Domain Structures and Pinning in Oxide Superconductors
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DOMAIN STRUCTURES AND PINNING IN OXIDE SUPERCONDUCTORS ALEXANDER L. ROYTBURD University of Maryland, NIST, Gaithersburg, MD
College Park, MD 20742 20899
ABSTRACT The domain structure of oxide superconductors arises as a result of twinning associated with the tetragonal-orthorhombic transition inside a restricted volume (a grain in a polycrystal, an epitaxial layer, or a part of an initial single crystal). A thermodynamic theory of the size and arrangement of the domains has been developed. There are two types of interfaces in equilibrium domain structures: coherent twin boundaries and boundaries between polytwin layers with microstresses. Elastic vortex-interface interactions have been estimated. INTRODUCTION In recent years there has been considerable interest in the twin structures of oxide HTSC and its effect on Tc and pinning of vortices in these materials (e.g., [1,2]). In the frame of a general concept of elastic domains [3-5] we will consider the equilibrium twin structures formed inside the restricted, partially or completely, volume of a crystal. It will be shown that the twin structures can be hierarchical with interal microstresses at interfaces. An estimation of energy of the interaction between a vortex and interface microstresses will be given. Structural Domains
(Twins).
Self-Strains.
Elastic Domains
If, in the course of a phase transition, a newly formed phase has a symmetry lower than an initial phase, then differently oriented domains of a new phase or structural domain arise. They are related to each other as twins. Any phase transition in crystals is accompanied by a self-strain [4], and different structural domains correspond to different self-strain. In a tetragonal (T) - orthorhombic (0) transition, two domains are formed (Fig. l)with the self strains:
- o60OO eQ0eoo 00ooo/ 61 where
o-20oI c)
6 =-&eC,zcO. e,,=(a-a,)/a7. e6 =(6-cxr)a,, 6 c
a,b,c
(C -C7)/C,
are the lattice parameters of the O-phase; ar, C.7 of the
T-phase. We neglected the concentration change at the transformation, so E -1, and e. _ 112, where 11 is the order parameter in the tetragonal phase, et, is the twin shear which transforms one Mat. Res. Soc. Symp. Proc. Vol. 169. @1990 Materials Research Society
802
domain into another. If the domains contact along the planes of the twinning shear (110). or (lM0). there are no internal Therefore there are no stresses between them (Fig. 1c, d). stresses in an unrestricted pack of plane-parallel domains, or a polytwin, as well, in some set of polytwins (Fig. 2,d, f, e). However, if the orthorhombic phase forms in a restricted region, internal stresses arise at the boundary of the region with the surrounding material. Then, structural domains can act as elastic domains reducing the internal stresses and their elastic energy [3-5].
ft
1 gb c--2 I.'
III
I
I Fig. 1: The structure domain and self-strains at the tetragonal-orthorhombic transformation.
d
I
.e
Fig. 2: The transformation in an epitaxial layer.
2D-restriction: Domain Structures in an Epitaxial Layer If a
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