Willis cluster

The parent structure of the anion-deficient fluorite structure phases is the cubic fluorite structure (Fig. 4.7). As in the case of the anion-excess fluorite-related phases, diffraction patterns from typical samples reveals that the defect structure is complex, and the true defect structure is still far from resolved for even the most studied materials. For example, in one of the best known of these, yttria-stabilized zirconia, early studies were interpreted as suggesting that the anions around vacancies were displaced along < 111 > to form local clusters, rather as in the Willis 2 2 2 cluster described in the previous section, Recently, the structure has been described in terms of anion modulation (Section 4.10). In addition, simulations indicate that oxygen vacancies prefer to be located as second nearest neighbors to Y3+ dopant ions, to form triangular clusters (Fig. 4.11). Note that these suggestions are not... 

The theoretical interpretation of the Willis clusters has been attempted by Cat-low 2). These authors employed the HADES program, a code used successfully for many ionic compounds. 

The calculation shows that the 2 2 2 and the 4 3 2 Willis clusters are essentially interstitial dimers stabilized by a coupled interstitial-lattice relaxation mechanism Oxidized (U ) cations localized at cation sites adjacent the cluster are also needed ... 

This affirmed necessity of positioning around the cluster, U (U ) cations is a very relevant fact, especially if coupled with the result of the channeling experiment reported above, which shows a displacement of uranium ions from their equilibrium positions. The Willis clusters can then be described also as molecularities in which the electronic charge... 

In fluorite-structure oxygen-deficient oxides MO2-X there is general agreement that the oxygen vacancy is the point-defect responsible for non-stoichiometry. Unfortunately, no direct observation is available of a basic cluster species for MO2-1 such as the Willis cluster in UO2+X. 

Figure 5.16 Willis clusters in UOj+y Open circles, oxygens small filled circles, uranium atoms in the UO2 structure. A 2 2 2 defect cluster consists of two interstitial oxygen atoms (large filled circles) and two normal oxygen atoms displaced from their ideal positions (open squares) to new interstitial positions (hatched circles). A 2 1 2 defect cluster would consist of one interstitial oxygen and two normal oxygens displaced from their ideal positions. (After Anderson, 19726.)...

Gerdanian (245) has developed a statistical-mechanical model for UO2 + X with small departure from stoichiometry to interpret the experimental values of AHq (244). His model is based on three types of defects—(a) f + 2Uy [Kroger and Vink notation (262)] in U02 [denoted by (a)], (b) 2 1 2 Willis cluster and two [denoted by (/)] in U02+ ,., and (c) 2 2 2 Willis clusters [denoted by (ii)] in U02+ (. The semi-grand partition function (SGPF) related to the defects... 

Figure 4.8 Structure of a Willis 2 2 2 structure (a) an empty Og cube (b) the stacking of four Og cubes in the UO2 structure (c) an Og cube containing a < 111 > interstitial oxygen ion (1d) an Og cube containing a < 110> interstitial oxygen ion and (e) the 2 2 2 cluster.

Yoder, J.A., M.G. Mueller, S. Wei, B.C. Corliss, D.M. Prather, T. Willis, R.T. Litman, J.Y. Djeu and G.W. Litman. Immune-type receptor genes in zebrafish share genetic and functional properties with genes encoded by the mammalian leukocyte receptor cluster. Proc. Natl Acad. Sci. USA 98 6771-6776, 2001. 

Presence of these interstices provides to the fluorite stmcture extremely specific features. In UO2 particularly, it allows for placement of some radioactive decay products, these sites are responsible for existence of hyperstoichiometric UO2+X phase, where the extra oxygen ions fill the empty interstitial sites in the fluorite lattice etc. First case is extremely important in radiation damaged UO2. Second one is cmcial in oxidation of pure UO2 in atmospheric conditions. Diffusion of atmospheric oxygen into the bulk of crystal brings excess oxygens into empty interstices. These become filled more or less randomly only at low x, at higher concentration of extra anions they form different types of clusters, including so-called 2 2 2 Willis dimers Willis), tetra- and pentameric defects clusters of cuboctahedral symmetry Allen and Tempest). Last defects appear due to interaction of extra anions with intrinsic crystal FP defects (anion Frenkel pairs, i.e. anion vacancies and anion interstitials). 

The maximum reactivity change rate for accidental withdrawal of two control banks is set such that peak linear heat rate and the departure from nucleate boiling ratio limitations are not challenged (Section 4.3.1.4.1 of Reference 6.1). Reactivity addition associated willi an accidental withdrawal of a control bank or banks is limited by the maximum rod speed (set at 1.14 m (45 inches) per minute for both rod cluster control assemblies and grey rod cluster assemblies) and by the worth of each bank (Section 4.3.1.4.2 of Reference 6.1). 

Viau L, Willis AC et al (2007) Ruthenium cluster chemistry monodentate bis(diphenylphosphino)acetylene-ligated cluster modules in chain and dendrimer formation. J Organomet Chem 692 2086-2091... 

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