Effective Field Approach For Mixed Ferroelectric Systems

Mixed ferroelectrics usually refer to ferroelectric materials that consist of two or more end materials, such as partially deuterated triglycine sulfate (TGS1-x/DTGSx) and partially deuterated triglycine selenate (TGSe1-x/DTGSex), or solid solution such as Pb(ZrxTi1-x)O3 and (KxNa1-x)NbO3 systems. The physical properties of these materials can be manipulated by adjusting their composition rate. This advantage makes the mixed ferroelectric materials more practical in applications. However, experimental data reveals that the physical properties, such as the Curie temperature and the spontaneous polarization, in these systems are not linearly related with their composition rate as expected. Many works have been devoted to the non-linearity of the composition dependence of the Curie temperature. The correlation effect and zero-point vibrations have been proposed to responsible for the nonlinear relationship. But fully understanding this problem needs more theoretical works.Effective field approach has been approved a successful method to describe the phase transition property in ferroelectrics. It is a simple in mathematics but rich in physics method. In its origin version, this method has already been applied to the second order phase transition properties in homogeneous ferroelectric systems. With including higher order terms of polarizations, properties in first order phase transitions can be also well described. With inclusion of zero-point energy, this approach can be extended to describe the dielectric behavior of quantum paraelectrics.The aim of this work is to throw some lights on the influence of compositional dependence of phase transition properties in mixed ferroelectrics from theoretical side using effective field approach. At first step of this work, a concise version of effective field with two sub-lattice systems has been developed to describe the phase transition property inmixed ferroelectrics. The two sub-lattices stand for the two end materials respectively, and a coupling between the two sub-lattice systems has been assumed. The effective field strength at either sub-lattice is proportional to its composition rate. From this model, the compositional dependence of the Curie temperature, spontaneous polarization and the dielectric susceptibility have been obtained.It was found from this model that the coupling strength between the two sub-lattice systems plays a crucial role in the composition dependence of the Curie temperature. When coupling strength is the average of the effective field strength in their individual subsystems, the Curie temperature follows linear relation with its composition rate, otherwise non-linear relationship will be followed. Weak coupling reduces the Curie temperature in the mix system, and the deviation from linear relation reaches maximum around 0.5 of composition rate. Fairly quantitative fitting of theoretical results with that of partially deuterated triglycine sulfate (TGS)1-x(DTGS)x and partially deuterated triglycine selenate (TGSe)1-x(DTGSe)x have been obtained, and revealed that the deviation of Curie temperature from their linear relationship in these two mixed systems is attributed to the weak coupling strength, which is about 80% of the average value of their individual system. This approach was further extended by C. David et al to three sub-lattice model, and the Curie temperature in tungsten bronze ferroelectrics has been obtained, and in fairly good agreement with the experimental data.The temperature dependence of the spontaneous polarization and that of the dielectric susceptibility have been obtained for different composition rate and different coupling strength in mixed systems. The influence of the dipolar contribution and the number of the dipole moment on the spontaneous polarization and dielectric constant hasbeen studied too. It is found that the dipolar moment can both change the saturation polarization and shift the Curie temperature, but the effective field strength can only change the Curie temperature. These results can well reproduce the p...