Ab-initio Calculations of the Relaxor Ferroelectric Na1/2Bi1/2TiO3 and its Solid Solutions

The necessity of substituting PbZrxTi(1−x)O3 by lead-free piezoelectric materials in numerous applications, such as sensors, actuators and ultrasonic transducers, has lead to a large number of research activities on perovskite solid solutions based on Na1/2Bi1/2TiO3 in recent years. The present dissertation deals with the characterization of the relaxor ferroelectric Na1/2Bi1/2TiO3 (NBT) in terms of structure and ferroelectric properties as a function of various parameters such as chemical order/disorder, hydrostatic pressure and alloying with other lead-free perovskites by computational methods. For this analysis it is necessary to combine ab-initio calculations with Landau theory and group theoretical tools. Part I begins in Ch. 1 with the motivation of this work. In Ch. 2, a brief overview of the regulatory framework, which triggered research activities in the field of lead-free piezoelectrics, is given and an example how lead can be substituted by other elements with similar properties. Afterwards the development concepts for these materials are introduced in Ch. 3. They are borrowed from the lead-containing perovskite solid solution PbZrxTi(1−x)O3, i.e. the presence of stereochemically active cations and solid solution formation with a morphotropic phase boundary. In Ch. 4, first relaxor ferroelectrics are introduced and the importance of chemical order/disorder discussed. Finally, the crystal structures of pure Na1/2Bi1/2TiO3 and four selected lead-free solid solutions are presented. The introduction closes in Ch. 5 with a listing of 13 specific questions this work aims to answer. In Part II the methods employed in this work are introduced. We start our investigations on the atomistic level using quantum mechanics. The atomistic simulations are performed in the Density Functional Theory (DFT) framework, which will be introduced on a very basic level, in Ch. 6. Some important remarks on the technique of structure optimization and mechanical boundary conditions will be given and a new nomenclature characterizing local structures of low symmetry will be presented, which is very similar to the well-known Glazer notation. Phase transitions are well described within the phenomenological Landau theory outlined in Ch 7. Landau theory allows to expand the free energy of a system in terms of its so-called order parameters. The application of Landau theory on the order parameters and displacive phase transitions relevant in Na1/2Bi1/2TiO3 requires also knowledge of some group theoretical tools, which will be introduced in Ch. 8. These tools are not only necessary for the Landau treatment, they are enormously useful in the analysis of calculated crystal structures in an ultimately systematic way in terms of symmetry-adapted distortion modes. The amplitudes of these (frozen-in) distortion modes can be directly used as order parameters in the Landau potentials. As Landau theory and group theory both are absolutely concrete but not demonstrative at all, both chapters contain numerous examples, which are all relevant for the understanding of this work. After introduction of the methods, the results will be discussed in Part III. The results are divided into five chapters. In Ch. 9 first the problem of chemical order will be treated in the cubic perovskite structure, accompanied by the question, whether it is possible to change the ordering tendency by application of hydrostatic pressure or chemical substitution. Afterwards the complexity of the structures is enhanced by including lattice distortions like polar displacements and octahedral tilts in Ch. 10. Here also the question of phase stabilities under hydrostatic pressure is addressed, together with the investigation of possible phase coexistence and formation of chemically ordered nanoregions. Afterwards the experimentally relevant phases R3c, Pbnm and P4bm will be compared in two representative chemical configurations, in order to investigate the effects of chemical order and hydrostatic pressure on the presence of different lattice distortions by using the group theoretical analysis in Ch. 11. This analysis helps us to identify the dominating distortion modes active in these phases. Landau theory then gives insights into the coupling interactions between these. In Ch. 12 Landau potentials are derived and energies obtained from DFT calculations, under systematic variation of atomic displacements induced by the separate distortion modes, allow the determination of the coefficients of the Landau potential. Ch. 13 finally treats the question of the possibility of morphotropic phase boundary predictions in NBT-based solid solutions. The method of determining pressure-induced phase transitions in pure NBT from Ch. 10 is extended to solid solutions in order to predict composition-induced phase transitions. Part IV starts by answering the initially posed 13 questions based on the findings of this work and finalises with a concluding discussion of the results and abilities of atomistic simulations and an outlook on possible future works