Nonlocal self-organization of long stacking faults from highly strained nanocomposite film of complex oxide

Elastic strain and defects are important key words for controlling structure and properties in films. While epitaxial strain and misfit dislocations have been discussed in conventional films, the evolution of strain and defect can be significantly varied by nanocomposite strain and complicated defects in oxides. In the present study, long stacking faults with a spacing of 5–30 nm and a length of $>500\mathrm{nm}$ were self-organized by ex situ annealing highly strained nanocomposite films of $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{7–\delta }\left(\mathrm{YBCO}\right)+\mathrm{BaM}{\mathrm{O}}_3\left(M=\mathrm{Hf},\mathrm{Sn}\right)$. It is surprising that the nonlocal nature of stacking faults, namely, the structural correlation over $>500\mathrm{nm}$, was observed in spite of the local configuration of the nanocomposite interface. This kind of structural variation was not observed in the pure $\mathrm{YBCO}$ film without nanorods, even when the same annealing was performed. A strain energy analysis showed that the stacking fault formation led to the strain energy minimum by reducing the nanocomposite strain. The layered structure of YBCO stacking faults and the large nanocomposite strain realized the present nonlocal self-organization, which is not observed in the conventional systems with epitaxial strain and misfit dislocations.

Figure 1

Bright-field TEM images of (a) the no-anneal $\mathrm{YBCO}+\mathrm{BSO}$, (b) the annealed $\mathrm{YBCO}+\mathrm{BSO}$, (c) the no-anneal $\mathrm{YBCO}+\mathrm{BHO}$, and (d) the annealed $\mathrm{YBCO}+\mathrm{BHO}$ films. The post–ex situ annealing formed the stacking faults in (b,d).

Figure 2

Bright-field TEM image of the annealed pure YBCO film.

Figure 3

HAADF-STEM image of the annealed $\mathrm{YBCO}+\mathrm{BHO}\left(4.7\right)$ film. Enlarged views of the CuO-deficient layer (top right) and the ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$-type stacking faults (bottom right) are also shown. (b) The calculation model for Cu-deficient stacking fault [supercell size $\left(A\right)=4$; concentration of Cu deficiencies $\left(x\right)=2/8$; stacking fault $\mathrm{spacing}=1$ unit cell YBCO]. (c) Stacking fault energy [${\varepsilon }_{\mathrm{SF}}$ for reactions (1a) and (2a)] as a function of the concentration of Cu deficiency in stacking fault.

Figure 4

(a) $2\theta \text{−}\omega$ scan results in the no-anneal and annealed $\mathrm{YBCO}+\mathrm{BHO}\left(4.7\right)$ films. RSM results of the (b) no-anneal and (c) annealed $\mathrm{YBCO}+\mathrm{BHO}\left(4.7\right)$ films. The reciprocal lattice unit (r.l.u) is defined with respect to the lattice parameter of STO ($a_{\mathrm{STO}}=3.905\AA$). BHO-content dependence of lattice parameters [(d) BHO, (e) YBCO] in the no-anneal and annealed $\mathrm{YBCO}+\mathrm{BHO}$ films. Solid and open symbols denote the lattice parameters in the no-anneal and annealed film, respectively. The lines show the lattice parameters determined by elastic strain, which was calculated using the finite element method elastic calculation in [10, 20]. $r=1.9$ was obtained from the analysis.

Figure 5

(a) HAADF-STEM and GPA for (b) ${\varepsilon }_{xx}$ and (c) ${\varepsilon }_{zz}$ in the annealed $\mathrm{YBCO}+\mathrm{BHO}\left(4.7\right)$ film. Dashed lines show the YBCO/BHO interface. Three stacking faults are observed as indicated by arrows in (a).

Figure 6

(a) Schematic illustration of the important structural factors to determine the present film structure. Energy of dislocations, stacking faults, and elastic strain as a function of the elastic component in mismatch, $f_{\mathrm{elastic}}$ for (b) the $\mathrm{YBCO}+\mathrm{BSO}$ and (c) the $\mathrm{YBCO}+\mathrm{BHO}$.