Tuesday, November 11, 2008

Multiscale Modeling for Nuclear Reactor Materials

For a variety of phenomena, it is true that physical interactions between constituents at a variety of length and time scales, starting from the smallest and cascading upward to the largest relevant scale - contribute to the macroscopic behaviour. While a strictly reductionist viewpoint would be misleading, it is nevertheless true that these interactions exist in a hierarchy of length scales, with the lower cutoff at the atomic scale and the upper cutoff at the 'continuum limit' in the millimeter length scale. This is true in particular of reactor materials that are subject to neutron irradiation (they may also be subjected to alpha or gamma radiation).

A neutron flux, for example, will impact an atom, and attempt to dislodge it from its lattice site, in what is called a 'primary knock-on' event. If the dislodgement is successful, the atom becomes an interstitial, and a vacancy is created at the original location. Such a primary knock-on event, which creates that point defect, is estimated to take as little as one-hundredth of a nanosecond (10^-11 seconds), while the atom is displaced over a length scale of the order of a nanometer(the lattice parameter of most metals is just under 1 nm).

The vacancy and interstitial atom function as a bound pair, known as the Frenkel pair. Many of the plasticity properties of the metal are determined by the behaviour of the population of Frenkel pairs that are created during the course of the irradiation. Point defects and Frenkel pairs can form clusters, and clusters grow by aggregation, forming voids where vacancies within them have accumulated. The formation of voids leads to swelling, which is an isotropic volume expansion of the metal that can be, for significant radiation doses, upto several tens of percent in magnitude. This can cause a considerable change in the linear dimensions as well (this scales as the cube root of the swelling percent).

Another phenomenon that can occur, depending on the mechanics of defect-vacancy formation, is growth, where volume remains constant but there is a change in shape of the metallic object. Usually, both swelling and growth occur, at different locations within the irradiated material. In addition, a phenomenon known as irradiation creep can occur, which is the slow deformation of the metal under constant mechanical and radiative stress.

It is interactions like these, and phenomena that occur when they aggregate over successively longer length (and time) scales within the reactor material that eventually have observable consequences on components that have dimensions of the order of meters, i.e., on the macroscopic scale. These consequences include onset of plasticity, fracture, or embrittlement.

Phenomena such as defect clustering and diffusion, formation of dislocations (a dislocation being formed whenever a regular pattern of defects significantly distorts the crystalline order), formation of separate phases and radiation-induced segregation also occur in the irradiated metal, each of which, depending on conditions, can contribute to the onset of plasticity or the start of fracture in a metal.

Zipping up a description starting from the lowest relevant length (and time) scale, up to the longest relevant length (and time) scale, using the most appropriate physical description at each scale - under conditions of high thermomechanical and radiative stress - is the challenge of Multiscale Materials Modeling under Irradiation (MMM-I). A certain amount of coarse graining is inevitable when this is attempted, and both sequential and parallel approaches are possible, as well as hybrid approaches that utilize elements of both methods.


My presentation Multi-scale Modeling of Radiation-Induced-Dislocation Pinning in Oxide-Dispersion Strengthened Steels (ODSS)- Part 1 and Multi-scale Modeling of Radiation-Induced-Dislocation Pinning in Oxide-Dispersion Strengthened Steels (ODSS)- Part 2 describe these ideas and my work in progress, in more detail, in the context of oxide dispersion strengthened steels, which have been suggested as possible reactor materials for new generation reactors in view of their superior creep strength under both radiative and thermomechanical stress, as well as corrosion resistance. This is the focus of my current work.

The Fall 2008 Meeting of the Materials Research Society in Boston has Symposium W on Computational Materials Design by Multiscale Modeling.