Source code for mchammer.ensembles.canonical_ensemble

"""Definition of the canonical ensemble class."""

from ase import Atoms
from ase.units import kB
from typing import List

from .. import DataContainer
from ..calculators.base_calculator import BaseCalculator
from .thermodynamic_base_ensemble import ThermodynamicBaseEnsemble

[docs] class CanonicalEnsemble(ThermodynamicBaseEnsemble): r"""Instances of this class allow one to simulate systems in the canonical ensemble (:math:`N_iVT`), i.e. at constant temperature (:math:`T`), number of atoms of each species (:math:`N_i`), and volume (:math:`V`). The probability for a particular state in the canonical ensemble is proportional to the well-known Boltzmann factor, .. math:: \rho_{\text{C}} \propto \exp [ - E / k_B T ]. Since the concentrations or equivalently the number of atoms of each species is held fixed in the canonical ensemble, a trial step must conserve the concentrations. This is accomplished by randomly picking two unlike atoms and swapping their identities. The swap is accepted with probability .. math:: P = \min \{ 1, \, \exp [ - \Delta E / k_B T ] \}, where :math:`\Delta E` is the change in potential energy caused by the swap. The canonical ensemble provides an ideal framework for studying the properties of a system at a specific concentration. Properties such as potential energy or phenomena such as chemical ordering at a specific temperature can conveniently be studied by simulating at that temperature. The canonical ensemble is also a convenient tool for "optimizing" a system, i.e., finding its lowest energy chemical ordering. In practice, this is usually achieved by simulated annealing, i.e., the system is equilibrated at a high temperature, after which the temperature is continuously lowered until the acceptance probability is almost zero. In a well-behaved system, the chemical ordering at that point corresponds to a low-energy structure, possibly the global minimum at that particular concentration. Parameters ---------- structure Stomic configuration to be used in the Monte Carlo simulation; also defines the initial occupation vector. calculator Calculator to be used for calculating the potential changes that enter the evaluation of the Metropolis criterion. temperature Temperature :math:`T` in appropriate units, commonly Kelvin. boltzmann_constant Boltzmann constant :math:`k_B` in appropriate units, i.e., units that are consistent with the underlying cluster expansion and the temperature units. Default: eV/K. user_tag Human-readable tag for ensemble. Default: ``None``. random_seed Seed for the random number generator used in the Monte Carlo simulation. dc_filename Name of file the data container associated with the ensemble will be written to. If the file exists it will be read, the data container will be appended, and the file will be updated/overwritten. data_container_write_period Period in units of seconds at which the data container is written to file. Writing periodically to file provides both a way to examine the progress of the simulation and to back up the data. Default: 600 s. ensemble_data_write_interval Interval at which data is written to the data container. This includes for example the current value of the calculator (i.e., usually the energy) as well as ensembles specific fields such as temperature or the number of atoms of different species. Default: Number of sites in the :attr:`structure`. trajectory_write_interval Interval at which the current occupation vector of the atomic configuration is written to the data container. Default: Number of sites in the :attr:`structure`. sublattice_probabilities Probability for picking a sublattice when doing a random swap. This should be as long as the number of sublattices and should sum up to 1. Example ------- The following snippet illustrate how to carry out a simple Monte Carlo simulation in the canonical ensemble. 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 import bulk >>> from icet import ClusterExpansion, ClusterSpace >>> from mchammer.calculators import ClusterExpansionCalculator >>> # 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 >>> structure = prim.repeat(3) >>> for k in range(5): >>> structure[k].symbol = 'Ag' >>> # set up and run MC simulation >>> calc = ClusterExpansionCalculator(structure, ce) >>> mc = CanonicalEnsemble(structure=structure, calculator=calc, ... temperature=600, ... dc_filename='myrun_canonical.dc') >>> # carry out 100 trial swaps """ def __init__(self, structure: Atoms, calculator: BaseCalculator, temperature: float, user_tag: str = None, boltzmann_constant: float = kB, random_seed: int = None, dc_filename: str = None, data_container: str = None, data_container_write_period: float = 600, ensemble_data_write_interval: int = None, trajectory_write_interval: int = None, sublattice_probabilities: List[float] = None) -> None: self._ensemble_parameters = dict(temperature=temperature) # add species count to ensemble parameters symbols = set([symbol for sub in calculator.sublattices for symbol in sub.chemical_symbols]) for symbol in symbols: key = 'n_atoms_{}'.format(symbol) count = structure.get_chemical_symbols().count(symbol) self._ensemble_parameters[key] = count super().__init__( structure=structure, calculator=calculator, user_tag=user_tag, random_seed=random_seed, data_container=data_container, dc_filename=dc_filename, data_container_class=DataContainer, data_container_write_period=data_container_write_period, ensemble_data_write_interval=ensemble_data_write_interval, trajectory_write_interval=trajectory_write_interval, boltzmann_constant=boltzmann_constant) if sublattice_probabilities is None: self._swap_sublattice_probabilities = self._get_swap_sublattice_probabilities() else: self._swap_sublattice_probabilities = sublattice_probabilities @property def temperature(self) -> float: """ Current temperature. """ return self._ensemble_parameters['temperature'] def _do_trial_step(self): """ Carries out one Monte Carlo trial step. """ sublattice_index = self.get_random_sublattice_index(self._swap_sublattice_probabilities) return self.do_canonical_swap(sublattice_index=sublattice_index)