Quantification Driving Force and Bond Stress

Inspecting Figs. 3.24b and 3.25, one can find that the surface network is composed of one-dimensional -2-(l/2)-(l/2)-2-2-(l/2)-(l/2) rhombi chains along the (11) directions. Labels 1 and 2 represents the valences of h- and dipole, respectively. The electrostatic charges of the Rh (1/2) and the Rh (2) are not equal and the Rh is slightly positive compared with the Rh that has a negative nature. 

The strength of interaction is in the order 2-2 (l/2)-(l/2) 0 2-(l/2). The repulsion between the 2-2 or (l/2)-(l/2), and the slight attraction between the 2-(l/2) determines that the distance of 2—2 or (l/2)-(l/2) is longer than the distance of (1/2)—2. Rhombus formation displaces the Rh atoms along the (11) direction, and consequently, leads to the overall rhombi-chain network at the surface. The alternate attraction and repulsion along the chain will squeeze the 2-(1/2) closer without otherwise a response of bond tension to equilibrate the electrostatic force along the chain. 

From Fig. 3.26a, b, it is seen that the bond expands by an amount AL/L — l/cosO — 1 = 1.2 %, which is negligible and, therefore, the mechanism of bond-tension-increase rather than the mechanism of bond-compression-release dominates in the Rh(001)-(4.y/2 x 4.y2)R45°-160 phase transition. 

Without knowing the exact dipole moment, one may assume that Coulomb interaction dominates along the rhombi chain that contains infinite number of atoms (n 100 is sufficient for calculation). The Coulomb potential V, and the electrostatic force F,- acting on the fth atom in the rhombi chain are  

As a component of the electrostatic force F,-, the in Fig. 3.26b balances the bond tension T and hence the clock rotation of the unit ceU  

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