Surface energy and surface stress tensor in an atomistic model

Price, C.W.; Hirth, J. P.

doi:10.1016/0039-6028(76)90344-7

Cited by 39 publications

(16 citation statements)

References 18 publications

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“…A more complete analysis gives [19] Y = Yo + 2f(B + 211 -3 + f '/f)/t (38) where Yo is the modulus value for a bulk material, 11 is a factor that depends on Poisson's ratio and is close to unity, and f ' is equal to 3f/Oe. Calculations of f ', which can be considered an "excess surface modulus," have shown that it can be negative [19,47,48]. For many (100) and (111) oriented fcc metal surfaces, the magnitude of f '/f is significantly smaller than B [19], so that, according to Equation (38), the modulus should always be enhanced when t is reduced below about 5 nm.…”

Section: A Strains and Elastic Modulus Variations In Ultrathin And Amentioning

confidence: 99%

“…The surface was modeled as a linear array of atoms connected by springs, and the atoms sat in a sinusoidal potential that represented the underlying lattice. The stability of the surface was characterized by a parameter P which, for the case of a (100) oriented surface of a simple cubic metal, was given by [9] P = rca(f -7)/2(2kW) 1/2, (47) where a is the lattice parameter, f and T are the surface stress and surface free energy of the unreconstructed surface, k is a spring constant associated with surface bonds, and W is the peak-to-peak amplitude of the sinusoidal surface-substrate interaction potential. If I PI < 1, an unreconstructed surface is stable; otherwise, a surface reconstruction is expected.…”

Section: Surface Reconstructions Of Clean Metal Surfacesmentioning

confidence: 99%

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Surface and interface stress effects in thin films

Cammarata

1994

Progress in Surface Science

880

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: A Strains and Elastic Modulus Variations In Ultrathin And Amentioning

confidence: 99%

Section: Surface Reconstructions Of Clean Metal Surfacesmentioning

confidence: 99%

Surface and interface stress effects in thin films

Cammarata

1994

Progress in Surface Science

880

414

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“…9 There have also been several atomistic studies devoted to the computational determination of surface elastic constants of crystalline materials. [10][11][12][13][14] However, when it comes to bicrystal interfaces, only limited number of studies have been reported on the atomistic calculations of interface energy and interface stress. 15,16 Furthermore, no interface elastic modulus tensor has ever been considered rigorously by atomistic simulations; this fact motivated the current study.…”

Section: Introductionmentioning

confidence: 99%

Atomistic calculations of interface elastic properties in noncoherent metallic bilayers

et al. 2008

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The paper describes theoretical and computational studies associated with the interface elastic properties of noncoherent metallic bicrystals. Analytical forms of interface energy, interface stresses, and interface elastic constants are derived in terms of interatomic potential functions. Embedded-atom method potentials are then incorporated into the model to compute these excess thermodynamics variables, using energy minimization in a parallel computing environment. The proposed model is validated by calculating surface thermodynamic variables and comparing them with preexisting data. Next, the interface elastic properties of several fcc-fcc bicrystals are computed. The excess energies and stresses of interfaces are smaller than those on free surfaces of the same crystal orientations. In addition, no negative values of interface stresses are observed. Current results can be applied to various heterogeneous materials where interfaces assume a prominent role in the systems' mechanical behavior.

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“…For example, Gc+ = 1150MPa, G c_ = 1240MPa, and G c = 885 MPa [1]. Considering maximum hydrogenation and relations (1)-(I 5), we obtain values of the parameters do+l and do_ 1 by using a known procedure [5] and data presented in [7][8][9]. In particular, we found do+ -do+ 1 do+ 1 = -3.64 V; 8~~ -do+l -0.025, do--do-I ~-1 = -4.9V; 8~~ = do-I = 0.0278.…”

Section: Formulation Of a Strength Criterion For Bimetallic Platesmentioning

confidence: 99%

“…where V 1 is the Volta potential, q = 1.6 9 10 -19 C is the charge of an electron, W 2 is the interaction energy of an electron with the solvent. If, for instance, hydrogenation decreases the parameters Wr+ and W r_ by 10 and 5%, respectively, compared to the work function of the metal into air, 6+ and or_ are reduced by 1.57 and 2.06%, respectively.…”

Section: Investigation Of the Effect Of Hydrogenation On The Mechanicmentioning

confidence: 99%

Energy characteristics of a newly formed and hydrogenated metal surface in a corrosive medium

Soprunyuk¹,

Yuzevych²

1998

Mater Sci

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We determine the strength of contacting steel specimens in a corrosive medium using the modified chemical potentials ~ of the conduction electrons. The potentials are related to integral physical quantities that characterize the hydrogen content in the surface layers of the plates and are evaluated by an experimental procedure based on measurement of the surface tension and energy. A new strength criterion involving the potentials 9 is constructed.In investigating the strength of bimetallic plates in a corrosive medium, the traditional parameters and the corresponding criteria are insufficient [1]. It is expedient to analyze the thermodynamic parameters of the interface in detail and to relate them to the ultimate strength and integral physical quantities that characterize the hydrogen content in the surface layers of the plates. For this purpose, it is fruitful to use information on the kinetics of hydrogen release on a newly formed and hydrogenated surface of the metal [2] and a procedure of calculation of integral characteristics of the concentration (for hydrogen) distribution in the surface layers [3]. If we consider the principles of construction of strength criteria connected with diagnostics of the surface of specimens [4], we obtain a large collection of thermodynamic parameters and new procedures that will bring us closer to our aim. Namely, we wish to establish features that would characterize the state of bimetallic plates under service conditions and allow us to construct a strength criterion for such plates hydrogenated from a corrosive medium. Statement of the ProblemLet us consider a newly formed surface of a metal that developed in splitting of bonds in a corrosive medium. Restricting ourselves to a description of absorption of hydrogen on the metallic surface, we evaluate the change in the thermodynamic electric potential ~ of the electric double layer [5]. Since a bimetallic plate consists of two metals (+) and (-), we determine the change in tI)+ and ~_. The redistribution of the charge density of the conduction electrons o on the interface of the metal and the corrosive medium is calculated by the density functional method [6]. We approximate it in the following way [7]:where f2 is the density of free electrons of the metal, x is the coordinate axis with origin on the boundary of the metal and the corrosive medium (x > 0 corresponds to the metal, x < 0 to the surrounding medium), A is a constant, and x = Z is the distance between the boundary of the metal and the surface on which the charge density of the conduction electrons is ~/2.The width of the electric double layer Z on the metal-air surface is determined in terms of the work function of the metal W [7]: Z= (~k)(2-( R-1) arctan (W) 0"5 -/R)~Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv.

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Surface energy and surface stress tensor in an atomistic model

Cited by 39 publications

References 18 publications

Surface and interface stress effects in thin films

Surface and interface stress effects in thin films

Atomistic calculations of interface elastic properties in noncoherent metallic bilayers

Energy characteristics of a newly formed and hydrogenated metal surface in a corrosive medium

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