7. Defects in β''- and β'''- Barium Hexa-aluminates
7.3 Intrinsic Defects
Although their chemical formulae are the same, the BAM structure is more stable than the β'' phase, which also can be seen from the fact that β''-alumina is metastable without Mg or Li, while β-alumina can exist as its own. The stability of the β''' phase is actually higher than the β'' phase but lower than BAM. Since the difference in reaction enthalpy is not very large, the β'' & β''' phases may intergrow with BAM structure, but β''' phase normally will not exist in the manufactured BAM material, because more magnesia and alumina are needed. The high stability of the BAM phase is the reason it is widely used as the phosphor host material instead of the other phases.
were chosen, normally the number of the selected positions was in the range of 100 to 400 depending on the size of the unit cell. All of the special positions need to be considered, but one must check the positions selected by the program to make sure that the special positions are included, by looking at the plot of selected interstitial positions in a unit cell. In this way, all of the positions with only one symmetry operation should have been chosen if their sizes are larger than the threshold.
7.3.1 Intrinsic Defects of Barium β''-Alumina
Table VII.4 lists the positions and energies of vacancy and interstitial defects. The energies listed are the lowest ones for the defect class. For example, aluminum interstitials can reside at the anti-BR site or in the middle of the spinel block or in many other positions; however, the energy to reside in the middle of the spinel block was the lowest of all. Then this energy was described as the interstitial defect energy of aluminum and the mid-spinel block position was described as the interstitial position of aluminum. The aluminum vacancy tended to occur at the Al(1) position, similar to the configuration II of the BAM structure. The problem is that the 024 configuration seems to be more similar to the configuration I of BAM structure, because they both have lost the mirror symmetry at the barium-oxygen plane whereas configuration II keeps it. It seems that the change from the two-fold screw axis of BAM to the three-fold screw axis of the β'' phase does change the defect properties, although the changes may be small.
The oxygen vacancy occurred at the O(1) position and oxygen interstitial resided at the Al(1) site exactly as in configuration I of BAM. The Reidinger defect is not energetically favorable in the β'' phase which has no mirror symmetry across the barium- oxygen plane. The larger interstitial ions, Ba and Mg, will stay in the anti-BR positions which are associated with more open space. Aluminum entered into the three cation-layers in the middle of spinel block. It can be said that the properties of the intrinsic point defects are almost the same for both BAM and the β'' phase, which is not really a surprise if one takes account of the same chemical formula and their closely related structures. As was found for BAM, the thermally predominant defect in barium β''-alumina was the Ba Frenkel defect.
Table VII.4. Defect Energy of Barium β''-Alumina Point Defect Defect Energy
(eV)
Point Defect Defect Energy (eV)
''
VBa 16.64 ••
) 3 O(
V 24.90
''
VMg 29.34 ••
) 4 O(
V 24.60
'' '
) 1 Al(
V 56.94 ••
) 5 O(
V 25.06
'' '
) 2 Al(
V 58.68 ••
Bai -11.81
'' '
) 3 Al(
V 58.62 ••
Mgi -19.39
'' '
) 4 Al(
V 57.43 •••
Ali -42.98
•
• ) 1 O(
V 23.05 ''
Oi -14.8
•
• ) 2 O(
V 24.63
Intrinsic Defect Energy (eV)
Schottky 4.81
Al Frenkel 6.98
Ba Frenkel 2.42
Mg Frenkel 4.98
O Frenkel 4.13
7.3.2 Intrinsic Defects in Barium β'''-Alumina
Because the symmetry of the BR site has changed, the defect properties of β''' also changed. As shown in Table VII.5 the aluminum vacancy was still found to occurs at the Al(2) sites in the so-called cation-rich region, where three layers of cations reside in between two close-packed oxygen layers. There are two cation-rich regions in each spinel block of the β''' phase instead of the one in BAM. The middle cation-layer is occupied by the Al(4) ion and the other two cation-layers are occupied by Mg ions or a mix of Mg and Al ions. Thus, there are two types of cation-rich region, with different effective charges caused by the Mg substitution: [Mg-Al-Mg]2- and [Mg-Al-Al]1-. A Mg vacancy occurring in [Mg-Al-Al]1- was more energetically favorable than in the other position as a result of the local charge effect. The same effect caused the oxygen vacancy to occur close to the other cation-rich region with the more negative local charge.
Table VII.5. Defect Energies of Barium β'''-Alumina Point Defect Defect Energy
(eV)
Point Defect Defect Energy (eV)
''
VBa 16.88 ••
) 3 O(
V 23.93
''
VMg 27.62 ••
) 4 O(
V 24.58
'' '
) 1 Al(
V 55.57 ••
) 5 O(
V 23.80
'' '
) 2 Al(
V 54.83 ••
) 6 O(
V 22.65
'' '
) 3 Al(
V - ••
) 7 O(
V 25.48
'' '
) 4 Al(
V 58.40 ••
Bai -11.19
'' '
) 5 Al(
V - ••
Mgi -18.53
'' '
) 6 Al(
V 55.70 •••
Ali -44.21
•
• ) 1 O(
V 24.53 ''
Oi -15.91
•
• ) 2 O(
V 22.62
Intrinsic Defect Energy (eV)
Schottky 3.80
Al Frenkel 5.31
Ba Frenkel 2.85
Mg Frenkel 4.55
O Frenkel 4.13
Large cations, Mg and Ba, as interstitial ions, occupied the anti-BR position in the conduction plane. The small Al ion stayed inside the spinel block. As in BAM, the aluminum interstitial resided in the octahedral site of the cation-rich region, where oxygen layers were not strictly close-packed. The oxygen interstitial appeared in the Al(1) layer close to a vacant octahedral site. Because the mirror symmetry across the barium-oxygen plane has been destroyed and because of the size of the large barium ion, the oxygen interstitial can not be stabilized by forming a Reidinger defect that is mirror symmetric about the conduction plane. Actually, the calculated intrinsic defect properties are exactly the same for the structure I of BAM, which is not surprising since their structures are very similar, in addition to the similarity of the Mg distribution.