Molecular Dynamic Simulations of Nickel Nanowires at Various Temperatures

Transcription

1 Intenatonal Jounal of Scentfc and Innovatve Mathematcal Reseach (IJSIMR Volume 2, Issue 3, Mach 204, PP ISS X (Pnt & ISS (Onlne Molecula Dynamc Smulatons of ckel anowes at Vaous Tempeatues M.M. Ash Physcs depatment, Faculty of scence, Menoufa Unvesty, Egypt, M. D. Staostenkov 2I. I. Polzunov Alta State Techncal Unvesty, Banaul, Russa. Abstact: The mechancal popetes of ckel nanowes have been studed at vaous tempeatues usng molecula dynamcs smulatons. Molecula Dynamcs (MD smulatons have been caed out on pue ckel ( cystal wth face-centeed cubc (FCC lattce upon applcaton of unaxal tenson at nanolevel wth a speed of 20 m/s. The defomaton coesponds to the decton <00>. To the calculated block of cystal - fee bounday condtons ae appled n the dectons <00>, <00>. Mose potental was employed to cay out thee dmensonal molecula dynamcs smulatons. MD smulaton used to nvestgate the effect of tempeatue of nanowe on the natue of defomaton and factue. Tempeatue effect on the extenson popety of metal nanowe s dscussed n detal. The mechancal stengths and the mechancal stan of the nanowes decease lnealy wth the nceasng tempeatue. The featue of defomaton enegy can be dvded nto fou egons: quas-elastc, plastc, flow and falue. Expements have shown that when the tempeatue nceases the fst stage of defomaton was naowed, and the second stage was wdened. The esults showed that beakng poston depended on tempeatue. The smulaton esults at nanoscale play an mpotant ole on the mechancal behavos of nanostuctues. Keywods: mechancal popetes, molecula dynamcs smulatons, nanowe, Mose potental.. COMPUTER SIMULATIO MODEL The obect of nvestgaton s taken alloy. Alloy stuctue s pesented n the fom of a facecenteed cubc cell. In ths pape fo calculatng the dynamcs of the atomc stuctue of the molecula dynamcs method usng paed Mose potental functon []. Mose pa potental s wtten as: ( D e e 2 ( Whee KL, KL, D KL - paametes defnng the nteacton of pas of atoms of type K and L; - the dstance between the atoms. The potental enegy of a system of atoms s epesented as: E 2, ( KL (2 Whee - adus vectos of -th atom. When consdeng a closed system, the foce actng on the - th atom, wll be: F d KL, d( ( (3 Mathematcal model of the molecula dynamcs method [2-5] descbes a system of odnay ARC Page 30

2 M.M. Ash & M. D. Staostenkov dffeental equatons of moton of ewton. The equaton of moton n the classcal fom s epesented by: d υ d m F υ,2,..., (4 dt dt Whee m and v - mass and velocty of -th atom - tme. To solve the system of odnay dffeental equatons by numecal Eule method wth half-step. Tempeatue of the atoms n a pefect cystal, calculated usng the fomula: T 2 k 3 k b 3 k b I m v 2 (5 Whee k b, Boltzmann constant and K, s the total Knetc enegy. Fg. Atomc confguatons of 2x2x36 nanowe ckel unde extenson loadng at tme 75 ps at dffeent tempeatues (a T=0 K, plastc defomaton occu (b T=300K, plastc defomaton occu (ct =500K, beak-up occu(d T=000K, plastc defomaton occu (e T=500K, plastc defomaton occu. Compute smulaton usng Mose potental s employed to cay out thee dmensonal molecula dynamcs smulatons of the mechancal popetes of ckel nanowe. We studed the extenson popetes of ckel nanowes at dffeent tempeatues fom 0 K to 700 K, whch s adusted evey 0-3 seconds. The estmated sze of the cystal unt was fo vaous expements of 728 atoms (6 atoms along the edges and 96 atoms n heght, 296 atoms (9 atoms along the edges and 72 atoms n heght and 3456 atoms (2 atoms along the edges at the bottom and 48 - n heght. The dependence of mechancal popetes on smulaton tempeatue has also been studed [6-9]. The yeld stength deceases wth nceasng tempeatue. Low yeld stength at hgh tempeatue s because of the fact that the themal fluctuatons ovecomng the enegy bae fo dslocaton nucleaton. Intenatonal Jounal of Scentfc and Innovatve Mathematcal Reseach (IJSIMR Page 302

3 Molecula Dynamc Smulatons of ckel anowes at Vaous Tempeatues In the study the followng paametes wee montoed: the stoed stan enegy, the dffuson coeffcents of the components n the dectons, the oveall dffuson coeffcent, the knetc and potental enegy of the cystal. 2. RESULTS AD DISCUSSIO, TEMPERATURE EFFECT The mechancal popety at dffeent tempeatues Wth MD smulatons, the unaxal tenson of the nckel nanowes ae studed at dffeent tempeatues fom 0 to 700 K. Fgue 2 gves the stess stan elatonshps of the 6x6x96 nanowes subected to unaxal tenson at tempeatues 300 K. The stan was defned as: Ԑ = l l 0 l 0 Whee l was the stetchng length and l 0 was the length ust afte elaxaton. The stess n the tensle decton was calculated as: (6 σ = (7 V F Whee V efes to volume of atom. Wth the nceasng ntal stan, stess nceases lnealy at dffeent tempeatues. Ths pocess coesponds to the elastc defomaton of the nanowe. Wth the nceasng stan, stess decease as shown n the stess stan esponse of the nanowe, ndcatng the begnnng of the plastc defomaton of the nanowe. the stess stan cuves ae smooth at low tempeatues, wheeas, some mnpeaks exhbt at hgh tempeatues. It s obseved that the fst yeld stess deceases as the tempeatue nceases (Fg. 3. When the plastc defomaton of the nanowe begns, the dop of the fst yeld stess also deceases. In ode to clealy study these chaactes, n Fg. 4, we show the aveage statstcal esults of the fst yeld stan, the fst yeld stess (σ at dffeent tempeatues. The aveage esult s fom 300 samples at each tempeatue, and tempeatues fom 0 to 700 K. As shown n Fg. 4, the fst yeld stan deceases when the tempeatue nceases. Fom 0 to 700 K, an abupt decease s dentfed and the fst yeld stans ae.25 (00 K and 0.2 (700 K wth alloy 2x2x48,.6 (0 K and 0.07 (700 K wth alloy 9x9x72 and.46 (00 K and (700 K wth alloy 6x6x96. The bgge stan at low tempeatue ndcates that the nanowe mantans ts elastc defomaton fo long tme. Wheeas, the smalle stan at hgh tempeatue llustates that the plastc defomaton begns quckly. Defomaton of the nanowe s n a fast stage of the atomc damage pocess at hgh tempeatue. Fgue.2. The stess stan elatonshps of the 6x6x96 nanowes subected to unaxal tenson at tempeatues 300 K. Intenatonal Jounal of Scentfc and Innovatve Mathematcal Reseach (IJSIMR Page 303

4 M.M. Ash & M. D. Staostenkov Table. Results of MD smulaton of unaxal tensle loadng wth 2x2x28 ckel nanowe. umbe of atoms=3456. Ultmate knetc enegy of the Stan at max. stess Tempeatue stength (GPa system, ev Fg. 3. The cuves of stess wth tempeatues. Fg 4. The cuves of stan wth tempeatues. Intenatonal Jounal of Scentfc and Innovatve Mathematcal Reseach (IJSIMR Page 304

5 Molecula Dynamc Smulatons of ckel anowes at Vaous Tempeatues 3. COCLUSIO The new concept of usng nanowes as buldng blocks fo logc and memoy ccuts makes t vey necessay to fully undestand the mechancal behavos of these nanowes. Molecula dynamcs smulatons have been caed out to nvestgate the mechancal behavos of ckel nanowe. The effect of tempeatue on mechancal popetes was nvestgated by MD smulatons. The stess stan elaton of nanowe s obtaned. The tempeatue effect on the extenson popetes s dscussed n detal. Tempeatue exhbted a geat effect on the mechancal popetes of nanowes. Study on the mechancal popetes of metal nanowes can gve us moe fundamental undestandng of nanoscale machnes fom atomstc motons. The defomatons of the nanowes wee obseved at low, mddle, and hgh tempeatues, espectvely. The nvestgaton on the confguaton, stess, elastcty, yeldng and defomaton wll contbute to the desgn, manufactue and manpulaton of nano-devces. Ths study of mechancal popetes of metal nanowes wll be helpful to the desgn, manufactue and manpulaton of nano-devces. REFERECES [] H. Raf-Taba, Modellng the nano-scale phenomena n condensed matte physcs va compute-based numecal smulatons, Phys. Rep.325, 239 (2000. [2] Kozlov E.V., Popov L.E., Staostenkov M.D., Calculaton of the Mose potental fo sold gold, Russan Physcs Jounal Т С [3] L.A. Gfalco, V.G. Weze, Applcaton of the Mose Potental Functon to Cubc Metals, Physcal Revew 4 ( [4] Dmtev S.V., Ovchaov A.A., Staostenkov M.D., Kozlov É.V., Physcs of the Sold State Т С [5] Mkhal Staostenkov, Alexande Yashn, kta Snca, Stuctual Tansfomaton n anowes CuAu I wth Supestuctue of L0 of Tetagonal Symmety at Un-Axal Tenson Defomaton, Key Engneeng Mateals (Volumes pp [6] X. Yang, L. Lu, P. Zha, Q. Zhang // Computatonal Mateals Scence 44 ( [7] Potekaev A.I., Dudnk E.A., Popova L.A., Staostenkov M.D. Russan Physcs Jounal Т С [8] M.D. Staostenkov, B.F. Demyanov, S.L. Kustov, E.G. Svedlova, E.L. Gakhov // Computatonal Mateals Scence 4 ( [9] M.M. Ash, M.D. Staostenkov, EFFECT OF VOLUME O THE MECHAICAL PROPERTIES OF ICKEL AOWIRE, Mate.Phys.Mech.(MPMo, Vol. 8, 203, pages Intenatonal Jounal of Scentfc and Innovatve Mathematcal Reseach (IJSIMR Page 305