An Updated Thermodynamic Modeling of the Al-Zr System

Abstract

International audienceThe thermodynamic modelling of the binary Al-Zr system has been carried out using the CALPHAD approach, based on available experimental and theoretical data for phase diagram and thermodynamic properties. A set of self-consistent thermodynamic parameters was established. The liquid phase and the terminal fcc_A1(Al), bcc_A2(Zr), hcp_A3(Zr) solid solutions were treated as disordered solutions, using the Redlich-Kister expressions for the excess Gibbs energy, and the intermetallic phases were considered to be line compounds. A satisfactory agreement was achieved between the experimental data and the calculated results

Critical evaluation of experimental data of solution enthalpy of zirconium in liquid aluminum

“…According to the Wang's and Fischer's assessments [53] or this work (Table 5), the enthalpy of Reaction (2), corresponding to the Al 3 Zr formation in the calorimeter, is equal to -216.1, -209.1, -214.5±5.2 kJ.mol −1 respectively, in agreement with the measured thermal effect in our tests, equal to -219.1 ±5 kJ.mol −1 .…”

“…Phonon calc. C Al 3 Zr p (T) Esin et al [45] Derivative of ∆H Al 3 Zr (T ) Serebrennikov et al [48] Derivative of ∆H Al 3 Zr (T ) Kemsies et al [60] DSC 300-825 K Quantum Espresso GGA-PBE -184.4 Table 5: Numerical values for the calculation of ∆H 2 (T ) for T=996.15 K involved in reaction (2), according to the Wang's [52], the Fischer's [53] assessments and this work. 1 Table 6: Solubilities (C s in wt.%) in liquid aluminum, diffusion coefficients in liquid aluminum (D 0 in m 2 .s −1 ) for different transition metals at 1023 K from Eremenko et al [37] and densities at the melting temperature from different authors.…”

“…− ∆H Zr(hcp) (298.15K) + ∆E [19,47,49] only overestimated by 5% whereas they seem to invalidate the lowest values by [43,45] as well as the highest one by [50]. For ∆H Al 3 Zr (T ) ( Table 3), Wang et al [52] and Fischer et al [53] selected the values of Esin et al [45,48] who determined heat contents of Al 3 Zr from adiabatic calorimetry measurements between 300 and 2000 K. Esin's data are not very well documented. In addition the heat capacity values recently reported in [60] are significantly different from Esin's data.…”

“…More recently, very different ∆ f H Al 3 Zr (298.15K) values obtained by using a technique coupling thick multilayer foils and differential scanning calorimetry were reported by Weihs et al [49] and Fischer et al [50]. Finally, different assessments of the Al-Zr phase diagrams have been published [44,[51][52][53], in particular the two most recent and complete ones, from Wang et al [52], Fischer et al [53], and Tamim et al [54], reflecting the absence of consensus on the ∆ f H Al With the Quantum Espresso code [55], we have performed DFT simulations within the GGA-PBE approximation to calculate ∆ f H Al 3 Zr (0K) for the stable D0 23 structure of Al 3 Zr, the zero-point energies, and the enthalpic terms described within the framework of the harmonic approximation, in order to evaluate the order of magnitude of the vibrational contributions. Theoretically, the enthalpy of formation at 0K resulting from an ab initio calculation corresponds to only electronic contributions.…”

Progress on phase equilibria of the Al Si Zr system at 700 and 900 °C

“…Coupling with the thermodynamic descriptions of the Al-Si [22], Al-Zr [28] and Si-Zr [29] binary systems, and Gibbs energy description of the τ1 phase adopted from ref [19], phase equilibrium between τ1, liquid, SiZr and Si2Zr phases was calculated with the Pandat software [34]. Phase constituents of alloy Al25Si50Zr25 from 700 to 1200 °C are shown in Fig.…”