Structural Evolution Induced by Interfacial Lattice Mismatch in Self-Organized YBa 2 Cu 3 O 7- Nanocomposite Film

Transcription

1 Structural Evolution Induced by Interfacial Lattice Mismatch in Self-Organized YBa 2 Cu 3 O 7- Nanocomposite Film Tomoya Horide, Fumitake Kametani, Satoru Yoshioka, Takanori Kitamura, Kaname Matsumoto SUPPLEMENTARY INFORMATION Figure S1 shows the H and L scan results for the BZO (103) and YBCO (108) peaks in the YBCO+BZO(4.1) and YBCO+BZO(8.2) films. From the peaks, the lattice parameters in Figure 2D and 2E were obtained. In the YBCO+BZO(8.2) film, the BZO (103) peak was observed at H=-0.92 and L=2.81. H <L/3 indicates that the out-of-plane lattice parameter of BZO in nanorods was smaller than its in-plane lattice parameter. Figure S1. The H and L scan results for the BZO (103) and YBCO (108) peaks in the (a) YBCO+BZO(4.1) and (b) YBCO+BZO(8.2) films. The symbols and lines show the experimental results and smoothed curves, respectively. S1

2 We used the five parameters to compare the XRD results with the FEM results. Strain is calculated in the FEM analysis, whereas the lattice parameters are obtained from XRD results. Strain is defined by (a-a 0 )/a 0, where a and a 0 are the lattice parameters in strained and unstrained states. To compare the XRD and FEM results, the definition of strain should be carefully discussed. In this case, the influence of the strain-induced oxygen-vacancy formation should be considered to estimate the lattice parameters in the unstrained state. The strain in the YBCO+BMO films is given by the following: ε = a(nanorod+vacancy) a(vacancy) a(vacancy) (S1) where a(nanorod+vacancy) denotes the lattice parameter in the presence of both nanorods and the strain-induced oxygen-vacancies, and a(vacancy) is the lattice parameter in the presence of only the oxygen vacancies. In addition, a 0 denotes the lattice parameter without nanorods or oxygen vacancies, namely, the lattice parameter in the pure YBCO film. We obtained the strain dependence of the oxygen vacancy concentration for the YBCO+BMO films from Figure 2E and Figure 4A, whereby the a(vacancy) was estimated from the relationship between the lattice parameter and oxygen content in bulk YBCO. 32 The lattice parameter calculated using the definition of (S1) is shown in Figure S2. On the other hand, when the strain-induced oxygen-vacancy formation does not significantly affect the lattice parameters in the unstrained state, the strain can be simply expressed by the following definition: ε = a(nanorod+vacancy) a 0 a(vacancy) (S2) The lattice parameter calculated using the definition of (S2) is also shown in Figure S2. The lattice parameters obtained under the definition of (S1) and (S2) are almost the same, and therefore, we used the definition (S2) to obtain the lattice parameters in Figure 2D and 2E. S2

3 Figure S2. The lattice parameters, c of YBCO calculated using the FEM results in the definition of (S1) and (S2). The FEM calculation in the YBCO+BZO was performed for a nanorod diameter of 5 nm. S3

4 Figure S3 shows the BSO volume fraction dependence of the lattice parameters in the YBCO+BSO films. Similar to the YBCO+BZO, the XRD results are in good agreement with the FEM results with f elastic =0.027, r=1.9, a BSO =4.24 Å, a YBCO,0 =3.865 Å, and c YBCO,0 =11.68 Å. The lattice parameter of bulk BSO is 4.12 Å, and substitution of Y for M in BMO increased a BSO from the value in bulk BMO. The reports on Ba(Sn,Y)O 3 powders indicated that a BSO =4.24 Å was obtained by the substitution of Y in 40-50% Sn sites. 50 Figure S3. Lattice parameters of (a) BSO and (b) YBCO as a function of BSO content in the YBCO+BSO films. Points and lines show XRD and FEM results, respectively. The FEM calculation was performed for a nanorod diameter of 5 nm and 10 nm. S4

5 Figure S4A shows the dislocation energy, elastic strain energy, and total strain energy calculated using Equations (1) and (2) for the nanocomposite film. The smallest total strain energy is obtained at the f elastic range between 0.02 and 0.06, and the energy minimum is at f elastic = The experimentally obtained f elastic (=0.027) is slightly different from f elastic =0.042 due to the estimation of cut-off length in E dis. To compare the strain accommodation in the nanocomposite and epitaxial films, the strain energy in the BZO/YBCO epitaxial films is also calculated, where the thickness of the BZO film is set to 10 nm (the nanorod diameter). The elastic strain energy is given by the following: E elastic = E film 1 ν ε xx 2 t (S3) On the other hand, the dislocation energy is defined as follows: E dis = μ b 2 4π(1 ν) R Ln ( ) 2f dislocation b b (S4) where f dislocation =f 0 f elastic, the cut-off distance, R=t, and dislocation spacing is b /f dislocation. The energy minimum is observed at f elastic = This shows that the energy minimum is obtained at a much larger f elastic in the nanocomposite films. Figure S4. The elastic strain energy, dislocation energy, and total strain energy as a function of f elastic in (a) the nanocomposite film with a nanorod diameter of 10 nm and (b) the conventional epitaxial film with a thickness of 10 nm. S5

6 Figure S5 shows the dependence of pdos (Cu3d, O2p) on the interface position in the two types of YBCO/BZO interface models. The interfaces in Figure S5A and S5D were parallel to the a-axis and b-axis of YBCO, respectively, and the results in Figure 3D correspond to Figure S5B. Regardless of the interface models (interface directions), the pdos of Cu3d and O2p was significantly varied in the first and second layers near the interface, and this electronic effect is the origin of the atomic relaxation, i.e., the interface distortion. Figure S5. The dependence of pdos (Cu3d, O2p) on the interface position in the calculation model where the interface was parallel to the a-axis (b, c) and b-axis (e, f). (a) and (d) show the interface models, and (a) corresponds to the model of Figure 3(d). The YBCO reference denotes the 10-layers-YBCO model without the interface. S6

7 Figure S6 shows the XANES spectrum in the wide energy range. The XANES spectrum was normalized by the converged intensity at high energy. Regardless of samples, the normalized intensity was 1 in Figure S6, showing that the intensity normalization was appropriately performed and that the difference at the peak intensity resulted from the variation in electronic states, not from an inconsistent data analysis. Figure S6. The XANES spectrum in the wide energy range. Regardless of samples, the normalized intensity converged at 1. S7

8 Figure S7 shows the T c -c relation for the cooling times of 30 min and 60 min. Almost the same behavior was observed for both 30 min. and 60 min, which indicates that the cooling time of 30 min was long enough that the YBCO films were fully oxidized during the cooling. In addition, Figure S7 shows the T c behavior for the strain-induced oxygen-vacancy formation calculated at different temperatures. The oxygen vacancy concentration obtained from the relationship of ~exp(-e OV /kt) depends on temperature (T). However, Figure S7 indicates that the influence of temperature is extremely small, and the results are unchanged at T(= ºC). Figure S7. The T c -c relation in the nanocomposite YBCO films for the cooling times of 30 min. and 60 min. The T c behavior, which was obtained from the relationship of ~exp(-e OV /kt) for T=200, 400, and 700 ºC, is also shown. S8

9 Figure S8 summarizes the atomic-scale structure of the YBCO+BMO nanocomposite film. The lattice mismatch between YBCO and BMO is accommodated by the elastic strain, and relaxed by the misfit dislocations, where the elastic and dislocation components are determined by the minimum strain energy. A large lattice mismatch is elastically accommodated in the BMO nanorods due to the volume fraction effect. The elastic strain in YBCO increases the oxygen vacancy concentration by decreasing the oxygen vacancy formation energy. Another feature of the structure is the interface distortion, which has a thickness that is limited to a few unit-cells. The interface distortion is determined by the interface atomic bonding and the electron screening in YBCO. YBCO matrix BMO nanorod inside Strain-induced oxygen-vacancy Very large elastic strain Large lattice mismatch Interface distorted region Misfit dislocation Electronical effect from BMO Elastic strain Figure S8. Summary of the structure of the YBCO+BMO nanocomposite film. Reference 50. Wang, Y.; Chesnaud, A.; Bevillon, E.; Dezanneau, G.; Properties of Y-Doped BaSnO 3 Proton Conductors. Solid State Ionics 2012, 214, S9