On the determination of the surface stress of copper and platinum

Wasserman, Harvey J.; Vermaak, J. S.

doi:10.1016/0039-6028(72)90127-6

Cited by 197 publications

(122 citation statements)

References 10 publications

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“…The elastic energy per unit area can be expressed as Yt~ 2. According to Equation (28), the change in the film-substrate interface energy per unit area can be expressed as 2(g -~o)¢. The work per unit area to stretch the film surface can be (44) (45) Most analyses of the thermodynamics of epitaxy only consider effects of the first two terms on the right hand side of Equation (44).…”

Section: Thermodynamics Of Epitaxymentioning

confidence: 99%

Surface and interface stress effects in thin films

Cammarata

1994

Progress in Surface Science

882

414

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Surface and interface stresses in solids are defined and their role in the thermodynamics of solids is presented. A discussion concerning the physical meaning of these quantities is given, along with a review of selected theoretical calculations and experimental measurements. It is shown that for a solid phase with one or more of its dimensions smaller than about 10 nm, the surface and interface stresses can be principal factors in determining the equilibrium structure and behavior of the solid. In particular, the effects of surface and interface stresses on thin films are reviewed along with the related topic of surface reconstructions in metals.

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Section: Thermodynamics Of Epitaxymentioning

confidence: 99%

Surface and interface stress effects in thin films

Cammarata

1994

Progress in Surface Science

882

414

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“…Lattice contractions of Ag, Au, Cu, Pd and Pt nanoparticles obtained from electron diffraction micrographs [19,21,29,30] are used to compare with our theoretical predictions as shown in Fig. 3a-e, respectively.…”

Section: Analysis Of the Size Effect Of Nanoparticle Surface Energy Dmentioning

confidence: 99%

“…The bulk surface energy density ϕ 0b is taken from Sheng et al [40]. The bulk lattice constant a 0 is from the existing experimental studies [19,21,[29][30][31]. The Young's moduli, bulk moduli and atomic diameters have been given by Ouyang et al [15] and Sheng et al [40].…”

Section: Analysis Of the Size Effect Of Nanoparticle Surface Energy Dmentioning

confidence: 99%

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Size effect of the surface energy density of nanoparticles

2015

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The surface energy density of nanoparticles exhibits an obviously size-dependent behavior. However, how the surface energy density changes with the diameter of nanoparticles is still ambiguous. Based on a recently developed continuum theory considering the size effect in nanomaterials, theoretical analysis is carried out for various fcc metallic nanoparticles. Surface lattice contractions of nanoparticles are predicted and compared with the existing experimental data. As a result, the surface energy density decreases with the increase of nanoparticle diameter. Such a variation trend of surface energy density is contrary to the prediction of existing theoretical models but well consistent with the previously atomistic simulations and density functional calculations. The results in this paper provide a further understanding of the surface effect of nanoparticles, which should be helpful for the design of nanoscale devices or nanomaterials related to nanoparticles, such as NEMs and nanoparticlereinforced composites.

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“…Expansion of the lattice parameter is generally observed in oxides such as CeO 2 [4][5][6], Fe 2 O 3 [7], MgO [8], TiO 2 (rutile) [9], ZrO 2 [10], BaTiO 3 [11], cubic PbTiO 3 [12], and BiFeO 3 [13]. In contrast, contraction in the lattice parameter, is observed in most metals, such as Au [14][15][16], Ag [17][18][19][20], Sn [21], Bi [21,22], Pt [15,23], Si [24], Cu [25], Ni [25], Pd [26,27], ZnS and CdSe [28,29]. Shrinkage of the Cu-Cu distance up to 9% for very small sizes has been reported by Apai,et al in [25].…”

Section: Introductionmentioning

confidence: 99%

Thickness Effect on Fluctuation of Electron States in Thin Film and Implications for Lattice Constant Change Due to Size Reduction

Amalia

Viridi

Abdullah

2017

J. Math. Fund. Sci.

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Abstract. We propose a model for predicting the fluctuation of electron states in thin films as a function of film thickness. The model is derived based on the assumption of the existence of potential barrier fluctuation on the film surface. Since the wave functions of electrons in the film are determined by the boundary conditions of the potential on the film surface, the potential fluctuation on the film surface implies fluctuation of the electron states in the film. The model was extended to predict the effect of size on the lattice constant of thin films or nanoparticles.

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On the determination of the surface stress of copper and platinum

Cited by 197 publications

References 10 publications

Surface and interface stress effects in thin films

Surface and interface stress effects in thin films

Size effect of the surface energy density of nanoparticles

Thickness Effect on Fluctuation of Electron States in Thin Film and Implications for Lattice Constant Change Due to Size Reduction

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