EFFECT OF VOLUME ON THE MECHANICAL PROPERTIES OF NICKEL NANOWIRE

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1 Materals Physcs and Mechancs 18 (2013) Receved: October 6, 2013 EFFECT OF VOLUME ON THE MECHANICAL PROPERTIES OF NICKEL NANOWIRE M.M. Ash 1,2*, M.D. Starostenkov 2 1 Physcs department, Faculty of Scence, Menoufa Unversty, Egypt 2 I.I. Polzunov Alta State Techncal Unversty, Barnaul, Russa, *e-mal: mohamedeash2@yahoo.com Abstract. Molecular Dynamcs (MD) smulatons have been carred out on pure nckel (N) crystal wth face-centered cubc (FCC) lattce upon applcaton of unaxal tenson at nanolevel wth a speed of 20 m/s. Morse potental was employed to carry out three dmensonal molecular dynamcs smulatons. MD smulaton was used to nvestgate the effect of volume of N nanowre on the nature of deformaton and fracture. The engneerng stress tme dagrams obtaned by the MD smulatons of the tensle specmens of these N nanowres show a rapd ncrease n stress up to a maxmum followed by a gradual drop to zero when the specmen fals by ductle fracture. The feature of deformaton energy can be dvded nto four regons: quas-elastc, plastc, flow and falure. The nature of deformaton, slppng, twnnng and neckng was studed. Stress decreased wth ncreasng volume and the breakng poston ncreases. 1. Introducton Fgure1 shows MD smulaton model of N nanowres generated from a bulk fcc N crystal wth the lattce parameter of 3.52 Å. Let x, y, and z coordnate axes represent the [100], [010] and [001] crystallographc drectons, respectvely. The ntal lengths of the MD models are denoted by Lx, Ly, and Lz, respectvely, wth z denotng the length drecton of the N nanowres. Seven nanowres of dfferent volume are consdered at the temperatures correspondng to 300 K and 1000 K. Fg. 1. MD smulaton model of 24x24x24 N nanowre. 2013, Insttute of Problems of Mechancal Engneerng

2 54 M.M. Ash, M.D. Starostenkov All of them have free surfaces n the length drecton. In the MD smulaton, the perodc boundary condtons are appled n both x and y drectons. The deformaton corresponds to the drecton <001>. To the calculated block of crystal - free boundary condtons are appled n the drectons <100>, <010>. 2. Potental model and smulaton methods In ths paper for calculatng the dynamcs of the atomc structure of the method of molecular dynamcs usng pared Morse potental functon [1-4], sutable n terms of ther computng tme and qualty of results. Morse par potental s wrtten as: KLr KLr KL ( r) DKL KLe KLe 2, (1) where KL, KL, D KL are parameters defnng the nteracton of pars of atoms of type K and L; r s the dstance between the atoms. The ntal veloctes of partcles are a Maxwell Boltzmann dstrbuton correspondng to a gven temperature. They are gven by N( v) N 2 m mv exp( ), (2) 2 kt 2kT where N(v) denotes the number of partcles whch have velocty v; k s Boltzmann s constant, and T s temperature. To keep the system temperature, the followng correcton s requred: T fnal d v v, (3) Ta fnal where v s the velocty of the partcle after correcton; T d and T a are the desred temperature and actual temperature of system, respectvely. The ntal confguraton of the molecular dynamcs smulaton s shown n Fg. 1. In the atomstc smulatons the stress on m plane and n n-drecton σ mn s calculated by [5-7]: m n m m n 1 m 1 ( ) v v r j rj rj mn [ ], (4) N V 2V r r s j j j where N s s the number of partcles contaned n the regon S and S s defned as the regon of atomc nteracton; r and r are two components of the vector from atom to j; V s the volume assgned to atom and gven by m j n j 3 4 a V, (5) 3 where r a. (6) 1 j 2 2 rj The form expressed n Eq. (4) contans two terms on the m rght hand sde. The frst s a knetc part and caused by atomc motons and the second s a potental part and affected by

3 Effect of volume on the mechancal propertes of nckel nanowre the nteractve forces of atoms The stran n the z-drecton s calculated by: 55, (7) where l s the stretchng length n the z-drecton and l 0 s ts ntal length. Usng Eqs. (4) and (7), the stress stran curve can be yelded; and then the elastc modulus of the materal can be obtaned from the curve. Generally, the mechancal propertes are dependent on the loadng condton, volume of the nanowres and temperature. The object of nvestgaton s taken dfferent nanowres of N alloy. Alloy structure s presented n the form of a face-centered cubc cell. We study the effect of volume on the mechancal propertes of smulaton nanowres at a temperatures correspondng to 300 K and 1000 K. The estmated sze of the crystal unt was for varous experments of 63 atoms (5 atoms along the edges at the bottom and 5 - n heght) to atoms (40 atoms along the edges at the bottom and 40 - n heght). 3. Results and dscusson Snce the breakng and the yeldng of N nanowres are of man nterest n ths work (Table 1 and 2), t seems to be reasonable to adopt small L x, L y and L z for the smulatons. To save the computng tme, the dmensons of the MD models used n the followng smulatons are set to be Lx=Ly=Lz and Lz changes from 5 to 40. The nature of deformaton, slppng, twnnng and neckng were studed. Table. 1. The typcal MD results of dfferent system at 300 K ncludng the tme requred to attan atomc break, the number of atoms, ntal length, breakng length, yeldng tme, yeldng stress and yeldng stran and the calculated fnal breakng poston. Breakng Yeldng pont System N l 0 l t b, t, l Poston σ, GPa z1. Ԑ nm ps nm 1 5x5x x10x x20x x24x x30x x36x x40x Four stages of deformaton. The experments were obtaned plots of the stored energy of deformaton of the tme, reflectng the processes n the nanowre durng deformaton. There are four stages of deformaton: the quas-elastc deformaton (I), plastc deformaton (II), the breakng (flow) (III), and falure (IV). At all volumes, n the frst stage there was almost lnear ncrease n stress. The ntal stage quas-elastc area there s only relatve dsplacement of atoms and there are no defects. Therefore, n ths regon the energy stored vares perodcally. Ths stage s completed n 15 ps for 10x10x10 N nanowre and 40 ps for 36x36x36. The sharp fall takes place only at the pont of transton from the frst to second stages of deformaton (Fg. 2 a and 2 c). Experments have shown that when the volume ncreases the frst stage of deformaton was wdened, and also the second stage was wdened.

4 56 M.M. Ash, M.D. Starostenkov Table. 2. The typcal MD results of dfferent system at 1000 K ncludng the tme requred to attan atomc break, the number of atoms, ntal length, breakng length, yeldng tme, yeldng stress and yeldng stran and the calculated fnal breakng poston. breakng Yeldng pont System N l z0 l t b, t, l Poston σ, GPa z1. Ԑ nm ps nm 1 5x5x x10x x20x x24x x30x x36x x40x Fg. 2. the dependence of the stored energy of deformaton of the experment at 300 K for nckel-10 x 10x 10 (a), the relaton of stress wth tme at temperatures 300 K for nckel-10 x 10 x 10 (b), the dependence of the stored energy of deformaton of the experment at 300 K for nckel-36 x 36x 36 (c) and the relaton of stress wth tme at temperatures 300 K for nckel-36 x 36x 36 (d) Volume effect on stress. Fgure 3 shows the stress length relatons obtaned from the smulatons for temperature at 300 K as lsted n Table 1. As t can be seen from the fgure, the smulated stress decreased wth ncreasng volume. However, further analyss for hgh temperature at 1000 K (Table 2) shows that the stress length results exhbt a large oscllaton about a mean curve (Fg. 3); however, the magntudes of the oscllaton can be reduced wth ncreasng number of atoms. Fgure 3 shows a decrease n strength wth ncreasng nanowre volume at the stran rate of s 1 for all temperatures. Ths s a smaller s softer effect. The effect of smaller s softer occurs for the nanowres wth

5 Effect of volume on the mechancal propertes of nckel nanowre 57 smaller volume and the self-smlar hardenng effect occurs for those nanowres wth hgh volume. Fg. 3. The smulated ultmate strength of ultrathn N nanowres as a functon of nanowre length for dfferent temperatures. The neck of the nanowre forms after the slps happened, and the deformatons have been carred manly through the elongaton of the neck. Beyond the neck regon, atomc structures have no sgnfcant changes. The atomc rearrangements n the neck regon nduce the zgzag ncrease de-crease n stress as the stran s ncreased. The atoms, close to the narrowest regon of the neck, are hghly dsordered. At the pont of breakng, we observe a one-atom thck. Wth further pullng of the nanowre, the bond between the two atoms lyng n the one-atom breaks and then the rupture happens Plastc deformaton. We now dscuss the plastc deformaton smulatons of the N nanowre. Beyond the elastc lmt, the nanowres are not able to retan the structure and the plastc deformaton starts to take place n order to accommodate the appled compressve unaxal loadng. In order to study the plastc deformaton process of N nanowres that arses beyond the elastc lmt. Fg. 4. Deformaton of 40x40x40 N nanowre under tenson. Plastc deformaton of dslocaton slps, slppng doman and twns at tme 100 ps.

6 58 M.M. Ash, M.D. Starostenkov Wth the volume ncreasng furthermore, we fnd that sldng happens (see Fg. 4 and 5), and many atoms rearrange n the neck regon. Sgnfcant neckng occurs at small volume. Through further analyss, we fnd that after the formaton of the neck, the plastc deformatons have been carred manly through the reconstructon and rearrangement of the neck regon. Beyond ths regon, the nanowre keeps ordered structure and have no sgnfcant change. Fg. 5. Deformaton of 40x40x40 N nanowre under tenson super-plastcty deformaton of dslocaton slps, slppng doman and twns (a) at tme 400 ps, (b) 5 th XOZ plane at tme 400 ps. Fgure 6 a shows the cluster produced on 5 th XOY plane at tme 600 ps for 40 x 40 x 40 nanowre under tenson. Fgure 6 b shows the gamma for deformaton of 40 x 40 x 40 N nanowre under tenson 5th XOY plane at tme 600 ps. Fg. 6. Deformaton of 40x40x40 N nanowre under tenson 5 th XOY plane at tme 600 ps (a) wth clusters, (b) Gamma for (a) Breakng. Fgure 7 and 8 presents the breakng poston for N nanowres. Unlke the stress, the breakng poston ncreases wth ncreasng volume. Fgure 4 and 5 shows the varaton of breakng poston wth the Volume (ndcated by the sde length) of the crosssecton. Surface atoms play an mportant role n the mechancal behavors of nano structures,

7 Effect of volume on the mechancal propertes of nckel nanowre 59 and the volume effect commonly found n small-scale systems s the surface effect. The results showed that breakng poston depended on the nanowre length. If the breakng poston s predctable, the nanowre can be strengthened near the breakng poston to avod falure. Although the sngle breakng case s not predctable, many breakng cases show a statstc feature. Fg.7. Hstograms of the breakng poston wth breakng length L z measured n unts of N at T=300 K. Fg. 8. Hstograms of the breakng poston wth breakng length L z measured n unts of N at T=1000 K. Fgure 9 presents the representatve snapshots of N nanowres wth dfferent Volume at the breakng moment. In most cases, the fnal breakng poston occurs at the central part of the nanowre when t s short, as the nanowre length ncreases the breakng poston gradually shfts to the ends Smulaton for one atom long (z drecton). Fgures 10 and 11 present the representatve snapshots of 70 x 70 x 1 N nanowres at 300 K dfferent amount of tme. Pores produced at 30 ps, number and sze of these pores ncreases. Falure occurs quckly as the breakng tme for ths smulaton s 53 ps.

8 60 M.M. Ash, M.D. Starostenkov Fg. 9. Snapshots of N nanowres wth dfferent volume at the breakng moment at T =1000 K. The experments were obtaned plots of the stored energy of deformaton of the tme, reflectng the processes n the nanowre durng deformaton (Fg. 12 a). There are two stages of deformaton: the quas-elastc deformaton (I), the breakng (flow) (II). The ntal stage quas-elastc area there s only relatve dsplacement of atoms and there are no defects. Therefore, n ths regon the energy stored vares perodcally but completely dfferent from Fg. 2. Ths stage s completed n 18 ps for 70 x70 x 1 N nanowre. Fg. 10. Snapshots of the atomc confguraton rearrangement of 70 x 70 x1 N nanowre at 300 K. The confguratons presented correspond to the followng tmes: 0 ps, 30 ps, 40 ps, 50 ps and 53 ps.

9 Effect of volume on the mechancal propertes of nckel nanowre 61 Fg. 11. Snapshots of the XOY rearrangement of 70 x70 x1 N nanowre at a temperature of 300 K. The confguratons presented correspond to the followng tmes: (a) 0 ps, (b) 10 ps, (c) 30 ps. Fg. 12. The dependence of the stored energy of deformaton of the experment at 300 K for nckel-70 x 70x 1 (a), the relaton of stress wth tme at temperatures 300 K for nckel-70 x 70 x 1 (b). 4. Conclusons Molecular dynamcs smulaton results about N nanowre at 300 K and 1000 K temperatures are presented. The mechancal propertes of N nanowre for these temperatures are dfferent. The stress tme and stress length curves for nanowres are smulated. The breakng and yeld stress of nanowres are dependent on the volume and temperature. The neckng, plastc deformaton, slppng doman, twnng, clusters, mcrospores and break-up phenomena of nanowre are demonstrated. Stress decreases wth ncreasng nanowre volume and temperature. The fnal breakng poston occurs at the central part of the nanowre when t s short, as the nanowre length ncreases the breakng poston gradually shfts to the ends. Reference: [1] E.V. Kozlov, L.E. Popov, M.D. Starostenkov // Russan Physcs Journal 15 (3) (1972) 395. [2] L.A. Grfalco, V.G. Wezer // Physcal Revew 114 (1959) 687. [3] S.V. Dmtrev, A.A. Ovcharov, M.D. Starostenkov, É.V. Kozlov // Physcs of the Sold State 38 (6) (1996) 996. [4] G.M. Poletaev, Atomc mechansms of dffuson n metallc systems wth fcc lattce, D. Sc.

10 62 M.M. Ash, M.D. Starostenkov Thess (I.I. Polzunov Alta State Techncal Unversty, Barnaul, 2006). [5] X. Yang, L. Lu, P. Zha, Q. Zhang // Computatonal Materals Scence 44 (2009) [6] Potekaev A.I., Dudnk E.A., Popova L.A., Starostenkov M.D. // Russan Physcs Journal 51 (10) (2008) [7] M.D. Starostenkov, B.F. Demyanov, S.L. Kustov, E.G. Sverdlova, E.L. Grakhov // Computatonal Materals Scence 14 (1999) 146.