Applications of Ab Initio Modeling to Materials Science ... - OSTI.GOV

LM-04K037 May 27, 2004

Applications of Ab Initio Modeling to Materials Science: Grain Boundary Cohesion and Solid State Diffusion GA Young, R Najafabadi, W Strohmayer, J Vollmer, C Thompson, W Hamm, C Geller, E Wimmer, J Sticht, A Mavromaras and J Harris

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Applications of Ab Initio Modeling to Materials Science: Grain Boundary Cohesion and Solid State Diffusion Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

George A. Young, Reza Najafabadi, Walter Strohmayer, James Vollmer, Charles Thompson, William Hamm

Lockheed Martin Corporation Schenectady, NY 12301-1072 Clint Geller

Bechtel Bettis, Inc. West Mifflin, PA 15122-0079 Erich Wimmer, Jurgen Sticht, Alexander Mavromaras, John Harris

Materials Design Inc. Angel Fire, NM 87710-1318 1

Background „

I. Grain boundary cohesion „

„

„ „

Metallurgical understanding Account for multiple elements Effect of H concentration Mechanisms of embrittlement „ „

He embrittlement SCC resistance

„

II. Solid State Bulk Diffusion „ „

„

„

„

Work of Wolverton et al. Proof of principle for H in nickel Determination of D0 and Q from first principles H diffusion in HCP Ti and Zr H diffusion in FCC Fe – effect of lattice parameter

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Computational Procedure: Pure nickel, Σ5{100} twist grain boundary, 0 K

Relaxation of pure grain boundary

(

Determination of impurity site and relaxation

∆ EGriffith = ESurface − E

impurity Surface

Cleavage

)

Relaxation of free surfaces

 impurity  −  EGrain − EGrain  Boundary   Boundary

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Geometry of impurity atoms on nickel Σ5 {100} Interstitial impurities pure Ni

H

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

B

C

4

Geometry of impurity atoms on nickel Σ5 {100} Substitutional impurities He

P

S

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

Cr

Fe

5

Structure / energy mapping: degree and extent of electronic interactions Electronic charge changes around a P impurity atom in Ni

(a)

Gain (red), loss (green)

(b)

Gain

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

(c)

Loss

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Tendency to migrate to grain boundary, surface, or bulk (Note boron)

Segregation Energy (kJ/mol)

500.0 Impurity Prefers the Grain Boundary or Free Surface

Grain boundary Surface

400.0

300.0

200.0

100.0

0.0 La

He

O

Pb

Li

S

H

C

Zr

P

Fe

Mn

Nb

Cr

Mo

B

Impurity Prefers the Bulk

-100.0

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Fundamental effects of impurities on grain boundary strength Griffith Energy (J/m2)

4.5 4.0

Strengthens Grain Boundary

3.5 Weakens Grain Boundary

3.0 2.5

H +B

+P H

H +C

+L i H +S

B

H

M o

r C

b N

Fe M n

P

Zr

C

H

Li

Pb

O

e H

La

S

Impurity Atom or Atom Pair

N iS

N ig ick m e a- l { 0 5 {0 01} 01 ) T Pla w ne is tG B

2.0

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Metallurgical strengthening of grain boundaries „

Boron a known strengthener of Ni grain boundaries

„

Theories (Donachie from Superalloys Source Book): „ „

„

Boron alters grain boundary precipitate structure Boron has a beneficial interaction with a deleterious element (e.g. ties up sulfur ?) Boron reduces the grain boundary diffusivity (slows S segregation ?)

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Why does boron promote grain boundary strength (but carbon doesn’t) ?

B-2p electrons overlap with Ni-3d → bonding Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Mechanism of “He Embrittlement” 10 5 „

„

„

B + n → Li + He 1 0

After irradiation and annealing, He bubbles on nickel grain boundaries have been observed But you embrittle before you observe physical bubbles – intrinsic He embrittlement (see Mills et al.) Need to assess B loss and Li embrittlement, kinetics of He and Li diffusion

7 3

4 2

α n

B

Li

Bill Mills et al. 7th Env. Deg. Proceedings

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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B loss + Li embrittlement + He embrittlement Boron transmutation releasing helium and lithium

~1 µm

α B

Boron loss, helium atoms, and lithium atoms all lower the grain boundary toughness

~3 µm

Li

Li n

Helium and lithium collect at the grain boundary. Is the rate of Li > He?

Li He

He

¤ Need to understand kinetics of Li and He migration back to grain boundary Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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He and Li embrittlers, B strengthener Griffith Energy (J/m2)

4.5 4.0

Strengthens Grain Boundary

3.5 Weakens Grain Boundary

3.0 2.5

H +B

+P H

H +C

+L i H +S

B

H

M o

r C

b N

Fe M n

P

Zr

C

H

Li

Pb

O

e H

La

S

Impurity Atom or Atom Pair

N iS

N ig ick m e a- l { 0 5 {0 01} 01 ) T Pla w ne is tG B

2.0

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Effect of H concentration on cleavage energy with and without S and P impurities 4.0

„

„

No significant synergistic effects S and H act additively

)

3.5

-2

Linear superposition good first approximation

Cleavage Energy (J m

„

Ni Σ5(001)

P+H

3.0 only H S+H

2.5

2.0

1.5 0

20

40

60

80

100

H Concentration (%) Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Need to account for multiple effects: (1) GB strength and (2) effect on H uptake

KI @ max load (ksi%in)

120

X-750 BH Data from Grove and Petzold Precracked Subsize Charpy Specimen 200oF Distilled Water Each datapoint is a different heat

100

80

60

40 1

2

3

4

5

Grain Boundary Phosphorus (at. %) Relative Grain Boundary Strength = − 4.86[ He] − 3.77[ Pb] − 1.58[ Li ] − 1.00[ H ] − 0.86[C ] − 0.18[ Zr ] + 0.23[ P] + 0.41{Fe] + 0.45[ Mn] + 1.09[ Nb] + 1.27[Cr ] + 2.64[ B] Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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SCC of X-750: Similar heats with different response to SCC initiation and growth X-750 Condition HTH (2025oF/1hr + 1300oF/20 hrs) Heat A B

Ni 72.43 71.47

Cr 15.54 15.25

Fe 7.93 8.15

Ti 2.60 2.66

Heat A (Good) B (Bad)

Al 0.79 0.73

YS (ksi) 118 117

Mn 0.07 0.15

UTS (ksi) 172 176

C 0.039 0.043

B 0.0037 0.0022

P 0.007 0.002

% El

%RA

27 26

32 36

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

S 0.001 0.002

Nb+Ta 0.86 0.97

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Heat “B” shows shorter initiation times and faster crack growth rates

# of Failed Specimens

5

500 days Exposure

1000 days Exposure

0/4

3/4

Heat

CGR at 680oF K=35 ksi√in

A

1.1 mils/day

B

1.8 mils/day

4

3/4

4/4

3

2

1

0 Heat A A Heat

Heat BB Heat

Heat A A Heat

Heat BB Heat

X-750 HTH, 90 ksi Net Section Stress, T=640oF

See Young et al. in 11th International Symposium on Environmental Degradation of Materials in Nuclear Power Systems – Water Reactors, Skamania, WA, August 2003. Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Heat A - typical Cr23C6 carbides Heat B - unusually high # of Ni23B6 Loss of atomic boron „

No Cr depletion around borides

Heat A

Heat B

M23C6

„

Ni23B6

Faster SCC initiation and growth „

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Summary „

Ab Initio atomistic modeling gives unique insight into metallurgical effects „

„

„

Explain alloying effects: Boron intrinsically strengthens Ni grain boundaries by helping to fill the Ni 3d orbital De-convolute complex embrittlement phenomena: boron transmutation / stress corrosion cracking Quantitatively assess the effects of multiple grain boundary impurities

Embrittling

Neutral

Strengthening

Al He O Pb Li S H C Zr P Fe Mn Nb Cr Mo B Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Ab Initio Modeling of Solid State Diffusion: Hydrogen in Structural Metals

20

Ab initio modeling of solid state diffusion „

Phonon capability in MedeA/VASP is a significant advance, allowing accurate determination of things like enthalpy, and entropy as a function of

temperature Æ free energy

„

„

Phonons enable first principles studies of diffusion, solubility, etc. that are often experimentally difficult and subject to significant controversy, e.g. H diffusion in Al, Ti, O solubility in Ni, etc. Examples „ „

Chris Wolverton on H in Al Present work on H in Ni, Ti, Zr, and Fe

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Experimental difficulties in diffusion „ „ „ „ „

„

„

Often large noise / small signal Oxide or other surface films often diffusion barriers Effects of traps often not considered May be difficult to ensure “lattice diffusion” control Electrochemical methods: charging solutions can degrade sample (pitting) Vacuum methods: time lag between charging and measurement etc., etc.

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Hydrogen diffusion in aluminum

„

„

„

Young and Scully, Acta Mat. Vol. 46, No. 18, pp. 63376349 Wolverton et al., Phys. Rev. B, 69, 144109, 2004

-7

10

600

0

20

10-3

D -8

10

10-4

A E

C

B

-9

10

10-5

10-10

H*

F K

I

-11

10

10-6 Lattice F

10-7

J A Eichenauer 61 B Matsuo 67 C Ishimura 79 D Papp 81 E Outlaw 82 F Hashimoto 83 G Ichikawa 86 H* Maienschein 88 I Saitoh 94 J Braun 94 K Present Work

-12

10

10-13 -14

10

10-8 Dislocations

Vacancies G

* Diffusivity of hydrogen, estimated from tritium permeability data

-15

10

1.0

1.5

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

2.0

2.5

3.0

3.5

Diffusivity (cm 2 /sec)

„

H diffusion both fundamental and technically important to Al and Al alloys Large controversy in literature See:

D iffusivity (m 2 /sec)

„

Temperature (oC) 400 300 200 100

10-9 10-10 10-11 4.0

3 -1 1/T x 10 (K )

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Barrier for lattice diffusion is relatively low, vacancies are strong trapping states

Ed#1 Ed# 2 Ed#3 Desorption Energies in Aluminum (kJ/mol) Researcher Young (experimental) Wolverton (ab initio)

Lattice

Dislocation

Vacancy

15.3 ±4.8

43.5 ±17.5

84.8±32.2

17

---

52

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Diffusion Equation – see Wert and Zener Phys. Rev. Vol. 76, No. 8, Oct. 15, 1949, pp. 1169-1175.

„ „

„ „ „ „ „

n: α: a: ν: ∆S: ∆H: R:

D = n α a 2 ν exp{∆S / R} exp{− ∆H / R T } 144424443 D0 number of nearest neighbor jump sites numeric coefficient that depends on the location of the interstitial positions lattice parameter (net jump distance, l) vibrational frequency activation entropy activation enthalpy (Q) gas constant, T: temperature

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Diffusion procedure: consider temperature dependence of ∆S and ∆H (and ν)

D = n α l ν exp{∆S (T ) / R} exp{− ∆H (T ) / R T } 2

„ „ „ „ „

Determine low energy site n, α, and l Determine low energy path Vibrational frequency (relatively T independent) } ν Entropy change f (T) } ∆S Enthalpy change f (T) } ∆H

}

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Octahedral site and indirect diffusion path via transition state

O’

0.0

TS’

84.0

M

T TS

O

44.3 49.1

0.0

28.8 37.4

44.3 49.1 kJ/mol

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Vibrational frequency via VASP/Phonon pure Ni

„

„

„

Frequency at stable octahedral site =25.8 THz Frequency in tetrahedral site =39.9 THz (less space than octahedral interstice) At the transition state, negative eigenvalue → imaginary frequency

Ni – Hoct

Ni – HTS

Ni – Htet

49.9 THz

50

39.3 THz

40

30

25.8 THz

20

10

0

R

X Γ M R

Γ R

X Γ M R

Γ Γ

L

Z

Γ R

X Γ M R

Γ

-10

-20

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

-22.6 THz

28

Temperature has little effect on the vibrational frequency of H in nickel (0 K to ~1000 K) a = 3.492 Å (T=0)

a = 3.581 Å (2.5 % expanded)

30 25.8 THz 21.3 THz 20

10

0 R

X

Γ

M

R

Γ

R

X

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

Γ

M

R

Γ

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∆S and ∆H vary with temperature. Typical assumption of constant D0 is an approximation Hydrogen in Nickel Octahedral Interstice 3000

2000

2500

1000

2000 1500 1000 500 0

Energy (kJ/mol)

Entropy (J/mol-K)

Temperature (oF) 0

500

1000

1500

2000

2500

3000

H

0 -1000

S

-2000

A

-3000 -4000

Entropy Energy

-5000

0

500

1000

Temperature (K) Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

1500

2000 30

Variation of Q and D0 with temperature: note “balance” at temperatures >200 K

H Diffusion in Nickel

0.08

0.96

0.06

0.94

0.04

2

exp(-Q/RT)

0.98

D0 (cm /sec)

0.10

1.00

D0 0.92

0.02

0.90

0.00 2000

0

500

1000

1500

Temperature (K) Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Excellent agreement between first principles calculations and experimental methods o

Diffusivity (cm2/sec)

55

14 0

26 0

44 0

74 0

10-3

13 40

Temperature ( F) TCurie=676oF

10-4

Best fits to experimental data above and below TCurie [Volkl]

10-5 10-6 10-7

The Present Study Data of Bockris 1970

10-8 10-9

Experiment Calculation

0. 00 35

0. 00 30

0. 00 25

0. 00 20

0. 00 15

0. 00 10

0. 00 05

10-10 -1

1/T (K ) Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Large disagreement in experimental data for αTi. Modeling line gives an impressive “best fit” 55

14 0

26 0

44 0

74 0

10-3

13 40

Temperature (oF)

Diffusivity (cm2/s)

10-4 10-5

Wasilewski 1954 Q=51.8 kJ/mol Papazoglou 1969 Q=61.5

10-6

Kolachev 1969 Q=46.0 Phillips 1974 Q=60.3 Brauer, 1976, 1982 Q=31 Nazimov 1976 Q=23.85 Nazimov 1976 Q=57.74 Doerr 1979 Kunz 1982 Q=46.6 Abdul-Hamid 1996 Present Study

10-7 10-8 10-9 10-10 10-11

Hydrogen Diffusion in α-Ti 0. 00 35

0. 00 30

0. 00 25

0. 00 20

0. 00 15

0. 00 10

0. 00 05

10-12

Reciprocal Temperature (K-1) Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Limited data for H in α-Zr. Results for H in Ni and α-Ti give confidence that modeling is accurate

55

14 0

26 0

44 0

74 0

10-3

13 40

Temperature (oF)

Diffusivity (cm2/s)

10-4 10-5

oct-TS-oct

10

-6

Mazzolai 1976 Q=56.9 kJ/mol Kearns 1972 Q=44.59 Present Study

10-7 10-8 10-9

Hydrogen Diffusion in α-Zr

10

0. 00 35

0. 00 30

0. 00 25

0. 00 20

0. 00 15

0. 00 10

0. 00 05

-10

Reciprocal Temperature (K-1) Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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For γ-Fe: Larger than typical error between calculated and experimental lattice parameter

Metal

Computed Lattice Parameters (Å)

Experimental Lattice Parameters (Å)

Deviation (%)

Ni

a=3.492

3.5239

-0.9

Ti

a=2.904 c=4.652

2.950 4.683

-1.6 -0.7

Zr

a=3.213 c=5.210

3.233 5.148

-0.6 +1.2

γ-Fe

a=3.433

3.6599

-6.2

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Calculations for H diffusion in γ-Fe highlight the strong effect of the lattice parameter, a 70 Activation Energy (kJ/mol)

Hydrogen Diffusion in γ-Fe 65 60 55 50 45 40

VASP GGA Experimental a=3.43 Angstroms

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

VASP with lattice parameter forced to a=3.53 Angstroms

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Summary of parameters

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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Summary „

„

Excellent agreement between first principles calculation of H diffusion in nickel Calculations help resolve controversy in systems where experimental data are in disagreement: „

H in α-Ti

and guide predictions where there are sparse data: „

„

„

„

H in α-Zr

Results for H in γ-Fe show strong influence of lattice

parameter

Calculations give new insight into diffusion paths and temperature dependencies Techniques have broad applicability to Materials Science, e.g. diffusion, solubility, entropy, enthalpy, free energy, …

Medea User’s Group Meeting, Orcas Island, WA, June 17-20, 2004

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