The Process Syntax¶

In kMC language a process is uniquely defined by a configuration before the process is executed, a configuration after the process is executed, and a rate constant. Here this model is used to define a process by giving it a :

condition_list
action_list
rate_constant

As you might guess each condition corresponds to one before, and each action coresponds to one after. In fact conditions and actions are actually of the same class or data type: each condition and action consists of a coordinate and a species which has to be or will be at the coordinate. This model of process definition also means that each process in one unit cell has to be defined explicitly. Typically one a single crystal surface one will have not one diffusion per species but as many as there are equivalent directions :

species_diffusion_right

species_diffusion_up

species_diffusion_left

species_diffusion_down

while this seems like a lot of work to define that many processes, it allows for a very clean and simple definition of a process itself. Later you can use geometric measures to abstract these cases as you will see further down.

Adsorption¶

Let’s start with a very simple and basic process: molecular adsorption of a gas phase species, let call it A on a surface site. For this we need a species

from kmcos.types import *
kmc_model = kmcos.create_kmc_model()

A = Species(name='A')
kmc_model.add_species(A)

empty = Species(name='empty')
kmc_model.add_species(empty)

and the coordinate of a surface site

layer = Layer(name='default')
kmc_model.add_layer(layer)
layer.sites.append(Site(name='a'))
coord = kmc_model.lattice.generate_coord('a.(0,0,0).default')

which is for now all we need to define an adsorption process:

adsorption = Proces(name='adsorption_A_a',
                    condition_list=[Condition(coord=coord,
                                              species='empty')],
                    action_list=[Action(coord=coord,
                                        species='A')])
kmc_model.add_process(adsorption)

Now this wasn’t hard, was it?

Diffusion¶

Let’s move to another example, namely the diffusion of a particle to the next unit cell in the y-direction. You first need the coordinate of the final site

final = kmc_model.lattice.generate_coord('a.(0,1,0).default')

and you are good to go

diffusion_up = Process('diffusion_A_up',
                       condition_list=[Condition(coord=coord,
                                                 species='A'),
                                       Condition(coord=final,
                                                 species='empty')],
                       condition_list=[Condition(coord=coord,
                                                 species='empty'),
                                       Condition(coord=final,
                                                 species='A')],
kmc_model.add_process(diffusion_up)

You can complicated this ad infinitum but you know all elements needed to define processes.

Avoid Double Counting¶

Finally a word of warning: double counting is a phenomenon sometimes encountered for those process where there is more than one equivalent direction for a process and the coordinates within the process are also equivalent. Think of dissociative oxygen adsorption. Novices typically collect all possible directions (e.g. right, up, left, down) and then define this process for each direction. This may be incorrect, depending on how the rate constant value was defined. If the rate constant represents a net rate for adsorption / desorption from a pair of sites, (from an average or from a single transition state that bridges two sites), then the right,up,left, down procedure will have double counted the process because e.g. adsorption_up is the same processes as adsorption_down, just executed from one site above or below. One can compensate by dividing each adsorption rate constant by 2 and also each desorption rate constant by 2. One can also avoid double counting by only defining geometrically equivalent sites one time per unit cell: a simple trick is to only consider processes in the positive directions, for example.

However, note that if there are two transition state possibilities (one above one site, one above the other site) due to a heterolytic cleavage transition state, then there are supposed to be double processes and it is not double counting, just two paths that achieve the same reactants and products. Most rate constants in the literature for dissociative adsorption are defined as an average for the two sites, or involve a single homolytic transition state, and thus most cases of dissociate adsorption should have a single process between up and down as well as between left and right (yielding two processes, not four, for a simple cubic system).

Taking It Home¶

A process consists of conditions, actions and a rate constant
double counting is best avoided from the beginning