Modeling Hydrogen Permeation through a TiO 2 Film and Palladium

Transcription

1 Modeling Hydrogen Permeation through a TiO 2 Film and Palladium Zack Qin, Y. Zeng, P.R. Norton, and D.W. Shoesmith Department of Chemistry and Surface Science Western Western University London, Ontario, Canada N6A 5B7 1

2 Titanium and Its Alloys 2

3 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 alloys. From AECL report From AECL report

4 Influence of Oxide Films Ti is generally covered by a thin passive oxide (TiO 2 ) film. The impermeability of this film is the limiting feature preventing HIC in Ti-alloys. The mechanism by which TiO 2 influences H permeation is complicated and still not well established. Water H 2 O H 2 Aqueous Environment O 2- H abs Passive Oxide Oxide Growth Ti 4+ TiO 2 TiOOH Oxide Transformation H + Ti Metal Oxidation TiH x Hydride Formation Metal 4

5 Key Questions J H? Time? H H + H 2 Ti Ti Oxide Solution Can hydrogen permeate the oxide film? How much the hydrogen entering the oxide can reach the underlying metal? How long does it take for the absorbed hydrogen to permeate through the oxide? 5

6 Hydrogen Permeation Measurements Ar gas H Charging System (i 0 = 80 na/cm 2 ) Potentiostat (E = 0.18 V SCE ) Pt RE Specimen RE Pt H + H + H charging solution (0.27M NaCl) TiO 2 /Pd Testing solution (0.01M KI) 6

7 Hydrogen Permeation Curve Anodic Current Density H-charging starts on TiO 2 Film Time lag H transport through TiO 2 and Pd H to Pd/sol n interface Steady-State H Permeation Current Stop H-charging Time PdI formation on Pd, leading to a background current < 2 na/cm 2 H reoxidation at Pd/sol n interface H discharge 7

8 Hydrogen Permeation Model constant charging current constant anodic potential TiO TiO 2 2 Pd Pd H + H + H abs H H + H H H H 2 H trap 0 X L TiO2 L Pd 8

9 Hydrogen Permeation in Pd 2 Pd Pd Pd Pd Pd CD (,) xt = D H C (,) (,) (,) 2 D xt CA xt + CT xt t x t reversible absorption: t Pd Pd Pd Pd Pd C (,) xt = k C (,) xt k C (,) xt A A D D A irreversible trapping: Pd Pd Pd CT (,) xt Pd CT (,) xt = kt 1- CD (,) xt S t CT boundary conditions: initial Pd Pd D C ( x= 0, t t ) = f x Pd C ( x= 0, t > t ) = 0 D H D off H off Pd C ( x= L,) t = 0 D Pd conditions: C ( xt, = 0) = C ( xt, = 0) = C ( xt, = 0) = 0 i0 F D A T 9

10 Simulation vs Experiment for Pd 0.8 H permeation (i/i 0 ) x x x x10 4 Time (seconds) 10

11 Evolution of H Profiles in Pd Steady-state achieved in >14 hrs. Reversible absorption is fast, and, hence, always at local equilibrium. Irreversible trapping sites are saturated after 6 hrs (~ time lag). 11

12 TiO 2 Deposited on Pd Large geometric scale variations in TiO 2 and Pd (24nm:0.1mm) Three approaches: Actual dimensions but different mesh densities simulations appear to yield reasonable results for certain parameter values but not for others. Different length scales in the TiO 2 and Pd the diffusion and absorption parameters are normalized accordingly. However, normalization of the flux is ambiguous at the TiO 2 /Pd interface. Thin layer approximation (Sandwich model) the thin TiO 2 film is replaced by a boundary layer sandwiched between a hypothetical fast diffusion layer (FDL) and the Pd. 12

13 Sandwich Model TiO 2 FDL Pd x L FDL L Pd The FDL is a hypothetical layer in which diffusion is so fast that it has a little effect on the subsequent TiO 2 and Pd. The thin TiO 2 film is replaced by an interior boundary layer between the FDL and the Pd. Diffusion in TiO 2 is incorporated as interior boundary conditions. The Pd is governed by the mass balance equations as stated. 13

14 Simulation vs Experiment for TiO 2 /Pd H permeation (i/i 0 ) x x x x10 5 Time (seconds) 14

15 Sensitivity to Model Parameters Effect of H diffusion in TiO 2 : D H TiO2 = m 2 /s D H TiO2 = m 2 /s D H TiO2 = m 2 /s Effect of TiO 2 thickness: L TiO2 = 12 nm L TiO2 = 24 nm L TiO2 = 36 nm 15

16 Simulation for Other Current Since the permeation parameters are material specific, they should not be dependent on the charging current density. The parameters obtained from the simulations at 80 na/cm 2 fit well to the permeation curve charging at 40 na/cm 2, even the experimental permeation curves appear quite different. 16

17 Conclusions Models describing hydrogen permeation through a thin TiO 2 film deposited on Pd were developed and solved using COMSOL Multiphysics. The model simulation reproduced the experimental permeation curves and yielded values of the permeation parameters, such as diffusion coefficients, absorption and desorption rate constants, trapping rate constants, and saturation concentrations. The value of D in TiO 2 is three orders of magnitude lower than that in Ti metal, indicating that hydrogen transport through the oxide is responsible for the strong retardation of TiO 2 films on hydrogen permeation. While focused specifically on the TiO 2 /Pd system, the models can be readily adapted to other material systems. 17

18 Electrochemical and Corrosion Studies at Western Thank You Acknowledgements Funded by National Science & Engineering Research Council of Canada 18