EVOLUTION OF DEFECTS AND DEFECT CLUSTERS IN b-SiC ...

EVOLUTION OF DEFECTS AND DEFECT CLUSTERS IN b-SiC IRRADIATED AT HIGH TEMPERATURE JIANQI XI,a PENG ZHANG,a* CHAOHUI HE,a MINGJIE ZHENG,b HANG ZANG,a DAXI GUO,a and LI MAa a

Xi’an Jiaotong University, Department of Nuclear Science and Technology, Xi’an, China University of Wisconsin–Madison, Materials Science and Engineering Department Madison, Wisconsin

b

Received October 31, 2013 Accepted for Publication March 2, 2014 http://dx.doi.org/10.13182/FST13-740

A molecular dynamics study has been performed to investigate the generation and evolution of damage states in irradiated b-SiC at high temperature. It is found that most of the C antisites (SiC) are created during the early collisional phase, while the Si antisites (CSi) are significantly produced during the thermal spike phase. A modified near-neighbor point defect density (NPDD) is introduced to study the spatial aggregation of different defects during the displacement cascades, and feature of defect clusters evolution is analyzed in details. The dominated types of vacancy clusters after the displacement cascades are two- and three-size chainlike ones.

And the vacancy NPDD (V-NPDD) decreases as the recoil energy increases. Furthermore, after the thermal spike phase, there is an additional annealing process during which the interstitials and antisites turn into defect clusters, respectively.

I. INTRODUCTION

temperature regime,8–14 while some other physical problems at high temperatures have not been well understood. Experimental investigations on the generation and evolution of microstructural defects were performed at high temperature.15–19 Cavity produced in b-SiC by the neutron irradiation was reported at temperature above 1523 K (Ref. 15). However, in our scope of knowledge, the micro-mechanism of the cavity production and void swelling in SiC has not been clearly revealed. L. Snead et al.15,16 reported that the interstitial clusters would transform into some complex clusters such as Frank faulted loops and even dislocation networks at high temperature. Meanwhile, molecular dynamics simulation performed by Farrell et al.20 showed that, upon 10 keV Si ion bombardments, there was no direct dependence of temperature on the number of vacancies, vacancy clusters and SiC. On the other hand, the C and Si replacement, CSi

Being one of the most promising candidates for structural components of nuclear reactors, silicon carbide (SiC) endures neutron irradiation.1–7 However, irradiation environment inevitably induce various defects such as Frenkel pairs, antisites and even complex clusters which will modify local microstructure and thus deteriorate the mechanical properties. Although many studies of the irradiation effects in b-SiC have been carried out for decades, there are still many problems unsolved. Especially, there is a lack of understanding on the formation and evolution of microstructural defects irradiated at high temperature. Until now, the knowledge about the microstructural change in SiC during irradiation has been mainly limited to the low-to-intermediate *E-mail: [email protected] FUSION SCIENCE AND TECHNOLOGY

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KEYWORDS: molecular dynamics simulation, defects and defect clusters, displacement cascade Note: Some figures in this paper may be in color only in the electronic version.

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EVOLUTION OF DEFECT CLUSTERS IN SiC IRRADIATED AT HIGH TEMPERATURE

formation and the reduced damage generation behavior were found to be related with the irradiated temperature. However, it is worth to note that some other significant features including the clustering of interstitials and antisites, the spatial aggregation of defects, as well as the morphology of defect clusters in the cascades are needed to be studied thoroughly, which are important for modeling at the longer timescale simulation. In this work, we investigate the evolution of defects and defect clusters in b-SiC during the displacement cascades with 1 keV and 10 keV Si primary knock-on atoms (PKAs) at high temperature ranging from 1300 K to 1800 K. The mechanism of the evolution is analyzed on the atomic scale. Additionally, the influence of the PKA energy and irradiated temperature on the defect evolution is carefully studied. Finally, the morphology of defect clusters has been recorded in a database for longer timescale study.

1. Thermal equilibration: Random velocities are assigned to all atoms following the Gaussian distribution at the beginning of the MD simulation, and these velocities are rescaled at every timestep to maintain the desired temperature. This phase is set to equilibrate for 10 ps with a 1 fs timestep. 2. Thermostat-skin velocity scaling: Interior region thermostat is removed. Thermostat skin maintains at the desired temperature. The system is allowed to equilibrate for 10 ps with a 1 fs timestep to diminish the deviation from the change in the ensemble. The equilibration time for the both phases is longer than that of Farrell’s.20 3. Initial cascade: PKA instantaneous velocity is applied. The system is then allowed to evolve for 0.2 ps with a 0.01 fs timestep to ensure that the PKA has enough time to dissipate its kinetic energy.

II. MODELING METHODS II.A. Simulation Setup

Molecular dynamics simulations have been performed with the LAMMPS parallel code21 to study the process of displacement cascade. Periodic boundary conditions are applied in all three directions. A Langevin thermostat is adopted to the five sides of the simulation box to avoid the unphysical energy propagation. The sixth side of the box contains the Si PKA and no thermostat is set there to avoid the artificial energies introduced to the cascade. The Tersoff/ ZBL potential22 is used to describe the interactions between Si and C atoms. The low-energy (1 keV) simulations are performed in a cube with 15|15|15 unit cells containing 27000 atoms, and the high-energy (10 keV) simulations are performed with the box containing 640000 atoms (40|40|50 unit cells). The thermostat region for 1 keV and 10 keV cascades is a 2- and 4-cell thick layer, respectively. The lattice parameter used in this work takes the experimentally determined values of 0.436 nm (Ref. 23). The simulation box is necessary to contain the full dynamics to avoid the influence of collision cascades on these thermostat layers. After a thermal equilibration process, the Si PKA in the top-center of the simulation cell is given an instantaneous velocity corresponding to the kinetic energy of 1 keV or 10 keV in the [4 11 –95] direction to avoid the channeling effect.8,20 With different random number generator seeds to the velocity scaling thermostat function,20 10 runs for the low-energy cascades and 5 runs for the high-energy cascades are performed for every different temperature. To prevent the drift of the system due to the PKA movement, the whole system is re-centered every timestep, and the net linear momentum of atoms is also zeroed every 236

timestep.24 A multiple-phase timestep procedure is employed to ensure that no atom travels farther than 20% of the nearest neighbor distance in a single timestep.20 This method minimizes the anomalous behaviors as discussed in Ref. 25. All cascade simulations are performed in the following phases as described by Farrell et al.20:

4. Intermediate evolution: System equilibrates for 1.8 ps with a 0.1 fs timestep in this phase. 5. Final equilibration: System is needed to evolve for 10 ps with a 1 fs timestep. The total time from the PKA excitation to the end of the final phase is 12 ps. II.B. Cascade Analysis

The occurrence of point defects has been identified in the light of the referenced criterion that an atom is displaced if it is beyond a sphere radius equal to half the nearestneighbor distance.26 The cut-off distance is chosen to be 0.095 nm (Ref. 26). An atom is considered as an interstitial if it is not within half the nearest-neighbor distance from the lattice site. A site is vacant if no atom exists within half the nearest-neighbor distance of the site. A site occupied by a wrong atom type is designated as an antisite. Many authors have obtained different results with different geometric criteria such as the small Lindemann spheres centered on lattice sites,27 spheres with the size of half a nearestneighbor distance,26,28 and Wigner-Seitz cells.29 Although the trend for any given method is roughly identical,30 none of those definitions are truly satisfactory in describing highly damaged regions. Furthermore, it is reported that the number of vacancy according to our method is larger than that defined by Wigner-Seitz.26,30 The formation of defect clusters was discussed from Farrell et al.20 The cutoff for the vacancy and antisite cluster is 0.22 nm (Ref. 20), while it ranges from 0.17 nm to 0.22 nm for the interstitial cluster. The lower bound is

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calculated from the distance between atoms as the dumbbell interstitial.31 Therefore, the dumbbell interstitial could not be considered as an interstitial cluster in our present work. Defect clusters are classified by a modified cluster index (a, b, c, d, e) (Ref. 32) to analyze their morphologies. Here a represents the number of point defects in one cluster; b the number of near-neighbors in one cluster; c the maximum near-neighbors around one point defect in the cluster; d the ratio of the number of Si point defects to the number of C point defects in one cluster; e the morphology of the cluster (1 for the isolated point defect, 2 for the line cluster, 3 for the tetrahedral cluster, OTHER for the remaining morphologies). Some typical snapshots in the systems are depicted in Fig. 1. In addition, the modified near-neighbor point defect density (NPDD) is used to reflect the extent of the spatial aggregation of point defects,32 which is defined as the ratio of the number of near-neighbors to the number of isolated point defects in one cluster. For example, the NPDD of the defect cluster (2, 1, 1, 1, 2) is 1/2 in Fig. 1. During the cascade, the NPDD is obtained by averaging the NPDD of each defect cluster in each run. Therefore, the larger NPDD means the higher ratio of the defect cluster to the isolated point defect in the system.

III. RESULTS AND DISCUSSION III.A. Cascade Generation and Evolution

In order to characterize the evolution of the displacement cascades, the total number of vacancy and antisite defects with different energy cascades is plotted in Fig. 2 as a function of time. Since the number

of interstitial and vacancy defects during the cascades is equal to each other, here we just show the change of vacancy defect. The number of the vacancy during the collisional phase in 1 keV and 10 keV cascades reaches a maximum at about 0.1 ps and 0.16 ps, respectively. Then it decreases during the thermal spike phase as expected. It is noted that the lifetime of the thermal spike is 0.9 ps for 1 keV cascades (except that at 1800 K) and 1.84 ps for 10 keV cascades, which is in consistent with Farrell’s results, about 1.95 ps (Ref. 20). In addition, it is noted that there is no direct dependence of temperature on the number of the vacancy and antisite during the cascades as shown in Fig. 2, which is in good agreement with the previous study by Farrell et al.20 Figure 3 shows the evolution of CSi and SiC antisite defects at different temperatures in 1 keV and 10 keV cascades. Like the evolution behavior of the antisite defects at low temperature,9 most of SiC are generated as a result of the replacement events at high temperature during the collisional phase before the displacement spike. On the other hand, CSi is significantly created during the thermal spike phase, in contrast to those at low temperature.9 Meanwhile, there is a slight decrease in the number of SiC after the displacement spike. These results are in agreement with the study by Farrell et al.20 The bond energies of homogeneous bonds have been cited to explain these phenomena. It is found that the bond energy of Si-Si (2.32 eV/bond) is weaker than that of C-C (3.68 eV/bond) as discussed in Ref. 33. Therefore, during the thermal annealing process, Si-Si bonds would easily be annihilated, inducing the decrease in the number of SiC antisite. Another interesting feature is observed that some Si vacancies are metastable to transform into the nearestneighbor vacancy-antisite complex VC -CSi (VSi ?VC {CSi )

Fig. 1. Several kinds of clusters with their modified cluster index, where the light and dark spheres represent the C or Si species. Near-neighbors are connected by lines. FUSION SCIENCE AND TECHNOLOGY

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Fig. 2. The total number of the vacancy and antisite as a function of time for the 1 keV and 10 keV Si cascades at different temperatures, ranging from 1300 and 1800 K. (a) and (b) the total number of the vacancy and antisite during the 1 keV cascade, respectively. (c) and (d) the total number of the vacancy and antisite during the 10 keV cascade, respectively.

during the thermal spike phase which is consistent with the results obtained by molecular dynamics34 and ab initio simulation.35 However, this transformation would not occur in the equilibration phase within the MD timescale as discussed in our previous work.36 These vacancyantisite complexes would become the source of antisite pairs by annealing with interstitials.37 The formation energy (Ef) of VC -CSi complex and VSi is calculated to be 4.84 eV and 6.47 eV, respectively, which is in the range of 4.1–7.3 eV for Vc-Csi and 6.0–8.1 eV for VSi as a function of Fermi level obtained by ab initio simulation.37 In addition, the binding energy (Eb) of VC -CSi complex is calculated to be 0.63 eV for the neutral state, which is also comparable with the results, ranging from 1.0 eV to 1.2 eV for different charge states.38 238

III.B. The Evolution of Spatial Aggregation of Point Defects

Furthermore, the evolutions of the vacancy NPDD (V-NPDD) during the 1 keV and 10 keV cascades are depicted in Fig. 4. It can be seen that the peaks of the V-NPDD for 1 keV and 10 keV cascades appear before the displacement spikes in Figs. 2a and 2c at 0.03 ps and 0.08 ps, respectively. Moreover, the combination of the evolution of the V-NPDD and the vacancy shown in Figs. 2a and 2c can provide new insights into the behavior of the point defect generation and recovery, as well as the vacancy cluster evolution. In Fig. 4, two declining stages of the V-NPDD can be obviously identified in different lines for 1 keV and 10 keV cascades. In the first stage (I) from the peak of the V-NPDD to the displacement spike, it is


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Fig. 3. The number of the SiC and CSi antisite as a function of time for 1 keV and 10 keV Si cascades at different temperatures, ranging from 1300 to 1800 K. (a) and (b) the number of the SiC and CSi during the 1 keV cascade, respectively. (c) and (d) the number of the SiC and CSi during the 10 keV cascade, respectively.

expected that the reduced degree of the spatial aggregation of vacancies is dominated by the significant generation of isolated point defects as shown in Figs. 2a and 2c. Meanwhile, in the second declining stage (II) throughout the thermal spike phase, it is indicated that the recombination of interstitial-vacancy defect plays an important role in reducing the V-NPDD values to decrease the degree of the vacancy clustering during the thermal spike phase. It is found that the higher the PKA energy, the lower the V-NPDD as shown in Fig. 4, indicating that the lower ratio of the vacancy cluster to the monovacancy is produced in the higher energy cascades. Additionally, it is revealed that the evolution of spatial aggregation of vacancies is largely independent on the irradiated temperature in our simulation for both energy cascades. The aggregation evolution of the interstitial (I-NPDD) and the antisite (A-NPDD) in the 10 keV FUSION SCIENCE AND TECHNOLOGY

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cascade has been investigated, shown in Figs. 5a and 5b, respectively. There is a significant scattering of the I-NPDD in Fig. 5a, due to the easier mobility of interstitial atoms at high temperature. It is noted that the I-NPDD reaches a maximum at about 0.6 ps in the cases above 1400 K and then shows a slight decline in the following phases, which is in contrast with the quenching-in mechanism for the low temperature cascades.9 From this observation, it is speculated that there is an additional annealing process in the clustering of defects after the thermal spike phase for the high temperature cascades. In order to confirm this speculation, these 10 keV cascades above 1400 K are successively extended for about 100 ps. The results show that there is a substantial change of the damage state produced at high temperatures, while the total number of defects is unchanged after 12 ps. It is found that the I-NPDD will become

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Fig. 4. The evolution of the V-NPDD as a function of time for 1 keV and 10 keV Si cascades at different temperatures, ranging from 1300 to 1800 K. Distinctive stages of the V-NPDD are plotted by the solid and dash line for 1 keV and 10 keV cascades, respectively. The first stage (I) ranges from the peaks of the V-NPDD to the displacement spike and the second stage (II) ranges throughout the thermal spike phase.

Fig. 5. The evolution of the NPDD as a function of time for 10 keV Si cascades at different temperatures, ranging from 1300 to 1800 K. (a) for the I-NPDD and (b) for the A-NPDD.

stable at about 40 ps, and the A-NPDD at about 60 ps in the 1800 K cascade. However, the V-NPDD will be always stable during the 100 ps due to the higher diffusion barrier for the vacancy, roughly 2.35 eV for VSi and 4.10 eV for VC (Ref. 39). 240

III.C. Cluster Analysis

In order to investigate the morphology of the defect cluster, the modified cluster index (a, b, c, d, e) is used to characterize the defect cluster evolution during the


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10 keV cascades above 1400 K. For the vacancy clusters, it is noted that the favorite vacancy cluster indexes are the (2, 1, 1, 1, 2) and (3, 2, 2, 1/2, 2) which are independent on the irradiated temperature. And the final percentage of them at 100 ps is about 6% and 3%, respectively. It is meant that the chainlike structure (LINE) is dominant in the vacancy cluster after the high-temperature cascades, which is in accordance with Farrell’s results.20 The formation and binding energies of these vacancy clusters at the equilibrium system are calculated. For the divacancy (VSi -VC ), Ef is 8.16 eV, which is in good agreement with the results of 7.75 eV (Ref. 40) and 7.22 eV (Ref. 41). The binding energy, Eb is 3.27 eV, which is consistent with the previous simulations, about 4.3 eV (Ref. 40) and 3.34 eV (Ref. 41). For the trivacancy (VC -VSi -VC ), Ef, 11 eV, is in agreement with the result of 8.7 eV (Ref. 40). And the binding energy Eb, 2.12 eV, is smaller than the binding energy of di-vacancy consistent with the result in Ref. 40, roughly 4 eV. It is meant that these small vacancy clusters are stable at high temperature. The percentage of the morphology of other complex defect clusters is less than 1% which can be negligible. For the interstitial clusters, it is seen that the clusters containing two interstitial atoms, namely two-size interstitial clusters, are the most favorite ones after the cascades, about 10%, which is different from the Weber’s finding that the size of the interstitial clusters is less than four at the room temperature.9,42–44 Further investigations are performed to study the evolution of the interstitial clusters with different morphologies. It is noted that the percentage of the chainlike interstitial clusters containing three atoms shows a similar trend to the I-NPDD evolution in Fig. 5a. The interstitial clusters containing two atoms will become stable during the following 100 ps process. However, as for the three-size interstitial clusters, the percentage will decrease below 1%. It is indicated that at high temperature those two-size interstitial clusters still meet the quenching-in mechanism, while the three-size interstitial clusters will be annealed in the successive relaxation process. These results are different from Jiang et al.45 who reported that the most stable one is the (CBC )3 cluster combining with three C-CS001T split interstitials. The deviation may be due to the fact that the initial system in Jiang’s study is a perfect crystal while the present work deals with the MD system after the cascades. And those (CBC )3 may be the energy minimized configuration after annealing a long time beyond the MD timescale we considered. In order to investigate the two-size interstitial cluster(Chex )2 , another simulation is performed in a perfect crystal at 1800 K as shown in Fig. 6a. After fully annealed, this cluster is changed into(Chex )3 -VC . Specifically, the nearest-neighbor C atom displaces from its original site and is absorbed by the two-interstitial cluster. After that, there is a symmetrical three-interstitial cluster surrounding one C vacancy as shown in Fig. 6b. The formation energies of (Chex )3 -VC and (CBC )3 cluster FUSION SCIENCE AND TECHNOLOGY

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defects are calculated to be 6.95 eV and 12.24 eV, respectively. It is indicated that the referenced defect clusters from Jiang et al.45 are difficult to observe in our simulation. Furthermore, the stable configuration of the threeinterstitial cluster after 12 ps cascades is studied as shown in Fig. 7a. It is found that two C interstitial atoms in this cluster will recombine with the surrounding C vacancies during the additional 100 ps annealing process. The lifetime of this cluster during the annealing process is determined at the different annealing temperatures. To improve the statistics, five simulations are performed at each temperature where the defect recovery occurs. The data are analyzed by assuming that the temperature dependence of t is described by the Arrhenius expression t~t0 exp(Er =kB T) ,

ð1Þ

where t0 is a preexponential factor, Er is the energy barrier of the cluster recombination with the surrounding vacancies, and kB is the Boltzmann constant. The lifetime t of this cluster is plotted on the logarithmic scale as a function of the inverse irradiated temperature (1000/T) in Fig. 7b. According to the fitting line, the energy barrier and preexponential factor are determined to be 0.90 eV and 0.09 ps, respectively. It is indicated that the three-interstitial cluster will not be stable at high temperature. This result further verifies that there is an additional annealing process for the clustering of interstitial defects. For the antisite clusters, the favorite cluster is the antisite-pair, which is in the percentage of about 30%. The formation energy of the antisite-pair is calculated to be 3.90 eV which is in consistent with the results of the ab initio simulation38 (3.95 eV and 4.43 eV with single-f (SZ) and double-f polarized (DZP) basis sets, respectively). The binding energy is found to be 2.85 eV which is in good agreement with the previous ab initio simulation of 2.8 eV (Ref. 46).

IV. CONCLUSIONS

The high temperature cascades produced by the 1 keV and 10 keV Si recoils have been simulated on the atomic scale, and several interesting points are presented. Firstly, it is revealed that the lifetime of the thermal relaxation largely depends on the recoil energy. Secondly, it is found that there are two distinctive generation stages for the CSi and SiC antisite defects. A large proportion of the SiC antisite defects are generated as a result of the replacement events at high temperature during the early collisional phase, and there is a slight decrease in SiC during the thermal spike phase. However, the CSi antisite defects are significantly created by the defect heterogeneous recombination and the reaction VSi ?VC {CSi during

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Fig. 6. The configuration of the two-interstitial at 1800 K in a perfect crystal. (a) The initial configuration of the two-interstitial cluster, (b) the relaxed configuration after fully annealed. The small-light sphere represents the C interstitial marked by digit; the large-light the Si lattice site and small-dark the C lattice site.

Fig. 7. The stable configuration and the lifetime of the three-interstitial cluster. (a) The stable initial configuration of the three-interstitial cluster during the additional annealing process. The small-light sphere represents the C interstitial marked by digit; the large-light the Si lattice site and small-dark the C lattice site. (b) The lifetime of this cluster at different temperatures.

the thermal spike phase. Beyond this, it is noted that there is no direct dependence of temperature on the number of vacancies and antisites for both energy cascades. Our analysis of the V-NPDD evolution for 1 keV and 10 keV cascades indicates that regardless of the simulation temperatures, the aggregation of vacancies is relatively small, and there are two distinctive declining stages for the clustering during the cascades. On the other hand, it is indicated that the higher the PKA energy, the lower the ratio of the vacancy cluster to the monovacancy defect. In the use of the modified cluster index of the vacancy, it is determined that the final dominated vacancy clusters are the di-vacancy and tri-vacancy ones. And the stable interstitial cluster is the two-size one at high temperature, which is different from the low temperature cascades. 242

In addition, it is seen that the three-size interstitial clusters will have an additional annealing process after the thermal spike phase in the high temperature (above 1400 K) cascades. Furthermore, we find that the clustering of the antisite will mainly occur during the thermal spike phase due to the heterogeneous recombination. And the morphology of the most antisite clusters is the antisitepair. Finally, based on our current results, it is expected that those defect clusters formed in the cascades will play an important role in their nucleation and growth at high temperature. Nevertheless, more work is needed to provide further evidence for the evolution mechanism involved in the high-temperature relaxation, such as the antisite clustering and the interstitial cluster dissociation on a longer timescale.


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ACKNOWLEDGMENTS This work was financially supported by National Natural Science Foundation of China (No. 11305122), China Postdoctoral Science Foundation (2013M532052) and the fundamental research fund for the central universities under the grant No. 08142041 and 08143097. Jianqi Xi was supported by the Nuclear Youth Fund from Defect Physics Computing Centre in the Institute of Nuclear Technology, Xi’an Jiaotong University. The computation work is partially supported by the cluster Hua-I in Xi’an Jiaotong University.

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