2. Bulk Pr oxides
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Each Pr atom in cubic PrO2 has eight oxygen neighbours |
The simplest Pr oxide is PrO2. It crystallizes in the CaF2 structure which can be visualized as the zinc blend structure with anion sites occupied by Ca (or praseodymium) atoms, and the cation and tetrahedral interstitial sites occupied by F (or oxygen) atoms. Thus, every Pr atom is eightfold-coordinated and every O atom is fourfold coordinated. All Pr atoms in PrO2 are Pr(IV) and each has transferred four electrons to oxygen atoms.
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Each Pr atom in cubic Pr2O3 has six oxygen neighbours |
When a quarter of the oxygen atoms is removed from the crystal, this charge transfer is reduced to three electrons per metal atom and Pr2O3 with Pr(III) is formed. Every Pr atom has now six O neighbors and every O atom retains four Pr neighbors. The atomic structure of remains closely related to that of PrO2: the oxygen vacancies are ordered in a 2×2×2 simple cubic array made of Pr fcc cubes, each fcc cube containing two O vacancies. Such a cubic Pr2O3 is stable under high vacuum. When deposited on Si(001) by electron beam evaporation, it grows with the (110) axis normal to the substrate. Therefore, our calculations are done nearly exclusively for Pr2O3; the dioxide is treated mostly as a reference to calibrate the pseudopotential for tetravalent Pr. This is necessary because one cannot a priori exclude that Pr(IV) atoms appear in certain structures of the interfacial region. However, up to now we have not identified any structures containing Pr(IV) which are stable under the conditions during growth and annealing of MBE Pr oxide layers.
The calculated lattice constant of Pr2O3 is 11.074 Å, less by 0.3% than the experimental 11.115 Å, and the bulk modulus is 280 GPa. LDA calculations yield 2.0 eV for the offset between bulk Si and bulk Pr2O3 valence band maxima.
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Pr(III) in PrOx may have one O neighbour more, Pr(IV) may have one O neighbour less |
There are also numerous mixed phases of Pr oxides, containing both Pr(III) and Pr(IV) atoms and having a composition of n(Pr2O3)·m(PrO2). The defected fluorite (vacancy) structure of the oxide is retained in these crystals, hence at least some of the Pr atoms have seven neighbors. Typical composition of praseodymium oxide is Pr6O11, corresponding to an ordered (Pr2O3)·4(PrO2) phase.