IOP PUBLISHING NANOTECHNOLOGY Nanotechnology 20 (2009) 465709 (7pp) doi:10.1088/0957-4484/20/46/465709 Ideal strength on clusters from first principles: the Ti 13 case M Salazar Villanueva 1,2,3 , A H Romero 1,3 and A Bautista Hern´ andez 2 1 Cinvestav, Unidad Quer´ etaro, Libramiento Norponiente 2000, Real de Juriquilla, CP 7230, Quer´ etaro, Mexico 2 Facultad de Ingenier´ ıa, Universidad Aut´ onoma de Puebla, Apartado Postal J-39, CP 72570, Puebla, Mexico E-mail: martin.salazar@fi.buap.mx and aromero@qro.cinvestav.mx Received 6 March 2009, in final form 9 September 2009 Published 22 October 2009 Online at stacks.iop.org/Nano/20/465709 Abstract The mechanical behavior of a Ti 13 cluster, based on total energy mechanical quantum calculations is studied. The cluster geometry has been optimized and good agreement with previous reports has been found. Axial strain is applied along one of the principal axes and the changes on the energetic and vibrational properties of the system are followed. To characterize the cluster stability as a function of strain, vibrational frequencies and total energy have been calculated, to obtain the cluster maximum load tolerance for compression (C ) and tensile (T ). If the maximum load is defined through a vibrational instability, it happens to be two and half, and three times larger than when the maximum total energy is considered (C and T respectively). As a result of the induced strain along of the C 5 symmetry element, the cluster changes its point group symmetry from I h to D 5d , with an energy difference of 1.17 eV (for compression) and 0.33 eV (for tension) with respect to the ground state geometry. The electronic changes are also characterized, as function of the strain, by following the modifications of the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) and changes on the total atomic population. 1. Introduction Small titanium clusters have attracted the attention of theoreticians and experimentalists in the last few years, mainly because they have shown a large potential in nanotechnology. Namely, in applications such as pigment fabrication, used to characterize corrosion, hydrogen storage, photocatalyzers and solar cells [1–11], most of those properties are system and structurally dependent and it is necessary to see their effect in the final product. Between the many interesting cluster structural properties, one exhibited by titanium is the so called formation of magic numbers [12], which is a unique relation between, stability, geometrical symmetry and atomic number. This relation has been observed in experiments [16] as well as in theoretical studies [13–15]. The first magic numbers in small titanium clusters correspond to 7, 13 and 15 atoms [12, 16]. For example, a complete structural and electronic characterization, as a function of the atomic number, has been reported in [13–15, 17]. Much more recently, 3 Authors to whom any correspondence should be addressed. researchers have directed their attention to the modification of the electronic and structural properties of these finite systems by application of external fields, such as pressure, temperature, electromagnetic fields, etc. Recently Krauss et al [18] have studied the compressibility of silver (10 nm) and gold (30 nm) nanoparticles and found an unexpected behavior as a function of size. Principally, they found that nanoparticles have a significantly higher stiffness than the corresponding bulk materials. The results of these experiments have motivated theoretical studies of mechanical properties of small molecular nano-structured components such as nano-films, nano-wires (tubes and cylinders) and nano-dots (clusters) [19–27]. Just as in crystalline systems [28], the ideal strength in clusters could be defined as the energy inflexion point in an energy versus strain curve, which corresponds to a maximum in the load– strain diagram. The dependence of the mechanical response is also controlled by the vibrational instabilities and they need to be also considered within a mechanical study of any given system. Therefore, in order to have a unique definition of the ideal strength for finite systems, inclusion of the vibrations as 0957-4484/09/465709+07$30.00 © 2009 IOP Publishing Ltd Printed in the UK 1