CALCULATION AND AUTO-PLOTTING OF THE STABLE EQUILIBRIUM P-T PHASE-DIAGRAM OF AN N-COMPONENT SYSTEM COMPOSED OF N+2 PHASES

Based on thermodynamic principles, the following equation is derived in the present work DELTA(r)G(m)(p,T) = DELTA(r)G(m)(p(i),T(i)) - DELTA(r)S(m)(T - T(i)) + DELTA(r)V(m)(p - p(i)), which serves as the universal thermodynamic basis of the sign function matrix (SFM) approach for identifying the metastable extensions of the univariant curves about a stable invariant point in a p-T space. (In the above equation p(i) and T(i) are the pressure and temperature at the invariant point, respectively; DELTA(r)G(m), DELTA(r)H(m), DELTA(r)S(m) and DELTA(f)V(m) are molar Gibbs free energy, enthalpy, entropy and volume changes of the reaction, respectively.) The slope (partial derivative p/partial derivative T) of each univariant curve at the invariant point can be found with Clapeyron equation or with the reverse curve-fitting technique. Based on the work of Cheng et al.[1], the application of SFM has been transformed in this study from a method for qualitative description into one for quantitative depiction, and it provides us a new, simple and easy method for auto-plotting of the stable equilibrium p-T phase diagram of an n-component system composed of n + 2 phases.