TEM and DFT Study of Basal-plane Inversion Boundaries in SnO 2 -doped ZnO

: In our recent study (Ribić et al. 2020) we reported the structure of inversion boundaries (IBs) in Sb 2 O 3 -doped ZnO. Here, we focus on IBs that form in SnO 2 -doped ZnO. Using atomic resolution scanning transmission electron microscopy (STEM) methods we confirm that in SnO 2 -doped ZnO the IBs form in head-to-head configuration, where ZnO 4 tetrahedra in both ZnO domains point towards the IB plane composed of a close-packed layer of octahedrally coordinated Sn and Zn atoms. The in-plane composition is driven by the local charge balance, following Pauling's principle of electroneutrality for ionic crystals, according to which the average oxidation state of cations is 3+. To satisfy this condition, the cation ratio in the IB-layer is Sn 4+ : Zn 2+ =1:1. This was confirmed by concentric electron probe analysis employing energy dispersive spectroscopy (EDS) showing that Sn atoms occupy 0.504 ± 0.039 of the IB layer, while the rest of the octahedral sites are occupied by Zn. IBs in SnO 2 -doped ZnO occur in the lowest energy, IB 3 translation state with the cation sublattice expansion of ΔIB (Zn–Zn) of +91 pm with corresponding O-sublattice contraction ΔIB (O–O) of –46 pm. Based on quantitative HRTEM and HAADF–STEM analysis of in-plane ordering of Sn and Zn atoms, we identified two types of short-range distributions, (i) zigzag and (ii) stripe. Our density functional theory (DFT) calculations showed that the energy difference between the two arrangements is small (~6 meV) giving rise to their alternation within the octahedral IB layer. As a result, cation ordering intermittently changes its type and the direction to maximize intrinsic entropy of the IB layer driven by the in-plane electroneutrality and 6-fold symmetry restrictions. A long-range in-plane disorder, as shown by our work would enhance quantum well effect to phonon scattering, while Zn 2+ located in the IB octahedral sites, would modify the bandgap, and enhance the in-plane conductivity and concentration of carriers. (PBE) generalized gradient approximation [72] is applied to exchange correlation A regular (4 × × grid of is used to sample the 3D Brillouin zone for the bulk and 1 × 2 × 1 for supercells. We used 0.02 Ry of the Gaussian spreading for Brillouin-zone integration and Marzari-Vanderbilt cold smearing. and the stripe only two, which is the lowest possible minimum. Our DFT calculations show that stripe distribution has only slightly lower energy (6 meV/ f.u. ) than the zigzag distribution, which makes them thermodynamically very competitive. The energy difference arises mainly from larger variation in the bond lengths and angles in the zigzag model (Fig. 6c) compared to the more symmetric stripe model (Fig. 6d). Such small energy difference is easily overcome kinetically and both variants would be expected in real IB-layers.


Introduction
Nonohmic properties of ZnO ceramics with a complex metal-oxide additions attracted researchers already 50 years ago for its use in varistor applications [1]. Successive studies were discovering new additives [2,3] and processing methods [4] to improve varistor's properties. The first to investigate the role of Sn addition in ZnO varistor ceramics were Gould and Carter [5], who recorded power-law dependence of current density on applied voltage, which they interpreted in terms of space-charge-limited conduction controlled by an exponential distribution of traps. In nearly the same time, grain growth and electrical properties of complex ZnO-based varistor compositions with SnO 2 additions were investigated by Milošević et al. [6]. As SnO 2 , as a dopant, did not significantly improve varistor properties, it had gone forgotten, until Daneu et al. [7] discovered the most unusual phenomenon, when studying grain growth in ZnO-Bi 2 O 3 -SnO 2 ceramics. On small additions of SnO 2 the ZnO grains grew significantly larger than without its addition. This alone would not be alarming, if then with higher additions of SnO 2 the ZnO grain size would not decrease. What was happening? How the low additions of a dopant first enhance the grain growth of the main phase, while increasing addition of the same dopant then inhibits its growth. The authors found that every ZnO grain in the final microstructure contains an inversion boundary (IB). Each grain with such IB grows on the expense of 'normal' ZnO grains until they dominate the microstructure. With higher amount of added SnO 2 , more IBs form in the initial ZnO grains, and final grain sizes are smaller. This behavior was called 'IB-induced grain growth' and was shown to be the key mechanism to tune grain growth in ZnO ceramics from a fine-to coarsegrained by a strict control of IBs [8][9][10][11][12][13]. Meanwhile, other researchers were exploring varistor properties of mixed ZnO/SnO 2 ceramics [14].
IBs in ZnO have soon been studied by electron microscopy methods. In structural and spectroscopic investigation of Sb-rich IBs, Rečnik et al. [15] reported that IBs in ZnO are always triggered by specific IB-forming dopant and that they compose an octahedral IB layer of cations with an average oxidation state of 3+. For Sn, being in the oxidation state of 4+, they suggested that it would constitute an octahedral IB layer together with Zn 2+ in the ratio of 1:1. For the first time implementing the new method for quantitative chemical analysis of interfaces [16], Daneu et al. accurately measured the composition of Sn-rich IB and proposed the model of its local structure [17]. With spectroscopic and structural analysis of IBs in SnO 2 -doped ZnO it was unequivocally shown that, controlled by the charge balance rule [15], Sn constitutes exactly one half of the IB layer.
In polycrystalline thin films IBs are not easy to detect, and their preparation would necessitate a plan-view TEM sample preparation [51]. More readily, IBs are observed in diverse nanostructures. Deng et al. [52] noticed IBs in Sn-doped ZnO nanobelts, extending along the longer [011 -0] axis of the belts, beautifully demonstrating the IB-induced anisotropic growth mechanism [10]. Similar conclusions were made by other authors [53,54]. Observation of IBs in Sn-doped ZnO nanobelts and nanowires was followed by highly competitive studies of their atomic structure using scanning transmission electron microscopy (STEM) methods [55][56][57][58][59]. While most of these studies correctly interpret the translation state of Sn-rich IBs, their lack in understanding of the local charge balance [15] is reflected in erroneous interpretation of the occupancy and arrangement of Sn atoms in the IB-plane. While it is generally known that Sn alone cannot produce a stable tail-to-tail inversion [10] further deficiency in these studies is seen in their knowledge on stabilization of parallel Snrich IBs. Not being aware of contamination with Ga [55], In [57], Si [58] or Al [59] in their experiments, they report on growing pure polytypoidic SnO 2 (ZnO:Sn) m nanowires, instead of fully characterizing these fascinating mixed homologous phases with potentially interesting physical properties. Namely, in addition to Fe and Ti, these dopants are known to stabilize tail-to-tail configuration of IBs [60][61][62][63][64][65], enabling growth of mixed homologous structures with Sn-rich IBs, as this was clearly demonstrated by Eichhorn et al. [60] and Hoemke et al. [63] for gallium and aluminum additions. While regardless of their synthesis route, the literature data has a broad agreement on the translation state of Sn-rich IBs in ZnO and octahedral coordination of Sn, there are still ambiguities about the occupancy, and thus no consent about the arrangement Sn atoms in the IB-layer. In the present study we investigated the structure and chemistry of basal-plane IBs in SnO 2 -doped ZnO ceramics by means of high-resolution transmission electron microscopy (HRTEM), high-angle annular dark-filed (HAADF) and annular bright filed (ABF) STEM methods to study the local structure, and energy dispersive X-ray spectroscopy (EDS) to determine the chemical composition of Sn-rich IBs in ZnO. Experimental studies are complemented by structure modeling and density functional theory (DFT) calculations to identify the lowest energy cation distributions in the IB-layer.

Materials and Experimental Procedures 2.1 Sample preparation
The pellets of ZnO with Bi 2 O 3 and SnO 2 additions were prepared by mixing the oxide powders and sintered at 1200 °C for 2 hours. Here, SnO 2 addition acts as grain growth modifier [12] whereas Bi 2 O 3 is added as fast oxygen ion conductor [66] increasing grain boundary resistivity in varistor compositions. Details of sample processing are given in ref. [7]. The pellets were cut and polished, and cross-sections were etched in diluted HCl to reveal ceramic microstructure with IBs. Prior to observations the samples were sputtered by a thin layer of carbon to improve conductivity. TEM samples were prepared according to the standard sample preparation procedure by ultrasonic cutting ceramic pellets into 3 mm disks (Sonicut 380, SBT Ltd., California, USA), grinding and dimpling (Dimple Grinder, Gatan Inc., Pennsylvania, USA) and Ar + ion-milling (Pips 691, Gatan Inc., California, USA) at an angle of 10° until perforation for TEM observations.

Electron microscopy
Scanning electron microscopy (JSM-5800, Jeol Inc., Tokyo, Japan) was used to inspect the microstructures. Transmission electron microscopy (TEM) investigations of the samples were performed using a field-emission-gun TEM (JEM-2010F, Jeol Inc., Japan) with an ultra-high-resolution pole piece, operated at 200 kV. The microscope is equipped with a Si (Li) EDS detector fitted into an atmospheric thin-window EDS spectrometer (Link ISIS 300, Oxford Instruments, England) that was used to acquire series of EDS spectra for quantification of Sn content in the IB-layer. Experimental HRTEM images were recorded in thin crystal part near high-contrast conditions, i.e. Scherzer focus and first reverse passband to facilitate identification of atomic column positions. Image simulations were performed using multislice algorithm (EMS software [67]) employing electron-optical parameters of the microscope: C s = 0.48 mm, Δf = 8 nm and θ c = 1.2 mrad. High resolution HAADF-and ABF-STEM images of IBs in SnO 2 -doped ZnO were recorded using a dedicated probe corrected scanning transmission electron microscope (JEM-ARM200CF, Jeol Ltd., Tokyo, Japan) operated at 200 kV.

Structural modeling
For initial supercells, unit-cell parameters of ZnO were used according to Kisi & Elcombe [68]: a = 3.2501 Å, c = 5.2071 Å, u = 0.3817. Structural modeling was performed following the methodology described by Ribić et al. [69]. Briefly, the models were generated by CrystalMaker ® software [70] in such a manner that IB-plane is placed at the center of the supercell at the middle of its longer A-axis running parallel with the polar c-axis of ZnO. IB stacking and polarity inversion disrupts the lattice periodicity along the supercell A-axis, whereas the structure is periodic along the B-and C-axes. The continuity of the supercells was handled by adding an 8-Å-thick vacuum layer between the adjacent supercells along the non-periodic A-axis and adequate numbers of H-atoms were added to super-cell terminations to preserve the overall charge neutrality. Two different cations ordering were contemplated into the models, following the well-known IB 3 stacking sequence for Sn-rich IBs [17].

DFT calculations
The methodology of ab-initio calculations adhered to the methodology described by Ribić et al. [69]. Structural relaxations were based on the density functional theory (DFT) as implemented in the Quantum-Espresso code [71]. The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation [72] is applied to exchange correlation functional. Atomic potentials are described by ultrasoft pseudopotentials, with the 3d electrons of Zn included in the valence shell. Single particle electronic wavefunctions are expanded into plane-waves up to a kinetic energy cut-off at 30 Ry. A regular (4×4×4) grid of k-points is used to sample the 3D Brillouin zone for the bulk and 1×2×1 for supercells. We used 0.02 Ry of the Gaussian spreading for Brillouin-zone integration and Marzari-Vanderbilt cold smearing.

General characteristics of the Sn-doped ZnO ceramics
Already with small additions of SnO 2 (0.1 mol%) IBs are observed in ZnO grains, indicating that rather than forming a solid solution, SnO 2 instantly triggers the formation of IBs when added to ZnO, as described by Daneu et al. (2000). Fig. 1a shows a typical microstructure, where every ZnO grain contains a planar defect intersecting the grain. The inversion nature of these defects is revealed by the orientation of triangular etch-pits, that are inverted across the IB plane. Bright-field TEM image and the corresponding electron diffraction pattern in Fig. 1b [69]. This indicates that we either have no long-range ordering, or the distribution of Sn-atoms is random in the IB-plane.

Local chemistry of the Sn-rich IBs
In order to solve the local structure of IBs an exact concentration of Sn in the IBplane is the most essential information. The most suitable technique is EDS analysis of the boundary region. When detecting Sn in the IB plane some authors assumed a full monolayer of Sn [55,56], while others suggested a partial occupation of IBs with Sn [59,60,63], and attempted to resolve this issue by different indirect techniques, such as measuring differences in the intensity profiles in STEM images [56,59], that gave inconclusive results. Regardless these new attempts, the most reliable approach is still the one suggested by Walther et al. [16,17], that relies on recording series of EDS spectra with series of different parallel beams, all centered at the single position on IB. Concentric electron probe (CEP) method, implementing EDS (or EELS), eliminates unwanted effects of variations in sample thickness largely improving the accuracy, while a high number of acquired spectra improves the precision [16]. Compared to the spatial difference method [73], CEP method provides 10 2 -times better accuracy, and as much as 10-times improved precision [15][16][17], which is revolutionary for any quantitative analytical technique, especially the one measuring chemical compositions at atomic scale. Apart from quantitative determination of the dopant concentration, CEP method provides important information on the mode of dopant distribution in the area of interest, which is shown by the dependence of intensity ratio of traced elements (Sn and Zn) vs. beam radius. For example, if the dependence is asymptotic, approaching a finite intensity ratio, the dopant is present also in bulk material [74], however when the dependence is linear, the dopant stems only from the boundary [15].
The results of CEP/EDS method, implemented on Sn-rich IBs are shown in Fig. 2. Three CEP series, from small (limited by the boundary width) to large beam diameters (limited by the EDS detection limit of minor element), were measured on three different IBs. Linear dependence, as shown in Fig. 2, indicates that the Sn signal stems only from the IB plane, and that any Sn, if present in bulk ZnO, is below the detection limit. This suggests that Sn is not present in solid solution, as proposed by some theoretical studies [75], but immediately forms an IB as soon as it enters the ZnO structure. Reproduced after Daneu et al. [17].
This result is a very important experimental evidence for the interpretation of physical properties, as bandgap, electron conductivity and optical transmittance . Linear regression of measured data points, normalized with respect to thickness dependent threshold [15], gives a slope κ of 11.97 with a correlation coefficient R 2 =0.9249. The slope is inversely proportional to the concentration of dopant, x Sn , expressed in terms the apparent boundary width, w Sn , that acquires its physical meaning when compared to a real lattice plane of the planar defect (d IB ≈ c/2), w Sn = x Sn ·d IB , where the dopant concentration is measured [16]: = κ · r + 1; κ = (1) with I Zn and I Sn corresponding to the intensities of measured elements, and k Zn and k Sn to their EDS k-factors, respectively. Hence, the apparent boundary width, w Sn = 0.1312 ± 0.0099 nm. Assuming the width of one basal plane in ZnO structure [68] c/2 = 0.26035 nm, the fractional occupancy of cation sites, x Sn , on the IB-plane is 0.504 ± 0.039, i.e. meaning that ½ of the IB layer is occupied by Sn 4+ and the other ½ by Zn 2+ atoms. This value exactly corresponds to the expected fractional occupancy for dopants with oxidation state of 4+, predicted by the charge balance model for IBs in ZnO [15]. In line with this model, shown in Fig. 3, charge balance on IB is distributed locally, following Pauling's rule of electroneutrality in ionic crystals. According to this principle, each O splits its charge equally to its neighbors. In ZnO structure, the ZnO 4 tetrahedra are linked by corners, which represent O-atoms. In each such corner 4 tetrahedra are connected, three from the same layer, and another from the adjacent layer. Each O-atom thus splits its charge to four Zn-atoms, receiving 4-times ½·eˉ, that compensates its oxidation state of 2+. If now the same principle is applied to the octahedral IB layer, one can conclude that, each O-atom of MO 6 octahedra, also has only 4 neighbors, just the same as in the ZnO structure. This is because the O-sublattice is unchanged, only the cations occupy different interstices within the hexagonal close packed (hcp) lattice. Each cation in octahedral site thus receives 6-times ½·eˉ as there are 6 oxygens bonded to each octahedral M-cation. Consequently, the average charge of M-cations is 3+. If we now turn to the IB plane, composed of close-packed layer of MO 6  π of any oxidation state, as long as their average oxidation state is 3+. In the case of Sn 4+ , this cation can thus occupy only ½ of the octahedral sites, while the rest is occupied by Zn 2+ giving rise to complex 2D structures with an uncommon octahedral coordination of Zn. Fig. 3. Charge balance at the IB in ZnO according to Rečnik et al. [15]. White arrows indicate charge contributions from the O-atoms in tetrahedral and octahedral sites, yielding oxidation states of 2+ and 3+, respectively. The increase in the oxidation state in octahedral sites is due to the increased coordination number. The red arrows indicate the polar c-axis orientations across the IB-layer.
With time passed and a load of new publications in the field, the description of charge balance conditions on IBs [15] and accurate spectroscopic determination of the quantity of Sn in the IB layer [17], appear to have been lost. Without the use of proper analytical methodology and failing to study the previous work on Sn-rich IBs, Cao et al. [55] concluded that IBs in their SnO 2 (ZnO:Sn) m nanowires are fully occupied by Sn. Similar conclusions were drawn a year later by Park et al. [56], followed by three further studies [57][58][59], where Tan et al. [59] nicely shows an intensity undulation in HAADF-STEM image indicating that the IB-layer is probably not fully occupied by Sn. On the other hand, it is great to read the studies by Eichhorn et al. [60] and Hoemke et al. [63] that have built on this knowledge and constructed fascinating modulated structures with parallel Sn-rich basal-plane IBs making use of either Ga 2 O 3 or Al 2 O 3 additions to stabilize the transient tail-to-tail configuration inbetween, respectively.

Translation of the Sn-rich IBs
To study the structure of IBs we inspected ZnO grains near [ projections. Using HAADF-STEM imaging of the Sn-rich IBs it is rather straightforward to observe the increased intensity of the atomic columns constituting the IB plane, indicating the presence of heavy atoms. Fig. 4a   Further we can observe that the size of octahedra varies along the IBplane. This can be seen by a slight, but consistent alternating contraction/dilatation in Opositions at the focus plane of high-angular scanning. This variation is indicative of cations with a higher and lower oxidation states, imposing stronger or weaker attraction to the surrounding O-atoms, respectively. Measuring distances from STEM images is highly unreliable due to scanning distortions [76]. The simplest way to obtain some rough approximation of structural information is elimination of systematic distortions caused by sample drift during scanning. This can be done by geometrical correction of STEM image using real-space reference, which in our case is bulk ZnO. Once the images are corrected for systematic distortions, they can be used to measure the apparent expansion in the cation sublattice across the IB-plane (Zn-IB-Zn). The d IB(Zn-Zn) distance, 1 measured from several STEM images, normalized to bulk ZnO, amounts to 6.12 ± 0.10 Å. This value is slightly larger than the d IB(Zn-Zn) distance of the Sb-rich IB 3 reported by Ribić et al. [69] based on quantitative HRTEM (5.99 ± 0.05 Å), but we must keep in mind that the variations in the reported IB expansions measured from STEM images may be considerable. Park et al. [56] reported the d IB(Zn-Zn) distance of 6.02 Å for the SnO 2 -doped ZnO nanobelts, which is similar to that of the Sb-doped nanorods [77]. Other STEM images in their work vary from 5.55-6.45 Å, with their DFT optimized model predicting a d IB(Zn-Zn) distance of 6.35 Å. Jiang et al. [58] determined a similar value in the SnO 2 (ZnO:Sn) m polytypoidic nanowires. The d IB(Zn-Zn) value reported by Eichhorn et al. [60] is considerably shorter, but we must keep in mind that these IBs are not directly comparable as they constitute a homologous [Sn 0.5 Zn 0.5 ]GaO 3 (ZnO) 3 phase. Shorter measured distances in homologous phases are probably due the presence of tail-to-tail inversion in vicinity that may influence head-to-head dilatation.

Cation distribution in the Sn-rich IBs
Visualizing cation distribution within the IB-layer is not an easy task. Ideally, we want to directly image the IB-plane along the [0001] axis of ZnO. The problem is that the IBplane is buried within layers of ZnO, and there is no nondestructive way to remove them. Focused ion-beam (FIB) cutting of (0001) ZnO lamella with IB turns out to be unsuccessful because of deep damage, Ga + ion implantation, and the final TEM lamellae are too thick for structural work. Another approach is to search the conventional TEM sample for [0001] oriented ZnO grains and finding the IB in thin crystal foil. If IB does not exit exactly to the thin part of the crystal, the information on cation distribution is overshadowed by superimposed ZnO layers. Our HAADF-STEM and HRTEM image simulations demonstrate that already with more than 10-ZnO-layers (~2.6 nm thickness) on both sides of an IB-layer, no contrast features from IB can be observed. As there is no amplitude contrast produced by an in-plane IB to facilitate their identification at low magnifications, search for such crosssections would need to be done in high-resolution mode, which is further complicated by rapid evaporation of ZnO due to electron irradiation. We therefore have to rely on conservative edge-on orientations, such as [21 -1 -0] and [011 -0], and look forward to obtain all the information necessary to reconstruct 2D cation ordering in the IB plane from these projections [15]. When studying Sn-rich IBs at high resolution, we realize that all important contrast features are averaged out in crystal foils thicker than ~10 nm. This problem also appears to be the main obstacle in solving the cation distribution in Sn-rich IBs by other authors [55][56][57][58][59], where only the latest work shows some contrast variations along the IB-plane in [011 -0] projection. Why this appears to be such a problem? Unlike in Sb-rich IBs, where we have pure Sb and Zn columns in any of 〈011 -0〉 projections [15], in Sn-rich IBs, no atomic column remains pure at longer distances. Therefore, if we are to obtain any information on cation ordering, we must work in a thin crystal foil, and fast, because of the evaporation of ZnO, especially in scanning mode. Under these conditions, we observe interesting contrast variations along the IB-plane that give us a valuable hint on possible cation ordering. These contrast features are generated by two cation distributions that satisfy 1:1 ratio of Sn and Zn: (i) zigzag ordering with cations of the same species are forming chains of octahedra though the IB layer, and (ii) stripe with the cations of the same species occupying octahedra in linear manner, as illustrated in Fig. 6.
Because the crystal foil is very thin we have a fair chance to observe sequences of pure cation distributions. The two characteristic arrangements are outlined in Fig. 5a, and the corresponding simulated images are shown in Figs. 5b and 5c. Under chosen imaging conditions, near the first reverse passband of the contrast transfer function, bright dots in the image roughly correspond to the position of cation columns. In the first arrangement, strong and weaker bright dots are alternating along the interface, while the second arrangement is characterized by doublets of strong and weak dots. As seen by simulations, the intensity of bright dots along the IB-plane directly corresponds to the positions of Sn-columns, while the weaker dots inbetween correspond to the Zn-columns.

DFT study of cation ordering in the Sn-rich IBs
The 1:1 distribution of two atomic species is optimally accomplished in the square packing of atoms, i.e. chessboard arrangement. In a hexagonal close packing, such as that in the IB layer, monotonous distribution of two species in 1:1 ratio is not possible. To satisfy the charge balance requirements (Section 3.2) we must destroy the hexagonal in-plane symmetry of the octahedral IB layer. This instantly implies complex arrangements of the two cations. It can be shown that the simplest distributions are also the shortest-range, having the smallest periodic units. The zigzag ordering suggested by Daneu et al. [17] seems a good solution for short-range distribution of the two cations in the IB plane, however this alone is not sufficient to generate a maximum degree of freedom for cation ordering. Here we add stripe distribution, which has a half smaller repeat unit compared to zigzag ordering and helps increasing the entropy of the IB layer.
The two cationic arrangements, zigzag and stripe, are illustrated in Figs. 6a and 6b. Both distributions maintain Sn:Zn ratio at 1:1 at short range. These two arrangements have the shortest possible repeat units, with the zigzag containing four cations, and the stripe only two, which is the lowest possible minimum. Our DFT calculations show that stripe distribution has only slightly lower energy (6 meV/f.u.) than the zigzag distribution, which makes them thermodynamically very competitive. The energy difference arises mainly from larger variation in the bond lengths and angles in the zigzag model (Fig. 6c) compared to the more symmetric stripe model (Fig. 6d). Such small energy difference is easily overcome kinetically and both variants would be expected in real IB-layers. If we take a close look at the HRTEM image in Fig. 5a, we indeed see segments of both elementary distributions, as well as their combinations. As both configurations are energetically equivalent and the system tends to randomize Sn and Zn atoms as much as possible, the elementary segments are only stable at short lengths, barely enough that we observe them in a very thin crystal foil. As the crystal thickness increases, we see less and less clearly any of the two sequences, as the cation ordering changes the type and the direction, intermittently, at any moment, to maximize the layer entropy that is driven by local charge balance. This is the main reason why we do not observe ordering in diffraction patterns or high-resolution images of Sn-rich IBs in thick crystals.
While Sn-doped IB already acts as a quantum well for scattering of phonons [78], the long-range in-plane disorder, as a high entropy 2D object, additionally contributes to phonon dissipation. On the other hand, Zn 2+ located in very uncommon octahedral sites, would modify the bandgap, and possibly also enhance the in-plane conductivity of carriers. Theoretical studies of IBs have recently shown a great potential in studying potential barriers in ZnO [79,80]. To study the long-range ordering of cations in the Sn-rich IBs, molecular dynamic calculations on larger scale should be performed. This can be computationally demanding but knowing the exact in-plane structure can contribute to better understanding physical properties important for optoelectronic, thermoelectrics, varistors and other applications.

Conclusion
We investigated the head-to-head basal plane inversion boundaries in Sn doped ZnO wurtzite structure using HRTEM and STEM analysis and DFT calculations. Even small additions of SnO 2 (0.1 mol%) trigger the formation of IBs in ZnO grains, indicating the high preference of SnO 2 in forming planar defects rather than a solid solution with ZnO. Understanding the local structure of the Sn-rich IBs has been shown to be very important for the interpretation of physical properties of Sn-doped ZnO materials, such as bandgap, electron conductivity and optical transmittance. Here we revised published data on structural properties in the Sn-doped ZnO IBs, and attempted to add the missing part, which refers to inplane cation ordering in IB layer. To summarize important aspects of structural characterization discussed in this paper: • The positions of O-columns shown by ABF-STEM confirm head-to-head inversion of the Sn-rich IBs in ZnO, and illustrates that cations in the IB-plane occupy octahedral interstices. • As shown by quantitative CEP/EDS analysis, the Sn-rich IBs obey the stringent 3+ rule for the average oxidation state of octahedral cations comprising a basalplane IB. Following this rule, one half of the IB-layer is occupied by Sn 4+ , and the other half by Zn 2+ cations. • The translation state of the Sn-rich IBs corresponds to the Aβ−Bα−AβC−γB−βC (IB 3 ) sequence, and is consistent with the observations in the other studies, suggesting that this is likely the only stable IB configuration in SnO 2 -doped ZnO. • Based on the quantitative HRTEM and HAADF-STEM analysis of in-plane ordering of Sn and Zn atoms two types of short-range distributions were identified, zigzag and stripe. DFT calculations showed that both cation distributions are energetically equivalent and randomly alternate throughout the structure, what can be also observed on HRTEM images.