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["José C. Conesa" <jcconesa@icp.csic.es>]

Dear collegues,
  Several authors now think that gamma alumina is not just a spinel 
structure where some cation positions are vacant; rather, stacking 
faults (affecting in reality only the Al sublattice; the O sublattice is not 
affected by them) would appear extensively, giving upon complete 
ordering a delta alumina phase in which one lattice vector could be 
equal to 3/2 times one of the spinel cubic cell vectors, something that 
is not possible without faults. This would be made possible thanks to 
the decrease in the number of cations, much like Magnéli phases 
appear in rutile-type phases when you create anion vacancies.
  A good discussion of these issues in alumina, and an explicit 
proposal of one such stacked fault structure (on the basis of previous 
modeling and experimental works), is given in M. Digne et al., J. 
Catalysis 226 (2004) 54. A strong indication that structures with 
stacking faults can provide lower energy than any mere cation-
defective spinel structure is presented in a modeling work by G. Paglia 
et al. in prb 71 (2005) 224115. TEM observation of faults in alumina 
nanorods (said to be of gamma phase) is reported in W.F. Li et al., 
Phil. Mag. 85 (2005) 3809. A good rationalisation of the fault ordering 
is found in A. Lefebvre et al., Phil. Mag. 85 (2005) 2211, indicating that 
different types of delta-alumina phases might exist and comparing 
them with previous experimental data reported by several authors.
   I do not know whether these structures would have dielectric 
properties significantly different from those of a mere cation-deficient 
spinel (a charge density analysis made using VASP, reported in prb 72 
(2005) 035116 by E. Menéndez-Poupin et al., who present also a 
defective spinel model, gives a nearly negligible difference); but, just in 
case it might be so, I thought it convenient to provide this information.
  By the way, cation-deficient spinel M2X3 structures, with well ordered 
cation vacancies, do exist in nature: see gamma-Fe2O3 (A.N. 
Shmakov et al., J. Appl. Cryst. 28 (1995) 141), with all vacancies in 
octahedral positions, and beta-In2S3 (G.A. Steigman et al., Acta Cryst. 
19 (1965) 967), with all vacancies in tetrahedral positions. Both are 
tetragonal, with c axis=3 times that of the parent spinel; the first one 
(primitive lattice) has 160 atoms/primitive cell, the second one 
(centered lattice) only 40.
  Hope this helps.
  Best regards,
Jose C. Conesa
Instituto de Catalisis y Petroleoquimica, CSIC
Campus de Cantoblanco
28049 Madrid  -  Spain
Phone Nr. 34-91-5854766
Fax Nr. 34-91-5854760