Thermodynamic calculation of Al-Mn-Zn system
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1 Thermodynamic calculation of Al-Mn-Zn system Tian Wang Supervisor: Dr. Mamoun Medraj 1
2 Content Introduction Thermodynamic calculation approach Thermodynamic modeling of Al-Mn, Al-Zn, Mn-Zn system. Thermodynamic calculation of Al-Mn-Zn ternary system. Conclusion 2
3 Introduction Phase diagrams are the foundation in performing basic materials research in such fields as solidification, crystal growth, joining, phase transformation, etc. Also, a phase diagram also serves as a road map for materials design and process optimization. In an alloy with several alloying elements, the phase relationships are very complex. In order to investigate and understand these complex phase relationships effectively, it is very useful to develop thermodynamic databases containing model parameters giving the thermodynamic properties of all phases as functions of temperature and composition. Using Gibbs free energy minimization software such as FactSage. 3
4 Thermodynamic Calculation Approach Collect thermochemical and phase equilibrium data Select thermodynamic models for each phase Optimize model parameters Obtain Gibbs energy functions for each phase in the system Describe known diagrams Predict unknown higher order multicomponent diagrams 4
5 Gamma (FCC) T(C) Al12Mn Alpha (CBCC) Al6Mn T(C) Al4Mn T( C) Alpha(CBCC) Thermodynamic modeling of Al-Mn, Al-Zn, Mn-Zn system Al - Zn Liquid 1177 o C 1271 o C 1314 o C Delta (BCC) o C 1047 o C 1001 o C Delta (BCC) Epsilon (HCP) 1046 o C 1068 o C Gamma (FCC) o C 816 o C 858 o C o C 511 o C Al11Mn 4 Al 8 Mn 5 Beta (CUB) 600 Liquid Al_Fcc Al_Fcc + Al_Fcc#2 Zn_Hcp 0 Mn - Zn Mole fraction, Mn 200 Al_Fcc + Zn_Hcp Zn/(Al+Zn) (mol/mol) Zn(HCP)+Zn13Mn Zn9Mn Zn8Mn5 Liquid Delta(BCC) Epsilon(HCP) Zn3Mn ZnMn Gamma (FCC) Beta(CUB) Three binary phase diagrams were calculated by current ternary model Modified Quasichemical Model(MQM) for the liquid phase. Substitutional Solution Model (SSM) for the solid solution Stoichiometric Model(ST) for the compound 5 Mn/(Mn+Zn) (mol/mol)
6 The advantages of Modified Quasichemical Model(MQM) It permits the composition of maximum short range ordering in a binary system to be freely chosen It expresses the energy of pair formation as a function of composition which can be expanded as a polynomial in the pair fraction The coordination numbers are permitted to vary with the composition The model can be extended to multicomponent systems 6
7 Equation of each model MQM is the change in the Gibbs energy for the formation of 2 moles of A-B pair are the parameters of model which related to the temperature SSM The Gibbs energy, per mole of the phase for the A-B binary system is given by: where C and D are the parameters to be determined during the optimization ST where p and q are the site fractions in the two sublattices of the compound ApBq and the C and D values are to be optimized using experimental data. 7
8 Thermodynamic calculation of Al-Mn-Zn ternary System A simple extrapolation of the Al-Mn, Al-Zn and Mn-Zn system to construct the ternary Al-Mn-Zn has been carried out using Kohler extrapolation technique without the use of any ternary interaction parameter. For modeling purposes, Alpha_CBCC, Beta_CUB, Delta_BCC and Gamma_FCC phases in both Al-Mn and Mn-Zn system were formally treated as the same phase. The thermodynamic properties of these phase were estimated from the binary model parameters. The previous optimizations of the Al-Mn, Al-Zn and Mn-Zn systems were combined in order to calculate the polythermal projection of the liquidus of the Al-Mn-Zn system. The thermodynamic properties of the ternary liquid phase were calculated by the MQM from the binary model parameters 8
9 Calculated liquidus projection of Al-Mn-Zn system The polythermal or liquidus projection is a two dimensional representation of the ternary liquidus surface on the Gibbs triangle which is mainly composed of several constant temperature lines called liquidus isotherms. Al - Mn - Zn Projection (Liquid) Mn Al - Mn - Zn Projection (Liquid) Mn oC 950oC 900oC 850oC 800oC 750oC 700oC 650oC 600oC 600oC 650oC Zn3Mn(s) 700oC 750oC 800oC 850oC Mn(s2) Mn(s) Mn 4Al 11(s) Zn3Mn(s) MnAl4(s) 1000oC Mn4Al11(s) 850oC 950oC Al MnAl4(s) 800oC 750oC MnAl 6(s) Al(s) oC mole fraction Calculated invariant reactions and critical points in the Al- Mn Zn system (table) 5 Zn 9Mn(s) Zn(s) Zn Al Al(s) MnAl 6(s) Zn Number Reaction T ( o C) Type Composition (at %) * Mn Al Zn 1 L Al_fcc + Al12Mn + Al6Mn E L Al11Mn4+ Mn_cbcc +MnZn E L Al11Mn4 + Mn_cbcc + MnZn E L + Mn_cbcc MnZn3 + MnZn P L + MnZn3 Mn4Al11 +MnZn P L + MnZn3 Al11Mn4 +MnZn P L Al11Mn4+Mn_cbcc + MnZn E L +MnZn9 Al11Mn4 +MnZn P L + MnZn13 Al11Mn4 + `Zn(HCP) P L Al 11 Mn 4 + Al4Mn+Zn(HCP) E
10 Zoomed Zn-rich corner Arrows indicated the descending temperature direction 10
11 Temperature/ o C Temperature/ o C Temperature/ o C Temperature/ o C Temperature/ o C Calculated liqudus temperature compared with the experimental results Al 81 Mn 14 Zn L Al 75 Mn 13 Zn 12 Al 75 Mn 16 Zn 9 Al 80 Mn 14 Zn 6 Al 83 Mn 13 Zn L 950 L 900 Delta_Mn+L Delta_Mn+L Delta_Mn+L L+MnAl Zn/at% (Mn=0.14) L+MnAl Zn/ at% (Mn=0.13) Delta_Mn+liquid+MnAl Zn/at% (Mn=0.16) Al 56 Mn 14 Zn L Al 80 Mn 14 Zn 6 Al 80 Mn 15 Zn 5 L+Mn 4 Al 11 L Al 54 Mn 14 Zn 32 Al 60 Mn 14 Zn Delta_Mn+L Delta_Mn+L+MnAl (s) 4 Al 58 Mn 14 Zn L+MnAl 4 (s) FCC+MnAl 4 Delta_Mn+L Mn/at% (Al=0.8) Delta_Mn+liquid+MnAl Zn/at% (Mn=0.14) 11
12 Al/at% Calculated Isothermal section (vertical section at 400oC) Al Al - Mn - Zn 400 o C Mn alpha + beta beta D8_10 + beta D8_10 + g-brass + beta D8_10 + Zn_Hcp Zn_Hcp + D8_10 + Mn 4 Al 11 (s) Zn_Hcp + MnAl 4 (s) + Mn 4 Al 11 (s) FCC + MnAl 4 (s) Zn_Hcp + FCC + MnAl 4 (s) FCC + MnAl 6 (s) mole fraction H + beta Zn FCC+MnAl6+MnAl4 FCC+MnAl4 FCC+MnAl6+MnAl4 FCC+MnAl4+T Zn/at% FCC+MnAl6 Calculated isothermal section compared with experimental results 12
13 Conclusion Thermodynamic modeling and calculation is a useful way to predict the complex system. Current calculation shows some discrepancies because the absence of ternary compounds data and ternary interaction parameters. Further experimental results will be used to construct and model the Al-Mn-Zn system. 13
14 Thank you 14
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