Basics of Calphad modelling. Bengt Hallstedt Institute for Materials Applications in Mechanical Engineering, RWTH Aachen University, Aachen, Germany

Transcription

1 Basics of Calphad modelling Bengt Hallstedt Institute for Materials Applications in Mechanical Engineering, RWTH Aachen University, Aachen, Germany

2 Contents The Calphad method The SGTE unary (element) data Modelling of the Al-Li system 2

3 What is Calphad? Acronym for CALculation of PHAse Diagrams Basic ideas developed by Larry Kaufman in the 1960 s Based on the theory of heterogeneous equilibria J.W. Gibbs in the 1870 s Marriage between constitution science (phase diagrams) and thermochemistry Mathematical description (models) of the Gibbs energy of each phase Phase diagrams + complete thermochemistry 3

4 Books about Calphad Saunders, Miodownik 1998 Lukas, Fries, Sundman 2007 Hillert, 1998,

5 Thermochemistry and phase diagrams Thermochemistry Phase diagrams

6 The Calphad method Binary systems + (Important) Ternary systems + Extrapolations = Real alloys (several elements) 6

7 The Calphad method 7

8 Phase diagrams Microstructure formation Microstructure Phase transformations X210CrW12 8

9 Thermodynamic data for the pure elements 9

10 The inverted pyramid Ternary (117480) Binary (4005) Elements (90) 10

11 Elements (and single compounds) Normally not included in Calphad Gibbs energy: G H ref = A + BT + CTlnT + DT 2 + E/T + FT 3 Heat capacity: c P = C 2DT 2ET 2 6FT 2 H G G T T P K c P H G 2 T T 2 P T P 11

12 Lattice stabilities For elements there is world-wide consensus on using the so called SGTE unary database. This is essentially contained in: A.T. Dinsdale, Calphad, 15, (1991). (2238 citations on ). Since then the descriptions of a few elements have been modified and some elements added. The current version can be found at There is now a world-wide tendency develop a new set of element data. A Ringberg workshop (RUW) was held in March 2013 to lay the foundations and the results have been published in the Jan issue of physica status solidi b. 12

13 Thermodynamic models 13

14 Gibbs energies: simple solutions General: G m = G i TS ideal + E G m For each phase: G m = x A G A + x B G B + RT(x A lnx A + x B lnx B ) + x A x B [ 0 L + (x A x B ) 1 L + ] Redlich-Kister polynomial

15 Sublattice models: CEF (compound energy formalism) (A,B) n (C,D) q Site fractions: y A = N A /(N A + N B ) General: G m = G i TS ideal + E G m G m = y A y C G AC + y A y D G AD + y B y C G BC + y B y D G BD + RT[n(y A lny A + y B lny B ) + q(y C lny C + y D lny D )] + y A y B y C L A,B:C + y A y B y D L A,B:D + y A y C y D L A:C,D + y B y C y D L B:C,D + y A y B y C y D L A,B:C,D M. Hillert and L.-I. Staffansson, Acta Chem. Scand., 24[10], (1970) M. Hillert, J. Alloys Compd., 320, (2001)

16 The Al-Li system (B. Hallstedt, O. Kim, Int. J. Mater. Res., 98, (2007)) 16

17 Selection of phases Find a review paper and/or previous Calphad evaluation A.J. McAlister, BAPD, 3, (1982) N. Saunders, ZMK, 80, (1989) 17

18 Selection of models (A.J. McAlister, BAPD, 3, (1982)) Liquid: (Al,Li) Redlich-Kister Fcc-Al and Al 3 Li (L1 2 ): Four sub-lattice addon (compound energy formalism; CEF) Bcc-Li and AlLi (B32): Four sub-lattice addon (CEF) Al 2 Li 3 and Al 4 Li 9 : ΔG = A + BT (Neumann-Kopp; Δc P = 0) 18

19 Phase diagram data 19

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21 Terminal solubility (of Li in fcc-al) Early data have high impurity contents, such as K, Na and Fe 21

22 Terminal solubility (of Li in fcc-al) 22

23 Side note on ternary (or higher) systems XRD is generally not suitable for composition determination. Instead diffusion couples combined with metallography, EDX/WDX is often useful. The figure shows tielines from an Fe-Cr-Mo diffusion couple determined by WDX. J.-O. Andersson, N. Lange, Metall. Trans. A, 19A, (1988) 23

24 Liquidus/Solidus/Invariant reactions In most cases thermal analysis was used, often supported by isothermal annealing, quenching and metallography 24

25 Thermodynamic data 25

26 Calorimetric and ab initio data All ab initio! Liquid From emf Heat capacity data and enthalpies of formation by calorimetry are missing 26

27 Chemical potential of Li Methods: Electromotive force (emf) Knudsen Effusion Mass Spectrometry (KEMS) 27

28 Coulometric titration 28

29 Thanks to DFG for generous funding within SFB 761 (and other projects)! 29

30 Thank you for your attention! 30