Structural Entities and Configurational Entropy
Redox Energetics of Perovskite-related Oxides
Let us for a while return to Ba2In2O5. Although configurations with alternating layers of InO4tetrahedra and InO6-octahedra dominate at low temperatures disorder is not negligible. The range
of different configurations of this type close in energy give rise to significant disorder and imply
that the configurational entropy is not negligible even below 2000 K. Still, our results are in line
with the entropy of the disordered phase being considerably lower than the ideal value. The
number of possible sites available for the oxygen atoms is large but strong structural correlations
due to the preference for particular structural polyhedra imply that these will be far from
randomly occupied. This is of major importance for the redox energetics of non-stoichiometric
compounds.
Non-stoichiometry – partial pressure of oxygen relationships for selected perovskites
Practical uses perovskite-related oxides are in many cases related to the variable oxidation state
of the metal, e.g. catalytic activity, superconductivity and mixed ionic/electronic conductivity.
The redox energetics of non-stoichiometric perovskite-related oxides can in many cases be
rationalized in terms of the relative stability of the oxidation states involved and the
configurational entropy of the system. The first term is the major one and a number of systems
can be adequately described with an enthalpy of oxidation that is independent of composition.
The stability of a given oxidation state is related to the structure of the oxide and the large
difference in redox behavior e.g. between hexagonal and cubic SrMnO3-δ is due to the low
stability of hypothetical hexagonal SrMnO2.5 and thus to polyhedron preference energetics that is
largely dependent on the crystal structure. The same polyhedron preference lead to a lower than
ideal entropy and the shape of non-stoichiometry versus partial pressure of oxygen curves
depends on the configurational entropy.
Redox energetics of perovskite-type oxides
E. Bakken, T. Norby, S. Stølen
Journal of Materials Chemistry 2002, 12, 317-323.
Enthalpies of oxidation of CaMnO3-d, Ca2MnO4-d and SrMnO3-d – deduced redox properties
L. Rørmark, A.B. Mørch, K. Wiik, S. Stølen, T. Grande
Chemistry of Materials 2001, 13, 4005-4013.
Heat capacity of SrFeO3-d – configurational entropy of structural entities in grossly nonstoichiometric oxides
C. Haavik, E. Bakken, T. Norby, S. Stølen, T. Atake, T. Tojo
Dalton Transcations 2003, 361-368.
Redox energetics of SrFeO3-d – a coulometric titration study
E. Bakken, S. Stølen, T. Norby, R. Glenne, M. Budd
Solid State Ionics 2004, 167, 367-377.
The entropic contribution to the redox energetics is less easily understood; there are no clear
periodic trends. Still it is evident that the vibrational density of states is the more important
factor. The entropy connected with structural, magnetic and electronic transitions is much
smaller than the total vibrational entropy.
On the entropic contribution to the redox energetics of SrFeO3-δ
C. Haavik, T. Atake, H, Kawaji, S. Stølen
Physical Chemistry Chemical Physics 2001, 3, 3863-3870.
Energetics of the spin transition in LaCoO3
S. Stølen, F. Grønvold, H. Brinks, T. Atake, H. Mori
Physical Review B 1997, 55, 14103-14106.
Defect Clusters in Wüstite at High Pressure
Wüstite, Fe1-yO, has been extensively studied partly because of its complex defect chemistry and
phase relations and partly because of its proposed presence in the lower mantle; it is formed in a
phase transition at around 660 km, where spinel and garnet give way to the minerals Mgperovskite and Mg-wustite.
Even though the phase is grossly non-stoichiometric it seems clear that the residual entropy at
zero K is negligible. Thus again a significant degree of short-range-order must be present. In
order to establish phase relations in the Fe-O system at high temperature and pressure relevant
for reactions in the zone between upper and lower mantle the stability of different defect clusters
must be considered.
Geometry of the [4:1]0 cluster
The effect of pressure on the defect structure and phase relations of wüstite, Fe1 xO, was studied
by high-pressure X-ray diffraction and lattice energy simulations. Both the experiments and the
simulations suggest that the bulk modulus of wüstite does not vary significantly with
composition, and moreover does not seem to depend on the defect structure of the compound.
Thermodynamic modeling using a composition independent bulk modulus of 150 GPa suggests a
significant widening of the stability field of wüstite relative to iron and magnetite at high
pressure. This conclusion is in general agreement with the increased binding energy of defect
clusters in wüstite at high pressure.
Stability field of wüstite at high pressure (T = 900 K)
Calculation of the phase boundaries of wüstite at high pressure
S. Stølen, F. Grønvold
Journal of Geophysical Research 1996, 101, 11531-11540
Heat capacity and thermodynamics properties of nearly stoichiometric wüstite from 13 to 450 K
S. Stølen, R. Glöckner, F. Grønvold, T. Atake, S. Izumisawa
American Mineralogist 1996, 81, 973-981
Effect of pressure on defect clustering in wüstite – high pressure diffraction and lattice energy
simulations
C. Haavik, S. Stølen, M. Hanfland, C.R.A. Catlow
Physical Chemistry Chemical Physics 2000, 2, 5333-5340
Equation of state of magnetite and its high-pressure modification - thermodynamics of the Fe-O
system at high pressure
C. Haavik, S. Stølen, H. Fjellvåg, M. Hanfland, D. Haüserman
American Mineralogist 2000, 85, 514-523