Grain Growth Simulation of [001] Textured Ybco Films Grown on (001) Substrates with Large Lattice Misfit: Prediction of
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77 Mat. Res. Soc. Symp. Proc. Vol. 403 ©1996 Materials Research Society
using minimization of grain boundary energy as the driving force. The application of the Potts Model in this simulation and the general description of the computer algorithm are explained elsewhere [11-14]. ORIGIN OF COINCIDENCE EPITAXY BETWEEN FILM AND SUBSTRATES For an one-to-one normal epitaxial growth, the lattice mismatch is limited to within 3% between the substrate and the overgrown film. The concept of coincidence epitaxy (CE) is used to describe the film grown on substrate with a large lattice misfit. Here, we allow the rotation of two lattice planes of the film and the substrate such that film crystal orientations corresponding to a small elastic strain and a high density of near lattice coincidence sites are obtained. The upper limit of elastic strain at the interface is set at 3% and the reciprocal of the planar density of coincidence sites aryaco at 29 for MgO substrates and aYBco at 20 for YSZ substrates. The CE model was explained in greater detail and was used for the YBCO on MgO substrate in earlier studies [1,4]. The problem with these earlier studies was the numbers of distinct misorientations predicted by CE [4] were too large to match the experimental observations where only a handful of misorientations were observed. Clearly, extensive grain growth contributed to the difference. Here, we have simulated grain growth for three different YBCO/substrate systems. The first simulation involves [001] textured YBCO films grown on (001) MgO. Since lattice parameters, ayBco = 3.87 A and amgo = 4.22A, the misfit between them for perfect square-on-square alignment is 8.9%. The number of total allowable YBCO grain orientations (n) on MgO is 16. They are 450, ±340, ±310, ±26.50, ±220, ±18.50, ±12.50, ±100, and 00. Therefore, the number of distinct misorientations (m) between two YBCO grains is 64, (m=n2 /4). The misorientation at the boundary is generated by taking the difference of any two CE orientations combination. The next two cases involve 6.27% and 4.54% lattice misfits for lattice parameters aysz = 5.14A, 5.24A and aYBco = 3.869,. The number of allowable grain orientations (n) is eight for both cases, therefore m is 16. The allowable CE orientations for the 6.27% YSZ case are 450, ±40.5', ±18.5', ±12.5°, and 00, while for the 4.54% YSZ case are 450, ±310, ±18.50, ±140, and 00. GENERATION OF GRAIN BOUNDARY ENERGY VS. MISORIENTATION FOR [001] TILT BOUNDARIES In the grain growth simulation, we have ignored the interfacial energy of YBCO with substrates for reason stated earlier. The only driving force is the grain boundary energy which depends solely on the misorientation between the neighboring grains. Here, we have not considered the influence of the boundary inclination on boundary energy. A stable microstructure is established by minimizing the total grain boundary energy of the configuration. The calculation of grain boundary energy of [001] tilt boundaries for YBCO polycrystalline film is categorized into four groups. (a) L
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