Towards automated phase isolation Danny Ritchie , Matthew S. Dyer,Vladimir V. Gusev,Michael W. Gaultois, Vitaliy Kurlin,Matthew J. Rosseinsky University of Liverpool, UK A novel probabilistic algorithm for the experimental determination of the composition of unknown phases is presented. A linear mapping of fractional compositions is first found, which exploits chemical restrictions to represent all feasible compositions in an affine geometric space of minimum dimensionality. A sampled composition is assumed to yield one unknown phase and several known phases. Relative weight fractions of the detected known phases, obtained from Powder X-Ray Diffraction, are then used to construct a multivariate normal distribution estimating the average composition of the known phases. Using this distribution, a probability density for the unknown phase is obtained from a computationally optimized projection of the distribution through the point corresponding to the sampled composition. In conjunction with iterative batch sampling methods, simulated exploration of phase fields constructed from either experimental or computational data show an average of less than 3 batches of 3 samples are required to obtain the unknown phase with 95% purity. This is across a range of intermetallic and ionic, ternary and quaternary phase fields, where the simulated relative weight fractions deviate from the true values with a root mean squared error of 6%. The probabilistic construction of the method makes it robust to various types of experimental error, including the formation of amorphous phases undetected by PXRD, sublimation of elements and reactions with crucibles. The nature of the technique permits phase fields containing an arbitrary number of elements.
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