ABSTRACT
C. Calcium Magnetoplumbite Surfaces 1. Low Dipole Surfaces
3. Other Low Dipole Surfaces
Table IX contains the calculated relaxed surface energies of the calcium
Table IX. Relaxed Surface Energies of Calcium Magnetoplumbite
Surface γ (J/m2)
{100} 2.39
{110} 2.64
{120} 2.74
{012} 2.31
{112} 3.08
{122} 2.67
magnetoplumbite system. Only the lowest relaxed surface energy planes of symmetrically equivalent surfaces have been included. One feature common to all of these surfaces is that the Al3+ ions relax into the surface structure. Only the Al3+ ions coordinated with O2- ions that have relaxed to positions above the original surface are exposed. In most cases, the Ca2+ ion is exposed or close enough to the surface in their initial configuration to relax to an exposed position. The area of exposed surface per unit cell is also larger than for the {100}
surfaces.
Dangling O2- ions are considered to be ions that have relaxed to positions above the unrelaxed surface plane. These O2- ions are associated with higher surface energies. The O2- ions in these dangling positions increase the potential energy of the surface and lead to their relatively higher surface energies.
The {110} surface, shown in Figure 3.9, has two exposed Ca2+ ions (A and B). An O2- ion (C) has relaxed to a position above the final surface but not above the unrelaxed surface. The first Ca2+ ion (A) is coordinated with the raised O2- ion, which also has two neighboring Al3+ ions. The coordination of the O2- ion with these cations partially satisfies its bonds; therefore, its position is stabilized. The first Ca2+ position is stabilized by the raised O2- ion. The second Ca2+ ion (B) is situated in a highly coordinated position, coordinated with six O2- ions on the same plane. The {110} surface has the third lowest surface energy of the low dipole surfaces. The stabilization of the raised O2- ion probably decreases the surface energy as does the exposure of the two Ca2+ ions.
The {120} surface, see Figure 3.10, has two dangling O2- ions, one (A) of which is coordinated with two Al3+ ions, the other (B) being coordinated by two Al3+ ions and a Ca2+
ion. This surface also has three exposed Ca2+ ions. The calculated surface energy is higher than that of the {110} surface. Each of the exposed Ca2+ ions is coordinated with four O2- ions. Even though there are three exposed Ca2+ ions, the lack of a Ca2+ ion near the second dangling O2- increases its site potential and thus the surface energy, compared to the {110}
surface.
The lowest surface energy of low dipole surfaces of the calcium magnetoplumbite system is the {012} orientation, see Figure 3.11. This surface only has one exposed Ca2+ ion.
Figure 3.9. Relaxed {110} surface of calcium magnetoplumbite.
Ions are color coded as follows: red - O2-, white - Al3+, and green - Ca2+. Surface image is of four blocks of unit cells of the modeled surface area. The Ca2+ ion (A) is
coordinated with the O2- ion (C) relaxed to a position above the original surface. The Ca2+ ion (B) is coordinated with six O2- ions.
Figure 3.10. Relaxed {120} surface of calcium magnetoplumbite.
Ions are color coded as follows: red - O2-, white - Al3+, and green - Ca2+. Surface image is of four blocks of unit cells of the modeled surface area. Dangling O2- ion (A) is
coordinated with a two Al3+ ions. Dangling O2- ion (B) is coordinated with two Al3+ and one Ca2+ ion.
Figure 3.11. Relaxed {012} surface of calcium magnetoplumbite.
Ions are color coded as follows: red - O2-, white - Al3+, and green - Ca2+. Surface image is of four blocks of unit cells of the modeled surface area. Ion A is a dangling O2- ion coordinated with one Ca2+ and three Al3+ ions.
Figure 3.12. Relaxed {112} surface of calcium magnetoplumbite.
Ions are color coded as follows: red - O2-, white - Al3+, and green - Ca2+. Surface image is of four blocks of unit cells of the modeled surface area. The O2- ion (A) has relaxed to a position above the original surface. The Ca2+ ion (B) occupies an exposed position.
There is a dangling O2- ion (A) which has a neighboring Ca2+ and three Al3+ ions. One would expect a higher surface energy than that calculated, due to the dangling O2- ion and only one exposed Ca2+ ion. The explanation for this surface having such a relatively low surface energy is that there are three, instead of two, Al3+ ions coordinated with the dangling O2- ion.
The long and short-range potential, ignoring the polarization energy, between the three Al3+
ions and the dangling O2- ion is -6.09 eV. Calculating the potential with only two Al3+ ions, based on the average distance of the three Al3+ ions, results in the higher potential of -4.06 eV. The addition of the third Al3+ ion further stabilizes the O2- ion, so that the overall surface energy of this configuration is lower than those of the other low dipole surfaces.
The {112} surface, see Figure 3.12, has one dangling O2- ion (A) and one exposed Ca2+ ion (B). The dangling O2- ions is coordinated with two Al3+ ions. The combination of a dangling O2- ion coordinated with only two Al3+ ions and one exposed Ca2+ ions leads to the high surface energy of this surface.
There are three dangling O2- ions in the relaxed {122} surface, seen in Figure 3.13.
There are two exposed Ca2+ ions. The first Ca2+ ion (A) has also relaxed to a position above the unrelaxed surface. There are three closely neighboring O2- ions which act to stabilize the Ca2+ ion's (A) position. Two of the dangling O2- ions (B and C) are stabilized by two neighboring Al3+ ions. The third (D) has both an Al3+ and a Ca2+ ion acting as stabilizers.
The calculated lower surface energy for the {112} than the {120} surface is interesting because of the greater number of dangling O2- ions and the lower number of exposed Ca2+
ions in the {112} surface. Examination of the calculated results shows that the repulsive energy term is higher in the {120} surface than the {122} surface. The smaller size of the surface area per unit cell of the {120} surface, 321.7 A2, causes neighboring O2- ions to relax to positions where the repulsive energy is higher than in the larger, 326.4 A2, {122} surface.
These surfaces do not appear to be as sensitive to the number of Ca2+ being in an exposed surface position as they are in the {100} surfaces. The orientation of the crystal is such that the size of non-exposed Ca2+ ions does not hinder the relaxation in the mirror plane. The more important factor in determining the lowest surface energy is then the coordination of the exposed atoms and the relative amount of repulsion between neighboring
Figure 3.13. Relaxed {122} surface of calcium magnetoplumbite.
Ions are color coded as follows: red - O2-, white - Al3+, and green - Ca2+. Surface image is of four blocks of unit cells of the modeled surface area. The Ca2+ ion (A) has relaxed to a position above the original surface. The dangling O2- ions (B and C) are each coordinated with two Al3+ ions. The dangling Ca2+ ion (A) and an Al3+ ion are coordinated to the third dangling O2- ion (D).
ions.