First Principles Calculation Of (K_1-xNa_x)NbO₃ Solid Solutions

Piezoelectric ceramic is an important high-tech ceramic materials, which has a wide range of applications, such as electronic and microelectronic devices. Nowadays, mostly high performance piezoelectric ceramic are Lead-based ceramics, and Pb is toxic. Lead-based ceramics damage both human health and the environment in its production, usage and waste treatment process. It was not until 2004, Y. Saito from Toyota, Japan reported that d33 of (K_0.50Na_0.50)_0.97Li_0.03(Nb_0.80Ta_0.20)O₃ and (K_0.44Na_0.52Li_0.04)(Nb_0.86Ta_0.10Sb_0.04)O₃ Piezoelectric Ceramics were 230 pC/N and 300 pC/N, respectively. While KNN with the same components but prepared by template grain growth (TGG) method had d₃₃ of 373 pC/N and 416 pC/ N. The report set off a study of KNN-based lead-free piezoelectric ceramic materials boom.From then people do much research on the KNN-based lead-free piezoelectric ceramic materials to improve its piezoelectric performance, mainly by doping. However, these efforts concentrated in experiments, theoretical work, especially the calculation of doped KNN system, is rare. In experiment, piezoelectric performance of KNN is improved mainly by means of doping, so it is benefit to understand the doping mechanism and doping effect on piezoelectric performance from the view point of atomic scale. Therefore, in this thesis structural properties and electronic structures of KNN are investigated by first-principles calculation.First-principles implement density functional theory (DFT) under Born-Oppenheimer approximation and give result of the ground state energy. Then the ground state of lattice structures, phonon dispersion and elastic constants can be obtained. In recent years, first principles calculation has been gradually extended to complex systems (such as doped systems, solid solutions and superlattices, etc.) and low-dimensional systems (such as solid surface, nanotubes, quantum wells and quantum dots, etc.). The theoretical analysis provided by first-principle calculation can not only explain the experimental phenomena, but can also provide a theoretical guide for the experiment.In this thesis, we applied this method to perovskite-type KNN under different phase structure and doped system. In our calculations, CASTEP program, which is integrated in Materials Studio package, is used. CASTEP is based on the density functional theory, using plane wave pseudopotential method (PWP) to calculate the electronic structure. The main work of this thesis is as follows:1) The lattice constants, electronic structure and total energy of KNN are calculated by using virtual crystal approximation (VCA) method. It is found that in both phases KNN, the lattice constant do not vary monotonic with the changes in Na content, in contrast, a mutation exists. The mutation of lattice constant occurrs at about 40% to 60% Na content. The total energy of KNN decreases with increasing Na content, but at Na content of 40% to 60%, a mutation of slope exists, which is consistent with lattice constant mutation at Na content of 40% to 60%. This can be recognized as morphotropic phase boundary (MPB) in the KNN at Na content of 40% to 60%. Electronic structure calculations of KNN show that, when K: Na = 1, KNN solid solution under both phase are indirect band gap, under tetragonal phase the band gap is 1.8 eV and under orthogonal phase the band gap is 2.5 eV. Through the analysis of density of states (DOS), it is found that in the both phase, Nb and O atoms are strongly covalent, while the A and O atoms are the ionic.2) The electronic structure and lattice structure of Li or Ta doped KNN are calculated by supercell method. Through the analysis of formation energy of Li or Ta doped KNN, it is found that in tetragonal phase KNN it is easier for Li to substitute Na atoms than K; the other way around, in orthogonal phase KNN, it is easier for Li to substitute K atoms than Na. Ta dopant has no effect on the direct band gap of KNN. Compared with orthogonal phase KNN, in tetragonal phase it is easier for Ta to substitute Nb atoms.