Analysing atom lattices — Atomap 0.4.3.dev1 documentation

After finding and refining the atom lattices as shown in Finding the atom lattice, the atomic structure can be analysed through
Ellipticity of the atomic columns
Monolayer separation
Angle between monolayers
Integration of atomic columns
Making line profiles
Plotting a pair distribution function
In this tutorial we will use a dummy image containing two sublattices. Different structural distortions have been introduced in the image, and this tutorial will study these distortions. The plots that are made are simple plots that clearly shows the structural changes in the sublattices. It is also possible to make more fancy figures for publications (such as in the paper presenting Atomap), and some tips for doing this are shown in the plotting section of the guide.
The procedure for finding and refining the sublattices in fantasite is similar as in Images with more than one sublattice.
Fantasite is shown in the left image, and it is possible to see some variations in ellipticity and atom positions with the naked eye. The right figure shows the atom positions after the refinement. As refinement of the sublattice can be time consuming, it is a good idea to save the final atom lattice.
The atom lattice can be loaded:
atomap.atom_lattice.Atom_Lattice is an object containing the sublattices, and other types of information. The fantasite atom lattice contains two sublattices (red and blue dots in the image above). Atom positions, sigma, ellipticity and rotation for the atomic columns in a sublattice can be accessed via attributes in the sublattice object.
Similarly, properties of a single atomic column atomap.atom_position.Atom_Position can be accessed in atomap.sublattice.Sublattice.atom_list. The atomap.atom_position.Atom_Position object contain information related to a specific atomic column.
The atomap.atom_plane.Atom_Plane objects contain the atomic columns belonging to the same specific plane. Atom plane objects are defined by the direction vector parallel to the atoms in the plane, for example (58.81, -41.99). These can be accessed by:
Atom planes for a specific direction can also be accessed:
Elliptical atomic columns may occur when atoms parallel to the electron beam have shifted position in the plane perpendicular to the beam. In the image, circular atomic columns have an ellipticity () of 1, as sigma_x = sigma_y (). Ellipticity is defined as
The ellipticity map shows the magnitude of the ellipticity. Values are interpolated, giving a continuous map. The sublattice B was generated without any ellipticity, and the image to the right is fairly flat, as expected. In sublattice A, a region with elliptical atomic columns is clearly visible. The ellipticity gradient is perfectly in line with how the dummy image of fantasite has been generated. Maps gives nice visualization of gradual change.
The atomap.sublattice.Sublattice.plot_ellipticity_map() function calls atomap.sublattice.Sublattice.get_ellipticity_map(), which calls atomap.sublattice.Sublattice.get_property_map().
While the ellipticity map nicely visualizes the magnitude (and gradual change) of the ellipticity, it does not show the direction of the ellipticity. In vector (quiver) plots (plot_ellipticity_vectors()) both the rotation and magnitude are visualized, through the length and angle of the arrows. There is one arrow for each atom position. This type of visualization also reveals that the ellipticity of the atomic columns have an alternating directionality.
In this function, a value of 1 is subtracted from the magnitude of the ellipticity. This makes it easier to study changes in ellipticity, as the 0-point of the plot is set to the perfect circle. atomap.plotting.plot_vector_field() is called, and this function uses Matplotlib’s quiver plot function.
As Atomap knows the positions of all atoms, it can also tell you if you have any variations in the unit cell sizes or other types of structural distortions. For example, Atomap has been used to study oxygen octahedron tilt patterns in perovskite thin films.
In this example, Atomap finds the distance between monolayers. “Distance between monolayers” is defined in the figure below (a). The distance is measured between an atomic column and the nearest monolayer, as shown in this figure. The values for monolayer separation is attributed to the midpoint of the atom and monolayer.
This is found by using the get_monolayer_distance_map(), which returns a stack of HyperSpy images. In this signal the navigation axis is a zone vector (the values in the zone axis tuple are in principle the vector parallel to the monolayer) and the signal axes shows monolayer separation at each atom position. get_monolayer_distance_map() can also take in a subset of zone vectors, but the default is to find the monolayer separation for all the zone axes.
The left image shows the monolayer separation for one zone axis, namely the separation between the monolayers drawn up by red lines in the right figure. Clearly, the position of the B atomic columns are changed in the middle of the image, where every second monolayer is closer and further apart from the atom.
An alternative to plotting the monolayer separation is the difference in distance from an atom to the two neighbouring atoms in the monolayer with get_atom_distance_difference_map(). In some cases, this is a more robust way of finding superstructures as this method only shows the variations in distance, not the total distance. The “distance difference” is defined in the below figure. The value of the distance difference is attributed to the position of the middle atom.
The B-sublattice of fantasite has two different domains of structural distortion. As seen above, the monolayers in (0.0, -30.0) direction are alternatively closer and further apart. The corresponding distance difference will be the distance difference for atoms in the orthogonal planes (index 0, value (15.0, 0.0), shown below).
The left image shows the monolayers, with the resulting distance dif