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Chessboard/diamond nano-structures and the A-site deficient, Li1/2-3x Nd1/2+xTiO3, defect perovskite solid solution Ray L Withers, Laure Bourgeois, Amanda Snashall, Yun Liu, Lasse Noren, Christian Dwyer, and Joanne Etheridge Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/cm303239d • Publication Date (Web): 18 Dec 2012 Downloaded from http://pubs.acs.org on December 19, 2012

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Chessboard/diamond nano-structures and the A-site deficient, Li1/2-3x Nd1/2+xTiO3, defect perovskite solid solution Ray L. Withers*, Laure Bourgeois#, Amanda Snashall, Yun Liu, Lasse Norén, Christian Dwyer# and Joanne Etheridge# Research School of Chemistry, College of Physical and Mathematical Sciences, The Australian National University, ACT 0200, Australia #Monash Centre for Electron Microscopy (MCEM) and Department of Materials Engineering, Monash University, VIC 3800, Victoria. Keywords: LNT perovskites, chessboard/diamond nanoscale ordering, transmission electron microscopy, dielectric properties

ABSTRACT: The crystal chemical origin of nano-scale chessboard/diamond ordering in perovskite-related solid solutions of composition Li0.5-3xNd0.5+xTiO3 (LNT, x~0.02 – 0.12) is investigated. Experimental and simulated scanning transmission electron microscopy (STEM) images are found to be consistent with the compositional modulation model proposed by previous authors. However these earlier models do not satisfactorily explain other features observed in high-resolution STEM and TEM images, such as the two-dimensional {100} lattice fringes with the same periodicity, √2ap x √2ap, as the local LNT unit cell viewed along the [001] direction (where ap is the parent perovskite unit cell parameter). Based on bond valence sum calculations, we propose a new set of crystal structures for LNT in which Li ions are primarily bonded to only two O ions, and order one-dimensionally with √2ap periodicity. Bright-field STEM image simulations performed for this new model reproduced the experimentally observed √2ap lattice fringes, thus strongly suggesting that the finer features of the high-resolution (S)TEM images are the result of Li ion ordering and associated local structural relaxation. In this new model, the LNT chessboard supercell then results from the ordered combinations of two sub-lattices: the Li ion sub-lattice and its translational variants on the one hand, and the Nd0.5TiO3 sub-lattice and its oxygen octahedral tilt twin variants on the other. Dielectric measurements indicate the presence of long-lived polar clusters that are easily activated under an applied electric field. This suggests that these clusters consist of spatially correlated Li ions.

nation and understanding of such materials is an ex1. Introduction traordinarily difficult challenge. The realization that the A-site deficient, perovskite-related solid solutions of chessboard type, self-assembled nano-structure characgeneral formula Li0.5-3xLn0.5+xTiO3, where Ln = La, Pr, Nd teristic of these materials (see e.g. that characteristic of and Sm and x typically runs from ~ 0.02 to ~ 0.12 [1], the LNT, x = 0.067, sample shown in Fig.1) is, at least in are amongst the best Li ion conductors known (particuprinciple, a well-ordered part of the one overall, apparlarly for Ln = La) as well as promising candidates for use ently continuously tuneable, crystal structure type [8-10] as solid electrolytes in lithium secondary batteries [1,2]. has been a significant recent development. So has the Compounds of this type also exhibit a relatively high dierecently reported, combined TEM and neutron powder lectric constant (ε = 75), reasonably high quality factors diffraction modelling study of Li0.25Nd0.583TiO3 [9], the y (Q.f = 2000 GHz) and a negative temperature coefficient 1/12 member of the Li3yNd2/3-yTiO3 (LNT) solid solution = of resonant frequency (τcf ~ -274 ppm/oC) in the com(see the 14x28x2 supercell reported for this composition mercially important microwave frequency range (see e.g. in [9] and shown in Fig.2, the latter obtained from the Table 1 of [3]). The latter property means that they can ICSD database; note y here = 1/6 - x in terms of the be used to temperature compensate the intrinsic high Li0.5-3xNd0.5+xTiO3 formulation given above). positive τcf of materials such as CaTiO3, leading to a In these latter contributions, Guiton et al [8,9] interrange of promising CaTiO3-based microwave elecpreted the coupled nano-chessboard/diamond type mitroceramics [3]. crostructure of this material in terms of periodic octaheOn the structural side, there have been numerous indral tilt twinning (see the tilt twin boundaries labelled vestigations of these materials [2,4-10]. The size, comwith the symbol t in Fig.2 and giving rise to the nanoplexity and longer range variability of the 'nano-domain chessboard type contrast, see e.g. the top half of Fig.1a) structure' typically observed (see e.g. Fig.1a-b), coupled combined with 2-D periodic phase separation (somewhat with the difficulty in determining the positions of the analogous to spinodal decomposition [11] and giving rise light Li ions as well as the location of the necessarily vato the diamond type contrast, see e.g. the bottom region cant A sites, means that an atomistic structure determiACS Paragon Plus Environment


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of Fig.1a) into compositionally distinct Li0.5Nd0.5TiO3 (y = 1/6) diamond-shaped regions separated by Nd2/3TiO3 (y = 0) boundary regions (see Fig.2). This interpretation led the authors to claim that the LNT system represents “.. the first example of a truly periodic (compositionally tuneable) two-dimensional nanometer-scale phase separation in any inorganic material.. ” [8].

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es (see e.g. Fig.1c) and of the structure proposed (Fig.2), and on the other hand, the typical strong dependence of such HRTEM images upon parameters such as thickness, defocus and partial ionicity, the HRTEM evidence presented is provisional and requires further investigation. Likewise, while the contrast observed in the relatively low resolution, high-angle annular dark field (HAADF) scanning (S)TEM image shown in Fig.1c of [8] does indeed suggest some compositional variation between the diamond-shaped and the boundary regions, a more quantitative analysis of this contrast to determine the origin and extent of this compositional variation has not yet been reported. In particular, whether this contrast is compatible with the proposed periodic phase separation into compositionally distinct Li0.5Nd0.5TiO3 diamond shaped regions separated by Nd2/3TiO3 boundary regions was not explored. Before the claim of “ .. (compositionally tuneable) nmscale phase separation ..” [8] can be accepted, the following questions need to be more thoroughly investigated: (1) Is the diamond type contrast characteristic of the Li3yNd2/3-yTiO3 solid solution really consistent with phase separation into compositionally distinct Li0.5Nd0.5TiO3 (y = 1/6) and Nd2/3TiO3 (y = 0) regions?, (2) Why is there necessarily an anti-phase relationship of the larger diamond shaped domain regions across the boundary regions?, (3) What determines the overall nano-scale periodicity? (note that while the composition-dependent model of Guiton and Davies, see Fig.3 of [8], determines the relative amounts of the proposed Li0.5Nd0.5TiO3 and Nd2/3TiO3 regions, it says nothing as to the overall periodicity) and (4) Where exactly are the Li ions and perovskite A site vacancies distributed within the overall structure? The purpose of the current paper is to report the results of a detailed TEM/STEM, dielectric properties and crystal chemical investigation of the Li0.5-3xNd0.5+xTiO3 solid solution system in an attempt to move towards an answer to some of the above crucial questions. As described below, we confirm the existence of a compositional modulation (question (1)), propose alternative structural models for the location of the Li ions (question (4)), and suggest possible answers to questions (2) and (3).

Figure 1. "Nano-chessboard" ordering characteristic of the LNT, x = 0.067) sample viewed under bright-field TEM. One super-cell is shown boxed in white in the middle region of (a). Arrows in (a) point to regions exhibiting rectangular shaped contrast similar to the so-called "stripe phases". The area framed in (b) and shown at higher magnification in (c) reveals the underlying parent perovskite sub-structure (lattice parameter ap, unit cell shown in white in (c)) as well as two sets of (110)p lattice fringes (black arrows) typical of LNT on the local scale (a unit cell with side √2ap, shown in yellow).

2. Experimental and Image Simulation Procedures Synthesis. A Li(0.5-3x)Nd(0.5+x)TiO3 sample with x = 0.067 (LNT6.7) was synthesized via solid state reaction from high purity (≥ 99.9%) Nd2O3, TiO2 and Li2CO3 powders. All starting materials were initially heat treated at low temperatures (< 120 °C) for ~ 12 hours to remove any adsorbed water prior to weighing. The resultant powder was then mixed, milled under ethanol for a period longer than 20 minutes and pressed into a pellet. These pellets were then sintered in air at a temperature of 1350 °C for 36 hours with intermediate re-grindings, re-pressings and checking of the XRD patterns at 12 hourly intervals. The relatively high 1350 °C annealing temperature of this sample was employed in order to maximize the resultant density of the ceramic pellets obtained. The density of the resultant 36 hour sintered pellet was 4.604 gm/cm3 as measured by the Archimedes' method, ~ 88 % of theoretical density. This LNT6.7

The image analysis and other evidence provided for this interpretation, however, was at best only qualitative [8,9] and requires more detailed consideration before this model can be considered to be well-established. In their work, Guiton et al. used high-resolution transmission electron microscopy (HRTEM) multislice image simulations, for example, to support their proposed structural model (see Fig.4 of [8]). No mention, however, was made of whether the particular thickness and defocus values used were in agreement with the actual thickness of the particular crystal region to which they were ‘matched’ or whether the reported agreement continued at differing thicknesses and defocus values. Given, on the one hand, the complexity of the observed HRTEM imag-

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sample was used for the dielectric properties measurements described below. An additional sample at a different composition, for comparison purposes, was also synthesized following Robertson et al [1]. This sample had the composition x = 0.04 (LNT4; nominal composition Li0.38Nd0.54TiO3). Nd2O3 powder was first heated to 1000 °C overnight in order to remove any hydrate/hydroxide while Li2CO3 powder and nanometre-sized TiO2 powder were heated to 130 °C to remove adsorbed water. The resultant powders were then mixed together in the appropriate ratio, hand milled and pressed to a pellet which was initially calcined at 600 °C for 2 h, followed by further heating at 1050 °C for 24 h. The sample was then crushed, handground, re-pelleted and sintered at 1200 °C for 24 h (with a ramp-rate of 10 °C/min). The sample was finally sintered a second time at 1200 °C for 14h using the same ramp-rate.

Figure 2. One unit cell of the crystal structure proposed by Guiton & Davies for the nano-chessboard phase (ICSD code 160439). For the sake of clarity only Nd ions in the partially occupied Nd layer at z=1/2 are shown (black). The occupancy of these sites is 0.33. Yellow spheres correspond to Li, blue spheres to Ti, and red spheres to O. The region boxed in red was that used for the STEM image simulations shown in Fig. 6. The lattice vectors for the local LNT unit cell, a, b, and for the parent perovskite cell, ap and bp, are shown.

During sintering the pellet was placed on platinum foil dusted with a thin layer of LNT powder with the same nominal composition as the pellet and then covered with more powder. Finally, a lid was placed on the alumina crucible. This was done in order to minimise lithium loss during the sintering process as well as any ion exchange reaction with the alumina crucibles. X-ray Diffraction (XRD). XRD powder patterns of all three samples were taken using a Siemens X-Ray Diffractometer with CuKα2 radiation stripped from the resultant patterns. For the determination of accurate average structure unit cell lattice parameters, a Guinier-Hägg Camera was employed using Si (Sietronics GD#1) as an internal standard. The average structure unit cell dimensions were refined using the software package "Unitcell" [12].

Dielectric Properties. For dielectric properties measurements of the LNT6.7 sample, the upper and lower surface areas of the polished cylindrical pellet sample were coated with silver paste to form a parallel plate capacitor. The silver paste was heat treated at 550 °C for 30 minutes to achieve good electrical contact. Dielectric permittivity and dielectric loss tangent (tan δ) spectra as well as an impedance spectrum were then measured over the frequency range 100 Hz – 1MHz using a high precision LCR Meter (Agilent 4284A). Transmission Electron Microscopy. Transmission electron microscope (TEM) investigations of the resultant LNT samples were carried out at room temperature using a Philips EM 430 TEM, a JEOL 2100F field emission gun (FEG)-TEM and a double-aberration corrected Titan3 80-300 FEG-TEM on crushed grains of the powder samples dispersed onto holey carbon-coated

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copper grids. The 2100F was operated at 200 kV and the EM 430 and Titan TEMs at 300 kV. Scanning (S)TEM was performed in bright-field (BF) and high-angle annular dark field (HAADF) modes on the Titan microscope, using a convergence semi-angle of 15 mrad, a BF-STEM collection semi-angle of 11.6 mrad, a HAADF-STEM collection inner semi-angle of 52 mrad and outer semiangle of ~200 mrad. In this instrument the partial spatial coherence is such that, with the spherical aberration corrected, this convergence angle generates an electron beam diameter on the specimen of ~1.2 Å and therefore generates atomic resolution images with a comparable spatial resolution [13]. The high-resolution (S)TEM images are shown unprocessed except for very minor contrast and intensity adjustments. LNT was found to be electron beam sensitive in both TEM and STEM modes, therefore requiring great care to minimise its exposure to the electron beam. Electron beam sensitivity was considerably reduced at higher accelerating voltages (300 kV, compared with 200 kV), with minimal observable beam damage taking place under 1 minute at room temperature for beam exposures typical of high-resolution imaging. Image Simulations. BF- and HAADF-STEM image simulations were conducted using multislice calculations incorporating thermal diffuse scattering via a frozen phonon approach (see Ref. [14] and references therein). The simulations were performed for a subset of the crystal structure proposed by Guiton, Wu & Davies [9] for the nano-chessboard super-cell – see the region boxed in red in Fig.2. The simulated cells had lateral size 30.4 Å x 30.4 Å, different thicknesses ranging from 7.7 nm to 77 nm, and were sampled using 512 x 512 pixels (to give a maximum scattering angle of about 216 mrad). Microscope parameters matched those used in the experiment as specified above. The calculations assume a Gaussianshaped effective source size of 1 Å.

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Indexation is with respect to a C-centred orthorhombic, but metrically tetragonal, average structure unit cell with refined unit cell lattice parameters a = b = 3.8244(6) x√2 = 5.408(1) Å and c = 7.675(2) Å, corresponding to an a = ap+bp, b = -ap+bp, c = 2cp; a* = ½(ap*+bp*), b* = ½(-ap*+bp*), c* = ½ cp*, subscript p for parent perovskite sub-structure, setting. (The reason for choosing a C-centred orthorhombic cell over a smaller primitive tetragonal cell will become apparent in the TEM section below). In the case of the x = 0.04 sample, the equivalent refined unit cell parameters were 3.8213(4) x√2 = 5.404(1) Å and c = 7.675(1) Å, respectively. Note that no reflections that broke C-centreing were observed from either sample and that only the doubling of the parent perovskite sub-structure c axis dimension is immediately apparent in the lab XRD data, in the form of the hkl, l odd reflections in Fig.3. Note that the √2c/a ratio was slightly greater than 2 in both cases with refined values of 2.007(1) and 2.008(1) respectively. 3.2 TEM. Fig.4a shows a typical single domain, untwinned [001] zone electron diffraction pattern (EDP) of the (3+2)-D incommensurately modulated, nanochessboard phase, in this case from the x = 0.067 sample. Indexation is with respect to the basis vector set M* = {a*= 1/2(ap*+bp*), b*= 1/2(-ap*+bp*), c* = 1/2 cp*, q1 = ε(a*-b*), q2 = ε(a*+b*)}. From Fig.4a, ε~ 0.036(2) and ε~ 0.035(2) corresponding to a 28ap – 29ap, or 10.7–11.1 nm 'supercell' along the parent ap and bp directions. One such large 'supercell' of this type is highlighted in white in the middle region of Fig.1a. While the nano-chessboard array (see Fig.1b and the top half of Fig.1a) and diamond type contrast (see the bottom half of Fig.1a) associated with these supercells can clearly be rather well-ordered over considerable distances, it is also apparent that there can also be considerable variability in the sizes and shapes of these supercells over longer length scales (also see Figs.S1, S2 and S3). This meso-scale variability in the sizes and shapes of the supercells, not surprisingly, could be expected to make the higher order harmonic satellite reflections in the corresponding EDP's disappear, as is observed experimentally both here as well as in earlier work (cf. e.g. Fig.4a with Fig.2 of [8]).

3. Results 3.1 XRD. The LNT6.7 sample annealed for 36 hours was homogeneous with no obvious trace of any impurity phase, as also was the LNT4 sample. Fig.3 shows a typical XRD pattern of the LNT6.7 sample.

Figure 3. XRD powder pattern of the LNT6.7 sample.

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Chemistry of Materials (according to the model of Guiton and Davies [8,9]) corresponds to the octahedral tilt twinned (see the dashed lines labelled with the symbol t in Fig.2), a = ap+bp, b =-ap+bp, c = 2cp, Li1/2Nd1/2TiO3 structure (see the basic structure cell outlined in the bottom left quadrant of Fig.2, and the a and b lattice fringes marked by black arrows in Fig.1c) while the planar interfaces can be thought of as corresponding to the two largely orthogonal Nd-rich, Nd2/3TiO3 regions running essentially perpendicular to the a and b directions (again see Fig.2). The reciprocal lattice reflections of the simpler basic structure (H = ha*+kb*+lc*) are then split to give rise to new Bragg reflections at g = H + 1/d1 (m-H.R1) a* + 1/d2 (n-H.R2) b*, where m and n are integers, d1 and d2 are the average spacings between the Nd-rich, Nd2/3TiO3 regions and R1 and R2 the shift vectors across the Ndrich, Nd2/3TiO3 regions. The observed positions of the spots in Fig.4a then imply that R1 = R2 = 1/2 [a+b] (so that H.R1 = H.R2 = 1/2 (h+k)) and 1/d1 = |(q1+q2)|, 1/d2 = |(-q1+q2)|. The required 1/2 [a+b] shift vectors are confirmed experimentally by high-resolution TEM imaging (see the black arrows in Fig.1c), in agreement with earlier work (see Fig.4 in Ref[8]). The only systematic extinction condition observed in the case of the nano-chessboard phase is F(HKLMN) = 0 unless H+K+M+N is even, requiring the existence of the superspace centreing operation {x1+1/2, x2+1/2, x3, x4+1/2, x5+1/2}. This superspace centreing operation is saying that the resultant (1/ε1) ap x (1/ε2) bp x 2cp superstructure (highlighted in white in the [001] images shown in Fig.1a) must be C-centred. It is also consistent with the interface modulated structure approach described above. The most likely ideal superspace group symmetry for this (3+2)-d modulated structure is then Cmmm(ε1,ε2,0; ε1, ε2,0). Fig.4b shows an apparently single-phase type zone axis EDP of the nano-chessboard phase. The EDP is indexed according to the same (a*, b*, c*, q1, q2) basis set as for Fig.4a. The observed relationship |g11000| ~ 2|g00100| reflects the fact that c* = 1/2 cp*, i.e. c = 2cp, as manifest in high-resolution TEM and STEM images (see Fig.5). A bright-field (BF) STEM image projected down the same direction (equivalent to projecting along one of the parent perovskite unit cell edges shown in Fig.2) is shown in Fig.5 (see the top and bottom regions). The central region in Fig.5 corresponds to an [001] zone axis orientation and exhibits the characteristic diamond-type contrast. Insets a and b, at the top and in the middle of Fig.5 respectively, show high-resolution, high-angle annular dark field (HAADF)-STEM images characteristic of the [110] and [001] regions. The brightest dots correspond to the heavy Nd atom columns (atomic number ZNd=60) while the smaller dots are either the lighter Ti columns (ZTi =22) (in both insets) or Nd atom columns with low occupancy (inset (b), for [110] view – see arrows). These images are consistent with the √2x√2x2 average crystal structure of Li1/4Nd7/12TiO3 reported in [9], and shown overlaid on the HAADF-STEM images in Fig.5. The twinned nature of the entire crystalline region shown in Fig.5, with an [001] oriented crystal at the centre of the image and [110] oriented crystals at the top and

Figure 4. Selected-area electron diffraction patterns indexed using the (a*, b*, c*, q1, q2) basis set (see text) and taken along the (a) [001] and (b) [110] zone axes respectively.

Further examples of supercell size and shape variability, and in particular the existence of a separate, but related, stripe phase, are shown in Fig.S1 and Fig.S2. Similar features have been reported in other systems, such as NaLaMgWO6 [15]. These local variations in size and shape were evident regardless of the sample composition (see Fig.S2). However it is important to note that there is no measurable difference in the average size or shape of the supercell across the two different compositions we have investigated, contrary to what has been reported previously [8]. The characteristic spot splitting observed around the (absent) h+k odd and (allowed) h+k even reflections in Fig.4a is strongly reminiscent of so-called interface modulated structures (see e.g. [16,17] and references contained therein) characterized by a simple basic structure modified by the periodic introduction of planar interfaces or boundaries across which the simpler basic structure is displaced by a so-called shift vector R [16,17]. In the current case, the ‘simple’ basic structure

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bottom regions of the image, reveals that the zigzag contrast visible in the [001] crystal lines up with the dark and white band contrast visible in the [110] crystal regions: the darker and wider bands in the [110] crystals are aligned with the zigzags that are darker and wider along the [1 -10] direction of the [001] crystal. This band contrast can be regarded as the projected view along [110] of the zigzag contrast; it is therefore consistent with the columnar nature of the nano-chessboard ordering along [001], as originally suggested by Guiton & Davies [10]. The observed spatial relationship between the zigzag and band contrasts is probably a consequence of the twin boundaries between the three crystals.

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To understand the nature of the nanochessboard/diamond type ordering, one must now explain the origin of the nano-chessboard, zigzag and band contrasts observed by TEM and STEM. HR-STEM imaging provides some partial answers to this question. Fig.6 shows HR-STEM images in HAADF (a), (c), (f) and BF (b), (d), (g) modes for an [001] oriented region. As expected, the zigzag contrast marking the boundary between the diamond-shaped tiles manifests itself differently in the BF image, where it is dark, than in the HAADF image, where it is light. Intensity profiles (Fig.6e) taken across the rectangular regions highlighted in Fig.6c and Fig.6d provide more detail regarding the behaviour of the boundary contrast and its possible origin. The boundary region is indicated by the doubleheaded black arrow below each profile (Fig.6e).

Figure 5. BF-STEM image of a crystal oriented along [001] (middle part of image) surrounded by [110] oriented crystals (top and bottom parts of image) in LNT6.7. The [001] region displays dark zigzag contrast, lining up with dark band contrast in the [110] regions. This demonstrates the columnar morphology of the nano-chessboard ordering. The insets show high-resolution high-angle annular dark field (HAADF)-STEM images characteristic of the [110] and [001] regions, top and bottom, respectively. The local LNT unit cell and crystal structure are overlayed in each inset. Arrows in the inset for a [110] oriented crystal (top) indicate evidence of the variable occupancy of the Nd columns in the (002) layers between the fully Nd occupied layers (bright dots).

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Figure 6. High-resolution STEM images in (a), (c), (f) HAADF and (b), (d), (g) BF modes of an [001] oriented region exhibiting nano-chessboard ordering in LNT4. The strong dark boundary contrast separating diamond-shaped domain regions in the BFSTEM images (b), (d), (g) corresponds to a much weaker light contrast in the HAADF-STEM images ((a), (c), (f)). Intensity profiles over the rectangular areas shown in (c) and (d) are presented in (e). The blue profile corresponds to intensities integrated over a single row of atom columns, and the red profile to intensities integrated over four rows of atom columns. The black double-sided arrow in (e) is an estimate of the light/dark boundary region in the HAADF/BF-STEM images. The grey arrows represent the small patch of similar contrast at the centre of the diamond-shaped domains. The regions boxed in (c) and (d) are shown enlarged in (f) and (g), respectively, with simulated images based on Fig. 2, inset for a 77 nm thickness. The intensity profiles shown in (h) were taken across the same simulated images, with the blue profile corresponding to a single row of atom column and the red profile to four rows, as in (c), (d), (e). Weak streaks connecting positions corresponding to neighbouring Nd atom columns in the BF image (see arrows) are highlighted by arrows in (g).

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The blue areas in Fig.6e correspond to profiles along a single row of Nd and Ti atoms (see the thin rectangles in Fig.6c,d), whilst the red curves correspond to profiles integrated across four rows of Nd and Ti atoms (see the thicker rectangles in Fig.6c,d). These profiles show that, in the HAADF-STEM image, the absolute value of the peaks located at the nominal Nd and Ti positions, increases slightly in the boundary region, whilst the background intensity increases significantly. In the BF image, the absolute value of the troughs located at the nominal Nd and Ti positions, as well as the background intensity, decrease significantly in the boundary region. Intensity profiles across simulated HAADF and BF-STEM images (insets in Fig.6f and Fig.6g, respectively) are displayed in Fig.6h. Image simulations for the HAADF and BF-STEM modes were performed for a subset of the supercell structure proposed by Guiton & Davies (see Fig. 2). The simulations reproduce qualitatively the experimentally observed small increase in the Nd, Ti and Nd+Ti intensity peaks and in the background intensity at the boundaries. More specifically, the small change in atomic number (Z)-contrast observed experimentally across the boundary is reproduced in the simulations. This finding, valid for the entire range of thicknesses considered in the simulations (7-77 nm, see Fig.S4), may seem unexpected: the observed and simulated increase in image intensity across the presumably Nd-rich boundary region is much less than that predicted through a naive application of the ~Z2 formula [18] to the actual 17% increase in Nd atom concentration at the boundary predicted by the phase separation model [8,9]). This apparent discrepancy is actually a consequence of the complicated scattering dynamics of Ångström-scale electron beams in complex atomic structures a few hundred Ångströms thick [19]. Therefore the small increase in Z-contrast observed at the boundaries is consistent with an enrichment in Nd atoms, as proposed by Guiton & Davies [8]. However it is important to note that to determine which and how much Nd (and possibly Li) ions reside at the boundary requires a detailed quantitative analysis of the STEM image contrast, which in turn requires a quantitative knowledge of instrumental parameters such as partial spatial and temporal coherence, residual aberrations, the response of the detectors, specimen thickness [20] and, above all, a plausible starting model for the atomic structure. This represents a major study in its own right and is beyond the scope of the present work. Whereas the simulated HAADF-STEM image based on Guiton & Davies' crystal structure (ICSD code number 160439) is consistent with experimental observations, the simulated BF-STEM image (Fig.6g) is not. Although the intensity profiles (Fig.6h) across the simulated image are qualitatively similar to the experimental profiles (Fig.6e), it is clear that the simulated and experimental BF images exhibit significant differences: the narrow streaks connecting neighbouring Nd columns in the experimental image (see arrows in Fig.6g) do not appear in the simulation (inset in Fig.6g). Furthermore, the vertical and horizontal streaks through neighbouring Nd and Ti columns visible in the simulation are not detected in the experimental image. These observations remained valid for the entire range of thicknesses considered in the

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simulations – see Fig.S4. This implies that, whilst a good approximation for the heavier Nd and Ti atoms, Guiton & Davies' structural model requires modification regarding the arrangement and position of the lithium (and/or oxygen) atoms. An important aspect of experimental HRTEM images reported previously [8] and in the present study (Fig.1c, Figs.S1 and S2), namely the {100} LNT lattice fringes in the diamond shaped Li-rich regions, has not been explained satisfactorily so far. These lattice fringes are also observed in BF-STEM images, as shown in Fig.7. As in the HRTEM images, the fringes run (mostly) along both (100) and (010) planes of the LNT structure between the Nd and Ti rows of atoms, and shift by /2 across the Nd-rich boundaries (see Fig.7a). Although the fringe contrast is weak, intensity profiles (insets in Fig.7a) confirm unequivocally the presence of brighter fringes with the characteristic {100} LNT spacing. Guiton et al. [8,9] proposed that “anti-ferroelectric like” Ti ion shifts are responsible for these features, and indeed, HRTEM multislice simulations [8] reproduced the experimentally observed fringes. These fringes do not appear in our BFSTEM image simulations (see Fig.6g, Fig.S4), however, because the structural model used (ICSD code number 160439, see also Fig.2) does not include the proposed basal plane Ti ion shifts. Despite the reported agreement between experimental and simulated HRTEM images [8], we strongly question the crystal chemical validity of invoking anti-ferroelectric-like Ti ion shifts of this type (in essence, independently of the local Li ion distribution and hence crystal chemically implausible) to explain the {100} LNT fringes [8,9], as detailed in Sec. 3.3 below. This observation has necessarily led us to propose quite new structural models in which any off-centre, basal plane Ti ion shifts are strongly coupled to, indeed induced by, the local Li ion distribution and in which the Li ions order locally in one dimension only; these models will be described in the following section. BF-STEM image simulations for e.g. model A of this type (see Fig.S5) yield clear (100) bright fringes for the entire large range of specimen thicknesses considered (8 to 77 nm). One such simulated image is inset in the experimental image of Fig.7b and is a very good match to the experimental image, especially considering the complexity of the structure and the extremely subtle effect expected from the presence of Li ions (atomic number Z = 3) beside the much heavier Nd ions (Z=60). However there remains one feature of the experimental BF-STEM images that is not reproduced in the simulated images: the streaks that connect the positions corresponding to neighbouring Nd atom columns (see Fig. 6g). This is discussed in Sec. 4. We also observe in both the BF and HAADF-STEM images a small, roughly “square” region at the centre of each diamond with similar contrast to that observed in the diamond boundary regions (see the grey arrows in the profiles, Fig.6e), suggesting they may have a similar structural origin and composition. The sides of this square are of approximately the same dimension as the width of the diamond boundary regions and also as the width of the small regions where the diamond boundary regions intersect, and which displays a similar contrast to the diamond regions. Furthermore, regions of the

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Chemistry of Materials Fig.8 shows (a) [001] and (b) [010] projections of this structure in the setting used in this paper ([010] and [100] in the P2/m (a = 5.41 Å, b = 7.71 Å, c = 5.41 Å; β= 90° setting), with the Nd ions in the same layer as the Li ions left out and the Li occupations set to 1. The local stoichiometry is then Li1/2Nd1/2TiO3, corresponding to the diamond regions. Note that the TiO6 octahedra are co-operatively rotated around the b axis (in this setting) by 15.44°, that the Li ions have been displaced completely away from the ideal perovskite A site positions occupied by the Nd ions to four co-ordinate, so-called 'square window' sites and that there exists layered ordering of the A cation positions along the c direction. This layered ordering is responsible for superlattice reflections such as e.g. 001* and 111* etc. in Fig.3.

same size as the central patch just mentioned, but with the lower Z-contrast characteristic of the diamond region (apart from its central patch), are observed at the intersection of the diamond boundaries. 3.3 Local crystal chemistry. In order to obtain further insight into the driving forces responsible for the complexity of the overall crystal structure, an understanding of the local crystal chemistry of the underlying average structure of the LNT perovskite phase is essential. Bond valence sum calculations were thus carried out using the P2/m (a = 5.41 Å, b = 7.71 Å, c = 5.41 Å and β= 90°; note the alternate setting to that given above) crystal structure reported for Li1/4Nd7/12TiO3 in [9] as a starting point. The reported fractional co-ordinates are listed in Table 1.

Figure 7. Experimental bright-field STEM image of an LNT4 sample, revealing the weak but ubiquitous white lattice fringes parallel to the [100] and [010] directions – see arrows. Intensity profiles across A to B and C to D confirm the presence of these fringes as higher intensity peaks (black-rimmed arrows). (b) shows an enlarged view of the bottom region in (a) in false colours to highlight the bright fringes (see arrows). A simulated image inset reproduces these fringes well. The simulation was for model A (Fig. 9) and thickness 77 nm (see Fig. S4).

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Figure 8. Structural models with ordered Li ions. (a), (b) Nd7/12Li1/4TiO3 structure from [9], viewed along [001] and [010], respectively. (c), (d) show model A, (e), (f) model B, and (g), (h) model C for Nd1/2Li1/2TiO3. This setting of a = b = 5.41 Å and c = 7.71 Å is consistent with that used throughout the text, but differs from the settings required by the specific space group of each model (see Tables 1, 3-5).

The 15.44° magnitude of octahedral rotation is essential in order to reduce the initial over-bonding of the Ti ions and under-bonding of the Nd ions for an ideal undistorted Pm3m perovskite structure. Thus the calculated bond valence sum, or apparent valence (AV), of the Ti4+ ion is reduced from an initial value of 4.55 for an unrotated, ideal perovskite structure to an acceptable value of 4.057 for the 15.44° rotated structure (see Row 1 of Table 2 below). Likewise, the apparent valence (AV) of the Nd3+ ion is increased from an initial value of 2.40 for an unrotated, ideal perovskite structure to an acceptable value of 3.193 for the 15.44° rotated structure (see the as reported Row 1 AV's listed in Table 2). It is worth pointing out at this stage that the magnitude of the primary modulation wave-vectors q1 = ε(a*-b*) and q2 = ε(a*+b*), ε~ 0.036 and ε~ 0.035, are clearly closely related to the magnitude of this octahedral rotation angle as follows: 1-cos(15.44°) = 0.0361! This is clearly no accident and strongly suggests that strain associated with the local octahedral rotations determines the overall superlattice periodicity). Table 1. Reported fractional coordinates of Li1/4Nd7/12TiO3 in space group P2/m, a = c = 5.41, b = 7.71 Å, β = 90° (see [9]). Atom Nd1 Nd2 Li1 Li2 Ti1 O1 O2 O3 O4 O5 O6

x 0.250 0.250 0.500 0.000 0.766 0.500 0.500 0.000 0.000 0.750 0.750

y 0.000 0.500 0.500 0.500 0.750 0.702 0.798 0.702 0.798 0.000 0.500

z 0.750 0.750 0.000 0.500 0.766 0.000 0.500 0.000 0.500 0.848 0.652

Table 2. Calculated Bond Valence Sums for the LNT average structure reported in [9]. P2/m, a = c = 5.41, b = 7.71 Å. AV(Li1)) AV(Li2) AV(Nd1) AV(Nd2) AV(Ti) As reported 1.762 1.670 3.193 3.193 4.057 Li adjusted 1.096 1.160 3.193 3.193 4.057

In the reported √2x2√2average structure reported for Li1/4Nd7/12TiO3 in the Supporting Information section of [9], the Ti ions undergo significant shifts along , away from the TiO6 octahedral centres (0.12 Å) towards one of the equatorial oxygen ions tilted upwards i.e. away from the Nd layer and towards the Li-containing layer – see the black arrows in Fig.8a above. These off-centre anti-ferroelectric type Ti shifts were introduced as an explanation for the {110}p lattice fringes observed in the HRTEM images [8,9]. However, as mentioned above, applying these Ti ionic displacements to the entire tilttwinned LNT supercell is crystal chemically implausible. Firstly, for these Ti shifts to be consistent with the fact that the {110}p lattice fringes run continuously across each diamond-shaped region and shift by 1/2 across the Nd-rich boundary regions, their direction must not change sign across the octahedral tilt twin boundaries within the diamond regions, but must change sign across the Nd-rich boundaries [8]. Consider two diagonally opposite quadrants in the diamond-shaped cell (Fig. 2). If the off-centre Ti ionic shifts for one quadrant are as shown in Fig.8a, in the diagonally opposite quadrant these Ti shifts must remain unchanged while the octahedra will be reflected across two orthogonal tilt boundaries, resulting in a shift of the origin of the original LNT cell by 1/2[110]. This is equivalent to reversing the displacements shown in Fig.8a and makes no crystal chemical sense at all. For a start, the equatorial oxygen

Occ. 1 0.167 0.5 0.5 1 1 1 1 1 1 1

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that it must now move towards is already over-bonded (AV = 2.20) by virtue of the fact that the 15.44° octahedral tilt has moved it away from the Li layer and towards the Nd layer. The last thing it therefore needs is a Ti moving towards it as required by the Guiton and Davies Ti shift model. This is borne out by bond valence sum calculations which show this oxygen becomes severely over-bonded if we reverse the Ti ion shifts (AV = 2.55!). Likewise the equatorial oxygen it moves away from is now even more severely under-bonded (AV = 1.34!). This is not crystal chemically credible. A further major problem with the Guiton and Davies Ti shift model is that the in-plane direction of displacement of the Ti ions is heavily dependent upon the local Li ion distribution as this strongly affects the calculated AV’s of the local oxygen atoms. As the Li ion distribution proposed by Guiton and Davies is not consistent with {100} LNT lattice fringes (see Fig.S6b) then neither can any induced Ti ion displacement pattern, at least not for opposite quadrants within the same nano-diamond region. Secondly, there is no convincing reason why such significant ionic shifts should occur, especially in the light of the proposed square window Li ion positions ([8,9], also see Fig.8a). In this case, the effect of the (large) 15.44° rotation is to heavily distort the initial square planar environment of the Li ions into a twisted diamond type environment with two far too short Li-O distances (~ 1.56 Å, each corresponding to a bond valence of ~ 0.78) and two much longer distances so that the Li ions effectively only bond significantly to two of the surrounding oxygen ions. The bond valence sum, or apparent valence (AV), of the Li ion is thereby raised from an initially near acceptable value of 1.18 in the square window site of an unrotated, ideal perovskite structure to quite unacceptable values of 1.762 for Li1 and 1.670 for Li2 for the 15.44° rotated structure (again, see Row 1 of Table 2). It is thus clear that the Li ions must be locally displaced a very significant distance away from the square window position in such a way that the two short Li-O bonds are increased by the same amount i.e. roughly towards one or other of the two possible ideal A site positions on either side of the square window position. The displacement directions and magnitudes of the shifts required for the Li ions can then be estimated from bond valence sum considerations and are ±0.11[101] = 0.84 Å, respectively, for the Li1 site, and ~ ± [0.08, 0, 0.1317] = 0.83 Å in the case of the Li2 ion (see Figs.8c and d). The pair of initially too short Li-O distances are thereby increased to ~ 1.78 Å corresponding to a bond valence of 0.43 valence units each. Both Li ions remain only bonded significantly to these two surrounding oxygen ions. (A rather similar displacement from the square window site positioning of the Li ions was recently also reported from an average structure refinement of the closely related Li0.3La0.567TiO3 phase, see [7]). The initial Li1 and Li2 positions of 1/2, 1/2, 0 and 0, 1/2, 1/2 given in [9] were thus adjusted to 0.61, 1/2, 0.11 and 0.08, 1/2, 0.6317 respectively and the AV's re-calculated (see Row 2 of Table 2). The calculated AV's of the Li ions are now acceptable at ~ 1.1. Note that only two of the eight possible Li ion positions per Li1/2Nd1/2TiO3 unit cell shown in Fig.S6a can be locally occupied and that the Li ion sites related by the 2fold rotation axis of the space group P2/m are far too

close together (1.67 Å separation distance) to be simultaneously occupied (see configurations with p,q both odd or both even, and p≠q, Fig.S6b). Likewise, the 2.183 Å separation distance separating Li ion sites across the centre of the ideal A site position also seem too close together for both these Li ion sites to be simultaneously occupied, given the minimum Li-Li separation distance in Li2O, for example, is 2.305 Å. The question now becomes: what is the local Li ion distribution within the local √2ap x √2ap x 2ap, Pm unit cell characteristic of the Li1/2Nd1/2TiO3 part of the overall superstructure? The existence of satellite reflections around the G ± 1/2 p* positions of reciprocal space in Fig.4a in conjunction with the associated existence of local {100} lattice fringes (see e.g. Fig.1c) suggests that Li ions originally separated by ap and bp (equivalent to 1/2 (a+b) and 1/2 (-a+b) in Fig.8b) should not be simultaneously occupied, thus precluding p = q configurations in Fig.S6b, including the Li ion distribution model of Guiton and Davies [8,9]. We thus believe the local structure of the Li-rich, Li1/2Nd1/2TiO3 region is a combination of the four remaining one-dimensionally Li ion ordered structures, three of which are shown in Fig.8c,d, Fig.8e,f and Fig.8g,h (their corresponding fractional coordinates are listed in Tables 3-5 below). Note that the fourth structure, model A', is the enantiomer of model A (see Fig.S6b). Bond valence sum calculations show that each of the structures listed give entirely plausible local crystal chemistries with similar calculated Gii values, less than 0.1 in each case. Table 3. Fractional coordinates of Li1/2Nd1/2TiO3 in space group Pm, a = c = 5.41, b = 7.71 Å, = 90° (model A) Atom Nd1 Nd2 Li1 Li2 Ti1 Ti2 O1 O2 O3 O4 O5 O6 O7 O8

x 0.250 0.750 0.89 0.08 0.744 0.256 0.500 0.500 0.000 0.000 0.750 0.750 0.250 0.250

y 0.000 0.000 0.500 0.500 0.733 0.733 0.702 0.798 0.702 0.798 0.000 0.500 0.000 0.500

z 0.750 0.250 0.11 0.6317 0.756 0.244 0.000 0.500 0.000 0.500 0.848 0.652 0.152 0.348

Occ. 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Table 4. Fractional coordinates of Li1/2Nd1/2TiO3 in space group Pm, a = c = 5.41, b = 7.71 Å, = 90° (model B) Atom Nd1 Nd2 Li1 Li2 Ti1 Ti2 O1 O2 O3 O4

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x 0.25 0.750 0.58 0.08 0.744 0.256 0.50 0.50 0.00 0.00

y 0.00 0.00 0.50 0.50 0.733 0.733 0.702 0.798 0.702 0.798

z 0.750 0.25 0.361 0.631 0.756 0.244 0.00 0.50 0.00 0.50

Occ. 1 1 1 1 1 1 1 1 1 1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

O5 O6 O7 O8

0.750 0.750 0.25 0.25

0.00 0.50 0.00 0.50

0.84 0.652 0.152 0.34

C. The dotted yellow and green lines indicate the zigzag arrangements of the Li ions.

1 1 1 1

In other words, the presence of octahedral tilt twinning ensures that all four possible equivalent combinations of the two-dimensional Li ion distribution with respect to the TiO3 octahedral distribution occur within each overall superstructure unit cell. Such combinations could also be achieved by a single structure in which the four possible Li ion configurations (models A, A', B and C) are statistically averaged through each Li ionic position being 1/4 occupied. Fig.10 shows the entire proposed LNT supercell, including the Nd-rich boundary regions (light purple), across which the two-dimensional sub-lattice of the Li ions is shifted by 1/2 (a+b). This shift enables each neighbouring set of four quadrants to display the same local structure, with the exception of the tilt boundary intersections. The Nd-rich regions do not extend to the tilt boundary intersections, as apparent in the HAADF-STEM images (see Fig.6). These experimental images also revealed the presence of a patch at the centre of each diamond-shaped domain; the HAADF-STEM image contrast of this patch suggested it is Nd-rich, like the boundaries between neighbouring diamond-shaped domains. For clarity this patch is not shown on Fig.10.

Table 5. Fractional coordinates of Li1/2Nd1/2TiO3 in space group Pmc21, b = c = 5.41, a = 7.71 Å, = 90° (model C) Atom Nd1 Li1 Ti1 O1 O2 O3 O4

x 0.0 0.5 0.2705 0.702 0.798 0.000 0.5

y 0.750 0.11 0.258 0.0 0.5 0.848 0.652

z 0.250 0.61 0.25 0.5 0.500 0.75 0.75

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Occ. 1 1 1 1 1 1 1

Note that each structure is characterised by local onedimensional ordering of the Li ions, and the four structures correspond to the four possible ways of achieving this ordering (see Fig.S6 and Fig.8). Note also that each structure gives rise to {100} lattice fringes but only along one direction (see the yellow lines in Fig.S6b). Our TEM experiments, however, strongly suggest average twodimensional ordering of the Li ions (see Fig. 8). Such two-dimensional ordering can be modelled by combining the structures of Model A and A' with those of Model B and C. The experimentally observed continuity of the Li ordering across the tilt boundaries then requires the combinations shown in Fig.9. Although the combinations shown may appear arbitrary, they are just the reflection of the fact that in each quadrant (as shown in Fig. 9), a single Li ion sub-lattice superimposes onto an octahedral sub-lattice with two tilt-twin boundaries. This superposition of two sub-lattices requires the combinations shown in Fig. 9, each combination consisting of two subtly different crystal structures (see Fig. 8).

Figure 9. Structural model for the Li ion ordering across the four quadrants of a diamond region separated by octahedral tilt twin boundaries (the black lines) and bounded by Ndrich regions (light purple). The Li ions are shown as yellow and green disks, to show their belonging to model A, A', B or

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Figure 10. Schematic of the proposed structural model for the Li ion ordering in the LNT supercell. The supercell vectors are shown in red.

3.4 Dielectric measurements. Given the usefulness of LNT for temperature compensation in dielectric applications, dielectric spectra were also collected as a function of temperature and frequency from liquid nitrogen up to 525 K. No peak in the dielectric loss tangent was observed below 300 K. Strong dielectric relaxation, however, was observed to occur above room temperature (see Figs.11a and b). Both the dielectric permittivity and the dielectric loss tangent show strong frequency dependence, indicative of a characteristic dielectric polarisation relaxation occurring over this temperature range. Note that the maximum temperature (Tm) of the dielectric loss tangent associated with this dielectric relaxation shifts systematically towards higher temperature with increasing frequency. Above ~ 50 kHz, however, the peak of the dielectric loss tangent (at ~ 490 K) becomes almost flat as a result of merging together with another peak from an even higher temperature range. The latter peak in the dielectric loss tangent is presumably induced by a high temperature conductive mechanism.

Taking the maximum temperature of the peak in the dielectric loss tangent temperature at Tm over the frequency range from 100 Hz to to 30 kHz, the frequency dependence of the peak positions in the loss tangent curves can be well modelled using the standard Arrhenius equation (fr = fo exp(-Ea/kT)) – see Fig. 11c. Here fr is the measuring frequency, fo is the relaxation frequency at infinite temperature (or attempt jump frequency), Ea represents a dipole activation energy, k is the Boltzmann constant and T is the peak temperature (Tm) of the dielectric loss curve at the particular measuring frequency. A fit of this type gives an activation energy Ea ~ 0.23 eV and an attempt jump, or freezing, frequency f0 ~ 1×1010 Hz. It is noteworthy that while the activation energy is not particularly high, the attempt jump frequency is extremely low relative to typical phonon frequencies. This implies the existence of relatively long-lived polar clusters that are easily activated but whose alignment under an applied electric field is quite slow. Presumably this is related to electric field driven, correlated displacements of the Li ions. The proposed one-

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dimensional ordering of Li ions in the nano-diamond regions (see Fig.S6b may well provide a mechanism for such correlated hopping of 1-D clusters of Li ions.

4. Discussion The above results show that one-dimensional Li ion ordering within an octahedral tilt-twinned structure is the most plausible origin for the observed {100} lattice fringes exhibited by Li0.5-3xNd0.5+xTiO3 solid solutions. One-dimensional ordering of the Li ions is a logical consequence of the local crystal chemistry. The four configurations of possible one-dimensional Li ordering offer the structural flexibility suggested by the large overall LNT supercell (~10 nm x 10 nm). In contrast, the large Ti ionic shifts invoked by previous authors are not consistent with bond valence calculations, although some smaller shifts of the Ti ions are induced by the local Li ion distribution. The fact that the √2 relationship between the local LNT unit cell in a diamond region and the parent perovskite unit cell is in most cases not detected in powder XRD also implies that the source of the local √2x√2 LNT unit cell is ordering of a low Z element such as Li. This observation is further supported by the fact that the LNT unit cell cannot be deduced from neutron diffraction either, a technique where the scattering factor for Li is also very small. The Li ordering is detected not only by electron diffraction (Fig. 4), but also by BF TEM and STEM imaging (Figs. 1, 5, 6, S1, S2). This work constitutes a case where the presence of Li has a measurable effect on the image contrast. The proposed zigzag ordering of the Li ions and the possibility that they hop rapidly from one site to another to generate the average {110} lattice fringes observed by HRTEM and BF-STEM are consistent with our dielectric measurements. Although such hopping would presumably take place in between neighbouring Nd ions, along the same directions where unusual streaks in the BFSTEM images (Fig.6g) were noted, it is unclear whether the two features are related. The streaks are very narrow and weak and hence not typical of contrast in STEM images typically associated with scattering from atomic columns. In order to understand and simulate the potential effect of Li-ion hopping on STEM image contrast, an understanding of the dynamics and correlations, if any, of the Li-ions would be needed. This would require a significant and highly sophisticated investigation beyond the scope of the present work.

Figure 11. The temperature-dependence of the (a) dielectric permittivity and (b) dielectric loss tangent measured over the frequency range from 100 Hz to 1 MHz of LNT6.7. (c) presents the measured relationship (dots) between the frequency-dependence of the dielectric polarisation and Tm (corresponding to the peak of the dielectric loss tangent), fitted using the Arrhenius equation (solid red line).

Finally, what is the origin of the chessboard/diamond nanostructure periodicity? The close relationship between the nanostructure periodicity in the form of the magnitude of the primary modulation wave-vectors q1 = ε(a*-b*) and q2 = ε(a*+b*), ε~ 0.036 and ε~ 0.035, and the magnitude of this octahedral rotation angle of 15.44°: 1-cos(15.44°) = 0.0361 strongly suggests that strain associated with the local octahedral rotations determines the overall superlattice periodicity. One may speculate that the combination of octahedral tilt twin boundaries and Li ion lattice antiphase bounda-

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ries act together to minimise the structural distortions generated by the ordered Li ions. The presence of patches of lower or higher Z-contrast at the diamond boundary intersections and tilt twin boundary intersections, respectively, is consistent with a complex interplay of chemical and strain factors. More sophisticated modelling tools such as ab-initio calculations are needed to determine the precise local crystal structure. Such structural models could in turn be used in more refined matching between experimental and simulated (S)TEM images and provide insight into the remarkable mesoscale ordering displayed by these LNT compounds.

thors are grateful to Dr Matthew Weyland for his advice and assistance regarding STEM on the Titan microscope.

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5. Conclusions The main result of this study is the demonstration via a combination of experimental and calculated brightfield scanning transmission electron microscopy images and crystal chemical considerations that the the observed {100} lattice fringes observed within the diamond shaped nanoscale regions observed in Li0.5-3xNd0.5+xTiO3 solid solutions are the result of local Li ion ordering and associated structural relaxation. Based on bond-valence calculations, models of the local crystal structure are proposed in which Li ions order two dimensionally. Simulated BF-STEM images show that the Li ion ordering can be observed experimentally, and are in fact consistent with experimental BF-STEM images. The resulting nano-chessboard supercell structure is then the combination of the Li ion sub-lattice and the octahedral tilttwinned sub-structure. The nature of the local Li ion ordering distribution is also consistent with the existence of correlated displacements of Li ions, as implied by dielectric measurements.

ASSOCIATED CONTENT Supporting Information. HRTEM and BF-STEM images, BF-STEM image simulations and Li ion distribution models. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author

* E-mail: [email protected] (RLW). Author Contributions

The manuscript was written through contributions of all authors./All authors have given approval to the final version of the manuscript./ Funding Sources

RLW, AS and YL acknowledge support from the Australian Research Council in the form of ARC Discovery and Linkage Grants. YL also acknowledges support from the ARC Future Fellowships program.

ACKNOWLEDGMENT Use of the facilities at the Monash Centre for Electron Microscopy is acknowledged. Funding from the Australian Research Council grant number LE0454166 and the Victorian State Government for the FEI Titan3 80-300 and JEOL 2100F FEG-TEMs, respectively, are acknowledged. The au-

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Nano-scale chessboard/diamond ordering characteristic of the LNT system.

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Diamond Nanostructures and the A ... - ACS Publications

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