Fast impurity diffusion in hcp Zr

The objective of this dissertation is to study the phenomenon of ultra-fast diffusion of Ni in hexagonal closed-packed Zr using atomistic simulating techniques. Our major concern is the lack of understanding on the impurity size effects and its relation to interstitial diffusion mechanisms in this lattice. We present an atomistic model based on an empirical many-body potential, with interatomic interactions written in the framework of the second moment approximation of the tight binding description for transition metals. The parameters of the potential to describe the impurity-host interactions are taken from fits of the potential form to the properties of Ni, Zr, and the alloy NiZr 2. Based on static calculations of equilibrium energy and volume of two other phases of the Ni-Zr diagrams, we find the cross interaction as fitted for the alloy to be suitable for a description of a Ni impurity in the Zr lattice. The model accounts for the exceptionally high values for the diffusion coefficient of small impurities in this material. Our results show that fast diffusion is due to a simple interstitial mechanism where the impurity jumps between adjacent octahedral sites with diffusion coefficients values calculated using Molecular Dynamics techniques between 10-6 105 cm 2/s in the temperature range of 900-1200 K, in excellent agreement with experimental values. Contrary to the long standing belief that fast diffusion was due to small ion-core overlap at the saddle point configurations, we demonstrate that, though small impurity sizes are needed for stabilizing the octahedral interstitial site, it is not the determining factor to allow for low saddle point configuration energies. Rather, fast diffusion is a direct consequence of apparent low frequency resonant modes in the local vibrational spectra of impurity and its Zr neighbors. These modes are characterized by collective participation of all atoms in the lattice. High frequency local modes are also present in the spectra, but they do not participate in the diffusion mechanism. These are decoupled from the lattice and only the impurity and its first neighbors are involved in the vibration. The local phonon spectra were calculated using the Recursion Method to obtain the appropriate dynamical response functions to external perturbations (Green functions). Resonances appear at 1.2 THz and 1.4 THz. The former is a two-fold degenerate mode which transforms according to the E, irreducible representation of the point group of the defect D3d, and has the appropriate symmetry required to drive diffusion perpendicular to the c-axis of the hcp lattice. The former is non-degenerate, transforms according to Al,, and its symmetry assists the diffusion process parallel to the c-axis. Fast diffusion in the model is predicted from static calculations of the diffusion coefficients within the harmonic approximation. We show that the resonances being at low frequencies decreases the activation energy for the diffusion process to values equal to . 60 eV and . 81 eV for diffusion parallel and perpendicular to the c-axis, respectively. Therefore, the combination of appropriate symmetries and low frequency character is the important ingredient in the model to allow for fast impurity diffusion to occur. The predicted dynamic behavior of the impurity is confirmed with extensive Molecular Dynamic trajectories calculated up to 14 ns. Fast diffusion is observed with migration energies equal to . 54 eV and . 71 eV in excellent agreement with experiments and with the static harmonic approximation results. Our model also reproduces the experimental values for the anisotropy ratio Dll/D± falling in the range of 3-5 for temperatures between 900 K and 1200 K. Temperature dependent anisotropy is inherited in the mechanism not only because the jump distances for impurity motion parallel and perpendicular to the c-axis are different, but also because diffusion in different directions are driven by different resonances. That diffusion occurs mostly by an octahedral-to-octahedral mechanism is verified with an statistics analysis of the residence time of the impurity in the interstitial site, which agree well with predicted Poisson distribution from the random walk theory. Random diffusion is shown not to be in contradiction with the strong correlations introduced by the resonances. This is demonstrated with the calculation of the velocity auto-correlation functions for the impurity during its trajectory in the lattice, from which we observe relaxation times associated with the correlations much smaller than the mean residence times obtained from the statistics. This implies that, for most of diffusion events, the impurity looses the memory from the previous jumps before it performs the next. For the few apparent jumps with residence time less than the relaxation time, the impurity is found to perform a forward double jump, in which the impurity basically skips one site. These do not contribute significantly to the fast diffusion process. Our results establish a different way to look into the problem of interstitial impurity diffusion in the hcp lattice, so far only discussed in terms of size effects, and set new directions for experiments in the field. Thesis Supervisor: Sidney Yip Title: Professor of Nuclear Engineering Thesis Supervisor: Kenneth Russell Title: Professor of Materials Science and Engineering