Meaning
Mathematical condition where all eigenvalues of a diffusion matrix are strictly positive ensures that atomic transport occurs in the direction of decreasing chemical potential. A positive definite matrix is mathematically required to guarantee that diffusion does not occur up a concentration gradient in a single-phase region. Chinese regulatory authorities require the submission of these matrix properties for high-temperature alloy certifications.
This mathematical check is the ultimate guarantee that thermodynamic simulations of alloy decay are physically sound.
Thermodynamic Stability
Stable mathematical systems require that the calculated atomic flux always results in positive entropy production. If the diffusion matrix fails to be a positive definite matrix, the simulated material would exhibit spontaneous unmixing, which is thermodynamically impossible in a stable phase. This mathematical verification is performed prior to any alloy release.
Certification Standard
Technical regulations published by MIIT require all multi-component models to include stability checks. Software platforms utilized by state factories must have built-in subroutines to verify the eigenvalues of calculated matrices. This prevents structural calculation errors in power generation equipment designs.
Operational Limit
Non-compliant materials or packages that do not meet these mathematical criteria are rejected during national design audits. Foreign engineering suppliers must submit technical documentation showing the eigenvalue analyses of their transport calculations. These rules safeguard industrial operations from incorrect material modeling.
