1. Determination of displacements and the strain field of metal sub-lattice
From contrast maxima in TEM images in [1-100], local lattice distortions at the pyramidal IDBs were observed over 3 - 4 atom columns. Lattice displacements and the strain field of metal sub-lattice in two-dimensions were for the first time visualized and measured using ‘DALI’ algorithm.
The quantified displacements were given by (0.55 ± 0.06, 0.16 ± 0.06) Å. Influences to positions of contrast maxima by variations of specimen thickness, defocus and crystal tilt were discussed in detail and might induce an additional error of max. (0.126 ± 0.067) Å horizontally.
The 2D strain was described as symmetric term ε and anti-symmetric term ω. The diagonal element ε11 of the strain ε exhibits a lattice dilatation of max. (4 ± 0.8)% at the pyramidal IDBs horizontally. The off-diagonal elements of the rotation field ω, proves lattice rotations by (1.9 ± 0.3)º with opposite signs at pyramidal IDBs. The strain exhibits a plane of mirror symmetry through the centre of triangular inversion domains IDBs.
2. Atomic structure of inversion domain boundaries by HR-TEM imaging
2.1 Basal IDB
From lattice image contrast and assignment of atom columns, a close-packed In monolayer at the basal IDB is proven with In in InO6 co-ordination. Comparing the exit-plane electron waves with the simulated ones, specimen thickness and tilt were estimated to be: t = (3.4 ± 0.25) nm and τ = (-0.5 ± 0.1°, -1.0 ± 0.1°), respectively. Finally, the atomic structure model of the basal IDB was refined iteratively.
2.2 Pyramidal IDB
The exit-plane wave of the pyramidal IDB in [2-1-10] zone axis was successfully reconstructed. Contrast from the weakly scattering oxygen was observed with a gradual positional transition across pyramidal IDB, directly proving the inversion of polar c axis of ZnO. From the determined atom positions, it proves In in trigonal bi-pyramidal co-ordination. There, we proposed an atomic structure model at the pyramidal IDB.
3. Determination of In contents at the pyramidal IDB
Z-contrast imaging was utilized to determine chemical compositions (Zn and In) at atomic resolution. At the basal IDBs, it confirms a close-packed In mono-layer. At the pyramidal IDBs, it indicates an In distribution over at least 3 atomic columns. Based on the structure models at the pyramidal IDBs, HAADF images of the pyramidal IDB in [1-100] were simulated with different In contents. From these results, a relation between intensity ratios and In contents per column was obtained within a thickness range of t ≤10 nm, which is treated as calibration curve. After comparison with intensity ratios from experimental images, the mean In contents in atom percent was quantified at the pyramidal IDBs. By HAADF image simulations, effects of crystal tilts up to 0.5° to peak positions was neglected. Finally, a three dimensional atomic structure model for the pyramidal IDB was proposed, with a distribution of 10%, 20%, 40%, 20% and 10% of In contents along basal planes, respectively.
Through a detailed structural study of In2O3(ZnO)m compounds by using phase-contrast and Z-contrast imaging at atomic resolution, In3+ atoms are determined with trigonal bi-pyramidal co-ordination and are distributed at the pyramidal IDBs. Hence, the atomic structure of the pyramidal IDBs with precise atoms positions was made possible. The proposed 3D atomic structure of the pyramidal IDB could be treated as the base structure of the materials of type RAO3(MO)m (with m≥7; R = Sc, Y, In Ho, Er, Tm, Yb, Lu; A = In, Ga, Al, Fe; and M = Mg, Mn, Fe, Co, Cu, Zn, Cd). The mechanism of forming inversion domain microstructures needs to be investigated further for better understanding physical properties of this group of materials forming homologous structures.