Proper permittivity for depolarization field in perfectly insulating ferroelectric and examination of background permittivity

Depolarization field Ed emerging from spontaneous polarization P S is considered to play an essential role in the characteristics of ferroelectrics. For the estimation of Ed, correct dc-permittivity ε d is necessary but is still a controversial issue such as background permittivity ε b.. This paper examines the permittivity ε _d in the case of 1-dimensional insulating single-domained ferroelectric, by noting that ε _ddepends on how P _Sis defined. This examination shows that ε _dshould be unity when experimental P _Sor self-consistent P _Sis used. Without relying on special theories, a generic consideration based on this results shows that 1-dimensional insulating single-domained ferroelectric having 1st order ferroelectric transition cannot exist thermodynamically.