Full energy range primary radiation damage model

A full energy range primary radiation damage model is presented here. It is based on the athermal recombination corrected displacements per atom (arc-dpa) model but includes a proper treatment of the near threshold conditions for metallic materials. Both ab initio (AIMD) and classical molecular dynamics (MD) simulations are used here for various metals with body-centered cubic (bcc), face-centered cubic (fcc), and hexagonal close-packed (hcp) structures to validate the model. For bcc and hcp metals, the simulation results fit very well with the model. For fcc metals, although there are slight deviations between the model and direct simulation results, it is still a clear improvement on the arc-dpa model. The deviations are due to qualitative differences in the threshold energy surfaces of fcc metals with respect to bcc and hcp metals according to our classical MD simulations. We introduce the minimum threshold displacement energy (TDE) as a term in our damage model. We calculated minimum TDEs for various metal materials using AIMD. In general, the calculated minimum TDEs are in very good agreement with experimental results. Moreover, we noticed a discrepancy in the literature for fcc Ni and estimated the average TDE of Ni using both classical MD and AIMD. It was found that the average TDE of Ni should be ∼70 eV based on simulation and experimental data, not the commonly used literature value of 40 eV. The most significant implications of introducing this full energy range damage model will be for estimating the effect of weak particle-matter interactions, such as for γ- and electron-radiation-induced damage.

Figure 1

Damage energy models displayed for face-centered cubic (fcc) Cu, with comparison with experiments and classical molecular dynamics (MD) simulations. When $N_d<1$, it is the probability to produce a stable Frenkel pair in each damage event. For the experimental reference damage data, we name them as Zinkle 1993 [12]; the damage energy of the experimental data is determined from the recoil energy [9]; the Cu interatomic potential used in this work are from Ref. [25]. $E_d^{\min }$ and $E_d^{\mathrm{avr}}$ in our modified model were calculated from classical MD simulations for self-consistency.

Figure 2

Damage production in body-centered cubic (bcc) metals. Classical and ab initio molecular dynamics (MD) simulations, as well as the athermal recombination corrected displacements per atom (arc-dpa) model and our low-energy extension are compared. For our own classical MD simulations, the reference numbers are the interatomic potentials used in this work; for the reference damage data using classical MD simulations, we name them as last name of the interatomic potential developer and publication year of the potential for better comparison; for the density functional theory (DFT) reference data, we name them as last name of first author and publication year. The reference numbers for reference classical MD data contain both simulation works and potential development works (some of the potential developers also performed simulations). Reference data: V: Johnson 1989 [28, 29]; Fe: Calder 1993 [31, 32], Marinica 2007 [33], Olsson 2016 [18]; Nb: Lin 2017 [35]; W: Ackland 1987 [9, 38]; Björkas 2009 [9, 39]. Interatomic potentials used in this work: V [30], Fe [34], Nb [36, 37], W [40, 41]. $E_d^{\min }$ and $E_d^{\mathrm{avr}}$ were calculated from classical MD simulations for self-consistency. The error bars correspond to standard deviation.

Figure 3

Damage production in face-centered cubic (fcc) metals. Classical molecular dynamics (MD) simulations, experimental data, as well as the athermal recombination corrected displacements per atom (arc-dpa) model and our low-energy extension are compared. For our own classical MD simulations, the reference numbers are the interatomic potentials used in this work; for the reference damage data using classical MD simulations, we name them as last name of the interatomic potential developer and publication year of the potential for better comparison; for the experimental reference data, we name them as last name of first author and publication year. The reference numbers for reference classical MD data contain both simulation works and potential development works. Reference data: Al: Ercolessi 1994 [42, 43]. Ni: Cleri 1993 [45, 46]; Cu: Zinkle 1993 [12], Averback 1998 [8], Sabochick 1991 [9, 48]; Ag: Merkel 1977 [49]. Interatomic potentials used in this work: Al [44], Ni [36, 47], Cu [25], Ag [50, 51]. $E_d^{\min }$ and $E_d^{\mathrm{avr}}$ were calculated from classical MD simulations for self-consistency. The damage energy in the experimental data was determined from the recoil energy for Cu [9] and Ag [27]. The error bars correspond to standard deviation.

Figure 4

Damage production in hexagonal close-packed (hcp) metals. Classical molecular dynamics (MD) simulations, as well as the athermal recombination corrected displacements per atom (arc-dpa) model and our low-energy extension are compared. For our own classical MD simulations, the reference numbers are the interatomic potentials used in this work; for the reference damage data using classical MD simulations, we name them as last name of the interatomic potential developer and publication year of the potential for better comparison. The reference numbers for reference classical MD data contain both simulation works and potential development works. Reference data: Ti: Ackland 1992 [52, 53]; Zr: Ackland 1995 [52, 55]. Interatomic potentials used in this work: Ti [53, 54], Zr [47]. $E_d^{\min }$ and $E_d^{\mathrm{avr}}$ were calculated from classical MD simulations for self-consistency. The error bars correspond to standard deviation.

Figure 5

The cumulative distribution function (CDF) of threshold displacement energy (TDE) distributions in Fe, Ag, and Cu. For our own classical molecular dynamics (MD) simulations, the reference numbers are the interatomic potentials used in this work. The dashed black lines are the CDF of uniformly distributed TDEs, which is the ideal assumption used in the modified model. The dashed gray lines are the average TDE calculated from classical MD simulations. The interatomic potentials are Fe [34], Ag [50], Cu [25]. The experimental references are King 1981 [10] and King 1983 [11].