Utilising unit-cell twinning operators to reduce lattice thermal conductivity in modular structures: Structure and thermoelectric properties of Ga2O3(ZnO)9

Abstract The Ga2O3(ZnO)m family of homologous compounds have been identified as potential thermoelectric materials, but properties are often limited due to low densification. By use of B2O3 as an effective liquid phase sintering aid, high density, high quality ceramic samples of Ga2O3(ZnO)9 have been synthesised. The atomic structure and local chemical composition of Ga2O3(ZnO)9 have been determined by means of high resolution X-ray diffraction and atomic resolution STEM-HAADF, EDS and EELS measurements. X-ray analysis showed that the compound crystalizes in the Cmcm orthorhombic symmetry. Atomically resolved HAADF-STEM images unambiguously showed the presence of nano-sized, wedge-shaped twin boundaries, parallel to the b-axis. These nano-scale structural features were chemically investigated, for the first time, revealing the exact distributions of Zn and Ga; it was found that Ga ions occupy sites at the junction of twin boundaries and inversion boundaries. HAADF-EDS analysis showed that the calcination step has a significant impact on crystal structure homogeneity. By use of a sintering aid and optimization of processing parameters the ceramics achieved a low thermal conductivity of 1.5–2.2 W/m.K (for the temperature range 300–900 K), a power factor of 40–90 μW/K.m2, leading to a ZT of 0.06 at 900 K. The work shows a route to exploit nanoscale interface features to reduce the thermal conductivity and thereby enhance the thermoelectric figure of merit in complex thermoelectric materials.


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INTRODUCTION
The application of traditional thermoelectric metallic alloys is restricted by several challenges.
For instance, alloy sublimation at elevated temperatures limits their reliability and operational range. Meanwhile the low abundance, cost and environmental impact of key constituent elements is driving the search towards more environmental friendly alternatives, such as oxides [1][2][3], which can operate over broader and more demanding temperature ranges. Selection criteria for candidate materials include the need for both high electrical conductivity and low thermal conductivity. The typical thermoelectric figure of merit (ZT) of oxide materials is lower than that of their alloy counterparts, but the interesting crystal structures exhibited by nano-periodic oxides, make them promising candidates for thermoelectric applications.
Recently, the Ga 2 O 3 (ZnO) m homologous compounds [4][5][6][7][8][9] have attracted attention as potential thermoelectric materials due to the presence of naturally occurring twinned nanostructures, which readily scatter phonons, thereby reducing the thermal conductivity. The first Ga 2 O 3 (ZnO) m compounds were synthesised by Nakamura et al. [10]. They proposed a "distorted" wurtzite structure for the solid solution range of (Ga 2 O 3 ) x (ZnO) 1-x (0≤x≤0.093) instead of a layered type structure. Subsequently, Kimizuka et al. [11] reported the formation of Ga 2 O 3 (ZnO) m homologous compounds with an orthorhombic Cmcm space group. It was suggested that Ga atoms can only occupy tetrahedral sites in Ga 2 O 3 (ZnO) m [11], and thus why they do not crystallise isostructurally with LuFe 3 (ZnO) m [12]. Later, Li et al. [13]  The exact structures of the Ga 2 O 3 (ZnO) 9 homologous compound and specifically the occupancy of the Zn and Ga lattice sites are not well established [4][5][6][7][8]14]. This is, in part, due to analytical limitations of the radiation techniques, arising from the close proximity of the atomic numbers of Zn and Ga, making the exact determination of the site occupancy of Ga and Zn in the twin boundaries and the accompanying inversion boundaries very difficult. The presence of Gainduced, non-periodic twin boundaries and inversion boundaries on the ሼ011 ത 3ሽ planes of ZnO has been reported [9,15], showing segregation of Ga in the twin and inversion boundaries.
The twinned crystal structure of the Ga 2 O 3 (ZnO) m compounds tends to encourage anisotropic, plate-like grains which are difficult to densify in ceramic form. Michiue et al. [6] synthesised polycrystalline Ga 2 O 3 (ZnO) 9 at 1723 K and achieved a density of only 57% theoretical. By the use of Cold Isostatic Pressing (CIP) the density was increased to 73%, which is still modest by the standards of most functional ceramics. However, the electrical conductivity of the low density sample was as high as 13 S/cm, which was comparable with that exhibited by the more expensive indium analogue, In 2 O 3 (ZnO) 9 [16]. In view of the encouraging electrical conductivity reported for the very low density Ga 2 O 3 (ZnO) 9 ceramics [6], and the fact that the layered structure materials are expected to have low thermal conductivity [17], the Ga 2 O 3 (ZnO) 9 ceramics should exhibit enhanced and potentially useful thermoelectric properties if the problem of very low density can be addressed.
In this study, we synthesised and investigated the crystal structure and thermoelectric properties of ceramic Ga 2 O 3 (ZnO) 9 . We selected this member of the homologous series because of the promising thermoelectric properties [6], although recognising that limited structural data had been reported [5,6]. To enhance density we employed B 2 O 3 as a sintering aid to both reduce the processing temperatures and increase sample quality [18].
In view of the uncertainties concerning structural details of Ga 2 O 3 (ZnO) 9 and the fact that nano-scale features in the microstructure have a significant impact on thermoelectric properties [6,9,19], we employed X-ray diffraction and electron microscopy techniques. The exact crystal structure of Ga 2 O 3 (ZnO) 9 was determined by combined high resolution X-ray diffraction and atomic resolution analytical Scanning Transmission Electron Microscopy (STEM) techniques; namely High and Medium Angle Annular Dark Field imaging (HAADF and MAADF, respectively), Energy Dispersive X-ray spectroscopy (STEM-EDS) and Electron Energy Loss spectroscopy (STEM-EELS). The atomically resolved HAADF-and MAADF-STEM images unambiguously showed the presence of nano-sized features; these structural features were chemically investigated, for the first time, revealing the exact distribution Zn and Ga in Ga 2 O 3 (ZnO) 9 . pressed in a 20 mm die at ~25 MPa and then sintered in air for 2, 4 and 12 h at 1673 K, under powder bed of the same composition; samples are denoted as 2H, 4H and 12H respectively. One set of samples were sintered at 1673 K for 4 h without being calcined; these are denoted as NC.

MATERIALS AND METHODS
The microstructures of the polished surfaces of the samples were analysed using Philips® XL30 (FEG)-SEM HKL ® microscope equipped with an energy-dispersive X-ray (EDX) detector. Initial X-ray diffraction studies and phase identification of the calcined powders were carried out using a Philip PANalytical X'Pert Pro ® diffractometer with Cu Kα radiation, for 2θ ranging from 10° to 100° in steps of 0.017. For Synchrotron Radiation X-ray Powder Diffraction (SR-XPD) study, the sintered pellets were ground and mounted in a 0.5 mm borosilicate glass capillary, which was irradiated with the I11 beamline (λ = 0.825625(10) Å and E=15 keV) at the Diamond Light Source over the 0-100° 2θ range. Rietveld full-profile refinement [20] was undertaken using Topas 5.0 [21]. here the collection semi-angle (spectrometer acceptance angle) was 36 mrad. EELS spectrum images (EELS SI) were acquired by rastering serially across a defined area of the specimen, recording an EEL spectrum at each position. EELS SI data for chemical mapping were de-noised by Principal Component Analysis using the MSA Cime -EPFL plugin [22] for Digital Micrograph. EELS chemical maps, namely Zn L 2,3 were subsequently produced by integrating pixel-by-pixel the intensity edges) over a fixed energy window of 40 eV above the edge onset, after subtraction of the decaying background using a standard power law fitting function.
Atomic-resolution Energy-dispersive X-ray spectroscopy (EDS) was performed in an FEI Themis Electron Microscope operated in STEM mode at 200 kV. EDS acquisition was carried out using a Super-X detector system (ChemiSTEM technology). EDS spectrum images were acquired by continuously rastering serially across a defined area of the specimen, recording cumulative EDS spectra at each position. EDS chemical maps were produced by integrating the intensity of the Zn K α and Ga K α absorption peaks, respectively.
The Electrical Conductivity of the samples was measured using the four-probe method, and their Seebeck coefficient was measured using the differential method. Both properties were measured simultaneously from room temperature to 873 ‫ܭ‬ in an ULVAC ® ZEM-3 ® using 2x2x12mm samples. The thermal conductivity (ߢ) was determined from the thermal diffusivity (ߙ), heat capacity ‫ܥ(‬ ) and density (ߩ), using the relationship: The thermal diffusivity of the samples was measured using the Laser Flash Technique (LFT) in an Argon atmosphere at atmospheric pressure using the NETZCH ® LFA 427 ® . The heat capacity was measured by the Differential Scanning Calorimeter Netzsch ® STA 449 C ® in a reducing atmosphere. Density was determined by the Archimedes method.

3.1.Optimization of the Microstructure
Following trial experiments, a calcination temperature of 1473 K was adopted. It enabled development of a significant fraction of the target phase Ga 2 O 3 (ZnO) 9 (denoted as Z 9 GO), without excessive particle growth, although both ZnO and ZnGa 2 O 4 , were present in the powder ( Figure 1a). A range of sintering temperatures were explored. At and below 1623 K, the products were of low density (less than 90% theoretical) and still contained the ZnGa 2 O 4 secondary phase.
Temperatures above 1673 K led to microcracks and unnecessary volatilisation of ZnO. Samples sintered at 1673 K for 2 to 12 hours (denoted as 2H to 12H etc) were single-phase ( Figure 1b), crack-free, high density and typically 90% theoretical, independent of the sintering time.

3.2.Atomic scale characterization
As mentioned earlier, the refinement the crystal structure, and explicitly the relative occupancy of the lattice sites in Ga and Zn, is particularly challenging solely from XRD data. In order to better inform the structure refinement, atomic scale structural and chemical information is needed. For this we turn to local probe techniques and more specifically electron microscopy.
High precision STEM imaging and analysis as well as atomically resolved chemical mapping were performed in order to obtain the relative occupancy of atomic columns in Zn and Ga.  Figure S1 in the in the supplementary information provided). The well-ordered nano-TB are marked with parallel white lines (Figure 3b). The ݉ + 1 = 10 atomic columns in between the wedge shaped nano-TB boundaries are observed, as reported in previous HRTEM studies [13].
The width of the nano-twins is uniform throughout the region screened in Figure 3, corresponding to ݉ + 1 = 10 atomic columns. The stacking sequence in the modular structure of the Ga 2 O 3 (ZnO) m compounds must be described considering both, the twin and inversion boundaries as structure building operators [4,14,15][9]. Recently Guilmeau et al. [9] showed that in HAADF images of heavily twinned ZnO doped with 4mole% Ga, the twin widths were generally large, about 100 nm, and the inversion boundaries appeared as dark bands mid-way between the twin boundaries. However, in the present samples there is no variation in the contrast of the HAADF image of sample 4H (Figure 3a,b). This is possibly because of the smaller width of twin in this sample.
In contrast to the 4H-Z 9 GO sample, the HAADF-MAADF-STEM images of the corresponding NC-Z 9 GO sample (prepared without calcination processing stage, Figure 3c  This finding is in good agreement with the predictions of Barf et al. [15], based on their lowresolution EELS study, and the Guilmeau et al. [9] HAADF-STEM-EDS study of twin boundaries of Ga doped ZnO. It should be noted that in the Guilmeau et al study [9], the Ga EDS signal was not clearly resolved. However, based on the Zn deficiency in the EDS map at the TBs it was concluded [9] that the TBs should be rich in Ga. The experimental observations by Barf et al. [15] and Guilmeau et al. [9] were supported by the theoretical calculations [14] for a low end member of the homologous series (Z 6 GO); it was predicted that twin boundaries on the ሼ011 ത 3ሽ

3.3.XRD refinement
For the structural refinement, the crystal structure parameters given in the ሺ3 + 1) dimensions using the superspace formalism presented by Michiue et al. [5] (and converted to three dimensional format by the same group [6]) was used as a starting point to further improve the structural model. In the prosed model [6], Zn has been considered as the main element for all the lattice sites throughout of the entire crystal structure. This is the same for the distribution of Ga but with much lower content compared to the Zn to maintain the stoichiometry. However, our

HAADF-STEM-EDS data showed very different site occupancies specifically for both Ga and
Zn. Therefore, the elemental distribution data from both HAADF-STEM imaging and atomic resolution EDS mapping was used for site occupancies of Zn and Ga in the input structural file for Rietveld refinement of the synchrotron X-ray diffraction data.
The modified structural parameters (coordinates and site occupancies for Ga) based on electron microscopy observations from the sample 4H-Z 9 GO were used to perform a Rietveld refinement on the SR-XPD data, using the suggested Cmcm space group [6]. Cell dimensions, lattice parameters, peak shape, site occupancies, thermal displacement parameters and background were refined; the final lattice parameters obtained through the Rietveld refinement, are shown in Table 1, along with the goodness of fit (GOF) and the R indexes (R wp and R p ). The refined coordinates for Zn, Ga and O and their site occupancies are listed in Table S1. All the reflections are fully indexed with the optimized crystal structure obtained. The refined lattice parameters were not significantly affected by the sintering time; a slight increase in the unit cell volume is observed for the 4H sample due to slightly higher values for unit cell dimensions, a and b. The result of the Rietveld refinement of the full spectrum for 4H -Z 9 GO sample is shown in Figure 5.

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The resulting crystal structure from the Rietveld refinement of sample 4H-Z 9 GO is shown in

3.4.Thermoelectric Properties
The thermoelectric properties of the Z 9 GO compounds are presented in Figure 7. All the samples show n-type behavior, with high Seebeck coefficients that increase with increasing temperature (Figure 7a). The Seebeck coefficients for sample 4H are in the range of -210 and -300 µV/K, and across all samples they are as high as -340 µV/K. In comparison with other homologous compounds, these Seebeck coefficients are at least comparable with or higher (at high temperatures) than most other materials, including the much more expensive indium analogue In 2 O 3 (ZnO) 9 [16,[23][24][25].
All the samples show semiconductor behaviour from room temperature up to 600 K, then metal-like behaviour at higher temperatures ( Figure 7b). However, the total variation in electrical conductivity across the full temperature range is modest (~10%). This consistency in electrical conductivity has been noted previously for ZnO ceramics heavily doped with Ga, and was attributed to tunnelling effects induced by superlattice interfaces which limit the electrical conductivity of Ga-ZnO materials [26]. Among the samples investigated, the sample sintered for M A N U S C R I P T

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19 samples in this study with 90% theoretical density are in the same range as those reported by Michiue et al [6] which had much lower densities (70% theoretical). Very different processing conditions were used in the two studies; higher sintering temperatures and longer times by Michiue et al [6] along with an 'open' sintering atmosphere. The use of B 2 O 3 in the present study was critical for achieving high densities, but its ultimate presence in the grain boundaries may have had a deleterious effect on electrical conductivity.
All the samples showed very low thermal conductivity of 2.3 to 1.5 W/K.m (Figure 7c). These values are the lowest reported for homologous compounds based on ZnO heavily doped with Ga 9 and Indium analogues [16,23]. Commonly, all the samples show limited variation in thermal conductivity with temperature (Figure 7c), this being more pronounced for 4H-Z 9 GO. The contribution of lattice thermal conductivity (ߢ ) to total thermal conductivity was calculated by assuming a Wiedemann-Franz relationship and a constant Lorentz number, ( ‫ܮ‬ = ߨ ଶ ݇ ଶ /3݁ ଶ = 2.44 × 10 ି଼ ܹΩ‫ܭ‬ ିଶ ). Data for the two components are presented in Figure S3. It is clear that lattice thermal conductivity dominates, being two orders of magnitude larger than the electronic component. This suggests that the total thermal conductivity is mainly controlled by the complex crystal structure exhibited by these homologous compounds and the low thermal conductivity is intimately linked to the range of nano-scale features acting as phonon scattering centers. In particular we propose that the following factors control the thermal conductivity response of The collected data in Figure 8 shows that increasing the level of Ga significantly increases the Seebeck coefficients but dramatically reduces electrical conductivity and thermal conductivity.
The net reduction in electrical conductivity with increasing Ga content is ascribed to a reduction in carrier concentration and mobility [8,9]  Guilmeau et al. [9]. Intrinsically, these homologous series compounds are not yet suitable in their own right as viable thermoelectric materials, but understanding and exploiting the nanostructured planar defects in other complex-structured materials could be very valuable.
To summarize, we have confirmed that boron oxide is effective in aiding the synthesis of dense, high quality samples of Ga 2 O 3 (ZnO) 9 as the first essential requirement for further improvement of the properties through control of the processing parameters. Following optimization of the processing parameters, the overall figure of merit sample was doubled by including calcination step to homogenize the width of the nano-twinned region, as confirmed by atomic resolution imaging.

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A C C E P T E D ACCEPTED MANUSCRIPT 24 We have shown, for the first time, the existence of the inversion domain boundaries in Z 9 GO.
Moreover, we have determined the chemistry and cation-oxygen environment for this material.
Our data shows that the crystal structure of Z 9

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Highlights • High quality ceramic Ga 2 O 3 (ZnO) 9 has been synthesised • Very low thermal conductivity for an oxide of 1.5 to 2.2 W/m.K has been achieved • HAADF-STEM showed the presence of nano-sized, wedge-shaped twin boundaries • The nano-scale features, chemically investigated for the first time, revealed the Zn and Ga distribution • Ga ions occupy the sites at the interfaces of twin boundaries and inversion boundaries