1. Ni-Al-Mo Single Crystal Rafting Studies
Shuwei Ma, Tresa.M.Pollock
The University of Michigan, Ann Arbor, MI
MEANS Group Meeting, Columbus, OH
April, 4, 2007

2. Previous Models of Rafting
Elastic model
Rafting direction is determined by the sign of lattice misfit, modulus mismatch and applied load direction. γ’
P type rafting
Plastic-elastic model γ
Take into account the contribution from plastic deformation in γ channels (continuum). Rafting direction is determined only by the sign of lattice misfit and applied load direction.
N type rafting

3. Accounting for Local Stress Fields with Phase Field Model
Phase field modeling was applied to evaluate elastic and plastic driving force in the Ni-Al-Mo system.
External applied stress
Dislocation
configuration
Microstructure
Stress Field
Misfit stress
Dislocation stress
Dislocation movement
Microstructure evolution
Initial channel filling and relaxation: PF dislocation model
Rafting: PF binary diffusion model
Stress due to modulus mismatch
Modulus mismatch between /’
Michael Mills’s plot

4. Objective
Provide a complete experimental data set in model Ni-Al-Mo single crystals for phase field modeling.
This information includes:
Misfit (sign and magnitude)
Plastic strain processes in g matrix
Elastic modulus
Diffusion
Rafting kinetics

5. References
Many properties have already been measured in a large set of Ni-Al-Mo single crystals
M.Fahrmann, W.Hermann, E, Fahrmann, A.Boegli, T.M.Pollock. Materials Science and Engineering A260 (1999) pp
O.Paris, M.Fahrmann, E.Fahrmann, T.M.Pollock and P.Fratzl. Acta mater. Vol.45, No.3, 1997, pp
M.Fahrmann, E.Fahrmann, O.Paris, P.Fratzl, and T.M.Pollock. Superalloy 1996, pp
M.Fahrmann, P.Fratzl, O.Paris, E.Fahrmann and W.C.Johnson. Acta Metall.Mater, Vol.43, No.3, pp
M.Fahrmann, E.Fahrmann, T.M.Pollock, W.C.Johnson. Metallurgical and materials Transactions A. pp

6. Experimental Methods
1. Observation of rafting and coarsening of g’ precipitate:
SAXS (small angle X-ray scattering)
Quantitatively image analysis on TEM and SEM ( Fourier Analysis)
2. Misfit measurement
Hot stage X-ray diffraction on over-aged sample, unconstrained misfit. (210) diffraction.
3. Elastic Constant measurement
Free-free beam resonance technique.
4. Diffusion data

7. Ternary Ni-Al-Mo Phase Diagram
Single Crystal Compositions 
Vg’60%
Vg’10%

8. Coherency Stress and Precipitate Coarsening in Ni-Al-Mo Alloys
Vg’0.1 

9. Coherency Stress and Precipitate Coarsening in Ni-Al-Mo Alloys
13 at% Mo
8 at% Mo
5 at% Mo
The coarsening rate decreases with increasing Mo content of alloy
A change in the rate controlling mechanism of coarsening from long range diffusion of Al to long range diffusion of Mo in this series of alloys.

10. Misfit And Rafting in Experimental Alloys

11. Misfit and Rafting in Experimental Ni-Al-Mo system
R1, Positive misfit d > 0
R3, Negative misfit, d < 0
Elastic and plastic rafting models can predict these observation.
Do rafting kinetics distinguish elastic and plastic effects?

12. Young’s Modulus

13. Elastic Stiffness of g and g’ phases in Ni-Al-Mo

14. Elastic Modulus Mismatch
R3, d=-0.5%
R1, d=+0.5%
For Elastic model:
For elastically anisotropic materials, the term Eg’-Eg has to be replaced by the differential C*, i.e, (C11-C12)g’- (C11-C12)g

15. Average Precipitate Aspect Ratio During Creep
Creep condition: 980°C/130MPa.
For Elastic model:
R1 alloy with positive misfit has a lower rate of rafting in spite of less Mo. C*R3>C*R1. Effect of elastic modulus mismatch?

16. Role of Matrix Plasticity in the Rafting Kinetics
Ni-13.3Al-8.8Mo (at%)
Misfit, d=-0.5%,
Vg’=0.60

17. Microstructure Evolution During Stress Annealing and Aging for Pre-strained interface
The microstructure in samples pre-strained in tension or compression rafted during subsequent aging in a direction as if the former load was still present, whereas a sample with isotropically relaxed interfaces did not show directional coarsening;
The microstructure in a sample pre-strained in tension rafted under an applied compressive stress initially in a direction opposite to what is generally observed in compression for this alloy.
Kinetics and the driving force of rafting are greatly affected by the state of the g/g’ interfaces.

18. Suggestions
Channel dislocations and modulus mismatch could both affect the rafting. This may be reflected in differences in rafting kinetics.
It is necessary to combine channel dislocations and modulus mismatch to evaluate their relative contributions via phase field modeling.
Does phase field modeling have sufficient fidelity to evaluate elastic + plastic driving force in the Ni-Al-Mo system?

19. THANK YOU!

20. Microstructure Evolution During Aging (980C/4hrs)
State a
2mm
State c
2mm
State b
2mm
State d
2mm

21. Microstructure Evolution During Compression Creep (980C/130MPa)
1hrs
8hrs
1mm
1mm
Initially fully coherent
(State a)
partially coherent,
pre-strain in tension
State b

22. Microstructure Evolution During Stress Annealing and Aging for Pre-strained interface
1mm
1mm
Stress annealed
in compression
Ordinary ageing