The interatomic interaction in V and alloy V-4Ti was described on the base of modern potentials of interatomic interactions which took into account the interaction of screened ions at small interatomic distances and allowed to simulate correctly radiation damage.  The main characteristics of atomic displacement cascades in simulated crystallites were calculated: the number of defects at diﬀerent stages of cascade development, the size of the radiation-damaged regions, and an analysis of the estimation of the number, types and sizes of the surviving radiation defects in crystallites. The results obtained are compared for vanadium and alloy V-4T

Boev, A. O.

Lipnitskii, A. G.

Nelasov, I. V.

Zolnikov, K. P.

English

DSpace at Belgorod State University

Journal of Physics: Conference SeriesPAPER • OPEN ACCESSMolecular dynamics simulation of primary radiation damage in vanadiumand alloy V-4TiTo cite this article: A O Boev et al 2019 J. Phys.: Conf. Ser. 1147 012087 View the article online for updates and enhancements.This content was downloaded from IP address 93.157.144.7 on 29/05/2020 at 10:16Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing LtdXXXIII International Conference on Equations of State for MatterIOP Conf. Series: Journal of Physics: Conf. Series 1147 (2019) 012087IOP Publishingdoi:10.1088/1742-6596/1147/1/0120871Molecular dynamics simulation of primary radiationdamage in vanadium and alloy V-4TiA O Boev1,2, K P Zolnikov2, I V Nelasov1 and A G Lipnitskii11 National Research University “Belgorod State University”, Pobedy Street 85, Belgorod308015, Russia2 Institute of Strength Physics and Material Science of the Siberian Branch of the RussianAcademy of Sciences, Akademicheskii 2/4, Tomsk 634021, RussiaE-mail: boev.anton.olegovich@gmail.comAbstract. In the framework of the molecular dynamics method, simulation of the primaryradiation damage in crystallites of bcc both V and alloy V-4Ti was carried out. The initialtemperature of the crystallites was 700 K, which corresponds to the operating temperatureof the alloy when used as the material of the first wall of a thermonuclear reactor. Theinteratomic interaction in V and alloy V-4Ti was described on the base of modern potentialsof interatomic interactions which took into account the interaction of screened ions at smallinteratomic distances and allowed to simulate correctly radiation damage. The impact of thedecay particle on the atoms of the simulated crystallites, as a result of which a cascade ofatomic displacements was generated, was simulated by assigning a pulse to one of the latticeatoms, the primary knocked out atom. The main characteristics of atomic displacement cascadesin simulated crystallites were calculated: the number of defects at different stages of cascadedevelopment, the size of the radiation-damaged regions, and an analysis of the estimation of thenumber, types and sizes of the surviving radiation defects in crystallites. The results obtainedare compared for vanadium and alloy V-4Ti.1. IntroductionAlloys based on the V–Ti system are known for their low radiation swelling, which is achievedthrough the addition of 4–5% titanium. The influence of titanium on the radiation damage ofvanadium was studied by computer simulation methods in [1–6], but the influence of titanium ongeneration of point defects at the stage of development of atomic cascade displacements (ballisticstage in [7]) has not been considered so far. At this stage the kinetic energy of incident particleis redistributing among the lattice atoms through the elastic interaction. The number of latticeatoms displaced from the nodes increases in an abrupt way and reaches a maximum. The resultof the second (recombination) stage, whose time scale is several picoseconds, is the formationof a set of point and clustered defects formed by a cascade of atomic displacements known asthe primary state of the material after radiation damage. In the third stage, the defects that“survived” after recombination continue to evolve as a result of the diffusion displacements ofthe atoms (main state). In [8], the first stage of damage in pure vanadium was studied bymolecular dynamics (MD) methods using interatomic potentials calculated in the framework ofthe centrally symmetric approximation. The authors of this paper [8] showed that vacanciesremain in the central part of the simulated cell in the resulting structure, while interstitialsXXXIII International Conference on Equations of State for MatterIOP Conf. Series: Journal of Physics: Conf. Series 1147 (2019) 012087IOP Publishingdoi:10.1088/1742-6596/1147/1/0120872leave the periphery. At this time, small vacancy and interstitial clusters are formed, which aredistributed along the simulated cell, mainly as point defects. In this paper we carried out astudy of the influence of titanium on the formation and evolution of defects in the alloy V–Tiformed as a result of the development of atomic displacement cascades at the atomic level byMD simulation using interatomic interaction potentials for the V–Ti system [3, 9], taking intoaccount the angular dependence in the interatomic interactions.2. Formalism of simulationThe simulated crystallites of V and V-4Ti had the shape of a cube of bcc lattice with periodicboundary conditions in the directions [100], [010] and [001]. The size of the crystallites waschosen proceeding from the primary knocked out atom (PKA) energy. We used 128 000-nodesamples (12 nm in edge length) for PKA energies 5 keV and below, and 432 000-node samples(18 nm in edge length) for higher PKA energies. The initial temperature of the simulatedcrystallites was 700 K, which corresponds to the operating temperature of the alloy when usedas the material of the first wall of a thermonuclear reactor [10]. The crystallite of V-4Ti differsfrom one of pure vanadium in that 4% vanadium atoms are randomly replaced by titanium.The V–Ti potentials [3] used in this paper correctly predict the melting temperature ofvanadium, the thermal expansion of vanadium, and the interaction of titanium atoms withintrinsic point defects in the bcc lattice of vanadium. These properties of the potentials areimportant for the correct simulation of the radiation damage, since the effects of radiationswelling essentially depend on the homological temperature and characteristics of point defectsand their complexes.We used an original MD program package optimized for Message Passing Interface (MPI)parallel calculations on the basis of our interatomic potentials. During MD simulation,firstly, each sample was kept at a given temperature and zero pressure using a Nose–Hooverthermostat [11] and Berendsen barostat [12], respectively, at 700 K during 20 ps (NPTensemble). Next we set a vanadium atom in the center of the crystallite a velocity correspondingto PKA energy with a random vector orientation. To obtain the statistics, for every value ofPKA energy we used 10 samples with a random orientation of the velocity vector of PKA. Thenwe continued kept our samples using NPT ensemble with changing the MD time step.The MD time step changed depend on the maximum velocity of the atom in the modelcrystallite based on the position that PKA can not pass a distance greater than 0.02 A˚ in onestep. Based on the estimate, minimal time step was chosen 0.02 fs for PKA energies 10 keVand below, and 0.005 fs for greater PKA energies. Maximum time step was 1 fs for all values ofPKA energy.We analyzed the evolution of damage regions in the crystallites by visualization using theOVITO package [13,14] with Wigner–Seitz defect analyze modifier.3. Results and discussionFrom the results of simulation, we obtained the dependence of changes in the number of Frenkelpairs with time during the 0.5–20 keV cascades of atomic displacements. The observed generaltrends and differences of the displacement cascades in the crystallites of pure vanadium and thealloy V-4Ti are illustrated in figure 1 by the example of the PKA energies of 1, 10, and 20 keV.As can be seen in figure 1, both pure vanadium and the alloy V-4Ti tend to increase thenumber of surviving Frenkel pairs at the end of the cascade with increasing energy of PKA. Thepresence of titanium does not affect the amount of these pairs. A small influence of titaniumtakes place in the decrease in the maximum number of Frenkel pairs during the peak of thecascade at high energies considered in this paper, as seen in figure 1 in for the case of 20 keVdisplacement cascade. The absence of strong differences in the numbers of Frenkel pairs in theXXXIII International Conference on Equations of State for MatterIOP Conf. Series: Journal of Physics: Conf. Series 1147 (2019) 012087IOP Publishingdoi:10.1088/1742-6596/1147/1/01208730 2 4 6 8 10 12Time, ps020040060080010001200Number of Frenekel pairsPure V 5 keVV-4Ti 5 keVPure V 10 keVV-4Ti 10 keVPure V 20 keVV-4Ti 20 keVFigure 1. The number of Frenkelpairs in crystallites of pure V andalloy V-4Ti as a function of timefor a PKA energy of 1, 10 and20 keV. Results were averaged overthe 10 simulated crystallites withrandom orientation of the PKAvelocity vector.Figure 2. Point defects in the simulated crystallite containing 432 000 atoms in pure vanadium(a) and in alloy V-4Ti (b) at the peak time and at the time of main state in 12 ps for purevanadium (c) and alloy V-4Ti (d). Vacancies and SIAs are shown blue and red, respectively.PKA energy is 20 keV.XXXIII International Conference on Equations of State for MatterIOP Conf. Series: Journal of Physics: Conf. Series 1147 (2019) 012087IOP Publishingdoi:10.1088/1742-6596/1147/1/0120874Cluster size048121620PKA energy, keV51020Number of clusters050100150200250300350400Figure 3. Distribution of vacancy clusters by their sizes in pure vanadium (grey color) and inalloy V-4Ti (red) for PKA energies of 1, 5, 10, 15, and 20 keV. The total number of clusters for10 crystallites is given for each energy of PKA.case of pure vanadium and alloy V-4Ti at the same energy can be attributed to the proximity ofthe masses of these elements and to the relatively small concentration of titanium in the alloy.A more noticeable effect of titanium is manifested in the structural differences of the radiationdamaged region. Figure 2 presents a comparison of the structures of pure vanadium and alloyV-4Ti in the peak time and by the time of 12 ps (main state after the displacement cascade) bythe example of the crystallites with a maximum energy of 20 keV considered in this work.As can be seen in figure 2, in the alloy V-4Ti at a main state, the radiation damaged regionis more compact, interstitial atoms are located closer to the center of the damage region, and inpure vanadium they go to large distances, which on average are 2 times larger. This differenceis due to the higher mobility of interstitial atoms in pure vanadium.One of the characteristic features of the structure of the radiation damaged region is theformation of the vacancy complexes and complexes of self-interstitial atoms (SIA). Figure 3shows the histogram of vacancy clusters size distribution as a function of the PKA energy.Clusters were determined by the cluster analysis method implemented in the software packageOVITO. The cutoff parameter selected a certain threshold value, which is equal to the distanceto the second coordination sphere in vanadium (3.03 A˚ [15]).As can be seen from the results of the analysis of the vacancy clusters presented in figure 3, theeffect of titanium leads to a systematic decrease in the size of the surviving vacancy clusters incomparison with pure vanadium. In the latter, clusters are formed up to the size of 19 vacanciesat the energy of 20 keV. However, most survived vacancies do not form complexes. This agreeswith the results of modeling cascades in pure vanadium using other interatomic potentials [8].In the case of the alloy V-4Ti, the number of monovacancies is greater than in pure vanadium,despite the fact that the total number of surviving Frenkel pairs is practically the same in pureV and alloy V-4Ti, as noted earlier (also see figure 1). This is explained by the high bindingenergy of vacancies with titanium atoms in the bcc lattice of vanadium [6]. The vacancy trappingXXXIII International Conference on Equations of State for MatterIOP Conf. Series: Journal of Physics: Conf. Series 1147 (2019) 012087IOP Publishingdoi:10.1088/1742-6596/1147/1/0120875by titanium constrains the formation of vacancy complexes. As for interstitial atoms, in bothmaterials they are in most cases in free form, or form clusters of two or three atoms.4. ConclusionIn this paper, MD simulations of cascades of atomic displacements for pure vanadium and alloyV-4Ti were carried out. Comparison of simulation results allowed revealing common featuresand differences of stages of cascades for the investigated materials. Doping of 4% titaniumdoes not affect the number of surviving Frenkel pairs in the bcc lattice of vanadium for all ofthe considered PKA energies in the interval 0.5–20 keV. The differences are manifested in theatomic structure of the region of the cascade development. In the case of the alloy V-4Ti, a largefraction of vacancies are in small-sized clusters, mainly remaining in the form of monovacancies.Interstitial atoms, in both pure vanadium and alloy V-4Ti, practically do not form clusters,except for a small number clusters containing 2 or 3 SIAs. Moreover, interstitial atoms in purevanadium propagate to larger distances from the center of the cascade region, in comparisonwith the alloy V-4Ti.AcknowledgmentsThe work was performed with financial support from the Russian Foundation for Basic Research(grant No. 17-308-50026).References[1] Zhang C, Zhang P, Li R, Zhao J and Dong C 2013 J. Nucl. Mater. 442 370–6[2] Deng L, Zhang X, Tang J, Deng H, Xiao S and Hu W 2016 J. Alloys Compd. 660 55–61[3] Boev A O, Nelasov I V, Maksimenko V N, Lipnitskii A G, Saveliev V N and Kartamyshev A I 2017 DefectDiffus. Forum 375 153–66[4] Psakhie S G, Zolnikov K P, Kryzhevich D S, Zheleznyakov A V and Chernov V M 2009 Crystallogr. Rep. 541002–10[5] Korchuganov A V, Zolnikov K P, Kryzhevich D S and Psakhie S G 2017 Russ. Phys. J. 60 170–4[6] Boev A O, Aksyonov D A, Kartamyshev A I, Maksimenko V N, Nelasov I V and Lipnitskii A G 2017 J.Nucl. Mater. 492 14–21[7] Psakhie S G, Zolnikov K P, Kryzhevich D S, Zheleznyakov A V and Chernov V M 2009 Fiz. Mezomekh. 1220–8[8] Alonso E, Caturla M J, de la Rubia T D and Perlado J M 2000 J. Nucl. Mater. 276 221–9[9] Lipnitskii A G and Saveliev V N 2016 Comput. Mater. Sci. 121 67–78[10] Impagnatiello A, Toyama T and Jimenez-Melero E 2017 J. Nucl. Mater. 485 122–8[11] Hoover W G 1985 Phys. Rev. A 31 1695[12] Berendsen H J C, Postma J P M, van Gunsteren W F, DiNola A and Haak J R 1984 J. Chem. Phys. 813684–90[13] Stukowski A 2009 Modell. Simul. Mater. Sci. Eng. 18 015012[14] Stukowski A and Albe K 2010 Modell. Simul. Mater. Sci. Eng. 18 085001[15] Souidi A, Becquart C S, Domain C, Terentyev D, Malerba L, Calder A F, Bacon D J, Stoller R E, OsetskyYu N and Hou M 2006 J. Nucl. Mater. 355 89–103

Molecular dynamics simulation of primary radiation damage in vanadium and alloy V-4Ti

http://dspace.bsu.edu.ru/bitstream/123456789/31155/1/Boev_Molecular.pdf

Molecular dynamics simulation of primary radiation damage in vanadium and alloy V-4Ti

Abstract

Similar works

Full text

Available Versions

DSpace at Belgorod State University