KNbO_3/NaNbO_3超晶格及KNbO_3畴结构的第一性原理研究
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摘要
由于铁电材料具有极好的压电﹑介电和热释电性能,以及广阔的应用前景,一直受到人们的广泛关注和重视。基于这类材料广泛和潜在的应用价值,对铁电体的理论研究具有重要的学术意义。早期的理论研究带有很强的经验性,例如,朗道-德文希尔热力学理论、软模理论及横场Ising模型等都着眼于拟合实验结果,然后再利用这些模型预测新的实验结果。近年来,基于第一性原理(first principles)计算的理论研究发展迅速。与其它的理论工具相比,它具有计算结果精确、不依赖实验参量等特点,引起理论工作者的极大兴趣。
本论文基于第一性原理的计算,展开了以下几个方面的研究:
1.外延应力的变化对KNbO3/NaNbO3超晶格晶体结构、声子、自发极化和介电常数的影响。首次得到了KNO1unit cell/NNO1unit cell超晶格随外延应变的相图。
2.钙钛矿结构的铁电晶体KNbO3的180°畴结构。计算了畴壁的位置、厚度和畴壁能,而且还估算了畴壁移动的势垒高度。
The theoretical study of ferroelectrics and related materials can facilitate their applications. New practical applications can also be desined through better understanding on ferroelectric properties and ferroelectric phase transitions. Ferroelectrics have been widely used in the fields of microelectronics and optoelectronics owing to their many excellent properties, such as piezoelectricity, thermoelectricity and dielectric effect. The occurrance of ferroelectrics order is directly related to the changes of crystal structure and electronic structure, reflecting the balance between short-range and long-range forces.The intrinsical origin of ferroelectricity has been investigated for a long time and people just begin to gain deeper understanding on the subject.
Previous theoretical investigations were strongly empirical, for example, the Landau theory, lattice dynamic models and pseudo-spin model et al. They were used firstly to fit the experimental results and then predict new experimental results based on the semi-emperical models. Some of the theoretical results from these models are helpful to understand the mechanism of ferroelectric phase transition and are important for the application of ferroelectric material. In resent years, first principles calculation has been used to study ferroelectrics and it has become a powerful tool in this field. Based on the basic formula of quantum mechanics and some reasonable approximations, first principle calculations can be used to study crystal systems starting from the level of electronic structure. In the calculations, the solid is regarded as a particles’system that consists of electrons and nuclei. Using the basic formula of quantum mechanics, the total energy of the system is first calculated and then the ground state of the system is confirmed. The total energy calculation is performed according to the electronic structure of the atoms and the geometric configuration of nuclei involved. As the media of interaction among ions, electrons and their energy states are the basic objects in the calculations. Compared with other theoretical tools, the results from first principles calculations are more accurate in certain aspects and are independent of experimental data.
First principle’s calculations on ferroelectric systems performed through this thesis can be summarized below:
1. Due to their scientific importance as well as potential technological applications, artificial superlattices have been extensively studied in recent years. It is now possible to fabricate artificial superlattices composed of alternating two or more ultrathin epitaxial oxide layers owing to the fast development of oxide thin film growth techniques. Ferroelectric superlattices have been found to improve functional properties and may even produce new functionalities.
Excellent piezoelectric and dielectric properties of Pb(Zr_(1-x)Tix)O_3(PZT) with composition close to the morphotropic phase boundary (MPB) have made it the primary choice for making transducers, actuators and many microelectronic devices since its discovery in the 1950s. However, because of the lead oxide toxicity, the development of lead-free materials with properties comparable to the lead based compounds has become more and more urgent as environmental issues and attracted more attention in recent years. So far, quite a few environmentally friendly lead-free piezoelectric systems have been identified, among them, (K0.5Na0.5)NbO3 [abbreviated as KNN], which is at the morphotropic phase boundary (MPB) composition of the KNbO3-NaNbO3 solid solution system, is considered one of the most promising candidates for piezoelectric applications.
Using first principle’s calculations, we have obtained the phase diagram with respect to the epitaxial misfit strain for the KNO 1unit cell/NNO1unit cell superlattice. The system is tetragonal for large compressive strain with the polarization along [001] (P4mm phase) and orthorhombic with polarization along [110] (Amm2 phase) for natural state and tensile strain. At the intermediate level of in-plane compressive strain, monoclinic structure is stable and its polarization component along [001] decreases whereas the polarization component along [110] direction increases with the increase of misfit strain from -1.25% to -0.1%. The critical strain levels causing phase transitions from P4mm to Cm and from Cm to Amm2 were determined to be -1.25% and -0.1%, respectively, based on the analysis on the zone-center soft phonon frequencies. The polarization amplitude is the highest in the orthorhombic phase, reaching more than 70μC/cm2, which is 80% more than that of the tetragonal phase. The natural structure without misfit strain is orthorhombic Amm2 phase. We also found that the ferroelectric state with orthorhombic Amm2 structure is the ground state by comparing its total energy with that of the paraelectric centrosymmetric state with the same lattice constant.
So far KNbO3-NaNbO3 superlattice has not been produced to allow direct comparison between our theoretical results and experiment observations, but ceramic form of KNN: (K0.5Na0.5)NbO3 has the perovskite structure with space group Amm2.
2. The domain structure and the properties of the domain boundaries play an important role in the performance of many ferroelectric materials. Mechanical and electrical characteristics, such as the piezoelectric constants,the permittivity and coercive field, are often significantly influenced by the domain structures. In particular, the thickness and the interfacial energy of the domain walls are important parameters in understanding the switching kinetics and fatigue mechanism in ferroelectric materials. The width affects the wall mobility, and the energy determines how easily new domain walls may be introduced during the polarization reversal process. Thus, for a thorough understanding of the physical processes associated with the switching and fatigue behavior of a ferroelectric material, an accurate microscopic description of the underlying domain walls and their dynamics is needed.
Using a first-principles ultrasoft-pseudopotential approach we have investigated the atomistic structure of the 180°domain boundary in the ferroelectric perovskite compound KNbO3. We have computed the position, thickness and creation energy of the domain wall, and obtained an estimate of the barrier height for their motion. We find that Rz =0.93 which is the ratio betweenδFE (the displacement of the metal atom relative to an oxygen atom in the NbO2 plane) of the specified lattice plane and its value in the undistorted ferroelectric bulk phase already for the NbO2 first-neighbor plane(to be compared with the value of 0.8 reported in the case of PbTiO3),and the ferroelectric distortion is essentially fully recovered to its bulk value by the KO second-layer plane. The orientation of the polarization thus changes abruptly over a distance of less than two lattice constants, leading to a very narrow domain wall with a width of one to two lattice constants. The narrowness of the 180°domain walls is experimentally supported by the results from atomic force microscopy which show that the width of a domain wall is of the order of a few lattice constants.The energy of the K centered domain wall is calculated to be 7.58 mJ/m2, about a factor of 1/2 lower than the energy of the Nb centered domain wall.The barrier height for a jump to the nearest-neighbor lattice position is 7.58 mJ/m2.The ferroelectric distortion in the unit cells furthest away from domain wall are fully restored. Our calculated domain wall energy densities agree very well with published theoretical values of BaTiO_3(6 mJ/m2) several years ago. These values are significantly smaller than those reported in the case of PbTiO3(132 mJ/m2).
In a word, in this dissertation, the changes of crystal structure, zone-center phonon, polarization and dielectric constant with epitaxial strain in KNbO3/NaNbO3 (KNO/NNO) superlattice and the thickness,domain wall energy et al in 180°domain of KNbO3 have been studied using first-principle’s density functional theory (DFT) within the local-density approximation (LDA).
本论文基于第一性原理的计算,展开了以下几个方面的研究:
1.外延应力的变化对KNbO3/NaNbO3超晶格晶体结构、声子、自发极化和介电常数的影响。首次得到了KNO1unit cell/NNO1unit cell超晶格随外延应变的相图。
2.钙钛矿结构的铁电晶体KNbO3的180°畴结构。计算了畴壁的位置、厚度和畴壁能,而且还估算了畴壁移动的势垒高度。
The theoretical study of ferroelectrics and related materials can facilitate their applications. New practical applications can also be desined through better understanding on ferroelectric properties and ferroelectric phase transitions. Ferroelectrics have been widely used in the fields of microelectronics and optoelectronics owing to their many excellent properties, such as piezoelectricity, thermoelectricity and dielectric effect. The occurrance of ferroelectrics order is directly related to the changes of crystal structure and electronic structure, reflecting the balance between short-range and long-range forces.The intrinsical origin of ferroelectricity has been investigated for a long time and people just begin to gain deeper understanding on the subject.
Previous theoretical investigations were strongly empirical, for example, the Landau theory, lattice dynamic models and pseudo-spin model et al. They were used firstly to fit the experimental results and then predict new experimental results based on the semi-emperical models. Some of the theoretical results from these models are helpful to understand the mechanism of ferroelectric phase transition and are important for the application of ferroelectric material. In resent years, first principles calculation has been used to study ferroelectrics and it has become a powerful tool in this field. Based on the basic formula of quantum mechanics and some reasonable approximations, first principle calculations can be used to study crystal systems starting from the level of electronic structure. In the calculations, the solid is regarded as a particles’system that consists of electrons and nuclei. Using the basic formula of quantum mechanics, the total energy of the system is first calculated and then the ground state of the system is confirmed. The total energy calculation is performed according to the electronic structure of the atoms and the geometric configuration of nuclei involved. As the media of interaction among ions, electrons and their energy states are the basic objects in the calculations. Compared with other theoretical tools, the results from first principles calculations are more accurate in certain aspects and are independent of experimental data.
First principle’s calculations on ferroelectric systems performed through this thesis can be summarized below:
1. Due to their scientific importance as well as potential technological applications, artificial superlattices have been extensively studied in recent years. It is now possible to fabricate artificial superlattices composed of alternating two or more ultrathin epitaxial oxide layers owing to the fast development of oxide thin film growth techniques. Ferroelectric superlattices have been found to improve functional properties and may even produce new functionalities.
Excellent piezoelectric and dielectric properties of Pb(Zr_(1-x)Tix)O_3(PZT) with composition close to the morphotropic phase boundary (MPB) have made it the primary choice for making transducers, actuators and many microelectronic devices since its discovery in the 1950s. However, because of the lead oxide toxicity, the development of lead-free materials with properties comparable to the lead based compounds has become more and more urgent as environmental issues and attracted more attention in recent years. So far, quite a few environmentally friendly lead-free piezoelectric systems have been identified, among them, (K0.5Na0.5)NbO3 [abbreviated as KNN], which is at the morphotropic phase boundary (MPB) composition of the KNbO3-NaNbO3 solid solution system, is considered one of the most promising candidates for piezoelectric applications.
Using first principle’s calculations, we have obtained the phase diagram with respect to the epitaxial misfit strain for the KNO 1unit cell/NNO1unit cell superlattice. The system is tetragonal for large compressive strain with the polarization along [001] (P4mm phase) and orthorhombic with polarization along [110] (Amm2 phase) for natural state and tensile strain. At the intermediate level of in-plane compressive strain, monoclinic structure is stable and its polarization component along [001] decreases whereas the polarization component along [110] direction increases with the increase of misfit strain from -1.25% to -0.1%. The critical strain levels causing phase transitions from P4mm to Cm and from Cm to Amm2 were determined to be -1.25% and -0.1%, respectively, based on the analysis on the zone-center soft phonon frequencies. The polarization amplitude is the highest in the orthorhombic phase, reaching more than 70μC/cm2, which is 80% more than that of the tetragonal phase. The natural structure without misfit strain is orthorhombic Amm2 phase. We also found that the ferroelectric state with orthorhombic Amm2 structure is the ground state by comparing its total energy with that of the paraelectric centrosymmetric state with the same lattice constant.
So far KNbO3-NaNbO3 superlattice has not been produced to allow direct comparison between our theoretical results and experiment observations, but ceramic form of KNN: (K0.5Na0.5)NbO3 has the perovskite structure with space group Amm2.
2. The domain structure and the properties of the domain boundaries play an important role in the performance of many ferroelectric materials. Mechanical and electrical characteristics, such as the piezoelectric constants,the permittivity and coercive field, are often significantly influenced by the domain structures. In particular, the thickness and the interfacial energy of the domain walls are important parameters in understanding the switching kinetics and fatigue mechanism in ferroelectric materials. The width affects the wall mobility, and the energy determines how easily new domain walls may be introduced during the polarization reversal process. Thus, for a thorough understanding of the physical processes associated with the switching and fatigue behavior of a ferroelectric material, an accurate microscopic description of the underlying domain walls and their dynamics is needed.
Using a first-principles ultrasoft-pseudopotential approach we have investigated the atomistic structure of the 180°domain boundary in the ferroelectric perovskite compound KNbO3. We have computed the position, thickness and creation energy of the domain wall, and obtained an estimate of the barrier height for their motion. We find that Rz =0.93 which is the ratio betweenδFE (the displacement of the metal atom relative to an oxygen atom in the NbO2 plane) of the specified lattice plane and its value in the undistorted ferroelectric bulk phase already for the NbO2 first-neighbor plane(to be compared with the value of 0.8 reported in the case of PbTiO3),and the ferroelectric distortion is essentially fully recovered to its bulk value by the KO second-layer plane. The orientation of the polarization thus changes abruptly over a distance of less than two lattice constants, leading to a very narrow domain wall with a width of one to two lattice constants. The narrowness of the 180°domain walls is experimentally supported by the results from atomic force microscopy which show that the width of a domain wall is of the order of a few lattice constants.The energy of the K centered domain wall is calculated to be 7.58 mJ/m2, about a factor of 1/2 lower than the energy of the Nb centered domain wall.The barrier height for a jump to the nearest-neighbor lattice position is 7.58 mJ/m2.The ferroelectric distortion in the unit cells furthest away from domain wall are fully restored. Our calculated domain wall energy densities agree very well with published theoretical values of BaTiO_3(6 mJ/m2) several years ago. These values are significantly smaller than those reported in the case of PbTiO3(132 mJ/m2).
In a word, in this dissertation, the changes of crystal structure, zone-center phonon, polarization and dielectric constant with epitaxial strain in KNbO3/NaNbO3 (KNO/NNO) superlattice and the thickness,domain wall energy et al in 180°domain of KNbO3 have been studied using first-principle’s density functional theory (DFT) within the local-density approximation (LDA).
引文
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