Enhanced current transport at grain boundaries in high-T c superconductors R. F. Klie 1 , J. P. Buban 2 , M. Varela 3 , A. Franceschetti 3,4 , C. Jooss 5 , Y. Zhu 1 , N. D. Browning 6 , S. T. Pantelides 3,4 & S. J. Pennycook 3,4 Large-scale applications of high-transition-temperature (high-T c ) superconductors, such as their use in superconducting cables, are impeded by the fact that polycrystalline materials (the only practical option) support significantly lower current densities than single crystals 1–6 . The superconducting critical current den- sity ( J c ) across a grain boundary drops exponentially if the misorientation angle exceeds 28–78. Grain texturing reduces the average misorientation angle, but problems persist 7,8 . Adding impurities (such as Ca in YBa 2 Cu 3 O 72d ; YBCO) leads to increased J c (refs 9, 10), which is generally attributed to excess holes introduced by Ca 21 substituting for Y 31 (ref. 11). However, a comprehensive physical model for the role of grain boundaries and Ca doping has remained elusive. Here we report calculations, imaging and spectroscopy at the atomic scale that demonstrate that in poly-crystalline YBCO, highly strained grain-boundary regions contain excess O vacancies, which reduce the local hole concentration. The Ca impurities indeed substitute for Y, but in grain-boundary regions under compression and tension they also replace Ba and Cu, relieving strain and suppressing O-vacancy formation. Our results demonstrate that the ionic radii are more important than their electronic valences for enhancing J c . The enhancement of grain-boundary J c in poly-crystalline YBCO has now been widely reported, induced by Ca doping of both weak-linked high-angle 9,10 , and strongly-coupled low-angle, grain boundaries 12,13 . However, Ca doping has been shown to reduce T c . The ideal dopant, which has yet to be found, would improve the grain-boundary J c , but not adversely affect other superconducting properties, such as the T c of the grains. It is usually assumed that the doping mechanism is electronic in nature, resulting in reduction of the intrinsic grain-boundary charge 9,10,14 , modification of the bulk screening length 9,10 or reduction of both charge and strain fields 13,15 . However, a comprehensive atomic-scale model has not yet been found that can explain the impact of grain boundaries and Ca impurities on the critical current density. Single-crystal studies show that Ca 2þ substitutes for Y 3þ where it acts as a hole dopant 11 . Song et al. (personal communication, and ref. 16) have found that Ca segregates in grain boundaries, and it was generally believed that Ca replaces Y there as well. However, strains of more than 10% can occur at the dislocation cores that comprise grain boundaries, with severe consequences. For example, SrTiO 3 grain boundaries are intrinsically non-stoichiometric owing to such high strains 17,18 . Similar effects are expected in YBCO. The formation energies required for substituting an isolated Ca dopant on different lattice sites in YBCO (in an oxidizing environ- ment) as a function of biaxial strain in the a–b plane were calculated from first principles, and are shown in Fig. 1a. In unstrained YBCO, Ca substitutes for Y as expected 19 . In regions under compressive strain, however, substitution for Ba is increasingly possible and becomes energetically favourable at strains greater than ,6%. Similarly, in regions under tensile strain, substitution for Cu becomes favourable. In contrast, strain has only a small effect on substitution for Y. Clearly, the relative ionic sizes drive the defect formation LETTERS Figure 1 | First-principles calculations of Ca and O vacancy formation energy in bulk YBCO. a, Energy required to substitute Ca on different lattice sites in YBCO as a function of biaxial strain. It can be energetically favourable for Ca to replace Y, Ba or Cu, depending on the local strain. b, Formation energy of O vacancies in bulk YBCO (left panel), in undoped YBCO under 5% tensile strain in the a–b plane (central panel), and in Ca-doped YBCO under 5% tensile strain (right panel), simulating the expanded regions at grain boundaries. For doped grain boundaries where Ca substitutes Cu, the O vacancy formation energy increases significantly. 1 Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA. 2 Institute of Engineering Innovation, The University of Tokyo, Tokyo, 113-8656, Japan. 3 Condensed Matter Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA. 4 Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA. 5 Institut fu ¨r Materialphysik, University of Go ¨ttingen, 37073 Go ¨ttingen, Germany. 6 Department of Chemical Engineering and Materials Science, University of California-Davis, Davis, California 95616, USA. Vol 435|26 May 2005|doi:10.1038/nature03644 475 © 2005 Nature Publishing Group