This is a example of analysis of the dimensionality of a structure using
ase.geometry.dimensionality.analyze_dimensionality() function. This is
useful for finding low-dimensional materials, such as 1D chain-like
structures, 2D layered structures, or structures with multiple dimensionality
types, such as 1D+3D.
The example below creates a layered MoS2 structure and analyzes its dimensionality.
import ase.build from ase.visualize import view from ase.geometry.dimensionality import analyze_dimensionality atoms = ase.build.mx2(formula='MoS2', kind='2H', a=3.18, thickness=3.19) atoms.cell[2, 2] = 7.0 atoms.set_pbc((1, 1, 1)) atoms *= 3 intervals = analyze_dimensionality(atoms, method='RDA') m = intervals print(sum([e.score for e in intervals])) print(m.dimtype, m.h, m.score, m.a, m.b) atoms.set_tags(m.components) view(atoms)
Coloring the atoms by their tags shows the distinct bonded clusters, which in this case are separate layers.
Each component in the material can be extracted, or “isolated”,
ase.geometry.dimensionality.isolate_components() function as
the example below demonstrates.
import numpy as np import ase.build from ase import Atoms from ase.visualize import view from ase.geometry.dimensionality import isolate_components # build two slabs of different types of MoS2 rep = [4, 4, 1] a = ase.build.mx2(formula='MoS2', kind='2H', a=3.18, thickness=3.19) * rep b = ase.build.mx2(formula='MoS2', kind='1T', a=3.18, thickness=3.19) * rep positions = np.concatenate([a.get_positions(), b.get_positions() + [0, 0, 7]]) numbers = np.concatenate([a.numbers, b.numbers]) cell = a.cell atoms = Atoms(numbers=numbers, positions=positions, cell=cell, pbc=[1, 1, 1]) atoms.cell[2, 2] = 14.0 # isolate each component in the whole material result = isolate_components(atoms) print("counts:", [(k, len(v)) for k, v in sorted(result.items())]) for dim, components in result.items(): for atoms in components: print(dim) view(atoms, block=True)
The method is described in the article:
P.M. Larsen, M. Pandey, M. Strange, and K. W. JacobsenPhys. Rev. Materials 3 034003, 2019
A preprint is available here.
More examples here: Dimensionality analysis of ICSD and COD databases.
analyze_dimensionality(atoms, method='RDA', merge=True)¶
Performs a k-interval analysis.
In each k-interval the components (connected clusters) are identified. The intervals are sorted according to the scoring parameter, from high to low.
- atoms: ASE atoms object
The system to analyze. The periodic boundary conditions determine the maximum achievable component dimensionality, i.e. pbc=[1,1,0] sets a maximum dimensionality of 2.
- method: string
Analysis method to use, either ‘RDA’ (default option) or ‘TSA’. These correspond to the Rank Determination Algorithm of Mounet et al. and the Topological Scaling Algorithm (TSA) of Ashton et al.
- merge: boolean
Decides if k-intervals of the same type (e.g. 01D or 3D) should be merged. Default: true
- intervals: list
List of KIntervals for each interval identified. A KInterval is a namedtuple with the following field names:
- score: float
Dimensionality score in the range [0, 1]
- a: float
The start of the k-interval
- b: float
The end of the k-interval
- dimtype: str
The dimensionality type
- h: tuple
The histogram of the number of components of each dimensionality. For example, (8, 0, 3, 0) means eight 0D and three 2D components.
- components: array
The component ID of each atom.
- cdim: dict
The component dimensionalities
Isolates components by dimensionality type.
Given a k-value cutoff the components (connected clusters) are identified. For each component an Atoms object is created, which contains that component only. The geometry of the resulting Atoms object depends on the component dimensionality type:
- 0D: The cell is a tight box around the atoms. pbc=[0, 0, 0].
The cell has no physical meaning.
- 1D: The chain is aligned along the z-axis. pbc=[0, 0, 1].
The x and y cell directions have no physical meaning.
- 2D: The layer is aligned in the x-y plane. pbc=[1, 1, 0].
The z cell direction has no physical meaning.
3D: The original cell is used. pbc=[1, 1, 1].
- atoms: ASE atoms object
The system to analyze.
- kcutoff: float
The k-value cutoff to use. Default=None, in which case the dimensionality scoring parameter is used to select the cutoff.
- components: dict
key: the component dimenionalities. values: a list of Atoms objects for each dimensionality type.