An epitaxial growth mechanism of oxide superconductor films has been investigated by using computer graphics for the combination of orthorhombic Ba
2YCu
3O
7-x with substrate crystals of SrTiO
3, MgO, and ZrO
2. The (001) plane of Ba
2YCu
3O
7-x has been shown to fit well the (100) plane of these substrate crystals. A crystallographic fit has also been demonstrated between the (110) plane of Ba
2YCu
3O
7-x and the (110) plane of SrTiO
3. Detailed investigation of atomic arrangements has indicated some differences in the ionic interaction at the superconductor-substrate interface among SrTiO
3, MgO, and ZrO
2 substrates. For the combination of the (001) plane of Ba
2YCu
3O
7-x and the (100) plane of SrTiO
3, various layers of Ba
2YCu
3O
7-x and SrTiO
3 are possible to provide arrangements of ions which stabilize the electrostatic interaction at the interface. Although the Ba-O layer of Ba
2YCu
3O
7-x does not provide such a stable interaction with the MgO (100) plane, the Cu-O layer of Ba
2YCu
3O
7-x can favorably interact with the MgO (100) plane. As for ZrO
2 (100) plane, ionic arrangements at the oxide layer is favorable only for the interaction with Y
3+ layer of Ba
2YCu
3O
7-x while the Zr-O layer of ZrO
2 can interact with both Ba-O layer and Cu-O layer of Ba
2YCu
3O
7-x.
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