Monte Carlo Simulation On Ferroelectric And Thermoelectric Properties Of Polycrystalline Materials

Grain growth is the most common grain evolution phenomenon in polycrystalline materials, such as metal, alloy and ceramic, and it has a significant impact on the performance of the materials. For most materials, the grain size and its' distribution are the key factors dominating their physical and chemical properties. Therefore, there is crucial theoretical and engineering meaning to investigate the grain growth kinetics of the polycrystalline materials systematically. In recent years, many material researchers have simulated the grain growth using Monte Carlo method, and this technology has become a very powerful tool in this application. This method can not only get the information of grain size change, but also observe the evolution of the grain morphology intuitionally. Consequently, it is necessary to explore the influence of the polycrystalline grain texture on the material performance from the theoretical point of view.Since the twenty-first century, high technology and new materials have been developing rapidly. Ferroelectric material is an important kind of electronic functional material, also it is considered to be an intelligence basis material having the most prospects in application. It has broad academic interest and application in the field of high-performance microelectronics and photoelectron integrated component, such as micro-sensors and optical modulator, which makes ferroelectric ceramics highly attractive by many researchers in the field of material science, condensed matter physics, microelectronics and information science and so on. Compared with the ferroelectric single crystal, polycrystalline ferroelectric ceramics has more advantages exampled by easy preparation, lower-cost, and also they can be processed to any shapes. Moreover, ferroelectric ceramics can be prepared by natural sintering from the amorphous power, so there maybe exist grain boundary, impurities, and defects and so on, which can be manipulated in order to achieve required characteristics. Since the nano-material emerged in 1980's, the grain size effect of ferroelectric ceramics has been attracted more attention. As is well known, domain structure of the ferroelectric ceramics is one of the key factors that affect its properties greatly. Accordingly, the study of the relationship between the properties and the grain size of ferroelectric ceramics becomes a subject of much attention in the field of this kind material. So far, there is few rather than no report on the simulation of the physical properties of polycrystalline ferroelectrics based on the simulation of grain growth.Polycrystalline thermoelectric material is another kind of semiconductor functional materials being able to convert electric energy to thermal energy directly. In comparation with the traditional cooling and power generation technology, thermoelectric conversion technology is limited in many applications because of its low efficiency. Hence, it is of great practical significance to investigate the performance of thermoelectric material to further improve its conversion efficiency. Generally, the confinement effect obtained through multiple interfaces, which is considered as grain boundary, can effectively reduce the propagation of phonons in all directions. Meanwhile, the interface effect is usually used to reduce the thermal conductivity by phonon scattering. Consequently, we mainly focus on the issue that how to coordinate the confinement effect and the interface effect to improve the thermoelectric performance.With the development of the computational material science, besides the experiment and theory, the computer simulation has become another important approach to study the microstructure evolution of the material. In consideration of the importance of simulating the properties of polycrystalline materials, the aim of the dissertation is to introduce the Potts-Ising model and Monte Carlo method firstly. Then different effects, including size effect, on the ferroelectric properties and dielectric properties of polycrystalline ferroelectrics are studied based on the simulation of grain growth. The thermoelectric properties of polycrystalline thermoelectric material are also simulated and investigated.In the first chapter, a brief introduction of the significance and methods of the grain growth simulation is given, especially for Monte Carlo method and Potts-Ising model we have developed recently. By comparing two modified Monte Carlo methods on the simulation of grain growth, more accurate strategy has been obtained to reflect the grain growth properties near the steady-state and further improve the efficiency of the simulation method. In the second half of the first chapter, a general review of the investigation of the ferroelectric, thermoelectric properties of polycrystalline ferroelectrics and the thermoelectric material is addressed. Then the significance on the simulation of the polycrystalline materials is briefly discussed, as most of the simulation works have been done is focused on the ferroelectric single crystal structures. At the end of this chapter, Monte Carlo determination of the width threshold for Ising strips as an example is shown to demonstrate the validity of the method and model in this work.In chapter 2, polarization switching in polycrystalline ferroelectrics with and without fixed dipolar defects has been investigated respectively using Potts-Ising model and Monte Carlo method. Two processes are considered in our simulation. In the first one, the grain texture of ferroelectric ceramics are produced from Potts model, and then Ising model is implemented in the obtained polycrystalline texture to produce the domain pattern, hysteresis loop and switching current. For normal ferroelectric ceramics, the influence of the external conditions including the temperature, amplitude and frequency of ac electric field on the hysteresis loop has been investigated in detail. The results show that increasing temperature results in the decrease of both the coercive field and remanent polarization. Meanwhile, the increase in frequency or amplitude of the applied electric field results in the enlarger of the hysteresis loop area. The followed simulation results indicated that with the increase of the grain size, both the coercive field and the remanent polarization increase, and more grains change from single-domain to multi-domain. There is more domain nucleation during the polarization reversal when the grain size is smaller. This is the reason that smaller grain size result in lower coercive field. This implies that the defect has the ability to decrease the remnant polarization P_r as well as the coercive field E_c. It is interesting to note from the results of domain pattern evolution process under an applied electric field using this scheme, a different domain named extended domain has been obtained. The domain nucleation mostly occurs at the grain boundaries in ferroelectric ceramics without defect rather than at the defect points in the ceramics with defect. The peak of the switching current has been found to be lower with the increasing defect concentration and the decreasing average grain size.In chapter 3, Monte Carlo simulation of dielectric susceptibility and domain pattern evolution of the relaxor ferroelectrics upon the Potts-Ising glass model is performed. The effect of grain size, amplitude and frequency of the applied electric field on the dielectric susceptibility has been investigated. The dielectric susceptibility increases and the T_m shifts to lower temperature with increasing average grain size or decreasing frequency or decreasing amplitude of the applied electric field. Moreover, the value of the relaxation parameterγestimated from the linear fit of the modified Curie-Weiss law further confirmed that this model can reproduce the relaxation property. The changing trend of the relaxation parameter with the average grain size or the frequency is well consistent with the experimental observation. The difference between the domain evolution of relaxor ferroelectrics and that of normal ferroelectrics subjected to an applied ac field mainly happens in the number of the domain nucleation as the applied ac field reversed, and then a series of accompanied differences appear, such as the mode of the domain growth.In chapter 4, a scheme has been primarily developed that can simulate the electronic and thermoelectric properties of polycrystalline structures. Polycrystalline texture is created in a two-dimensional scale from Potts model using Monte Carlo method at the first step. Afterwards, the grain boundary potential function is created using order parameters of the model, and the grain boundaries are assumed either as potential barriers or as wells. Near free electron model is employed to construct the system Hamiltonian. The two-dimensional time-independent Schrodinger equation is solved numerically to obtain Eigen-values. Subsequently the thermoelectric properties including seebeck coefficient (S) and electrical conductivity (σ) have been calculated from these eigen-values. The simulation results show that the ground state electrons are easily confined at the largest grain. The calculated seebeck coefficient decreases, while the electrical conductivity increases monotonically, with the increasing grain size. Most significantly, the electrical conductivity decreases drastically with the increasing applied electric field and it shows an oscillatory behavior with different lattice site due to the potential barriers. The model is verified with the experimental data and proved to be a promising approach for simulating thermoelectric properties in ceramic samples. In addition, the thermoelectric conductivity is also obtained using Monte Carlo method.Chapter 5 summarized the main results of this dissertation, and further possible extension is previewed. This could be the first attempt to simulate the ferroelectric and thermoelectric properties of polycrystalline texture using Potts-Ising model on the basis of the simulation of grain growth.