Atomistic simulations of tensile and bending properties of single-crystal bcc iron nanobeams Pär A. T. Olsson, 1, * Solveig Melin, 1 and Christer Persson 2 1 Division of Mechanics, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden 2 Division of Material Science, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden Received 7 May 2007; revised manuscript received 15 August 2007; published 28 December 2007 In this paper, we report the results of a systematic study of the elastic properties of nanosized single-crystal wires and beams of bcc iron. Both tensile and bending stiffnesses have been determined employing molecular statics simulations for specimens of different sizes and three different crystallographic orientations. We also analyze the influence of circular cross sections and rounded edges compared to square cross sections with sharp edges for one of the crystallographic orientations. The simulations show that there is a size dependence in Young’s modulus and that different crystallographic orientations display different elastic behaviors. There are bands of deviating Young’s modulus over the cross sections in the direction 45° from the surfaces emanating from the edges, giving the cross section a heterogeneous character. Rounding the edges, or making the cross section circular, has little influence on the average Young’s modulus, but it does influence the distribution over the cross section and, consequently, the aforementioned bands. DOI: 10.1103/PhysRevB.76.224112 PACS numbers: 62.25.+g, 62.20.Dc, 62.20.-x I. INTRODUCTION With the introduction, fast development, and increasing use of nanoelectromechanical systems NEMS, the me- chanical properties of nanostructures have become of consid- erable interest. NEMS are characterized by their small di- mensions, spanning from hundreds down to only a few nanometers, resulting in components of extraordinary force sensitivity, very low mass, high attainable eigenfrequencies, and, sometimes, intriguing magnetic properties. This allows NEMS to act as sensors in highly sensitive detectors in ap- plications involving, e.g., molecular interactions and cell adhesion. 1–7 The low density of defects and the high surface to volume ratio provide the structure with mechanical prop- erties that deviate significantly from those of macroscopic single crystals. Hence, macroscopic continuum mechanical generalizations to the nanoscale may no longer be valid. 8–10 In the literature, a vast number of papers addressing the issue of mechanical properties of nanostructures have been published. Specially designed experiments to obtain the elas- tic properties involve mainly two types of setups, e.g., bent cantilever beams 8,10–14 and cantilever resona- tors. 1–4,9,13,15,16 The two methods differ in the sense that the first is static and uses the continuum mechanical relation between the deflection and the applied force of a cantilever beam to obtain Young’s modulus. The latter is, on the other hand, dynamic and the elastic properties are conceived by measuring the spectrum of eigenfrequencies and, through continuum mechanical considerations, Young’s modulus is calculated. Experiments indicate that, as the dimensions of a structure reach a certain threshold, surface effects are no longer neglectable. Mechanical properties are reported to de- viate significantly from bulk properties, and these deviations are material specific. For instance, it has been observed that for chromium, 10 silicon 15 and gallium nitride, 16 there is a decrease in Young’s modulus with decreasing size, whereas for polypyrrole, 12–14 silver, 14 and lead, 14 it has been reported that Young’s modulus increases with decreasing size. Alongside the experimental research, a great deal of the- oretical investigations of the elastic properties of nanostruc- tures have been performed. 17–19 Using simple linear nearest neighbor interactions, it has been found that, depending on how the height of the structure is measured, the bending stiffness for a two-dimensional 2D single-crystal strip of discrete particles takes on different values. This effect does, however, vanish as the number of planes goes toward infinity. 17 Similar results has been found for Young’s modu- lus of 2D hexagonal closed-packed structures and three- dimensional face-centered cubic crystals. Furthermore, it has been reported that this height ambiguity can lead to that Young’s modulus may both increase and decrease with in- creasing size. 18,19 Different numerical techniques have been employed to simulate the elastic and the plastic behaviors of nanostruc- tures. In the literature, there are basically three types of mo- lecular dynamics simulations that are used to monitor the elastic behavior of a nanostructure; structural frequency re- sponse simulations, 20 tensile tests, 21–29 and beam bending simulations. 30 In Ref. 20, the mechanical properties for quartz crystal oscillators have been investigated, and it was argued that it is not sufficient to approximate Young’s modu- lus with only surface and bulk atoms, but the edge atoms must also be taken into account. Consequently, when ap- proximating Young’s modulus, the cross sections were di- vided into three parts, bulk, surfaces, and edges, and contri- butions from each part were regarded so that an approximate fit to a polynomial with coefficients that were weights corre- sponding to the individual part’s area divided by the full area could be found. Metallic films and nanowires have been investigated by several investigators. 21–30 The elastic properties of copper films and wires have been simulated through molecular stat- ics MS simulations using embedded atom method multi- body potentials. It has been observed that different orienta- tions display very different behaviors, i.e., some orientations display increasing Young’s modulus whereas others display decreasing Young’s modulus with increasing size. These findings have been confirmed with ab initio simulations from which it has also been found that there is a correlation be- tween the redistribution of the electron density over the sur- PHYSICAL REVIEW B 76, 224112 2007 1098-0121/2007/7622/22411215 ©2007 The American Physical Society 224112-1