Discontinuous surface tension[1] (Fig. 1) of a restricted solid-on-solid (RSOS) model with point contact type step-step attraction (p-RSOS model)[1-3] is calculated numerically by using the product wave-function renormalization group (PWFRG) method[4].   The discontinuous surface tension induces a merging of steps at low temperatures near the equilibrium.   The side surface of the merged step becomes smooth contrary to the capillary wave instability.   As a result, the speed of motion of the merged step becomes slower than the dissolved steps.

   The microscopic energy Hamiltonian of the p-RSOS model is as follows:

where h(i,j) represents the surface height at the site (i,j) on a square lattice, ε represents a microscopic step energy, ε_int (ε_int<0) represents a microscopic step-step attractive energy, and δ(a,b) represents Kronecker delta.

   Due to the sticky character of steps in the p-RSOS model, the surface free energy per projected area of the vicinal surface (Fig. 1) does not have the form of the ‘one-dimensional free fermion universal type’ or the ‘Gruber- Mullins- Pokrovsky- Talapov (GMPT) universal type’ but has a discontinuous one.

 References

 [1] N. Akutsu, Phys. Rev. E 86, (2012) 061604.  PRE Kaleidoscope Images: December 2012.

 [2] N. Akutsu, J. Phys.: Condens. Matter 23 (2011) 485004.

[3] N. Akutsu, Appl. Surf. Sci. 256 (2009) 1205; J. Cryst. Growth, 318 (2011) 10.

[4] T. Nishino and K. Okunishi, J. Phys. Soc. Jpn. 64 (1995) 4084.   Y. Hieida, K. Okunishi and Y. Akutsu, Phys. Lett. A 233 (1997) 464; New J. of Phys. 1 (1999) 7.

Fig. 1 Surface free energies per projected area f(p) (left figures) and surface tensions γ_surf(p)(right figures).    p=(∂z(x,y)/∂p_x, ∂z(x,y)/∂p_y) represents the surface gradient, p=|p|=tanθ represents the surface slope, and θ represents the tilted angle of the surface. ε_int/ε=-0.5.     (a) and (d) k_BT/ε=0.35, (b) and (e) k_BT/ε=0.36, and (c) and (f) k_BT/ε=0.37.

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1. Pinning of steps near equilibrium without impurities, adsorbates, or dislocations