Segregation energy, defect energy, surface defect energy and change in surface energy for the {100} surface of barium β(I)-alumina. MnAl segregation energy, defect energy, surface energy and change in surface energy for the {001} surface of the alkaline earth hexa-aluminates.
ABSTRACT
INTRODUCTION
The increasing complexity of the materials used in today's society has led experimental researchers to improve and invent new characterization techniques. The study of surface defects via atomistic surface modeling has the potential to provide a better understanding of surface properties, particularly in catalysis and biomaterials.
Hexa-Aluminates
- Magnetoplumbite Crystal Structure
- Barium β(I)-Alumina Crystal Structure
- Barium β(II)-Alumina Crystal Structure
The B(5) sites are coordinated with three oxygens in the mirror plane and three oxygens in the spinel block. It was found that there was little difference in the lattice energy for the different defect half-cell distributions.
Surface Science
These data show the surface composition and depth profile of the species in the sample. This may lead to questions about the validity of the surface structure for larger size samples.39.
Computational Materials Science
Using the solutions for the matrix, calculations of the total energy and excitation spectra can be compared with experimental data. Relaxation is the adjustment of the atomic coordinates relative to the initial configuration due to the minimization of the system's energy.
Perfect Lattice Simulations
- Description of a Perfect Lattice
- Lattice Energy Minimization
- Calculation of Crystal Properties
- Description of a Defective Lattice
- Defect Energy Minimization
The subscript ijk represents the labels of the central atom i and the two bonded atoms j and k. The forces associated with the three-body terms are usually much smaller in magnitude than the Coulombic and short-range forces. The Davidon-Fletcher-Powell algorithm76 can be used to compute the matrix H. The matrix H is updated at each iteration using the following equation:.
Surface Energy Calculations 1. Description of a Surface
- Surface Energy Minimization
- Surface Defect Energy Calculations
The dipole created by the surface defect induces dipoles in the rest of the crystal. The ionic displacements and the energy of the continuum must be modified to use planar integrals for the surface planes.
Interatomic Potentials
Crystal chemistry was also found to affect the number of termination planes. The increases observed for the {110} and {112} orientations in the barium magnetoplumbite structure are also due to the larger size of the Ba2+ cation.
Calcium Magnetoplumbite Surfaces 1. Low Dipole Surfaces
- Other Low Dipole Surfaces
- The {001} Surface
The shell of the Ca2+ can relax more than the core of the Ca2+ ion. Dipole moments normal to the surface can be reduced by relaxation of the Ca2+ shell. The second possible explanation for the higher surface energy calculated for the (1_0) surface is that the "opposite" side of the lattice is modeled.
The symmetry of the modeled planes indicates that the (1_0) surface should still relax to the same equilibrium position and thus the same surface energy. In a real crystal, the area of the (1_0) surface would be equal to the area of the symmetrically equivalent (100) and (010) surfaces. Stabilization of the raised O2- ion probably lowers the surface energy, as does the exposure of the two Ca2+ ions.
The lowest surface energy of the low-dipole surfaces of the calcium magnetoplumbite system is the {012} orientation, see Figure 3.11. Inspection of the calculated results shows that the repulsion energy term is higher on the {120} surface than on the {122} surface. All peaks of O2- ions lie on this line in the unrelaxed surface structure.
Strontium Magnetoplumbite Surfaces 1. Low Dipole Moment Surfaces
The number of patterned terminations is different from the calcium magnetoplumbite system due to the larger size of the Sr2+ ion. The calculated results for the strontium magnetolead system are similar to those of the calcium magnetolead system. The unit cell of strontium magnetoplumbite is larger than that of the calcium magnetoplumbite system because of the size of the Sr2+ ion.
The relatively high surface energy is due to the highly polarized environment of the first Sr2+ ion. The combination of the higher site potential of the fourth Sr2+ ion and the two dependent O2- ions leads to relatively high surface energy. The high coordination of the Sr2+ ions overcomes any increase in surface energy due to the low coordinated pendant O2- ion.
The relaxed position of the three dangling O2- ions results in the high energy of this surface orientation even though there are three exposed Sr2+ ions. The high surface energy is due to the positions of the upper Sr2+ (A) and O2- ions. The coordination of Sr2+ and O2- ions becomes the most important factor in the surface energy of an orientation.
Barium Magnetoplumbite Surfaces 1. Low Dipole Moment Surfaces
- Other Low Dipole Moment Surfaces
The coordination of the Ba2+ ion is seen to influence the surface energy of the end face. The second role that its size plays is the increase in the polarizability of the Ba2+ ion. There are no dangling O2 ions relaxing in places above the rest of the surface.
This surface is smooth, and therefore no O2 ions occupy positions above the original plane of the surface. This surface has the lowest surface energy of the low dipole surfaces, excluding the {100} orientation. The decrease in surface energy due to the exposure of the Ba2+ ions is lost by dangling O2 ions and the repulsive Coulombic forces between adjacent Ba2+ ions.
Coordination of O2- ions affects the surface energy of the surface, but to a lesser extent than exposure to Ba2+ ions. The result of the surface energy calculation of the (001) surface in the middle spinel block is a surface energy of 9.21 J/m2. Wrinkling on the relaxed surface creates space for the release of Al3+ ions.
Comparison of Magnetoplumbite Surfaces
The decrease in surface energy for the barium magnetoplumbite is due to its larger size. The second reason for the increase in surface energy for the larger cation is due to the size of the mirror plane. These two factors result in the increase of surface energy with increasing cation size.
Although Ba2+ is the largest of the cations, it does not reduce relaxation in the mirror plane. The smaller size of the cation allows the relaxation to occur more easily below the surface. This effect of divalent size on surface energy is more important for surfaces with mirror planes perpendicular to the surface, i.e. the surfaces and {120}.
The initial configuration of the low energy termination for the strontium magnetoplumbite system is not present in the calcium magnetoplumbite system. The larger unit cell size of the strontium magnetoplumbite system creates this additional low dipole moment termination plane. The relaxed surface energy of the {001} surface decreases with increasing size of the divalent cation.
Barium β(I)-Alumina Surfaces
- Surfaces Other Than the {001} Surface
The most striking difference in the structures is in the arrangement of the rows of O2 ions. However, the number of exposed Ba2+ ions does affect the surface energy of the end face. Increasing the number of Ba2+ ions reduces the surface energy of similar structures due to the high polarizability of the Ba2+ ions.
This greater polarizability reduces the polarization energy of the surface and therefore reduces the surface energy. Given similar structures, however, an increase in the number of exposed Ba2+ ions decreases the polarization energy of the surface and thus the surface energy. The main influence of the surface energy of these orientations is due to the O2 ion position.
Surfaces with constraints on the relaxation of the rows of O2 ions show an increase in surface energies. This increases the coordination of the Al3+ ions and reduces the polarization energy of the surface. The similarity of the surface structure to the bulk structure leads to a small difference in the surface and bulk energies.
Barium β(II)-Alumina Surfaces
- Surfaces Other Than The {001} Surface
- Comparison of Surfaces of the Barium Phases
We note that the calculation of the lowest surface energy {001} surface in barium β(I)-alumina led to the lowest surface energy calculations for the magnetoplumbite systems. One of the surface Ba2+ ions (A) occupies a relaxed position that is highly coordinated to the neighboring O2- ions. Two of the exposed Ba2+ ions (B and C) lie on a line containing the scaled O2- ions that run parallel to the channel.
Four of the exposed Ba2+ ions (A, B, C and D) have only three O2- coordinated in the surface plane. The low coordination of the exposed Ba2+ ions and the very high number of dependent O2- ions results in the highest surface energy calculated for the barium β(II)-aluminum structure. The high surface energy of these two surfaces was expected from visual examination of the surface images.
The density of surface atoms is an important factor in the calculated surface energy for a particular orientation. The charge compensation defects in the mirror plane and the middle spinel block thus do not affect the surface energy of the O2- and Al3+ layers. A simple model was used to determine whether the surface energy of barium magnetoplumbite can be stabilized by surface energy effects.
Defects in Alkaline Earth Hexa-Aluminates
- Bulk Defects in Alkaline Earth Hexa-Aluminates
- Surface Defects in Alkaline Earth Hexa-Aluminate
- Effect of Surface Defects on Phase Stability of Barium Magnetoplumbite Five cases of surface defects were examined using the same model used to determine
The first is when there is a negative segregation energy and a reduction in surface energy. The second possibility is when there is a positive segregation energy and an increase in surface energy. The third possibility is when there is a negative segregation energy and an increase in surface energy.
The fourth is when the segregation energy is positive and there is a decrease in surface energy. In the fourth case, the lowering of the surface energy must overcome the positive segregation energy. In each of these defect surfaces there is a negative segregation energy and an increase in surface energy.
For each of these defects there is a positive segregation energy and an increase in surface energy. The energy of segregation never overcomes the decrease in surface energy for a crystal of any size. Due to the negative segregation energy and the decrease in surface energy, the defect will always occupy a position on the surface.
Stratton, “Defect Structure and Transport in Oxygen Excess Cerium Oxide-Uranium Oxide Solid Solutions,” pp. Hamda, “Effect of the Surface Structure of Supported Palladium Catalysts on the Direct Decomposition Activity of Nitric Oxide,” J. Tasker, “The Surface Energies, Surface Tensions, and Surface Structure of the Alkali Halide Crystals,” Philos.
Lawrence, “The Role of Defects and Impurities on the Surface, Interface, and Bulk of Chromium(III) Oxide”; Ph.D. Norgett, "A Born Model Calculation of the Energies of Vacancies, Ion Interstitials, and Inert Gas Atoms in Calcium Fluoride", J. Norgett, "A General Formulation of the Problem of Calculating the Energies of Lattice Defects in Ionic Crystals," UKAEA AERE Harwell Report, AERE-R 7650, 1974.
