The validity of the linear elasticity theory is examined at the nanometer scale by investigating the vibrational properties of silver and gold nanoparticles whose diameters range from about 1.5 to 4 nm. Comparing the vibration modes calculated by elasticity theory and atomistic simulation based on the Embedded Atom Method, we first show that the anisotropy of the stiffness tensor in elastic calculation is essential to ensure a good agreement between elastic and atomistic models. Second, we illustrate the reduction of the number of vibration modes due to the diminution of the number of atoms when reducing the nanoparticles size. Finally, we exhibit a breakdown of the frequency-spectra scaling of the vibration modes and attribute it to surface effects. Some critical sizes under which such effects are expected, depending on the material and the considered vibration modes are given.
Bimetallic nanoalloys such as nanoparticles and nanowires are attracting significant attention due to their vast potential applications such as in catalysis and nanoelectronics. Notably, Pd-Pt nanoparticles/nanowires are being widely recognized as catalysts and hydrogen sensors. Compared to unary systems, alloys present more structural complexity with various compositional configurations. Therefore, it is important to understand energetically preferred atomic structures of bimetallic nanoalloys. In this study, we performed a series of simulated annealing Monte Carlo simulations to predict the …
We present a computational study for the equilibrium shape of gold nanoparticles. By linking extensive quantum-mechanical calculations, based on Density-Functional Theory (DFT) to Wulff construction, we predict equilibrium shapes that are in good agreement with experimental observa- tions. We discuss the effect of the interactions between a nanoparticle and the encapsulating material on the equilibrium shape. As an example, we calculate adsorption of CO on several different Au(hkl) and use the results to explain the experimentally observed shape change of Au nanoparticles.
We discuss the roles of continuum linear elasticity and atomistic calculations in determining the formation volume and the strain energy of formation of a point defect in a crystal. Our considerations bear special relevance to defect formation under stress. The elasticity treatment is based on the Green's function solution for a center of contraction or expansion in an anisotropic solid. It makes possible the precise definition of a formation volume tensor and leads to an extension of Eshelby's result for the work done by an external stress during the transformation of a continuum inclusion (P…
The shape of metal nanoparticles embedded in dielectric matrices influences the optical properties of the composite material. Swift heavy ion irradiation can induce a controllable shape transformation in gold and other metals embedded in amorphous silicon dioxide, where the particles elongate along the direction of the ion beam. The details of this transformation are not fully understood, but it is presumably related to nanometer-scale phase transitions induced by individual ion impacts. The phenomenon has been reproduced using atomistic simulations, although the time scale limitations and the…
We observe using ab initio methods that localized surface plasmon resonances in icosahedral silver nanoparticles enter the asymptotic region already between diameters of 1 and 2 nm, converging close to the classical quasistatic limit around 3.4 eV. We base the observation on time-dependent density-functional theory simulations of the icosahedral silver clusters Ag$_{55}$ (1.06 nm), Ag$_{147}$ (1.60 nm), Ag$_{309}$ (2.14 nm), and Ag$_{561}$ (2.68 nm). The simulation method combines the adiabatic GLLB-SC exchange-correlation functional with real time propagation in an atomic orbital basis set us…
We present classical molecular dynamics calculations of the behavior of copper and gold nanoparticles on a graphene sheet, sheared with a constant applied force $F_{\rm a}$. The force $F_{\rm s}$ acting on the particle from the substrate depends on the material of the nanoparticles (Au or Cu), and exhibits a sawtooth dependency on time, which we attribute to local commensurability between the metal nanoparticle surface atomic positions with the graphene lattice. The time-averaged value of $F_{\rm s}$ (the friction force) acting on Au nanoparticles increases linearly with the contact area, havi…
Understanding and mastering the mechanical properties of metallic nanoparticles is crucial for their use in a wide range of applications. In this context, we use atomic-scale (Molecular Dynamics) and continuous (Finite Elements) calculations to investigate in details gold nanoparticles under deformation. By combining these two approaches, we show that the elastic properties of such nanoobjects are driven by their size but, above all, by their shape. This outcome was achieved by introducing a descriptor in the analysis of our results enabling to distinguish among the different nanoparticle shap…
We present a detailed atomistic picture of the oxidation mechanism of Co nanoparticles and its impact on magnetism by experimentally following the evolution of the structure, chemical composition, and magnetism of individual, gas-phase grown Co nanoparticles during controlled oxidation. The early stage oxidation occurs in a twostep process characterized by (i) the initial formation of small CoO crystallites randomly distributed across the nanoparticle surface, until their coalescence leads to structural completion of the oxide shell and passivation of the metallic core; (ii) progressive conver…
The dislocation core is an important region as it controls many important properties of materials. Elasticity breaks down in the core and the stress, force, and energy diverge at the dislocation line. We consider three commonest methods employed in Discrete Dislocation Dynamics (DDD) simulations to eliminate these singularities: (1) considering a cutoff parameter, (2) spreading the Burgers vector (CAWB theory), and (3) using gradient elasticity. Each of these methods includes an extra length parameter to regularize the elastic fields. In this article, we show that these regularization paramete…
A finite-deformation crystal-elasticity membrane model for Transition Metal Dichalcogenide (TMD) monolayers is presented. Monolayer TMDs are multi-atom-thick two-dimensional (2D) crystalline membranes having atoms arranged in three parallel surfaces. In the present formulation, the deformed configuration of a TMD-membrane is represented through the deformation map of its middle surface and two stretches normal to the middle surface. Crystal-elasticity based kinematic rules are employed to express the deformed bond lengths and bond angles of TMDs in terms of the continuum strains. The continuum…
The atomic pair distribution function (PDF) for nano-particles has to be corrected with a shape factor, also known as form factor, in order to take size and shape effects into consideration. For most anisotropic shapes an analytical formulation of the shape factor is a challenge. In this paper, we present a new method to numerically compute the shape factor using atomistic model. This numerical method to calculate PDF for a wide range of geometrical shapes is demonstrated. In addition, a fitting formulation, which effectively converts the numerical shape factors for some selected geometrical s…
Signature of surface anisotropy in the spin-flip neutron scattering cross section of spherical nanoparticles: atomistic simulations and analytical theory
Energetically the single sheet of graphite (graphene) is more stable than the nanotube. The energy difference between the two systems can be directly related to the strain energy involved in rolling up the graphene sheet to form the nanotube. We have carried out first principle electronic structure calculations and evaluated the strain energy as a function of the nanotube radius. The dependence of the strain energy on the diameter of the nanotube has been found by several groups to be welldescribed by a continuum elasticity model. We attempt to examine why this is the case and show where atomi…
By introducing the divergence of a vector potential into the Lagrangian, a Lagrangian framework is developed to incorporate surface energy into elasticity. Besides the Euler-Lagrange equation and natural boundary condition, a new boundary constitutive equation is derived from the variation of the Lagrangian and configuration on which the Lagrangian is defined. On the boundary surface, explicit expression of the vector potential with respect to field variable and surface curvature is determined. Based on this framework, an elastic model with relevance to the surface energy is established. The Y…
Modeling point defects at an atomic scale requires careful treatment of the long-range atomic relaxations. This elastic field can strongly affect point defect properties calculated in atomistic simulations because of the finite size of the system under study. This is an important restriction for ab initio methods which are limited to a few hundred atoms. We propose an original approach coupling ab initio calculations and linear elasticity theory to obtain the properties of an isolated point defect for reduced supercell sizes. The reliability and benefit of our approach are demonstrated for thr…
Atomistic simulations are performed to probe the anisotropic deformation in the compressions of face-centred-cubic metallic nanoparticles. In the elastic regime, the compressive load-depth behaviors can be characterized by the classical Hertzian model or flat punch model, depending on the surface configuration beneath indenter. On the onset of plasticity, atomic-scale surface steps serve as the source of heterogeneous dislocation in nanoparticle, which is distinct from indenting bulk materials. Under [111] compression, the gliding of jogged dislocation takes over the dominant plastic deformati…
The atomistic structure of metallic glasses is closely related to properties such as strength and ductility. Here, Ni1-xBx metallic glass nanoparticles of two different sizes are compressed under quasi-hydrostatic high-pressure conditions in order to understand structural changes under stress. The structural changes in the nanoparticles were tracked using in situ high-pressure X-ray diffraction (XRD). The ambient pressure pair-distribution functions generated from XRD showed that the smaller sized nanoparticles had a more compact amorphous structure with lower coordination number. XRD showed t…
Vibrational mode frequencies and damping are calculated for an elastic sphere embedded in an infinite, homogeneous, isotropic elastic medium. Anisotropic elasticity of the sphere significantly shifts the frequencies in comparison to simplified calculations that assume isotropy. New low frequency Raman light scattering data are presented for silicon spheres grown in a SiO2 glass matrix. Principal features of the Raman spectrum are not correctly described by a simple model of the nanoparticle as a free, isotropic sphere, but require both matrix effects and the anisotropy of the silicon to be tak…
By combining continuum elasticity theory and tight-binding atomistic simulations, we work out the constitutive nonlinear stress-strain relation for graphene stretching elasticity and we calculate all the corresponding nonlinear elastic moduli. Present results represent a robust picture on elastic behavior of one-atom thick carbon sheets and provide the proper interpretation of recent experiments. In particular, we discuss the physical meaning of the effective nonlinear elastic modulus there introduced and we predict its value in good agreement with available data. Finally, a hyperelastic softe…
The size-dependent phase stability of gamma-Al2O3 was studied by large-scale molecular dynamics simulations over a wide temperature range from 300 to 900 K. For the gamma-Al2O3 crystal, a bulk transformation to alpha-Al2O3 by an FCC-to-HCP transition of the O sublattice is still kinetically hindered at 900 K. However, local distortions of the FCC O-sublattice by the formation of quasi-octahedral Al local coordination spheres become thermally activated, as driven by the partial covalency of the Al-O bond. On the contrary, spherical gamma-Al2O3 NPs (with sizes of 6 and 10 nm) undergo a crystalli…
We report a comprehensive study of aqueous halide adsorption on nanoparticles of gold and palladium that addresses several limitations hampering the use of atomistic modeling as a tool for understanding and improving wet-chemical synthesis and related applications. A combination of thermodynamic modeling with density functional theory (DFT) calculations and experimental data is used to predict equilibrium shapes of halide-covered nanoparticles as a function of the chemical environment. To ensure realistic and experimentally relevant results, we account for solvent effects and include a large s…
We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical (2nd-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products …
Conducting polymers have wide technological applications in sensors, actuators, electric and optical devices, solar cells etc. To improve their operational performance, mechanical, thermal, electrical and optical properties, such polymers are doped with carbon allotrope nanofillers. Functionality of the novel nanocomposite polymers may be stipulated by size characteristics of nanoparticles and the polymer, different physical effects like charge transfer in such objects etc. We characterize and analyze structure, elastic, electric properties and of novel polymer nanocomposites, isotactic polypr…
We study mutual alignment and interactions between colloidal particles of dissimilar shapes and dimensions when dispersed in a nematic host fluid. Convex pentagonal and concave starfruit-shaped nanoprisms and microspheres induce dipolar or quadrupolar director structures. The ensuing elastic pair interactions between microspheres and nanoprisms are highly dependent on the nanoparticle shape being omnidirectionally attractive for convex prisms but strongly anisotropic for concave prisms. Elastic deformations due to spherical particles cause well-defined alignment of complex-shaped nanoparticles…
Some issues that arise when modeling elastic energy for binary alloys are discussed within the context of a Keating model and density functional calculations. The Keating model is based on atomistic modeling of elastic interactions in binary alloy using harmonic springs with species dependent equilibrium lengths. It is demonstrated that the continuum limit for the strain field are the usual equations of linear elasticity for alloys and that they correctly capture the coarse-grained displacement field. In addition, it is established that Euler-Lagrange equation of the continuum limit of the ela…
Max-Planck-Institut für Eisenforschung（马克斯·普朗克钢铁研究所）；Technische Universität Darmstadt（达姆施塔特工业大学）；DeepMetis
The elastic properties of materials derive from their electronic and atomic nature. However, simulating bulk materials fully at these scales is not feasible, so that typically homogenized continuum descriptions are used instead. A seamless and lossless transition of the constitutive description of the elastic response of materials between these two scales has been so far elusive. Here we show how this problem can be overcome by using Artificial Intelligence (AI). A Convolutional Neural Network (CNN) model is trained, by taking the structure image of a nanoporous material as input and the corre…
