Observers

SiteOccupancyObserver

class mchammer.observers.SiteOccupancyObserver(cluster_space, sites, super_cell, interval=None)[source]

This class represents a site occupation factor (SOF) observer.

A SOF observer allows to compute the site occupation factors along the trajectory sampled by a Monte Carlo (MC) simulation.

Parameters:
  • cluster_space (icet.ClusterSpace) – cluster space from which the allowed species are extracted
  • sites (dict(str, list(int))) – dictionary containing lists of sites that are to be considered, which keys will be taken as the names of the sites
  • super_cell (ase.Atoms) – an atoms object that represents a typical super cell, which is used to determine the allowed species
  • interval (int) – observation interval during the Monte Carlo simulation
tag

name of observer

Type:str
interval

observation interval

Type:int

Example

The following snippet illustrate how to use the site occupancy factor (SOF) observer in a Monte Carlo simulation of a surface slab. Here, the SOF observer is used to monitor the concentrations of different species at the surface, the first subsurface layer, and the remaining “bulk”. A minimal cluster expansion is used with slightly modified surface interactions in order to obtain an example that can be run without much ado. In practice, one should of course use a proper cluster expansion:

from ase.build import fcc111
from icet import ClusterExpansion, ClusterSpace
from mchammer.calculators import ClusterExpansionCalculator
from mchammer.ensembles import CanonicalEnsemble
from mchammer.observers import SiteOccupancyObserver

# prepare reference structure
prim = fcc111('Au', size=(1, 1, 10), vacuum=10.0)
prim.translate((0.1, 0.1, 0.0))
prim.wrap()
prim.pbc = True  # icet requires pbc in all directions

# prepare cluster expansion
cs = ClusterSpace(prim, cutoffs=[3.7], chemical_symbols=['Ag', 'Au'])
params = [0] + 5 * [0] + 10 * [0.1]
params[1] = 0.01
params[6] = 0.12
ce = ClusterExpansion(cs, params)
print(ce)

# prepare initial configuration based on a 2x2 supercell
atoms = prim.repeat((2, 2, 1))
for k in range(20):
    atoms[k].symbol = 'Ag'

# set up MC simulation
calc = ClusterExpansionCalculator(atoms, ce)
mc = CanonicalEnsemble(atoms=atoms, calculator=calc, temperature=600,
                       data_container='myrun_sof.dc')

# set up observer and attach it to the MC simulation
sites = {'surface': [0, 9], 'subsurface': [1, 8],
         'bulk': list(range(2, 8))}
sof = SiteOccupancyObserver(cs, sites, atoms, interval=len(atoms))
mc.attach_observer(sof)

# run 1000 trial steps
mc.run(1000)

After having run this snippet one can access the SOFs via the data container:

print(mc.data_container.data)
get_observable(atoms)[source]

Returns the site occupation factors for a given atomic configuration.

Parameters:atoms (Atoms) – input atomic structure.
Return type:Dict[str, List[float]]
return_type

Data type of the observed data.

Return type:type

BinaryShortRangeOrderObserver

class mchammer.observers.BinaryShortRangeOrderObserver(cluster_space, structure, interval, radius)[source]

This class represents a short range order (SRO) observer for a binary system.

Parameters:
  • cluster_space (icet.ClusterSpace) – cluster space used for initialization
  • structure (ase.Atoms) – defines the lattice which the observer will work on
  • interval (int) – observation interval during the Monte Carlo simulation
  • radius (float) – the maximum radius for the neigbhor shells considered
tag

human readable observer name (BinaryShortRangeOrderObserver)

Type:str
interval

observation interval

Type:int

Example

The following snippet illustrate how to use the short-range order (SRO) observer in a Monte Carlo simulation of a bulk supercell. Here, the parameters of the cluster expansion are set to emulate a simple Ising model in order to obtain an example that can be run without modification. In practice, one should of course use a proper cluster expansion:

from ase.build import bulk
from icet import ClusterExpansion, ClusterSpace
from mchammer.calculators import ClusterExpansionCalculator
from mchammer.ensembles import CanonicalEnsemble
from mchammer.observers import BinaryShortRangeOrderObserver

# prepare cluster expansion
# the setup emulates a second nearest-neighbor (NN) Ising model
# (zerolet and singlet ECIs are zero; only first and second neighbor
# pairs are included)
prim = bulk('Au')
cs = ClusterSpace(prim, cutoffs=[4.3], chemical_symbols=['Ag', 'Au'])
ce = ClusterExpansion(cs, [0, 0, 0.1, -0.02])

# prepare initial configuration
nAg = 10
atoms = prim.repeat(3)
atoms.set_chemical_symbols(nAg * ['Ag'] + (len(atoms) - nAg) * ['Au'])

# set up MC simulation
calc = ClusterExpansionCalculator(atoms, ce)
mc = CanonicalEnsemble(atoms=atoms, calculator=calc, temperature=600,
                       data_container='myrun_sro.dc')

# set up observer and attach it to the MC simulation
sro = BinaryShortRangeOrderObserver(cs, atoms, interval=len(atoms), radius=4.3)
mc.attach_observer(sro)

# run 1000 trial steps
mc.run(1000)

After having run this snippet one can access the SRO parameters via the data container:

print(mc.data_container.data)
get_observable(atoms)[source]

Returns the value of the property from a cluster expansion model for a given atomic configurations.

Parameters:atoms (Atoms) – input atomic structure
Return type:Dict[str, float]
return_type

Data type of the observed data.

Return type:type

ClusterCountObserver

class mchammer.observers.ClusterCountObserver(cluster_space, atoms, interval)[source]

This class represents a cluster count observer.

A cluster count observer enables one to keep track of the decoration of clusters along the trajectory sampled by a Monte Carlo (MC) simulation. For example, using this observer, several canonical MC simulations could be carried out at different temperatures and the temperature dependence of the number of nearest neigbhors of a particular species could be accessed with this observer.

Parameters:
  • cluster_space (icet.ClusterSpace) – cluster space to define the clusters to be counted
  • atoms (ase.Atoms) – defines the lattice that the observer will work on
  • interval (int) – observation interval during the Monte Carlo simulation
tag

human readable observer name

Type:str
interval

observation interval

Type:int
get_observable(atoms)[source]

Returns the value of the property from a cluster expansion model for a given atomic configuration.

Parameters:atoms (Atoms) – input atomic structure
Return type:dict
return_type

Data type of the observed data.

Return type:type

ClusterExpansionObserver

class mchammer.observers.ClusterExpansionObserver(cluster_expansion, interval=None, tag='ClusterExpansionObserver')[source]

This class represents a cluster expansion (CE) observer.

A CE observer allows to compute a property described by a CE along the trajectory sampled by a Monte Carlo (MC) simulation. In general this CE differs from the CE that is used to generate the trajectory. For example in a canonical MC simulation the latter would usually represent an energy (total or mixing energy) whereas the former CE(s) could map lattice constant or band gap.

Parameters:
  • cluster_expansion (icet.ClusterExpansion cluster expansion model) – to be used for observation
  • tag (str) – human readable observer name (default: ClusterExpansionObserver)
  • interval (int) – observation interval during the Monte Carlo simulation
tag

name of observer

Type:str
interval

observation interval

Type:int
get_observable(atoms)[source]

Returns the value of the property from a cluster expansion model for a given atomic configuration.

Parameters:atoms (Atoms) – input atomic structure.
Return type:float
return_type

Data type of the observed data.

Return type:type