nonlinear
effect also contributes to the induced Polarization. If the dielectric permittivity of a material is very high, it usually implies that its structure allows for a mode of ionic displacements, which is very sensitive to external poling perturbations.
BaxSr1-xTiO3 is a classical material used in microwave technology due to its high dielectric permittivity and appreciable dielectric nonlinearity. In this material, one of the polar optical phonon modes is responsible for its enhanced dielectricof a DC bias or by cooling it below TC = 120 C, Fig. 2.3b. In a simple model, the ferroelectric part of the polarization Pi can be associated with a displacement of the B-site ion from its central position, ni, and can be written as
Pi ¼ eðBÞ v ni ð2:27Þ where v is the unit cell volume, and eðBÞ is the charge of the B-site ion.
In this model, at temperatures higher than TC = 120 C, ni ¼ 0, whereas at temperatures below TC = 120 C, ni 6¼ 0. Thus, in the framework used above, setting To equal to TC, one qualitatively describes the evolution of the structure of
BaTiO3 while cooling from the paraelectric to ferroelectric phase. It occurs that the
Landau theory enables a quite good qualitative description of many properties of ferroelectrics. However, in some cases, the scheme needs the involvement of more terms than given by (2.23) and (2.24). What follows in this chapter, the Landau framework given by these or more advanced forms of these equations will be used repeatedly. The Landau theory provides a description for the polarization response of ferroelectrics. Using (2.2), (2.19), and (2.24), one finds the dielectric permittivity of a ferroelectric under DC bias, E, given by the following expression: eðEÞ ¼ eb þ
1
a þ 3bP2 ð2:28Þ where P should be calculated from (2.24).
2.1.2.2 Paraelectric Phase
In the paraelectric phase (T [To) in the absence of a DC field, P ¼ 0 and (2.28) yield the dielectric permittivity of the ferroelectric as e ¼ eb þ
1
BaxSr1-xTiO3 is a classical material used in microwave technology due to its high dielectric permittivity and appreciable dielectric nonlinearity. In this material, one of the polar optical phonon modes is responsible for its enhanced dielectricof a DC bias or by cooling it below TC = 120 C, Fig. 2.3b. In a simple model, the ferroelectric part of the polarization Pi can be associated with a displacement of the B-site ion from its central position, ni, and can be written as
Pi ¼ eðBÞ v ni ð2:27Þ where v is the unit cell volume, and eðBÞ is the charge of the B-site ion.
In this model, at temperatures higher than TC = 120 C, ni ¼ 0, whereas at temperatures below TC = 120 C, ni 6¼ 0. Thus, in the framework used above, setting To equal to TC, one qualitatively describes the evolution of the structure of
BaTiO3 while cooling from the paraelectric to ferroelectric phase. It occurs that the
Landau theory enables a quite good qualitative description of many properties of ferroelectrics. However, in some cases, the scheme needs the involvement of more terms than given by (2.23) and (2.24). What follows in this chapter, the Landau framework given by these or more advanced forms of these equations will be used repeatedly. The Landau theory provides a description for the polarization response of ferroelectrics. Using (2.2), (2.19), and (2.24), one finds the dielectric permittivity of a ferroelectric under DC bias, E, given by the following expression: eðEÞ ¼ eb þ
1
a þ 3bP2 ð2:28Þ where P should be calculated from (2.24).
2.1.2.2 Paraelectric Phase
In the paraelectric phase (T [To) in the absence of a DC field, P ¼ 0 and (2.28) yield the dielectric permittivity of the ferroelectric as e ¼ eb þ
1