# Presentation: 488528

## 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

*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*

-  Need for Multicomponent Diffusion Data & Simulations
-  Review of Multicomponent Diffusion Basics
-  Structure of Diffusion Mobility Database
-  Optimization to obtain mobility parameters:
-  from measured diffusion coefficients (normal approach)
-  from measured diffusion profiles (new work)

**Notes:**
Title page and outline for talk. 
Acknowledge  co-authors 
Thank organizers
Workshop

## AIM Strategy

*Rapid Experiments *
* *
*Diffusion Multiples*
*** **Experiments & Characterization *
*Grain Size Experiments & Characterization*

- Ni

- W

- Ta

- NiAl

- R88

**Notes:**
Current motivation work; big picture
Review of AIM project and how NIST is involved.
GE --  land base turbines
Goal not only to rapidly develop materials models and use the models to predict mechanical properties, but also to the develop materials such that the process can be reverse.  That is, mechanical properties can be specified and the materials models can be used to develop the desired materials.  The important element in this process is that the material models are developed in such a way that designers have confidence in the models uncertainty predictions so that the develop materials can be used with less experimental testing needed to qualified the properties for use. 

The aspect of the project that is driving the current NIST work is the desire to correctly predicted gamma prime phase fraction, composition as function solidifcation practices and heat treatment.  Knowing the gamma prime composition and phase fraction distribution is critical for predicting the many of the mechanical properties, including strength and creep resistance. 

Critical issue:  With continuous cooling after casting:  multi-modal phase fraction distributions.  (PICTURE).  Need to predict this.   
The precipitation modeling is done using the Precipi-Calc software, which uses a multicomponent thermodynamics and diffusion mobilities to calculate second phase transformations.  This software code needs composition dependent diffusion coefficients of the matrix composition as an input.   The DICTRA software calculate these multicomponent diffusion coefficients, but it needed a diffusion mobility database to do so.  So NIST has developed a multicomponent diffusion mobility database for the Ni-rich fcc phase and now is the process of evaluating the database.  It is the challenges of evaluating the multicomponent diffusion database that I would like to focus on this morning.

## AIM Precipi-Calc simulation of multi-modal ’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
- Assume 3D spherical particle: need to add elastic energy effects
- t < 100 s low nucleation rate
- 100 s < t < 150 s  Primary ’ is formed
- 150 s < t < 350 s  Primary ’ grows
- 400 s Secondary ’ precipitates
- 500 s Tertiary ’ precipitates

**Notes:**
Precipi-Calc application of NIST diffusion database.

However, before the changes of multicomponent diffusion.  A brief review of the success that has been achieved using multicomponent thermodynamics and diffusion mobilities.

As I mentioned, Questek has developed a precipitation code that can predict the multi-modal gamma-prime size distribution.  I would just like present the result one such calculation.  Emphasizing that each temperature and grid point a composition dependent multicomponent diffusion matrix must be calculated for the matrix (gamma) phase.  

Review output.   Phase Fraction ,  Radius, Volume fraction,  Temperature profile  

->  Multi-modal distribution for continuous cooling of R88.

## Multicomponent Diffusion

***Review***

- Fick’s first law for Flux, *J**i*

- Fick’s second law

**Notes:**
Review of multicomponent diffusion.  

Fick’s second law (mass conversation)

So now that I have showed how one might use a multicomponent diffusion database in a real application. What do I mean by a multicomponent diffusion coefficient matrix...

For R88  (Interdiffusion:  n=Ni)   7x7 matrix  at each grid point at each temperature.

Need efficient way to store data.  Can’t store diffusion coefficient:  Used methodology of Kirklday and applied Agren and Anderson :  Define diffusion coefficients as the products of a diffusion mobility matrix and thermodynamic factor matrix.  

Develop diffusion mobility database.

## Multicomponent Diffusion Database Structure

- Inputs:
- Calphad Thermodynamics
- Diffusion experiments  (unary, binary, ternary systems)
- Tracer diffusivity,
- Intrinsic diffusivity,
- Interdiffusion coefficients/Marker motion
-  Optimize value of mobilities, *M**i* ,* *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)
- Add terms		  if necessary to fit ternary data, etc.

**Notes:**
How diffusion mobility database is constructed based on Calphad approach.

## Optimization of Experimental Diffusion Coefficients

**Experimental **
**diffusion data**

**Mobility  M=f (c,T)**

**Calculate diffusion **
**Coefficients D = f(c,T)**

- Distance

- Composition

**Diffusion profile **
**   ******** ****Diffusion Coefficient**

- Composition

- Log (Mobility)

- T = 1150 °C

- T = 1050 °C

- T = 950 °C

- Ni - Al

- For a binary:

**Notes:**
Optimization of diffusion coefficients to develop diffusion mobility database.   
Determine mobility parameters as a function of composition and temperature based available literature data defining binary and ternary diffusion quantities. 

## Examples of Optimized Binary Interactions Ni-Al-Cr-Co-Fe-Hf-Nb-Mo-Re-Ta-Ti-W

***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

**Notes:**
Results of diffusion mobility database development for fcc phase of Ni-rich phases.
Database includes Ni-Al-Co-Cr-Fe-Hf-Nb-Mo-Re-Ta-Ti-W.  
Examples of assessed mobility parameter fits to experimental data.

## Optimization of  Ni-W 

- Tracer diffusivity data

- Interdiffusion data

- Data from Karuanaratne et al., *Mater. Sci&Eng.* **281** (2000) 229.

- Data from Monma et. Al., *JIM*, **28** (1964) 197.

- Data from Monma et. Al., *JIM*, **28** (1964) 197.

**Notes:**
Binary Ni-W example of optimization base on diffusion coefficients

Green self diffusion

## Challenge: Analysis of Diffusion Multiples /Multicomponent Diffusion Cannot determine diffusion coefficients from experimental data 

**Notes:**
Multicomponent challenge.  

Note use mobility and thermodynamic database with DICTRA to simulate diffusion couple
Enter end compositions and geometry, time,temperature

Good fit on appear but how do we evaluate it .   Can we develop a method to assess the error associated with the mobility parameters

Mention workshops

## Example : René-88/IN-100; 1000 h at 1150 °C

***Example : René-88/IN-100; 1000 h at 1150 °C***

- Experimental data from J. C. Zhao,
- GE-GR, Schenectady, NY

- At 1150 °C equilibrium
- phase fractions
-   René-88: f = 1
-   IN-100: f = 0.638   f’ = 0.362

**Additional ********’ GE couples analyzed**:
- René-95/ René-88	ME3/IN718
- IN100/ME3		U720/IN718
- IN100/ René-88	René-95/U720
- IN718/IN100		U720/ME3
- René-95/IN718	ME3/ René-95
- ME3/ René-88	IN100/U720

**Notes:**
Example of multicomponent-multiphase diffusion couple.
Note gamma prime presence.  

## Diffusion Database Optimization Scheme

**Notes:**
Approach to develop optimization scheme base on composition profiles.

Note: Lars Hoglund with Thermo-Calc Software is also working on a similar code with uses a MatLab interface and has achieve similar results. 

## Test Example: Binary Ni-Co

*Interdiffusion Coefficient obtained by Boltzmann-Matano method*

**Notes:**
Test example: Ni-Co    Experimental data for system.

## Programming Elements and Inputs

***Programming Elements and Inputs***

-  Error Definition:

* **z**0 *= Error associated with location of Matano plane

-  Change selected mobility parameters

*a*

*b*

*W**i**(z)= *Weighting function
-  Currently set to equal 1

**Notes:**
Define programming elements and initial mobility parameter inputs

Error define as a least square fit.    Error between calculated and measured at each grid point 

Z0  describes error associated with defining the matano interface

Changing binary interactions and binary end members  (mobility of Co in pure Ni and mobility of Ni in pure Co)  

Constant temperature.

## Ni-Co: Optimization Results

**Notes:**
Results of binary optimization:  comparison of composition profiles.

## Optimization Results:  Diffusion Coefficient 

**Notes:**
Results of binary optimization:  Comparison of composition-dependent diffusion coefficient

If self diffusion coefficients were optimized could achieve better fit for the given experimental data.    

## Ternary Example:  Ni-5.13Al-9.77Cr/Ni-2.39Al-19.34Cr (at.%)

***Ternary Example:******  ******Ni-5.13Al-9.77Cr/Ni-2.39Al-19.34Cr (at.%)***

*For a single couple cannot determine the interdiffusion coefficients using the BM method*

- Reference

- Binary interactions zeroed

- T = 1100 °C
- t = 1000 h

- T = 1100 °C
- t = 1000 h

- Reference

- Binary interactions zeroed

**Notes:**
Ternary single phase example:   Ni-Al-Cr    Idealize 
Reference profile : DICTRA calculation with Ni-Al-Cr assessment by Engstrom and Agren  
Initial profile:  Change Al and Cr binary mobility parameters to zero.

## Diffusion Database Optimization Scheme

- 1 couple
- 2 profiles

- Changing 9 binary interactions

- Input Experimental File
- (Composition Profiles)

- Run DICTRA
- (via python)

- Thermodynamic
- Database

- Diffusion Mobility
- Database

- Compare composition profiles

- Calculate Error
- (via Mathematica)

- Minimize Error f(Mi)

- Change Mi Run new simulation

**Notes:**
Approach to develop optimization scheme base on composition profiles.

## Optimization Results: 9 parameters

- t = 1000 h

***Optimization Results: 9 parameters***

- AlAlCr=335000    CrAlCr= 487000 	   NiAlCr=211000
- AlAlNi=-166517   CrAlNi=-118000     NiAlNi=-23068
- AlCrNi=-53200    CrCrNi=-68000       NiCrNi=-81000

- Reference

- Binary Interactions zero

- T = 1100 °C
- t = 1000 h

**Notes:**
Optimization results: Comparison of composition profiles

## Goal:  Ni/Rene-88

***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

**Notes:**
Self explanatory:  Goal single phase multicomponent system

## Diffusion Database Optimization Scheme

- 1 couple
- 7 profiles

- Changing 2 binary end members
- 	     2 binary interactions

**Notes:**
Approach to develop optimization scheme base on composition profiles.

## Ti Profile from Ni/Rene-88

## Summary

- Multicomponent Ni-base diffusion mobility
- Based on optimization of available diffusion coefficient data
- Comparison of simulation results with experiments shows good agreement
- Optimization based on composition profiles
- Method
- Relates profiles to mobility parameters
-  Provides ability to asses error associated with mobility parameters
- 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/Rene88  (1 couples, fixed T, 7 profiles, 4 parameters, *z**0*)
- Improved optimization strategy needed
- Multicomponent single phase (*Need to consider more than 1 couple*)
- Multicomponent multiphase
- Programming additions needed
- Weighting functions
- Other error definitions

**Notes:**
Self-explanatory