On the measurement of surface free energy and surface tension of solid metals

Kumikov, V.K.; Khokonov, Kh. B.

doi:10.1063/1.332209

Cited by 290 publications

(102 citation statements)

References 43 publications

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“…6 would qualitatively improve if a correction for the different temperatures could be made. Other experimental studies of Pb surface free energies, which have claimed to represent the (111) orientation, report values close to 570-600 mJ/m 2 but these high values are more likely due to vicinal or ill-defined rough surfaces [83,84].…”

Section: Comparison Of Theory and Experimentsmentioning

confidence: 99%

The three-dimensional equilibrium crystal shape of Pb: Recent results of theory and experiment

Bonzel

Scheffler

2007

Appl. Phys. A

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The three-dimensional equilibrium crystal shape (ECS) is constructed from a set of 35 orientation-dependent surface energies of fcc Pb which are calculated by density functional theory in the local-density approximation and distributed over the [110] and [001] zones of the stereographic triangle. Surface relaxation has a pronounced influence on the equilibrium shape. The (111), (100), (110), (211), (221), (411), (665), (15,1,1), (410) and (320) facets are present after relaxation of all considered surfaces, while only the low-index facets (111), (100) and (110) exist for the unrelaxed ECS. The result for the relaxed Pb crystal state is in support of the experimental ECS of Pb at 320-350 K. On the other hand, approximating the surface energies of vicinal surfaces by assuming a linear relationship between the Pb(111) first-principles surface energy and the number of broken bonds of surface atoms leads to a trivial ECS that shows only (111) and (100) facets, with a sixfold symmetric (111) facet instead of the correct threefold symmetry. It is concluded that the broken bond rule in this simple linear form is not a suitable approximation for obtaining the proper three-dimensional ECS and correct step formation energies.PACS 05.70.Np; 61.50.Jr; 68.35.Md; 71.15.Mb IntroductionThe surface free energy is a fundamental property of solids and liquids. For crystalline solids it is generally anisotropic, i.e., it depends on the orientation of the surface. In this case the surface free energy is particularly difficult to measure, especially for structurally and chemically well-defined surfaces [1][2][3][4]. Hence it is not surprising that many theoretical attempts have been undertaken to generate hopefully trustworthy values of this quantity. Some were empirical, starting from surface free energies of liquids (e.g., metals) and transposing them to the solid state [5,6]. Other semi-empirical studies have been summarized by Galanakis et al. [7]. More recently, full potential first principles calculations have produced surface energies of many crystalline materials [7][8][9][10][11][12][13][14][15][16][17][18] mostly for low-index orientations. Although there can be considerable scatter in theoretical values for a single material and orientation [16,19], it has been suggested by u Fax: +49 2461 61 2950, E-mail: h.bonzel@fz-juelich.de some authors that the lack of experimental surface energy data for well-defined orientations may be replaced by ab initio calculations [15,17,20].Theoretical attempts of describing the more or less complete anisotropy of the surface free energy of crystals by invoking attractive pairwise atomic interaction potentials have been numerous, beginning in 1931 with the work by Stranski et al. [21][22][23][24][25][26] followed by others [27][28][29][30]. A different phenomenological description of the anisotropy and to some extent of the temperature dependence of the surface free energy was based on the terrace-step-kink model of a crystalline surface [31] assuming the existence of steps of monoat...

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Section: Comparison Of Theory and Experimentsmentioning

confidence: 99%

The three-dimensional equilibrium crystal shape of Pb: Recent results of theory and experiment

Bonzel

Scheffler

2007

Appl. Phys. A

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“…According to (5) and (6), knowing the temperature, particle size reduction rate dR/dt, and Р ∞ (Т), one can determine the value of σ. These expressions adequately describe evaporation kinetics of liquid Pb particles and crystalline Ag particles [6] at values of σ close to handbook ones.…”

Section: Kinetics Of Evaporation Of Small Particles and Surface Energymentioning

confidence: 99%

“…Analysis of known methods for the determination of the wetting contact angles θ shows that the use of traditional methods [1,40] for studying wetting in ultradispersed systems is quite limited. In view of these, new methods [41,42] were developed that allowed to investigate wetting in ultradispersed systems with different types of contact interaction (i.e., applicable both at θ < 90°, and for [6,7,22,[31][32][33][34][35][36] (the dotted lines are extrapolation of dependencies σ l (T) to the area of supercooling state) ■ -creep data [5], ⊕ -small particles evaporation data [7], □ -data for Fe [39] It is evident that there is a common tendency observed for all of the preceding metals manifested in the fact that the values of σ s have nonlinear temperature dependence. With relative temperatures below T/T s ≤ (0.85-0.9) the temperature coefficient for these metals becomes approximately constant and makes module (0.3-0.4) mJ/m 2 K (Figure 4).…”

Section: Wetting In Condensed Filmsmentioning

confidence: 99%

“…These values agree well with available literature data on σ s for bulk samples obtained by other methods. data [6,7,22,[31][32][33][34][35][36] (the dotted lines are extrapolation of dependencies σ l (T) to the area of supercooling state) -creep data [5], ⊕ -small particles evaporation data [7], -data for Fe [39] …”

Section: Decrease In Small Particles Melting Temperature and Surface mentioning

confidence: 99%

“…While methods available for the liquid phase enable to determine reliably not only the value but also the temperature dependence of surface energy [1][2][3], for the solid phase the accuracy of existing methods, as a rule, does not allow to trace its temperature dependence [4,5]. Therefore, the following approach is justified: what information can be obtained about surface energy of the condensed matters on studies of various properties and processes in small size samples [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

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Surface Energy and Wetting in Island Films

Дукаров¹,

Kryshal²,

Sukhov³

2015

Wetting and Wettability

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The chapter describes the fundamental aspects of the effects of scale on surface phenomena in condensed films. Experimental and theoretical data for the size and temperature dependencies of the surface energy (including the solid phase); wetting of solid surfaces and free thin films by small metal particles are discussed. Several modern methods of contact angle measurement in small-sized systems based on the optical and electron microscopy methods are described.

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