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Combinatorial experiments involve synthesis of sample libraries with lateral composition gradients requiring spatially-resolved characterization of structure and properties.Due to maturation of combinatorial methods and their successful application in many fields, the modern combinatorial laboratory produces diverse and complex data sets requiring advanced analysis and visualization techniques. In order to utilize these large arXiv:1904.07989v2 [cond-mat.mtrl-sci] 30 Apr 2019 data sets to uncover new knowledge, the combinatorial scientist must engage in data science. For data science tasks, most laboratories adopt common-purpose data management and visualization software. However, processing and cross-correlating data from various measurement tools is no small task for such generic programs. Here we describe COMBIgor, a purpose-built open-source software package written in the commercial Igor Pro environment, designed to offer a systematic approach to loading, storing, processing, and visualizing combinatorial data sets. It includes (1) methods for loading and storing data sets from combinatorial libraries, (2) routines for streamlined data processing, and (3) data analysis and visualization features to construct figures. Most importantly, COMBIgor is designed to be easily customized by a laboratory, group, or individual in order to integrate additional instruments and data-processing algorithms.Utilizing the capabilities of COMBIgor can significantly reduce the burden of data management on the combinatorial scientist.

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.