Stability and symmetry breaking in metal nanowires: The nanoscale free-electron model

Urban, Daniel F.; Bürki, J.; Stafford, Charles; Grabert, Hermann

doi:10.1103/physrevb.74.245414

Cited by 17 publications

(53 citation statements)

References 44 publications

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“…These observations form the basis for the nanoscale free-electron model (NFEM [11,29,41]) which considers electrons in the wire to be free (other than being confined within the wire) and non-interacting. The former works best for s-shell metals, such as alkali and to some extent noble metals like gold, but has also been shown to perform well for metals whose Fermi surface in the extended zone scheme is nearly spherical, such as Al [14].…”

Section: The Modelmentioning

confidence: 99%

“…The theory, however, is limited to wires with a cylindrical symmetry. Urban et al [9,11], using a stability analysis of metal nanowires subject to non-axisymmetric perturbations, showed that, at certain mean radii and aspect ratios, Jahn-Teller deformations breaking cylindrical symmetry can be energetically favorable, leading to an additional class of stable nanowires with non-axisymmetric cross sections.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we use these results and those of Urban et al [9,11] to construct a more general theory of lifetimes of nanowires with both axisymmetric and nonaxisymmetric cross-sections, as functions of temperature, strain, and other thermodynamic variables.…”

Section: Introductionmentioning

confidence: 99%

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Lifetimes of metal nanowires with broken axial symmetry

et al. 2015

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We present a theoretical approach for understanding the stability of simple metal nanowires, in particular monovalent metals such as the alkalis and noble metals. Their cross sections are of order one nanometer so that small perturbations from external (usually thermal) noise can cause large geometrical deformations. The nanowire lifetime is defined as the time required for making a transition into a state with a different cross-sectional geometry. This can be a simple overall change in radius, or a change in the cross section shape, or both. We develop a stochastic field theoretical model to describe this noise-induced transition process, in which the initial and final states correspond to locally stable states on a potential surface derived by solving the Schrödinger equation for the electronic structure of the nanowire numerically. The numerical string method is implemented to determine the optimal transition path governing the lifetime. Using these results, we tabulate the lifetimes of sodium and gold nanowires for several different initial geometries.

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Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lifetimes of metal nanowires with broken axial symmetry

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“…It is thus particularly suitable as a model of metal nanowires, and successfully describes many of their equilibrium [2,11,12,15,18,19] and dynamical [3,4,9,16,20] properties in simple physical terms.…”

Section: The Nanoscale Free-electron Modelmentioning

confidence: 99%

“…It has been shown, using the NFEM [4,12], that the quantum confinement of electrons in the cross-section of the wire provide electron-shell effects-similar to those well-known in cluster physics [13]-that compete with surface effects, and stabilize cylindrical wires for a finite range around magic radii [11,12], as well as a number of number of wires with broken axial symmetry [14,15].…”

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confidence: 91%

Front propagation into unstable metal nanowires

Bürki

2007

Phys. Rev. E

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Long, cylindrical metal nanowires have recently been observed to form and be stable for seconds at a time at room temperature. Their stability and structural dynamics is well described by a continuum model, the nanoscale free-electron model, which predicts cylinders in certain intervals of radius to be linearly unstable. In this paper, I study how a small, localized perturbation of such an unstable wire grows exponentially and propagates along the wire with a well-defined front. The front is found to be pulled, and forms a coherent pattern behind it. It is well described by a linear marginal stability analysis of front propagation into an unstable state. In some cases, nonlinearities of the wire dynamics are found to trigger an invasive mode that pushes the front. Experimental procedures that could lead to the observation of this phenomenon are suggested. Front propagation into unstable states occurs in many areas of physics, chemistry, and biology (see Ref.[1] for a recent review), and is often related to pattern formation mechanisms. In this paper, I show that metal nanowires, whose dynamics can be described by a continuum model, the nanoscale free-electron model (NFEM) [2,3,4], exhibit such front propagation into unstable cylinders.Recent transmission electron microscopy experiments [5,6,7,8] have observed gold and silver nanowires to form long cylinders, with diameters of order one nanometer, that are stable for seconds at a time at room temperature. A theoretical description within the NFEM shows [3,9] that such self-assembly is natural if conditions are such that the atom mobility allows the wire to explore its configuration space and reach its equilibrium shape, as is the case at room temperature for these metals.Due to the high number of surface atoms-with low coordination numbers-in such nanowires, surface effects are particularly important, and favor wire breakup due to the Rayleigh instability [10,11]. It has been shown, using the NFEM [4,12], that the quantum confinement of electrons in the cross-section of the wire provide electron-shell effects-similar to those well-known in cluster physics [13]-that compete with surface effects, and stabilize cylindrical wires for a finite range around magic radii [11,12], as well as a number of number of wires with broken axial symmetry [14,15].The NFEM [2,3,4] is a continuum model where the atomic structure is replaced by a uniform, positively charged background, and the emphasis is put on the electronic structure. An extension of the model [3] includes ionic dynamics through surface self-diffusion, which is expected to dominate the structural dynamics in such thin wires. One of its important predictions is that a random wire naturally evolves into a universal equilibrium shape consisting of a perfect cylinder of a magic radius, connected to thicker leads [3,9]. Recently, the rich kink dy- * Electronic address: buerki@physics.arizona.edu namics of the NFEM has been described [16], and shown to be qualitatively similar to the thinning mechanism of gold nanowires ...

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A jellium model analysis on quantum growth of metal nanowires and nanomesas

Han

2008

Front. Phys. China

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A simple jellium model is used to investigate the stability of a metal nanowire as a function of its size. The theoretical results from the model indicate the quantum selectivity of preferable radii of nanowires, in apparent agreement with the experimental observations. It is consequently suggested that a series of stable "magic numbers" and "instability gaps" observed in the synthesis experiments of Au nanowires is mainly attributed to the quantum-mechanical behavior. These stable radii can be achieved by rearranging atoms during the formation of nanowires. The model is also used to analyze the growth of Au nanomesas on a graphite surface, and the puzzling growth behavior of Au nanomesas can be reasonably explained.Keywords jellium model, free electrons, quantum size effects, metal nanowires, metal nanomesas PACS numbers 81.10. Aj, 36.40.Qv ½ ÁÒØÖÓ Ù Ø ÓÒA metal nanostructure often exhibits a size-dependent feature arising from quantum confinement when its structural dimension is comparable to the electron Fermi wavelength, a phenomenon referred to as the quantum size effect (QSE). The QSE can have two distinct sizedependent manifestations: a property anomaly at certain selected size, i.e., the so-called "magic" size, or an oscillatory size-dependent property. For example, metal nanoclusters are anomalously stable when they contain a magic number of atoms [1−5]; a chain of transition metal atoms shows an oscillatory magnetic moment with increasing chain length [6]; and, metal nanofilms display a periodic oscillation of stability with increasing film thickness [7,8]. The size-dependency of physical properties of metal nanostructures has attracted much interest because it is of importance not only in fundamental physics but also in many targeted potential applications, e.g., electronic device technology, nanocatalysts, sensors, biological interfaces, and functional materials. However, the measurement and interpretation of properties relevant to metal nanostructures manifests a considerable theoretical and experimental challenge [2−5] because, as mentioned above, the big difference in properties often exists between a metal nanostructure and its bulk counterpart.Nanowires, belonging to one type of nanostructure, can be produced by employing various experimental techniques that have burgeoned in the past decade. Such experiments on alkali metals [9−11], noble metals [12−14], Al [15][16][17] and Bi [18] have revealed an oscillatory behavior in nanowire electrical conductivity as a function of its diameter. Suspended Au nanowires formed in an ultra-high vacuum have been reported as exhibiting a series of stable "magic numbers" and "instability gaps" [19]. Although some theoretical analyses on metal nanowires have been made to connect this magic sequence to the electron shell structure, the physical origin is still not very clear [16, 20−25].Nanomesas, belonging to another type of nanostructure, can grow on a semiconductor or insulator surface in vacuum evaporation-deposition experiments, and often adopt a flat-to...

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Stability and symmetry breaking in metal nanowires: The nanoscale free-electron model

Cited by 17 publications

References 44 publications

Lifetimes of metal nanowires with broken axial symmetry

Lifetimes of metal nanowires with broken axial symmetry

Front propagation into unstable metal nanowires

A jellium model analysis on quantum growth of metal nanowires and nanomesas

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