The theoretical model of fcc ultrathin film

Abstract

A three-dimensional lattice model is constructed to theoretically study the size effects on the elastic properties of ultrathin films with face-center-cubic crystal structure. The lattice model directly takes the discrete nature in the thickness direction into account and treats the deformations along the film plane with continuum mechanics. Only the interactions between the nearest and second nearest atoms are considered in this model and represented as harmonic springs. The constitutive relation of the ultrathin film is then derived using the energy approach and the analytical expressions of the elastic moduli of ultrathin films, including in-plane, out-plane Young's modulus and Poisson's ratio, are obtained. Moreover, the analytical expressions of ultrathin films with different crystal orientations are also formulated. It is shown that the ultrathin film along in-plane directions may be stiffer or softer than its bulk counterpart, but it is always softer along the out-plane direction.

Nondestructive Measurement of the Evolution of Layer-Specific Mechanical Properties in Sub-10 nm Bilayer Films

“…This is a major challenge because the mechanical properties of thin films determine their strength, flexibility, and reliability in a host of nanostructured electronic, photovoltaic, and thermoelectric devices. Moreover, while a departure from bulk mechanical properties has long been expected and observed for nanoscale materials, , the precise mechanisms, magnitude, and even sign of these changes are still open questions, which cannot be addressed without new approaches to nanoscale metrology.…”

Elastic Compliance and Stiffness Matrix of the FCC Lennard-Jones Thin Films: Influence of Thickness and Temperature

“…In our case, the film is so thin that the two external surfaces are not independent: the elastic constants in the direction perpendicular to the surface exhibit dependence with the film thickness. Another explanation could be found in the work of Chang 26 et al 99 who have proposed a lattice model where only the total strain energy density of an ultrathin film is taken into account, without any consideration of surface effect. They have observed a size dependence of the elastic constants, in particular for the out-of-plane stiffness coefficient C 13 .…”

“…[90][91][92][93][94] These simple models show that surface relaxations occur over few atomic layers: the effects are thus enhanced in ultrathin films or multilayers. [65][66][67][95][96][97][98][99][100][101][102][103][104][105] The simple decomposition of the elastic properties in a bulk + surface contribution, and the expected linear dependence with the inverse system size, remain controversial. 64,66,88,97,106,107 Furthermore, the effect of temperature is not so frequently studied.…”

“…On the other hand, nonspecific mechanical properties of solid may be studied by using simple pairwise additive interactions like the Lennard-Jones potential. − These simple models show that surface relaxations occur over few atomic layers: the effects are thus enhanced in ultrathin films or multilayers. − ,− The simple decomposition of the elastic properties in a bulk + surface contribution, and the expected linear dependence with the inverse system size, remain controversial. ,,,,, Furthermore, the effect of temperature is not so frequently studied. , The following study thus focuses on a simple Lennard-Jones thin film model to determine the effect of both the film thickness and the temperature on its elastic properties. We present the model and methods, in particular the two numerical deformation experiments used to calculate the elastic constants of the thin film.…”

Fracture Behavior Transition in (001) Cracked Metal Nanoplates Induced by the Surface Effect

“…For extremely small nanostructures, the induced stress may exceed the critical stress of the material, causing phase transformation without an external load . Moreover, the surfaces can alter the mechanical properties of the nanostructures, such as the elastic modulus ,− and strength. − Nanostructures also exhibit different fracture modes depending on their sizes, owing to the size dependence of dislocation nucleation and capacity. , …”