Effects of Space Charge, Dopants, and Strain Fields on Surfaces and   Grain Boundaries in YBCO Compounds
  Statistical thermodynamical and kinetically-limited models are applied to study the origin and evolution of space charges and band-bending effects at low angle [001] tilt grain boundaries in YBa$_2$Cu$_3$O$_7$ and the effects of Ca doping upon them. Atomistic simulations, using shell models of interatomic forces, are used to calculate the energetics of various relevant point defects. The intrinsic space charge profiles at ideal surfaces are calculated for two limits of oxygen contents, i.e. YBa$_2$Cu$_3$O$_6$ and YBa$_2$Cu$_3$O$_7$. At one limit, O$_6$, the system is an insulator, while at O$_7$, a metal. This is analogous to the intrinsic and doping cases of semiconductors. The site selections for doping calcium and creating holes are also investigated by calculating the heat of solution. In a continuum treatment, the volume of formation of doping calcium at Y-sites is computed. It is then applied to study the segregation of calcium ions to grain boundaries in the Y-123 compound. The influences of the segregation of calcium ions on space charge profiles are finally studied to provide one guide for understanding the improvement of transport properties by doping calcium at grain boundaries in Y-123 compound. 
H.B. Su and D.O. Welch