Abstract
I review the multiple successes of the discrete hard-wired dopant network model ZZIP, and comment on the equally numerous failures of continuum models, in describing and predicting the properties of ceramic superconductors. The prediction of transition temperatures can be regarded in several ways, either as an exacting test of theory, or as a tool for identifying theoretical rules for defining new homology models. Popular “first principle” methods for predicting transition temperatures in conventional crystalline superconductors have failed for cuprate HTSC, as have parameterized models based on CuO2 planes (with or without apical oxygen). Following a path suggested by Bayesian probability, we find that the glassy, self-organized dopant-network percolative model is so successful that it defines a new homology class appropriate to ceramic superconductors. The reasons for this success in an exponentially complex (Non-Polynomial Complete, NPC) problem are discussed, and a critical comparison is made with previous polynomial (PC) theories. The predictions are successful for the superfamily of all ceramics, including new non-cuprates based on FeAs in place of CuO2.
Highlights
The prediction of transition temperatures Tc is rightly considered to be one of the most difficult problems in theoretical physics
The results are quite disappointing, as they yield a scatter-shot plot [28], which means that the traditional chemical approach is too simple to explain HTSC
We begin by realizing that volume factors they are not known in detail, can be included implicitly in the analysis by focusing initially not on Tc (Y ), but rather on the largest transition temperatures Tcmax(Y ), where Y is any other chemical factor
Summary
The prediction of transition temperatures Tc is rightly considered to be one of the most difficult problems in theoretical physics. Other examples of Tc predictions are the proton orderdisorder transition in high-pressure ice, where the predicted and experimental values are 98 K and 72 K, respectively (KOH doping) [6], and strained thin-film ferroelectrics, where large shifts in the Curie temperature Tc are predicted, and there is a good agreement between theory and experiment after correcting the domain effects [7]. The values of Tc calculated by self-consistent fields with frozen magnons are in generally good agreement with experiment within about 20%, even for complex ternary alloys with mixed ferro- and antiferromagnetic interactions [8] All of these successful calculations have occurred in well-ordered crystals; methods based on ideal lattice models may not be successful for strongly disordered materials like ceramic superconductors
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