The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity is obtained by making a specific coordinate transformation and by using the method of time-dependent invariant.
Piezoresponse Force Spectroscopy(PFS)is a powerful technique widely used for measuring the nanoscale electromechanical coupling of the ferro-/piezo-electric materials.However,it is found that certain nonferroelectric ...Piezoresponse Force Spectroscopy(PFS)is a powerful technique widely used for measuring the nanoscale electromechanical coupling of the ferro-/piezo-electric materials.However,it is found that certain nonferroelectric materials can also generate the“hysteresis-loop-like”responses from the PFS measurements due to many other factors such as electrostatic effects.This work therefore studies the signal of the contact resonance frequency during the PFS measurements.By comparing the results from ferroelectric and non-ferroelectric materials,it is found there are distinct differences between these two types of materials in the variation of the contact resonance frequency during the PFS measurements.A momentary and sharp increase of the contact resonance frequency occurs when the domain is switched by applying the DC bias,which can be regarded as a unique characteristic for the ferroelectric materials.After analyzing the reliability and mechanism of this method,it is proposed that the contact resonance frequency variation at the coercive bias is capable to differentiate the electromechanical responses of the ferroelectric and non-ferroelectric materials during the PFS measurements.展开更多
文摘The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity is obtained by making a specific coordinate transformation and by using the method of time-dependent invariant.
基金the financial support by Ministry of Education,Singapore,through National University of Singapore(NUS)under the Academic Research Fund(ARF)of grant number R-265-000-596-112the post-graduate scholarship provide by NUSthe support for post-doctoral research fellow from ARF of R-265-000-596-112 by Ministry of Education,Singapore.
文摘Piezoresponse Force Spectroscopy(PFS)is a powerful technique widely used for measuring the nanoscale electromechanical coupling of the ferro-/piezo-electric materials.However,it is found that certain nonferroelectric materials can also generate the“hysteresis-loop-like”responses from the PFS measurements due to many other factors such as electrostatic effects.This work therefore studies the signal of the contact resonance frequency during the PFS measurements.By comparing the results from ferroelectric and non-ferroelectric materials,it is found there are distinct differences between these two types of materials in the variation of the contact resonance frequency during the PFS measurements.A momentary and sharp increase of the contact resonance frequency occurs when the domain is switched by applying the DC bias,which can be regarded as a unique characteristic for the ferroelectric materials.After analyzing the reliability and mechanism of this method,it is proposed that the contact resonance frequency variation at the coercive bias is capable to differentiate the electromechanical responses of the ferroelectric and non-ferroelectric materials during the PFS measurements.
