摘要
The surface free energy (SFE) of (1× 1)-surfaces of crystals, without reconstructionand adsorption, is calculated using a bond-broken mode. In the mode, the potentialenergy of the crystals is treated as a sum of the energies of the bonds connectingpair-wise atoms (u-bonds). The SFE is calculated based on the bond energy and thearea density of dangling bonds which depends on the structure of the surface. Theresults provide a general expression for the SFE in terms of the bond energy (E)and the bond length (do) of the crystal and Miller indices hkl. The anisotropy ofthe SFE is therefore completely determined with the expression. As the examples,considering the nearest-neighboring bonding, the SFEs of sc, fcc, bcc and cth (cubictetrahedral) crystals are discussed, respectively. Wulff plots of bcc and fcc crystalsare then obtained. The equilibrium forms (EFs) of these crystals ave consequentlygot from their Wulff plots, respectively. It is found that the EFs of bcc and fcc arerespectively the rhombic dodecahedron and the truncated-octahedron that are their firstBrillouin zones, respectively.
The surface free energy (SFE) of (1× 1)-surfaces of crystals, without reconstructionand adsorption, is calculated using a bond-broken mode. In the mode, the potentialenergy of the crystals is treated as a sum of the energies of the bonds connectingpair-wise atoms (u-bonds). The SFE is calculated based on the bond energy and thearea density of dangling bonds which depends on the structure of the surface. Theresults provide a general expression for the SFE in terms of the bond energy (E)and the bond length (do) of the crystal and Miller indices hkl. The anisotropy ofthe SFE is therefore completely determined with the expression. As the examples,considering the nearest-neighboring bonding, the SFEs of sc, fcc, bcc and cth (cubictetrahedral) crystals are discussed, respectively. Wulff plots of bcc and fcc crystalsare then obtained. The equilibrium forms (EFs) of these crystals ave consequentlygot from their Wulff plots, respectively. It is found that the EFs of bcc and fcc arerespectively the rhombic dodecahedron and the truncated-octahedron that are their firstBrillouin zones, respectively.
