Unprecedented phase transition sequence in the perovskite Li0.2Na0.8NbO3

Dixon, C.A.L.; McNulty, J.A.; Huband, S.; Thomas, P.A.; Lightfoot, P.

doi:10.1107/S2052252517002226

research papers

IUCrJ

Volume 4| Part 3| May 2017| Pages 215-222

ISSN: 2052-2525

https://doi.org/10.1107/S2052252517002226

CHEMISTRY | CRYSTENG

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Unprecedented phase transition sequence in the perovskite Li_0.2Na_0.8NbO₃

Charlotte A. L. Dixon,^a Jason A. McNulty,^a Steven Huband,^b Pamela A. Thomas ^b and Philip Lightfoot ^a ^*

^aSchool of Chemistry and EaStCHEM, University of St Andrews, St Andrews KY16 9ST, Scotland, and ^bDepartment of Physics, University of Warwick, Coventry CV4 7AL, England
^*Correspondence e-mail: pl@st-andrews.ac.uk

Edited by A. Fitch, ESRF, France (Received 19 January 2017; accepted 9 February 2017; online 8 March 2017)

The perovskite Li_0.2Na_0.8NbO₃ is shown, by powder neutron diffraction, to display a unique sequence of phase transitions at elevated temperature. The ambient temperature polar phase (rhombohedral, space group R3c) transforms via a first-order transition to a polar tetragonal phase (space group P4₂mc) in the region 150–300°C; these two phases correspond to Glazer tilt systems a⁻a⁻a⁻ and a⁺a⁺c⁻, respectively. At 500°C a ferroelectric–paraelectric transition takes place from P4₂mc to P4₂/nmc, retaining the a⁺a⁺c⁻ tilt. Transformation to a single-tilt system, a⁰a⁰c⁺ (space group P4/mbm), occurs at 750°C, with the final transition to the aristotype cubic phase at 850°C. The P4₂mc and P4₂/nmc phases have each been seen only once and twice each, respectively, in perovskite crystallography, in each case in compositions prepared at high pressure.

Keywords: perovskite; ferroelectric; powder neutron diffraction.

1. Introduction

Perovskites continue to fascinate solid-state scientists, both for their chemical and structural diversity and for their ever-growing list of physical and chemical properties and applications (Chakhmouradian & Woodward, 2014 ; Jeon et al., 2014 ). Considerable effort in the last few years has focused on alkali metal niobate perovskites for their promising piezoelectric and electro-optic properties (Jo et al., 2009 ; Saito et al., 2004 ). Within this family, the Li_xNa_1 − xNbO₃ (hereafter abbreviated LNN-X, where X represents the % Li composition) system has been shown to display some curious features at ambient temperature (Peel et al., 2013 ). Detailed crystallographic characterization of this system at elevated temperatures has only been reported for one specific composition, LNN-12 (Mishra et al., 2015 ). As part of a more comprehensive study of the high-temperature phase diagram of LNN-X we now report a detailed study of LNN-20 by high-resolution powder neutron diffraction. This reveals some unique structural behaviour, including two very rare structural variants of perovskite, based on an unusual combination of tilting of NbO₆ octahedra.

2. Experimental

2.1. Synthesis

LNN-20 was prepared by traditional ceramic methods. Stoichiometric amounts of Na₂CO₃ (99.9% Sigma-Aldrich), Li₂CO₃ (99.9% Sigma-Aldrich) and Nb₂O₅ (99.9% Alfa Aesar) were dried at 100°C for 24 h, ground for a period of 30 min and pressed into pellets of approximately 10 mm diameter and 5 mm thickness. The pellet was then annealed at 1000°C for a period of 24 h, before being cooled at a rate of 10° min⁻¹. We assume no deviation of alkali metal content due to volatility, and a fixed Li/Na and (Li,Na)/Nb ratio in the subsequent analysis.

2.2. Powder diffraction

Sample purity was analysed by powder X-ray diffraction using a Rigaku miniflex 600 X-ray diffractometer using Cu Kα_1,2 (λ = 1.54056, 1.54439 Å) radiation. Powder neutron diffraction (PND) data were collected on the HRPD instrument at the ISIS facility at selected temperatures between 20 and 900°C. The sample was contained in a cylindrical vanadium can. For data analysis, two detector banks, centred at ∼ 168° and 90°, and covering d-spacing ranges of 0.7 < d < 2.6 Å and 0.9 < d < 4.0 Å, respectively, were used. Data were analysed by the Rietveld method, using the GSAS/EXPGUI package (Larson & Von Dreele, 1994 ; Toby, 2001 ), and interpretation of the results was assisted using symmetry mode analysis via the ISODISTORT suite (Campbell et al., 2006 ). A consistent refinement strategy was used in each case, including 3, 2, 18 and 6 parameters to model instrumental variables, scale factors, background and peak-shapes for each dataset, together with appropriate lattice parameters, atomic coordinates (Li and Na constrained to be equal) and atomic displacement parameters (Li and Na constrained to be equal, and some additional constraints, detailed later).

2.3. Second-harmonic generation (SHG)

A polycrystalline powder sample of LNN-20 was contained in glass cells capable of withstanding a high-temperature study. Calibration of the furnace was then performed, followed by null checks, before the sample was placed in a small furnace consisting of an aperture normal to the orientation of the sample. Through these apertures an intense beam (100 mJ, 100 ms pulse) was exposed to the sample from a Q-switched Nd:YAG laser (λ = 1064 nm) following the setup of Kurtz & Perry (1968 ). Filtration with a green filter of the scattered radiation was carried out to remove traces of the fundamental beam whilst the second harmonic signal (if any was present) was measured using a photomultiplier (PMT) and subsequently displayed on an oscilloscope as signal versus time. A beam splitter and photodiode were utilized to monitor the fundamental beam, allowing for the necessary corrections to variations in the laser output. The intensity of the second harmonic was then normalized by dividing by the square of the intensity of the incident beam (Kurtz & Perry, 1968). Repeat measurements as a function of temperature were made to remove the effects of any residual strain from the sample preparation and to ensure the reproducibility of the results.

2.4. Dielectric measurements

Pellets were electroded with Ag paste (RS components) or sputtered Au. Dielectric measurements were performed with a Wayne Kerr 6500B impedance analyser with the sample mounted in a tube furnace. Capacitance and loss data were recorded in the frequency range 100 Hz–10 MHz on heating and cooling at a rate of 2 K min⁻¹ over the temperature range ambient to approximately 600°C.

3. Results and discussion

3.1. Thermal evolution of the crystal structure

3.1.1. Room temperature to 500°C

At ambient temperature the PND data can be successfully modelled using a majority perovskite phase of space-group symmetry R3c, in agreement with our earlier work (Peel et al., 2013). There is a minor additional rhombohedral phase present all the way to 900°C; this phase corresponds to a LiNbO₃-like material, essentially isostructural to the majority perovskite phase, but of composition close to LiNbO₃. The co-existence of two distinct rhombohedral phases has been noted in our previous work (Peel et al., 2013), with the Li-rich phase being labelled `Li-R3c' in that work. Two phase refinements suggest a phase fraction, constant versus T, of only ∼ 3% for the Li-R3c phase. Thus for simplicity, and to allow more valid comparisons of the various models to be discussed for the majority perovskite phase, we have chosen not to incorporate this minor phase into all of the refinements presented here. It is most clearly seen at the highest temperatures, and is highlighted in a two-phase refinement of the data at 900°C (see Fig. S3 of the supporting information). All further discussions omit reference to the minor Li-R3c phase.

The majority rhombohedral phase, which corresponds to the Glazer tilt system a^-a^-a^-, but also includes an additional polar distortion, may be considered isostructural with the low-temperature form of NaNbO₃ (and as a less distorted version of the stable phase of LiNbO₃). On warming to 150°C a second phase is seen to appear, which becomes the only phase present by 300°C (these two phases co-exist at temperatures of 150, 200 and 250°C, with phase fractions of ∼ 74/26, 20/80 and 7/93%, respectively, which provides evidence of a first-order phase transition).

Careful Rietveld analysis is required to ascertain the exact nature of the higher-temperature phase. Perovskite crystallography is often dominated by the presence of characteristic `octahedral tilt' distortions: in simple cases (i.e. for a 2 × 2 × 2 array of corner-linked octahedra) there are options of `in-phase' or `out-of-phase' tilts relative to each of the three axes of the parent cubic phase. The possible combinations of these tilts were first classified by Glazer (1972 ) and subsequently re-assessed using group-theoretical methods to produce 15 unique possibilities (Howard & Stokes, 1998 ). Thus, for example, the Glazer symbol a^-a^-a^- signifies equal out-of-phase tilts around all three axes of the parent cubic phase. The simplest and least ambiguous means of determining which tilt system is present is to identify characteristic peaks in the diffraction pattern which are due to either in-phase or out-of-phase tilts. These independent sets of peaks may be designated by the labels M and R, or more specifically M₃⁺ (in-phase tilt) and R₄⁺ (out-of-phase tilt).

Key portions of the diffraction patterns of LNN-20 at 100°C and 300°C are shown in Fig. 1. It can be readily seen that superlattice peaks (due predominantly to octahedral tilting) are located at R positions only in the former, but at both R and M positions in the latter; in other words, in addition to out-of-phase tilts, the higher-temperature phase contains in-phase tilts. The key question is `what are the directions of the constituent tilts relative to the cubic parent phase'?

Figure 1
Portions of Rietveld refinement carried out on PND data at (a) 100°C and (b) 300°C. In (a) the peaks in the region 2.2–2.3 Å arise from the subcell; the peak near 2.35 Å in both (a) and (b) is due to the R₄⁺ tilt mode. The additional peaks (`doublets' near d = 2.09 and 2.48 Å) in (b) are due to the M₃⁺ tilt mode. The small peak near d = 2.14 Å is from the vanadium sample holder and the `shoulder' near d = 2.27 Å is due to the minority Li-R3c phase.

The analysis of Howard & Stokes (1998) suggests four possible structural models comprising both types of tilts, designated a⁺a⁺c^-, a⁰b⁺c^-, a⁺b^-b^- and a⁺b^-c^-. The first three of these were each tested against the PND data at 300°C [the latter has unnecessarily low (monoclinic) symmetry and is discarded]. The first two models are described in space groups P4₂/nmc and Cmcm, respectively, with unit cells of approximate metrics 2 × 2 × 2 a_p, where a_p represents the aristotype cubic perovskite unit-cell parameter. Both these models give good quality fits, whereas the a⁺b^-b^- option (space group Pnma, which corresponds to the most common perovskite tilt system, with unit-cell metrics approximately $[\sqrt 2]$ × 2 × $[\sqrt 2]$ a_p), does not adequately describe the observed peak splittings.

Further details of the two most promising models, P4₂/nmc and Cmcm, are given in Table 1, together with several models representing non-centrosymmetric subgroups of P4₂/nmc (see later). Both centrosymmetric structural models have the same number of variable atomic parameters (coordinates plus isotropic displacement parameters) which makes direct numerical comparison of fit quality straightforward. In addition to the significantly improved fit (χ²), the a⁺a⁺c^- (P4₂/nmc) model can be seen graphically to be significantly better (Fig. 2). Moreover the atomic displacement parameters for the O atoms show much more uniform behaviour [U_iso (Å²) values for the three distinct O atoms in the P4₂/nmc and Cmcm models, respectively are 0.0152 (7), 0.0136 (7), 0.0179 (4) and 0.0137 (6), −0.0028 (6), 0.0348 (10)] – a clear indication that the octahedral tilt behaviour is modelled correctly in the a⁺a⁺c^- model and incorrectly for a⁰b⁺c^-.

Table 1
Comparison of the respective Rietveld refinements for the two chosen centrosymmetric models proposed for the phase at 300°C, together with the feasible non-centrosymmetric subgroups of P4₂/nmc

N_ref defines the total number of variable parameters refined, N_xyz is the number of variable atomic coordinates and N_{U_iso} the number of isotropic atomic displacement parameters (ADPs) refined. Occupancies of the A-sites are fixed at 80% Na/20% Li in each case, with Li/Na at each particular site having the same ADP. For the non-centrosymmetric models, O atom ADPs were constrained in pairs according to the parent phase, as appropriate

Space group	χ²	N_ref	N_xyz	N_{U_iso}
P4₂mc	3.513	55	17	7
$[P {\overline 4} m2]$	4.263	55	17	7
P4₂2₁2	4.428	50	12	7
$[P{\overline 4}2_1c]$	4.582	51	13	7
P4₂/nmc	4.553	44	7	7
Cmcm	6.692	44	7	7

Figure 2
Portion of Rietveld refinement (PND) of LNN-20 at 300°C modelled in (a) Cmcm; (b) P4₂/nmc and (c) P4₂mc space groups.

The above analysis confirms the tilt system of the phase present at 300°C to be a⁺a⁺c^-. However, this assumes the phase to be centrosymmetric. Second harmonic generation offers a sensitive powder technique with the ability to establish the centrosymmetric or non-centrosymmetric nature of a crystalline phase, independently of diffraction data. We therefore carried out second-harmonic generation (SHG) measurements as a function of temperature, as shown in Fig. 3.

Figure 3
SHG data generated from a sample of LNN-20 showing clear SHG response to at least 450°C on heating.

This experiment clearly shows a significant SHG signal to at least 450°C, thus supporting the presence of a non-centrosymmetric phase. Hence, the simplest non-centrosymmetric subgroups of P4₂/nmc were considered, and these models are presented in Table 1. All four potential models were treated similarly with the same set of `standard' refined parameters, as described in §2.1. Atomic coordinates and displacement parameters were then refined for each of the models with displacement parameters constrained for those crystallographic sites that were `split' in two upon distortion to the lower symmetry phase. It can be seen that the P4₂mc model provides the best description of the phase present in the region 300 < T < 500°C, consistent with both the observed tilt system and the presence of SHG signal. We note that this is the only polar subgroup; the other three subgroups tested are non-centrosymmetric but not polar. The final, refined model for space group P4₂mc at 300°C is presented in Table 2, and the corresponding Rietveld fit in Fig. 4. One further point here is worthy of comment: the U_iso values of the A-site cations may suggest a possible partial ordering of Li/Na over these sites (Li has a negative scattering length); we tested this, but no clear-cut ordering pattern or significant lowering of agreement parameters was observed.

Table 2
Crystallographic data for LNN-20 at 300°C modelled in the P4₂mc space group [a = 7.7706 (2), c = 7.8498 (3) Å]

Atom	Wycoff position	x	y	z	100 × U_iso (Å²)
Na1†	2c	0	0.5	0.726 (3)	4.1 (3)
Na2	2c	0	0.5	0.258 (6)	4.1 (3)
Na3	2b	0.5	0.5	0.253 (3)	0.2 (4)
Na4	2a	0	0	0.236 (2)	−0.7 (3)
Nb1	8f	0.2489 (5)	0.7493 (5)	0	0.48 (2)
O1	4e	0.2281 (8)	0.5	0.4843 (7)	1.39 (9)
O2	4e	0.2781 (8)	0.5	0.0552 (7)	0.75 (7)
O3	4d	0.2864 (8)	0	0.5538 (8)	0.75 (7)
O4	4d	0.2115 (8)	0	0.0026 (6)	1.39 (9)
O5	8f	0.2858 (10)	0.7874 (11)	0.2655 (4)	1.52 (4)

†Positions Na1–Na4 have fixed occupancy Na_0.8Li_0.2; the derived U_iso values (especially the unphysical value for Na4) illustrate the possibility of a slight Na/Li ordering.

Figure 4
Portion of Rietveld refinement (PND) of LNN-20 at 300°C using the P4₂mc model.

3.1.2. 500 < T < 850°C

In addition to the SHG signal (Fig. 3), which supports the presence of a non-centrosymmetric LNN-20 phase to at least 450°C, dielectric data support an additional structural event in the region of 450–500°C (Fig. 5).

Figure 5
Relative permittivity data for LNN-20 at selected frequencies, obtained on cooling.

Further corroborating evidence of a phase transition in this region could be seen from the PND data, with a sharp merging of several peaks when the temperature was elevated from 450°C to 500°C. For completeness the data at 500°C were modelled in the P4₂mc space group and whilst the χ² was lower for P4₂mc over P4₂/nmc (2.75 and 3.17, respectively) this was most likely an artefact due to the increased degrees of freedom in the lower symmetry space group; indeed it was found that the model was not stable upon full, unrestrained refinement. Key superlattice peaks corresponding to both M-point and R-point tilts are still observed above 500°C, however. In light of this, the models for each of the standard a⁺a⁺c^-, a⁰b⁺c^- and a⁺b^-b^- tilt systems, previously discounted for the phase at 300°C, were trialled as fits to this new (presumed centrosymmetric) phase at 500°C. Of these three tilt systems the fit to the P4₂/nmc model was clearly the most satisfactory at this temperature (χ² value for P4₂/nmc = 3.175, Pnma = 4.045, Cmcm = 4.442). Evolution of the lattice parameters versus temperature, based on the P4₂mc (250–450°C), P4₂/nmc (500–700°C) and subsequent higher temperature phases is shown in Fig. 6. We note, in particular, the marked tetragonal distortion in the P4₂mc phase field, related to the polar cation displacements along c. This distortion disappears on entering the pseudo-cubic P4₂/nmc phase, but an enhanced tetragonality reappears at 750°C, with the gradual emergence of a new phase. Finer temperature increments would be necessary to establish a more precise point for the P4₂mc to P4₂/nmc phase transition, but this clearly occurs in the range 450°C to 500°C, consistent with the SHG, dielectric data and PND.

Figure 6
Normalized lattice parameters versus T, obtained from Rietveld refinement of PND data. For the tetragonal phases, the a lattice parameter is represented by red circles and c by blue triangles. In regions where phase co-existence occurs, only the majority phase present at each temperature is shown.

As the centrosymmetric P4₂/nmc space group remained the best fit to the diffraction data in the region 500 ≤ T ≤ 600°C, a single phase refinement using this model was carried out over these temperatures. Upon reaching 650°C further structural changes were indicated in the diffraction data, with a developing asymmetry of several peaks. This new phase was seen to `grow in' as the temperature was increased to 800°C where complete loss of the superlattice peaks attributed to the R₄⁺ out-of-phase tilt mode occurs, suggesting complete conversion to the emergent phase. For a centrosymmetric perovskite with only M₃⁺ (in-phase) tilts, the analysis of Howard & Stokes (1998) suggests three possible tilt systems; a⁺a⁺a⁺ (space group $[Im{\overline 3}]$ ), a⁰b⁺b⁺ (I4/mmm) and a⁰a⁰c⁺ (P4/mbm). Of these, the a⁺a⁺c^- to a⁰b⁺b⁺ transition is expected to be second order; clearly this is not the case here. The other two options are required to be first order, compatible with the phase co-existence observed here. The cubic a⁺a⁺a⁺ option can easily be discounted, thus leaving the tilt system a⁰a⁰c⁺ (P4/mbm) as the only viable option.

The tetragonal model P4/mbm with a⁰a⁰c⁺ tilt system was indeed confirmed to provide the best fit. A two phase refinement of P4₂/nmc and P4/mbm models was carried out for 650 ≤ T ≤ 750°C, with a single phase refinement in the P4/mbm space group for the 800°C diffraction data (Fig. 7). Elevation of the temperature to 850°C resulted in the loss of all remaining superlattice peaks, signalling the disappearance of the in-phase tilt along the c-axis. All subsequent data were therefore fitted to the aristotype cubic space group $[Pm{\overline 3}m]$ .

Figure 7
Portion of Rietveld refinement (PND) of LNN-20 at 800°C using the P4/mbm model.

3.2. Discussion

The phase transition sequence reported here (R3c – P4₂mc – P4₂/nmc – P4/mbm – $[Pm{\overline 3}m]$ ) is unique in perovskite crystallography. Moreover, the unusual structural variants displaying the a⁺a⁺c^- tilt system (space groups P4₂/nmc and P4₂mc) present throughout the intermediate temperature range studied here have only been previously reported twice and once each, respectively. The general trends in octahedral tilt preferences versus temperature (i.e. from `in-phase' tilts only at high temperature to `out-of-phase' tilts only at low temperature) mirror those in NaNbO₃ itself (Megaw, 1974 ; Peel et al., 2012 ), although the specific details are quite different in the two cases, with NaNbO₃ showing more complex, longer-range tilt sequences. Such longer-range superlattices can be definitively ruled out for LNN-20 from the present data.

The crystal structure of the ambient temperature, R3c, phase has been discussed previously (Peel et al., 2013). The crystal structure of the P4₂mc phase at 300°C is shown in Fig. 8. Corresponding bond lengths and selected bond angles are given in Table 3. Fig. 9(a) shows the distortion of the NbO₆ octahedron. The off-centre displacement of the Nb atom, along the polar c-axis, is evident, and resembles that in much simpler tetragonal ferroelectric perovskites (without octahedral tilting) such as the ambient-temperature phase of BaTiO₃. In contrast to this difference of ∼ 0.243 Å in axial Nb—O bond lengths, the corresponding ab-plane bond lengths are roughly equal. The thermal evolution of these Nb—O bonds is shown in Fig. 10, and this clearly shows the centralization of the Nb atoms within its octahedral site as the P4₂mc – P4₂/nmc transition is approached. The variation in the two octahedral tilt mode, M₃⁺ and R₄⁺, versus temperature across the P4₂mc – P4₂/nmc phase region is shown in Fig. 11. The M₃⁺ mode amplitude shows a uniform reduction with increasing temperature, whereas the R₄⁺ mode exhibits a step change at the 500°C transition, presumably in order to accommodate the transition to the centrosymmetric state.

Table 3
Bond lengths and selected bond angles of the P4₂mc phase at 300°C, Na—O bond lengths over 2.7 Å are not reported

Na—O	Bond length (Å)	Nb—O	Bond length (Å)	Nb—O—Nb	Bond angle (°)
Na1—O1 × 2	2.597 (17)	Nb—O1	1.963 (4)	Nb—O1—Nb	167.8 (4)
Na1—O5 × 4	2.365 (3)	Nb—O2	1.999 (4)	Nb—O2—Nb	150.8 (4)
Na2—O1 × 2	2.51 (3)	Nb—O3	1.999 (4)	Nb—O3—Nb	151.1 (4)
Na2—O2 × 2	2.69 (3)	Nb—O4	1.969 (4)	Nb—O4—Nb	163.3 (4)
Na2—O3 × 2	2.31 (3)	Nb—O5	2.125 (3)	Nb—O5—Nb	156.77 (10)
Na3—O2 × 2	2.322 (17)	Nb—O5'	1.882 (3)
Na4—O3 × 2	2.644 (12)
Na4—O4 × 2	2.460 (15)
Na4—O4 × 2	2.664 (15)

Figure 8
Crystal structure of the P4₂mc phase at 300°C showing (a) the view down the a-axis highlighting in-phase tilting in this direction, and off-centring of Nb atoms along the polar c-axis and (b) the out-of-phase tilt along the c-axis.

Figure 9
Schematic of NbO₆ octahedron in the P4₂mc phase at 300°C highlighting the polar Nb displacement (difference between Nb—O5 and Nb—O5′ bond lengths ∼ 0.243 Å). The symmetry operators acting upon the Nb—O5 and Nb—O5′ bonds are x, y, z and $[1-y, 1-x, -{1\over 2} + z]$ , respectively.

Figure 10
Thermal evolution of Nb—O bond lengths over the region 300 < T < 500°C, showing a decrease in the off-centring of the Nb atom within the NbO₆ octahedron as the P4₂mc – P4₂/nmc phase transition is approached.

Figure 11
Thermal evolution of the two tilt modes throughout the P4₂mc – P4₂/nmc phase field. Note the discontinuous evolution of the R₄⁺ mode.

As suggested earlier, the a⁺a⁺c^- Glazer tilt system has only been observed very rarely: twice in its aristoype form, space group P4₂/nmc (Leinenweber & Parise, 1995 ; Shimura et al., 2017 ), once in the polar form, P4₂mc, also observed here (Aimi et al., 2014 ), and additionally in a B-site ordered variant, space group P4₂/n (Solana-Madruga et al., 2016 ). Each of these earlier reports relate to compounds prepared at high pressure, viz. CaFeTi₂O₆ (Leinenweber & Parise, 1995), MnLnMnSbO₆ (Solana-Madruga et al., 2016), CaMnTi₂O₆ (Aimi et al., 2014) and LnMn(Ga_0.5Ti_0.5)₂O₆ (Shimura et al., 2017). Each of these high-pressure-prepared phases incorporate unusually small cations (Fe²⁺ or Mn²⁺) at the A-site, and consequently exhibit complete A-site cation ordering across geometrically distinct sites. In particular the Fe²⁺ or Mn²⁺ cations in CaFeTi₂O₆ and CaMnTi₂O₆ occupy two distinct sites of approximately tetrahedral and square-planar geometry, each having four significantly shortened A—O contacts. Although it is tempting to suggest that such a structure might be chosen in the present case in order to permit a degree of Li/Na ordering, there is insufficient evidence from the present data to support this possibility. Aimi et al. (2014) reported ferroelectric hysteresis at room temperature in CaMnTi₂O₆, and a phase transition to the paraelectric P4₂/nmc phase at 630 K. Unusually they show that this transition has a partial order–disorder nature, with the square-planar Mn site (only) displaying disorder in the P4₂/nmc phase. Again, no evidence for such an occurrence can be definitively gleaned from the present study. The off-centre displacement of the B-site cation (Ti⁴⁺) in CaMnTi₂O₆ has a similar magnitude to that reported for Nb⁵⁺ here (Fig. 9). However, the geometries of the A-site cations are quite different between LNN-20 and CaMnTi₂O₆. Rather than having well defined four-coordinate geometries the A-sites in LNN-20 have a less regular geometry, as shown in Figs. S5 and S6.

The third tetragonal polymorph observed in the present study (the P4/mbm phase) is observed in the high-temperature phase diagram of NaNbO₃, and also occurs in the variable-temperature phase diagram of several other perovskites, for example, NaMgF₃ (Knight et al., 2015 ) and CsSnI₃ (Yamada et al., 1991 ). On transforming to the cubic phase at 850°C, the remaining in-phase tilts are lost, although some evidence for residual localized octahedral tilting can be inferred from the anisotropic nature of the O atom displacement parameters [U¹¹ = 0.0094 (5), U³³ = 0.0677 (4) Å²].

4. Conclusions

The thermal evolution of the phase behaviour and crystal structure of the perovskite ferroelectric Li_0.2Na_0.8NbO₃ (LNN-20) has been characterized using powder neutron diffraction, supported by second-harmonic generation and dielectric measurements. Persistence of a non-centrosymmetric perovskite phase was confirmed up to at least 500°C. The phase progression is determined as R3c – P4₂mc – P4₂/nmc – P4/mbm – $[Pm\bar 3m]$ on increasing temperature from ambient to 900°C. This phase transition sequence demonstrates the identification of two rare phases with regard to the perovskite structure: both the polar P4₂mc and centrosymmetric P4₂/nmc phases have the Glazer tilt system a⁺a⁺c^-, and each structure type has been reported only once or twice previously in a perovskite. The ultimate reasons for Li_0.2Na_0.8NbO₃ to adopt such an unusual sequence of phases remains to be determined.

Supporting information

Link https://doi.org/10.17630/c97a6cc7-05e8-4f3a-b881-0ee334dee69d
Raw powder neutron diffraction data

Crystal structure: contains datablocks LNN20R3C_publ, LNN20R3C_overall, LNN20R3C_phase_1, LNN20R3C_phase_2, LNN20R3C_p_01, LNN20R3C_p_02. DOI: https://doi.org/10.1107/S2052252517002226/fc5017sup1.cif

Crystal structure: contains datablocks P42NMC_publ, P42NMC_overall, P42NMC_phase_1, P42NMC_phase_2, P42NMC_p_01, P42NMC_p_02. DOI: https://doi.org/10.1107/S2052252517002226/fc5017sup2.cif

Crystal structure: contains datablocks LNN20_P4MBM_800C_publ, LNN20_P4MBM_800C_overall, LNN20_P4MBM_800C_phase_1, LNN20_P4MBM_800C_phase_2, LNN20_P4MBM_800C_p_01, LNN20_P4MBM_800C_p_02. DOI: https://doi.org/10.1107/S2052252517002226/fc5017sup3.cif

Crystal structure: contains datablocks LNN20_900C_CUBIC_publ, LNN20_900C_CUBIC_overall, LNN20_900C_CUBIC_phase_1, LNN20_900C_CUBIC_phase_2, LNN20_900C_CUBIC_p_01, LNN20_900C_CUBIC_p_02. DOI: https://doi.org/10.1107/S2052252517002226/fc5017sup4.cif

Crystal structure: contains datablocks LNN20_P42MC_300C_publ, LNN20_P42MC_300C_overall, LNN20_P42MC_300C_phase_1, LNN20_P42MC_300C_phase_2, LNN20_P42MC_300C_p_01, LNN20_P42MC_300C_p_02. DOI: https://doi.org/10.1107/S2052252517002226/fc5017sup5.cif

Computing details top

(LNN20R3C_phase_1) top

Crystal data top

Li_0.20Na_0.80NbO₃	c = 13.7441 (3) Å
M_r = 160.68	V = 354.52 (2) Å³
Trigonal, R3c	Z = 6
a = 5.45750 (13) Å	T = 293 K

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Na1	0.0	0.0	0.2519 (3)	0.0013 (5)*	0.8
Nb1	0.0	0.0	−0.00223 (9)	−0.0022 (2)*
O1	0.09883 (15)	0.3391 (2)	0.06489	0.00549 (18)*
Li1	0.0	0.0	0.2519 (3)	0.0013 (5)*	0.2

Geometric parameters (Å, º) top

Na1—Na1ⁱ	3.8956 (1)	Nb1—O1	1.8890 (12)
Na1—Na1ⁱⁱ	3.8956 (1)	Nb1—O1^xi	1.8890 (12)
Na1—Na1ⁱⁱⁱ	3.8956 (1)	Nb1—O1^xii	1.8890 (12)
Na1—Na1^iv	3.8956 (1)	Nb1—O1^iv	2.1019 (12)
Na1—Na1^v	3.8956 (1)	Nb1—O1^xxiii	2.1019 (12)
Na1—Na1^vi	3.8956 (1)	Nb1—O1^xxiv	2.1019 (12)
Na1—Nb1	3.493 (4)	Nb1—Li1^xix	3.379 (4)
Na1—Nb1^vii	3.379 (4)	Nb1—Li1^xx	3.3336 (12)
Na1—Nb1ⁱ	3.3725 (13)	Nb1—Li1^xxi	3.3336 (12)
Na1—Nb1ⁱⁱ	3.3725 (13)	Nb1—Li1^xxii	3.3336 (12)
Na1—Nb1ⁱⁱⁱ	3.3725 (13)	Nb1—Li1^iv	3.3725 (13)
Na1—Nb1^viii	3.3336 (12)	Nb1—Li1^v	3.3725 (13)
Na1—Nb1^ix	3.3336 (12)	Nb1—Li1^vi	3.3725 (13)
Na1—Nb1^x	3.3336 (12)	O1—Na1	3.054 (3)
Na1—O1	3.054 (3)	O1—Na1^xxii	2.567 (3)
Na1—O1^xi	3.054 (3)	O1—Na1^v	2.3596 (7)
Na1—O1^xii	3.054 (3)	O1—Na1^vi	3.1274 (5)
Na1—O1ⁱ	2.3596 (7)	O1—Nb1	1.8890 (12)
Na1—O1ⁱⁱ	3.1274 (5)	O1—Nb1ⁱⁱⁱ	2.1019 (12)
Na1—O1^xiii	2.3596 (7)	O1—Li1^xxii	2.567 (3)
Na1—O1^xiv	3.1274 (5)	O1—Li1^v	2.3596 (7)
Na1—O1^xv	3.1274 (5)	Li1—Nb1^vii	3.379 (4)
Na1—O1^xvi	2.3596 (7)	Li1—Nb1ⁱ	3.3725 (13)
Na1—O1^viii	2.567 (3)	Li1—Nb1ⁱⁱ	3.3725 (13)
Na1—O1^xvii	2.567 (3)	Li1—Nb1ⁱⁱⁱ	3.3725 (13)
Na1—O1^xviii	2.567 (3)	Li1—Nb1^viii	3.3336 (12)
Nb1—Na1	3.493 (4)	Li1—Nb1^ix	3.3336 (12)
Nb1—Na1^xix	3.379 (4)	Li1—Nb1^x	3.3336 (12)
Nb1—Na1^xx	3.3336 (12)	Li1—O1ⁱ	2.3596 (7)
Nb1—Na1^xxi	3.3336 (12)	Li1—O1^xiii	2.3596 (7)
Nb1—Na1^xxii	3.3336 (12)	Li1—O1^xvi	2.3596 (7)
Nb1—Na1^iv	3.3725 (13)	Li1—O1^viii	2.567 (3)
Nb1—Na1^v	3.3725 (13)	Li1—O1^xvii	2.567 (3)
Nb1—Na1^vi	3.3725 (13)	Li1—O1^xviii	2.567 (3)

Nb1^vii—Na1—Nb1ⁱ	110.89 (6)	Na1^xix—Nb1—O1	119.23 (3)
Nb1^vii—Na1—Nb1ⁱⁱ	110.89 (6)	Na1^xix—Nb1—O1^xi	119.23 (3)
Nb1^vii—Na1—Nb1ⁱⁱⁱ	110.89 (6)	Na1^xix—Nb1—O1^xii	119.23 (3)
Nb1^vii—Na1—Nb1^viii	70.94 (6)	Na1^xix—Nb1—O1^iv	49.39 (3)
Nb1^vii—Na1—Nb1^ix	70.94 (6)	Na1^xix—Nb1—O1^xxiii	49.39 (3)
Nb1^vii—Na1—Nb1^x	70.94 (6)	Na1^xix—Nb1—O1^xxiv	49.39 (3)
Nb1^vii—Na1—O1ⁱ	96.81 (8)	Na1^xx—Nb1—Na1^xxi	109.88 (6)
Nb1^vii—Na1—O1^xiii	96.81 (8)	Na1^xx—Nb1—Na1^xxii	109.88 (6)
Nb1^vii—Na1—O1^xvi	96.81 (8)	Na1^xx—Nb1—Na1^iv	71.0252 (18)
Nb1^vii—Na1—O1^viii	38.43 (5)	Na1^xx—Nb1—Na1^v	71.0252 (18)
Nb1^vii—Na1—O1^xvii	38.43 (5)	Na1^xx—Nb1—Na1^vi	178.17 (12)
Nb1^vii—Na1—O1^xviii	38.43 (5)	Na1^xx—Nb1—O1	113.15 (3)
Nb1ⁱ—Na1—Nb1ⁱⁱ	108.02 (6)	Na1^xx—Nb1—O1^xi	50.02 (6)
Nb1ⁱ—Na1—Nb1ⁱⁱⁱ	108.02 (6)	Na1^xx—Nb1—O1^xii	136.69 (3)
Nb1ⁱ—Na1—Nb1^viii	71.0252 (18)	Na1^xx—Nb1—O1^iv	65.77 (4)
Nb1ⁱ—Na1—Nb1^ix	71.0252 (18)	Na1^xx—Nb1—O1^xxiii	118.93 (7)
Nb1ⁱ—Na1—Nb1^x	178.17 (12)	Na1^xx—Nb1—O1^xxiv	44.69 (4)
Nb1ⁱ—Na1—O1ⁱ	32.83 (3)	Na1^xxi—Nb1—Na1^xxii	109.88 (6)
Nb1ⁱ—Na1—O1^xiii	86.96 (4)	Na1^xxi—Nb1—Na1^iv	71.0252 (18)
Nb1ⁱ—Na1—O1^xvi	140.04 (10)	Na1^xxi—Nb1—Na1^v	178.17 (12)
Nb1ⁱ—Na1—O1^viii	82.87 (3)	Na1^xxi—Nb1—Na1^vi	71.0252 (18)
Nb1ⁱ—Na1—O1^xvii	147.43 (10)	Na1^xxi—Nb1—O1	136.69 (3)
Nb1ⁱ—Na1—O1^xviii	96.84 (3)	Na1^xxi—Nb1—O1^xi	113.15 (3)
Nb1ⁱⁱ—Na1—Nb1ⁱⁱⁱ	108.02 (6)	Na1^xxi—Nb1—O1^xii	50.02 (6)
Nb1ⁱⁱ—Na1—Nb1^viii	71.0252 (18)	Na1^xxi—Nb1—O1^iv	44.69 (4)
Nb1ⁱⁱ—Na1—Nb1^ix	178.17 (12)	Na1^xxi—Nb1—O1^xxiii	65.77 (4)
Nb1ⁱⁱ—Na1—Nb1^x	71.0252 (18)	Na1^xxi—Nb1—O1^xxiv	118.93 (7)
Nb1ⁱⁱ—Na1—O1ⁱ	140.04 (10)	Na1^xxii—Nb1—Na1^iv	178.17 (12)
Nb1ⁱⁱ—Na1—O1^xiii	32.83 (3)	Na1^xxii—Nb1—Na1^v	71.0252 (18)
Nb1ⁱⁱ—Na1—O1^xvi	86.96 (4)	Na1^xxii—Nb1—Na1^vi	71.0252 (18)
Nb1ⁱⁱ—Na1—O1^viii	96.84 (3)	Na1^xxii—Nb1—O1	50.02 (6)
Nb1ⁱⁱ—Na1—O1^xvii	82.87 (3)	Na1^xxii—Nb1—O1^xi	136.69 (3)
Nb1ⁱⁱ—Na1—O1^xviii	147.43 (10)	Na1^xxii—Nb1—O1^xii	113.15 (3)
Nb1ⁱⁱⁱ—Na1—Nb1^viii	178.17 (12)	Na1^xxii—Nb1—O1^iv	118.93 (7)
Nb1ⁱⁱⁱ—Na1—Nb1^ix	71.0252 (18)	Na1^xxii—Nb1—O1^xxiii	44.69 (4)
Nb1ⁱⁱⁱ—Na1—Nb1^x	71.0252 (18)	Na1^xxii—Nb1—O1^xxiv	65.77 (4)
Nb1ⁱⁱⁱ—Na1—O1ⁱ	86.96 (4)	Na1^iv—Nb1—Na1^v	108.02 (6)
Nb1ⁱⁱⁱ—Na1—O1^xiii	140.04 (10)	Na1^iv—Nb1—Na1^vi	108.02 (6)
Nb1ⁱⁱⁱ—Na1—O1^xvi	32.83 (3)	Na1^iv—Nb1—O1	128.21 (7)
Nb1ⁱⁱⁱ—Na1—O1^viii	147.43 (10)	Na1^iv—Nb1—O1^xi	42.63 (2)
Nb1ⁱⁱⁱ—Na1—O1^xvii	96.84 (3)	Na1^iv—Nb1—O1^xii	66.10 (3)
Nb1ⁱⁱⁱ—Na1—O1^xviii	82.87 (3)	Na1^iv—Nb1—O1^iv	62.86 (6)
Nb1^viii—Na1—Nb1^ix	109.88 (6)	Na1^iv—Nb1—O1^xxiii	136.45 (4)
Nb1^viii—Na1—Nb1^x	109.88 (6)	Na1^iv—Nb1—O1^xxiv	115.31 (4)
Nb1^viii—Na1—O1ⁱ	92.85 (3)	Na1^v—Nb1—Na1^vi	108.02 (6)
Nb1^viii—Na1—O1^xiii	38.79 (3)	Na1^v—Nb1—O1	42.63 (2)
Nb1^viii—Na1—O1^xvi	147.78 (6)	Na1^v—Nb1—O1^xi	66.10 (3)
Nb1^viii—Na1—O1^viii	34.33 (3)	Na1^v—Nb1—O1^xii	128.21 (7)
Nb1^viii—Na1—O1^xvii	84.62 (7)	Na1^v—Nb1—O1^iv	136.45 (4)
Nb1^viii—Na1—O1^xviii	98.76 (9)	Na1^v—Nb1—O1^xxiii	115.31 (4)
Nb1^ix—Na1—Nb1^x	109.88 (6)	Na1^v—Nb1—O1^xxiv	62.86 (6)
Nb1^ix—Na1—O1ⁱ	38.79 (3)	Na1^vi—Nb1—O1	66.10 (3)
Nb1^ix—Na1—O1^xiii	147.78 (6)	Na1^vi—Nb1—O1^xi	128.21 (7)
Nb1^ix—Na1—O1^xvi	92.85 (3)	Na1^vi—Nb1—O1^xii	42.63 (2)
Nb1^ix—Na1—O1^viii	84.62 (7)	Na1^vi—Nb1—O1^iv	115.31 (4)
Nb1^ix—Na1—O1^xvii	98.76 (9)	Na1^vi—Nb1—O1^xxiii	62.86 (6)
Nb1^ix—Na1—O1^xviii	34.33 (3)	Na1^vi—Nb1—O1^xxiv	136.45 (4)
Nb1^x—Na1—O1ⁱ	147.78 (6)	O1—Nb1—O1^xi	98.18 (4)
Nb1^x—Na1—O1^xiii	92.85 (3)	O1—Nb1—O1^xii	98.18 (4)
Nb1^x—Na1—O1^xvi	38.79 (3)	O1—Nb1—O1^iv	168.61 (6)
Nb1^x—Na1—O1^viii	98.76 (9)	O1—Nb1—O1^xxiii	88.973 (13)
Nb1^x—Na1—O1^xvii	34.33 (3)	O1—Nb1—O1^xxiv	89.498 (15)
Nb1^x—Na1—O1^xviii	84.62 (7)	O1^xi—Nb1—O1^xii	98.18 (4)
O1ⁱ—Na1—O1^xiii	118.61 (3)	O1^xi—Nb1—O1^iv	89.498 (15)
O1ⁱ—Na1—O1^xvi	118.61 (3)	O1^xi—Nb1—O1^xxiii	168.61 (6)
O1ⁱ—Na1—O1^viii	87.17 (6)	O1^xi—Nb1—O1^xxiv	88.973 (13)
O1ⁱ—Na1—O1^xvii	133.17 (13)	O1^xii—Nb1—O1^iv	88.973 (13)
O1ⁱ—Na1—O1^xviii	69.14 (4)	O1^xii—Nb1—O1^xxiii	89.498 (15)
O1^xiii—Na1—O1^xvi	118.61 (3)	O1^xii—Nb1—O1^xxiv	168.61 (6)
O1^xiii—Na1—O1^viii	69.14 (4)	O1^iv—Nb1—O1^xxiii	82.21 (5)
O1^xiii—Na1—O1^xvii	87.17 (6)	O1^iv—Nb1—O1^xxiv	82.21 (5)
O1^xiii—Na1—O1^xviii	133.17 (13)	O1^xxiii—Nb1—O1^xxiv	82.21 (5)
O1^xvi—Na1—O1^viii	133.17 (13)	Na1^xxii—O1—Na1^v	104.43 (7)
O1^xvi—Na1—O1^xvii	69.14 (4)	Na1^xxii—O1—Nb1	95.65 (6)
O1^xvi—Na1—O1^xviii	87.17 (6)	Na1^xxii—O1—Nb1ⁱⁱⁱ	92.18 (7)
O1^viii—Na1—O1^xvii	65.14 (8)	Na1^xxii—O1—Li1^v	104.43 (7)
O1^viii—Na1—O1^xviii	65.14 (8)	Na1^v—O1—Nb1	104.54 (5)
O1^xvii—Na1—O1^xviii	65.14 (8)	Na1^v—O1—Nb1ⁱⁱⁱ	96.52 (7)
Na1^xix—Nb1—Na1^xx	70.94 (6)	Na1^v—O1—Li1^v	0.0
Na1^xix—Nb1—Na1^xxi	70.94 (6)	Nb1—O1—Nb1ⁱⁱⁱ	154.86 (4)
Na1^xix—Nb1—Na1^xxii	70.94 (6)	Nb1—O1—Li1^v	104.54 (5)
Na1^xix—Nb1—Na1^iv	110.89 (6)	O1ⁱ—Li1—O1^xiii	118.61 (3)
Na1^xix—Nb1—Na1^v	110.89 (6)	O1ⁱ—Li1—O1^xvi	118.61 (3)
Na1^xix—Nb1—Na1^vi	110.89 (6)	O1^xiii—Li1—O1^xvi	118.61 (3)

Symmetry codes: (i) y−x−2/3, y−1/3, z+1/6; (ii) y−x+1/3, y−1/3, z+1/6; (iii) y−x+1/3, y+2/3, z+1/6; (iv) y−x−1/3, y−2/3, z−1/6; (v) y−x−1/3, y+1/3, z−1/6; (vi) y−x+2/3, y+1/3, z−1/6; (vii) y−x, y, z+1/2; (viii) x−1/3, y−2/3, z+1/3; (ix) x−1/3, y+1/3, z+1/3; (x) x+2/3, y+1/3, z+1/3; (xi) −y, x−y, z; (xii) y−x, −x, z; (xiii) −y+1/3, −x−1/3, z+1/6; (xiv) −y+1/3, −x+2/3, z+1/6; (xv) x−2/3, x−y−1/3, z+1/6; (xvi) x+1/3, x−y+2/3, z+1/6; (xvii) −y+2/3, x−y+1/3, z+1/3; (xviii) y−x−1/3, −x+1/3, z+1/3; (xix) y−x, y, z−1/2; (xx) x−2/3, y−1/3, z−1/3; (xxi) x+1/3, y−1/3, z−1/3; (xxii) x+1/3, y+2/3, z−1/3; (xxiii) −y+2/3, −x+1/3, z−1/6; (xxiv) x−1/3, x−y+1/3, z−1/6.

(LNN20R3C_phase_2) top

Crystal data top

Li_0.95Na_0.5NbO₃	c = 13.870 (3) Å
M_r = 158.58	V = 320.15 (6) Å³
Trigonal, R3cH	Z = 6
a = 5.1627 (6) Å	T = 293 K

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Li1	0.0	0.0	0.2829	0.01*	0.95
Nb1	0.0	0.0	0.0	0.01*
O1	0.0492	0.3446	0.0647	0.01*
Na	0.0	0.0	0.2829	0.01*	0.5

Geometric parameters (Å, º) top

Li1—Nb1ⁱ	3.0111 (7)	Nb1—Na^xviii	3.0617 (3)
Li1—Nb1ⁱⁱ	3.3887 (3)	Nb1—Na^xii	3.3887 (3)
Li1—Nb1ⁱⁱⁱ	3.3887 (3)	Nb1—Na^xiii	3.3887 (3)
Li1—Nb1^iv	3.3887 (3)	Nb1—Na^xiv	3.3887 (3)
Li1—Nb1^v	3.0617 (3)	O1—Li1^xviii	2.2422 (3)
Li1—Nb1^vi	3.0617 (3)	O1—Li1^xiii	2.0736 (2)
Li1—Nb1^vii	3.0617 (3)	O1—Nb1	1.8929 (2)
Li1—O1ⁱⁱ	2.0736 (2)	O1—Nb1^iv	2.1160 (3)
Li1—O1^viii	2.0736 (2)	O1—Na^xviii	2.2422 (3)
Li1—O1^ix	2.0736 (2)	O1—Na^xiii	2.0736 (2)
Li1—O1^v	2.2422 (3)	Na—Li1ⁱⁱ	3.7720 (4)
Li1—O1^x	2.2422 (3)	Na—Li1ⁱⁱⁱ	3.7720 (4)
Li1—O1^xi	2.2422 (3)	Na—Li1^iv	3.7720 (4)
Li1—Naⁱⁱ	3.7720 (4)	Na—Li1^xii	3.7720 (4)
Li1—Naⁱⁱⁱ	3.7720 (4)	Na—Li1^xiii	3.7720 (4)
Li1—Na^iv	3.7720 (4)	Na—Li1^xiv	3.7720 (4)
Li1—Na^xii	3.7720 (4)	Na—Nb1ⁱ	3.0111 (7)
Li1—Na^xiii	3.7720 (4)	Na—Nb1ⁱⁱ	3.3887 (3)
Li1—Na^xiv	3.7720 (4)	Na—Nb1ⁱⁱⁱ	3.3887 (3)
Nb1—Li1^xv	3.0111 (7)	Na—Nb1^iv	3.3887 (3)
Nb1—Li1^xvi	3.0617 (3)	Na—Nb1^v	3.0617 (3)
Nb1—Li1^xvii	3.0617 (3)	Na—Nb1^vi	3.0617 (3)
Nb1—Li1^xviii	3.0617 (3)	Na—Nb1^vii	3.0617 (3)
Nb1—Li1^xii	3.3887 (3)	Na—O1ⁱⁱ	2.0736 (2)
Nb1—Li1^xiii	3.3887 (3)	Na—O1^viii	2.0736 (2)
Nb1—Li1^xiv	3.3887 (3)	Na—O1^ix	2.0736 (2)
Nb1—O1	1.8929 (2)	Na—O1^v	2.2422 (3)
Nb1—O1^xix	1.8929 (2)	Na—O1^x	2.2422 (3)
Nb1—O1^xx	1.8929 (2)	Na—O1^xi	2.2422 (3)
Nb1—O1^xii	2.1160 (3)	Na—Naⁱⁱ	3.7720 (4)
Nb1—O1^xxi	2.1160 (3)	Na—Naⁱⁱⁱ	3.7720 (4)
Nb1—O1^xxii	2.1160 (3)	Na—Na^iv	3.7720 (4)
Nb1—Na^xv	3.0111 (7)	Na—Na^xii	3.7720 (4)
Nb1—Na^xvi	3.0617 (3)	Na—Na^xiii	3.7720 (4)
Nb1—Na^xvii	3.0617 (3)	Na—Na^xiv	3.7720 (4)

Nb1ⁱ—Li1—O1ⁱⁱ	110.164 (5)	Nb1^v—Na—Nb1^vi	114.942 (2)
Nb1ⁱ—Li1—O1^viii	110.164 (5)	Nb1^v—Na—Nb1^vii	114.942 (2)
Nb1ⁱ—Li1—O1^ix	110.164 (5)	Nb1^v—Na—O1ⁱⁱ	95.878 (2)
Nb1ⁱ—Li1—O1^v	44.586 (7)	Nb1^v—Na—O1^viii	43.593 (6)
Nb1ⁱ—Li1—O1^x	44.586 (7)	Nb1^v—Na—O1^ix	149.1051 (3)
Nb1ⁱ—Li1—O1^xi	44.586 (7)	Nb1^v—Na—O1^v	38.006 (3)
O1ⁱⁱ—Li1—O1^viii	108.770 (5)	Nb1^v—Na—O1^x	84.890 (4)
O1ⁱⁱ—Li1—O1^ix	108.770 (5)	Nb1^v—Na—O1^xi	112.884 (8)
O1ⁱⁱ—Li1—O1^v	89.720 (7)	Nb1^v—Na—Na^xxiv	58.3540 (9)
O1ⁱⁱ—Li1—O1^x	153.970 (2)	Nb1^v—Na—Na^xxv	58.3540 (9)
O1ⁱⁱ—Li1—O1^xi	80.956 (8)	Nb1^v—Na—Na^xxiii	128.998 (10)
O1^viii—Li1—O1^ix	108.770 (5)	Nb1^v—Na—Na^xii	51.002 (10)
O1^viii—Li1—O1^v	80.956 (8)	Nb1^v—Na—Na^xiii	121.6460 (9)
O1^viii—Li1—O1^x	89.720 (7)	Nb1^v—Na—Na^xiv	121.6460 (9)
O1^viii—Li1—O1^xi	153.969 (2)	Nb1^vi—Na—Nb1^vii	114.942 (2)
O1^ix—Li1—O1^v	153.969 (2)	Nb1^vi—Na—O1ⁱⁱ	43.593 (6)
O1^ix—Li1—O1^x	80.956 (8)	Nb1^vi—Na—O1^viii	149.1051 (3)
O1^ix—Li1—O1^xi	89.720 (7)	Nb1^vi—Na—O1^ix	95.878 (2)
O1^v—Li1—O1^x	74.880 (11)	Nb1^vi—Na—O1^v	84.890 (4)
O1^v—Li1—O1^xi	74.880 (11)	Nb1^vi—Na—O1^x	112.884 (8)
O1^x—Li1—O1^xi	74.881 (11)	Nb1^vi—Na—O1^xi	38.006 (3)
Li1^xv—Nb1—O1	118.300 (6)	Nb1^vi—Na—Na^xxiv	58.3540 (9)
Li1^xv—Nb1—O1^xix	118.300 (6)	Nb1^vi—Na—Na^xxv	128.998 (10)
Li1^xv—Nb1—O1^xx	118.300 (6)	Nb1^vi—Na—Na^xxiii	58.3540 (9)
Li1^xv—Nb1—O1^xii	48.059 (7)	Nb1^vi—Na—Na^xii	121.6460 (9)
Li1^xv—Nb1—O1^xxi	48.059 (7)	Nb1^vi—Na—Na^xiii	51.002 (10)
Li1^xv—Nb1—O1^xxii	48.059 (7)	Nb1^vi—Na—Na^xiv	121.6460 (9)
Li1^xv—Nb1—Na^xv	0.0	Nb1^vii—Na—O1ⁱⁱ	149.1051 (3)
Li1^xv—Nb1—Na^xvi	76.793 (3)	Nb1^vii—Na—O1^viii	95.878 (2)
Li1^xv—Nb1—Na^xvii	76.793 (3)	Nb1^vii—Na—O1^ix	43.593 (6)
Li1^xv—Nb1—Na^xviii	76.793 (3)	Nb1^vii—Na—O1^v	112.884 (8)
O1—Nb1—O1^xix	99.373 (7)	Nb1^vii—Na—O1^x	38.006 (3)
O1—Nb1—O1^xx	99.373 (7)	Nb1^vii—Na—O1^xi	84.890 (4)
O1—Nb1—O1^xii	166.3117 (11)	Nb1^vii—Na—Na^xxiv	128.998 (10)
O1—Nb1—O1^xxi	88.604 (9)	Nb1^vii—Na—Na^xxv	58.3540 (9)
O1—Nb1—O1^xxii	90.191 (9)	Nb1^vii—Na—Na^xxiii	58.3540 (9)
O1—Nb1—Na^xv	118.300 (6)	Nb1^vii—Na—Na^xii	121.6460 (9)
O1—Nb1—Na^xvi	102.794 (2)	Nb1^vii—Na—Na^xiii	121.6460 (9)
O1—Nb1—Na^xvii	141.9619	Nb1^vii—Na—Na^xiv	51.002 (10)
O1—Nb1—Na^xviii	46.834 (8)	O1ⁱⁱ—Na—O1^viii	108.770 (5)
O1^xix—Nb1—O1^xx	99.373 (7)	O1ⁱⁱ—Na—O1^ix	108.770 (5)
O1^xix—Nb1—O1^xii	90.191 (9)	O1ⁱⁱ—Na—O1^v	89.720 (7)
O1^xix—Nb1—O1^xxi	166.3117 (11)	O1ⁱⁱ—Na—O1^x	153.970 (2)
O1^xix—Nb1—O1^xxii	88.604 (9)	O1ⁱⁱ—Na—O1^xi	80.956 (8)
O1^xix—Nb1—Na^xv	118.300 (6)	O1^xxiv—Na—Na^xxiv	65.081 (10)
O1^xix—Nb1—Na^xvi	46.834 (8)	O1^xxiv—Na—Na^xxv	149.6584 (1)
O1^xix—Nb1—Na^xvii	102.794 (2)	O1^xxiv—Na—Na^xxiii	101.072 (5)
O1^xix—Nb1—Na^xviii	141.9619	O1^xxiv—Na—Na^xii	78.928 (5)
O1^xx—Nb1—O1^xii	88.604 (9)	O1^xxiv—Na—Na^xiii	30.3416 (1)
O1^xx—Nb1—O1^xxi	90.191 (9)	O1^xxiv—Na—Na^xiv	114.919 (10)
O1^xx—Nb1—O1^xxii	166.3117 (11)	O1^viii—Na—O1^ix	108.770 (5)
O1^xx—Nb1—Na^xv	118.300 (6)	O1^viii—Na—O1^v	80.956 (8)
O1^xx—Nb1—Na^xvi	141.9619	O1^viii—Na—O1^x	89.720 (7)
O1^xx—Nb1—Na^xvii	46.834 (8)	O1^viii—Na—O1^xi	153.969 (2)
O1^xx—Nb1—Na^xviii	102.794 (2)	O1^xxvi—Na—Na^xxiv	101.072 (5)
O1^xii—Nb1—O1^xxi	80.209 (11)	O1^xxvi—Na—Na^xxv	65.081 (10)
O1^xii—Nb1—O1^xxii	80.209 (11)	O1^xxvi—Na—Na^xxiii	149.6584 (1)
O1^xii—Nb1—Na^xv	48.059 (7)	O1^xxvi—Na—Na^xii	30.3416 (1)
O1^xii—Nb1—Na^xvi	76.660 (3)	O1^xxvi—Na—Na^xiii	114.919 (10)
O1^xii—Nb1—Na^xvii	42.5084 (13)	O1^xxvi—Na—Na^xiv	78.928 (5)
O1^xii—Nb1—Na^xviii	120.651 (9)	O1^ix—Na—O1^v	153.969 (2)
O1^xxi—Nb1—O1^xxii	80.209 (11)	O1^ix—Na—O1^x	80.956 (8)
O1^xxi—Nb1—Na^xv	48.059 (7)	O1^ix—Na—O1^xi	89.720 (7)
O1^xxi—Nb1—Na^xvi	120.651 (9)	O1^xxvii—Na—Na^xxiv	149.6584 (1)
O1^xxi—Nb1—Na^xvii	76.660 (3)	O1^xxvii—Na—Na^xxv	101.072 (5)
O1^xxi—Nb1—Na^xviii	42.5084 (13)	O1^xxvii—Na—Na^xxiii	65.081 (10)
O1^xxii—Nb1—Na^xv	48.059 (7)	O1^xxvii—Na—Na^xii	114.919 (10)
O1^xxii—Nb1—Na^xvi	42.5084 (13)	O1^xxvii—Na—Na^xiii	78.928 (5)
O1^xxii—Nb1—Na^xvii	120.651 (9)	O1^xxvii—Na—Na^xiv	30.3416 (1)
O1^xxii—Nb1—Na^xviii	76.660 (3)	O1^v—Na—O1^x	74.880 (11)
Na^xv—Nb1—Na^xvi	76.793 (3)	O1^v—Na—O1^xi	74.880 (11)
Na^xv—Nb1—Na^xvii	76.793 (3)	O1^v—Na—Na^xxiv	27.850 (3)
Na^xv—Nb1—Na^xviii	76.793 (3)	O1^v—Na—Na^xxv	60.249 (7)
Na^xvi—Nb1—Na^xvii	114.942 (2)	O1^v—Na—Na^xxiii	94.073 (13)
Na^xvi—Nb1—Na^xviii	114.942 (2)	O1^v—Na—Na^xii	85.927 (13)
Na^xvii—Nb1—Na^xviii	114.942 (2)	O1^v—Na—Na^xiii	119.751 (7)
Li1^xviii—O1—Li1^xiii	121.808 (3)	O1^v—Na—Na^xiv	152.150 (3)
Li1^xviii—O1—Nb1	95.160 (10)	O1^x—Na—O1^xi	74.881 (11)
Li1^xviii—O1—Nb1^iv	87.354 (14)	O1^x—Na—Na^xxiv	94.073 (13)
Li1^xviii—O1—Na^xviii	0.0	O1^x—Na—Na^xxv	27.850 (3)
Li1^xviii—O1—Na^xiii	121.808 (3)	O1^x—Na—Na^xxiii	60.249 (7)
Li1^xiii—O1—Nb1	117.304 (3)	O1^x—Na—Na^xii	119.751 (7)
Li1^xiii—O1—Nb1^iv	93.898 (7)	O1^x—Na—Na^xiii	152.150 (3)
Li1^xiii—O1—Na^xviii	121.808 (3)	O1^x—Na—Na^xiv	85.927 (13)
Li1^xiii—O1—Na^xiii	0.0	O1^xi—Na—Na^xxiv	60.249 (7)
Nb1—O1—Nb1^iv	140.347 (3)	O1^xi—Na—Na^xxv	94.073 (13)
Nb1—O1—Na^xviii	95.160 (10)	O1^xi—Na—Na^xxiii	27.850 (3)
Nb1—O1—Na^xiii	117.304 (3)	O1^xi—Na—Na^xii	152.150 (3)
Nb1^xxiii—O1—Na^xviii	87.354 (14)	O1^xi—Na—Na^xiii	85.927 (13)
Nb1^xxiii—O1—Na^xiii	93.898 (7)	O1^xi—Na—Na^xiv	119.751 (7)
Na^xviii—O1—Na^xiii	121.808 (3)	Na^xxiv—Na—Na^xxv	86.368 (10)
Nb1ⁱ—Na—Nb1^v	76.793 (3)	Na^xxiv—Na—Na^xxiii	86.368 (10)
Nb1ⁱ—Na—Nb1^vi	76.793 (3)	Na^xxiv—Na—Na^xii	93.632 (10)
Nb1ⁱ—Na—Nb1^vii	76.793 (3)	Na^xxiv—Na—Na^xiii	93.632 (10)
Nb1ⁱ—Na—O1ⁱⁱ	110.164 (5)	Na^xxiv—Na—Na^xiv	180.0
Nb1ⁱ—Na—O1^viii	110.164 (5)	Na^xxv—Na—Na^xxiii	86.368 (10)
Nb1ⁱ—Na—O1^ix	110.164 (5)	Na^xxv—Na—Na^xii	93.632 (10)
Nb1ⁱ—Na—O1^v	44.586 (7)	Na^xxv—Na—Na^xiii	180.0
Nb1ⁱ—Na—O1^x	44.586 (7)	Na^xxv—Na—Na^xiv	93.632 (10)
Nb1ⁱ—Na—O1^xi	44.586 (7)	Na^xxiii—Na—Na^xii	180.0
Nb1ⁱ—Na—Na^xxiv	52.205 (7)	Na^xxiii—Na—Na^xiii	93.632 (10)
Nb1ⁱ—Na—Na^xxv	52.205 (7)	Na^xxiii—Na—Na^xiv	93.632 (10)
Nb1ⁱ—Na—Na^xxiii	52.205 (7)	Na^xii—Na—Na^xiii	86.368 (10)
Nb1ⁱ—Na—Na^xii	127.795 (7)	Na^xii—Na—Na^xiv	86.368 (10)
Nb1ⁱ—Na—Na^xiii	127.795 (7)	Na^xiii—Na—Na^xiv	86.368 (10)
Nb1ⁱ—Na—Na^xiv	127.795 (7)

Symmetry codes: (i) y−x, y, z+1/2; (ii) y−x−2/3, y−1/3, z+1/6; (iii) y−x+1/3, y−1/3, z+1/6; (iv) y−x+1/3, y+2/3, z+1/6; (v) x−1/3, y−2/3, z+1/3; (vi) x−1/3, y+1/3, z+1/3; (vii) x+2/3, y+1/3, z+1/3; (viii) −y+1/3, −x−1/3, z+1/6; (ix) x+1/3, x−y+2/3, z+1/6; (x) −y+2/3, x−y+1/3, z+1/3; (xi) y−x−1/3, −x+1/3, z+1/3; (xii) y−x−1/3, y−2/3, z−1/6; (xiii) y−x−1/3, y+1/3, z−1/6; (xiv) y−x+2/3, y+1/3, z−1/6; (xv) y−x, y, z−1/2; (xvi) x−2/3, y−1/3, z−1/3; (xvii) x+1/3, y−1/3, z−1/3; (xviii) x+1/3, y+2/3, z−1/3; (xix) −y, x−y, z; (xx) y−x, −x, z; (xxi) −y+2/3, −x+1/3, z−1/6; (xxii) x−1/3, x−y+1/3, z−1/6; (xxiii) y−x+1/3, y+2/3, z−5/6; (xxiv) y−x−2/3, y−1/3, z−5/6; (xxv) y−x+1/3, y−1/3, z−5/6; (xxvi) −y+1/3, −x−1/3, z−5/6; (xxvii) x+1/3, x−y+2/3, z−5/6.

(P42NMC_phase_1) top

Crystal data top

Li_0.20Na_0.80NbO₃	c = 7.8182 (3) Å
M_r = 160.68	V = 477.65 (2) Å³
Tetragonal, P4₂/nmc	Z = 8
a = 7.81632 (16) Å	T = 773 K

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Na1_1	0.25	0.25	0.7405 (13)	0.0268 (5)*	0.8
Na1_2	0.75	0.25	0.25	0.0268 (5)*	0.8
Na1_3	0.75	0.25	0.75	0.0268 (5)*	0.8
Nb1_1	0.0	0.0	0.0	0.00703 (18)*
O1_1	0.25	−0.0332 (5)	0.0329 (3)	0.0187 (7)*
O1_2	0.25	0.0308 (5)	0.4777 (4)	0.0172 (7)*
O1_3	−0.0329 (3)	0.0329 (3)	0.25	0.0190 (5)*
Li1	0.25	0.25	0.7405 (13)	0.0268 (5)*	0.2
Li2	0.75	0.25	0.25	0.0268 (5)*	0.2
Li3	0.75	0.25	0.75	0.0268 (5)*	0.2

Geometric parameters (Å, º) top

Na1_1—Na1_1ⁱ	3.9091 (1)	Nb1_1—O1_2	1.9765 (6)
Na1_1—Na1_1ⁱⁱ	3.9091 (1)	Nb1_1—O1_3	1.9880 (6)
Na1_1—Na1_2ⁱⁱⁱ	3.9089 (2)	Nb1_1—O1_3^xxvi	1.9880 (6)
Na1_1—Na1_2ⁱⁱ	3.9089 (2)	Nb1_1—Li1^xiv	3.428 (6)
Na1_1—Na1_3^iv	3.9089 (2)	Nb1_1—Li1ⁱ	3.342 (6)
Na1_1—Na1_3	3.9089 (2)	Nb1_1—Li1	3.428 (6)
Na1_1—Nb1_1^v	3.428 (6)	Nb1_1—Li1	3.342 (6)
Na1_1—Nb1_1ⁱⁱ	3.342 (6)	Nb1_1—Li2^iv	3.3848 (1)
Na1_1—Nb1_1^vi	3.428 (6)	Nb1_1—Li2^xxiii	3.3848 (1)
Na1_1—Nb1_1^vii	3.342 (6)	Nb1_1—Li3^xxiv	3.3848 (1)
Na1_1—Nb1_1^viii	3.428 (6)	Nb1_1—Li3^xxiii	3.3848 (1)
Na1_1—Nb1_1^ix	3.342 (6)	O1_1—Na1_1^xiv	3.182 (7)
Na1_1—Nb1_1^x	3.428 (6)	O1_1—Na1_1ⁱ	2.745 (8)
Na1_1—Nb1_1^xi	3.342 (6)	O1_1—Na1_2^xxiii	2.786 (3)
Na1_1—O1_1^v	3.182 (7)	O1_1—Na1_3^xxiii	2.399 (3)
Na1_1—O1_1ⁱⁱ	2.745 (8)	O1_1—Nb1_1	1.9879 (6)
Na1_1—O1_1^vi	3.182 (7)	O1_1—Nb1_1^xvii	1.9879 (6)
Na1_1—O1_1^vii	2.745 (8)	O1_1—Li1ⁱ	2.745 (8)
Na1_1—O1_2	2.675 (9)	O1_1—Li2^xxiii	2.786 (3)
Na1_1—O1_2ⁱⁱ	2.525 (8)	O1_1—Li3^xxiii	2.399 (3)
Na1_1—O1_2^xii	2.675 (9)	O1_2—Na1_1	2.675 (9)
Na1_1—O1_2^vii	2.525 (8)	O1_2—Na1_1ⁱ	2.525 (8)
Na1_1—O1_3ⁱⁱ	2.7883 (5)	O1_2—Na1_2ⁱⁱⁱ	3.058 (4)
Na1_1—O1_3^vii	2.7883 (5)	O1_2—Na1_3^xxiii	2.826 (3)
Na1_1—O1_3^ix	2.7883 (5)	O1_2—Nb1_1ⁱⁱ	1.9765 (6)
Na1_1—O1_3^xi	2.7883 (5)	O1_2—Nb1_1^xi	1.9765 (6)
Na1_2—Na1_1ⁱ	3.9089 (2)	O1_2—Li1	2.675 (9)
Na1_2—Na1_1^xiii	3.9089 (2)	O1_2—Li1ⁱ	2.525 (8)
Na1_2—Na1_1	3.9089 (2)	O1_2—Li3^xxiii	2.826 (3)
Na1_2—Na1_1	3.9089 (2)	O1_3—Na1_1ⁱ	2.7883 (5)
Na1_2—Na1_3^xiv	3.9091 (1)	O1_3—Na1_1	2.7883 (5)
Na1_2—Na1_3	3.9091 (1)	O1_3—Na1_2^iv	2.400 (3)
Na1_2—Nb1_1^xv	3.3848 (1)	O1_3—Na1_3^xxiii	3.127 (3)
Na1_2—Nb1_1ⁱⁱ	3.3848 (1)	O1_3—Nb1_1	1.9880 (6)
Na1_2—Nb1_1^xii	3.3848 (1)	O1_3—Nb1_1^xi	1.9880 (6)
Na1_2—Nb1_1^xvi	3.3848 (1)	O1_3—Li1ⁱ	2.7883 (5)
Na1_2—Nb1_1^xvii	3.3848 (1)	O1_3—Li1	2.7883 (5)
Na1_2—Nb1_1^ix	3.3848 (1)	O1_3—Li2^iv	2.400 (3)
Na1_2—Nb1_1^xviii	3.3848 (1)	Li1—Nb1_1^v	3.428 (6)
Na1_2—Nb1_1^xix	3.3848 (1)	Li1—Nb1_1ⁱⁱ	3.342 (6)
Na1_2—O1_1ⁱⁱ	2.786 (3)	Li1—Nb1_1^vi	3.428 (6)
Na1_2—O1_1^xvi	2.786 (3)	Li1—Nb1_1^vii	3.342 (6)
Na1_2—O1_1	2.786 (3)	Li1—Nb1_1^viii	3.428 (6)
Na1_2—O1_1	2.786 (3)	Li1—Nb1_1^ix	3.342 (6)
Na1_2—O1_2ⁱ	3.058 (4)	Li1—Nb1_1^x	3.428 (6)
Na1_2—O1_2^xx	3.058 (4)	Li1—Nb1_1^xi	3.342 (6)
Na1_2—O1_2	3.058 (4)	Li1—O1_1ⁱⁱ	2.745 (8)
Na1_2—O1_2	3.058 (4)	Li1—O1_1^vii	2.745 (8)
Na1_2—O1_3^xv	2.400 (3)	Li1—O1_2	2.675 (9)
Na1_2—O1_3^xii	2.400 (3)	Li1—O1_2ⁱⁱ	2.525 (8)
Na1_2—O1_3^xvii	2.400 (3)	Li1—O1_2^xii	2.675 (9)
Na1_2—O1_3^xviii	2.400 (3)	Li1—O1_2^vii	2.525 (8)
Na1_3—Na1_1	3.9089 (2)	Li1—O1_3ⁱⁱ	2.7883 (5)
Na1_3—Na1_1^xv	3.9089 (2)	Li1—O1_3^vii	2.7883 (5)
Na1_3—Na1_1	3.9089 (2)	Li1—O1_3^ix	2.7883 (5)
Na1_3—Na1_1	3.9089 (2)	Li1—O1_3^xi	2.7883 (5)
Na1_3—Na1_2	3.9091 (1)	Li2—Nb1_1^xv	3.3848 (1)
Na1_3—Na1_2^v	3.9091 (1)	Li2—Nb1_1ⁱⁱ	3.3848 (1)
Na1_3—Nb1_1^xxi	3.3848 (1)	Li2—Nb1_1^xii	3.3848 (1)
Na1_3—Nb1_1ⁱⁱ	3.3848 (1)	Li2—Nb1_1^xvi	3.3848 (1)
Na1_3—Nb1_1^vi	3.3848 (1)	Li2—Nb1_1^xvii	3.3848 (1)
Na1_3—Nb1_1^xvi	3.3848 (1)	Li2—Nb1_1^ix	3.3848 (1)
Na1_3—Nb1_1^viii	3.3848 (1)	Li2—Nb1_1^xviii	3.3848 (1)
Na1_3—Nb1_1^ix	3.3848 (1)	Li2—Nb1_1^xix	3.3848 (1)
Na1_3—Nb1_1^xxii	3.3848 (1)	Li2—O1_1ⁱⁱ	2.786 (3)
Na1_3—Nb1_1^xix	3.3848 (1)	Li2—O1_1^xvi	2.786 (3)
Na1_3—O1_1ⁱⁱ	2.399 (3)	Li2—O1_1	2.786 (3)
Na1_3—O1_1^xvi	2.399 (3)	Li2—O1_1	2.786 (3)
Na1_3—O1_1	2.399 (3)	Li2—O1_3^xv	2.400 (3)
Na1_3—O1_1	2.399 (3)	Li2—O1_3^xii	2.400 (3)
Na1_3—O1_2ⁱⁱ	2.826 (3)	Li2—O1_3^xvii	2.400 (3)
Na1_3—O1_2^xvi	2.826 (3)	Li2—O1_3^xviii	2.400 (3)
Na1_3—O1_2	2.826 (3)	Li3—Nb1_1^xxi	3.3848 (1)
Na1_3—O1_2	2.826 (3)	Li3—Nb1_1ⁱⁱ	3.3848 (1)
Na1_3—O1_3ⁱⁱ	3.127 (3)	Li3—Nb1_1^vi	3.3848 (1)
Na1_3—O1_3^xvi	3.127 (3)	Li3—Nb1_1^xvi	3.3848 (1)
Na1_3—O1_3^ix	3.127 (3)	Li3—Nb1_1^viii	3.3848 (1)
Na1_3—O1_3^xix	3.127 (3)	Li3—Nb1_1^ix	3.3848 (1)
Nb1_1—Na1_1^xiv	3.428 (6)	Li3—Nb1_1^xxii	3.3848 (1)
Nb1_1—Na1_1ⁱ	3.342 (6)	Li3—Nb1_1^xix	3.3848 (1)
Nb1_1—Na1_1	3.428 (6)	Li3—O1_1ⁱⁱ	2.399 (3)
Nb1_1—Na1_1	3.342 (6)	Li3—O1_1^xvi	2.399 (3)
Nb1_1—Na1_2^iv	3.3848 (1)	Li3—O1_1	2.399 (3)
Nb1_1—Na1_2^xxiii	3.3848 (1)	Li3—O1_1	2.399 (3)
Nb1_1—Na1_3^xxiv	3.3848 (1)	Li3—O1_2ⁱⁱ	2.826 (3)
Nb1_1—Na1_3^xxiii	3.3848 (1)	Li3—O1_2^xvi	2.826 (3)
Nb1_1—O1_1	1.9879 (6)	Li3—O1_2	2.826 (3)
Nb1_1—O1_1	1.9879 (6)	Li3—O1_2	2.826 (3)
Nb1_1—O1_2^xxv	1.9765 (6)

Nb1_1ⁱⁱ—Na1_1—Nb1_1^vii	111.5 (3)	O1_1^xvi—Na1_2—O1_3^xii	115.47 (5)
Nb1_1ⁱⁱ—Na1_1—Nb1_1^ix	71.56 (15)	O1_1^xvi—Na1_2—O1_3^xvii	115.47 (5)
Nb1_1ⁱⁱ—Na1_1—Nb1_1^xi	71.56 (15)	O1_1^xvi—Na1_2—O1_3^xviii	64.53 (5)
Nb1_1ⁱⁱ—Na1_1—O1_1ⁱⁱ	36.48 (7)	O1_1—Na1_2—O1_1	74.93 (15)
Nb1_1ⁱⁱ—Na1_1—O1_1^vii	98.0 (3)	O1_1—Na1_2—O1_3^xv	64.53 (5)
Nb1_1ⁱⁱ—Na1_1—O1_2	36.25 (8)	O1_1—Na1_2—O1_3^xii	115.47 (5)
Nb1_1ⁱⁱ—Na1_1—O1_2ⁱⁱ	90.94 (5)	O1_1—Na1_2—O1_3^xvii	64.53 (5)
Nb1_1ⁱⁱ—Na1_1—O1_2^xii	86.7 (2)	O1_1—Na1_2—O1_3^xviii	115.47 (5)
Nb1_1ⁱⁱ—Na1_1—O1_2^vii	144.09 (10)	O1_1—Na1_2—O1_3^xv	115.47 (5)
Nb1_1ⁱⁱ—Na1_1—O1_3ⁱⁱ	36.45 (7)	O1_1—Na1_2—O1_3^xii	64.53 (5)
Nb1_1ⁱⁱ—Na1_1—O1_3^vii	146.6 (4)	O1_1—Na1_2—O1_3^xvii	115.47 (5)
Nb1_1ⁱⁱ—Na1_1—O1_3^ix	97.05 (14)	O1_1—Na1_2—O1_3^xviii	64.53 (5)
Nb1_1ⁱⁱ—Na1_1—O1_3^xi	84.68 (12)	O1_3^xv—Na1_2—O1_3^xii	180.0
Nb1_1^vii—Na1_1—Nb1_1^ix	71.56 (15)	O1_3^xv—Na1_2—O1_3^xvii	90.0
Nb1_1^vii—Na1_1—Nb1_1^xi	71.56 (15)	O1_3^xv—Na1_2—O1_3^xviii	90.0
Nb1_1^vii—Na1_1—O1_1ⁱⁱ	98.0 (3)	O1_3^xii—Na1_2—O1_3^xvii	90.0
Nb1_1^vii—Na1_1—O1_1^vii	36.48 (7)	O1_3^xii—Na1_2—O1_3^xviii	90.0
Nb1_1^vii—Na1_1—O1_2	86.7 (2)	O1_3^xvii—Na1_2—O1_3^xviii	180.0
Nb1_1^vii—Na1_1—O1_2ⁱⁱ	144.09 (10)	O1_1ⁱⁱ—Na1_3—O1_1^xvi	89.90 (16)
Nb1_1^vii—Na1_1—O1_2^xii	36.25 (8)	O1_1ⁱⁱ—Na1_3—O1_1	120.06 (9)
Nb1_1^vii—Na1_1—O1_2^vii	90.94 (5)	O1_1ⁱⁱ—Na1_3—O1_1	120.06 (9)
Nb1_1^vii—Na1_1—O1_3ⁱⁱ	146.6 (4)	O1_1^xvi—Na1_3—O1_1	120.06 (9)
Nb1_1^vii—Na1_1—O1_3^vii	36.45 (7)	O1_1^xvi—Na1_3—O1_1	120.06 (9)
Nb1_1^vii—Na1_1—O1_3^ix	84.68 (12)	O1_1—Na1_3—O1_1	89.90 (16)
Nb1_1^vii—Na1_1—O1_3^xi	97.05 (14)	Na1_1ⁱ—Nb1_1—Na1_1	180.0
Nb1_1^ix—Na1_1—Nb1_1^xi	111.5 (3)	Na1_1ⁱ—Nb1_1—O1_1	55.17 (12)
Nb1_1^ix—Na1_1—O1_1ⁱⁱ	36.48 (7)	Na1_1ⁱ—Nb1_1—O1_1	124.83 (12)
Nb1_1^ix—Na1_1—O1_1^vii	98.0 (3)	Na1_1ⁱ—Nb1_1—O1_2^xxv	53.17 (13)
Nb1_1^ix—Na1_1—O1_2	86.7 (2)	Na1_1ⁱ—Nb1_1—O1_2	126.83 (13)
Nb1_1^ix—Na1_1—O1_2ⁱⁱ	90.94 (5)	Na1_1ⁱ—Nb1_1—O1_3	56.43 (15)
Nb1_1^ix—Na1_1—O1_2^xii	36.25 (8)	Na1_1ⁱ—Nb1_1—O1_3^xxvi	123.57 (15)
Nb1_1^ix—Na1_1—O1_2^vii	144.09 (10)	Na1_1—Nb1_1—O1_1	124.83 (12)
Nb1_1^ix—Na1_1—O1_3ⁱⁱ	97.05 (14)	Na1_1—Nb1_1—O1_1	55.17 (12)
Nb1_1^ix—Na1_1—O1_3^vii	84.68 (12)	Na1_1—Nb1_1—O1_2^xxv	126.83 (13)
Nb1_1^ix—Na1_1—O1_3^ix	36.45 (7)	Na1_1—Nb1_1—O1_2	53.17 (13)
Nb1_1^ix—Na1_1—O1_3^xi	146.6 (4)	Na1_1—Nb1_1—O1_3	123.57 (15)
Nb1_1^xi—Na1_1—O1_1ⁱⁱ	98.0 (3)	Na1_1—Nb1_1—O1_3^xxvi	56.43 (15)
Nb1_1^xi—Na1_1—O1_1^vii	36.48 (7)	O1_1—Nb1_1—O1_1	180.0
Nb1_1^xi—Na1_1—O1_2	36.25 (8)	O1_1—Nb1_1—O1_2^xxv	91.2 (2)
Nb1_1^xi—Na1_1—O1_2ⁱⁱ	144.09 (10)	O1_1—Nb1_1—O1_2	88.8 (2)
Nb1_1^xi—Na1_1—O1_2^xii	86.7 (2)	O1_1—Nb1_1—O1_3	90.97 (13)
Nb1_1^xi—Na1_1—O1_2^vii	90.94 (5)	O1_1—Nb1_1—O1_3^xxvi	89.03 (13)
Nb1_1^xi—Na1_1—O1_3ⁱⁱ	84.68 (12)	O1_1—Nb1_1—O1_2^xxv	88.8 (2)
Nb1_1^xi—Na1_1—O1_3^vii	97.05 (14)	O1_1—Nb1_1—O1_2	91.2 (2)
Nb1_1^xi—Na1_1—O1_3^ix	146.6 (4)	O1_1—Nb1_1—O1_3	89.03 (13)
Nb1_1^xi—Na1_1—O1_3^xi	36.45 (7)	O1_1—Nb1_1—O1_3^xxvi	90.97 (13)
O1_1ⁱⁱ—Na1_1—O1_1^vii	107.5 (3)	O1_2^xxv—Nb1_1—O1_2	180.0
O1_1ⁱⁱ—Na1_1—O1_2	62.99 (17)	O1_2^xxv—Nb1_1—O1_3	88.55 (15)
O1_1ⁱⁱ—Na1_1—O1_2ⁱⁱ	83.51 (10)	O1_2^xxv—Nb1_1—O1_3^xxvi	91.45 (15)
O1_1ⁱⁱ—Na1_1—O1_2^xii	62.99 (17)	O1_2—Nb1_1—O1_3	91.45 (15)
O1_1ⁱⁱ—Na1_1—O1_2^vii	169.0 (3)	O1_2—Nb1_1—O1_3^xxvi	88.55 (15)
O1_1ⁱⁱ—Na1_1—O1_3ⁱⁱ	61.64 (10)	O1_3—Nb1_1—O1_3^xxvi	180.0
O1_1ⁱⁱ—Na1_1—O1_3^vii	120.4 (2)	Na1_1ⁱ—O1_1—Na1_2^xxiii	163.72 (19)
O1_1ⁱⁱ—Na1_1—O1_3^ix	61.64 (10)	Na1_1ⁱ—O1_1—Na1_3^xxiii	98.69 (19)
O1_1ⁱⁱ—Na1_1—O1_3^xi	120.4 (2)	Na1_1ⁱ—O1_1—Nb1_1	88.35 (11)
O1_1^vii—Na1_1—O1_2	62.99 (17)	Na1_1ⁱ—O1_1—Nb1_1^xvii	88.35 (11)
O1_1^vii—Na1_1—O1_2ⁱⁱ	169.0 (3)	Na1_1ⁱ—O1_1—Li3^xxiii	98.69 (19)
O1_1^vii—Na1_1—O1_2^xii	62.99 (17)	Na1_2^xxiii—O1_1—Na1_3^xxiii	97.59 (13)
O1_1^vii—Na1_1—O1_2^vii	83.51 (10)	Na1_2^xxiii—O1_1—Nb1_1	88.67 (9)
O1_1^vii—Na1_1—O1_3ⁱⁱ	120.4 (2)	Na1_2^xxiii—O1_1—Nb1_1^xvii	88.67 (9)
O1_1^vii—Na1_1—O1_3^vii	61.64 (10)	Na1_2^xxiii—O1_1—Li3^xxiii	97.59 (13)
O1_1^vii—Na1_1—O1_3^ix	120.4 (2)	Na1_3^xxiii—O1_1—Nb1_1	100.58 (10)
O1_1^vii—Na1_1—O1_3^xi	61.64 (10)	Na1_3^xxiii—O1_1—Nb1_1^xvii	100.58 (10)
O1_2—Na1_1—O1_2ⁱⁱ	124.33 (8)	Na1_3^xxiii—O1_1—Li3^xxiii	0.0
O1_2—Na1_1—O1_2^xii	79.7 (3)	Nb1_1—O1_1—Nb1_1^xvii	158.84 (19)
O1_2—Na1_1—O1_2^vii	124.33 (8)	Nb1_1—O1_1—Li3^xxiii	100.58 (10)
O1_2—Na1_1—O1_3ⁱⁱ	60.83 (13)	Nb1_1^xvii—O1_1—Li3^xxiii	100.58 (10)
O1_2—Na1_1—O1_3^vii	121.9 (3)	Na1_1—O1_2—Na1_1ⁱ	97.43 (13)
O1_2—Na1_1—O1_3^ix	121.9 (3)	Na1_1—O1_2—Nb1_1ⁱⁱ	90.58 (9)
O1_2—Na1_1—O1_3^xi	60.83 (13)	Na1_1—O1_2—Nb1_1^xi	90.58 (9)
O1_2ⁱⁱ—Na1_1—O1_2^xii	124.33 (8)	Na1_1ⁱ—O1_2—Nb1_1ⁱⁱ	98.48 (12)
O1_2ⁱⁱ—Na1_1—O1_2^vii	85.5 (4)	Na1_1ⁱ—O1_2—Nb1_1^xi	98.48 (12)
O1_2ⁱⁱ—Na1_1—O1_3ⁱⁱ	64.36 (11)	Nb1_1ⁱⁱ—O1_2—Nb1_1^xi	162.7 (2)
O1_2ⁱⁱ—Na1_1—O1_3^vii	113.2 (3)	Na1_1ⁱ—O1_3—Na1_1	165.02 (13)
O1_2ⁱⁱ—Na1_1—O1_3^ix	64.36 (11)	Na1_1ⁱ—O1_3—Na1_2^iv	97.49 (6)
O1_2ⁱⁱ—Na1_1—O1_3^xi	113.2 (3)	Na1_1ⁱ—O1_3—Nb1_1	87.1 (2)
O1_2^xii—Na1_1—O1_2^vii	124.33 (8)	Na1_1ⁱ—O1_3—Nb1_1^xi	90.1 (2)
O1_2^xii—Na1_1—O1_3ⁱⁱ	121.9 (3)	Na1_1ⁱ—O1_3—Li2^iv	97.49 (6)
O1_2^xii—Na1_1—O1_3^vii	60.83 (13)	Na1_1—O1_3—Na1_2^iv	97.49 (6)
O1_2^xii—Na1_1—O1_3^ix	60.83 (13)	Na1_1—O1_3—Nb1_1	90.1 (2)
O1_2^xii—Na1_1—O1_3^xi	121.9 (3)	Na1_1—O1_3—Nb1_1^xi	87.1 (2)
O1_2^vii—Na1_1—O1_3ⁱⁱ	113.2 (3)	Na1_1—O1_3—Li2^iv	97.49 (6)
O1_2^vii—Na1_1—O1_3^vii	64.36 (11)	Na1_2^iv—O1_3—Nb1_1	100.54 (9)
O1_2^vii—Na1_1—O1_3^ix	113.2 (3)	Na1_2^iv—O1_3—Nb1_1^xi	100.54 (9)
O1_2^vii—Na1_1—O1_3^xi	64.36 (11)	Na1_2^iv—O1_3—Li2^iv	0.0
O1_3ⁱⁱ—Na1_1—O1_3^vii	176.9 (4)	Nb1_1—O1_3—Nb1_1^xi	158.93 (18)
O1_3ⁱⁱ—Na1_1—O1_3^ix	104.93 (13)	Nb1_1—O1_3—Li2^iv	100.54 (9)
O1_3ⁱⁱ—Na1_1—O1_3^xi	74.98 (13)	Nb1_1^xi—O1_3—Li2^iv	100.54 (9)
O1_3^vii—Na1_1—O1_3^ix	74.98 (13)	O1_3^xv—Li2—O1_3^xii	180.0
O1_3^vii—Na1_1—O1_3^xi	104.93 (13)	O1_3^xv—Li2—O1_3^xvii	90.0
O1_3^ix—Na1_1—O1_3^xi	176.9 (4)	O1_3^xv—Li2—O1_3^xviii	90.0
O1_1ⁱⁱ—Na1_2—O1_1^xvi	74.93 (15)	O1_3^xii—Li2—O1_3^xvii	90.0
O1_1ⁱⁱ—Na1_2—O1_1	129.05 (9)	O1_3^xii—Li2—O1_3^xviii	90.0
O1_1ⁱⁱ—Na1_2—O1_1	129.05 (9)	O1_3^xvii—Li2—O1_3^xviii	180.0
O1_1ⁱⁱ—Na1_2—O1_3^xv	115.47 (5)	O1_1ⁱⁱ—Li3—O1_1^xvi	89.90 (16)
O1_1ⁱⁱ—Na1_2—O1_3^xii	64.53 (5)	O1_1ⁱⁱ—Li3—O1_1	120.06 (9)
O1_1ⁱⁱ—Na1_2—O1_3^xvii	64.53 (5)	O1_1ⁱⁱ—Li3—O1_1	120.06 (9)
O1_1ⁱⁱ—Na1_2—O1_3^xviii	115.47 (5)	O1_1^xvi—Li3—O1_1	120.06 (9)
O1_1^xvi—Na1_2—O1_1	129.05 (9)	O1_1^xvi—Li3—O1_1	120.06 (9)
O1_1^xvi—Na1_2—O1_1	129.05 (9)	O1_1—Li3—O1_1	89.90 (16)
O1_1^xvi—Na1_2—O1_3^xv	64.53 (5)

Symmetry codes: (i) −y+1/2, x, z−1/2; (ii) −y+1/2, x, z+1/2; (iii) −y+1/2, x−1, z+1/2; (iv) x−1, y, z; (v) x, y, z+1; (vi) −x+1/2, −y+1/2, z+1; (vii) y, −x+1/2, z+1/2; (viii) −x+1/2, y, z+1; (ix) −y+1/2, −x+1/2, z+1/2; (x) x, −y+1/2, z+1; (xi) y, x, z+1/2; (xii) −x+1/2, −y+1/2, z; (xiii) −y+3/2, x, z−1/2; (xiv) x, y, z−1; (xv) x+1, y, z; (xvi) y+1, −x+1/2, z+1/2; (xvii) −x+1/2, y, z; (xviii) x+1, −y+1/2, z; (xix) y+1, x, z+1/2; (xx) y+1, −x+1/2, z−1/2; (xxi) x+1, y, z+1; (xxii) x+1, −y+1/2, z+1; (xxiii) −y+1/2, x−1, z−1/2; (xxiv) x−1, y, z−1; (xxv) y, −x+1/2, z−1/2; (xxvi) y, x, z−1/2.

(P42NMC_phase_2) top

Crystal data top

LiNbO₃	c = 13.880 (7) Å
M_r = 147.84	V = 325.74 (14) Å³
Trigonal, R3cH	Z = 6
a = 5.2057 (15) Å	T = 773 K

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Li1	0.0	0.0	0.2829	0.01*
Nb1	0.0	0.0	0.0	0.01*
O1	0.0492	0.3446	0.0647	0.01*

Geometric parameters (Å, º) top

Li1—Nb1ⁱ	3.0133 (14)	Nb1—Li1^xiv	3.0859 (8)
Li1—Nb1ⁱⁱ	3.4111 (8)	Nb1—Li1^xv	3.0859 (8)
Li1—Nb1ⁱⁱⁱ	3.4111 (8)	Nb1—Li1^xvi	3.4111 (8)
Li1—Nb1^iv	3.4111 (8)	Nb1—Li1^xvii	3.4111 (8)
Li1—Nb1^v	3.0859 (8)	Nb1—Li1^xviii	3.4111 (8)
Li1—Nb1^vi	3.0859 (8)	Nb1—O1	1.9054 (5)
Li1—Nb1^vii	3.0859 (8)	Nb1—O1^xix	1.9054 (5)
Li1—O1ⁱⁱ	2.0889 (5)	Nb1—O1^xx	1.9054 (5)
Li1—O1^viii	2.0889 (5)	Nb1—O1^xvi	2.1265 (6)
Li1—O1^ix	2.0889 (5)	Nb1—O1^xxi	2.1265 (6)
Li1—O1^v	2.2522 (6)	Nb1—O1^xxii	2.1265 (6)
Li1—O1^x	2.2522 (6)	O1—Li1^xv	2.2522 (6)
Li1—O1^xi	2.2522 (6)	O1—Li1^xvii	2.0889 (5)
Nb1—Li1^xii	3.0133 (14)	O1—Nb1	1.9054 (5)
Nb1—Li1^xiii	3.0859 (8)	O1—Nb1^iv	2.1265 (6)

Nb1ⁱ—Li1—O1ⁱⁱ	110.024 (10)	Li1^xii—Nb1—O1^xvi	48.275 (16)
Nb1ⁱ—Li1—O1^viii	110.024 (10)	Li1^xii—Nb1—O1^xxi	48.275 (16)
Nb1ⁱ—Li1—O1^ix	110.024 (10)	Li1^xii—Nb1—O1^xxii	48.275 (16)
Nb1ⁱ—Li1—O1^v	44.803 (16)	O1—Nb1—O1^xix	99.603 (17)
Nb1ⁱ—Li1—O1^x	44.803 (16)	O1—Nb1—O1^xx	99.603 (17)
Nb1ⁱ—Li1—O1^xi	44.803 (16)	O1—Nb1—O1^xvi	166.346 (3)
O1ⁱⁱ—Li1—O1^viii	108.913 (10)	O1—Nb1—O1^xxi	88.32 (2)
O1ⁱⁱ—Li1—O1^ix	108.913 (10)	O1—Nb1—O1^xxii	89.92 (2)
O1ⁱⁱ—Li1—O1^v	89.507 (16)	O1^xix—Nb1—O1^xx	99.603 (17)
O1ⁱⁱ—Li1—O1^x	154.040 (5)	O1^xix—Nb1—O1^xvi	89.92 (2)
O1ⁱⁱ—Li1—O1^xi	80.698 (19)	O1^xix—Nb1—O1^xxi	166.346 (3)
O1^viii—Li1—O1^ix	108.913 (10)	O1^xix—Nb1—O1^xxii	88.32 (2)
O1^viii—Li1—O1^v	80.698 (19)	O1^xx—Nb1—O1^xvi	88.32 (2)
O1^viii—Li1—O1^x	89.507 (16)	O1^xx—Nb1—O1^xxi	89.92 (2)
O1^viii—Li1—O1^xi	154.041 (5)	O1^xx—Nb1—O1^xxii	166.346 (3)
O1^ix—Li1—O1^v	154.040 (5)	O1^xvi—Nb1—O1^xxi	80.54 (2)
O1^ix—Li1—O1^x	80.698 (19)	O1^xvi—Nb1—O1^xxii	80.54 (2)
O1^ix—Li1—O1^xi	89.507 (16)	O1^xxi—Nb1—O1^xxii	80.54 (2)
O1^v—Li1—O1^x	75.22 (3)	Li1^xv—O1—Li1^xvii	121.726 (6)
O1^v—Li1—O1^xi	75.22 (3)	Li1^xv—O1—Nb1	95.48 (2)
O1^x—Li1—O1^xi	75.22 (3)	Li1^xv—O1—Nb1^iv	86.92 (3)
Li1^xii—Nb1—O1	118.119 (13)	Li1^xvii—O1—Nb1	117.221 (6)
Li1^xii—Nb1—O1^xix	118.119 (13)	Li1^xvii—O1—Nb1^iv	94.115 (16)
Li1^xii—Nb1—O1^xx	118.119 (13)	Nb1—O1—Nb1^iv	140.268 (6)

Symmetry codes: (i) y−x, y, z+1/2; (ii) y−x−2/3, y−1/3, z+1/6; (iii) y−x+1/3, y−1/3, z+1/6; (iv) y−x+1/3, y+2/3, z+1/6; (v) x−1/3, y−2/3, z+1/3; (vi) x−1/3, y+1/3, z+1/3; (vii) x+2/3, y+1/3, z+1/3; (viii) −y+1/3, −x−1/3, z+1/6; (ix) x+1/3, x−y+2/3, z+1/6; (x) −y+2/3, x−y+1/3, z+1/3; (xi) y−x−1/3, −x+1/3, z+1/3; (xii) y−x, y, z−1/2; (xiii) x−2/3, y−1/3, z−1/3; (xiv) x+1/3, y−1/3, z−1/3; (xv) x+1/3, y+2/3, z−1/3; (xvi) y−x−1/3, y−2/3, z−1/6; (xvii) y−x−1/3, y+1/3, z−1/6; (xviii) y−x+2/3, y+1/3, z−1/6; (xix) −y, x−y, z; (xx) y−x, −x, z; (xxi) −y+2/3, −x+1/3, z−1/6; (xxii) x−1/3, x−y+1/3, z−1/6.

(LNN20_P4MBM_800C_phase_1) top

Crystal data top

Li_0.20Na_0.80NbO₃	c = 3.94101 (12) Å
M_r = 160.68	V = 122.18 (1) Å³
Tetragonal, P4/mbm	Z = 2
a = 5.56804 (12) Å	T = 1073 K

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Nb1	0.0	0.0	0.0	0.01413
Na1	0.0	0.5	0.5	0.03891	0.8
O1	0.0	0.0	0.5	0.06498
O2	0.2610 (2)	0.2390 (2)	0.0	0.04118
Li1	0.0	0.5	0.5	0.03891	0.2

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Nb1	0.0116 (12)	0.0116 (12)	0.019 (3)	0.0	0.0	0.0
Na1	0.046 (3)	0.046 (3)	0.025 (5)	−0.002 (4)	0.0	0.0
O1	0.089 (3)	0.089 (3)	0.016 (3)	0.0	0.0	0.0
O2	0.0305 (15)	0.0305 (15)	0.063 (2)	−0.0253 (16)	0.0	0.0
Li1	0.046 (3)	0.046 (3)	0.025 (5)	−0.002 (4)	0.0	0.0

Geometric parameters (Å, º) top

Nb1—Na1ⁱ	3.4108 (1)	Na1—O2^xx	2.8471 (13)
Nb1—Na1ⁱⁱ	3.4108 (1)	Na1—O2^xxi	2.8471 (13)
Nb1—Na1ⁱⁱⁱ	3.4108 (1)	Na1—O2^xxii	2.7249 (13)
Nb1—Na1	3.4108 (1)	Na1—O2^xxiii	2.7249 (13)
Nb1—Na1^iv	3.4108 (1)	O1—Nb1	1.9705 (1)
Nb1—Na1^v	3.4108 (1)	O1—Nb1^x	1.9705 (1)
Nb1—Na1^vi	3.4108 (1)	O1—Na1ⁱⁱ	2.7840 (1)
Nb1—Na1^vii	3.4108 (1)	O1—Na1	2.7840 (1)
Nb1—O1ⁱⁱⁱ	1.9705 (1)	O1—Na1^v	2.7840 (1)
Nb1—O1	1.9705 (1)	O1—Na1^vii	2.7840 (1)
Nb1—O2	1.9705 (1)	O1—Li1ⁱⁱ	2.7840 (1)
Nb1—O2^v	1.9705 (1)	O1—Li1	2.7840 (1)
Nb1—O2^viii	1.9705 (1)	O1—Li1^v	2.7840 (1)
Nb1—O2^ix	1.9705 (1)	O1—Li1^vii	2.7840 (1)
Nb1—Li1ⁱ	3.4108 (1)	O2—Nb1	1.9705 (1)
Nb1—Li1ⁱⁱ	3.4108 (1)	O2—Nb1^xv	1.9705 (1)
Nb1—Li1ⁱⁱⁱ	3.4108 (1)	O2—Na1ⁱⁱⁱ	2.8471 (13)
Nb1—Li1	3.4108 (1)	O2—Na1	2.8471 (13)
Nb1—Li1^iv	3.4108 (1)	O2—Na1^vi	2.7249 (13)
Nb1—Li1^v	3.4108 (1)	O2—Na1^vii	2.7249 (13)
Nb1—Li1^vi	3.4108 (1)	O2—Li1ⁱⁱⁱ	2.8471 (13)
Nb1—Li1^vii	3.4108 (1)	O2—Li1	2.8471 (13)
Na1—Nb1	3.4108 (1)	O2—Li1^vi	2.7249 (13)
Na1—Nb1^x	3.4108 (1)	O2—Li1^vii	2.7249 (13)
Na1—Nb1^xi	3.4108 (1)	Li1—Nb1	3.4108 (1)
Na1—Nb1^xii	3.4108 (1)	Li1—Nb1^x	3.4108 (1)
Na1—Nb1^xiii	3.4108 (1)	Li1—Nb1^xi	3.4108 (1)
Na1—Nb1^xiv	3.4108 (1)	Li1—Nb1^xii	3.4108 (1)
Na1—Nb1^xv	3.4108 (1)	Li1—Nb1^xiii	3.4108 (1)
Na1—Nb1^xvi	3.4108 (1)	Li1—Nb1^xiv	3.4108 (1)
Na1—Na1ⁱⁱⁱ	3.9410 (1)	Li1—Nb1^xv	3.4108 (1)
Na1—Na1^x	3.9410 (1)	Li1—Nb1^xvi	3.4108 (1)
Na1—Na1^v	3.9372 (1)	Li1—O1	2.7840 (1)
Na1—Na1^xvii	3.9372 (1)	Li1—O1^xi	2.7840 (1)
Na1—Na1^vii	3.9372 (1)	Li1—O1^xiii	2.7840 (1)
Na1—Na1^xviii	3.9372 (1)	Li1—O1^xv	2.7840 (1)
Na1—O1	2.7840 (1)	Li1—O2	2.8471 (13)
Na1—O1^xi	2.7840 (1)	Li1—O2^x	2.8471 (13)
Na1—O1^xiii	2.7840 (1)	Li1—O2^v	2.7249 (13)
Na1—O1^xv	2.7840 (1)	Li1—O2^xix	2.7249 (13)
Na1—O2	2.8471 (13)	Li1—O2^xx	2.8471 (13)
Na1—O2^x	2.8471 (13)	Li1—O2^xxi	2.8471 (13)
Na1—O2^v	2.7249 (13)	Li1—O2^xxii	2.7249 (13)
Na1—O2^xix	2.7249 (13)	Li1—O2^xxiii	2.7249 (13)

O1ⁱⁱⁱ—Nb1—O1	180.0	O1^xiii—Na1—O2^xxiii	119.236 (16)
O1ⁱⁱⁱ—Nb1—O2	90.0	O1^xv—Na1—O2^v	119.236 (16)
O1ⁱⁱⁱ—Nb1—O2^v	90.0	O1^xv—Na1—O2^xix	119.236 (16)
O1ⁱⁱⁱ—Nb1—O2^viii	90.0	O1^xv—Na1—O2^xxii	60.764 (16)
O1ⁱⁱⁱ—Nb1—O2^ix	90.0	O1^xv—Na1—O2^xxiii	60.764 (16)
O1—Nb1—O2	90.0	O2^v—Na1—O2^xix	92.63 (6)
O1—Nb1—O2^v	90.0	O2^v—Na1—O2^xxii	87.37 (6)
O1—Nb1—O2^viii	90.0	O2^v—Na1—O2^xxiii	180.0
O1—Nb1—O2^ix	90.0	O2^xix—Na1—O2^xxii	180.0
O2—Nb1—O2^v	90.0	O2^xix—Na1—O2^xxiii	87.37 (6)
O2—Nb1—O2^viii	180.0	O2^xxii—Na1—O2^xxiii	92.63 (6)
O2—Nb1—O2^ix	90.0	Nb1—O1—Nb1^x	180.0
O2^v—Nb1—O2^viii	90.0	Nb1—O1—Na1ⁱⁱ	90.0
O2^v—Nb1—O2^ix	180.0	Nb1—O1—Na1	90.0
O2^viii—Nb1—O2^ix	90.0	Nb1—O1—Na1^v	90.0
O1—Na1—O1^xi	180.0	Nb1—O1—Na1^vii	90.0
O1—Na1—O1^xiii	90.0	Nb1^x—O1—Na1ⁱⁱ	90.0
O1—Na1—O1^xv	90.0	Nb1^x—O1—Na1	90.0
O1—Na1—O2^v	60.764 (16)	Nb1^x—O1—Na1^v	90.0
O1—Na1—O2^xix	60.764 (16)	Nb1^x—O1—Na1^vii	90.0
O1—Na1—O2^xxii	119.236 (16)	Na1ⁱⁱ—O1—Na1	180.0
O1—Na1—O2^xxiii	119.236 (16)	Na1ⁱⁱ—O1—Na1^v	90.0
O1^xi—Na1—O1^xiii	90.0	Na1ⁱⁱ—O1—Na1^vii	90.0
O1^xi—Na1—O1^xv	90.0	Na1—O1—Na1^v	90.0
O1^xi—Na1—O2^v	119.236 (16)	Na1—O1—Na1^vii	90.0
O1^xi—Na1—O2^xix	119.236 (16)	Na1^v—O1—Na1^vii	180.0
O1^xi—Na1—O2^xxii	60.764 (16)	Nb1—O2—Nb1^xv	174.97 (11)
O1^xi—Na1—O2^xxiii	60.764 (16)	Nb1—O2—Na1^vi	91.74 (4)
O1^xiii—Na1—O1^xv	180.0	Nb1—O2—Na1^vii	91.74 (4)
O1^xiii—Na1—O2^v	60.764 (16)	Nb1^xv—O2—Na1^vi	91.74 (4)
O1^xiii—Na1—O2^xix	60.764 (16)	Nb1^xv—O2—Na1^vii	91.74 (4)
O1^xiii—Na1—O2^xxii	119.236 (16)	Na1^vi—O2—Na1^vii	92.63 (6)

Symmetry codes: (i) x, y−1, z−1; (ii) x, y−1, z; (iii) x, y, z−1; (iv) −y, x, z−1; (v) −y, x, z; (vi) −y+1, x, z−1; (vii) −y+1, x, z; (viii) −x, −y, z; (ix) y, −x, z; (x) x, y, z+1; (xi) x, y+1, z; (xii) x, y+1, z+1; (xiii) −x−1/2, y+1/2, z; (xiv) −x−1/2, y+1/2, z+1; (xv) −x+1/2, y+1/2, z; (xvi) −x+1/2, y+1/2, z+1; (xvii) −y, x+1, z; (xviii) −y+1, x+1, z; (xix) −y, x, z+1; (xx) −x, −y+1, z; (xxi) −x, −y+1, z+1; (xxii) y, −x+1, z; (xxiii) y, −x+1, z+1.

(LNN20_P4MBM_800C_phase_2) top

Crystal data top

LiNbO₃	c = 13.8773 (18) Å
M_r = 147.84	V = 330.04 (4) Å³
Trigonal, R3cH	Z = 6
a = 5.2404 (4) Å	T = 1073 K

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Li1	0.0	0.0	0.2829	0.01*
Nb1	0.0	0.0	0.0	0.01*
O1	0.0492	0.3446	0.0647	0.01*

Geometric parameters (Å, º) top

Li1—Nb1ⁱ	3.0127 (4)	Nb1—Li1^xiv	3.1055 (2)
Li1—Nb1ⁱⁱ	3.4287 (2)	Nb1—Li1^xv	3.1055 (2)
Li1—Nb1ⁱⁱⁱ	3.4287 (2)	Nb1—Li1^xvi	3.4287 (2)
Li1—Nb1^iv	3.4287 (2)	Nb1—Li1^xvii	3.4287 (2)
Li1—Nb1^v	3.1055 (2)	Nb1—Li1^xviii	3.4287 (2)
Li1—Nb1^vi	3.1055 (2)	Nb1—O1	1.9152 (1)
Li1—Nb1^vii	3.1055 (2)	Nb1—O1^xix	1.9152 (1)
Li1—O1ⁱⁱ	2.1012 (2)	Nb1—O1^xx	1.9152 (1)
Li1—O1^viii	2.1012 (2)	Nb1—O1^xvi	2.1342 (2)
Li1—O1^ix	2.1012 (2)	Nb1—O1^xxi	2.1342 (2)
Li1—O1^v	2.2595 (2)	Nb1—O1^xxii	2.1342 (2)
Li1—O1^x	2.2595 (2)	O1—Li1^xv	2.2595 (2)
Li1—O1^xi	2.2595 (2)	O1—Li1^xvii	2.1012 (2)
Nb1—Li1^xii	3.0127 (4)	O1—Nb1	1.9152 (1)
Nb1—Li1^xiii	3.1055 (2)	O1—Nb1^iv	2.1342 (2)

Nb1ⁱ—Li1—O1ⁱⁱ	109.898 (3)	Li1^xii—Nb1—O1^xvi	48.470 (4)
Nb1ⁱ—Li1—O1^viii	109.898 (3)	Li1^xii—Nb1—O1^xxi	48.470 (4)
Nb1ⁱ—Li1—O1^ix	109.898 (3)	Li1^xii—Nb1—O1^xxii	48.470 (4)
Nb1ⁱ—Li1—O1^v	44.999 (4)	O1—Nb1—O1^xix	99.808 (4)
Nb1ⁱ—Li1—O1^x	44.999 (4)	O1—Nb1—O1^xx	99.808 (4)
Nb1ⁱ—Li1—O1^xi	44.999 (4)	O1—Nb1—O1^xvi	166.3779 (7)
O1ⁱⁱ—Li1—O1^viii	109.041 (3)	O1—Nb1—O1^xxi	88.070 (6)
O1ⁱⁱ—Li1—O1^ix	109.041 (3)	O1—Nb1—O1^xxii	89.672 (5)
O1ⁱⁱ—Li1—O1^v	89.315 (4)	O1^xix—Nb1—O1^xx	99.808 (4)
O1ⁱⁱ—Li1—O1^x	154.1054 (14)	O1^xix—Nb1—O1^xvi	89.672 (5)
O1ⁱⁱ—Li1—O1^xi	80.466 (5)	O1^xix—Nb1—O1^xxi	166.3778 (7)
O1^viii—Li1—O1^ix	109.041 (3)	O1^xix—Nb1—O1^xxii	88.070 (6)
O1^viii—Li1—O1^v	80.466 (5)	O1^xx—Nb1—O1^xvi	88.070 (6)
O1^viii—Li1—O1^x	89.315 (4)	O1^xx—Nb1—O1^xxi	89.672 (5)
O1^viii—Li1—O1^xi	154.1054 (14)	O1^xx—Nb1—O1^xxii	166.3779 (7)
O1^ix—Li1—O1^v	154.1054 (14)	O1^xvi—Nb1—O1^xxi	80.828 (7)
O1^ix—Li1—O1^x	80.466 (5)	O1^xvi—Nb1—O1^xxii	80.828 (7)
O1^ix—Li1—O1^xi	89.315 (4)	O1^xxi—Nb1—O1^xxii	80.828 (7)
O1^v—Li1—O1^x	75.521 (7)	Li1^xv—O1—Li1^xvii	121.6533 (16)
O1^v—Li1—O1^xi	75.521 (7)	Li1^xv—O1—Nb1	95.772 (6)
O1^x—Li1—O1^xi	75.521 (7)	Li1^xv—O1—Nb1^iv	86.532 (9)
Li1^xii—Nb1—O1	117.956 (4)	Li1^xvii—O1—Nb1	117.1482 (16)
Li1^xii—Nb1—O1^xix	117.956 (4)	Li1^xvii—O1—Nb1^iv	94.309 (4)
Li1^xii—Nb1—O1^xx	117.956 (4)	Nb1—O1—Nb1^iv	140.1970 (16)

Symmetry codes: (i) y−x, y, z+1/2; (ii) y−x−2/3, y−1/3, z+1/6; (iii) y−x+1/3, y−1/3, z+1/6; (iv) y−x+1/3, y+2/3, z+1/6; (v) x−1/3, y−2/3, z+1/3; (vi) x−1/3, y+1/3, z+1/3; (vii) x+2/3, y+1/3, z+1/3; (viii) −y+1/3, −x−1/3, z+1/6; (ix) x+1/3, x−y+2/3, z+1/6; (x) −y+2/3, x−y+1/3, z+1/3; (xi) y−x−1/3, −x+1/3, z+1/3; (xii) y−x, y, z−1/2; (xiii) x−2/3, y−1/3, z−1/3; (xiv) x+1/3, y−1/3, z−1/3; (xv) x+1/3, y+2/3, z−1/3; (xvi) y−x−1/3, y−2/3, z−1/6; (xvii) y−x−1/3, y+1/3, z−1/6; (xviii) y−x+2/3, y+1/3, z−1/6; (xix) −y, x−y, z; (xx) y−x, −x, z; (xxi) −y+2/3, −x+1/3, z−1/6; (xxii) x−1/3, x−y+1/3, z−1/6.

(LNN20_900C_CUBIC_phase_1) top

Crystal data top

Li_0.20Na_0.80NbO₃	V = 61.42 (1) Å³
M_r = 160.68	Z = 1
Cubic, Pm3m	T = 1173 K
a = 3.94561 (3) Å

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Na1	0.0	0.0	0.0	0.04055	0.8
Nb1	0.5	0.5	0.5	0.01471
O1	0.0	0.5	0.5	0.04842
Li1	0.0	0.0	0.0	0.04054	0.2

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Na1	0.04055	0.04055	0.04055	0.0	0.0	0.0
Nb1	0.01471	0.01471	0.01471	0.0	0.0	0.0
O1	0.01035	0.06746	0.06746	0.0	0.0	0.0
Li1	0.04054	0.04054	0.04054	0.0	0.0	0.0

Geometric parameters (Å, º) top

Na1—Na1ⁱ	3.9456 (1)	Nb1—O1^xxiv	1.9728 (1)
Na1—Na1ⁱⁱ	3.9456 (1)	Nb1—Li1	3.4170 (1)
Na1—Na1ⁱⁱⁱ	3.9456 (1)	Nb1—Li1^iv	3.4170 (1)
Na1—Na1^iv	3.9456 (1)	Nb1—Li1^v	3.4170 (1)
Na1—Na1^v	3.9456 (1)	Nb1—Li1^xix	3.4170 (1)
Na1—Na1^vi	3.9456 (1)	Nb1—Li1^vi	3.4170 (1)
Na1—Nb1^vii	3.4170 (1)	Nb1—Li1^xx	3.4170 (1)
Na1—Nb1^viii	3.4170 (1)	Nb1—Li1^xxi	3.4170 (1)
Na1—Nb1^ix	3.4170 (1)	Nb1—Li1^xxii	3.4170 (1)
Na1—Nb1ⁱ	3.4170 (1)	O1—Na1	2.7900 (1)
Na1—Nb1^x	3.4170 (1)	O1—Na1^iv	2.7900 (1)
Na1—Nb1ⁱⁱ	3.4170 (1)	O1—Na1^v	2.7900 (1)
Na1—Nb1ⁱⁱⁱ	3.4170 (1)	O1—Na1^xix	2.7900 (1)
Na1—Nb1	3.4170 (1)	O1—Nb1ⁱ	1.9728 (1)
Na1—O1^x	2.7900 (1)	O1—Nb1	1.9728 (1)
Na1—O1ⁱⁱ	2.7900 (1)	O1—Li1	2.7900 (1)
Na1—O1ⁱⁱⁱ	2.7900 (1)	O1—Li1^iv	2.7900 (1)
Na1—O1	2.7900 (1)	O1—Li1^v	2.7900 (1)
Na1—O1^xi	2.7900 (1)	O1—Li1^xix	2.7900 (1)
Na1—O1^xii	2.7900 (1)	Li1—Nb1^vii	3.4170 (1)
Na1—O1^xiii	2.7900 (1)	Li1—Nb1^viii	3.4170 (1)
Na1—O1^xiv	2.7900 (1)	Li1—Nb1^ix	3.4170 (1)
Na1—O1^xv	2.7900 (1)	Li1—Nb1ⁱ	3.4170 (1)
Na1—O1^xvi	2.7900 (1)	Li1—Nb1^x	3.4170 (1)
Na1—O1^xvii	2.7900 (1)	Li1—Nb1ⁱⁱ	3.4170 (1)
Na1—O1^xviii	2.7900 (1)	Li1—Nb1ⁱⁱⁱ	3.4170 (1)
Nb1—Na1	3.4170 (1)	Li1—Nb1	3.4170 (1)
Nb1—Na1^iv	3.4170 (1)	Li1—O1^x	2.7900 (1)
Nb1—Na1^v	3.4170 (1)	Li1—O1ⁱⁱ	2.7900 (1)
Nb1—Na1^xix	3.4170 (1)	Li1—O1ⁱⁱⁱ	2.7900 (1)
Nb1—Na1^vi	3.4170 (1)	Li1—O1	2.7900 (1)
Nb1—Na1^xx	3.4170 (1)	Li1—O1^xi	2.7900 (1)
Nb1—Na1^xxi	3.4170 (1)	Li1—O1^xii	2.7900 (1)
Nb1—Na1^xxii	3.4170 (1)	Li1—O1^xiii	2.7900 (1)
Nb1—O1	1.9728 (1)	Li1—O1^xiv	2.7900 (1)
Nb1—O1^vi	1.9728 (1)	Li1—O1^xv	2.7900 (1)
Nb1—O1^xiv	1.9728 (1)	Li1—O1^xvi	2.7900 (1)
Nb1—O1^xxiii	1.9728 (1)	Li1—O1^xvii	2.7900 (1)
Nb1—O1^xviii	1.9728 (1)	Li1—O1^xviii	2.7900 (1)

O1^x—Na1—O1ⁱⁱ	90.0000 (7)	O1^xii—Na1—O1^xvi	60.0000 (2)
O1^x—Na1—O1ⁱⁱⁱ	90.0000 (7)	O1^xii—Na1—O1^xvii	120.0000 (2)
O1^x—Na1—O1	180.0	O1^xii—Na1—O1^xviii	120.0000 (2)
O1^x—Na1—O1^xi	60.0000 (4)	O1^xiii—Na1—O1^xiv	90.0000 (7)
O1^x—Na1—O1^xii	120.0000 (4)	O1^xiii—Na1—O1^xv	120.0000 (2)
O1^x—Na1—O1^xiii	60.0000 (4)	O1^xiii—Na1—O1^xvi	120.0000 (2)
O1^x—Na1—O1^xiv	120.0000 (4)	O1^xiii—Na1—O1^xvii	60.0000 (2)
O1^x—Na1—O1^xv	60.0000 (2)	O1^xiii—Na1—O1^xviii	60.0000 (2)
O1^x—Na1—O1^xvi	120.0000 (2)	O1^xiv—Na1—O1^xv	120.0000 (2)
O1^x—Na1—O1^xvii	60.0000 (2)	O1^xiv—Na1—O1^xvi	120.0000 (2)
O1^x—Na1—O1^xviii	120.0000 (2)	O1^xiv—Na1—O1^xvii	60.0000 (2)
O1ⁱⁱ—Na1—O1ⁱⁱⁱ	180.0	O1^xiv—Na1—O1^xviii	60.0000 (2)
O1ⁱⁱ—Na1—O1	90.0000 (7)	O1^xv—Na1—O1^xvi	90.0
O1ⁱⁱ—Na1—O1^xi	120.0000 (4)	O1^xv—Na1—O1^xvii	90.0
O1ⁱⁱ—Na1—O1^xii	60.0000 (4)	O1^xv—Na1—O1^xviii	180.0
O1ⁱⁱ—Na1—O1^xiii	120.0000 (4)	O1^xvi—Na1—O1^xvii	180.0
O1ⁱⁱ—Na1—O1^xiv	60.0000 (4)	O1^xvi—Na1—O1^xviii	90.0
O1ⁱⁱ—Na1—O1^xv	60.0000 (2)	O1^xvii—Na1—O1^xviii	90.0
O1ⁱⁱ—Na1—O1^xvi	120.0000 (2)	O1—Nb1—O1^vi	180.0
O1ⁱⁱ—Na1—O1^xvii	60.0000 (2)	O1—Nb1—O1^xiv	90.0
O1ⁱⁱ—Na1—O1^xviii	120.0000 (2)	O1—Nb1—O1^xxiii	90.0
O1ⁱⁱⁱ—Na1—O1	90.0000 (7)	O1—Nb1—O1^xviii	90.0
O1ⁱⁱⁱ—Na1—O1^xi	60.0000 (4)	O1—Nb1—O1^xxiv	90.0
O1ⁱⁱⁱ—Na1—O1^xii	120.0000 (4)	O1^vi—Nb1—O1^xiv	90.0
O1ⁱⁱⁱ—Na1—O1^xiii	60.0000 (4)	O1^vi—Nb1—O1^xxiii	90.0
O1ⁱⁱⁱ—Na1—O1^xiv	120.0000 (4)	O1^vi—Nb1—O1^xviii	90.0
O1ⁱⁱⁱ—Na1—O1^xv	120.0000 (2)	O1^vi—Nb1—O1^xxiv	90.0
O1ⁱⁱⁱ—Na1—O1^xvi	60.0000 (2)	O1^xiv—Nb1—O1^xxiii	180.0
O1ⁱⁱⁱ—Na1—O1^xvii	120.0000 (2)	O1^xiv—Nb1—O1^xviii	90.0
O1ⁱⁱⁱ—Na1—O1^xviii	60.0000 (2)	O1^xiv—Nb1—O1^xxiv	90.0
O1—Na1—O1^xi	120.0000 (4)	O1^xxiii—Nb1—O1^xviii	90.0
O1—Na1—O1^xii	60.0000 (4)	O1^xxiii—Nb1—O1^xxiv	90.0
O1—Na1—O1^xiii	120.0000 (4)	O1^xviii—Nb1—O1^xxiv	180.0
O1—Na1—O1^xiv	60.0000 (4)	Na1—O1—Na1^iv	90.0000 (7)
O1—Na1—O1^xv	120.0000 (2)	Na1—O1—Na1^v	90.0000 (7)
O1—Na1—O1^xvi	60.0000 (2)	Na1—O1—Na1^xix	180.0
O1—Na1—O1^xvii	120.0000 (2)	Na1—O1—Nb1ⁱ	90.0
O1—Na1—O1^xviii	60.0000 (2)	Na1—O1—Nb1	90.0
O1^xi—Na1—O1^xii	90.0000 (7)	Na1^iv—O1—Na1^v	180.0
O1^xi—Na1—O1^xiii	90.0000 (7)	Na1^iv—O1—Na1^xix	90.0000 (7)
O1^xi—Na1—O1^xiv	180.0	Na1^iv—O1—Nb1ⁱ	90.0
O1^xi—Na1—O1^xv	60.0000 (2)	Na1^iv—O1—Nb1	90.0
O1^xi—Na1—O1^xvi	60.0000 (2)	Na1^v—O1—Na1^xix	90.0000 (7)
O1^xi—Na1—O1^xvii	120.0000 (2)	Na1^v—O1—Nb1ⁱ	90.0
O1^xi—Na1—O1^xviii	120.0000 (2)	Na1^v—O1—Nb1	90.0
O1^xii—Na1—O1^xiii	180.0	Na1^xix—O1—Nb1ⁱ	90.0
O1^xii—Na1—O1^xiv	90.0000 (7)	Na1^xix—O1—Nb1	90.0
O1^xii—Na1—O1^xv	60.0000 (2)	Nb1ⁱ—O1—Nb1	180.0

Symmetry codes: (i) x−1, y, z; (ii) x, y−1, z; (iii) x, y, z−1; (iv) x, y, z+1; (v) x, y+1, z; (vi) x+1, y, z; (vii) x−1, y−1, z−1; (viii) x−1, y−1, z; (ix) x−1, y, z−1; (x) x, y−1, z−1; (xi) z−1, x, y−1; (xii) z−1, x, y; (xiii) z, x, y−1; (xiv) z, x, y; (xv) y−1, z−1, x; (xvi) y−1, z, x; (xvii) y, z−1, x; (xviii) y, z, x; (xix) x, y+1, z+1; (xx) x+1, y, z+1; (xxi) x+1, y+1, z; (xxii) x+1, y+1, z+1; (xxiii) z, x+1, y; (xxiv) y, z, x+1.

(LNN20_900C_CUBIC_phase_2) top

Crystal data top

LiNbO₃	c = 13.8744 (11) Å
M_r = 147.84	V = 331.65 (2) Å³
Trigonal, R3cH	Z = 6
a = 5.2537 (2) Å	T = 1173 K

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Li1	0.0	0.0	0.2829	0.01*
Nb1	0.0	0.0	0.0	0.01*
O1	0.0492	0.3446	0.0647	0.01*

Geometric parameters (Å, º) top

Li1—Nb1ⁱ	3.0121 (2)	Nb1—Li1^xii	3.1129 (1)
Li1—Nb1ⁱⁱ	3.1129 (1)	Nb1—Li1^xiii	3.1129 (1)
Li1—Nb1ⁱⁱⁱ	3.1129 (1)	Nb1—O1	1.9189 (1)
Li1—Nb1^iv	3.1129 (1)	Nb1—O1^xiv	1.9189 (1)
Li1—O1^v	2.1059 (1)	Nb1—O1^xv	1.9189 (1)
Li1—O1^vi	2.1059 (1)	Nb1—O1^xvi	2.1371 (1)
Li1—O1^vii	2.1059 (1)	Nb1—O1^xvii	2.1371 (1)
Li1—O1ⁱⁱ	2.2621 (1)	Nb1—O1^xviii	2.1371 (1)
Li1—O1^viii	2.2621 (1)	O1—Li1^xiii	2.2621 (1)
Li1—O1^ix	2.2621 (1)	O1—Li1^xix	2.1059 (1)
Nb1—Li1^x	3.0121 (2)	O1—Nb1	1.9189 (1)
Nb1—Li1^xi	3.1129 (1)	O1—Nb1^xx	2.1371 (1)

Nb1ⁱ—Li1—O1^v	109.8478 (16)	Li1^x—Nb1—O1^xvi	48.547 (3)
Nb1ⁱ—Li1—O1^vi	109.8478 (16)	Li1^x—Nb1—O1^xvii	48.547 (3)
Nb1ⁱ—Li1—O1^vii	109.8478 (16)	Li1^x—Nb1—O1^xviii	48.547 (3)
Nb1ⁱ—Li1—O1ⁱⁱ	45.077 (3)	O1—Nb1—O1^xiv	99.890 (3)
Nb1ⁱ—Li1—O1^viii	45.077 (3)	O1—Nb1—O1^xv	99.890 (3)
Nb1ⁱ—Li1—O1^ix	45.077 (3)	O1—Nb1—O1^xvi	166.3907 (4)
O1^v—Li1—O1^vi	109.0921 (17)	O1—Nb1—O1^xvii	87.969 (3)
O1^v—Li1—O1^vii	109.0920 (17)	O1—Nb1—O1^xviii	89.574 (3)
O1^v—Li1—O1ⁱⁱ	89.238 (3)	O1^xiv—Nb1—O1^xv	99.890 (3)
O1^v—Li1—O1^viii	154.1316 (9)	O1^xiv—Nb1—O1^xvi	89.574 (3)
O1^v—Li1—O1^ix	80.373 (3)	O1^xiv—Nb1—O1^xvii	166.3907 (4)
O1^vi—Li1—O1^vii	109.0921 (17)	O1^xiv—Nb1—O1^xviii	87.969 (3)
O1^vi—Li1—O1ⁱⁱ	80.373 (3)	O1^xv—Nb1—O1^xvi	87.969 (3)
O1^vi—Li1—O1^viii	89.238 (3)	O1^xv—Nb1—O1^xvii	89.574 (3)
O1^vi—Li1—O1^ix	154.1316 (9)	O1^xv—Nb1—O1^xviii	166.3907 (4)
O1^vii—Li1—O1ⁱⁱ	154.1316 (9)	O1^xvi—Nb1—O1^xvii	80.946 (4)
O1^vii—Li1—O1^viii	80.373 (3)	O1^xvi—Nb1—O1^xviii	80.946 (4)
O1^vii—Li1—O1^ix	89.238 (3)	O1^xvii—Nb1—O1^xviii	80.946 (4)
O1ⁱⁱ—Li1—O1^viii	75.642 (4)	Li1^xiii—O1—Li1^xix	121.6241 (9)
O1ⁱⁱ—Li1—O1^ix	75.642 (4)	Li1^xiii—O1—Nb1	95.888 (4)
O1^viii—Li1—O1^ix	75.642 (4)	Li1^xiii—O1—Nb1^xx	86.375 (5)
Li1^x—Nb1—O1	117.891 (2)	Li1^xix—O1—Nb1	117.1189 (9)
Li1^x—Nb1—O1^xiv	117.891 (2)	Li1^xix—O1—Nb1^xx	94.387 (3)
Li1^x—Nb1—O1^xv	117.891 (2)	Nb1—O1—Nb1^xx	140.1688 (9)

Symmetry codes: (i) y−x, y, z+1/2; (ii) x−1/3, y−2/3, z+1/3; (iii) x−1/3, y+1/3, z+1/3; (iv) x+2/3, y+1/3, z+1/3; (v) y−x−2/3, y−1/3, z+1/6; (vi) −y+1/3, −x−1/3, z+1/6; (vii) x+1/3, x−y+2/3, z+1/6; (viii) −y+2/3, x−y+1/3, z+1/3; (ix) y−x−1/3, −x+1/3, z+1/3; (x) y−x, y, z−1/2; (xi) x−2/3, y−1/3, z−1/3; (xii) x+1/3, y−1/3, z−1/3; (xiii) x+1/3, y+2/3, z−1/3; (xiv) −y, x−y, z; (xv) y−x, −x, z; (xvi) y−x−1/3, y−2/3, z−1/6; (xvii) −y+2/3, −x+1/3, z−1/6; (xviii) x−1/3, x−y+1/3, z−1/6; (xix) y−x−1/3, y+1/3, z−1/6; (xx) y−x+1/3, y+2/3, z+1/6.

(LNN20_P42MC_300C_phase_1) top

Crystal data top

Li_0.20Na_0.80NbO₃	c = 7.8499 (3) Å
M_r = 160.68	V = 474.01 (4) Å³
Tetragonal, P4₂mc	Z = 8
a = 7.7707 (2) Å	T = 573 K

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Na1_1	0.0	0.5	0.725 (3)	0.040 (3)*	0.8
Na1_2	0.0	0.5	0.256 (6)	0.040 (3)*	0.8
Na1_3	0.5	0.5	0.255 (3)	0.003 (4)*	0.8
Na1_4	0.0	0.0	0.237 (2)	−0.007 (3)*	0.8
Nb1_1	0.2487 (5)	0.7493 (5)	0.0	0.0048 (3)*
O1_1	0.2273 (8)	0.5	0.4835 (7)	0.0138 (9)*
O1_2	0.2779 (7)	0.5	0.0542 (7)	0.0075 (7)*
O1_3	0.2849 (8)	0.0	0.5540 (8)	0.0075 (7)*
O1_4	0.2107 (7)	0.0	0.0024 (6)	0.0138 (9)*
O1_5	0.2859 (11)	0.7875 (11)	0.2652 (4)	0.0154 (4)*
Li1_1	0.0	0.5	0.725 (3)	0.040 (3)*	0.2
Li1_2	0.0	0.5	0.256 (6)	0.040 (3)*	0.2
Li1_3	0.5	0.5	0.255 (3)	0.003 (4)*	0.2
Li1_4	0.0	0.0	0.237 (2)	−0.007 (3)*	0.2

Geometric parameters (Å, º) top

Na1_1—Na1_2	3.68 (3)	Nb1_1—O1_2	1.997 (4)
Na1_1—Na1_2ⁱ	4.17 (3)	Nb1_1—O1_3^xix	1.996 (4)
Na1_1—Na1_3ⁱⁱ	3.892 (2)	Nb1_1—O1_4^xv	1.970 (4)
Na1_1—Na1_3ⁱⁱⁱ	3.892 (2)	Nb1_1—O1_5	2.122 (3)
Na1_1—Na1_4ⁱⁱ	3.8865 (8)	Nb1_1—O1_5^xxxiv	1.885 (3)
Na1_1—Na1_4^iv	3.8865 (8)	Nb1_1—Li1_1^xxi	3.275 (11)
Na1_1—Nb1_1ⁱ	3.486 (13)	Nb1_1—Li1_2	3.39 (3)
Na1_1—Nb1_1ⁱⁱⁱ	3.275 (11)	Nb1_1—Li1_2^xxi	3.36 (3)
Na1_1—Nb1_1^v	3.486 (13)	Nb1_1—Li1_3	3.400 (13)
Na1_1—Nb1_1^vi	3.275 (11)	Nb1_1—Li1_3^xx	3.359 (13)
Na1_1—Nb1_1^vii	3.486 (13)	Nb1_1—Li1_4^xv	3.313 (11)
Na1_1—Nb1_1^viii	3.275 (11)	O1_1—Na1_1	2.590 (16)
Na1_1—Nb1_1^ix	3.486 (13)	O1_1—Na1_2	2.51 (3)
Na1_1—Nb1_1^x	3.275 (11)	O1_1—Na1_3	2.779 (14)
Na1_1—O1_1	2.590 (16)	O1_1—Na1_3ⁱⁱⁱ	3.003 (17)
Na1_1—O1_1^xi	2.590 (16)	O1_1—Nb1_1ⁱⁱⁱ	1.966 (4)
Na1_1—O1_3ⁱⁱ	3.078 (18)	O1_1—Nb1_1^viii	1.966 (4)
Na1_1—O1_3^xii	3.078 (18)	O1_1—Li1_1	2.590 (16)
Na1_1—O1_4ⁱⁱ	2.847 (13)	O1_1—Li1_2	2.51 (3)
Na1_1—O1_4^xii	2.847 (13)	O1_1—Li1_3	2.779 (14)
Na1_1—O1_5ⁱⁱⁱ	2.366 (3)	O1_2—Na1_2	2.68 (3)
Na1_1—O1_5^vi	2.366 (3)	O1_2—Na1_3	2.335 (17)
Na1_1—O1_5^viii	2.366 (3)	O1_2—Na1_3^xx	2.918 (18)
Na1_1—O1_5^x	2.366 (3)	O1_2—Nb1_1	1.997 (4)
Na1_1—Li1_2	3.68 (3)	O1_2—Nb1_1^xvii	1.997 (4)
Na1_2—Na1_1^xiii	4.17 (3)	O1_2—Li1_2	2.68 (3)
Na1_2—Na1_1	3.68 (3)	O1_2—Li1_3	2.335 (17)
Na1_2—Na1_3^xiv	3.8854 (2)	O1_3—Na1_1^xx	3.078 (18)
Na1_2—Na1_3	3.8854 (2)	O1_3—Na1_2ⁱⁱⁱ	2.30 (3)
Na1_2—Na1_4	3.888 (2)	O1_3—Na1_4ⁱⁱ	2.637 (12)
Na1_2—Na1_4^xv	3.888 (2)	O1_3—Nb1_1ⁱⁱⁱ	1.996 (4)
Na1_2—Nb1_1	3.39 (3)	O1_3—Nb1_1^xxix	1.996 (4)
Na1_2—Nb1_1ⁱⁱⁱ	3.36 (3)	O1_3—Li1_2ⁱⁱⁱ	2.30 (3)
Na1_2—Nb1_1^xi	3.39 (3)	O1_3—Li1_4ⁱⁱ	2.637 (12)
Na1_2—Nb1_1^vi	3.36 (3)	O1_4—Na1_1^xx	2.847 (13)
Na1_2—Nb1_1^xvi	3.39 (3)	O1_4—Na1_2^xx	2.97 (3)
Na1_2—Nb1_1^viii	3.36 (3)	O1_4—Na1_4	2.462 (16)
Na1_2—Nb1_1^xvii	3.39 (3)	O1_4—Na1_4^xviii	2.652 (16)
Na1_2—Nb1_1^x	3.36 (3)	O1_4—Nb1_1^xxvi	1.970 (4)
Na1_2—O1_1	2.51 (3)	O1_4—Nb1_1^xvii	1.970 (4)
Na1_2—O1_1^xi	2.51 (3)	O1_4—Li1_1^xx	2.847 (13)
Na1_2—O1_2	2.68 (3)	O1_4—Li1_4	2.462 (16)
Na1_2—O1_2^xi	2.68 (3)	O1_4—Li1_4^xviii	2.652 (16)
Na1_2—O1_3^xviii	2.30 (3)	O1_5—Na1_1^xxi	2.366 (3)
Na1_2—O1_3^xix	2.30 (3)	O1_5—Na1_2	3.1513 (19)
Na1_2—O1_4ⁱⁱ	2.97 (3)	O1_5—Na1_3	2.787 (12)
Na1_2—O1_4^xii	2.97 (3)	O1_5—Na1_4^xv	2.777 (12)
Na1_2—O1_5	3.1513 (19)	O1_5—Nb1_1	2.122 (3)
Na1_2—O1_5^xi	3.1513 (19)	O1_5—Nb1_1^viii	1.885 (3)
Na1_2—O1_5^xvi	3.1513 (19)	O1_5—Li1_1^xxi	2.366 (3)
Na1_2—O1_5^xvii	3.1513 (19)	O1_5—Li1_3	2.787 (12)
Na1_2—Li1_1	3.68 (3)	O1_5—Li1_4^xv	2.777 (12)
Na1_3—Na1_1^xx	3.892 (2)	Li1_1—Na1_2	3.68 (3)
Na1_3—Na1_1^xxi	3.892 (2)	Li1_1—Nb1_1ⁱⁱⁱ	3.275 (11)
Na1_3—Na1_2	3.8854 (2)	Li1_1—Nb1_1^vi	3.275 (11)
Na1_3—Na1_2^xxii	3.8854 (2)	Li1_1—Nb1_1^viii	3.275 (11)
Na1_3—Na1_3^xx	3.9250 (1)	Li1_1—Nb1_1^x	3.275 (11)
Na1_3—Na1_3ⁱⁱⁱ	3.9250 (1)	Li1_1—O1_1	2.590 (16)
Na1_3—Nb1_1	3.400 (13)	Li1_1—O1_1^xi	2.590 (16)
Na1_3—Nb1_1ⁱⁱⁱ	3.359 (13)	Li1_1—O1_4ⁱⁱ	2.847 (13)
Na1_3—Nb1_1^xxiii	3.400 (13)	Li1_1—O1_4^xii	2.847 (13)
Na1_3—Nb1_1^xii	3.359 (13)	Li1_1—O1_5ⁱⁱⁱ	2.366 (3)
Na1_3—Nb1_1^xxiv	3.400 (13)	Li1_1—O1_5^vi	2.366 (3)
Na1_3—Nb1_1^viii	3.359 (13)	Li1_1—O1_5^viii	2.366 (3)
Na1_3—Nb1_1^xvii	3.400 (13)	Li1_1—O1_5^x	2.366 (3)
Na1_3—Nb1_1^xxv	3.359 (13)	Li1_2—Na1_1	3.68 (3)
Na1_3—O1_1	2.779 (14)	Li1_2—Nb1_1	3.39 (3)
Na1_3—O1_1^xx	3.003 (17)	Li1_2—Nb1_1ⁱⁱⁱ	3.36 (3)
Na1_3—O1_1^xxiii	2.779 (14)	Li1_2—Nb1_1^xi	3.39 (3)
Na1_3—O1_1^xix	3.003 (17)	Li1_2—Nb1_1^vi	3.36 (3)
Na1_3—O1_2	2.335 (17)	Li1_2—Nb1_1^xvi	3.39 (3)
Na1_3—O1_2ⁱⁱⁱ	2.918 (18)	Li1_2—Nb1_1^viii	3.36 (3)
Na1_3—O1_2^xxiii	2.335 (17)	Li1_2—Nb1_1^xvii	3.39 (3)
Na1_3—O1_2^xii	2.918 (18)	Li1_2—Nb1_1^x	3.36 (3)
Na1_3—O1_5	2.787 (12)	Li1_2—O1_1	2.51 (3)
Na1_3—O1_5^xxiii	2.787 (12)	Li1_2—O1_1^xi	2.51 (3)
Na1_3—O1_5^xxiv	2.787 (12)	Li1_2—O1_2	2.68 (3)
Na1_3—O1_5^xvii	2.787 (12)	Li1_2—O1_2^xi	2.68 (3)
Na1_4—Na1_1^xviii	3.8865 (8)	Li1_2—O1_3^xviii	2.30 (3)
Na1_4—Na1_1^xx	3.8865 (8)	Li1_2—O1_3^xix	2.30 (3)
Na1_4—Na1_2^xxvi	3.888 (2)	Li1_3—Nb1_1	3.400 (13)
Na1_4—Na1_2	3.888 (2)	Li1_3—Nb1_1ⁱⁱⁱ	3.359 (13)
Na1_4—Na1_4^xviii	3.9250 (1)	Li1_3—Nb1_1^xxiii	3.400 (13)
Na1_4—Na1_4ⁱⁱ	3.9250 (1)	Li1_3—Nb1_1^xii	3.359 (13)
Na1_4—Nb1_1^xxvi	3.313 (11)	Li1_3—Nb1_1^xxiv	3.400 (13)
Na1_4—Nb1_1ⁱⁱⁱ	3.435 (12)	Li1_3—Nb1_1^viii	3.359 (13)
Na1_4—Nb1_1^xi	3.313 (11)	Li1_3—Nb1_1^xvii	3.400 (13)
Na1_4—Nb1_1^xxvii	3.435 (12)	Li1_3—Nb1_1^xxv	3.359 (13)
Na1_4—Nb1_1^xxviii	3.313 (11)	Li1_3—O1_1	2.779 (14)
Na1_4—Nb1_1^xxix	3.435 (12)	Li1_3—O1_1^xxiii	2.779 (14)
Na1_4—Nb1_1^xvii	3.313 (11)	Li1_3—O1_2	2.335 (17)
Na1_4—Nb1_1^x	3.435 (12)	Li1_3—O1_2^xxiii	2.335 (17)
Na1_4—O1_3^xviii	2.637 (12)	Li1_3—O1_5	2.787 (12)
Na1_4—O1_3^xxx	2.637 (12)	Li1_3—O1_5^xxiii	2.787 (12)
Na1_4—O1_4	2.462 (16)	Li1_3—O1_5^xxiv	2.787 (12)
Na1_4—O1_4ⁱⁱ	2.652 (16)	Li1_3—O1_5^xvii	2.787 (12)
Na1_4—O1_4^xxxi	2.462 (16)	Li1_4—Nb1_1^xxvi	3.313 (11)
Na1_4—O1_4^xxxii	2.652 (16)	Li1_4—Nb1_1^xi	3.313 (11)
Na1_4—O1_5^xxvi	2.777 (12)	Li1_4—Nb1_1^xxviii	3.313 (11)
Na1_4—O1_5^xi	2.777 (12)	Li1_4—Nb1_1^xvii	3.313 (11)
Na1_4—O1_5^xxviii	2.777 (12)	Li1_4—O1_3^xviii	2.637 (12)
Na1_4—O1_5^xvii	2.777 (12)	Li1_4—O1_3^xxx	2.637 (12)
Nb1_1—Na1_1^xiii	3.486 (13)	Li1_4—O1_4	2.462 (16)
Nb1_1—Na1_1^xxi	3.275 (11)	Li1_4—O1_4ⁱⁱ	2.652 (16)
Nb1_1—Na1_2	3.39 (3)	Li1_4—O1_4^xxxi	2.462 (16)
Nb1_1—Na1_2^xxi	3.36 (3)	Li1_4—O1_4^xxxii	2.652 (16)
Nb1_1—Na1_3	3.400 (13)	Li1_4—O1_5^xxvi	2.777 (12)
Nb1_1—Na1_3^xx	3.359 (13)	Li1_4—O1_5^xi	2.777 (12)
Nb1_1—Na1_4^xv	3.313 (11)	Li1_4—O1_5^xxviii	2.777 (12)
Nb1_1—Na1_4^xxxiii	3.435 (12)	Li1_4—O1_5^xvii	2.777 (12)
Nb1_1—O1_1^xix	1.966 (4)

Na1_2—Na1_1—Nb1_1ⁱⁱⁱ	57.4 (3)	Nb1_1^xxvi—Na1_4—O1_5^xi	149.5 (7)
Na1_2—Na1_1—Nb1_1^vi	57.4 (3)	Nb1_1^xxvi—Na1_4—O1_5^xxviii	99.3 (2)
Na1_2—Na1_1—Nb1_1^viii	57.4 (3)	Nb1_1^xxvi—Na1_4—O1_5^xvii	85.89 (19)
Na1_2—Na1_1—Nb1_1^x	57.4 (3)	Nb1_1^xi—Na1_4—Nb1_1^xxviii	72.0 (3)
Na1_2—Na1_1—O1_1	43.0 (3)	Nb1_1^xi—Na1_4—Nb1_1^xvii	71.4 (3)
Na1_2—Na1_1—O1_1^xi	43.0 (3)	Nb1_1^xi—Na1_4—O1_3^xviii	37.04 (15)
Na1_2—Na1_1—O1_5ⁱⁱⁱ	97.7 (5)	Nb1_1^xi—Na1_4—O1_3^xxx	100.9 (5)
Na1_2—Na1_1—O1_5^vi	97.7 (5)	Nb1_1^xi—Na1_4—O1_4	88.2 (5)
Na1_2—Na1_1—O1_5^viii	97.7 (5)	Nb1_1^xi—Na1_4—O1_4ⁱⁱ	94.48 (11)
Na1_2—Na1_1—O1_5^x	97.7 (5)	Nb1_1^xi—Na1_4—O1_4^xxxi	36.24 (15)
Nb1_1ⁱⁱⁱ—Na1_1—Nb1_1^vi	114.8 (6)	Nb1_1^xi—Na1_4—O1_4^xxxii	143.5 (3)
Nb1_1ⁱⁱⁱ—Na1_1—Nb1_1^viii	73.2 (3)	Nb1_1^xi—Na1_4—O1_5^xxvi	149.5 (7)
Nb1_1ⁱⁱⁱ—Na1_1—Nb1_1^x	73.0 (3)	Nb1_1^xi—Na1_4—O1_5^xi	39.57 (14)
Nb1_1ⁱⁱⁱ—Na1_1—O1_1	36.89 (17)	Nb1_1^xi—Na1_4—O1_5^xxviii	85.89 (19)
Nb1_1ⁱⁱⁱ—Na1_1—O1_1^xi	90.7 (5)	Nb1_1^xi—Na1_4—O1_5^xvii	99.3 (2)
Nb1_1ⁱⁱⁱ—Na1_1—O1_5ⁱⁱⁱ	40.3 (2)	Nb1_1^xxviii—Na1_4—Nb1_1^xvii	111.8 (6)
Nb1_1ⁱⁱⁱ—Na1_1—O1_5^vi	155.1 (8)	Nb1_1^xxviii—Na1_4—O1_3^xviii	100.9 (5)
Nb1_1ⁱⁱⁱ—Na1_1—O1_5^viii	94.4 (3)	Nb1_1^xxviii—Na1_4—O1_3^xxx	37.04 (15)
Nb1_1ⁱⁱⁱ—Na1_1—O1_5^x	93.9 (4)	Nb1_1^xxviii—Na1_4—O1_4	88.2 (5)
Nb1_1^vi—Na1_1—Nb1_1^viii	73.0 (3)	Nb1_1^xxviii—Na1_4—O1_4ⁱⁱ	143.5 (3)
Nb1_1^vi—Na1_1—Nb1_1^x	73.2 (3)	Nb1_1^xxviii—Na1_4—O1_4^xxxi	36.24 (15)
Nb1_1^vi—Na1_1—O1_1	90.7 (5)	Nb1_1^xxviii—Na1_4—O1_4^xxxii	94.48 (11)
Nb1_1^vi—Na1_1—O1_1^xi	36.89 (17)	Nb1_1^xxviii—Na1_4—O1_5^xxvi	99.3 (2)
Nb1_1^vi—Na1_1—O1_5ⁱⁱⁱ	155.1 (8)	Nb1_1^xxviii—Na1_4—O1_5^xi	85.89 (19)
Nb1_1^vi—Na1_1—O1_5^vi	40.3 (2)	Nb1_1^xxviii—Na1_4—O1_5^xxviii	39.57 (14)
Nb1_1^vi—Na1_1—O1_5^viii	93.9 (4)	Nb1_1^xxviii—Na1_4—O1_5^xvii	149.5 (7)
Nb1_1^vi—Na1_1—O1_5^x	94.4 (3)	Nb1_1^xvii—Na1_4—O1_3^xviii	37.04 (15)
Nb1_1^viii—Na1_1—Nb1_1^x	114.8 (6)	Nb1_1^xvii—Na1_4—O1_3^xxx	100.9 (5)
Nb1_1^viii—Na1_1—O1_1	36.89 (17)	Nb1_1^xvii—Na1_4—O1_4	36.24 (15)
Nb1_1^viii—Na1_1—O1_1^xi	90.7 (5)	Nb1_1^xvii—Na1_4—O1_4ⁱⁱ	94.48 (11)
Nb1_1^viii—Na1_1—O1_5ⁱⁱⁱ	94.4 (3)	Nb1_1^xvii—Na1_4—O1_4^xxxi	88.2 (5)
Nb1_1^viii—Na1_1—O1_5^vi	93.9 (4)	Nb1_1^xvii—Na1_4—O1_4^xxxii	143.5 (3)
Nb1_1^viii—Na1_1—O1_5^viii	40.3 (2)	Nb1_1^xvii—Na1_4—O1_5^xxvi	85.89 (19)
Nb1_1^viii—Na1_1—O1_5^x	155.1 (8)	Nb1_1^xvii—Na1_4—O1_5^xi	99.3 (2)
Nb1_1^x—Na1_1—O1_1	90.7 (5)	Nb1_1^xvii—Na1_4—O1_5^xxviii	149.5 (7)
Nb1_1^x—Na1_1—O1_1^xi	36.89 (17)	Nb1_1^xvii—Na1_4—O1_5^xvii	39.57 (14)
Nb1_1^x—Na1_1—O1_5ⁱⁱⁱ	93.9 (4)	O1_3^xviii—Na1_4—O1_3^xxx	114.1 (7)
Nb1_1^x—Na1_1—O1_5^vi	94.4 (3)	O1_3^xviii—Na1_4—O1_4	66.0 (4)
Nb1_1^x—Na1_1—O1_5^viii	155.1 (8)	O1_3^xviii—Na1_4—O1_4ⁱⁱ	84.8 (2)
Nb1_1^x—Na1_1—O1_5^x	40.3 (2)	O1_3^xviii—Na1_4—O1_4^xxxi	66.0 (4)
O1_1—Na1_1—O1_1^xi	86.0 (6)	O1_3^xviii—Na1_4—O1_4^xxxii	161.1 (6)
O1_1—Na1_1—O1_5ⁱⁱⁱ	67.8 (3)	O1_3^xviii—Na1_4—O1_5^xxvi	122.9 (3)
O1_1—Na1_1—O1_5^vi	125.0 (6)	O1_3^xviii—Na1_4—O1_5^xi	62.91 (14)
O1_1—Na1_1—O1_5^viii	67.8 (3)	O1_3^xviii—Na1_4—O1_5^xxviii	122.9 (3)
O1_1—Na1_1—O1_5^x	125.0 (6)	O1_3^xviii—Na1_4—O1_5^xvii	62.91 (14)
O1_1^xi—Na1_1—O1_5ⁱⁱⁱ	125.0 (6)	O1_3^xxx—Na1_4—O1_4	66.0 (4)
O1_1^xi—Na1_1—O1_5^vi	67.8 (3)	O1_3^xxx—Na1_4—O1_4ⁱⁱ	161.1 (6)
O1_1^xi—Na1_1—O1_5^viii	125.0 (6)	O1_3^xxx—Na1_4—O1_4^xxxi	66.0 (4)
O1_1^xi—Na1_1—O1_5^x	67.8 (3)	O1_3^xxx—Na1_4—O1_4^xxxii	84.8 (2)
O1_5ⁱⁱⁱ—Na1_1—O1_5^vi	164.6 (10)	O1_3^xxx—Na1_4—O1_5^xxvi	62.91 (14)
O1_5ⁱⁱⁱ—Na1_1—O1_5^viii	89.4 (6)	O1_3^xxx—Na1_4—O1_5^xi	122.9 (3)
O1_5ⁱⁱⁱ—Na1_1—O1_5^x	88.6 (6)	O1_3^xxx—Na1_4—O1_5^xxviii	62.91 (14)
O1_5^vi—Na1_1—O1_5^viii	88.6 (6)	O1_3^xxx—Na1_4—O1_5^xvii	122.9 (3)
O1_5^vi—Na1_1—O1_5^x	89.4 (6)	O1_4—Na1_4—O1_4ⁱⁱ	125.99 (12)
O1_5^viii—Na1_1—O1_5^x	164.6 (10)	O1_4—Na1_4—O1_4^xxxi	83.3 (6)
Na1_1—Na1_2—Nb1_1ⁱⁱⁱ	55.2 (6)	O1_4—Na1_4—O1_4^xxxii	125.99 (12)
Na1_1—Na1_2—Nb1_1^vi	55.2 (6)	O1_4—Na1_4—O1_5^xxvi	61.86 (17)
Na1_1—Na1_2—Nb1_1^viii	55.2 (6)	O1_4—Na1_4—O1_5^xi	126.3 (6)
Na1_1—Na1_2—Nb1_1^x	55.2 (6)	O1_4—Na1_4—O1_5^xxviii	126.3 (6)
Na1_1—Na1_2—O1_1	44.6 (7)	O1_4—Na1_4—O1_5^xvii	61.86 (17)
Na1_1—Na1_2—O1_1^xi	44.6 (7)	O1_4ⁱⁱ—Na1_4—O1_4^xxxi	125.99 (12)
Na1_1—Na1_2—O1_2	126.2 (7)	O1_4ⁱⁱ—Na1_4—O1_4^xxxii	76.2 (6)
Na1_1—Na1_2—O1_2^xi	126.2 (7)	O1_4ⁱⁱ—Na1_4—O1_5^xxvi	107.7 (5)
Na1_1—Na1_2—O1_3^xviii	133.4 (8)	O1_4ⁱⁱ—Na1_4—O1_5^xi	64.5 (2)
Na1_1—Na1_2—O1_3^xix	133.4 (8)	O1_4ⁱⁱ—Na1_4—O1_5^xxviii	107.7 (5)
Nb1_1ⁱⁱⁱ—Na1_2—Nb1_1^vi	110.4 (13)	O1_4ⁱⁱ—Na1_4—O1_5^xvii	64.5 (2)
Nb1_1ⁱⁱⁱ—Na1_2—Nb1_1^viii	71.1 (6)	O1_4^xxxi—Na1_4—O1_4^xxxii	125.99 (12)
Nb1_1ⁱⁱⁱ—Na1_2—Nb1_1^x	70.9 (6)	O1_4^xxxi—Na1_4—O1_5^xxvi	126.3 (6)
Nb1_1ⁱⁱⁱ—Na1_2—O1_1	35.6 (3)	O1_4^xxxi—Na1_4—O1_5^xi	61.86 (17)
Nb1_1ⁱⁱⁱ—Na1_2—O1_1^xi	90.1 (11)	O1_4^xxxi—Na1_4—O1_5^xxviii	61.86 (17)
Nb1_1ⁱⁱⁱ—Na1_2—O1_2	82.50 (14)	O1_4^xxxi—Na1_4—O1_5^xvii	126.3 (6)
Nb1_1ⁱⁱⁱ—Na1_2—O1_2^xi	143.61 (8)	O1_4^xxxii—Na1_4—O1_5^xxvi	64.5 (2)
Nb1_1ⁱⁱⁱ—Na1_2—O1_3^xviii	88.31 (18)	O1_4^xxxii—Na1_4—O1_5^xi	107.7 (5)
Nb1_1ⁱⁱⁱ—Na1_2—O1_3^xix	144.6 (3)	O1_4^xxxii—Na1_4—O1_5^xxviii	64.5 (2)
Nb1_1^vi—Na1_2—Nb1_1^viii	70.9 (6)	O1_4^xxxii—Na1_4—O1_5^xvii	107.7 (5)
Nb1_1^vi—Na1_2—Nb1_1^x	71.1 (6)	O1_5^xxvi—Na1_4—O1_5^xi	170.8 (8)
Nb1_1^vi—Na1_2—O1_1	90.1 (11)	O1_5^xxvi—Na1_4—O1_5^xxviii	106.25 (13)
Nb1_1^vi—Na1_2—O1_1^xi	35.6 (3)	O1_5^xxvi—Na1_4—O1_5^xvii	72.98 (11)
Nb1_1^vi—Na1_2—O1_2	143.61 (8)	O1_5^xi—Na1_4—O1_5^xxviii	72.98 (11)
Nb1_1^vi—Na1_2—O1_2^xi	82.50 (14)	O1_5^xi—Na1_4—O1_5^xvii	106.25 (13)
Nb1_1^vi—Na1_2—O1_3^xviii	144.6 (3)	O1_5^xxviii—Na1_4—O1_5^xvii	170.8 (8)
Nb1_1^vi—Na1_2—O1_3^xix	88.31 (18)	Na1_1^xxi—Nb1_1—Na1_2^xxi	67.4 (4)
Nb1_1^viii—Na1_2—Nb1_1^x	110.4 (13)	Na1_1^xxi—Nb1_1—Na1_3^xx	107.8 (3)
Nb1_1^viii—Na1_2—O1_1	35.6 (3)	Na1_1^xxi—Nb1_1—Na1_4^xv	72.30 (15)
Nb1_1^viii—Na1_2—O1_1^xi	90.1 (11)	Na1_1^xxi—Nb1_1—O1_1^xix	52.3 (3)
Nb1_1^viii—Na1_2—O1_2	82.50 (14)	Na1_1^xxi—Nb1_1—O1_2	113.2 (3)
Nb1_1^viii—Na1_2—O1_2^xi	143.61 (8)	Na1_1^xxi—Nb1_1—O1_3^xix	122.8 (3)
Nb1_1^viii—Na1_2—O1_3^xviii	144.6 (3)	Na1_1^xxi—Nb1_1—O1_4^xv	59.8 (2)
Nb1_1^viii—Na1_2—O1_3^xix	88.31 (18)	Na1_1^xxi—Nb1_1—O1_5	46.1 (3)
Nb1_1^x—Na1_2—O1_1	90.1 (11)	Na1_1^xxi—Nb1_1—O1_5^xxxiv	134.6 (3)
Nb1_1^x—Na1_2—O1_1^xi	35.6 (3)	Na1_2^xxi—Nb1_1—Na1_3^xx	70.7 (3)
Nb1_1^x—Na1_2—O1_2	143.61 (8)	Na1_2^xxi—Nb1_1—Na1_4^xv	108.6 (4)
Nb1_1^x—Na1_2—O1_2^xi	82.50 (14)	Na1_2^xxi—Nb1_1—O1_1^xix	48.0 (4)
Nb1_1^x—Na1_2—O1_3^xviii	88.31 (18)	Na1_2^xxi—Nb1_1—O1_2	128.2 (3)
Nb1_1^x—Na1_2—O1_3^xix	144.6 (3)	Na1_2^xxi—Nb1_1—O1_3^xix	139.6 (4)
O1_1—Na1_2—O1_1^xi	89.3 (15)	Na1_2^xxi—Nb1_1—O1_4^xv	61.3 (3)
O1_1—Na1_2—O1_2	81.58 (19)	Na1_2^xxi—Nb1_1—O1_5	113.6 (6)
O1_1—Na1_2—O1_2^xi	170.9 (15)	Na1_2^xxi—Nb1_1—O1_5^xxxiv	67.2 (6)
O1_1—Na1_2—O1_3^xviii	119.29 (11)	Na1_3^xx—Nb1_1—Na1_4^xv	179.0 (5)
O1_1—Na1_2—O1_3^xix	119.29 (11)	Na1_3^xx—Nb1_1—O1_1^xix	55.8 (2)
O1_1^xi—Na1_2—O1_2	170.9 (15)	Na1_3^xx—Nb1_1—O1_2	59.8 (3)
O1_1^xi—Na1_2—O1_2^xi	81.58 (19)	Na1_3^xx—Nb1_1—O1_3^xix	127.4 (3)
O1_1^xi—Na1_2—O1_3^xviii	119.29 (11)	Na1_3^xx—Nb1_1—O1_4^xv	131.5 (3)
O1_1^xi—Na1_2—O1_3^xix	119.29 (11)	Na1_3^xx—Nb1_1—O1_5	124.3 (5)
O1_2—Na1_2—O1_2^xi	107.6 (15)	Na1_3^xx—Nb1_1—O1_5^xxxiv	56.1 (5)
O1_2—Na1_2—O1_3^xviii	66.0 (8)	Na1_4^xv—Nb1_1—O1_1^xix	124.2 (2)
O1_2—Na1_2—O1_3^xix	66.0 (8)	Na1_4^xv—Nb1_1—O1_2	121.2 (3)
O1_2^xi—Na1_2—O1_3^xviii	66.0 (8)	Na1_4^xv—Nb1_1—O1_3^xix	52.8 (2)
O1_2^xi—Na1_2—O1_3^xix	66.0 (8)	Na1_4^xv—Nb1_1—O1_4^xv	47.6 (3)
O1_3^xviii—Na1_2—O1_3^xix	93.1 (17)	Na1_4^xv—Nb1_1—O1_5	56.5 (4)
Nb1_1ⁱⁱⁱ—Na1_3—Nb1_1^xii	110.0 (6)	Na1_4^xv—Nb1_1—O1_5^xxxiv	123.2 (6)
Nb1_1ⁱⁱⁱ—Na1_3—Nb1_1^viii	71.1 (3)	O1_1^xix—Nb1_1—O1_2	89.5 (3)
Nb1_1ⁱⁱⁱ—Na1_3—Nb1_1^xxv	70.5 (3)	O1_1^xix—Nb1_1—O1_3^xix	171.1 (3)
Nb1_1ⁱⁱⁱ—Na1_3—O1_1	35.80 (17)	O1_1^xix—Nb1_1—O1_4^xv	93.3 (3)
Nb1_1ⁱⁱⁱ—Na1_3—O1_1^xxiii	93.9 (6)	O1_1^xix—Nb1_1—O1_5	85.2 (3)
Nb1_1ⁱⁱⁱ—Na1_3—O1_2	87.70 (13)	O1_1^xix—Nb1_1—O1_5^xxxiv	95.6 (3)
Nb1_1ⁱⁱⁱ—Na1_3—O1_2^xxiii	144.37 (12)	O1_2—Nb1_1—O1_3^xix	86.3 (3)
Nb1_1ⁱⁱⁱ—Na1_3—O1_5	96.0 (3)	O1_2—Nb1_1—O1_4^xv	167.0 (3)
Nb1_1ⁱⁱⁱ—Na1_3—O1_5^xxiii	82.0 (2)	O1_2—Nb1_1—O1_5	84.9 (3)
Nb1_1ⁱⁱⁱ—Na1_3—O1_5^xxiv	142.5 (7)	O1_2—Nb1_1—O1_5^xxxiv	94.8 (4)
Nb1_1ⁱⁱⁱ—Na1_3—O1_5^xvii	34.13 (15)	O1_3^xix—Nb1_1—O1_4^xv	89.1 (3)
Nb1_1^xii—Na1_3—Nb1_1^viii	70.5 (3)	O1_3^xix—Nb1_1—O1_5	86.7 (3)
Nb1_1^xii—Na1_3—Nb1_1^xxv	71.1 (3)	O1_3^xix—Nb1_1—O1_5^xxxiv	92.5 (3)
Nb1_1^xii—Na1_3—O1_1	93.9 (6)	O1_4^xv—Nb1_1—O1_5	82.7 (4)
Nb1_1^xii—Na1_3—O1_1^xxiii	35.80 (17)	O1_4^xv—Nb1_1—O1_5^xxxiv	97.5 (4)
Nb1_1^xii—Na1_3—O1_2	144.37 (12)	O1_5—Nb1_1—O1_5^xxxiv	180.000 (5)
Nb1_1^xii—Na1_3—O1_2^xxiii	87.70 (13)	Na1_1—O1_1—Na1_2	92.4 (6)
Nb1_1^xii—Na1_3—O1_5	82.0 (2)	Na1_1—O1_1—Na1_3	173.3 (4)
Nb1_1^xii—Na1_3—O1_5^xxiii	96.0 (3)	Na1_1—O1_1—Nb1_1ⁱⁱⁱ	90.85 (19)
Nb1_1^xii—Na1_3—O1_5^xxiv	34.13 (15)	Na1_1—O1_1—Nb1_1^viii	90.85 (19)
Nb1_1^xii—Na1_3—O1_5^xvii	142.5 (7)	Na1_2—O1_1—Na1_3	94.3 (6)
Nb1_1^viii—Na1_3—Nb1_1^xxv	110.0 (6)	Na1_2—O1_1—Nb1_1ⁱⁱⁱ	96.4 (2)
Nb1_1^viii—Na1_3—O1_1	35.80 (17)	Na1_2—O1_1—Nb1_1^viii	96.4 (2)
Nb1_1^viii—Na1_3—O1_1^xxiii	93.9 (6)	Na1_3—O1_1—Nb1_1ⁱⁱⁱ	88.4 (2)
Nb1_1^viii—Na1_3—O1_2	87.70 (13)	Na1_3—O1_1—Nb1_1^viii	88.4 (2)
Nb1_1^viii—Na1_3—O1_2^xxiii	144.37 (12)	Nb1_1ⁱⁱⁱ—O1_1—Nb1_1^viii	167.0 (4)
Nb1_1^viii—Na1_3—O1_5	34.13 (15)	Na1_2—O1_2—Na1_3	101.5 (6)
Nb1_1^viii—Na1_3—O1_5^xxiii	142.5 (7)	Na1_2—O1_2—Nb1_1	92.0 (3)
Nb1_1^viii—Na1_3—O1_5^xxiv	82.0 (2)	Na1_2—O1_2—Nb1_1^xvii	92.0 (3)
Nb1_1^viii—Na1_3—O1_5^xvii	96.0 (3)	Na1_2—O1_2—Li1_3	101.5 (6)
Nb1_1^xxv—Na1_3—O1_1	93.9 (6)	Na1_3—O1_2—Nb1_1	103.16 (19)
Nb1_1^xxv—Na1_3—O1_1^xxiii	35.80 (17)	Na1_3—O1_2—Nb1_1^xvii	103.16 (19)
Nb1_1^xxv—Na1_3—O1_2	144.37 (12)	Na1_3—O1_2—Li1_3	0.0
Nb1_1^xxv—Na1_3—O1_2^xxiii	87.70 (13)	Nb1_1—O1_2—Nb1_1^xvii	152.0 (4)
Nb1_1^xxv—Na1_3—O1_5	142.5 (7)	Nb1_1—O1_2—Li1_3	103.16 (19)
Nb1_1^xxv—Na1_3—O1_5^xxiii	34.13 (15)	Nb1_1^xvii—O1_2—Li1_3	103.16 (19)
Nb1_1^xxv—Na1_3—O1_5^xxiv	96.0 (3)	Na1_2ⁱⁱⁱ—O1_3—Na1_4ⁱⁱ	103.6 (7)
Nb1_1^xxv—Na1_3—O1_5^xvii	82.0 (2)	Na1_2ⁱⁱⁱ—O1_3—Nb1_1ⁱⁱⁱ	104.1 (2)
O1_1—Na1_3—O1_1^xxiii	99.4 (7)	Na1_2ⁱⁱⁱ—O1_3—Nb1_1^xxix	104.1 (2)
O1_1—Na1_3—O1_2	82.64 (18)	Na1_2ⁱⁱⁱ—O1_3—Li1_2ⁱⁱⁱ	0.0
O1_1—Na1_3—O1_2^xxiii	178.0 (8)	Na1_4ⁱⁱ—O1_3—Nb1_1ⁱⁱⁱ	90.2 (2)
O1_1—Na1_3—O1_5	61.66 (19)	Na1_4ⁱⁱ—O1_3—Nb1_1^xxix	90.2 (2)
O1_1—Na1_3—O1_5^xxiii	115.8 (5)	Na1_4ⁱⁱ—O1_3—Li1_2ⁱⁱⁱ	103.6 (7)
O1_1—Na1_3—O1_5^xxiv	115.8 (5)	Nb1_1ⁱⁱⁱ—O1_3—Nb1_1^xxix	151.0 (4)
O1_1—Na1_3—O1_5^xvii	61.66 (19)	Nb1_1ⁱⁱⁱ—O1_3—Li1_2ⁱⁱⁱ	104.1 (2)
O1_1^xxiii—Na1_3—O1_2	178.0 (8)	Nb1_1^xxix—O1_3—Li1_2ⁱⁱⁱ	104.1 (2)
O1_1^xxiii—Na1_3—O1_2^xxiii	82.64 (18)	Na1_4—O1_4—Na1_4^xviii	100.20 (19)
O1_1^xxiii—Na1_3—O1_5	115.8 (5)	Na1_4—O1_4—Nb1_1^xxvi	96.13 (17)
O1_1^xxiii—Na1_3—O1_5^xxiii	61.66 (19)	Na1_4—O1_4—Nb1_1^xvii	96.13 (17)
O1_1^xxiii—Na1_3—O1_5^xxiv	61.66 (19)	Na1_4^xviii—O1_4—Nb1_1^xxvi	94.88 (17)
O1_1^xxiii—Na1_3—O1_5^xvii	115.8 (5)	Na1_4^xviii—O1_4—Nb1_1^xvii	94.88 (17)
O1_2—Na1_3—O1_2^xxiii	95.3 (8)	Nb1_1^xxvi—O1_4—Nb1_1^xvii	162.7 (4)
O1_2—Na1_3—O1_5	65.09 (17)	Na1_1^xxi—O1_5—Na1_3	97.8 (3)
O1_2—Na1_3—O1_5^xxiii	117.5 (5)	Na1_1^xxi—O1_5—Na1_4^xv	97.9 (3)
O1_2—Na1_3—O1_5^xxiv	117.5 (5)	Na1_1^xxi—O1_5—Nb1_1	93.6 (5)
O1_2—Na1_3—O1_5^xvii	65.09 (17)	Na1_1^xxi—O1_5—Nb1_1^viii	109.7 (5)
O1_2^xxiii—Na1_3—O1_5	117.5 (5)	Na1_1^xxi—O1_5—Li1_1^xxi	0.0
O1_2^xxiii—Na1_3—O1_5^xxiii	65.09 (17)	Na1_3—O1_5—Na1_4^xv	162.2 (3)
O1_2^xxiii—Na1_3—O1_5^xxiv	65.09 (17)	Na1_3—O1_5—Nb1_1	86.6 (6)
O1_2^xxiii—Na1_3—O1_5^xvii	117.5 (5)	Na1_3—O1_5—Nb1_1^viii	89.8 (6)
O1_5—Na1_3—O1_5^xxiii	176.6 (9)	Na1_3—O1_5—Li1_1^xxi	97.8 (3)
O1_5—Na1_3—O1_5^xxiv	73.32 (9)	Na1_4^xv—O1_5—Nb1_1	84.0 (5)
O1_5—Na1_3—O1_5^xvii	106.57 (10)	Na1_4^xv—O1_5—Nb1_1^viii	92.9 (6)
O1_5^xxiii—Na1_3—O1_5^xxiv	106.57 (10)	Na1_4^xv—O1_5—Li1_1^xxi	97.9 (3)
O1_5^xxiii—Na1_3—O1_5^xvii	73.32 (9)	Nb1_1—O1_5—Nb1_1^viii	156.74 (9)
O1_5^xxiv—Na1_3—O1_5^xvii	176.6 (9)	Nb1_1—O1_5—Li1_1^xxi	93.6 (5)
Nb1_1^xxvi—Na1_4—Nb1_1^xi	111.8 (6)	Nb1_1^viii—O1_5—Li1_1^xxi	109.7 (5)
Nb1_1^xxvi—Na1_4—Nb1_1^xxviii	71.4 (3)	O1_5ⁱⁱⁱ—Li1_1—O1_5^vi	164.6 (10)
Nb1_1^xxvi—Na1_4—Nb1_1^xvii	72.0 (3)	O1_5ⁱⁱⁱ—Li1_1—O1_5^viii	89.4 (6)
Nb1_1^xxvi—Na1_4—O1_3^xviii	100.9 (5)	O1_5ⁱⁱⁱ—Li1_1—O1_5^x	88.6 (6)
Nb1_1^xxvi—Na1_4—O1_3^xxx	37.04 (15)	O1_5^vi—Li1_1—O1_5^viii	88.6 (6)
Nb1_1^xxvi—Na1_4—O1_4	36.24 (15)	O1_5^vi—Li1_1—O1_5^x	89.4 (6)
Nb1_1^xxvi—Na1_4—O1_4ⁱⁱ	143.5 (3)	O1_5^viii—Li1_1—O1_5^x	164.6 (10)
Nb1_1^xxvi—Na1_4—O1_4^xxxi	88.2 (5)	O1_3^xviii—Li1_2—O1_3^xix	93.1 (17)
Nb1_1^xxvi—Na1_4—O1_4^xxxii	94.48 (11)	O1_2—Li1_3—O1_2^xxiii	95.3 (8)
Nb1_1^xxvi—Na1_4—O1_5^xxvi	39.57 (14)

Symmetry codes: (i) x, y, z+1; (ii) −y, x, z+1/2; (iii) −y+1, x, z+1/2; (iv) −y, x+1, z+1/2; (v) −x, −y+1, z+1; (vi) y−1, −x+1, z+1/2; (vii) −x, y, z+1; (viii) −y+1, −x+1, z+1/2; (ix) x, −y+1, z+1; (x) y−1, x, z+1/2; (xi) −x, −y+1, z; (xii) y, −x+1, z+1/2; (xiii) x, y, z−1; (xiv) x−1, y, z; (xv) x, y+1, z; (xvi) −x, y, z; (xvii) x, −y+1, z; (xviii) −y, x, z−1/2; (xix) y, −x+1, z−1/2; (xx) −y+1, x, z−1/2; (xxi) −y+1, x+1, z−1/2; (xxii) x+1, y, z; (xxiii) −x+1, −y+1, z; (xxiv) −x+1, y, z; (xxv) y, x, z+1/2; (xxvi) x, y−1, z; (xxvii) y−1, −x, z+1/2; (xxviii) −x, y−1, z; (xxix) −y+1, −x, z+1/2; (xxx) y, −x, z−1/2; (xxxi) −x, −y, z; (xxxii) y, −x, z+1/2; (xxxiii) −y, x+1, z−1/2; (xxxiv) −y+1, −x+1, z−1/2.

(LNN20_P42MC_300C_phase_2) top

Crystal data top

LiNbO₃	c = 13.818 (9) Å
M_r = 147.84	V = 324.64 (19) Å³
Trigonal, R3cH	Z = 6
a = 5.209 (2) Å	T = 573 K

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Li1	0.0	0.0	0.2829	0.01*
Nb1	0.0	0.0	0.0	0.01*
O1	0.0492	0.3446	0.0647	0.01*

Geometric parameters (Å, º) top

Li1—Nb1ⁱ	3.000 (2)	Nb1—Li1^xiv	3.0868 (11)
Li1—Nb1ⁱⁱ	3.4092 (11)	Nb1—Li1^xv	3.0868 (11)
Li1—Nb1ⁱⁱⁱ	3.4092 (11)	Nb1—Li1^xvi	3.4092 (11)
Li1—Nb1^iv	3.4092 (11)	Nb1—Li1^xvii	3.4092 (11)
Li1—Nb1^v	3.0868 (11)	Nb1—Li1^xviii	3.4092 (11)
Li1—Nb1^vi	3.0868 (11)	Nb1—O1	1.9043 (6)
Li1—Nb1^vii	3.0868 (11)	Nb1—O1^xix	1.9043 (6)
Li1—O1ⁱⁱ	2.0889 (7)	Nb1—O1^xx	1.9043 (6)
Li1—O1^viii	2.0889 (7)	Nb1—O1^xvi	2.1229 (8)
Li1—O1^ix	2.0889 (7)	Nb1—O1^xxi	2.1229 (8)
Li1—O1^v	2.2478 (9)	Nb1—O1^xxii	2.1229 (8)
Li1—O1^x	2.2478 (9)	O1—Li1^xv	2.2478 (9)
Li1—O1^xi	2.2478 (9)	O1—Li1^xvii	2.0889 (7)
Nb1—Li1^xii	3.000 (2)	O1—Nb1	1.9043 (6)
Nb1—Li1^xiii	3.0868 (11)	O1—Nb1^iv	2.1229 (8)

Nb1ⁱ—Li1—O1ⁱⁱ	109.932 (14)	Li1^xii—Nb1—O1^xvi	48.42 (2)
Nb1ⁱ—Li1—O1^viii	109.932 (14)	Li1^xii—Nb1—O1^xxi	48.42 (2)
Nb1ⁱ—Li1—O1^ix	109.932 (14)	Li1^xii—Nb1—O1^xxii	48.42 (2)
Nb1ⁱ—Li1—O1^v	44.95 (2)	O1—Nb1—O1^xix	99.75 (2)
Nb1ⁱ—Li1—O1^x	44.95 (2)	O1—Nb1—O1^xx	99.75 (2)
Nb1ⁱ—Li1—O1^xi	44.95 (2)	O1—Nb1—O1^xvi	166.369 (4)
O1ⁱⁱ—Li1—O1^viii	109.007 (15)	O1—Nb1—O1^xxi	88.14 (3)
O1ⁱⁱ—Li1—O1^ix	109.007 (15)	O1—Nb1—O1^xxii	89.74 (3)
O1ⁱⁱ—Li1—O1^v	89.37 (2)	O1^xix—Nb1—O1^xx	99.75 (2)
O1ⁱⁱ—Li1—O1^x	154.088 (7)	O1^xix—Nb1—O1^xvi	89.74 (3)
O1ⁱⁱ—Li1—O1^xi	80.53 (3)	O1^xix—Nb1—O1^xxi	166.369 (4)
O1^viii—Li1—O1^ix	109.007 (15)	O1^xix—Nb1—O1^xxii	88.14 (3)
O1^viii—Li1—O1^v	80.53 (3)	O1^xx—Nb1—O1^xvi	88.14 (3)
O1^viii—Li1—O1^x	89.37 (2)	O1^xx—Nb1—O1^xxi	89.74 (3)
O1^viii—Li1—O1^xi	154.088 (7)	O1^xx—Nb1—O1^xxii	166.369 (4)
O1^ix—Li1—O1^v	154.088 (7)	O1^xvi—Nb1—O1^xxi	80.75 (3)
O1^ix—Li1—O1^x	80.53 (3)	O1^xvi—Nb1—O1^xxii	80.75 (3)
O1^ix—Li1—O1^xi	89.37 (2)	O1^xxi—Nb1—O1^xxii	80.75 (3)
O1^v—Li1—O1^x	75.44 (4)	Li1^xv—O1—Li1^xvii	121.673 (8)
O1^v—Li1—O1^xi	75.44 (4)	Li1^xv—O1—Nb1	95.69 (3)
O1^x—Li1—O1^xi	75.44 (4)	Li1^xv—O1—Nb1^iv	86.64 (4)
Li1^xii—Nb1—O1	118.000 (19)	Li1^xvii—O1—Nb1	117.168 (8)
Li1^xii—Nb1—O1^xix	118.000 (19)	Li1^xvii—O1—Nb1^iv	94.26 (2)
Li1^xii—Nb1—O1^xx	118.000 (19)	Nb1—O1—Nb1^iv	140.216 (8)

Symmetry codes: (i) y−x, y, z+1/2; (ii) y−x−2/3, y−1/3, z+1/6; (iii) y−x+1/3, y−1/3, z+1/6; (iv) y−x+1/3, y+2/3, z+1/6; (v) x−1/3, y−2/3, z+1/3; (vi) x−1/3, y+1/3, z+1/3; (vii) x+2/3, y+1/3, z+1/3; (viii) −y+1/3, −x−1/3, z+1/6; (ix) x+1/3, x−y+2/3, z+1/6; (x) −y+2/3, x−y+1/3, z+1/3; (xi) y−x−1/3, −x+1/3, z+1/3; (xii) y−x, y, z−1/2; (xiii) x−2/3, y−1/3, z−1/3; (xiv) x+1/3, y−1/3, z−1/3; (xv) x+1/3, y+2/3, z−1/3; (xvi) y−x−1/3, y−2/3, z−1/6; (xvii) y−x−1/3, y+1/3, z−1/6; (xviii) y−x+2/3, y+1/3, z−1/6; (xix) −y, x−y, z; (xx) y−x, −x, z; (xxi) −y+2/3, −x+1/3, z−1/6; (xxii) x−1/3, x−y+1/3, z−1/6.

Acknowledgements

We thank STFC for the provision of neutron diffraction facilities at ISIS and Dr A. Daoud-Aladine for experimental assistance. We would also like to thank Dr F. D Morrison for access to dielectric measurements.

Biographical information

This is an Inaugural Article by Phil Lightfoot, who joined the Editorial Board of IUCrJ in 2016. Phil Lightfoot is Professor of Solid State Chemistry at the University of St Andrews. His first degree was in Chemistry at Oxford, where he remained to carry out a D.Phil with Professor Tony Cheetham. Two post-doctoral positions were held at Leeds University and Argonne National Lab, prior to taking a faculty position in St Andrews in 1990. His research interests have spanned many fields across solid state chemistry and crystallography, with the emphasis on designing, synthesising and understanding new functional materials. This has included early work on cuprate superconductors, polymer electrolytes, ab initio powder diffraction methods, porous solids and, more recently, studies of ferroelectric and magnetic oxides and fluorides. In total he has published nearly 300 papers, the majority of which involve a key role for crystallography and diffraction methods.

Funding information

Funding for this research was provided by: EPSRC (award No. EP/L505079/1).

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IUCrJ

Volume 4| Part 3| May 2017| Pages 215-222

ISSN: 2052-2525

https://doi.org/10.1107/S2052252517002226

CHEMISTRY | CRYSTENG

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