Molecular dynamics simulations of mass transport in chromium oxide scales
Jukka Vaari VTT Technical Research Centre of Finland
2 06/02/2013
Introduction
Thermal spray coatings provide corrosion resistance for low-alloy materials in high-temperature applications Goal: component lifetime prediction Means: atomistic, finite-element and thermodynamic modelling Starting point: simple model systems (Fe-Cr-O)
3 06/02/2013
1D corrosion model
Steel is divided into control volumes Chemical reactions obtained by assuming thermodynamic
equilibrium in each control volume Mass transfer between control volumes occurs via diffusion
position x
steel gas ( ) ( ) ( )
∂∂⋅
∂∂
=∂
∂x
xCxDxt
xC ipi
i,
4 06/02/2013
Classical molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules
however, movement of planets about sun can be done with MD a numerical solution of Newton’s equations for a system of interacting
particles the interaction is described in terms of a potential (a.k.a force field)
practical for times up to ns-µs, and for 105-107 atoms
5 06/02/2013
Diffusion in solid crystals
No mass diffusion in perfect lattice Diffusion requires defects
0D: point defects 1D: dislocations 2D: surfaces, grain boundaries
A random walk process driven by thermal energy
”Like human defects, those of crystals come in a seemingly endless variety, many dreary and depressing, and a few fascinating” - Ashcroft & Mermin, Solid State Physics, Ch. 30
6 06/02/2013
Defect structure of Cr2O3
A perfect lattice possible only at T = 0 K Defects present at finite temperatures
For intrinsic point defects in Cr2O3
For certain extrinsic defects (such as
substitutional Mg2+) EF can be as low as 2 eV Impurities determine the point defect
concentration (ppm range) Real Cr2O3 is a doped semiconductor with
charge carrier concentration dictated by impurity concentration
Nature of charge carrier can be modeled by writing out the defect reactions for mass and charge balance
Schottky defect 5.6 eV
Cation Frenkel defect 7.8 eV
7 06/02/2013
Model of the Cr2O3 crystal
Cr2O3 has an orthorhombic primitive cell Simulation model built using a triclinic lattice and a hexagonal unit
cell containing three primitive cells (12 Cr atoms, 18 O atoms) The model has 4000 hexagonal unit cells and 120000 atoms with
periodic boundary conditions • Schottky defects formed by
randomly deleting two Cr atoms and three O atoms to maintain charge neutrality
• Measures vacancy diffusion in both anion and cation lattices
• Defect concentrations 2e-4 … 8e-4 in each lattice
• No attempt to model defect concentration
8 06/02/2013
Interaction potential
A combined Buckingham-Coulomb potential has been widely used to model ionic crystals , rcut = 15 Å
Potential parameters A, ρ and C available for many metal-oxygen
pairs
Parameter set 1 [Lewis and Catlow 1985, Catlow 1977]
Parameter set 2 [Minervini et al 1999]
A (eV) r (Å) C (eV⋅Å6) A (eV) r (Å) C (eV⋅Å6)
Cr3+ – O2- 1734.1 0.301 0 1204.18 0.3165 0 O2- – O2- 22764 0.149 27.88 9547.96 0.2192 32
Cr3+ – Cr3+ Only Coulombic Only Coulombic
9 06/02/2013
Other computational details
Ionic diffusion constants determined from mean square displacement vs time curve Simulation temperatures 1300 K – 2000 K NPT ensemble Simulation timestep 1 fs Typical simulation time 400 ps Software: LAMMPS Hardware: Linux cluster ’Smokey’ (Intel Xeon 8-32 core CPU’s,
3.1…3.5 GHz)
( ) ( ) ( )[ ] DtrtrN
trN
iii 601 22 =−= ∑
10 06/02/2013
Typical MSD curves
Defect fraction 8.3⋅10-4, T=1500 K
11 06/02/2013
Parameter set 1: oxygen diffusion
Defect fraction 8.3⋅10-4
12 06/02/2013
Parameter set 2: oxygen diffusion
Horita et al, Solid State Ionics 179 (2008) 2216-2221: Ea=1.4 eV
Defect fraction 8.3⋅10-4
13 06/02/2013
Parameter set 2: chromium diffusion
Liu et al, Solid State Ionics 109 (1998) 247-257: Ea=0.3 eV Betova et al, VTT-R-04098-07: Ea=0.45 eV
Defect fraction 8.3⋅10-4
14 06/02/2013
Oxygen diffusion coefficient vs defect fraction
15 06/02/2013
Extrapolation to lower temperatures and defect fractions
Experimental data from Tsai et al, Materials Science and Engineering A212 (1996) 6-13.
Young et al, Journal of the Electrochemical Society: Solid-State Science and Technology vol. 134 pp. 2257-2260 • Die pressed Cr2O3 powder, high-temperature
sintering • Seebeck measurements • p-type semiconductivity • Electron hole concentration 2⋅10-4
• Chromium vacancy concentration 6.7⋅10-5
16 06/02/2013
Conclusions
Mass transport due to Schottky point defects in bulk α-Cr2O3 investigated using molecular dynamics Defect fraction a free parameter in the approach
Charge carrier concentrations from literature used as guidance Results sensitive to the potential used
Parameter set #2 more credible Diffusion constants approximately linearly dependent on defect
fraction Extrapolation to lower temperatures through Arrhenius plot Qualitative agreement with experiments