The third generation Calphad description of Al–C including revisions of pure Al and C

Third Generation of Unary Calphad Descriptions and the Avoidance of Re-Stabilized Solid Phases and Unexpected Large Heat Capacity

“…[9] 2 Problems Created by Using a Single Temperature Range for Unary Gibbs Energy This work is prompted by the publication of the paper ''A third generation Calphad description of Fe: revisions of fcc, hcp and liquid'' by He et al in this issue. [4] However, the problem of solid phase re-stabilization at high temperature noted in that work is also observed in the latest version of 3rd generation data for pure Al [3] and pure W. [5] It is obviously imminent to the method applied for these unary Calphad descriptions because the parameters a and b in Eq 1 are generally positive, resulting in an unlimited growth of C p of solid phases at high T, far above C p (Liquid).…”

“…This safely prevents by definition of the mathematical Gibbs energy function the violation of the EEC axiom and the incorrect re-stabilization of solid at high temperatures at the cost of a step in C p at EET. This is exemplified below for pure aluminum because it is a simple element without magnetic contribution and two different 3rd generation data, [2,3] can be shown for comparison. Figure 1 shows the thermodynamic functions of the stable Al phases FCC and Liquid.…”

“…If the calculation reaches the Equal-Entropy Temperature (EET) of the solid phase, the software will automatically suspend this solid phase.'' Similar statements are made for pure Al, [3] and pure W. [5] Currently (as of March 2022) the EEC is not implemented in the software Thermo-Calc, [11] but only in the latest software version of OpenCalphad (www.opencalphad. com).…”

“…In the third-generation data for pure elements [1][2][3][4][5] the molar Gibbs energy function of an element i in any crystalline phase u, is generally described by an equation of the following form…”

“…E 0 is a total energy at 0 K and the parameters a, b and n are determined from the molar heat capacity, C p , where n usually takes the values 2, 3 or 4. h E is the Einstein temperature for the phase u of this element. The focus of this work is on the proposal made for the latest version of the 3rd generation data to use a single set of these parameters in Eq 1 to cover the temperature range from 0 to 6000 K [3][4][5] as opposed to a second high temperature range. [2] Note that H SER i is the molar enthalpy of the element i at 298.15 K and 1 bar in its standard element reference (SER) state.…”