Invenstigation of isotope effect on phase transition temperature of perovskite type some crystals

ABSTRACTPhD. THESISINVENSTIGATION OF ISOTOPE EFFECT ON PHASETRANSITION TEMPERATURE OF PEROVSKITE TYPESOME CRYSTALSBahattin ERDİNÇDEPARTMENT OF PHYSICS INSTITUTE OF NATURAL ANDAPPLIED SCIENCES UNIVERSITY OF CUKUROVASupervisor: Assist. Prof. Dr. Faruk KARADAĞYear: 2006, Sayfa: 143Jury: Assist. Prof. Dr. Faruk KARADAĞProf. Dr. Emirullah MEHMETOVProf. Dr. Birgül YAZICIProf. Dr. Yüksel UFUKTEPEAsssoc. Prof. Dr. Oğuz GÜLSERENIn this thesis, the isotope effects on phase transition temperature, T0 , andgeneralized force constant, k f , in perovskite-type ferroelectrics is discussedtheoretically. Using the single-ion model and the quantum-mechanical electron-phonon interaction model with a higher order vertex term in Matsubara Greenfunction formalism at finite temperature; the theory of the reduced force constant ofthe soft optic phonon, both reduced mass dependency of the soft optic phonon andtemperature dependency of the generalized force constant corresponding to thetransverse optical phonon related to the ferroelectric phase transition, isotope effectson the properties of perovskite-type ferroelectric crystals and how their phasetransition temperature depends on atomic mass are obtained.The influence of quantum fluctuations on the Curie temperature Tc isconsidered nonempirically in the context of the single-ion model of Devonshire-Slater-Barrett for BaTiO3, KNbO3 where Ti, and Nb atoms are considered asferroelectrically active. The coefficients of Landau-Ginsburg free energy expansionare calculated using total energy ab- initio Hartree-Fock MOLCAO-SCF calculationsfor large many-atom clusters. Quantum shift, ∆TCquant , of Curie temperature for theseferroelectrics and of isotopic shift, ∆TCiso , for BaTiO3 at substitution of 46,50Ti for 48Tiare given.Key Words: Perovskite, Isotope effect, Green functions, Single-ion model.II