Fall 2002 DOE CSP Meeting
Atomistic Modeling of Corrosion:
Kinetic Monte Carlo and DFT
R. G. Kelly, M. Neurock, C. Taylor
Dept. of Materials Sci. & Engr.
Dept. of Chemical Engr.
University of Virginia
Charlottesville, VA
The Vision Thing
(Modeling Plans)
• Atomistic Modeling
– Quong (LLNL),
Neurock (UVa)
• Continuum Modeling
Ab initio
Energetics
KMC
– Kelly (UVa)
Rate constant
• Connect two levels of
modeling via
boundary condition
matching
Continuum mass
transport
E, pH, I(x,y,t)
(Original) Approach
• UVa Molecular Dynamics
– Energetics of Al-Cl-H2O interactions
• DFT to get energetics to feed into KMC
– Structure at Metal/Water Interface
– Kinetic Monte Carlo to get rate constants
– Interact with LLNL oxide modeling
• UVa Continuum Mass Transport Modeling
– Use 2-D mass transport model to rationalize both
transient and steady state BNL gel data
– Interact with BNL experimental studies
Objective
• Develop framework and capability to
connect corrosion modeling across length
and time scales
Aspects of Focus Lately
• DFT of Structure and Energetics
– In vacuum: Cl- adsorption onto Al metal
• Effect of introduction of water
– In solution and the effect of polarization
• Water on Pd and Cu
• Addition and removal of e-
COOL!
Al-Cl Dimer 5.2 eV (Expt)
Al-Cl Dimer 5.1 eV (DFT)
Chlorine binding energy
Chlorine binding energy
DFT Calculations of Effect of Applied Potential
on Structure of Interfacial Water
Neurock
C= +1 e
C=O
C=-1e
Pd-O
2.9 Å
Pd-O
2.5 Å
Pd-O
2.2 Å
Increasing potential across interface
• reorientation of the water molecules at the interface
• oxidative adsorption of water on Pt upon electron depletion
Application of Charge to a Cu (111) – H2O Interface
+2e-
+1e-
Neutral
-1e-
-2e-
Periodic slab DFT calculations
• 9 Cu atoms (3 layers), 8H2O molecules / unit cell
-3e-
Modes of Adsorption
+2 e-
+1 e-
-1 e-
-2 e-
Neutral
-3 e-
120
100
80
60
40
Oxidation
Reduction
20
0
-3
-2
-1
0
1
2
3
2
3
Electrons Added to Cu
3.3
3.1
Cu-O Bond Distance (A)
Effect of
Applied
Potential on
Structure at
Interface
Cu-O-H Angle (degrees)
140
2.9
Proton released
2.7
2.5
2.3
2.1
Oxidation
1.9
Reduction
1.7
1.5
-3
-2
-1
0
1
Electrons Added to Cu
So What
• Given structure, calculate energetics as a function
of addition/subtraction of electrons
• Can then determine reversible potentials on
measurable electrode scale (e.g., NHE)
– Water reduction
– Metal oxidation
– Metal oxide formation
• THEN can compare to experiment and hand off
values to KMC calculations
Related work at LLNL
The Structure of the TiO2/Water Interface
Leonard A. Harris and Andrew A. Quong
Lawrence Livermore National Laboratory
Water Adsorption on the (110)
Surface of Rutile TiO2
Half-layer Coverage
Molecular
Adsorption
(Eads = 0.896 eV/H2 O)
Dissociative
Adsorption - Type Ι
(Eads = 1.170 eV/H2 O)
Ti
O
H
Dissociative
Adsorption - Type ΙΙ
(Eads = 1.172 eV/H2 O)
Water Adsorption on the (110)
Surface of Rutile TiO2
Monolayer Coverage
Pure Molecular
Adsorption
(Eads = 1.089 eV/H2 O)
Pure Dissociative
Adsorption
(Eads = 0.996 eV/H2 O)
Ti
O
H
Mixed Molecular /
Dissociative Adsorption
(Eads = 1.105 eV/H2 O)
Water Adsorption on the (110)
Surface of Rutile TiO2
Bi-layer Coverage
1st Layer Molecular
Adsorption
(Eads = 0.902 eV/H2 O)
1st Layer Dissociative
Adsorption
(Eads = 0.835 eV/H2 O)
Ti
O
H
1st Layer Mixed Molecular /
Dissociative Adsorption
(Eads = 0.885 eV/H2 O)
Kinetic Monte Carlo Calculations
• Given rate constants for reactions
– By DFT, literature, measurement
• Enhance KMC methods
– Consider reactions as in literature, but also
account for presence of solution and its
alteration
• Local pH effect
• Local atomic structure (bonding)
• Local concentration
COOL!
Atomistic Framework of Pitting
Beginning
1. Cl- adsorption
2. Passive film breakdown
3. Dissol’n/repassivation
4. Stable pitting
Al metal bulk
Al
metal
bulk
Al
Al metal
metal bulk
bulk
Cl-
Na+
H+
Al3+
H2 O
Donghai Mei
Matt Neurock
Oxide Layer (Al2O3)
KMC Modeling of Pitting of Al and Al/Cu in Chloride Solution
Simple 3D Lattice-gas Model
Solution with Constant
Ion Concentration (C0)
Solution (Na +, Cl-, H2O)
Passive Oxide Layer (Al 2O3)
Aluminum Metal (Al)
Pits formed by continuous kinetic events (reaction + diffusion/migration)
Reaction rate calculation
 Ei 
ri = k i exp −

 RT 
k i = f ( E applied , pH , Neighbors )
E i = f ( E i ,0 , Neighbors)
M o d e l S y s t e m : Aluminum -copper alloy in aqueous NaCl solution environment
Reactions Considered
Breakdown of oxide layer
Cl-
Anodic dissolution
Al
O xide
+
k2
Cu
Metal ion hydrolysis
Al3+
+
H2O
Al(OH)2+ + ClAl(OH)Cl+ + H2O
Water Reduction
Al3+
+
3H2O
Al3+
+
3Cl-
2H2O
+
2e-
Water Dissociation
H+
Oxide Formation
2Al
k1
+
k3
k4
k5
k6
k7
k8
k9
k10
k11
k12
k13
k14
k15
Cl- +
(1)
E mpty
Al3+ + 3e–
(2)
Cu2+ + 2e–
(3,4)
Al(OH)2+ + H+
(5,6)
Al(OH)Cl+
(7,8)
Al(OH)2Cl +
Al(OH)3
+
H+
3H+
(11,12)
(13,14)
AlCl3
H2 (g)
(9,10)
+
2OH-
(15)
OH-
k16
k17
H2O
+ 3H2O
k18
k19
Al2O3 ( Oxide
xide ) + 6H+ + 6e–
Note: WAGs for rate constants in some cases
(16,17)
(18,19)
KMC Modeling of Localized Corrosion of Pure Al in Aqueous Chloride
Chloride Solution
Initial configuration
Evolution of pit
Legend
Al
Al2O3
Legend
Empty
Cl-
Al3+
H2O
Na+
Al(OH)2+
OH-
Effect of Copper Content and Configuration on
Pitting Process of
Al and Al-Cu
• Three configurations:
– randomly distribution
– a 3x3 column of Cu
– a cluster of 6-12 Cu atoms
Effect of Copper Content and Configuration
Al-Cu alloy layer
Cu distribution
Effect of Cu on Nanopit Morphology
Dish-like
4.5
4.0
3.5
3.0
r/h
2.5
Al-4Cu
2.0
Al-2Cu
1.5
Hemisphere
Tunnel
1.0
Pure Al
0.5
0.0
0
20
40
60
Time (s)
80
100
120
Effect of Cu on Pit pH
5.0
4.5
4.0
Al-4Cu
pH
3.5
Pure Al
3.0
2.5
Al-2Cu
2.0
1.5
0
20
40
60
Time(s)
80
100
120
Possible Future Paths
DFT
• Map out Cu electrochemistry
– Reduction of water (and oxygen?)
– Oxidation of metal
– Connect to known reversible potentials and
experimental measurements (e.g., water flipflop on Pd, initial Cu-OH)
• Extend to Al (bare metal) electrochemistry
• Extend oxide work to Al2O3
Possible Future Paths
KMC
• Understand what parameter(s) control the
evolution of pit shape in terms of the individual
reactions
• Definition of shape based on distribution of atoms
dissolved
• Understand what parameter(s) control pH and
other ion distributions
• Prediction of current density as f(t)
• Prediction of repassivation