Refined cascade model and Monte Carlo code for calculation of radiation damage of heterogeneous structures of multicomponent materials :: SPE RESST

Refined cascade model and Monte Carlo code for calculation of radiation damage of heterogeneous structures of multicomponent materials


Calculations of the concentration fields of point defects in irradiated structural materials and targets with complex three-dimensional (3D) geometry are relevant for many problems of radiation physics, nuclear and irradiation technologies. In particular, they are important for the optimal planning and analysis of the results of the simulation experiments on radiation materials science of the alternative options of nuclear power systems (HTGR, MSR, SCWR) of Generation IV and the traveling nuclear wave reactor (TWR) which are undertaken at the NSC KIPT hosted accelerators of ions and electrons. In these prospective studies, an important role plays the refinement of the physical models of the formation of radiation defects and the increase in the computational efficiency of the methods and computer programs used in the calculations.

A common measure of the primary radiation damage is the specific (per atom of the material) number of atomic displacements (dpa). The most adequate approach to the dpa calculations in multicomponent materials consists in atomistic computer simulation of atomic collisions cascades (ACCs) produced by primary knocked atoms (PKAs) generated by external irradiation. Traditionally, it is conducted by means of molecular dynamics (MD) or binary collisions approximation (BCA) methods. However, the existing atomistic simulation codes' capabilities of reproducing the conditions of real irradiation experiments in are either not provided at all (case of the vast majority of MD codes operating within the framework of the concept of "defects in a material") or are restricted to layered target geometries (as in the SRIM codes family routinely used for ion irradiation). The obvious motive for this is the extreme inefficiency of the atomic-level description of nontrivial macroscopically heterogeneous systems.

Modeling of the primary radiation damage of real subjects of irradiation is the prerogative of Monte Carlo codes (MCNP, MCU, MVP, PSG2, etc.). They offer wide possibilities of specification of complex designs of installations and targets, as well as of spatial and energy distributions of primary radiation sources. However, they are out of capability of direct simulation of defect production in collision cascades and apply to dpa calculations the approximate analytical method of Norgett-Robinson-Torrence (1973), known as the NRT standard. Although this method retains its importance as an operational practical standard of reactor dosimetry, it is formally applicable only to simple one-component materials and, unlike atomistic modeling, does not take into account the cascade efficiency of atomic displacement in complex atomic mixtures and transient effects near the interfaces in heterogeneous systems.

The task to merge the advantages provided by the codes of both these types was set and solved by us [28 (2012)] within the framework of the SPE RESST developed Geant4 Toolkit based multipurpose Monte Carlo code RaT 3.1. In the code, the physical models of elastic atom-atom scattering and ionization energy losses of ions were implemented, and coordinated with the models and data of the atomistic code SRIM2011 which simulates the ACC by means of the binary collision method. The Geant4 offered radiation transport simulation Monte Carlo algorithms were supplemented by the ACC-in-solid specific nonclassical algorithms of sampling of the mean free paths of atoms as well as of the impact parameters of atomic collisions. Thus, it has been managed to simulate the ACC in the framework of the general Monte Carlo simulations modeling scheme (see Fig. 1) and to create a computer code capable of consistent modeling of cascade radiation damage under irradiation of various kind (neutron, ion, electron, and also combined) on spatial scales from atomic (~nm) to macroscopic (~m). To our knowledge, this distinguishes the new version of the RaT code from all the general-purpose Monte Carlo codes.

Fig. 1 – Typical 100 keV energy PKA generated cascades in Nickel modeled by the standard code SRIM2011 (a) and the new version of the RaT 3.1 code (b)

The new version of the RaT code has been validated by comparing the simulation results with those of the SRIM2011 code calculations in the planar geometry of targets acceptable for both programs. The SRIM calculated secondary displacement functions of cascades in nickel irradiated by light (H, Ne), self- (Ni) and heavy (Xe) ions with energies from 100 eV to 1 MeV were reproduced with a relative error of not worse than 5%. For a multicomponent structural material, the stainless steel Х18Н10Т, modeling of spatial distributions of radiation defects was successfully benchmarked against the example of irradiation by 1.8 MeV chromium ions at the accelerator ESUVI, which is relevant for simulation studies of the NSC KIPT Institute of Solid State Physics, Materials Science and Technologies. As can be seen in Fig. 2, the corresponding implantation and damage profiles practically do not differ for both codes calculations.

Fig. 2 – The ion implantation and damage profiles of stainless steel irradiated by chromium ions calculated in different (full/quick damage) simulation modes of the standard code SRIM and by the RaT code using a new cascade model and in the NRT-standard approximation

The developed model of the RaT code has found a practical application for the analysis of the data of the unique simulation irradiation [32 (2012)] of prospective Generation IV Super-Critical Water-Cooled Reactor (SCWR) structural materials, Ni-Cr alloy Inconel 690 and Zr-1%Nb zirconium alloy, in a convective water flow at a temperature of 360°C and a pressure of 235 atm (see Figure 3), which had been performed at the NSC KIPT Science and Research Establishment "Accelerator" hosted electron linac LPE-10. Apparently, for this simulation experiment, a complex heterogeneous design of the target device and a significant heterogeneity of the radiation field are characteristic. The simulation allowed to calculate the required dosimetric parameters of the radiation effect on the samples, to reveal the effect of the alloys oxidation enhancement under irradiation, and its correlation with temperatures of samples.

Fig. 3 – Three-dimensional spatial distributions of the rate of accumulation of atomic displacements in tubes of the irradiation chamber and samples of alloys irradiated by 10 MeV electrons in the convective flow of a water coolant calculated using the cascade model of the RaT 3.1 code

Fig. 3 also illustrates the wide capabilities of the RaT code for modeling of geometrically complex (including randomly inhomogeneous [2 (2012)]) heterogeneous media of the propagation of radiation. Along with applications to simulation experiments in reactor materials science, it can find applications in the computational support of radiation technologies for ion implantation, ion-beam and ion-plasma processing of an inhomogeneous surface, as well as in radiation nanophysics. These promising applications are illustrated by the simulation results shown in Figs. 4 and 5.

Fig. 4 – A sketch of implantation of gallium arsenide, GaAs, with 100 keV energy silicon ions through the profiled mask of PMMA photoresist (a) and the RaT 3.1 code calculated spatial distributions of the implanted ions (б), the ion beam produced interstitial atoms (в), vacancies (г) and defects of replacement (д)

As it follows from Fig. 4, for the problems of ion implantation, the developed code allows to calculate, with nanometer spatial resolution, not only three-dimensional concentration fields of dopants implanted through (possibly profiled) resistive masks, but also the corresponding fields of primary production of defects of various types. By these parameters, it is comparable with the specialized packages, the technological process simulators, used in the modern electronic industry.

Figure 5 demonstrates the application of the RaT code to the forward-looking tasks of irradiation nanotechnology. The accumulation of radiation defects of various types in silicon nanowires (NW) with a characteristic transverse size of 4 nm under irradiation by ions of keV energies is considered.

Fig. 5 – Spatial distributions of vacancies (top) and interstitial atoms (bottom) formed by irradiating a nanowire with argon ions of different energies (the ion beam falls from below perpendicular to the axis of the nanowire)

The RaT code calculated energy dependences of the integral characteristics of the radiation damage of the nanowire are in qualitative agreement with the results of the paper S. Hoilijoki, E. Holmstrom, K. Nordlund, "Enhancement of Irradiation-Induced Defect Production in Si Nanowires", J. Appl. Phys. 110(2011)043540 in which defect formation under the indicated conditions was simulated by the method of stable molecular dynamics. A quantitative comparison showed that with the standard, for bulk silicon, value of the energy threshold for defect production, Ed = 15 eV, the RaT code lowers the number of defects by 60%. However, at Ed = 9 eV, the discrepancy is reduced to 10-15%. Such an analysis makes it possible to estimate the effective energy thresholds for the formation of defects in nanosystems, taking into account intrinsic effects of their size. The obtained values of threshold energies can be further used in routine process calculations of radiation damage to irradiated arrays of nanowires. Such a task seems inaccessible for the performance-limited MD simulation, but can be solved by the Monte-Carlo code RaT.