Special site-rules

Custom site-attributes

Sites in MonteCoffee, per default only contain a variable that determine their type named stype. Stype is used to analyze the rates and coverages over different sites in a system. However, to calculate reaction energies, it can be good to attach a coordination number to the class as well. This can simply be done by adding a parameter coordination_number to the constructor in user_sites.py as

class Site(SiteBase):

    def __init__(self, stype=0, covered=0, ind=None, lattice_pos=None, coordination_number=None):
        SiteBase.__init__(self, stype=stype, covered=covered, ind=ind,
        self.cn = coordination_number

Then the get_rate() methods of user_events.py can access the coordination number as

class A(EventBase):
def get_rate(self, system, site, other_site):
    return self.alpha*1000.*system.sites[site].cn

Using stype for everything

stype that belongs to a NeighborKMC.user_sites.Site object is useful to define special rules for performing events. For a binary alloy system with 10 different generalized coordination numbers we have 20 different types of sites, thus stype can take on the values from 0 to 19.

To use stype, let us assume that we have defined

from user_sites import Site
from user_system
s1 = Site(stype = 0, covered = 0, ind = 0)
s2 = Site(stype = 1, covered = 0, ind = 1)

One example of a special rule is to make events that are only possible if stype == 1:

class A(EventBase):

    def possible(self, system, site, other_site):
        if system.sites[site].stype == 1:
            return True
            return False

Another special rule is to return a different rate-constant based on stype

class A(EventBase):

    def get_rate(self, system, site, other_site):
        R = 1000*system.sites[site].stype+0.1
        return self.alpha*R

This can be useful when having multiple different sites on a nanoparticle. If we want to calculate the rate-constant based on transition state theory, a different reaction energy barrier can be defined for each site’s and neighbor-site’s type as

from user_constants import kB
import numpy as np
class A(EventBase):
    def get_rate(self, system, site, other_site):
        stype = system.sites[site].stype
        stype_other = system.sites[other_site].stype
        stype_avg = 0.5*(stype+stype_other)
        Ea = 1.08 + (4-stype_avg)*0.1
        return self.alpha*1E12*np.exp(-Ea/(kB*self.params["T"]))

Here, a transition state like rate constant is returned, with a pre-exponential factor of \(\dfrac{k_\mathrm{B}T}{h}\dfrac{Z^{ts}}{Z^{ini}} \approx 10^{12}\,\mathrm{s}^{-1}\) and the energy barrier is based on the average site-type number of the two sites.