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