On surface stress and surface tension

Vermaak, J. S.; Mays, C.W.; Kuhlmann‐Wilsdorf, D.

doi:10.1016/0039-6028(68)90118-0

Cited by 209 publications

(84 citation statements)

References 3 publications

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“…Indeed, pioneering experimental studies regarding the change of the lattice constant of tiny three dimensional crystallites were done in the early 1950s, 9 and somewhat later the connection of this observation to surface stress was established. 10 In these studies the contraction of small spherical metal crystals was explained through the radial forces applied by the surface to the inner part of the particles, laying out the basis for understanding our experimental observations.…”

Section: Introductionmentioning

confidence: 99%

Strain relaxation in small adsorbate islands: O on W(110)

et al. 2008

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Section: Introductionmentioning

confidence: 99%

Strain relaxation in small adsorbate islands: O on W(110)

et al. 2008

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“…The most importantly physical quantity characterizing surface effect is the surface free energy density, which is a reversible work necessary to create a unit of new surface area. 5 In the existing continuum mechanics models considering surface effect in nanomaterials, [6][7][8] surface free energy density is related to the deformation of nanomaterial surface and its derivative with respect to the surface strain leads to the surface stress. One of the representative works is the Gurtin and Murdoch model * Author to whom correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

Size-Dependent Surface Energy Density of Spherical Face-Centered-Cubic Metallic Nanoparticles

Wei¹,

Chen²

2015

j nanosci nanotechnol

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The surface energy density of nano-sized elements exhibits a significantly size-dependent behavior. Spherical nanoparticle, as an important element in nano-devices and nano-composites, has attracted many interesting studies on size effect, most of which are molecular dynamics (MD) simulations. However, the existing MD calculations yield two opposite size-dependent trends of surface energy density of nanoparticles. In order to clarify such a real underlying problem, atomistic calculations are carried out in the present paper for various spherical face-centered-cubic (fcc) metallic nanoparticles. Both the embedded atom method (EAM) potential and the modified embedded atom method (MEAM) one are adopted. It is found that the size-dependent trend of surface energy density of nanoparticles is not governed by the chosen potential function or variation trend of surface energy, but by the defined radius of spherical nanoparticles in MD models. The finding in the present paper should be helpful for further theoretical studies on surface/interface effect of nanoparticles and nanoparticle-reinforced composites.

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“…The theoretical formulation of surface free energy within the framework of continuum mechanics has drawn many interests. As pointed out by Shuttleworth [9] and Vermaak et al [10], surface energy is related to the deformation of solids' crystal faces, whose partial derivative with respect to the surface strain gives rise to a surface stress. Inspired by this basic idea, Gurtin and Murdoch [11,12] used a linearized constitutive law to formulate the surface free energy, based on which the surface elasticity theory was rigorously developed (G-M theory).…”

Section: Introductionmentioning

confidence: 99%

“…However, the size dependence of the surface energy density was not considered in these simulations. For nanomaterials with a large surface-to-volume ratio, the surface free energy density always shows a strong dependence on their characteristic scales [9,10,22]. A series of thermodynamic models were established to describe the size effect of surface energy density.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent surface energy density of typically fcc metallic nanomaterials

Zhang

Yao

Chen

2014

Computational Materials Science

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a b s t r a c tThe surface energy density of nano-sized structural elements exhibits an obvious size-dependent feature. To study this interesting phenomenon, atomistic calculations are carried out in the present paper for different face-centered-cubic (fcc) metallic nano-slabs. Lagrangian and Eulerian descriptions are adopted, respectively, in order to find the varying trends of surface energy densities in an initially un-deformed configuration and a current one. It is found that the Lagrangian surface energy density increases monotonically with an increase of the nano-slab's thickness in the former no matter what the surface orientation is; while the variation of the Eulerian one is indefinite. The surface relaxation parameters are further simulated for differently oriented surfaces, which gives a very good explanation for the differences between the Lagrangian and Eulerian surface energy densities. The results in this paper should be a useful supplement to theoretical studies on the surface/interface effect of nanomaterials.

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On surface stress and surface tension

Cited by 209 publications

References 3 publications

Strain relaxation in small adsorbate islands: O on W(110)

Strain relaxation in small adsorbate islands: O on W(110)

Size-Dependent Surface Energy Density of Spherical Face-Centered-Cubic Metallic Nanoparticles

Size-dependent surface energy density of typically fcc metallic nanomaterials

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