MD and OKMC simulations of the displacement cascades in nickel

MD and OKMC simulations of the displacement cascades in nickel 1 first-author 1 1 1 2 2 1 corresp Corresponding author: Hu Wang-yu, E-mail: wyuhu@hnu.edu.cn Corresponding author: Hu Wang-yu, E-mail: wyuhu@hnu.edu.cn wyuhu@hnu.edu.cn Department of Applied Physics, School of Physics and Electronics, Hunan University, Changsha 410012, China Department of Applied Physics, School of Physics and Electronics, Hunan University, Changsha 410012, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China The molecular dynamics (MD) method was used to investigate the displacement cascades with primary knock-on atom (PKA) energies of 2–40 keV at 100 K and 600 K. The migration energy of defects and their clusters were calculated by Nudged elastic band (NEB) method. Object Kinetic Monte Carlo (OKMC) was used to simulate the evolution of defects in Ni under annealing. In each annealing stage, the recombination mechanism was discussed and evolution of the defects under different cascade conditions was compared. It was found that the defects generated in high temperature cascades are more stable than those in the low temperature cascades. In addition, almost all the defects are annihilated during annealing process at low PKA energy. At PKA energy of 20–40 keV, however, a large number of defects would remain after annealing. Displacement cascades Molecular dynamics simulation Object Kinetic Monte Carlo; 1. Introduction 1 Thorium Molten Salt Reactor (TMSR) is considered as a candidate of the Generation 4 reactors [ 1 1 , 2 2 ] . Due to the excellent high temperature properties and corrosion resistance, Hastelloys are important structural materials for advanced nuclear reactors [ 3 3 , 4 4 ] . Ni is the major element in Hastelloys, and its irradiation property has been discussed for decades. By comparing the displacement cascades in Cu and Fe with Ni, King et al . [ 5 5 ] and Kwon et al . [ 6 6 ] found that more residual defects could be generated and more point defects were able to get clustered in Cu and Fe than those in Ni. Several interatomic potentials for Ni were used to investigate the effect of stacking fault energy (SFE) on cascade evolution [ 7 7 ] . The results showed that it was easier for the sacking fault tetrahedron (SFT) to form at lower SFE. Additionally, the spatial and time scales accessible to molecular dynamics (MD) simulation are only nanometers and nanoseconds. Therefore, MD simulation is limited for the practical prediction of microstructural evolution for long time scale. A solution to solve this problem is the application of the Object Kinetic Monte Carlo (OKMC) method together with MD, which has been successfully proved in defect simulations in Fe and Cu annealing [ 8 8 - 10 10 8-10 ] , by simulating the damage using the MD method. Based on the cascade simulations, Almazouzi [ 11 11 ] used the KMC method to describe the long term evolution of the defects in Ni and showed that the annealing temperature affected the fraction of the defects that escaped the KMC boundary strongly. Only the diffusion of mono-vacancy and di-vacancy were considered in the study and low primary knock-on atom (PKA) energy ( E P < 10 keV) cascades were simulated. It was found that almost 90% of the MD-produced defects might be freely migrating defects at annealing temperatures of > 500 K. However, the study did not considered the migration of big vacancy clusters, the influences of irradiation at high temperatures, and PKA energies on the evolution of the defects in Ni. Large clusters will form in the cascades under high energy at high temperature. So, it is necessary to consider the migrations for more types of defects. In this paper, we simulate the cascades in Ni at high energy and temperature. The Nudged elastic band (NEB) method is used to simulate the migration energies for more kinds of defects. The evolutions of defects are studied by the OKMC method. These methods can accurately describe the long term evolution of the defects produced by a displacement cascade, and we can be prepared for studying Hastelloy alloy in the future. 2. Simulation methods 1 In this paper, a modified analytic embedded-atom method (MAEAM) potential, which has been successfully applied to metallic systems, is used to do MD simulations. The energy of every atom ( E i ) in a crystal is given by <math display="block" id="M1"><mrow><msub><mi>E</mi><mi>i</mi></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mstyle displaystyle="true"><munder><mo>∑</mo><mrow><mi>j</mi><mo>≠</mo><mi>i</mi></mrow></munder><mrow><mi>φ</mi><mo stretchy="false">(</mo><msub><mi>r</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></mrow></mstyle><mo stretchy="false">)</mo><mo>+</mo><mi>F</mi><mo stretchy="false">(</mo><msub><mi>ρ</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>+</mo><mi>M</mi><mo stretchy="false">(</mo><msub><mi>P</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>,</mo></mrow></math> where Φ ( r ij ) is the pairwise interaction between atoms i and j with a pair separation of r ij ; M ( P i ) is the experiential modification item and F ( ρ i ) is the embedding energy. The potential functions are described in detail by Wang et al . [ 12 12 ] . The potential parameters for Ni are given in Table 1 Table 1 . 1 1 F 0 1 1 2.9545685 1 1 k c 1 1 0.05 1 1 n 1 1 0.355 1 1 k 0 1 1 −2.1557471e+02 1 1 ρ e 1 1 12.976133 1 1 k 1 1 1 1.3880198 1 1 P e 1 1 12.714634 1 1 k 2 1 1 −1.0619366 1 1 α 1 1 −1.6501104e−3 1 1 k 3 1 1 −9.6388310e−01 1 1 β 1 1 4.69 1 1 u 1 1 1 1.0 1 1 γ 1 1 5.41 1 1 u 2 1 1 1.5 In this paper, we use a modified MOLDY code to study the displacement cascades in Ni. All simulation blocks in a size of 60 a 0 ×60 a 0 ×60 a 0 (864,000 atoms) are firstly equilibrated at 100 K and 600 K for about 10 ps in NVT ensemble, where a 0 is the lattice constant of Ni. Then, a primary knock-on atom of E P = 2–40 keV is initialized in a block center. Five different directions are assigned to the PKA to get the statistical results. The cascade simulation time with MD is 10 ps under each radiation condition, so that the cascade region can be cooled down completely. The Wigner-Seitz cell method is utilized to identify the defects [ 13 13 ] . The distribution of defects obtained from the MD simulations is used as the input date for OKMC simulations [ 14 14 ] . Other input parameters for OKMC simulations are the migration energies of various defects in Ni. The NEB method is used to calculate the migration barriers [ 15 15 , 16 16 ] , which is easier and more reliable than the MD method in calculating the migration energies. The binding energies of different defects are calculated by the MD method. All the energies are calculated in the box of 10 a 0 ×10 a 0 ×10 a 0 . In order to find the most stable structure of defect clusters, all possible configurations of the defects of the same size are considered. A defect of the lowest formation energy and the biggest binding energy is the most stable structure. Based on the above results, the OKMC is mainly used to simulate the evolution of radiation-induced defects. The defects can be translated randomly or in accordance with the special direction in the crystal lattice. As used widely in radiation damage simulations, only the positions of transition objects are considered [ 17 17 , 18 18 ] . The objects which can be treated with OKMC codes include vacancies, self-interstitial atoms (SIAs) and their clusters. In this model, defects are assumed to be spherical and their specific atomic structures are ignored. Four types of events can be considered in these objects: 1) jump to a neighbor position; 2) recombination between anti-type defects or coarsening between none-anti-type defects; 3) emission of an element from a defect cluster; 4) annihilation and sink of mobile defects at grain boundaries, free surfaces or dislocations. The pre-factors of diffusion in annealing simulations are taken from the Ref [ 19 19 ]. The box size of OKMC simulations is (105 nm) 3 and periodic boundary conditions (PBC) is used in the simulations. Residual defects in the cascade collisions are annealed at 30–800 K and each simulation is repeated 20 times to ensure good statistics. 3. Results and Discussion 1 3.1. Validation of potential 2 The potential was tested and the defect formation energies of single vacancy ( E vac ), dumbbells in different directions ( E d-111 , E d-110 and E d-100 ), SIA initialized in octahedral or tetrahedral interstitial site ( E oct and E tet ), and the elastic constants ( C 11 , C 12 and C 44 ) were calculated, as shown in Table 2 Table 2 , together with the results of other authors. It can be seen that the stability order of the defects is E d-100 < E d-110 < E d-111 < E oct < E tet and the dumbbell in < 100 > direction has the lowest formation energy. Our results are closely related to the following studies on defects migration. The formation energies of different kinds of defects and elastic constants agree well with those from previous simulations [ 20 20 , 21 21 ] and experimental results [ 22 22 ].0.91 1 1 Authors 6 1 Defect formation energies (eV) 3 1 Elastic constant (GPa) 1 1   1 1 E vac 1 1 E d-111 1 1 E d-110 1 1 E d-100 1 1 E oct 1 1 E tet 1 1 C 11 1 1 C 12 1 1 C 44 1 1 This work 1 1 1.51 1 1 4.84 1 1 4.62. 1 1 4.00 1 1 5.23 1 1 6.10 1 1 260.7 1 1 150.7 1 1 126.0 1 1 MD [ 20 20 ] 1 1 1.95 1 1 5.31 1 1 — 1 1 5.26 1 1 5.28 1 1 6.64 1 1 257 1 1 155 1 1 136 1 1 DFT [ 21 21 ] 1 1 1.5–1.7 1 1 4.24 1 1 — 1 1 4.08 1 1 — 1 1 — 1 1 261.2 1 1 150.8 1 1 131.7 1 1 Exp. [ 22 22 ] 1 1 1.63 1 1 — 1 1 — 1 1 — 1 1 — 1 1 — 1 1 260 1 1 150 1 1 126 3.2. Defect production in Ni 1 Fig.1 Fig.1 shows the mean number of SIA-vacancy pairs ( N F ) value for the cascades of Ni in this work and other metals in Ref. [ 23 23 ] at 100 K (initial te mperature) at different PKA energies ( E P ), and the N F - E P curve at 600 K obtained in this work. The N F increases with E P . Only a few defects survive at E P < 10 keV. The number of defects is over 100 at E p > 40 keV. As atoms of high energy collide intensively, more defects are formed in the box. The defect production curve N F in log-log scales fits excellently the Bacon power law of N F =AE P m , where A =4.20 and m = 0.91 at 100 K in Ni, though they depend weakly on material and temperature. At 600 K( Fig.1b Fig.1b ), we have N F =2.82 E P 1.02 . Fig.2 Fig.2 shows the distributions of defects in stable state at 600 K with E P =2 keV and 40 keV. The box size was diminished six times in Fig.2(a) Fig.2(a) in order to observe the defect distribution clearly. At 2 keV, only a few individual defects remained in the box, while at 40 keV, the defects number reached one hundred. In this condition, clusters of self-interstitial atoms distribute at the center of collision region, surrounded by vacancies without the formation of stacking fault tetrahedral (SFT) structure. 3.3. Defect energetics 1 The migration energies of various defects are listed in Table 3 Table 3 . In this paper, a single defect (interstitial and vacancy) has a three-dimensional migration regime. The I 2 and I 3 ( I n means the cluster consists of n interstitial atoms) clusters have similar ground-state configurations of the < 100 > dumbbell. Larger defect clusters migrate via the one-dimensional mechanism without direction change. The dumbbells in the configuration of I 4 are not aligned, and not discussed here. The vacancies are assumed as immobile with the cluster size of > 4. Similar results were reported in Ref.[ 9 9 ]. Using the NEB method can simulate more types of the migration energies than MD method. The migration energies we obtained are compared with the experimental value. The migration energies of the single defect (V 1 and I 1 ) simulated by MD [ 11 11 ] are slightly lower than the experimental value. 1 1 Defect types 1 1 This work 1 1 MD simulated [ 11 11 ] 1 1 Measured 1 1 V 1 1 1 1.395 1 1 0.85 1 1 1.1/1.8 [ 24 24 ] 1 1 V 2 1 1 1.478 1 1 0.57 1 1 0.83 [ 25 25 ] 1 1 V 3 1 1 1.529 1 1 -- 1 1 — 1 1 V 4 1 1 1.501 1 1 -- 1 1 — 1 1 I 1   1 1 0.250 1 1 0.12 1 1 0.14-0.18  [ 26 26 ] 1 1 I 2 1 1 0.103 1 1 0.1 1 1 0.12 [ 27 27 ] 1 1 I 3 1 1 0.326 1 1 0.1 1 1 — It is believed that clusters are mobile, but the mobility decreases as defect size increases. The migration energies of SIA and SIA clusters are much lower than those of vacancy clusters, which leads to different behaviors during the evolution of defects. The binding energies of vacancies and interstitials in a cluster of size ( n ) are given by: <math display="block" id="M2"><mrow><msub><mi>E</mi><mrow><mtext>b-v</mtext></mrow></msub><mo>=</mo><mtext> </mtext><mn>0.35</mn><msup><mi>n</mi><mrow><mn>0.26</mn></mrow></msup><mo> </mo><mo> </mo><mo>,</mo></mrow></math> <math display="block" id="M3"><mrow><msub><mi>E</mi><mrow><mtext>b-I</mtext></mrow></msub><mo>=</mo><mtext> </mtext><mn>0.27</mn><msup><mi>n</mi><mrow><mn>2.19</mn></mrow></msup><mo> </mo><mo> </mo><mo> </mo><mo>.</mo></mrow></math> 3.4. Annealing simulations 2 Based on the results of MD simulations and NEB calculations, the evolution of defects in bulk Ni were studied with OKMC simulations. Fig. 3(a) Fig. 3(a) shows the evolution of defects in bulk Ni after displacement cascades at 100 K and 40 keV. The annealing process has three stages. Stage I corresponding to the correlated recombinations is observed at 112 K, mainly resulted from the recombination of the single interstitials and vacancies. In the simulations in Ref.[ 11 11 ], the Stage I temperature was 57 K, and was lower than the experimental value. At about 145 K, the clusters began to annihilate. Stage II begins at 338 K. This stage mainly due to recombination of the defect clusters. The temperature of Stage II agrees with the experimental value of 350 K. Stage III is attributed to the dissociation of defect clusters at about 535 K. After the annealing process, 61% defects are residual and all in the form of cluster. Fig. 3(b) Fig. 3(b) shows the simulated evolution process for defects produced in the cascades at 600 K and 40 keV. Most defects are annihilated at Stage I, which is similar to the Stage I at 100 K. But in Stage II, recombination of the defect clusters at 600K is significantly less than those at 100 K. And in Stage III the defect number keeps almost the same. This reason is that the defect clusters formed at the high temperature cascade are more stable than at the low temperature cascade. So that the defect clusters at the high temperature cascade are difficult to emit defects during the annealing process. After the annealing process, 69% defects remained in the box. Fig. 4 Fig. 4 shows the number of surviving defects during annealing, for E P = 2–40 keV at irradiation temperature of 600 K. It can be seen that Stage I temperature for E P =2 keV is obvious lower than those of the higher PKA energies. This is mainly due to different configurations of the defects. As shown in Fig 2(a) Fig 2(a) , the defects at E P = 2 keV are just individual defects, which are easier to migrate than clustered defects. For E P =2 keV, there was only one recombination stage in the annealing process, and all the defects were annihilated at last. At E P =10 keV, three stages appeared in the annealing process and no defects remained after annealing. At E P =20 keV, a modest increase of defect appeared, at annealing temperature of 550 K This is due to the new emission of defect in the annealing process. Previous analysis showed that under high PKA energy and irradiation conditions, defect clusters of large sizes could be generated. This kind of clustered defect can emit single defect to reduce its size. However, the increase in size of the point defect cluster will increase the binding energy and decrease the emission probability of the cluster. These defect clusters are difficult to annihilate. At E P =20 keV and 40 keV, there are still a large number of defects (58% and 69%) at annealing temperature of 800 K. 4. Conclusion 1 The MD method was used to investigate the displacement cascades and the N F - E P curve shows log-log scales. The migration energies calculated by NEB method agree well with experimental value. OKMC was used to simulate the evolutions of defects in Ni under different irradiation conditions. The evolution stages are as follows: Stage I at about 115 K, Stage II at about 350 K and Stage III at about 550 K. The defects generated in high temperature cascades are more stable than those in the low temperature cascades. At E P ≤10 keV, almost all the defects annihilate in the annealing process; while at E P ≥20 keV, about 60% of the defects remain after annealing process. References L Zhu , P Pu , S Du , et al . Simulation of neutron diffusion and transient analysis of MSR . Nucl Sci Tech , 2014 , 25 : 020601 . DOI: 10.13538/j.1001-8042/nst.25.020601 http://doi.org/10.13538/j.1001-8042/nst.25.020601 Simulation of neutron diffusion and transient analysis of MSR X Zhou and G Liu . Study of control rod worth in the TMSR . Nucl Sci Tech , 2013 , 24 : 010601 . DOI: 10.13538/j.1001-8042/nst.2013.01.003 http://doi.org/10.13538/j.1001-8042/nst.2013.01.003 Study of control rod worth in the TMSR J R Keiser . Compatibility studies of potential molten-salt breeder reactor materials in molten fluoride salts . Tennessee : Oak Ridge National Laboratory , 1977 . Compatibility studies of potential molten-salt breeder reactor materials in molten fluoride salts W G Liu , H Han , C L Ren , et al . The effect of Nb additive on Te-induced stress corrosion cracking in Ni alloy: a first-principles calculation . Nucl Sci Tech , 2014 , 25 ( 5 ): 050603 . DOI: 10.13538/j.1001-8042/nst.25.050603 http://doi.org/10.13538/j.1001-8042/nst.25.050603 The effect of Nb additive on Te-induced stress corrosion cracking in Ni alloy: a first-principles calculation W E King and R Benedek . Computer simulation study of the displacement threshold-energy surface in Cu . Phys Rev B , 1981 , 23 : 6335 - 6339 . DOI: 10.1103/PhysRevB.23.6335   http://doi.org/10.1103/PhysRevB.23.6335   Computer simulation study of the displacement threshold-energy surface in Cu J Kwon , W Kim and J H Hong . Comparison of the primary damage states in iron and nickel by molecular dynamics simulations . Radiat Eff Defect S , 2006 , 4 : 207 - 218 . DOI: 10.1080/10420150600704013 http://doi.org/10.1080/10420150600704013 Comparison of the primary damage states in iron and nickel by molecular dynamics simulations Z Yao , M J Caturla and R Schaublin , Study of cascades damage in Ni by MD with different interatomic potentials , J Nucl Mater , 2007 , 367 : 298 - 304 . DOI: 10.1016/j.jnucmat.2007.03.136 http://doi.org/10.1016/j.jnucmat.2007.03.136 Study of cascades damage in Ni by MD with different interatomic potentials M J Caturlaa , N Soneda , T. Diaz de la Rubia , et al . Kinetic Monte Carlo simulations applied to irradiated materials: The effect of cascade damage in defect nucleation and growth . J Nucl Mater , 2006 , 351 : 78 - 87 . DOI: 10.1016/j.jnucmat.2006.02.019 http://doi.org/10.1016/j.jnucmat.2006.02.019 Kinetic Monte Carlo simulations applied to irradiated materials: The effect of cascade damage in defect nucleation and growth C C Fu , J D Torre , F Willaime , et al . Multiscale modelling of defect kinetics in irradiated iron . Nat Mater , 2005 , 4 : 68 - 74 . DOI: 10.1038/nmat1286 http://doi.org/10.1038/nmat1286 Multiscale modelling of defect kinetics in irradiated iron F Gao , D J Bacon , A V Barashev , et al . Kinetic Monte Carlo Annealing Simulation of Damage Produced by Cascades in Alpha-Iron . Materials Research Society Symposium Proceedings . 1999 , 540 : 703 - 710 . Kinetic Monte Carlo Annealing Simulation of Damage Produced by Cascades in Alpha-Iron A Almazouzi , M J Caturla , T. Diaz de la Rubia , et al . Annealing kinetics of single displacement cascades in Ni: an atomic scale computer simulation , Mat Res Soc Symp Proc , 1999 , 540 : 685 - 690 . DOI: 10.1557/PROC-540-685 http://doi.org/10.1557/PROC-540-685 Annealing kinetics of single displacement cascades in Ni: an atomic scale computer simulation K Wang , S F Xiao , H Q Deng , et al . An atomic study on the shock-induced plasticity and phase transition for iron-based single crystals . Int J Plasticity , 2014 , 59 : 180 - 198 . DOI: 10.1016/j.ijplas.2014.03.007   http://doi.org/10.1016/j.ijplas.2014.03.007   An atomic study on the shock-induced plasticity and phase transition for iron-based single crystals W R Bowen and F Jenner . Dynamic ultrafiltration model for charged colloidal dispersions: a Wigner-Seitz cell approach . Chem Eng Sci , 1995 , 50 : 1707 - 1736 . DOI: 10.1016/0009-2509(95)00026-2 http://doi.org/10.1016/0009-2509(95)00026-2 Dynamic ultrafiltration model for charged colloidal dispersions: a Wigner-Seitz cell approach C Domain , C S Becquart and L Malerba . Simulation of radiation damage in Fe alloys: an object kinetic Monte Carlo approach . J Nucl Mater , 2004 , 335 : 121 - 145 . DOI: 10.1016/j.jnucmat.2004.07.037 http://doi.org/10.1016/j.jnucmat.2004.07.037 Simulation of radiation damage in Fe alloys: an object kinetic Monte Carlo approach G K Schenter , G Mills and H Jonsson . Reversible work based quantum transition state theory . J Chem Phys , 1994 , 101 : 8964 - 8971 . DOI: 10.1063/1.468447 http://doi.org/10.1063/1.468447 Reversible work based quantum transition state theory G Henkelman and H Jonsson . A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives . J Chem Phys , 1999 , 111 : 7010 - 7022 . DOI: 10.1063/1.480097   http://doi.org/10.1063/1.480097   A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives L Gámez , B Gámez , M J Caturla , et al . Object Kinetic Monte Carlo calculations of irradiated Fe-Cr dilute alloys: The effect of the interaction radius between substitutional Cr and self-interstitial Fe . Nucl Instrum Meth B , 2011 , 269 : 1684 - 1688 . DOI: 10.1016/j.nimb.2010.12.044 http://doi.org/10.1016/j.nimb.2010.12.044 Object Kinetic Monte Carlo calculations of irradiated Fe-Cr dilute alloys: The effect of the interaction radius between substitutional Cr and self-interstitial Fe C S Becquart and C Domain . An object Kinetic Monte Carlo Simulation of the dynamics of helium and point defects in tungsten . J Nucl Mater , 2009 , 385 : 223 - 227 . DOI: 10.1016/j.jnucmat.2008.11.027 http://doi.org/10.1016/j.jnucmat.2008.11.027 An object Kinetic Monte Carlo Simulation of the dynamics of helium and point defects in tungsten K Maier , H Mehrer , E Lessmann , et al . Self-diffusion in nickel at low temperatures . Phys Status Solidi B , 1976 , 78 : 689 - 698 . DOI: 10.1002/pssb.2220780230 http://doi.org/10.1002/pssb.2220780230 Self-diffusion in nickel at low temperatures F Cleri and V Rosato . Tight-binding potentials for transition metals and alloys . Phys Rev B , 1993 , 48 : 22 - 33 . DOI: 10.1103/PhysRevB.48.22   http://doi.org/10.1103/PhysRevB.48.22   Tight-binding potentials for transition metals and alloys H J Wollenberger . Physical Metallurgy . Amsterdam : Cahn R W, Haasen P . 1983 : 157 - 158 . Physical Metallurgy B W Zhang , W Y Hu and X L Shu . Theory of Embedded Atom Method and Its Application to Materials Science—Atomic Scale Materials Design Theory . 2003 : 84 - 85 Theory of Embedded Atom Method and Its Application to Materials Science—Atomic Scale Materials Design Theory J Bacon , F Gao and Y N Osetaky . Computer simulation of displacement cascades and the defects they generate in metals . Nucl Instrum Meth B , 1999 , 153 : 87 - 98 . DOI: 10.1016/S0168-583X(99)00041-5 http://doi.org/10.1016/S0168-583X(99)00041-5 Computer simulation of displacement cascades and the defects they generate in metals R W Siegl , M J Fluss and L C Smedskjaer . The Application of Position Annihilation in Materials Science . 1982 : 1 - 21 M J Fluss and L C Smedskjaer H Kronmuller . Vacancies and Interstitials in Metals . North-Holland : Seeger A . 1970 : 667 - 728 Vacancies and Interstitials in Metals S M Foiles , M I Baskes and M S Daw . Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys . Phys Rev B , 1986 , 12 : 7983 - 7991 . DOI: 10.1103/PhysRevB.33.7983   http://doi.org/10.1103/PhysRevB.33.7983   Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys P Ehehart . Properties and interactions of atomic defects in metal and alloys . Landolt-Bornstein , 1991 , 25 : 219 . Properties and interactions of atomic defects in metal and alloys 10.1007/s41365-016-0057-y Supported by the CAS Strategically Leading Program of the Chinese Academy of Sciences (XD02004140) and the National Natural Science Foundation of China (Nos. 51371080, 11076012) 2015-05-17 2015-07-20 2015-08-11 2016-05-09 2016-06-20 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2016 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-016-0057-y http://dx.doi.org/10.1007/s41365-016-0057-y . 2016 Nuclear Science and Techniques 03 27