Computer calculations of phase diagrams

Abstract

The thermodynamic route of establishing phase diagrams is a relatively recent activity, considering that tiff about the fifties most phase diagrams were determined by the measurement of certain physical property or quantitative microscopy using light optics or x-ray diffraction. The thermodynamic formalism used by Kaufman and Bernstein is explained and illustrated with examples of the development of hypothetical binary phase diagrams. The calculation of ternary phase diagrams can begin with the binary phase diagram data as a first approximation. However, to calculate a reasonably accurate ternary phase diagram a certain amount of ternary solution data is necessary. Various empirical equations have been proposed in the literature to express ternary thermodynamic data. Calculation of simple ternary isothermal sections is illustrated with the examples of Mo-V-W and Cd-Sn-Pb systems. The numerical techniques which involve the differentiation of thermodynamic parameters with respect to composition get more involved with the number of components becoming 3 or more. A simpler approach has been applied recently to find the minimum position on the Gibbs free energy surface.

A new approach to fabricate superconducting NbTi alloys

“…of Nb-Ti system [24] and other ductile-ductile systems such as Ag-Cu [15] and Ni-Ti [17]. (Figure 2b), even though the phase diagram suggests that there is limited solubility of Nb in -Ti at room temperature [25]. The scale of this microstructure is sufficiently coarse to be confident that this apparent mechanical alloying is not just an artefact from beam broadening or from the interfaces lying inclined to the observation direction.…”

“…According to the Nb-Ti binary phase diagram [25], a single β-phase region exists above 600 ºC for the Nb-47wt%Ti alloy, and a two-phase (α+β) region below 600 ºC. We thus expect that when our consolidated material is annealed at 350 ºC (in the two-phase region), further precipitation of α-Ti will occur from supersaturated -Nb(Ti).…”

Investigation on Solid-State Phase Transformations in a 2510 Duplex Stainless Steel Grade

“…The thermodynamic calculation was employed to represent the equilibrium condition of the investigated steel. The modeling used in this work is based on the CALPHAD method (CALculation of PHAse Diagrams) [21] and the software Thermo-Calc (Thermo-Calc Software, Solna, Sweden) [22] was used in connection with the thermodynamic database TCFe6. The method is based on the minimization of Gibbs free energy of the phases provided by the Fe-C-Si-Mn-Cr-Ni-Mo-N multicomponent system.…”

Investigation on Solid State Phase Transformations in a 2510 Duplex Stainless Steel Grade

“…Schematic of the heat treatments performed on the investigated material Thermodynamic calculation have been employed to represent the equilibrium condition of the investigated steel. The modelling used in this work is based on the CALPHAD method (CALculation of PHAse Diagrams) [21] and the software Thermo-Calc [22] has been used in connection with the thermodynamic database TCFe6. The method is based on the minimization of Gibbs free energy of the phases provided by the Fe-C-Si-Mn-Cr-Ni-Mo-N multi-component system.…”