| Ferroelectric materials have great application prospects in ultrasonic sensors,stress sensors and ferroelectric storage devices due to their excellent electrical and electromechanical properties.In order to improve the functional properties of ferroelectric materials,various defects have been introduced into ferroelectric materials.By introducing defect ions which are different from the valence state of original lattice ion,the properties of the ferroelectric material can be greatly changed,which makes the material suitable for different application scenarios.The doping that introduces impurities lower than the valence state of the original lattice ion is called acceptor doping,which is also called hard doping.Hard doped ferroelectric materials generally exhibit larger coercive fields,mechanical quality factors,better temperature stability,and lower dielectric loss than undoped ferroelectric materials.These excellent properties make hard doped ferroelectric materials suitable for high energy electromechanical devices.However,the current theoretical researches on the mechanism of acceptor doping are not mature enough.Researches on how to use the doping to modulate the properties of ferroelectric materials are not profound enough.Therefore,it is necessary to establish a set of phenomenological theory suitable for acceptor-doped ferroelectric materials and to study how the doping ions affect the piezoelectric and dielectric properties of ferroelectric materials.In this paper,the Landau-Devonshire theory and phase field method were used to establish a model for acceptor doped ferroelectric materials,and the effects of defect dipoles on the domain structures and macroscopic physical properties of ferroelectric materials were studied.Our works provides a theoretical basis for the characteristics of acceptor-doped ferroelectric materials.First,we created a phenomenological model including defect dipoles with fixed positions and orientations.The model includes Landau-Devonshire free energy,long-range electrostatic energy and elastic energy,gradient energy,and defect dipole energy.We discretized the electric field generated by defect dipoles and the time-dependent Ginzburg-Landau equation.Using the Landau coefficient of tetragonal phase zirconate titanate and the elastic constant,the parameters were normalized.The steady-state numerical solution of the Landau equation was solved under periodic boundary conditions.The domain structure under random and uniform oriented defect dipoles were studied to provide a theoretical basis for the influence of defect dipoles on the domain structure and physical properties of ferroelectric materials.We have quantitatively demonstrated the “volume effect” model of acceptor doping.According to the “symmetry-conforming short-range ordering” principle of defect dipoles,the arrangement of the defect dipoles are consistent with the direction of spontaneous polarizations.This arrangement described a stable domain structure obtained after poling and sufficient time aging.The hysteresis loop and the butterfly curve of this stable domain structure at different defect dipole concentrations were calculated.This built-in bias field is defined as the internal bias field.The variation of the internal bias field with the concentration of the defect dipole was calculated.The theoretical calculation results were found to be very consistent with the experimentally measured PZT(lead zirconate titanate)hysteresis loop.The piezoelectric coefficient and dielectric constant of the ferroelectric material containing the defect dipoles and their variation with the defect dipole concentration were calculated.The memory effect of the acceptor-doped ferroelectric system experiencing a ferroelectric-paraelectric-ferroelectric process was studied.The simulation showed that the ideal ferroelectric without the defect dipole has no memory effect,and the ferroelectric material doped with the defect dipoles can return to the initial state after the heating/cooling cycle.As the defect concentration increases,the recovery is faster.Then we turn the fixed defect dipole in the original model into a rotatable defect dipole.Using the potential function of oxygen vacancies,the defect dipole can be rotated with external conditions,and the state of the defect dipole was solved by kinetic Monte Carlo method.Combining the phase field method used above,a phenomenological model of a ferroelectric system with a rotatable defect dipole was established.This model can couple the evolution of ferroelectric domains with the rotation of defect dipoles.Using such a model,we can obtain the needed domain structure by modulating the poling time of the electric field.Simulations showed that too long or too short poling times were not conducive to obtain smaller domain size,moderate poling time can help to achieve the largest domain size and a larger piezoelectric coefficient.Then we studied on the de-aging process of ferroelectric materials by using the rotatable defect dipole model.By applying an alternating electric field on the aged ferroelectric material,the orientation of the defect dipole became gradually randomized.The hysteresis loop of the acceptor ferroelectric material at different frequencies and temperatures were calculated.The internal bias fields generated by the rotatable defect dipole ware calculated and their relationship with the electric field frequency and temperature was explored.The variation of the percentage of defect dipoles in all directions with the alternating electric field was calculated,and the influence on the hysteresis loop was studied.Microscopic domain structures at low and high frequencies were simulated.At low frequencies,there was enough time for the defect dipoles to keep up with the switching of the electric field and at low frequencies,due to the low mobility of oxygen vacancies,the defect dipoles were almost fixed.This research has guiding significance for the de-aging process of ferroelectric materials in practical applications. |
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