Calculation of the surface energy of fcc-metals with the empirical electron surface model

Surface Energy of Diamond Cubic Crystals and Anisotropy Analysis Revealed by Empirical Electron Surface Models

“…Every atom with the atoms of the nearest neighbor crystal plane forms one A bond, four B bonds and three C bonds, and with the atoms of the second neighbor crystal plane forms one B bond, two C bonds and two D bonds. So the equivalent dangling bond numbers on the (110) plane with the area of √2a For the (111) surface, the diamond cubic crystals have some specific structural properties, which differ from bcc-metals and fcc-metals [3,21]. As is shown in Figure 4 (a) (view along the <110> crystal direction), the (111) surface has two possible cleavage planes denoted by s 1 and s 2 , respectively.…”

“…It is almost impossible to find one type of potentials to reproduce the surface energies of all materials. The empirical electron surface model (EESM) [3,[20][21][22], based on empirical electron theory (EET) [3,20,23], has been found remarkably successful in predicting the surface energies for fcc-, bcc-and hcp-metals [3,[20][21][22]24]. The reliability of EET has been extensively examined in the fields of metals, alloys, metallic compounds and ceramics [25][26][27].…”

In the Search of Fundamental Inner Bond Strength of Solid Elements

“…There were already some attempts in literature to evaluate the effect of number of neighboring atoms and in some cases the effect of their relative atomic distances mostly for estimation of surface properties of pure metals in fcc, bcc, and hcp structures in [ 8 , 9 , 17 , 18 ] and [ 10 , 19 , 20 ], respectively. The value of bond energy in this literature is originated from either empirical electron theory, dangling bond analysis methods, atomic potential simulation, or density function theory which mostly are based on parameters such as covalent electron pairs, bond length, number of electron, contribution of couple effect between spin and orbit, bond capability, screen effect, electron density, and much other quantum chemistry information.…”

“…In their reports Zhang et al in [ 17 ] considered only the effect of 1st nearest neighbors for fcc metals, and Fu et al in [ 8 , 9 ] used up to 3rd nearest neighbors for fcc and bcc, respectively, and in [ 10 ] used up to 7th nearest neighbors for hcp structures, while Wu et al in [ 18 , 20 ] considered up to 12 slabs for fcc and hcp surfaces, respectively, and Matysina in [ 19 ] considered up to 3rd nearest neighbors effect for hcp crystal structures.…”

“…Moreover, in recent years bond energy calculation has been applied in estimation of surface properties through (atomic scale) broken bond model; thus the bond strength should be known between different neighboring atoms. In latest works of Fu et al in [ 8 – 10 ] these estimations have been mostly supported by complicated quantum chemistry information through empirical electron theory where the bond energy of neighboring atoms was evaluated from the value of bonding capability of covalent electron, screen factor upon the core electron, bond length, and the number of covalent electron pair. Obviously, lack of a simple and more engineering based procedure has been realized which leads to an inquiry for developing a generalized simple method.…”