National Aeronautics and Space Administration Kinetic Monte Carlo Simulations of Diffusion in Environmental Barrier Coating Materials Brian Good Materials and Structures Division NASA Glenn Research Center www.nasa.gov 1 National Aeronautics and Space Administration Motivation Ceramic Matrix Composite (CMC) materials offer a number of advantages for use in next-generation turbine engines. CMC components (e.g. SiC) experience corrosion and recession when exposed to conditions typical of a turbine engine in operation. In order to minimize corrosion, environmental barrier coatings (EBCs) are needed. Candidate coating materials should have high melting temperatures, coefficients of thermal expansion close to that of the coated part, and should exhibit no phase changes between room temperature and operating temperature. Candidate EBC materials include Y- and Yb mono- and disilicates. Bond coats are used to adhere the coating to the substrate. They are not chosen for their protective properties but may nevertheless offer a degree of protection, which may be important when cracks develop in the coating. Candidate bond coat materials include Hf silicate. www.nasa.gov 2 National Aeronautics and Space Administration Approach In an effort to better understand coating functionality we have performed kinetic Monte Carlo (kMC) computer simulations of oxygen diffusion in Yb Si O , Y Si O 2 2 7 2 2 7 and HfSiO . 4 We consider vacancy and interstitial diffusion, but not more complex mechanisms. Processes are assumed to be thermally activated. Migration barrier energies are computed using Density Functional Theory (DFT) Barrier energies are used to produce diffusivities using a kMC code developed in our laboratory. www.nasa.gov 3 National Aeronautics and Space Administration Related work • Zhou et al. studied the thermal and mechanical properties of β-Yb Si O via 2 2 7 experiment and density functional theory. • Provided insight into chemical bonding and its relationship to anisotropic properties. • Liu et al. performed a combined experimental/theoretical study of oxygen permeation in Y monosilicate using density functional theory (DFT). • Material crystalizes in monoclinic structure do may expect some similarities to materials considered, but unit cell contains four oxygens within tetrahedra, but also a single interstitial oxygen. • Identified two potential diffusion paths, and the migration barrier energies were computed. The first path connects two atoms on tetrahedral sites in neighboring tetrahedra, with a migration barrier energy of 3.93 eV. • The second path is similar, but with three intermediate stops at interstitial sites. The first step barrier energy is 3.25eV and the other are between 2.39 and 2.87eV. • Concluded that relatively large barriers resulted in low diffusivity 4 www.nasa.gov 4 National Aeronautics and Space Administration Yb Si O Structure 2 2 7 • Distorted monoclinic phase, space group C2/m (12). ! • Lattice parameters a=6.802Å, b=8.875Å, c=4.703Å, and β = 102.07°. ! • Unit cell contains two Yb Si O units 2 2 7 ! • All silicon atoms are tetrahedrally bonded to oxygen atoms. ! Yb (light blue, large), Si (dark blue, small), O (red) • All oxygen atoms are contained within Three distinct oxygen sites within pairs of tetrahedral structures that share a double-tetrahedral complex: common vertex ! 1 O1 at common vertex. 2 O2 pair with colinear bonds passing through O1. 4 O3 pairs in top and bottom planes of complex. www.nasa.gov 5 National Aeronautics and Space Administration Y Si O Structure 2 2 7 • Distorted monoclinic phase, space group P2 /c (14). 1 ! • Lattice parameters a=4.689Å, b=10.841Å, c=5.582Å, and β = 96.033°. ! • Unit cell contains two Y Si O units 2 2 7 ! • All silicon atoms are tetrahedrally bonded to oxygen atoms. ! Y (green, large), Si (dark blue, small), O (red) • All oxygen atoms are contained within pairs of tetrahedral structures that share a Four distinct oxygen sites within common vertex double-tetrahedral complex: 1 O1 at common vertex. 2 O2 pair with colinear bonds passing through O1. 2 O3 pair with colinear bonds passing through O1. 2 O4 pair with colinear bonds passing through O1. www.nasa.gov 6 National Aeronautics and Space Administration HfSiO Structure 4 • Tetragonal phase, space group I4 /amd 1 (141). ! • Lattice parameters a=6.569Å, c=5.967Å. ! • Unit cell contains four HfSiO units 4 ! • There is only a single oxygen site type. ! ! Hf (brown), Si (dark blue, small), O (red) www.nasa.gov 7 National Aeronautics and Space Administration Supercells (100) ! • Yb Si O 2 2 7 • Yb dislocate and Hf silicate structures are fairly open, Y dislocate less so. ! • A number of potential interstitial diffusion channels are evident. ! (001) • The existence of such channels suggests that interstitial diffusivity may be large. • Y Si O ! 2 2 7 • Open structure may also provide room for considerable relaxation, lowering the vacancy diffusion barriers. (001) • HfSiO 4 All three materials show possible low-energy interstitial paths. www.nasa.gov 8 National Aeronautics and Space Administration Infrequent event systems and the kMC method • Systems in which events of interest temporally separated, such that the time between events is much longer than the event durations. ! • Studying such a system using Molecular Dynamics (MD) can be very inefficient. ! • The kinetic Monte Carlo method is designed to study such systems. ! • kMC concentrates on the events of interest, and treats the evolution of the system between events statistically. ! • kMC requires that all events accessible to the system in its current state are known. ! • kMC does not produce exact atomic trajectories, as does MD. However, in the limit of uncorrelated events, the trajectories are statistically equivalent to those from MD simulations. 9 www.nasa.gov 9 National Aeronautics and Space Administration Diffusive hopping as an infrequent event system • Diffusion takes place via a variety of mechanisms. Diffusion via the thermally activated hopping of atoms among vacancies or vacant interstitial sites is common. ! • Atoms are typically confined within local potential minima and undergo thermal vibrations at frequencies on the order of 1013 s-1. ! • Escape from the local minima is possible, but on average an atom is confined for many vibrational periods before it escapes. ! • Under such conditions, immediately after a diffusive hop, thermal vibrations serve to cause the atom to lose any memory of its previous location. ! • In such circumstances, the hops may be considered uncorrelated. www.nasa.gov 10