A Method of Triangulated Irregular Network-Based Linear Interpolation of Phase Diagrams

Drawn phase diagrams often need to be transformed into digital form and interpolated so that numerical values are available in each diagram point for further computations. Triangulation is often used for such a typical task. However, there are cases where the common triangulation algorithms do not work correctly for interpolating phase diagrams. In phase diagrams, the temperature value monotonically changes between isotherms, but in some situations the temperature values are the same in all three vertices of the triangle, which contradicts the physics of the phase diagrams. This may happen if there is a narrow-curved valley with a flat bottom similar to the Rosenbrock banana function on the phase diagram. Such triangulation must be corrected to ensure a monotonic temperature change. A new method is proposed that constructs a triangulation based on the existing points of the isotherms, and if there are plateau areas in this triangulation (three vertices having the same temperature values) they are transformed into smaller triangles to ensure a monotonic change of temperature by adding weighted points to some of their sides. The method is based on building a rooted tree with triangles as nodes, while the roots of the trees are inclined triangles. The method was implemented as a computer program, and its successful practical application is demonstrated using the ternary phase diagram of the melting temperature of ferrochrome steel depending on the chromium and carbon contents. The algorithm is included in the HSC Chemistry 10 modeling and simulation software developed by Metso Outotec.