High Throughput Analysis of Multicomponent Diffusion Data C

High Throughput Analysis of Multicomponent Diffusion Data C. E. Campbell and W. J. Boettinger National Institute of Standards and Technology Gaithersburg, MD 20899 J-C. Zhao General Electric Company: Global Research Schenectady, NY Ø Need for Multicomponent Diffusion Data & Simulations Ø Review of Multicomponent Diffusion Basics Ø Structure of Diffusion Mobility Database Ø Optimization to obtain mobility parameters: • from measured diffusion coefficients (normal approach) • from measured diffusion profiles (new work) TMS Fall Meeting 2003: The Accelerated Implementation of Materials & Processes November 11, 2003 This work was partially funded by the GE-led DARPA AIM program

AIM Strategy R 88 Ni. Al Ni Ta W Rapid Experiments Material Models Diffusion Multiples Thermo-Calc g Experiments & Characterization DICTRA Precipi-Calc Grain Size Experiments & Characterization g’ Fast Track Grain size Property Models Yield Strength UTS Creep Fatigue Crack Growth

AIM Precipi-Calc simulation of multi-modal g’size distribution for Rene-88 • Validated against GE-Interrupt cooling experiments – GE-AE proprietary data: – Literature data: Mao (2001) • Thermodynamics: Thermo-tech Ni-Data • Diffusion: NIST Ni-mobility database • Thermal profile: DEFORM simulation of blank disk Particle Distribution Mean <R> Primary g’ Temp. profile • Assume 3 D spherical particle: need to add elastic energy effects t < 100 s low nucleation rate 100 s < t < 150 s Primary g’ is formed 150 s < t < 350 s Primary g’ grows 400 s Secondary g’ precipitates 500 s Tertiary g’ precipitates Volume Fraction Total # Particles/m 3

Multicomponent Diffusion Review Multicomponent diffusion matrix for René-88 composition using NIST database Fick’s first law for Flux, Ji René-88 at 1100 °C (x 10 -14 m 2/s) Fick’s second law Simulations need to compute the diffusion matrix for each composition encountered in diffusion profile at each time step. Approach enables efficient data storage

Multicomponent Diffusion Database Structure Ø Inputs: – Calphad Thermodynamics – Diffusion experiments (unary, binary, ternary systems) • Tracer diffusivity, • Intrinsic diffusivity, • Interdiffusion coefficients/Marker motion Ø Optimize value of mobilities, Mi , for all binaries consistent with available data – Composition and Temperature-dependent – Consistent with estimates of Metastable end members e. g. , FCC W – Optimized using code, DICTRA (Parrot) Ø Add terms if necessary to fit ternary data, etc.

Optimization of Experimental Diffusion Coefficients Estimate Mobility Compare experimental and calculated D Experimental Mobility M=f (c, T) diffusion data Simulate diffusion process Adjust Mobility Calculate diffusion Coefficients D = f(c, T) Ni - Al Composition Log (Mobility) Diffusion profile Diffusion Coefficient T = 1150 °C T = 1050 °C T = 950 °C Distance For a binary: Composition

Examples of Optimized Binary Interactions Ni-Al-Cr-Co-Fe-Hf-Nb-Mo-Re-Ta-Ti-W Ni-Co Interdiffusion with Ni 1400 o. C T = 1000 o. C Log (D) m 2/s Data from Ustad and Sorum, Phys. Stat. Sol. A 285 (1973) 285. Calculated 1325 o. C 1250 o. C 1200 o. C 1160 o. C Data from Komai et al. , Acta. Mater. , 46, (1998) 4443. Data from Karunaratne et al. , Mater. Sci. Eng. , A 281 (2000) 229. Atomic Percent Ni Weight Fraction Previous assessments: Ni-Al-Cr Engström and Ågren, Z. Metallkd. 87 (1996) 92. Ni-Al-Ti Matan et al. , Acta mater. , 46 (1998) 4587. Ni-Cr-Fe Jönsson, Z. Metallkd 85 (7): 502 -509, 1994. Current assessments: Ni-Co, Ni-Hf, Ni-Mo, Ni-Nb, Ni-Re, Ni-Ta, Ni-Ti, Ni-W Co-Cr, Co-Mo C. E. Campbell, W. J. Boettinger, U. R. Kattner, Acta Mat, 50 (2002) 775

Optimization of Ni-W Tracer diffusivity data Data from Monma et. Al. , JIM, 28 (1964) 197. Interdiffusion data Data from Karuanaratne et al. , Mater. Sci&Eng. 281 (2000) 229. Data from Monma et. Al. , JIM, 28 (1964) 197. Activation energies in the fcc phase Self activation energies Optimized parameters

Challenge: Analysis of Diffusion Multiples /Multicomponent Diffusion Cannot determine diffusion coefficients from experimental data Diffusion Multiple 1 Sample 8 Diffusion Couples R 88 R 95 IN 718 ME 3 IN 100 R 88/R 95 R 88/ME 3 R 95/IN 718//IN 100 R 88/IN 718 R 88/IN 100 R 95/ME 3/IN 100 Experimental data provides composition and phase fraction profiles as functions of distance. Is it possible to directly relate composition profiles to mobility parameters?

Example : René-88/IN-100; 1000 h at 1150 °C gg g+g´ At 1150 °C equilibrium phase fractions • René-88: fg = 1 • IN-100: fg = 0. 638 fg’ = 0. 362 Additional g+g’ GE couples analyzed: René-95/ René-88 IN 100/ME 3 IN 100/ René-88 IN 718/IN 100 René-95/IN 718 ME 3/ René-88 R 88 ME 3/IN 718 U 720/IN 718 René-95/U 720/ME 3/ René-95 IN 100/U 720 IN-100 gg g g g IN 100 Experimental data from J. C. Zhao, GE-GR, Schenectady, NY

Diffusion Mobility Database Thermodynamic Database Run DICTRA (via python) Compare composition profiles Input Experimental File (Composition Profiles) Calculate Error (via Mathematica) Minimize Error f(Mi) Change Mi and z 0, Run new simulation Diffusion Database Optimization Scheme

Test Example: Binary Ni-Co Interdiffusion Coefficient obtained by Boltzmann-Matano method

Programming Elements and Inputs Ø Error Definition: Shift Matano interface Wi(z)= Weighting function Ø Currently set to equal 1 Ø z 0 = Error associated with location of Matano plane Ø Change selected mobility parameters a b

Ni-Co: Optimization Results Initial Parameters Initial Optimized Parameters Distance shift z 0= -1. 58 mm

Optimization Results: Diffusion Coefficient Initial Parameters NIST MOB - Initial Optimized Parameters GE Experimental data BM analysis Distance shift z 0= -1. 58 mm

Ternary Example: Ni-5. 13 Al-9. 77 Cr/Ni-2. 39 Al-19. 34 Cr (at. %) For a single couple cannot determine the interdiffusion coefficients using the BM method T = 1100 °C t = 1000 h Reference Binary interactions zeroed

Diffusion Mobility Database Thermodynamic Database Run DICTRA (via python) Compare composition profiles Input Experimental File (Composition Profiles) 1 couple 2 profiles Calculate Error (via Mathematica) Minimize Error f(Mi) Changing 9 binary interactions Change Mi Run new simulation Diffusion Database Optimization Scheme

Optimization Results: 9 parameters T = 1100 °C t = 1000 h Reference Al. Cr=335000 Cr. Al. Cr= 487000 Al. Ni=-166517 Cr. Al. Ni=-118000 Al. Cr. Ni=-53200 Cr. Ni=-68000 T = 1100 °C t = 1000 h Optimized Ni. Al. Cr=211000 Ni. Al. Ni=-23068 Ni. Cr. Ni=-81000 Binary Interactions zero Al. Cr= 341099 Cr. Al. Cr= 397756 Al. Ni= -175812 Cr. Al. Ni=-117332 Al. Cr. Ni= -58013 Cr. Ni=-62614 Ni. Al. Cr=265578 Ni. Al. Ni=-24037 Ni. Cr. Ni=-89378

Goal: Ni/Rene-88 Optimization strategy Ni end-member term • Ti, Nb Ni binary interactions • Ni-Ti Ni-Nb • Ni-Cr Ni-Al Ni ternary interactions • Ni-Al-Cr • Ni-Al-Ti • Ni-Cr-Nb

Diffusion Mobility Database Thermodynamic Database Run DICTRA (via python) Compare composition profiles Input Experimental File (Composition Profiles) 1 couple 7 profiles Calculate Error (via Mathematica) Minimize Error f(Mi) Changing 2 binary end members 2 binary interactions Change Mi and z 0, Run new simulation Diffusion Database Optimization Scheme

Ti Profile from Ni/Rene-88 Experiment 4 parameters optimized Initial Ni-MOB = -386325 =-81000 =-367650 =-68000 Initial Ni-MOB Need to consider additional parameters: • Other binary interactions • Ternary interactions Optimized = -367867 =-93125 =-327697 =-70015 z 0= +7. 5 mm

Summary Ø Multicomponent Ni-base diffusion mobility • Based on optimization of available diffusion coefficient data • Comparison of simulation results with experiments shows good agreement Ø Optimization based on composition profiles Ø Method • Relates profiles to mobility parameters • Provides ability to asses error associated with mobility parameters Ø Examples • Binary: Ni-Co (1 couple, fixed T, 1 profile, 4 parameters, z 0) • Ternary: Ni-Al-Cr (1 couple, fixed T, 2 profiles, 9 parameters) • Multicomponent: Ni/Rene 88 (1 couples, fixed T, 7 profiles, 4 parameters, z 0) Ø Improved optimization strategy needed • Multicomponent single phase (Need to consider more than 1 couple) • Multicomponent multiphase Ø Programming additions needed • Weighting functions • Other error definitions