app_style sos command

Syntax:

app_style sos bond_energy keyword args 

• sos = application style name
• bond_energy = lateral bond energy between columns
• zero or more keyword/value pairs may be appended
• keyword = xsin

    xsin args = amp Lx Lz
      amp = amplitude of initial sine wave
      Lx  = wavelength of initial sine wave in x direction
      Lz  = wavelength pf initial sine wave in z direction (ignored if > 1.0e10) 
  

Examples:

app_style sos 1.0 xsin 5.5 20.0 1.0e+20
app_style sos 2.0 none 

Description:

The SOS (Solid-on-Solid) model is an on-lattice application that models a solid surface as a 1D or 2D lattice of sites. At each site an integer value represents the height of the surface at that site, so that collectively the heights of all the sites represent a surface profile with no overhangs or vacancies.

The Hamiltonian representing the energy of a site I is:

Hi = 1/2 J Sum_j |h_i - h_j| 

where J is the bond energy, specified through the bond_energy parameter, and h_i and h_j are the heights at sites I and J. Sum_j represents a sum over the nearest neighbors of i, e.g. the neighbors to the immediate left and right for a 1D lattice.

If the xsin keyword is used, an initial height profile is assigned by a sine function. If the z dependence is inactive (Lz > 1.0e10), this is

hi = round(amp*sin(2*pi*x/Lx)) 

If the z dependence is active, this is instead:

hi = round(amp * min(sin(2*pi*x/Lx), sin(2*pi*z/Lz))) 

This application performs Kawasaki dynamics, in which each event involves an "atom" hopping from one site to a neighboring site. That is, an event consists of site I losing one unit of height, and either site I+1 or I-1 simultaneously gaining one unit of height.

This application does not allow for use of a rejection KMC (rKMC) algorithm; only KMC options are supported. See this page for more information. For solution by a KMC algorithm, the probability of each "atom hop" event is min[P0, P0*exp(-dE/kT)], where P0 is a scaling factor, dE = Efinal - Einitial using the Hamiltonian defined above for the energy of the site, and T is the temperature of the system defined by the temperature command (which includes the Boltzmann constant k implicitly). The scaling factor P0 is given by 1/nn where nn is the number of nearest neighbors for each site.

The following additional commands are defined by this application:

Restrictions: none

Related commands:

app_style diffusion