Title : Transformation of scheil reaction scheme into the scheme of horizontal complexes and ruled surfaces computer models of TXY diagrams for catalytic materials
Abstract:
Chloride ternary systems based on LiCl–KCl are widely utilised as catalytic materials and electrolytes in spent nuclear fuel reprocessing, where the accumulation of lanthanide and actinide fission products necessitates precise knowledge of phase equilibria. However, traditional experimental determination of phase diagrams (PD) is resource‑intensive, and published diagrams frequently contain graphical errors or topological inconsistencies due to the complexity of 3D spatial structures. For instance, in the Ag–Cu–Ni system, a three‑phase subsolidus region was erroneously shown despite being forbidden by the phase reaction scheme, highlighting the need for rigorous verification of experimental and computational data [1]. Similarly, in pharmaceutical systems such as paracetamol‑caffeine‑aspirin, polymorphism of caffeine introduces ambiguity in the type of phase reaction (catatectic, peritectic, or mixed), and computer prototyping becomes essential for interpreting thermal analysis data and constructing reliable phase diagrams [2]. To address these challenges systematically, a comprehensive methodology has been developed for transforming the Scheil reaction scheme into a 3D framework of horizontal complexes and ruled surfaces [3]. The reaction scheme is first converted into a 2D scheme of invariant states and monovariant transitions, where each phase receives subscripts corresponding to its participation in invariant equilibria, fixing its trajectory. This 2D scheme is then translated into a 3D format, forming the PD skeleton consisting of tetrahedral horizontal complexes and connecting ruled surfaces. Subsequently, non‑ruled surfaces are added at the boundaries of single‑phase regions, with curvature correction. The technology has been successfully applied to construct 3D computer models for Li,M,K||Cl (M=Nd, Pr, La) systems, enabling cross‑validation of horizontal (at fixed temperature) and vertical (for specific compositions) material balances, as well as simulation of DTA spectra and electrical conductivity. The developed digital twins serve as effective tools for materials design, experimental data interpretation, and creation of "roadmaps" for targeted research in both catalytic and pharmaceutical systems, while also accelerating training of students and specialists in understanding complex phase diagrams.
