23rd Annual Conference on Fossil Energy Materials – May 12-14, 2009 – Pittsburgh, PA

Computational Design and Experimental Verification of Refractory Metal-Based Alloys Ömer Doğan, Michael Gao, Wren Chan, Paul King

2

New Energy Conversion Technologies and High-Temperature Structural Materials

Melting ToC

Densityg/cm3

Cr 1863 7.2

Hf 2231 13.3

Os 3033 22.6

Ni 1455 8.9

V 1910 6.1

Rh 1963 12.4

Ru 2334 12.4

Ir 2447 22.6

Nb 2469 8.6

Mo 2623 10.2

Ta 3020 16.6

Re 3186 21.0

W 3422 19.3

Refractory Metals and Ni

500 600 700 800 900 1000 1100 1300 1400 15001200

Temperature (ºC)

Ferritic St.

Austenitic St.

Ni Based Superalloys

Refractory Metal Based Alloys

Next Generation USC Plant Syngas Turbines

Hydrogen Turbines

Oxy-Fuel Turbines

Turbine blade substrate metal temperature (oC) and temperature capability of structural materials

Pros and Cons of Refractory Metals

Good high-temperature strength

High thermal conductivity, low CTE

Low ductility at low temperatures thus difficult to fabricate

Poor oxidation resistance at high temperatures

Cr has good corrosion resistance due to formation of Cr2O3 scale

Cr is relatively abundant; Cr has low density; high thermal conductivity

3

Key Property Requirements

Ductility at low temperaturesRequired for processing e.g. machining, rolling.ElongationArea reduction

Fracture toughness (i.e., resistance against crack propagation)

Minimum: 15-20MPa√m; preferred: ≥20-25MPa√m for structural applications

Creep resistance at high temperaturesCorrosion resistance against internal and external oxidation and nitridation at high temperatures

4

Cr Alloys Development

Holzwarth et al. J. Nucl. Mat. 300 (2002) 161Cr-5Fe-1Y2O3: 6.4MPa√m; DBTT 400-500oCCr-44Fe-5Al-0.3Ti-0.5Y2O3: forms dense Al2O3 surface layer, very brittle

Brady et al, ORNL, Script. Mater. 52 (2005) 815 and moreVarious Cr-Nb, Cr-Ta, Cr-Ni, Cr-Fe alloysCr-30Fe-6.3Ta-4Mo-0.5Ti-0.3Si-0.1La, 20MPa√m and 350 MPa at 1100oCCr-6wt%MgO-0.75wt%Ti: 10% elongation at RT (hot pressed and extruded)Cr-45Fe-6MgO-0.75Ti (wt%): 1% elongation and 650MPa@RT

5

What Controls Ductility of Metals?

Electronic properties of a solid determine its intrinsic mechanical property.Delocalized, mobile electrons contribute to high ductility; localized, immobile electrons cause low ductility.Formation of flexible bonds contribute to high ductility; strongdirectionality of bonds causes low ductility.Poisson’s ratio is commonly used as a ductility indicator. Metals with higher Poisson’s ratio tend to be more ductile. Rice-Thompson parameter is another ductility criterion. It considers the ease of dislocation emission compared to crack growth. The lower its value is, more ductile the metal will be.Other parameters include unstable twinning, dislocation mobility, etc.

6

Poisson's ratio

0.0 0.1 0.2 0.3 0.4 0.5

Elon

gatio

n (%

)

0

10

20

30

40

50

60

70 BeCrPuURuOsReRhIrThZnMgWCdMoCaCoNiZrTaAlCuTiHfAgVPdNbAuPtPbTl

Data from refs. [1]. S.F. Pugh, Phil. Mag., 45 (1954) 823; and [2]. Smithells Metals Ref. Book, 7th Ed. 1992

Elongation vs. Poisson’s Ratio

7

Poisson’s ratio Phil. Mag. Lett. 85 (2005) 77

Amorphous metals

0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.1

0.2

0.3

0.4

0.5

)/(26)/(23

BGBG

+−

=ν

G/B

νDesirable: high B, low GPoisson ratio measures the intrinsic properties of a solid. It can be predicted from first principles DFT calculations.

8

Validation of Computation

0

50

100

150

200

250

300

350

Al Zr Hf Nb Cr Ta Mo W

Bul

k M

odul

us (G

pa)

Cal.Exp.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

V Cr Nb Mo Ta W Al

Pois

son'

s ra

tio

CalExp

Bulk modulus

Poisson ratio

0

50

100

150

200

250

300

350

400

450

500

C11 C12 C44

Elas

tic c

onst

ants

(GPa

)

calexp[1][2][3]

Elastic constants

JOM 2008;60(7);61

[1] Phys Rev B 54 (1996) 4519 (tight binding)[2] Phys Rev B 62 (2000) 5136 (DFT full potential)[3] Phys Rev B 67 (2003) 134204 (DFT full potential)

9Nb V Ta Mo W

Pois

son

ratio

0.0

0.1

0.2

0.3

0.4

0.5

(a)

0.33

Nb V Ta Mo W

Ric

e-Th

omps

on ra

tio

0

2

4

6

8

10

12

14

16

(b)

)/(26)/(23

BGBG

+−

=ν

CB.Geller et al, Scripta Mater 52 (2005) 205, “A computational search for ductilizing additives to Mo)”

}110{

111[}110{

γ

><

=−bGTR paramter

}110{G><111b}110{γ Surface energy of (110) plane

J.R. Rice and R. Thomson: Ductile versus brittle behavior of crystals, Philosophical Magazine, 1974, 29, p.78.

General Hook’s law

Rice-Thompson ParameterPoisson’s Ratio

Shear modulus of (110) plane

Burgers vector along [111] direction

[ ])(1jjkkiiii E

σσνσε +−=

Poisson's ratio is the ratio of the relative contraction strain divided by the relative extension strain

brittle

ductile

[this study]

10

Zr Hf V Nb Re

Cha

nge

in P

oiss

on a

nd R

-T ra

tios

(%)

-60

-40

-20

0

20

40

60

ΔμΔR-T ratio

[1] CB.Geller et al, Scripta Mater 52 (2005) 205, “A computational search for ductilizing additives to Mo)”

Mo1X1 alloys [this study]

Mo3X alloys [1]

Ductilizing Mo via alloying

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Poisson ratio

Enthalpy

Moduli

Volume

Ti, V, Fe, Co, Ni, Zr, Nb, Mo, Ru, Rh, Pd, Hf, Ta, W, Re, Os, Ir, Pt

Ti, V, Fe, Co, Ni, Mo, Ru, Rh, W, Re, Os, Ir, Pt

Solubility

Cost

Major Constituents

X XX XX

X XXX XX

Ti, V, Fe, Co, Ni, Mo, W

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Cr-V-X Ternary Alloys

0.386

0.358 0.357 0.3560.339 0.337

0.318 0.318 0.31

0.276

0.244

0.4040.4090.4190.42

0

0.1

0.2

0.3

0.4

0.5

CrV_#

1CrV

_#2

CrV_#

3CrV

_#4

CrV_#

5CrV

_#6

CrV_#

7CrV

_#8

CrV_#

9CrV

_#10

CrV_#

11CrV

_#12

CrV_#

13CrV

_#14

CrV_#

15Po

isso

n's

ratio

13

Cr-Fe-X Ternary Alloys

0.3420.332

0.309

0.3790.358

0.3470.324

0

0.1

0.2

0.3

0.4

0.5

CrFe_#1 CrFe_#2 CrFe_#3 CrFe_#4 CrFe_#5 CrFe_#6 CrFe_#7

Pois

son'

s ra

tio

14

Cr-Mo-X Ternary Alloys

0.3350.32 0.319 0.317

0.37

0

0.1

0.2

0.3

0.4

0.5

CrMo_#1 CrMo_#2 CrMo_#3 CrMo_#4 CrMo_#5

Pois

son'

s ra

tio

15

Cr-Quartenary Alloys

0.324

0.303

0.328 0.334 0.3310.318

0.3540.345

0.363 0.3610.375

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Fe Ga Hf Mn Mo Re Si Ta Ti W Zr

Pois

son'

s ra

tio

16

Cr-Quinnary Alloys

0.324 0.325 0.3190.332

0.3750.3590.3650.368

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Al Fe Ga Mn Re Si Ti W

Pois

son'

s ra

tio

17

Cr-Hexagonary Alloys

0.281

0.324 0.332 0.330.35

0.3940.383

0.3980.39

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Fe5 Al Fe Ga Si Ti Mn Re W

Pois

son'

s ra

tio

18[12] J T Lenkkeri and E E Lahteenkorva, J. Phys. F: Metal Phys.. Vol. 8, No. 8, 1978, “An investigation of elastic moduli of vanadium-chromium alloys”

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Al Al

Al Al

Ti Ti

Ti Ti

Cr Cr

Cr Cr

bcc Cr15Al1

bcc Cr

Charge Density Plot: (1 1 0) Plane

bcc Cr15Ti1

[0 0 1]

[1 1 0]

[1 1 1] [1 1 1]

0.020.05

0.07

Cr Cr

Cr Cr

Cr Cr

Cr Cr

Cr Cr

Cr Cr

Cr

Cr

Cr

Cr

Cr

Cr

Cr

Cr

Cr

CrCr CrCr

CrCr

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SummaryPoisson ratio calculations agree with Rice-Thompson parameter calculations on selected pure elements and Mo binary alloysElastic properties of 25 binary, 27 ternary, 28 higher order Cr alloys were theoretically examined:– all transition metals selected enhance ductility of binary Cr alloys

while IIIA/IVA elements lower it– Calculation method verified

Most favorable elements in binary alloys are Ti, Zr, Hf, Nb, V, Ta– These alloys have a higher DOS at Fermi level– They tend to delocalize electrons.

Al tends to lower the ductility:– The alloy has lower DOS at Fermi level– Possible bond formation along <1 1 1> in the {1 1 0} plane.

Enhancement in bond directionality usually deteriorates ductility.

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Thermodynamic Assessment of Cr-RE,Mo-RE and V-RE Systems

22

Cr-Rare Earth Elements Alloys

• Rare earth elements are added to:– Absorb residual oxygen contents in the matrix and

thus enhance ductility.– Form rare earth oxides that strengthen the matrix and

enhance creep resistance • There are no accurate thermodynamic databases for

Cr-rare earth systems• There are no compound formation in these systems.• Insufficient experimental data on terminal solubility• Discrepancy in melting point of Cr

– 1907 or 1863oC?

23

Calculated Cr-La System

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Problems with La-rich Cr-La System

4-phase equilibria at 865oC:L, γLa, βLa, and Cr

Case a: Eutectic reaction: L Cr+γLaEutectoid reaction: γLa Cr+βLa

Case b: Eutectic reaction: L Cr+βLaPeritectic reaction: L+ γLa βLa

25

Calculated Cr-Y System

H. Okamoto: Journal of Phase Equilibirum, 1992, vol. 13, no. 1, pp. 100-101.

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Mo-Y

Ce-Mo La-Mo

Mo-RE Systems

27

Y-V

Ce-V La-V

V-RE Systems

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Summary• Cr-Ce, Cr-La and Cr-Y are thermodynamically assessed

– Self-consistent thermodynamic databases are obtained.– Current study predicts a likely peritectic reaction in the La-rich side

of the Cr-La system: L2+δLa βLa, which resolves the ambiguity of the currently accepted phase diagram.

– It also predicts a possible catetectic reaction in the Y-rich side of the Cr-Y system: βY L2+αY.

– Work on the Mo-RE and V-RE systems is continuing.• Future work needed:

– Melting point of high-purity Cr.– Polymorphic transformation temperature of γCe ↔ βCe.– La-rich side Cr-La phase diagram.– Y-rich side of Cr-Y phase diagram

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Milestones

• Evaluate promising Cr ternary systems using CALPHAD modeling, DFT total energy calculations, and experiments (09/30/2009)– In progress.

• Complete ductility calculations and experimental verifications on Cr based ternary and higher order alloys (09/30/2009).– Computational work is complete.– Experimental work is in progress.

• Identify second phase particles potentially increasing creep strength in a promising Cr based multi component system (09/30/2009). – In progress.

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DeliverablesPeer-reviewed journal articles

• First Principles Study of the Mechanical Properties of Mo-50at%X (X=Zr, Hf, V, Nb, Re) Alloys, Michael C. Gao, Ömer N. Doğan, Paul King, Michael Widom, To be submitted to ScriptaMaterialia (May 2009).

• Elastic and Thermodynamic Properties of Cr-V Binary Alloys Predicted from First Principles Calculations, Michael C. Gao, Ömer N. Doğan, Paul King, To be submitted to Scripta Materialia(May 2009).

• Thermodynamic Assessment of Cr-Rare Earth Systems, Wren Chan, Michael C. Gao, Ömer N. Doğan, Paul King, Anthony D. Rollett, Accepted for publication in Journal of Phase Equilibria and Diffusion (2009).

• The First-Principles Design of Ductile Refractory Alloys, Michael C. Gao, Ömer N. Doğan, Paul King, Anthony D. Rollett, Michael Widom, Journal of Metals, 2008, 7, 61-65.

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DeliverablesArticles in Conference Proceedings

• Integrated Design of Chromium Based Alloys for Fossil Energy Applications, Michael C. Gao, Ömer N. Doğan, Paul King, Proceedings of The 17th PlanseeSeminar, Reutte, Austria, May 25-29, 2009.

• Computational Design and Experimental Verification of Refractory Metal-Based Alloys, Proceedings of the 23rd Annual Conference on Fossil Energy Materials, Pittsburgh, PA, May 12-14, 2009.

• First Principles Design of Ductile Refractory Alloys: Ductility Criteria, Michael C. Gao, Ömer N. Doğan, Paul King, Supplemental Proceedings of the 138th Annual Meeting: Volume 1: Fabrication, Materials, Processing and Properties, TMS, 2009, 157-163.

• Thermodynamic Assessment of Cr-Rare Earth Systems, Wren Chan, Michael C. Gao, Ömer N. Doğan, Paul King, Supplemental Proceedings the 138th Annual Meeting: Volume 2: Materials Characterization, Computation and Modeling, TMS, 2009, 55-61.

• Integrated Design and Rapid Development of Refractory Metal-Based Alloys for Fossil Energy Applications, Proceedings of the 22nd Annual Conference on Fossil Energy Materials, Pittsburgh, PA, July 8-10, 2008.

• First Principles Design of Ductile Refractory Alloys, Michael C. Gao, Anthony D. Rollett, Michael Widom, Ömer N. Doğan, Paul King, Supplemental Proceedings of the 137th Annual Meeting: Volume 1: Materials Processing and Properties, TMS, 2008.

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DeliverablesPresentations

• Computational Design of High Performance Refractory Alloys for Ultra-High Temperature Applications: a Bottom-up Approach, Michael C. Gao, Ömer N. Doğan, Paul King, AeroMat’09, Dayton, OH, June 6-11, 2009.

• Integrated Design of Chromium Based Alloys for Fossil Energy Applications, Michael C. Gao, Ömer N. Doğan, Paul King, the 17th Plansee Seminar, Reutte, Austria, May 25-29, 2009.

• Computational Design and Experimental Verification of Refractory Metal-Based Alloys, the 23rd Annual Conference on Fossil Energy Materials, Pittsburgh, PA, May 12-14, 2009.

• Materials Development for Future Energy Conversion Systems, Ömer N. Doğan, Michael C. Gao, Paul King, presented at Materials Science Seminars at Oregon State University, Corvallis, OR, February 26, 2009.

• First Principles Design of Ductile Refractory Alloys: Ductility Criterion, Michael C. Gao, Ömer N. Doğan, Paul King, presented at TMS Annual Meeting & Exhibition, February 15-19, 2009, San Francisco, CA.

• Thermodynamic Assessment of Cr-Ce, Cr-La, and Cr-Y Systems, Wren Chan, Michael C. Gao, Ömer N. Doğan, Paul King, Anthony D. Rollett, presented at TMS Annual Meeting & Exhibition, February 15-19, 2009, San Francisco, CA.

• Computational Design of Refractory Alloys for Fossil Energy Applications, M.C. Gao, O.N. Dogan, P. King, presented at the 4th International Conference of Multiscale Materials Modeling, Tallahassee, FL, USA, October 27-31, 2008.

• Multiscale Computational Design of Ductile Refractory Alloys for Moderrn Fossil Energy Applications, M.C. Gao, O.N. Dogan, P. King, presented at the Materials Science & Technology 2008 Conference and Exhibition (MS&T’08), Pittsburgh, PA, USA, October 5-9, 2008.

• Integrated Design and Rapid Development of Refractory Metal-Based Alloys for Fossil Energy Applications, the 22rd Annual Conference on Fossil Energy Materials, Pittsburgh, PA, July 8-10, 2008.

• First Principles Design of Ductile Refractory Alloys, Michael C. Gao, Anthony D. Rollett, Michael Widom, Ömer N. Doğan, Paul King, presented at TMS Annual Meeting & Exhibition, March 9-13, 2008, New Orleans, LA.