a b s t r a c tProcessing-structure relationships are at the heart of materials science, and predictive tools are essential for modern technological industries insofar as structure dictates properties. Point defects can have a profound effect on structure and consequently properties, but their effect on crystal chemistry is still not generally known or understood. None of the very few theoretical models which exist for perovskites are suited to the doped and defective ceramics most commonly used in commercial devices; therefore, a new empirical approach is presented here. A predictive model for the effective size of anions as well as cation vacancies and ultimately the pseudocubic lattice constant of such perovskites, based solely on published ionic radii data, has been developed here. The model can also be used to derive ionic radii of cations in twelvefold coordination. Vacancies have an effective size due to both bond relaxation and mutual repulsion of coordinating anions, and as expected this size scales with the host cation radius, but not in a straightforward way. The model is able to predict pseudocubic lattice constants, calculate the effective size of anions and cation vacancies, and identify the effects of both cation ordering and second-order Jahn Teller distortions. A lower limit on the tolerance factor of stable oxide perovskites is proposed.

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and SEM Analysis Jatuporn Burns, TEM preparation Kevin Tolman, X-ray Diffraction AnalysisXiang Liu, TEM Data Collection v non-native oxide is somewhat porous, meaning that if the fuel storage environment changes, these locations may be points where corrosion would be initiated.Video images from the sampling operation indicate that the cut ends and locations where the elements were handled using a "friction tool" have retained the large white oxide blooms. Otherwise, the fuel elements have a neutral medium gray external appearance with little evidence of corrosive attack or surface alteration. The individual fuel plates are clearly visible through the side plate openings and show no sign of oxide alteration or damage. vi vii ACKNOWLEDGEMENTAssistance from Andy Gray, Alan Olaveson, Craig Carlson, Caleb Maynard, and Gary Landon for help in validation of the sampling tools and acquiring the samples from the ATR fuel elements, Claude Kimball for contract logistics and video review support, Marcie Anderson and Shawn Tigue for coordinating shipment, Al Carlson for retrieving video footage, Mark Taylor for Electron Microscopy Laboratory receipt scheduling, and Joanne Grimmett for receiving and completing the inter-building laboratory transfers is gratefully acknowledged.

Models for composition–structure relationships are useful in both the lab and industry, yet few exist for perovskites-containing extrinsic defects or cation ordering. In this work, an empirical model is used to predict the existence of A-site cation ordering. Specifically, four compositions in the Na(1−3x)/2La(1+x)/2TiO3 system (x = 0.0, 0.0533, 0.1733 and 0.225) were synthesized using a conventional solid-state mixed-oxide method. The structure of the x=0 end-member (Na0.5La0.5TiO3) has been reported in various space groups, but always with a random distribution of Na+ and La3+ on the A site; however, empirical modeling suggests that it is not only ordered but also that a small volume increase accompanies the ordering process. While no evidence of long-range A-site ordering is observed in this composition via X-ray or neutron diffraction, electron-diffraction data indicate short-range ordering of Na+ and La3+ ions, with the degree of cation ordering decreasing (but the scale of ordered domains and degree of vacancy ordering generally increasing) with increasing x. First-principles calculations via density functional theory support both conclusions that short-range ordering in Na0.5La0.5TiO3 is stable and that it results in a volume increase with respect to the disordered analog. A similar analysis has been conducted for the Li(1−3x)/2La(1+x)/2TiO3 and Na(1−3x)/2La(1+x)/2(Mg0.5W0.5)O3 solid solutions. These systems provide additional validation of the accuracy and versatility of the empirical modeling method used