Iron-technetium alloys are of relevance to the development of waste forms for disposition of radioactive technetium-99 obtained from spent nuclear fuel. Corrosion of candidate waste forms is a function of the local cohesive energy (
The development of long-term containment strategies for spent nuclear fuel requires a combination of careful experiments and theoretical studies so that the realistic lifetimes of these strategies can be confidently predicted. Currently, a number of different containment strategies are being considered, one of which involves the storage of certain fission products within a metallic alloy waste form [
Predictions of the long-term stability of this material can be obtained through the coupling of the results of accelerated testing studies with a rigorous, physics-based theoretical model. Corrosion is believed to be the chief process by which stored, spent nuclear fuel will degrade over time and have the potential to release radionuclides to the environment [
A schematic illustrating the many processes that need to be considered when building a model for the corrosion of candidate metal alloy waste forms.
One of the tools that can be applied to assist in the construction of lifetime prediction models is atomistic simulation. Contemporary atomistic modeling tools in the solid-state and molecular sciences allow the first-principles calculation of thermodynamic energies, activation barriers associated with phase-transformations, and the prediction of phase diagrams. First-principles modeling has been used by theorists at UNLV (Weck et al.) to explore the stability of Tc nanoparticles [
In the present work, we have applied atomistic modeling to illuminate a second set of corrosion reactions relevant to the iron-technetium system. The tendency for an atom to dissolve or be released from the metal by other means (such as diffusion through the passive film or ligand complexation) is related to the intrinsic stability of the atom in its local surface configuration (composition, coordination number, and local orientation, see Figure
Schematic rendering of the surface of an iron-technetium alloy (iron: yellow and technetium: gray) showing schematically that dissolution can involve either technetium or iron atoms and that corrosion processes will involve breaking apart the local bonding arrangements, which will vary from atom to atom.
Our strategy for computing the dissolution tendency of metal atoms in the iron-technetium binary system required the calculation of cohesive energies using the modified embedded atom method. It was necessary for us to construct a modified embedded atom potential that is accurate for the iron-technetium interactions. Modified embedded atom potentials for binary systems can be constructed by consulting accurate materials properties for the individual metals and their intermetallic phases, and these can be determined either from experiments, or higher-level theoretical calculations [
Density functional theory is a powerful theoretical technique developed by Hohenberg and Kohn for the determination of the electronic structure associated with a given crystallographic and/or molecular system [
Density functional theory has been implemented in numerous software packages that are commercially available. We utilized the Vienna Ab-initio Simulation Package (VASP) v.4.6.36 to solve for the electronic structures and energies for the reference structures studied in the iron-technetium binary system [
(a) Hexagonal close-packed crystal structure for Tc, (b) B2 crystal structure for the hypothetical iron-technetium intermetallic used as a reference for development of the modified embedded atom iron-technetium potential.
Systems parameters within VASP that were specified to expedite the computationally intensive quantum mechanical calculations are described briefly as follows: the projector augmented wave method (PAW) was used to treat the core electrons and core-valence interactions [
The modified embedded atom method is, in essence, a simplified approach to evaluating the energies and forces on atoms that is achieved by reducing and collecting the equations of density functional theory into a sum of single atom and pairwise expressions [
A modified embedded atom potential for iron was previously developed by Lee and Baskes [
The large-scale atomic/molecular massively parallel simulator (LAMMPS), developed at Sandia National Laboratory, was used to perform total energy computations, conjugate gradient optimizations, and molecular dynamics simulations of iron-technetium systems using the modified embedded atom method [
The modified embedded atom method involves the computation of system energies by summation of individual and pairwise atomic cohesive energies using the formulae
Attempts to estimate cohesive energies using counts of the number of nearest neighbors have been used in kinetic Monte Carlo simulations of alloy dissolution and nanoporous dealloying [
Density functional theory computations were performed for the hexagonal close-packed phase of technetium (Figure
Elastic moduli and lattice constants for hexagonal close-packed technetium and selected moduli for the iron-technetium B2 intermetallic taken from density functional theory and experimental data where available.
Tc | DFT | Experiment | Tc-Fe (DFT) | |
---|---|---|---|---|
320 | 306a, 281b | B, GPa | 290 | |
380 | 331a, 314b | 2.93 | ||
146 | 125a, 123b | Δ | + 0.325 | |
0.30 | 0.32a | |||
518 | 433b | |||
243 | 199b | |||
193 | 199b | |||
584 | 470b | |||
138 | 117b | |||
131 | ||||
2.72 | 2.74b | |||
1.603 | 1.605b |
aLove et al. [
bGuillermet and Grimvall [
Examination of Table
While the B2 iron-technetium intermetallic is not a known phase for the Tc-Fe binary system, it has composition within the known range of the iron-technetium sigma-phase intermetallic (40%–60%), and its symmetry is consistent with the body-centered cubic phase of iron (Figure
Following the procedure given by Baskes and Johnson [
Parameters for the modified embedded atom potentials for simulation of technetium, iron, and iron-technetium.
Parameter | Tc | Fea | Tc-Fe |
---|---|---|---|
3.853 | 2.866 | 2.537 | |
7.534 | 4.29 | ||
1 | 0.56 | ||
5.593 | 5.073 | 6.054 | |
2.0 | 0.36 | 2.0 | |
2.8 | 2.8 | 4.8 | |
4.209 | 2.6 | ||
25.8257 | 1.8 | ||
−15 | −7.2 | ||
1 | 4.15 | ||
0 | 1 | ||
0.665 | 1.0008 | ||
3 | 1 | ||
Δ | +0.325 |
aLee and Baskes [
Spherical clusters of technetium, iron, iron-technetium, and various core-shell combinations were modeled using the LAMMPS package. Spherical clusters based on technetium were generated based on a hexagonal close-packed parent lattice. Spherical clusters based on iron were generated using a body-centered cubic lattice, and spherical clusters based on iron-technetium were generated using the hypothetical iron-technetium B2 structure. Geometry optimizations as well as molecular dynamics simulations at 1000 K for 150 ps were performed on these systems so that the atoms could migrate to low-energy sites. Due to the geometry of the spherical particles, multiple different surface planes (and hence atomic configurations for the surface atoms) were sampled within each simulation. Example clusters are shown in Figure
Illustrations of the (a) technetium, (b) iron, and (c) iron-technetium spherical particles used in this work to simulate a variety of surface states. Technetium atoms are rendered in white and iron in brown. The structures shown are the structures obtained following annealing at 1000 K and conjugate gradient optimization of the atomic positions.
For the purposes of probing a greater set of surface ensembles, each of the spherical particles shown in Figure
Following this compilation process, we plotted the cohesive energy of technetium and iron atoms that occupy surface sites in the metal versus the number of nearest neighbors of technetium (#Tc) and the number of nearest neighbors of iron (#Fe). These cohesive energies are plotted in contour form for the two variables (#Tc and #Fe) in Figure
Cohesive energy contours (upper) and their standard deviation (lower) for iron and technetium components of iron-technetium alloy systems (left and right, respectively) plotted against the number of nearest neighbors of type Tc (
The cohesive energy plots shown in Figure
What is also apparent from Figure
In the lower portion of Figure
In this work, we have performed density functional theory computations for metallic technetium and iron-technetium intermetallic systems. We have used materials properties obtained from the density functional theory computations to develop a modified embedded atom method potential for the iron-technetium system. The materials properties calculated using density functional theory were in good agreement with the available experimental literature and were, therefore, used to parameterize the MEAM potential.
Simulations containing model surfaces of iron-technetium alloys in the iron-rich, technetium-rich, and 50-50 iron-technetium intermetallic limit were then performed. The simulations were designed to capture the variations in surface cohesive energies that occur as iron or technetium atoms are placed in different local compositional and coordination environments. We collated the local surface atom cohesive energies obtained from the various computations so that we could investigate how the local environments of iron or technetium atoms at the surface of hypothetical iron-technetium alloy waste forms may influence their corrosion behavior. The simulations indicated that the local bonding arrangements are very critical to the ultimate stability of these surface atoms. Generally speaking, increases in local coordination lead to more stable surface atoms; that is, more bonds to nearest neighbors will increase the energy required to dissolve or remove an atom from the alloy surface. Another observation that is revealed by this study is that technetium-rich environments are more noble, not only for technetium atoms on the surface, but also for iron atoms.
Our work also shows that a consideration of the local bonding environment, in terms of numbers of nearest neighbors, is not sufficient for computing or estimating the local cohesive energy and that variations in the particular way the atoms are situated about the central atom can lead to perturbations in the cohesive energy of up to 0.5 eV (as estimated by one standard deviation from the mean). Therefore, although linear relationships for dissolution and diffusion energies have been assumed in previous works, significant errors in these simulations may apply.
The modified embedded atom potential for iron-technetium alloys that we have developed in this work is currently being implemented within a kinetic Monte Carlo scheme, which we will apply in future work for the simulation of relative corrosion rates for iron and technetium in candidate metal alloy waste forms, as well as the differences in corrosion morphology and extending the potential to include other alloy components such as molybdenum and chromium. This technique will allow us to investigate the relative corrosion properties of different intermetallic and alloy phases and the roles of electrochemical potential and pH, and provide a starting point for more complex models that combine alternative surface processes such as oxidation, grain-boundary dissolution, and surface adsorption.
The authors acknowledge funding through the Fundamental Waste Form Science campaign under the auspices of the US DOE Fuel Cycle R&D under the direction of John Vienna, Waste Forms and Separations Campaign Manager. Helpful discussions with Dave Moore, Gordon Jarvinen, Scott Lillard, and Dave Kolman at Los Alamos National Laboratory are also acknowledged. The Los Alamos National Laboratory is operated by Los Alamos National Security LLC for the National Nuclear Security Administration of the U.S. Department of Energy under Contract no. DE-AC52-06NA25396. A portion of the research was performed using EMSL, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory.