Structure and formation of twins in the orthorhombic YBa₂Cu₃O_7-x

Structure and formation of twins in the orthorhombic phase of YBa₂Cu₃O_7-x samples, exhibiting bulk superconductivity at 90 K, are studied by transmission electron microscopy and modeling. Twinned domains with {110} twin boundaries form with separation λ which is dictated by energetic and geometrical requirements. Both of these requirements are related to Δa=b-a, where b and a are lattice parameters of the orthorhombic phase. Geometrical requirement leads to the estimate that the stable values of λ are integer multiples of d=ab/(√2Δa). In some samples λ's are regular, in others not. Deviation of λ from theoretically expected stable separations is interpreted as due to local variation of oxygen ordering and/or local elastic strain. The twin boundary has a structure different from the bulk orthorhombic phase and electron micrographs suggest that it has a width of 30-50 Å. In bulk samples twinned domains can be present at different stages of the growth process. These substructural variations suggest that samples are at metastable equilibrium and are consistent with samples being in the superconducting glassy state.