Reconciling Local Structure Disorder and the Relaxor State in (Bi1/2Na1/2)TiO3-BaTiO3

Lead-based relaxor ferroelectrics are key functional materials indispensable for the production of multilayer ceramic capacitors and piezoelectric transducers. Currently there are strong efforts to develop novel environmentally benign lead-free relaxor materials. The structural origins of the relaxor state and the role of composition modifications in these lead-free materials are still not well understood. In the present contribution, the solid-solution (100-x)(Bi1/2Na1/2)TiO3-xBaTiO3 (BNT-xBT), a prototypic lead-free relaxor is studied by the combination of solid-state nuclear magnetic resonance (NMR) spectroscopy, dielectric measurements and ab-initio density functional theory (DFT). For the first time it is shown that the peculiar composition dependence of the EFG distribution width (ΔQISwidth) correlates strongly to the dispersion in dielectric permittivity, a fingerprint of the relaxor state. Significant disorder is found in the local structure of BNT-xBT, as indicated by the analysis of the electric field gradient (EFG) in 23Na 3QMAS NMR spectra. Aided by DFT calculations, this disorder is attributed to a continuous unimodal distribution of octahedral tilting. These results contrast strongly to the previously proposed coexistence of two octahedral tilt systems in BNT-xBT. Based on these results, we propose that considerable octahedral tilt disorder may be a general feature of these oxides and essential for their relaxor properties

Influence of orbital contributions to the valence band alignment of Bi2O3, Fe2O3, BiFeO3, and Bi0.5Na0.5TiO3

The formation of an interface between Bi2O3, Fe2O3, BiFeO3, Bi0.5Na0.5TiO3, and the high work function metallic RuO2 is studied using photoelectron spectroscopy with in situ RuO2 deposition. Schottky barrier heights are derived and the valence band maximum energies of the studied materials are aligned with respect to each other as well as to other functional oxides like SrTiO3 and PbTiO3. The energy band alignment follows systematic trends compared to a large number of oxides, and can be understood in terms of the contribution of Fe 3d and Bi 6s/6p (lone pair) orbitals to electronic states near the valence band maximum. The results indicate that the valence band maxima are largely determined by the local environment of the cations, which allows to estimate valence band maximum energies of oxides with multiple cations from those of their parent binary compounds. The high valence band maximum of BiFeO3 is consistent with reported p-type conduction of acceptor doped material, while the high conduction band minimum makes n-type conduction unlikely

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

Comparative study of A-site order in the lead-free bismuth titanates M1/2Bi1/2TiO3

We investigate the possibility of enhancing chemical order in the relaxor ferroelectric Na1/2Bi1/2TiO3 upon substitution of Na+ by other monovalent cations M+ using total energy calculations based on density functional theory. All chemically available monovalent cations M+, which are Li, Na, Ag, K, Tl, Rb and Cs, are considered and an analysis of the structurally relaxed structures in terms of symmetry-adapted distortion modes is given in order to quantify the chemically induced structural distortions. We demonstrate that the replacement of Na+ by other monovalent cations can hardly alter the tendency of chemical order with respect to Na1/2Bi1/2TiO3. Only Tl1/2Bi1/2TiO3 and Ag1/2Bi1/2TiO3 show enhanced tendency for chemical ordering. Both heavy metals behave similar to the light alkali metals in terms of structural relaxations and relative stabilities of the ordered configurations. Although a comparison of the Goldschmidt factors of components (M TiO3)− reveals for Tl a value above the upper stability limit for perovskites, the additional lone-pair effect of Tl+ stabilizes the ordered structure

Theoretical prediction of morphotropic compositions in Na1/2Bi1/2TiO3-based solid solutions from transition pressures

In this article we present a method based on ab initio calculations to predict compositions at morphotropic phase boundaries in lead-free perovskite solid solutions. This method utilizes the concept of flat free energy surfaces and involves the monitoring of pressure-induced phase transitions as a function of composition. As model systems, solid solutions of Na1/2Bi1/2TiO3 with the alkali substituted Li1/2Bi1/2TiO3 and K1/2Bi1/2TiO3 and the alkaline earth substituted CaTiO3 and BaTi03 are chosen. The morphotropic compositions are identified by determining the composition at which the phase transition pressure equals zero. In addition, we discuss the different effects of hydrostatic pressure (compression and tension) and chemical substitution on the antiphase tilts about the [111] axis (a-a-a-) present in pure Na1/2Bi1/2TiO3 and how they develop in the two solid solutions Na1/2Bi1/2TiO3 – CaTiO3 and Na1/2Bi1/2TiO3 – BaTiO3. Finally, we discuss the advantages and shortcomings of this simple computational approach

Chemical order and local structure of the lead-free relaxor ferroelectric (Na1/2Bi1/2)TiO3

The A-site mixed perovskite sodium bismuth titanate (Na1/2Bi1/2)TiO3 (NBT) is investigated by means of first-principles calculations based on density functional theory. By studying different geometries with varying occupations of the A-site, the influence of chemical order on the thermodynamic stability and local structure is explored. We find that the hybridization of Bi 6sp with O 2p-states leads to stereochemically active Bi3+ lone pairs and increases the stability of structures with high Bi concentrations in {001}-planes. This goes along with displacive disorder on the oxygen sublattice, which up to now has been neglected in experimental studies. The calculated ordering energies are, however, small as compared to the thermal energy and therefore only short-range chemical order can be expected in experiments. Thus, it is conceivable that chemically ordered local areas can act as nucleation sites for polar nano-regions, which would explain the experimentally observed relaxor behavior of NBT

Octahedral tilt transitions in the relaxor ferroelectric Na1/2_{1/2}Bi1/2_{1/2}TiO3_3

The kinetics of octahedral tilt transitions in the lead-free relaxor material sodium bismuth titanate Na1/2Bi1/2TiO3 (NBT) is investigated by electronic structure calculations within density functional theory. Energy barriers for transitions between tetragonal, rhombohedral and orthorhombic tilts in cation configurations with [001]- and [111]-order on the A-sites are determined by nudged elastic band calculations. By tilting entire layers of octahedra simultaneously we find that the activation energy is lower for structures with 001-order compared to such with 111-order. The energetic coupling between differently tilted layers is, however, negligibly small. By introducing a single octahedral defect we create local tilt disorder and find that the deformation energy of the neighboring octahedra is less in a rhombohedral than in a tetragonal structure. By successively increasing the size of clusters of orthorhombic defects in a rhombohedral matrix with 001-order, we determine a critical cluster size of about 40 Å . Thus groups of about ten octahedra can be considered as nuclei for polar nanoregions, which are the cause of the experimentally observed relaxor behavior of NBT

Structure, Electronic Structure and Defect Formation Energies of LixCo1-yNiyO2 as a Function of x (0<x<1) and y (y = 0, 0.5, 1)

LixCoO2 and LixNiO2 (0.5<x<1) are prototype cathode materials in lithium ion batteries.Both systems show degradation and fatigue during electrochemical cycling. We have performed band structure calculations based on density-functional theory for a series of compounds Lix(Co,Ni)O2 (0<x<1). The distribution of the transition metals (TM) cobalt and nickel on TM sites as well as the electronic structure of these compounds is investigated with focus on the change of oxidation states of cobalt, nickel and oxygen during lithium de-intercalation. We also study the total energy as a function of the lithium content x, including the vibrational energy Ev and the formation energy of lithium vacancies E(VLi). It is found that Ev is small compared to E(VLi) and that E(VLi) is increasing with increasing x for all systems

Influence of orbital contributions to the valence band alignment of Bi2O3, Fe2O3, BiFeO3, and Bi0.5Na0.5TiO3

The formation of an interface between Bi2O3, Fe2O3, BiFeO3, Bi0.5Na0.5TiO3, and the high work function metallic RuO2 is studied using photoelectron spectroscopy with in situ RuO2 deposition. Schottky barrier heights are derived and the valence band maximum energies of the studied materials are aligned with respect to each other as well as to other functional oxides like SrTiO3 and PbTiO3. The energy band alignment follows systematic trends compared to a large number of oxides, and can be understood in terms of the contribution of Fe 3d and Bi 6s/6p (lone pair) orbitals to electronic states near the valence band maximum. The results indicate that the valence band maxima are largely determined by the local environment of the cations, which allows to estimate valence band maximum energies of oxides with multiple cations from those of their parent binary compounds. The high valence band maximum of BiFeO3 is consistent with reported p-type conduction of acceptor doped material, while the high conduction band minimum makes n-type conduction unlikely