Narrow Results

We study a thin-shell limit of micromagnetic energy for soft small ferromagnets. The relations between thickness of the magnet t, diameter l and magnetic exchange length w are t/l → 0 and tl/w² ≲ 1. We prove a Γ-convergence of the original 3D problem to a nonlocal 2D problem.

We provide a rigorous derivation of the compressible Reynolds system as a singular limit of the compressible (barotropic) Navier–Stokes system on a thin domain. In particular, the existence of solutions to the Navier–Stokes system with non-homogeneous boundary conditions is shown that may be of independent interest. Our approach is based on new a priori bounds available for the pressure law of hard sphere type. Finally, uniqueness for the limit problem is established in the one-dimensional case.

We present here an analysis of the regularity of minimizers of a variational model for epitaxially strained thin-films. The regularity of energetically-optimal film profiles is studied by extending previous methods and by developing new ideas based on transmission problems. The achieved regularity results relate to both the Stranski-Krastanow and the Volmer-Weber modes, the possibility of different elastic properties between the film and the substrate, and the presence of the surface tensions of all three involved interfaces: film/gas, substrate/gas, and film/substrate. Finally, geometrical conditions are provided for the optimal wetting angle, i.e. the angle formed at the contact point of films with the substrate. In particular, the Young–Dupré law is shown to hold, yielding what appears to be the first analytical validation of such law for a thin-film model in the context of Continuum Mechanics.

The behavior of a thin film made of a ferromagnetic material in the absence of an external magnetic field is described by an energy depending on the magnetization of the film verifying the saturation constraint. The free energy consists of an induced magnetostatic energy and an energy term with density including the exchange energy and the anisotropic energy. We study the behavior of this energy when the thickness of the curved film goes to zero. We show that the minimizers of the free energy converge to the minimizers of a local energy depending on a two-dimensional magnetization by Γ-convergence arguments.

In this communication, a quantum mechanical technique for treatment of effects of scattering transport at nanoscale in thin films is discussed. We implemented a rigorous treatment of scattering within the NEGF simulation platform. Results obtained by applying the rigorous scattering model to simulate the devices were used as a benchmark to validate a simple computationally-efficient, phenomenological treatment of scattering. The NEGF method is used to study the effect of electron confinement on silicon nano-films and wires. Electron confinement results in almost a factor of 3 decreases in the electrical conductivity of the 5 nm silicon film compared to the 10 nm film. Increase in the amount of confinement also leads to a 35% decrease in the conductivity of a 5 nm × 5 nm wire compared to the 5 nm film. Our simple model provides an excellent tradeoff between increased computational cost and the physics of scattering that needs to be captured in devices of the future.

Using thermodynamics approach, the present work analytically studies the effect of mismatch strains on the material properties of ferroelectric thin films. A one-dimensional model is first developed to illustrate the physical picture and the procedure of the theoretical approach. Then, the effect of non-equal mismatch strains is investigated by using the same theoretical approach.

It is well known that a circular hole in a blanket thin film causes strain concentration near the hole edge when the thin film is under tension. The increased strain level can be as high as three times of the applied tension. Interestingly, we show that, by suitably patterning an array of circular holes in a thin film, the resulting strain in the patterned film can be decreased to only a fraction of the applied tension, even at the hole edges. The strain deconcentration in the film originates from the following deformation mechanism: while initially planar, the film patterned with circular holes elongates by deflecting out of plane, so that a large tension induces only small strains. Using finite element simulations, we investigate the effects of geometric parameters (i.e., hole size, spacing, and pattern) and loading direction on the resulting strain in patterned thin films under tension. The large deformability of the patterned film is independent of materials and length scale, and thus sheds light on a potential architecture concept for flexible electronics.

This paper presents alternative analysis methodologies to extract the elastic modulus and hardness of the ultra-thin films from nanoindentation load-displacement data, especially when the film thickness is only few hundred nanometers or less. At such film thickness, the conventional analysis methods for nanoindentation usually do not give accurate film properties due to the substrate effect. The new methods are capable to show how to determine the film-only properties and how the substrates affect the nanoindentation measurement, especially for ultra thin films. These methods give accurate results for nanoindentation of various metallic, ceramic and polymeric films. It also reveals the differences between the use of high-resolution nanoindentation set-up and normal nanoindentation set-up on the same films. The relationships between the mechanical properties and film thickness are also discussed.

Gold and copper thin films are widely used in microelectromechanical system (MEMS) and nanoelectromechanical system (NEMS) devices. Nanoindentation has been developed in mechanical characterization of thin films in recent years. Several researchers have examined the effect of surface roughness on nanoindentation results. It is proved that the surface roughness has great importance in nanoindentation of thin films. In this paper, the surface topography of thin films is simulated using the extracted data from the atomic force microscopy (AFM) images. Nanoindentation on a rough surface is simulated using a three-dimensional finite-element model. The results are compared with the results of finite-element analysis on a smooth surface and the experimental results. The results revealed that the surface roughness plays a key role in nanoindentation of thin films, especially at low indentation depths. There was good compatibility between the results of finite-element simulation on the rough surface and those of experiments. It is observed that on rough films, at low indentation depths, the geometry of the location where the nanoindentation is performed is of major importance.

Using molecular-dynamics simulation, we study the phase transformations in Fe thin films induced by uni- and biaxial strain. Both the austenitic transformation of a body-centered cubic (bcc) film at the equilibrium temperature of the face-centered cubic (fcc)–bcc transformation and the martensitic transformation of an undercooled fcc film are studied. We demonstrate that different strain states (uni- or biaxial) induce different nucleation kinetics of the new phase and hence different microstructures evolve. For the case of the austenitic transformation, the direction of the applied strain selects the orientation of the nucleated grains of the new phase; the application of biaxial strain leads to a symmetric twinned structure. For the martensitic transformation, the influence of the strain state is even more pronounced, in that it can either inhibit the transformation, induce the homogeneous nucleation of a fine-dispersed array of the new phase resulting in a single-crystalline final state, or lead to the more conventional mechanism of heterogeneous nucleation of grains at the free surfaces, which grow and result in a poly-crystalline microstructure of the transformed material.

The development of long-wave Marangoni instability under the action of a heat flux modulated in time is studied. The critical Marangoni number for the deformational instability is obtained as a function of frequency.