Y. Lereah

Surface melting enhanced by curvature effects

Abstract Recent unambiguous experiments (melting of ultrafine particles, premelting at the surface of a bulk crystal, superheating, etc.) offer clear evidence of the key role of the surface in determining the melting of a material. In this work we concentrate our attention on spherical and non-spherical nanometric lead inclusions. We report experimental results on Pb/SiO and Pb/Al 2 O 3 systems obtained at different temperatures by two techniques: high-sensitivity optical reflectance and dark-field electron microscopy. The main result is the existence, below the melting temperature and at the surface of the inclusion, of a liquid layer whose thickness is much larger than that observed on the bulk (zero curvature). This thickness, which depends on local curvature, increases continuously with temperature until a uniform curvature of the solid core is attained; then the core melts suddenly. A phenomenological model, based on the minimization of the free energy, is proposed and reported in detail. It represents a significant improvement compared to previous theoretical approaches related to well-known thermodynamic size-effect models, particularly insofar as the agreement with the experimental results is concerned.

Generation of electron Airy beams

We report the first experimental generation and observation of Airy beams of free electrons. The electron Airy beams are generated by diffraction of electrons through a nanoscale hologram, that imprints a cubic phase modulation on the beams’ transverse plane. We observed the spatial evolution dynamics of an arc-shaped, self accelerating and shape preserving electron Airy beams. We directly observed the ability of electrons to self-heal, restoring their original shape after passing an obstacle. This electromagnetic method opens up new avenues for steering electrons, like their photonic counterparts, since their wave packets can be imprinted with arbitrary shapes or trajectories. Furthermore, these beams can be easily manipulated using magnetic or electric potentials. It is also possible to efficiently self mix narrow beams having opposite signs of acceleration, hence obtaining a new type of electron interferometer.Within the framework of quantum mechanics, a unique particle wave packet exists in the form of the Airy function. Its counterintuitive properties are revealed as it propagates in time or space: the quantum probability wave packet preserves its shape despite dispersion or diffraction and propagates along a parabolic caustic trajectory, even though no force is applied. This does not contradict Newton’s laws of motion, because the wave packet centroid propagates along a straight line. Nearly 30 years later, this wave packet, known as an accelerating Airy beam, was realized in the optical domain; later it was generalized to an orthogonal and complete family of beams that propagate along parabolic trajectories, as well as to beams that propagate along arbitrary convex trajectories. Here we report the experimental generation and observation of the Airy beams of free electrons. These electron Airy beams were generated by diffraction of electrons through a nanoscale hologram, which imprinted on the electrons’ wavefunction a cubic phase modulation in the transverse plane. The highest-intensity lobes of the generated beams indeed followed parabolic trajectories. We directly observed a non-spreading electron wavefunction that self-heals, restoring its original shape after passing an obstacle. This holographic generation of electron Airy beams opens up new avenues for steering electronic wave packets like their photonic counterparts, because the wave packets can be imprinted with arbitrary shapes or trajectories.

Solid-liquid transition in ultra-fine lead particles

Abstract We have studied the melting and the solidification of lead ultra-fine particles. We report on electron microscopy technique which enables the identification of the transition temperatures of each particle. The experimental results presented show a dependence of the melting and solidification temperatures on the particle size. The melting temperature results are compared with a new phenomenological model.

Time-resolved electron microscopy studies of the structure of nanoparticles and their melting

Abstract We review our quantitative results related to the physical properties of metallic nanoparticles that were obtained by time-resolved electron microscopy. These studies include the solid–liquid transition and structural instabilities. Surface melting has been demonstrated, quantitatively measured and analysed within the frainework of a phenomenological model. The nature of the liauid layer is discussed. Quantitative studies of the structural instabilities indicate a spontaneous appearance of twin defects inside the nanoparticles and their spontaneous disappearance. It has been found that this process is thermally activated.

Sculpturing the electron wave function using nanoscale phase masks.

Electron beams are extensively used in lithography, microscopy, material studies and electronic chip inspection. Today, beams are mainly shaped using magnetic or electric forces, enabling only simple shaping tasks such as focusing or scanning. Recently, binary amplitude gratings achieved complex shapes. These, however, generate multiple diffraction orders, hence the desired shape, appearing only in one order, retains little of the beam energy. Here we demonstrate a method in electron-optics for arbitrarily shaping electron beams into a single desired shape, by precise patterning of a thin-membrane. It is conceptually similar to shaping light beams using refractive or diffractive glass elements such as lenses or holograms - rather than applying electromagnetic forces, the beam is controlled by spatially modulating its wavefront. Our method allows for nearly-maximal energy transference to the designed shape, and may avoid physical damage and charging effects that are the scorn of commonly-used (e.g. Zernike and Hilbert) phase-plates. The experimental demonstrations presented here - on-axis Hermite-Gauss and Laguerre-Gauss (vortex) beams, and computer-generated holograms - are a first example of nearly-arbitrary manipulation of electron beams. Our results herald exciting prospects for microscopic material studies, enables electron lithography with fixed sample and beam and high resolution electronic chip inspection by structured electron illumination.

A Direct Observation of Low-Dimensional Effects on Melting of Small Lead Particles

The melting of small lead particles embedded in a silicon monoxide matrix has been studied by dark-field electron microscopy. Thomsons idea from 1888, that the melting temperature depends on the size of the particles and Faradays idea from 1860, that melting of the surface occurs below the bulk melting temperature, are demonstrated here straight-forwardly. The electron microscope pictures give the most direct observation on the existence of a molten surface layer in equilibrium with a solid core at temperatures below the melting point. The width of the molten layer is demonstrated to depend on the particle curvature as well as on temperature indicating a continuous transition. Quantitatively, it was found that for the small lead particles, the width of the molten layer is wider than the reported one for bulk lead.

Nanoscale oxygen octahedral tilting in 0.90(Bi1/2Na1/2)TiO3–0.05(Bi1/2K1/2)TiO3–0.05BaTiO3 lead-free perovskite piezoelectric ceramics

The oxygen octahedral tilted domains in 0.90(Bi1/2Na1/2)TiO3-0.5(Bi1/2K1/2)TiO3-0.5BaTiO3 lead-free perovskite piezoelectric ceramic have been studied by transmission electron microscopy (TEM). Selected-area electron diffraction patterns shows the 1/2ooo and 1/2ooe reflections, indicating the presence of antiphase (a-a-a-) and in-phase (aoaoc+) octahedral tilting, respectively. The morphology and distributions of these tilted domains are shown in the centered dark-field images. Further, the Bragg-filtered high-resolution TEM image reveals that the size of the in-phase tilted domains varies from 1 to 8 nm across. The ceramic contains the mixture of non-tilted and variants of the antiphase and in-phase tilted domains.

Hillock formation during electromigration in Cu and Al thin films: Three‐dimensional grain growth

The evolution of microstructure in Al and Cu thin film lines during electromigration has been studied using a transmission electron microscopy. Grain boundary migration was found to be critically involved in the electromigration induced hillock formation that can be described as a three‐dimensional growth of a single grain.

Large anisotropic conductance and band gap fluctuations in nearly round-shape bismuth nanoparticles.

Unlike their bulk counterpart, nanoparticles often show spontaneous fluctuations in their crystal structure at constant temperature [Iijima, S.; Ichihashi T. Phys. Rev. Lett.1985, 56, 616; Ajayan, P. M.; Marks L. D. Phys. Rev. Lett.1988, 60, 585; Ben-David, T.; Lereah, Y.; Deutscher, G.; Penisson, J. M.; Bourret, A.; Korman, R.; Cheyssac, P. Phys. Rev. Lett.1997, 78, 2585]. This phenomenon takes place whenever the net gain in the surface energy of the particles outweighs the energy cost of internal strain. The configurational space is then densely populated due to shallow free-energy barriers between structural local minima. Here we report that in the case of bismuth (Bi) nanoparticles (BiNPs), given the high anisotropy of the mass tensor of their charge carriers, structural fluctuations result in substantial dynamic changes in their electronic and conductance properties. Transmission electron microscopy is used to probe the stochastic dynamic structural fluctuations of selected BiNPs. The related fluctuations in the electronic band structure and conductance properties are studied by scanning tunneling spectroscopy and are shown to be temperature dependent. Continuous probing of the conductance of individual BiNPs reveals corresponding dynamic fluctuations (as high as 1 eV) in their apparent band gap. At 80 K, upon freezing of structural fluctuations, conductance anisotropy in BiNPs is detected as band gap variations as a function of tip position above individual particles. BiNPs offer a unique system to explore anisotropy in zero-dimension conductors as well as the dynamic nature of nanoparticles.

Spreading of a mercury droplet on thin gold films

The spreading of a small mercury droplet (150μm) on thin gold films is studied, using an optical microscope enhanced with a differential interference contrast system. The growing interfaces are analyzed in order to determine the roughness (α) and growth (β) exponents. For gold film thickness of 1500A we find that α=0.88±0.03 and β=0.76±0.03, while for gold thickness of 3000A, α=0.96±0.04 and β=1.00±0.04. Both sets of exponents satisfy the scaling relation α+α/β=2. In both systems the roughness exponent α crosses over to a value close to 0.5 in the final stages of the experiment and for relatively long length scales (order of a few microns).