**1. Introduction**

258 Nuclear Reactors

Zacarias Mesquita, A.; Cesar Rezende, H. (2007). *Power measure channels of the IPR-R1 TRIGA* 

Javidkia, F.; Hashemi-Tilehnoee, M.; Zabihi ,V. (2011) *A Comparison between Fossil and* 

Engineering, Proceedings of COBEM 2007, Brazil.

and Power Engineering, Vol. 5, 811-820.

*research nuclear reactor by thermal methods*, 19th International Congress of Mechanical

*Nuclear Power Plants Pollutions and Their Environmental Effects*, Journal of Energy

In the process of energy production via fission – and fusion in the years to come - both fuel components and structural materials within nuclear reactors can sustain substantial radiation damage. Regardless of the type of reactor, this damage initially appears in the form of local intrinsic point defects within the material – vacancies and interstitials. The point defects agglomerate, interact with the underlying microstructure and produce effects such as void swelling and irradiation creep. Vacancies provide a pathway for solutes to segregate to grain boundaries and dislocation leading to chemical inhomogeneities that translate into phase transformations and/or property variations in these materials, rendering them unsuitable for the desired application.

Many deleterious effects of irradiation on material properties—e.g. void swelling, irradiation creep, radiation-induced hardening and embrittlement—can be traced back to the formation of the aforementioned point defect clusters and gas bubbles. These effects include such phenomena as swelling, growth, phase change, segregation, etc. For example (Was 2007), a block of pure nickel, 1cm on a side, irradiated in a reactor (to a fluence of say, 1022 n/cm2) will measure 1.06cm on a side, representing a volume change of 20%. The volume change, or swelling, is isotropic and is due to the formation of voids in the solid. Other examples are irradiation growth which is distortion at constant volume, phase changes under irradiation where new phases form as a consequence of diffusion of supersaturated defect concentrations and radiation induced segregation.

In addition, the transmutation of reactor elements produces extrinsic defects such as hydrogen, deuterium and helium. For example, Zircalloy high-pressure-tubes used in light water reactors are known to absorb deuterium which can cause delayed hydride cracking (Cirimello, G. et al. 2006). Similarly, in Pebble Bed Modular reactors and in other technologies based on inert gas cooling, formation of ionic gas bubbles within both fuel and structural materials is common(Was 2007). This is critical in structural materials as their behaviour depends on their microstructure, which is in turn affected by neutron radiation.

Multiscale Materials Modeling of Structural Materials for Next Generation Nuclear Reactors 261

Fig. 1. Multiscale processes that govern deformation processes in irradiated materials

complexity in a single framework.

**2. Radiation damage in materials** 

mechanics methods.

The scientific challenge for next-generation extreme materials – whatever their composition – is to understand their failure modes, and to prolong their useful lifetimes by interrupting or arresting these failures. Damage starts with atomic displacements that create interstitials and vacancies, which then migrate and aggregate to form clusters and ever-larger extended structures. Eventually, the damage reaches macroscopic dimensions, leading to degradation of performance and failure. This problem is massively multiscale, covering nine orders of magnitude in its spatial dimension, and neither experiment nor theory has yet captured this

On the experimental side, *in situ* measurements of neutron irradiation with atomic or nanoscale resolution are needed to observe the initial damage processes, followed by coarsergrained experiments to capture migration, aggregation and ultimately macroscopic failure. The modeling challenge is equally dramatic: kinetic energy from an incident particle is transferred successively to electronic, atomic, vibrational and structural systems, requiring a

This chapter will review choices for structural materials for these environments, and review the methods and techniques available for simulating these materials at various length and time scales Methods that will be reviewed will include first principles calculations, molecular dynamics calculations, kinetic Monte Carlo methods, and microstructural

At the smallest scales, radiation damage is continually initiated with the formation of energetic primary knock-on atoms (PKA) primarily through elastic collisions with high-

diverse mix of theoretical formulations appropriate for different spatial scales.

Cladding materials are also exposed to fission product gasses produced in the fuel during operation.

The effect of irradiation on materials is a classic example of an inherently multiscale phenomenon, as schematically illustrated in Figure 1 for the case of deformation and plasticity in irradiated materials. Irradiation changes the properties of cladding and duct materials as follows: increase in the ductile to brittle transition temperature; reduction of fracture toughness from low temperature irradiation (below 400oC); irradiation creep, helium embrittlement (above ~500C) and swelling. Experimental irradiation programs can be conducted to test the irradiation induced mechanical property changes, but these take significant time and the conditions are limited. As a consequence, it is desirable and efficient to develop models with reliable predictive capabilities for both, design of new reactor components, and simulation of the in-service response of existing materials.

Although these phenomena have been known for many years (Olander 1981; de la Rubia, Zbib et al. 2000; Was 2007) , the underlying fundamental mechanisms and their relation to the irradiation field have not been clearly demonstrated. Most models and theories of irradiation induced deformation and mechanical behavior rely on empirical parameters fit to experimental data. With improvements in computational techniques and algorithms, it is now possible to probe structure-property connections through the elucidation of fundamental atomic mechanisms. Often, these mechanisms involve defects of different dimensionality that exist and interact with each other to significantly affect material properties.

For irradiated materials, point defects and clusters affect crystal plasticity. Dislocation-defect interactions may be associated with defects in the matrix, the modification of the local elastic constants due to the presence of defects and defect clusters and the effects of clusters and voids on the stacking fault energy. The formation of self interstitial loop rafts and the decoration of dislocations with self interstitial clusters have become important issues for understanding radiation hardening and embrittlement under cascade damage conditions(Wen, Ghoniem et al. 2005). Dislocation motion is thought to be the main mechanism for deformation, because a fairly high density of network dislocations are generated during irradiation, and the dislocation sink strength for point defects is much higher that the grain boundary sink strength for point defects. Computational studies of dislocation activity can be performed at several different length and time scales(Ghoniem, Busso et al. 2003) that are shown in Fig. 1.

Pertinent processes span more than 10 orders of magnitude in length from the sub-atomic nuclear to structural component level, and span 22 orders of magnitude in time from the sub-picosecond of nuclear collisions to the decade-long component service lifetimes (Odette, Wirth et al. 2001; Wirth, G.R. et al. 2004). Many different variables control the mix of nano/microstructural features formed and the corresponding degradation of physical and mechanical properties in nuclear fuels, cladding and structural materials. The most important variables include the initial material composition and microstructure, the thermomechanical loads, and the irradiation history. While the initial material state and thermomechanical loading are of concern in all materials performance-limited engineering applications, the added complexity introduced by the effects of radiation is a large concern for materials in advanced nuclear energy systems.

Cladding materials are also exposed to fission product gasses produced in the fuel during

The effect of irradiation on materials is a classic example of an inherently multiscale phenomenon, as schematically illustrated in Figure 1 for the case of deformation and plasticity in irradiated materials. Irradiation changes the properties of cladding and duct materials as follows: increase in the ductile to brittle transition temperature; reduction of fracture toughness from low temperature irradiation (below 400oC); irradiation creep, helium embrittlement (above ~500C) and swelling. Experimental irradiation programs can be conducted to test the irradiation induced mechanical property changes, but these take significant time and the conditions are limited. As a consequence, it is desirable and efficient to develop models with reliable predictive capabilities for both, design of new reactor

Although these phenomena have been known for many years (Olander 1981; de la Rubia, Zbib et al. 2000; Was 2007) , the underlying fundamental mechanisms and their relation to the irradiation field have not been clearly demonstrated. Most models and theories of irradiation induced deformation and mechanical behavior rely on empirical parameters fit to experimental data. With improvements in computational techniques and algorithms, it is now possible to probe structure-property connections through the elucidation of fundamental atomic mechanisms. Often, these mechanisms involve defects of different dimensionality that exist and interact with each other to significantly affect material

For irradiated materials, point defects and clusters affect crystal plasticity. Dislocation-defect interactions may be associated with defects in the matrix, the modification of the local elastic constants due to the presence of defects and defect clusters and the effects of clusters and voids on the stacking fault energy. The formation of self interstitial loop rafts and the decoration of dislocations with self interstitial clusters have become important issues for understanding radiation hardening and embrittlement under cascade damage conditions(Wen, Ghoniem et al. 2005). Dislocation motion is thought to be the main mechanism for deformation, because a fairly high density of network dislocations are generated during irradiation, and the dislocation sink strength for point defects is much higher that the grain boundary sink strength for point defects. Computational studies of dislocation activity can be performed at several different length and time scales(Ghoniem,

Pertinent processes span more than 10 orders of magnitude in length from the sub-atomic nuclear to structural component level, and span 22 orders of magnitude in time from the sub-picosecond of nuclear collisions to the decade-long component service lifetimes (Odette, Wirth et al. 2001; Wirth, G.R. et al. 2004). Many different variables control the mix of nano/microstructural features formed and the corresponding degradation of physical and mechanical properties in nuclear fuels, cladding and structural materials. The most important variables include the initial material composition and microstructure, the thermomechanical loads, and the irradiation history. While the initial material state and thermomechanical loading are of concern in all materials performance-limited engineering applications, the added complexity introduced by the effects of radiation is a large concern

components, and simulation of the in-service response of existing materials.

operation.

properties.

Busso et al. 2003) that are shown in Fig. 1.

for materials in advanced nuclear energy systems.

Fig. 1. Multiscale processes that govern deformation processes in irradiated materials

The scientific challenge for next-generation extreme materials – whatever their composition – is to understand their failure modes, and to prolong their useful lifetimes by interrupting or arresting these failures. Damage starts with atomic displacements that create interstitials and vacancies, which then migrate and aggregate to form clusters and ever-larger extended structures. Eventually, the damage reaches macroscopic dimensions, leading to degradation of performance and failure. This problem is massively multiscale, covering nine orders of magnitude in its spatial dimension, and neither experiment nor theory has yet captured this complexity in a single framework.

On the experimental side, *in situ* measurements of neutron irradiation with atomic or nanoscale resolution are needed to observe the initial damage processes, followed by coarsergrained experiments to capture migration, aggregation and ultimately macroscopic failure. The modeling challenge is equally dramatic: kinetic energy from an incident particle is transferred successively to electronic, atomic, vibrational and structural systems, requiring a diverse mix of theoretical formulations appropriate for different spatial scales.

This chapter will review choices for structural materials for these environments, and review the methods and techniques available for simulating these materials at various length and time scales Methods that will be reviewed will include first principles calculations, molecular dynamics calculations, kinetic Monte Carlo methods, and microstructural mechanics methods.

#### **2. Radiation damage in materials**

At the smallest scales, radiation damage is continually initiated with the formation of energetic primary knock-on atoms (PKA) primarily through elastic collisions with high-

Multiscale Materials Modeling of Structural Materials for Next Generation Nuclear Reactors 263

clustering, migration and gas and solute diffusion and trapping. Evolution of the underlying materials structure is thus governed by the time and temperature kinetics of diffusive and reactive processes, albeit strongly influenced by spatial correlations associated with the sink structure of the microstructure and the continual production of new radiation damage. Extended defects including dislocations, precipitate interfaces and grain boundaries, which exist in the original microstructure and evolve during irradiation, serve as sinks for point defect absorption and for vacancy – self-interstitial recombination and/or point defect –

The inherently wide range of time scales and the "rare-event" nature of the controlling mechanisms make modeling radiation effects in materials extremely challenging and experimental characterization is often unattainable. Indeed, accurate models of microstructure (point defects, dislocations, and grain boundaries) evolution during service are still lacking. To understand the irradiation effects and microstructure evolution to the extent required for a high fidelity nuclear materials performance model will require a

Furthermore, the kinetic processes controlling defect cluster and microstructure evolution, as well as the materials degradation and failure modes may not entirely be known. Thus, a substantial challenge is to develop knowledge of, and methodologies to determine, the controlling processes so that they can be included within the models. Essentially, this is to avoid the detrimental consequences of in-service surprises. A critical issue that needs to be addressed is not only the reliability of the simulation but also the accuracy of the model for

Fig. 2. Illustration of the length and time scales (and inherent feedback) involved in the multiscale processes responsible for microstructural changes in irradiated materials

combination of experimental, theoretical, and computational tools.

representing the critical physical phenomena.

**3. Multiscale materials models** 

impurity clustering.

energy neutrons. Concurrently, high concentrations of fission products (in fuels) and transmutants (in cladding and structural materials) are generated, which can cause pronounced effects in the overall chemistry of the material, especially at high burnup. The primary knock-on atoms, as well as recoiling fission products and transmutant nuclei quickly lose kinetic energy through electronic excitations (that are not generally believed to produce atomic defects) and a chain of atomic collision displacements, generating cascade of vacancy and self-interstitial defects. High-energy displacement cascades evolve over very short times, 100 picoseconds or less, and small volumes, with characteristic length scales of 50 nm or less, and are directly amenable to molecular dynamics (MD) simulations if accurate potential functions are available and chemical reactions are not occurring. If change in electronic structure need to be included, then ab initio MD is needed and this is beyond current capabilities.

In order to simulate the appropriate reactor conditions for all models, it is important to connect the parameters of the atomistic models with reactor conditions and the type of irradiation encountered. The radiation damage event is composed of several distinct processes concluded by a displacement cascade (collection of point defect due to the PKA) and by the formation of an interstitial –which occurs when the PKA comes to rest-. In order to simulate the radiation effects, it is important to determine the type of energetic particle interaction we wish to model. In nuclear reactors, neutrons and charged fission product particles are the dominant energetic species produced (Beta and Gamma rays are also produced, but these create less damage than the neutrons and charged particles). The type of reactor determines the nature of the dominant energetic particle interaction. The proposed study will focus on neutrons and He ions. The additional aspect to consider concerns the energy of the PKA, which in the case of D-T fusion reaction can reach the order of ~1MeV. These energies are out of reach of atomistic simulations. Nonetheless cascade event simulations at lower energies –ranging from 5to 45 KeV- can yield significant insight on the evolution of defect type and number as a function of PKA energy. Was (2007) and Olander (1981) have extensively documented how it is possible to determine the primary damage state due to irradiation by energetic particles. The simplest model is one that approximates the event as colliding hard spheres with displacement occurring when the transferred energy is high enough to knock the struck atom off its lattice site.

The physics of primary damage production in high-energy displacement cascades has been extensively studied with MD simulations(Was 2007). The key conclusions from those MD studies of cascade evolution have been that i) intra-cascade recombination of vacancies and self-interstitial atoms (SIAs) results in ~30% of the defect production expected from displacement theory, ii) many-body collision effects produce a spatial correlation (separation) of the vacancy and SIA defects, iii) substantial clustering of the SIAs and to a lesser extent, the vacancies occurs within the cascade volume, and iv) high-energy displacement cascades tend to break up into lobes, or sub-cascades which may also enhance recombination(Calder and Bacon 1993; Calder and Bacon 1994; Bacon, Calder et al. 1995; Phythian, Stoller et al. 1995).

It is the subsequent transport and evolution of the defects produced during displacement cascades, in addition to solutes and transmutant impurities, that ultimately dictate radiation effects in materials, and changes in material microstructure(Odette et al. 2001; Wirth et al. 2004). Spatial correlations associated with the displacement cascades continue to play an important role over much larger scales, as do processes including defect recombination, clustering, migration and gas and solute diffusion and trapping. Evolution of the underlying materials structure is thus governed by the time and temperature kinetics of diffusive and reactive processes, albeit strongly influenced by spatial correlations associated with the sink structure of the microstructure and the continual production of new radiation damage. Extended defects including dislocations, precipitate interfaces and grain boundaries, which exist in the original microstructure and evolve during irradiation, serve as sinks for point defect absorption and for vacancy – self-interstitial recombination and/or point defect – impurity clustering.

The inherently wide range of time scales and the "rare-event" nature of the controlling mechanisms make modeling radiation effects in materials extremely challenging and experimental characterization is often unattainable. Indeed, accurate models of microstructure (point defects, dislocations, and grain boundaries) evolution during service are still lacking. To understand the irradiation effects and microstructure evolution to the extent required for a high fidelity nuclear materials performance model will require a combination of experimental, theoretical, and computational tools.

Furthermore, the kinetic processes controlling defect cluster and microstructure evolution, as well as the materials degradation and failure modes may not entirely be known. Thus, a substantial challenge is to develop knowledge of, and methodologies to determine, the controlling processes so that they can be included within the models. Essentially, this is to avoid the detrimental consequences of in-service surprises. A critical issue that needs to be addressed is not only the reliability of the simulation but also the accuracy of the model for representing the critical physical phenomena.
