Molecular Dynamics Simulation on Plastic Deformation of Metallic Nanowires


Hideyuki Ikeda*, Yue Qi**, Tahir Çagin**, Konrad Samwer***,

William L. Johnson**** and William A. Goddard III**


*Department of Mechanical Engineering, Kagoshima National College of Technology,

Kagoshima 899-5193, Japan

** Materials and Process Simulation Center (139-74), California Institute of Technology,

CA 91125, USA

***Institut fuer Physik, Universitaet Augsburg, D 86135 Augsburg, Germany

****Keck Laboratory of Engineering Materials (138-78), California Institute of Technology,

CA 91125, USA


We have studied the initial stage of plastic deformation behavior of metallic nanowire of pure nickel, by using molecular dynamics methods. In these simulations, we applied uniform strain along c-axis at strain rate of 0.5%/100ps, 0.5%/10ps and 0.1%/2ps. We have observed the formation of stacking faults by movement of a partial dislocation, and the development of stacking faults to deformation twins at initial down event of stress-strain curve. Since twinning is also seen in at the slowest strain rate in our simulations and direct observation of nanometer-sized gold by high resolution transmission microscopy at very slow strain rate by Kizuka(i), the twinning seems to be a characteristic of deformation mechanism in metallic nanowires.

(Received April 13, 1999)

Keywords : nickel nanowire, molecular dynamic simulation, many-body potential, plastic deformation, partial dislocation, deformation twin



I. Introduction


Recent advanced technology of fabricating nanometer-sized materials coupled with demands for producing highly integrated and precise industrial productions have enabled and required to study various properties of nano-scale specimens(a-e).

Kizuka(f) observed in situ atomic process of the deformation of nanometer-sized gold under high-resolution transmission electron microscopy using a piezodriving specimen holder. He has found that slip and twinning are attributed to the deformation and proceed at every atomic layer in dislocation free nanometer-sized gold. While molecular dynamic simulations in deformations of nano-wires under high strain rate are also performed by Mehrez et al. (g-h) and Kitamura et al. (i-j). According to the report by Kitamura et al., the deformation of nickel nano-wire proceeds in such a way that after the first partial dislocation slide on (111) plane to create a stacking fault, the second partial dislocation goes through the plane and the combined slips of the partial dislocations bring about migration toward [101] direction on the slip plane. In general, the metallic single crystal deforms by twin mechanism under high strain rate or at low temperature. They have not referred to the formation of twins in plastic deformation of Ni nano-wire.

We have already reported the deformation behavior of FCC crystalline metallic nanowires studied by Molecular Dynamics (MD) simulations, and observed that the plastic deformation proceeds through twinning(m). In this article, we focus on the atomistic formation processes of stacking faults and the development to twins in early stage of plastic deformation.


II. Simulation Method and Model


The MD-simulations use the MSC Alloy Simulator(k), which employs the quantum Sutton-Chen (Q-SC) force field (f) to model the atomic interactions. The Q-SC describes the total potential energy of the metal as follows,

where rij is the distance between atoms i and j, u(rij) denotes a pair-wise potential energy between the cores of atoms i and j, and D i means a local density associated with atom i ,

The parameter a is a length parameter leading to a dimensionless form for u, and D , c is a dimensionless parameter scaling the attractive terms, D sets the overall energy scale, and m, n are integers such that n > m. These parameters are optimized to fit the 0K properties such as the cohesive energy, zero pressure condition and the bulk modulus of the fcc metals.

The specimens are constructed from the fcc crystal by taking 5x5x10 fcc unit cells (1000 atoms) with the long axis (c-axis) parallel to the tensile axis. Before deformation, each sample was allowed to relax at 300K for 110ps but with the sample length fixed. The deformation was applied uniformly in discrete steps at intervals of 1 ps (1000 MD steps). We took the boundaries in the c direction ([001]) as periodic (with an initial cell length of 10 fcc cubic cells) so that the wire is infinite in length, while the boundaries in the a and b directions are nonperiodic (with an initial cell length of 5 fcc cells). We studied the deformation behavior at constant strain rates, 0.5%/10ps, 0.1%/2ps and 0.5%/100ps.


III. Results and Discussions


The stress–strain curves of pure Ni nanowires tensiled by 0.5%/10ps, 0.1%/2ps and 0.5%/100ps are shown in Fig. 1. Both 0.5%/10ps and 0.1%/2ps are the same strain rate, but the latter is given the strain by 0.1% for each step. As shown in Fig. 1, their yield stresses are almost equal, although they show different curves after yielding. On the other hand, the curve for strain rate of 0.5%/100ps exhibits the lower yield stress (about 4 GPa) than the others, therefore the yield stress depends on a strain rate in accordance with the result by experimental measurements.

We have studied on the changes in atomstic arrangements at early stage of plastic deformation tensiled by 0.1%/2ps in order to confirm the formation of stacking faults and twins. We show the stress-strain curves of 0.1%/2ps and 0.5%/10ps. The curve of 0.1%/2ps is different from that of 0.5%/10ps, that is one extra peak ('c') and lower minimum stress ('e'). Then we examined all points of the curve at strain of 0.1%/2ps from strain of 0,076 to 0.083 in Fig. 2.

We schematically illustrate a twin which is created by the movements of partial dislocations on (111) planes. The first run of the dislocation forms a stacking fault, and the second run on upper or lower layer of (111) planes on which the first dislocation has run creates a twin from stacking fault. One of other {111} planes intersecting the twin inflects as drawn in Fig. 3. Therefore, we have colored several {111} planes in deformed Ni crystal in order to identify the stacking faults and twins.

Even before yielding state at strain of 0.076 (point 'a' in Fig. 2), we find the partial dislocation moving on the P2 plane as seen in Fig. 4. The dislocation is generated at the edge of the specimen where stress concentration is higher than any other parts of specimen. It has gone through the specimen from top to bottom, because of periodic boundary condition along c direction, and created a stacking fault on bottom, too (Fig. 5 (a)). This movement causes bending stress normal to c-axis, and then some atoms in area 'A' indicated in Fig. 5 have displaced by d=a/4[1-1 0]. The atoms in area 'A' started to move at strain of 0.077, which is the first point of beginning of stress down, and continued to decrease the stress to the point 'b'. Again another partial dislocation, b=a/6[1-2-1], is acting on P6 plane (Fig. 5 (b)). The displacement of d, however, cannot be corrected by this partial dislocation, because vector sum of them, d+b = (a/12) [5-7-2], does not translate atoms to right positions of fcc lattice. After the dislocation swept through whole P6 plane, new stacking fault has created on P4. This state is the first minimum stress at the middle point of (b) and (c) in Fig. 2. As the displacement vector cannot move atoms to right positions, above motion causes the irregular arrangement of atoms at the end point of the dislocation movement on P6. Hence an initiation of new partial dislocation is generating from these atoms (left bottom of P6 in Fig. 6 (a), (b)), and makes the increase in stress. This dislocation runs from the bottom part of specimen to the top on P1 with making deformation twin as seen in Fig. 7. After all, at the second minimum stress in Fig.2 (strain of 0.083), two twins and one stacking fault are created (Fig. 8).

In Fig. 9, we depict the snapshot pictures at strain of 0.25 deformed by 0.1%/2ps and 0.5%/100ps. Both specimens have thicker twins than those in Fig. 8. The twins are also created in the specimen at slowest strain rate that we simulated. So far as we studied, we cannot find the slip of (a/2)<110> or Heidenreich-Shockley type dislocations even at the slowest strain rate. In a bulk crystal, twinning proceeds with generation of partial dislocations from some source in crystal. However in a nanowire, the origin of a partial dislocation is a surface of crystal, that is an edge of specimen for square shaped nanowire which yields high stress concentration. Kizuka(f) mentions that the twinning are observed in deformation of gold nanowire displaced by less than 0.6nm/s. In our simulations, the defomation speed of slowest displacement is about 0.18m/s, we conjectured that twinning was the deformation mechanism due to the high strain rates. Although taking account of the differences of stacking fault energy between gold and nickel (the stacking fault energy of gold is about 1/4 or 1/5 of that of nickel), we cannot explain formation of the twin in gold nanowire at such a slow strain rate.

 We, therefore, suppose that twinning is a characteristic deformation mechanism for a nanowire specimen.


IV. Conclusions


We have performed the molecular dynamic simulations to study an atomistic deformation mechanism of nickel namowires with square cross section, and obtained following results.

(1) Yield stresses show strain rate dependence, which is lower yield stress at slower strain rate.

(2) Stacking faults have been formed by the movement of partial dislocations generated at edge of specimen on surface.

(3) At stress down event, a stacking fault develops to deformation twins by motion of a partial dislocation.

(4) We cannot find any Heidenreich-Shockley type dislocations.

(5) The twinning seems to be a characteristic deformation mechanism for a nanowire specimen.




Financial support was provided by Ministry of Education, Science, Sports and Culture, Government of Japan for HI, by DOE (DEFOG3 86ER45242) for KS and WLJ, by ARO (DAAH04-95-1-0233) for WLJ and WAG, and by NSF (CHE95-22179 and ACR-92-17368) and DOE-ASCI for YQ, TC and WAG. In addition, the facilities of the MSC are supported by grants from ARO-DURIP, BP Chemical, Exxon, Avery-Dennison, Owens-Corning, ARO-MURI, Asahi Chemical, Chevron and Beckman Institute.




(a) M. Brandbyge, J. Schiotz, M. R. Sorensen, P. Stoltze, K. W. Jacobsen, J.K. Norskov, L. Olesen, E. Laegsgaard, I. Stensgaard, F. Besenbacher : Phys. Rev. B, Condens. Matter , 52(1995), 8499-514.

(b) U. Landman, W. D. Luedtke, B. E. Salisbury, R. L. Whetten : Phys. Rev. Lett., 77(1996),1362-5.

(c) A. I. Yanson, G. R. Bollinger, H. E. van den Brom, N. Agrait, J. M. van Ruitenbeek : Nature, 395(1998),783-5.

(d) K. Liu, C. L. Chien, P. C. Searson : Phys. Rev. B, Condens. Matter, 58(1998), R14681-4.

(e) U. Landman : Solid State Commun., 107(1998), 693-708.

(f) T. Kizuka : Phys. Rev. B, 57(1998), 11 158-11 163

(g) H. Mehrez, S. Ciraci : Phys. Rev. B, Condens. Matter, 56(1997), 12632-42.

(h) H. Mehrez, S. Ciraaci, C. Y. Fong and S. Erkoc : J. Phys. Condens. Matter 9(1997),10843-10854.

(i) T. Kitamura, K. Yashiro, M. Iehara and R. Ohtani : Jpn. Soc. Mech. Eng.(in Japanese), 46(1997), 232-237.

(j) T. Kitamura, K. Yashiro and R. Ohtani : JSME A, 40 (1997), 430-435.

(m) Y. Qi, H. Ikeda, T. Çagin, K. Samwer, W. L. Johnson and W. A. Goddard III : Proceedings of MSC Meeting? Please let me know vol. no. and page etc.

(k) T. Çagin and W. A. Goddard III : MSC Alloy Simulator program. This uses Extended System Hamiltonian molecular dynamics for metals and alloys, 1997. Interfaced to Cerius2 Modelling environment using Software Developers Kit (SDK) of Molecular Simulation Inc. San Diego, CA.

(l) Y. Kimura, T. Çagin, Y. Qi, W. A. Goddard, III : Phys. Rev B1, submitted. (Please let me know vol. no. and page etc., if it is already published) For Sutton Chen potentials see A. P. Sutton : J. Chen, Phil. Mag. Lett. 61(1990), 139.