Surface energies of solid metals

Abstract

Measurements of surface energies of solid metals reported in the literature are collected and compared, and best values are suggested. A brief review is presented of theories of surface free energy 'Y and surface entropy S, and it is proposed that S ......., LO R per mole of surface atoms is a reasonable estimate. Using this value of S, surface energies 'Y 0 at OaK are deduced by extrapolation of experimental data from higher temperatures and correlated with cohesive energies H(O) at OaK. On the basis of this correlation, it is suggested that reasonable estimates of surface energy reliable to""""10 per cent may be obtained from "I A = "loA -TS where A = molar surface area, "loA = 0.25 H(O), and S = 1.0 R. Resume. On a rassemble dans la litterature les mesures d'energie superficielle de metaux solides. De leur comparaison l'auteur suggere les meilleures valeurs disponibles. On presente aussi une breve revue des theories concernant l'energie libre de surface Set l'entropie superficielle 'Y. La valeur de 1.0 R par mole d'atome superficiel est proposee pour S comme une estimation raisonnable. On utilise cette valeur de S pour en deduire l'energie superficielle 'Y Q a OaK par extrapolation des resultats experimen taux obtenus a temperatures plus elevees. Sur la base d'une correlation entre les resultats et les energies de cohesion H(O) a OaK, on suggere que des estimations des energies superficielles peuvent etre obtenues a ± 10% en u tilisant la relation "IA = "loA -TS ou A = surface molaire, "loA = 0.25 H(O), et S = 1.0 R.

Error estimates for density-functional theory predictions of surface energy and work function

“…Other estimates of S vib and S conf suggest a large uncertainty of ±50% should be attached to the RT m /A value [38]. However, as this term only contributes about 10% of the total surface energy (RT m /A ≈ 0.1γ SV ) [36], the dominant part of the uncertainty remains the conversion from γ LV to γ SV .…”

“…m [38], with N as Avogadro's number and V m the molar volume, the temperature-dependent transformation is…”

“…The former includes all vibrational modes associated with the surface, whereas the latter aims to describe the surface roughening observed when the material is heated. For both contributions a simplified approximation was proposed [38]. S vib was assumed to increase linearly from 0 to 0.8 R (where R is the universal gas constant) between 0 K and the Debye temperature T D ≈ 0.2T m .…”

High temperature fracture of boron carbide: experiments and simple theoretical models

“…For polycrystalline material an appropriate average has to be calculated, which is not a simple operation. An approximate average, however, may be calculated by using a simple model [28,29]. For compounds an "average" atom must be used.…”

The temperature‐dependent surface energy of ceramic single crystals

“…For example, Tyson's analysis gave the following equation:where γ and γ 0 are, respectively, the surface energies at temperature T and 0 K, S ≈ R is the molar surface entropy, A =1.612 N 1/3 V 2/3 is the molar surface area, V is the molar volume, and N and R are the Avogadro's number and the gas constant, respectively. The above equation can give reasonable predictions for metals . However, it will give significantly weak temperature dependence for ceramic single crystals (see Figure B).…”