This book is unique because it focuses specifically on the internal connections between several systems of crystal structures and their evolutionary behavior. To be unique, this book is not a compiled list of different functional materials, rather it is on the internal connection and evolutionary behavior between and in different structural systems which are often observed in oxide functional materials.
Symbols and Definitions
Fourier coefficient of the crystal potential Fourier transform of the Ilth atom in the unit cell Debye-Waller factor of the Ilth atom. Position of the IX atom in the unit cell X-ray absorption coefficient Intensity of the integrated X-ray line Fluorescence yield.
Introduction
Functional materials are clearly different from structural materials, and their physical and chemical properties are sensitive to a change in the environment such as temperature, pressure, electric field, magnetic field, optical wavelength, adsorbed gas molecules and pH. A key requirement in the preparation of materials is to control the structural and compositional evolution for achieving superior properties.
MIXED V ALENCES AND FUNCTIONALITY
This book discusses the intrinsic connections between several crystal structure systems commonly used in functional materials and their evolutionary behavior. Functional materials are described in terms of mixed valence and stoichiometry in order to understand the structural evolution and transformation of various material systems.
Structure, Bonding, and Properties
CRYSTAL STRUCTURE
Specification of the lattice parameters and the positions of all atoms in the unit cell is sufficient to characterize all essential aspects of a crystal structure. A chemical formula is also given that represents the ratio of different elements in the unit cell, such as LaMn03' This type of material is called a stoichiometric compound, and its structure can be fully represented by the structure of the unit cell.
COORDINATION NUMBER AND COORDINATION POLYHEDRON
In this case, the symbol 3 + 3 is used to represent the antimony coordination number, with the first 3 standing for the atoms in the first shell and the second 3 for those in the second shell. In this way, a polyhedron face can be assigned to each atom in the unit cell, the area of the polyhedron face directly facing the atom being a measure of the weighting factor in the previous calculation.
ISOTYPISM AND POLYMORPHISM
Polymorphisms containing structures with different stacking orders of the same layers are called polytypes. The surface structure may differ from the inner structure and changes with temperature; different modifications can therefore form on the same substrate at different temperatures.
STRUCTURE AND CHEMICAL BONDING
Chemical bonding in a solid depends on the atoms, the lattice, the coordination situation, the valence value and the environment of the crystal atoms. A is called the Madelung constant, which depends on the type of structure of an ionic compound, and R is half the average intermolecular distance.
CHAPTER 1
This is achieved by the smaller coordination number 6 of the ions in the NaCl type (Fig. 1.7b). In the case of the fluorite-type structure, an exchange between cation and anion also involves an exchange of the coordination numbers; i.e. the anions get coordination number 8 and the cations 4.
Rule 1: Coordination polyhedra
This discrepancy arises because Shannon's data for ionic radii are based on the assumption that the cation is at the center of the coordination polyhedron. Therefore, the coordination number of anions must be calculated using ionic radii derived from the assumption that the anion is at the center of the coordination polyhedron.
Rule 2: The electrostatic valence rule
Rule 3: Linking of polyhedra
The decrease in stability of the structure during the assembly of the polyhedra is due to the electrostatic repulsion between the cations. This applies when it is favorable to have the atoms in the centers of the polyhedra close to each other.
Linking of polyhedra having different cations
- LIGAND FIELD THEORY
- LIGAND FIELD STABILIZATION ENERGY
- COORDINATION POLYHEDRA OF TRANSITION METALS
- MOLECULAR ORBITAL THEORY
- BAND THEORY
- STRUCTURE TRANSFORMATION AND STABILITY 1. PHASE DIAGRAM
- PROPERTIES OF MATERIALS
- STRUCTURE AND PROPERTY
- SELECTIVITY, SENSITIVITY, REPRODUCIBILITY, AND RECOVERABILITY
- SUMMARY
The positions of the ligands are at the points on the axes of the coordinate system. However, the observed bond angle is not 90° due to the repulsive interaction of the electrons in the orbitals (for example in water it is 104°27'). In the following sections, some of the typical properties associated with functional materials are reviewed.
One obstacle in the memory application of ferroelectric BaTi03, for example, is domain switching fatigue. Therefore, the behavior of the structural evolution is closely related to the functionality of the material.
Sodium Chloride and Rutile-Related Structure Systems
ROCK SALT STRUCTURE
However, if the cations and anions have similar sizes and their lattices can interpenetrate, the two close-packed fcc or hcp sublattices can combine to form a close-packed structure. The chloride anion lattice penetrates the sodium cation lattice and positions itself at the midpoints between the two closely packed sodium cation layers; thus, ions with opposite charges attract to form a lower energy structure (Fig. 2.2b). The cations will shift from the center between the anion close-packed layers into the void positions of the close-packed layers as shown in fig. 2.2c, resulting in the structure transforming from rock salt to sphalerite.
NONSTOICHIOMETRIC COMPOUNDS WITH SODIUM CHLORIDE STRUCTURE STRUCTURE
So, the property of a defective titanium monoxide can be a conductor and a superconductor below 1.0K. Due to a partially filled d-electron energy band, TiO can not only have a metallic conductivity, but also a yellow-gold color and metallic luster due to a plasma cutoff CAp ~ 0.4 Jlm) in the reflectance spectrum. If there is no oxygen deficiency, but some titanium deficiency, the system is a non-stoichiometric compound TixO (or Ti01+x)' The structure of this phase, such as Tio.80 (or Ti01.25), differs from that of TiO. The whole system is a metallic conductor, and the two types of structures described above can intergrow in different proportions to maintain the average stoichiometry of the compound.
RUTILE STRUCTURE AND ITS FAMILY
If the next stack layer is the same, it should be on the voids of the triangles to form a tetrahedron unit, as shown in Figure 2.5b. These structural configurations fulfill the requirements of molecular orbital interaction and geometric symmetry. The different geometric assembly of the tetrahedra and octahedra gives the rutile, perovskite, and fluorite-type structures.
CHARACTERISTICS OF RUTILE STRUCTURES
The [001] projection of the unit cell showing the arrangement of the octahedron chains along the c-axis direction. In V02, for example, the vanadium cations are displaced from the centers of the octahedra, causing a structural transformation from rutile to monoclinic. Arrays of edge-sharing octahedra. a) The linear, zigzag, ring and sheet of octahedra formed by edge splitting.
EVOLUTION OF RUTILE-TYPE STRUCTURES
The unit cell can be selected from the center to the center of the rutile mosaics or the newly created large tunnels. The structure of ~-Ga203 projected onto (010) (a), and the stereoscopic view (b), where the rutile sheets are clearly visible. Doping of another valence cation in rutile can form a structure built from the rutile mosaic and the basic unit of the doped cation.
SUMMARY
If another element is doped into the rutile structure, the donor energy levels can locate in the gap and the system will be semiconducting. The unit cell will be changed from tetragonal to monoclinic and the cation-to-cation distances in the pairs will be shortened. The corner share connection can be changed to create different derivative structures, but the chains still exist.
Perovskite and Related Structure Systems
- UNIT CELL BY TAKING A CATION AS THE ORIGIN
The triangles formed by oxygen are the same except for the position of the A cation. The perovskite structure is formed by an alternating stacking of the (A03)4 and B cation layers parallel to (III). a) The stacking sequence of A cations, (b) the unit cell of perovskite, (c) the formation of the B06. A change in the valence of the A cation should have a much stronger effect because it is in the fundamental stack layer.
THE TOLERANCE FACTOR
- CONDUCTIVE PEROVSKITES
In these compounds, the titanium (e.g. cation B) is not located exactly in the center of the octahedron as shown in the figure. In the perovskite structure, the transition metal cations are at or around the center of the oxygen octahedron. These operations can increase the dimensions of the unit cell and change the structure of the Bravais cell.
CHAPTER 3
- BUILDING THE STRUCTURES OF HIGH TEMPERATURE SUPERCONDUCTORS USING PEROVSKITE STRUCTURE UNITS. As discussed in Section 3.2 there are many
- GIANT MAGNETORESISTANCE (GMR) AND COLOSSAL MAGNETORESISTANCE (CMR)
- OXYGEN MIGRATION AND IONIC CONDUCTIVITY OF PEROVSKITES Compounds with perovskite or perovskite-related structures usually can be used as
- ANION-DEFICIENCY INDUCED PEROVSKITE TO BROWNMILLERITE STRUCTURAL EVOLUTION
- ORDERED STRUCTURAL EVOLUTION INTRODUCED BY CATION SUBSTITUTION
- CONSTRUCTING NEW MATERIALS BY TAILORING
- SUMMARY
This new module is the building block of the structure of YBa2Cll40g. f) The structure of YBa2C~Og. The structural evolution in the order-disorder transition is the basis of the tunable transducer. Two possible mechanisms were proposed (Zhang, Levy, & Fert, 1992): spin-defined scattering at interfaces where the deposited layers meet, and spin-scattering in the interior (bulk) of the deposits.
Fluorite-Type and Related Structure Systems
BASIC FLUORITE STRUCTURE
For the fluorite structure, rMlrx must be greater than 0.732 if the basic structural unit is a simple cation-centered cubic. This means that the size of the oxygen anion is larger than the size of the cation. In this chapter, the structure of fluorite is described on the basis of cation-coordinated tetrahedra (Figure 4.1d).
FLUORITE STRUCTURE WITH ANION DEFICIENCY
Fluorite modules viewed along the [112] direction of the fluorite unit cell, showing local distorted waves. The arrangement of the two types of fluorite modules builds the ideal structure of pyrochlore, where the oxygen vacancies are indicated in these drawings by open circles labeled V. We find three types of units in which the origin of the fluorite unit cell is shifted down to [ 0,0,4].
CHARACTERISTICS OF FLUORITE AND FLUORITE-RELATED STRUCTURES
By varying the cycling of temperature (up and down) and/or oxygen partial pressure (high and low), the oxygen content of a high content rare earth oxide can be reversed. The rapid communication of oxygen anions with gaseous oxygen must be related to the surface characteristics of rare earth oxides. One of the characteristics of rare earth high oxides is a redox hysteresis loop.
STRUCTURAL AND COMPOSITIONAL PRINCIPLES OF RARE EARTH HOMOLOGOUS HIGHER OXIDES
Due to the obvious structural relationships between the fluorite substructure and the homologous series of superstructures, the fluorite unit cell is chosen as the basic module to model the structures. The modular unit cell of each member of the series must contain only the eight possible vacancies or a multiple, m, of the eight. The fluorite-type unit cell is defined as the basic module from which all members of the homologous series are composed.
