Modeling Hydrogen Permeation through a Thin TiO2 Film Deposited on Pd Usinga Thin TiO2 Film Deposited on Pd Using

COMSOL Multiphysics

Zack Qin, Y. Zeng, P. P. Norton, and D. W. Shoesmith

The University of Western OntarioLondon, Ontario, Canada N6A 5B7London, Ontario, Canada N6A 5B7

1

Presented at the COMSOL Conference 2009 Boston

Titanium and Its Alloys

2

Hydrogen-Induced Cracking (HIC)

Potentially susceptible to HIC as a consequence of H absorption

Absorbed hydrogen results in hydride formation and fast crack

growth leading to the cracking of Ti and its alloysgrowth leading to the cracking of Ti and its alloys.

HydrideLayer

Dense Band

Metal

3From AECL report 11608 From AECL report 11284

Influence of Oxide Films

Ti is generally covered by a thin passive oxide (TiO2) film.The impermeability of this film is the limiting feature preventingThe impermeability of this film is the limiting feature preventingHIC in Ti-alloys.Th h i b hi h TiO i fl H ti iThe mechanism by which TiO2 influences H permeation iscomplicated and still not well established.

H 2O H 2W ater AqueousEnvironm ent

Passive

O 2- H abs

4+

O xide G row th TiO 2

TiO O H O xide Transform ation

PassiveO xide

Ti4+

T i

G row th

M t lH ydride

Form ationTiH x

H +

4

M etalO xidation

Form ation M etal

Critical Questions

Can hydrogen permeateCan hydrogen permeate the oxide film?How much the hydrogenH+

H

JH ?How much the hydrogen entering the oxide can

H

H2

reach the underlying metal?

2

Time? How long does it take for the absorbed

Ti Ti Oxide Solution hydrogen to permeate through the oxide?

5

through the oxide?

TiO2 Deposited on Pd

Due to complications caused by formation of hydrides in Timetal, a thin TiO2 film deposited on a Pd foil was used.Pd was selected because of its high hydrogen solubility and rapidkinetics for hydrogen absorption and transport.

8 Resistance of deposited TiO

TiO

Micro-balance

Pump system

Pd

TiO

Micro-balance

Pump system

TiO

Micro-balance

Pump system

107

108 Resistance of deposited TiO2 Resistance of Passive Oxide on Ti-2

(Ω)

(Ωcm

2 )oxygen

TiO2

Pressure gauge

oxygen

TiO2

Pressure gauge

oxygen

TiO2

Pressure gauge

106

10

esis

tanc

e (

Ti

oxygen gasTi

oxygen gasTi

oxygen gas

0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 0105

10

Re

6

Temp. Controller

Temp. Controller

Temp. Controller

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0

Potential (V vs. SCE)

Hydrogen Permeation Measurements

P t ti t tH Ch iAr gas P t ti t tH Ch iAr gas P t ti t tH Ch iAr gas P t ti t tH Ch iAr gas PotentiostatH ChargingSystem

Ar gas PotentiostatH ChargingSystem

Ar gas PotentiostatH ChargingSystem

Ar gas PotentiostatH ChargingSystem

Ar gas(E = 0.18 VSCE)(i0 = 80 nA/cm2)

PtSpecimen RERE

PtSpecimen RERE

PtSpecimen RERE

PtSpecimen RERE

PtSpecimenRE

PtSpecimenRE

PtSpecimenRE

PtSpecimenRE

H+ H+H+ H+H+ H+H+ H+

H charging solution Testing solutionH charging solution Testing solutionH charging solution Testing solutionH charging solution Testing solution

7

g g(0.27M NaCl)

Testing solution(0.01M KI)

g g(0.27M NaCl)

Testing solution(0.01M KI)TiO2/Pd

g g(0.27M NaCl)

Testing solution(0.01M KI)

g g(0.27M NaCl)

Testing solution(0.01M KI)TiO2/Pd

Hydrogen Permeation Curvety

H-charging starts TiO Fil

Den

sit

H to Pd/sol’n i t f

Stop H-charging

on TiO2 Film

urre

nt

Time lag

interface

St d St t

odic

Cu

H transport through

Steady-State H Permeation

Current

An through

TiO2 and Pd

Time

H reoxidation at PdI formation on Pd,

leading to a background H discharge

8

Pd/sol’n interfaceleading to a background

current < 2 nA/cm2H discharge

Hydrogen Permeation Model

constantcharging current

constantanodic potential

TiO 2 Pdcharging current

H+

Pd

H+

anodic potentialTiO2

H+ H

H+

HH H

Habs

HH H

X0 X0

H2

Htrap

X0

LTiO2

X0

LPd

9

Hydrogen Permeation in Pd

2

( ) ( ) ( ) ( )Pd Pd Pd Pd PdC x t D C x t C x t C x t∂ ∂ ∂ ⎡ ⎤= − +⎣ ⎦2( , ) ( , ) ( , ) ( , )D H D A TC x t D C x t C x t C x tt x t

⎡ ⎤= +⎣ ⎦∂ ∂ ∂

Pd Pd Pd Pd Pd∂ibl ( , ) ( , ) ( , )Pd Pd Pd Pd PdA A D D AC x t k C x t k C x t

t∂

= −∂

reversible absorption:

⎛ ⎞irreversible trapping:

( , )( , ) 1- ( , )Pd

Pd Pd PdTT T DS

T

C x tC x t k C x tt C

⎛ ⎞∂= ⎜ ⎟∂ ⎝ ⎠

boundary conditions:

0( 0, )Pd PdH D off H

Pd

iD C x t t fx F

∂− = ≤ =

∂( 0, ) 0

( , ) 0

PdD off

PdD Pd

C x t t

C x L t

= > =

= =

i i i l

10

initial conditions: ( , 0) ( , 0) ( , 0) 0D A TC x t C x t C x t= = = = = =

Simulation vs Experiment for Pd

0.8)

0.6

atio

n (i/

i 0)

0.4

H p

erm

ea

0.2

0.0 2.0x104 4.0x104 6.0x104 8.0x104

0.0

11Time (seconds)

Evolution of H Profiles in Pd

Steady state achieved in >14 hrsSteady-state achieved in >14 hrs.Reversible absorption is fast, and, hence, always at equilibrium.Irreversible trapping sites are

12saturated after ~ 6 hrs.

TiO2 Deposited on Pd

Large geometric scale variations in TiO2 and Pd (24nm:0.1mm)

Three approaches:Actual dimensions but different mesh densities i l i i ld bl l f i

×simulations appear to yield reasonable results for certain parameter values but not for others. Different length scales in the TiO and Pd × Different length scales in the TiO2 and Pd the diffusion and absorption parameters are normalized accordingly. However, normalization of the flux is g yambiguous at the TiO2/Pd interface.Thin layer approximation (Sandwich model) h hi TiO fil i l d b b d l

√the thin TiO2 film is replaced by a boundary layer sandwiched between a hypothetical fast diffusion layer (FDL) and the Pd

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(FDL) and the Pd.

Sandwich ModelTiO2

FDL Pd

x

LFDL LPdLFDL LPd

The FDL is a hypothetical layer in which diffusion is so fastThe FDL is a hypothetical layer in which diffusion is so fast

that it has a little effect on the subsequent TiO2 and Pd.

The thin TiO2 film is replaced by an interior boundary layer

between the FDL and the Pd. Diffusion in TiO2 is incorporatedbetween the FDL and the Pd. Diffusion in TiO2 is incorporated

as interior boundary conditions.

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The Pd is governed by the mass balance equations as stated.

Simulation vs Experiment for TiO2/Pd

0.8

0.6

0.4on (i

/i 0)

0 2

0.4

erm

eatio

0 0

0.2

H p

e

0.0 5.0x104 1.0x105 1.5x105 2.0x105

0.0

15

Time (seconds)

Sensitivity to Model Parameters

Effect of TiO2 thickness: Effect of H diffusion in TiO2: 2 LTiO2 = 12 nm LTiO2 = 24 nm LTiO2 = 36 nm

2 DH

TiO2 = 10-16 m2/s DH

TiO2 = 10-17 m2/s DH

TiO2 = 10-18 m2/s

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LTiO2 36 nmDH 10 m /s

Conclusions

Models describing hydrogen permeation through a thin TiO2

film deposited on Pd were developed and solved using

COMSOL MultiphysicsCOMSOL Multiphysics.

The model simulation reproduced the experimental permeation

curves and yielded values of the permeation parameters

required to predict hydrogen absorption into Ti-alloys.q p y g p y

The value of D in TiO2 is three orders of magnitude lower than

h i i l i di i h h d h h hthat in Ti metal, indicating that hydrogen transport through the

oxide is responsible for the strong retardation of TiO2 films on

17hydrogen permeation.

Electrochemical and Corrosion Studies at Western

http://sun.chem.uwo.ca

Thank YouThank YouAcknowledgements

18

Funded by National Science & Engineering Research Council of Canada

Simulation Parameters

Value Description

i0 8 x10-4 A/m2 charging current density

fH 0.7325 / 0.6935 charging efficiency (Pd / TiO2+Pd)

t0 62000 / 149000 s charging time (Pd / TiO2+Pd)t0 62000 / 149000 s charging time (Pd / TiO2+Pd)

L0 1 x10-5 m FDL thickness

L1 2.4 x10-8 m TiO2 thickness

L2 0.0001 m Pd thickness

D0 1 x10-5 m2/s diffusion coefficient in FDL

D1 1 x10-17 m2/s diffusion coefficient in TiO21 2

D2 3.34 x10-11 m2/s diffusion coefficient in Pd

kA 1 s-1 absorption rate constant in Pd

k 0 0125 1 d i i PdkD 0.0125 s-1 desorption rate constant in Pd

kT 10 s-1 trapping rate constant in Pd

CTS 0.58 mol/m3 trapping saturation in Pd

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Sandwich Model Equations

FDL2

( ) ( ) ( )C x t D C x t D D D∂ ∂= >>FDL:

TiO2 interface

0 0 0 0 1 22( , ) ( , ) ( , )C x t D C x t D D Dt x

= >>∂ ∂

( )1D +2condition:

⎛ ⎞

( )11 2 0 0 0

1

( ) ( , ) ( , )DJ t C L t C L tL

+ −= − −

Steady-stateconcentrations:

0 0 1 20 0

0 1 2

02 0 2

( ) ( )

( ) ( )

ss H H

ss H

f i f i L LC x L xF D F D Df iC x L L x

⎛ ⎞= − + +⎜ ⎟⋅ ⎝ ⎠

= + −2 0 22

2

( ) ( )

( ) ( ) ; ( )ss ss ss SAA T T

D

C x L L xF DkC x C x C x Ck

+⋅

= =

1 1 0( , ) 0offD C x L t tx

∂= > =

∂Discharge boundary

202 0 2( , ) 0offC x L L t t= + > =conditions: