Non-statistical thermodynamic optimization

点击翻译按钮获取中文摘要

CALPHAD method is used for constructing thermodynamic models of phases via a simultaneous treatment of experimental data on the thermodynamic properties of phases and multiphase mixtures, and on the conditions of phase equilibria. Despite a thermodynamic flavour, the method is in fact a non-linear least squares technique resulting in a statistically optimal vector of models' parameters along with their covariance matrix. An analysis of the solution obtained requires that input data possess certain statistical characteristics. In particular, it is necessary to ascribe a reasonable experimental error to each measurement, and to ensure that its connotation conforms to that adopted in mathematical statistics. In reality, a painstaking analysis of experimental errors is often replaced with their estimations reflecting a personal opinion and experience of an expert proposing these estimations. Instead of speculating whether this widespread practice is good or bad, let us realize that it strips the "experimental errors" of their statistical meaning. It should also be noticed that in many contemporary publications, an accuracy of observations is not paid attention, that tables of experimental data are more and more frequently replaced with figures visualizing these data. It is not a problem to scan and digitize these illustrations; the problem is that scanning and digitizing lead to statistically meaningless quantities. It is not intended to commence a hopeless struggle against a reproachable way in which experimental knowledge is disseminated today. It is contemplated to augment the CALPHAD method by a new assessment technique based on the ideas and algorithms of a non-statistical treatment of experimental information formulated by Leonid V. Kantorovich and successfully employed for solving economic problems. The new procedure will yield not the vector of models' parameters, but a region (not necessarily convex) of their values within which one can try to satisfy additional criteria such as an absence of inverted miscibility gaps or false inflection points along phase boundaries. For any point from this region, it guaranteed that back-calculated quantities are confined within a non-statistical corridor of "ultimate errors" associated with all experimental observations.