2059	0.2234	0.05*
O2	0.9593	0.7211	0.2971	0.05*
O3	0.2415	0.9837	0.4224	0.05*

Bond lengths (Å)

La—O1	2.7950	La—O3	2.4116
La—O1	3.3275	La—O3	3.1111
La—O1	2.4517	La—O3	2.5662
La—O1	2.6772	Zn—O1	2.0883
La—O2	3.3459	Zn—O2	2.0938
La—O2	2.7820	Zn—O3	2.0880
La—O2	2.6919	Ti—O1	1.9513
La—O2	2.4403	Ti—O2	1.9548
La—O3	3.1988	Ti—O3	1.9576

 

Footnotes

¹Supplementary data for this paper are available from the IUCr electronic archives (Reference: WS5035 ). Services for accessing these data are described at the back of the journal.