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angle anisotropy approximation assumed atoms average axis c-sites calculated cations coherent concentration condition considerations constant contribution corresponding crystal curve defect density dependence determined diffusion direction discussed dislocations displacement effect elastic elastic scattering electron energy equation et al exist experimental experiments factor field flux lines follows force function garnet given gives important increasing Inelastic Scattering interaction interface ions lattice length limit magnetic materials measured Merwe metal method misfit mode neutron normal obtained parameter phase phonon Phys plane position potential present properties range rare earth reasonable reference region relation resolution respectively sample scattering cross section shown shows single solid solution space strain stress structure substrate superconducting surface Table temperature tetrahedral theory thermal thickness transition unit values vector X-ray