Grain segmentation

This modifier identifies the individual grains in a polycrystalline microstructure by grouping atoms in crystal regions having similar local lattice orientations. The algorithm works in three steps:

1. The local structural environment and orientation of each atom is determined using the Polyhedral template matching modifier.

2. A graph representation of the input structure is created using the neighbors of each atom, where each atom is a graph node and each neighbor bond is a graph edge.

3. Grains are formed by hierarchical clustering of the graph.

The modifier assigns a new property named Grain to each atom indicating which grain the atom belongs to (grain numeric identifier). The special grain identifier 0 is assigned to atoms that do not belong to any grain. The modifier furthermore computes a mean lattice orientation for each identified grain and outputs a list of the grains as a data table with the following per-grain information:

1. Numeric grain identifier

2. Grain size (in terms of the number of atoms belonging to the grain; whether grain boundary atoms are included depends on the Adopt orphan atoms option)

3. Display color (see option Color particles by grain below)

4. Crystal phase of the grain (see PTM structure types)

5. Mean lattice orientation (expressed as 4-component quaternion similar to the per-atom lattice orientations computed by the PTM modifier)

6. Center of mass of the grain (see below)

7. Radius and radius of gyration of the grain (see below)

The list of grains is ordered by size, starting with the largest grain (in terms of the number of atoms).

Calculation of centers of mass

The modifier computes the center of mass of every grain and outputs the coordinates as an additional column of the grain list. Grains that extend across periodic cell boundaries are correctly handled: the atomic coordinates are unwrapped along the bonds of the neighbor graph before the mean position is computed, using the minimum image convention.

However, if a grain is infinite (reconnecting to itself through periodic cell boundaries), the computed center will have some arbitrary value, because the center of mass of an infinite grain is not well-defined.

The algorithm calculates the center of mass using the atomic masses as weights. Mass information is taken from the Mass property of individual atoms if present or from the masses set at the level of particle types. If no per-atom masses have been specified, and if none of the particle types has a mass value, the algorithm assumes uniform weights for all atoms in the calculation.

The centers of mass also serve as the positions of the rows of the grain list. That means a text labels visual element attached to the grain list will place its labels right at the grains without any further setup.

Calculation of gyration radius

The modifier outputs two further columns measuring the spatial extent of every grain:

Radius

The radius of the smallest sphere centered at the grain’s center of mass that encloses all atoms of the grain, i.e. the distance of the atom furthest away from the center.

Radius of Gyration

The radius of gyration of the grain (in simulation units of length).

Both quantities are computed from the same unwrapped atomic coordinates as the centers of mass, which means grains extending across periodic cell boundaries are handled correctly. As for the center of mass, the values are not well-defined for an infinite grain reconnecting to itself through the periodic boundaries.

The calculation of the radius of gyration follows the compute gyration command of the LAMMPS simulation code and the Cluster analysis modifier of OVITO. It uses the same atomic masses as weights as the center of mass calculation, falling back to uniform weights if no mass information is available.

The Radius column doubles as the size of a grain when labeling the grain list with the Add text labels modifier: labels are then placed at the edge of each grain instead of right at its center of mass.

Caution

The grain segmentation algorithm is still considered experimental and has not been tested yet on many real-world microstructures. Please use this function with caution and help us improve the algorithm by reporting any issues you may observe when applying it to your simulations.

The grain segmentation algorithm is illustrated in the figures below. The local structural environment is determined for every atom using PTM (left). PTM also determines the local orientations (colored, middle) but does not explicitly group atoms into grains. Hierarchical clustering is used to identify grains (right).

Structure

Lattice orientation

Segmented grains

Algorithm selection

The modifier creates grains by performing hierarchical clustering on the nearest-neighbor atom graph. Two types of hierarchical clustering algorithms are implemented:

Graph Clustering (automatic / manual)

Graph edge weights are initialized as \(\exp(-d^2/3)\), where \(d\) is the misorientation in degrees between two neighboring atoms. Grains are built up by contracting edges using the Node Pair Sampling method of Bonald et al..

This algorithm produces good segmentations in a range of microstructure types. It performs well on low-angle grain boundaries and can discriminate between grains and sub-grains. A drawback is that the merge distance threshold parameter does not have an intuitive physical meaning.

The automatic mode alleviates this problem by choosing a good merge threshold automatically for you using a statistical analysis of the sequence of graph merging steps, stopping the merging of crystallite clusters as soon as a deviation from the regular exponential behavior is observed.

Minimum Spanning Tree

In this algorithm the graph gets replaced by its minimum spanning tree. The edge weights are the misorientation angles between neighboring atoms. Grains are built up by contracting edges in sorted order (by misorientation, low to high). The distance of a contraction (or merge) is simply the edge misorientation.

This is a fast algorithm which has lower memory usage. The merge distance has a simple interpretation (misorientation between neighboring atoms or crystal clusters) and is scale invariant. Drawbacks are that it can produce poor results in microstructures containing low-angle grain boundaries, and it performs poorly in the presence of local perturbations due to, e.g., thermal atomic displacements or elastic lattice distortions. This method is best suited for low-temperature simulations.

This approach is similar to that of Panzarino and Rupert. The key differences are the use of PTM (more robust structural determination), a faster algorithm (minutes instead of days), and the formulation as a hierarchical clustering problem (effects of cutoff choices are visible).

Parameters and options

Log merge threshold

Specifies the maximum graph edge contraction distance and determines the resulting number and sizes of grains. A lower threshold produces more (and smaller) grains; a larger threshold produces fewer (and larger) grains. The scatter plot (“Log merge distance” vs “Merge size”) can be used to select an appropriate merge threshold value. If the grains are well-separated, the scatter plot will contain a dense cluster at low distances, and a few isolated points at higher distances. An ideal threshold lies after the dense cluster, but before the isolated points (see screenshot). Note that this threshold parameter can be set to a negative value, because it is specified on a logarithmic distance scale.

Minimum grain size

Grains below this minimum number of atoms are dissolved. Atoms in sub-critical grains, which get dissolved, will become orphan atoms (see option Adopt orphan atoms).

Adopt orphan atoms

After clustering has been performed by the algorithm, some atoms might not be assigned to a grain, so-called “orphan” atoms (according to Hoffrogge and Barrales-Mora). This includes atoms that are part of grain boundaries. This option lets the modifier assign these orphan atoms to the nearest grain.

Handle coherent interfaces/stacking faults

This option lets the algorithm merge atoms having hexagonal crystal structures (e.g., HCP) with atoms having cubic structures (e.g., FCC) at stacking faults or other types of coherent crystal interfaces. Thus, stacking faults will become part of the surrounding grain if this option is enabled. Furthermore, atoms belonging to the cores of coherent twin boundaries will be attributed to one of the two adjacent grains.

Color particles by grain

This option assigns each grain a unique color for easier visualization of the grain structure.

Output bonds

Whether to visualize the edges of the initial neighbor graph as bonds between atoms. Local lattice disorientations are output as a bond property named Disorientation, which may be visualized using the Color coding modifier of OVITO. This output option is mainly meant for debugging purposes and has large memory requirements. It is not recommended for large datasets.

Example

The panel below illustrates the effect of varying the merge threshold in a polycrystalline graphene sample, using the Graph Clustering algorithm. A good segmentation into 6 grains is achieved using a merge threshold of 14 (left). Reducing the threshold to 13.5 reveals a subgrain structure in the largest grain (middle). A further reduction of the threshold to 12.5 splits the largest grain into three subgrains (right).

Note that the difference between subgrains and grains is not well defined. It is therefore up to the user to decide upon the best threshold value.

6 grains	7 grains	8 grains

See also

ovito.modifiers.GrainSegmentationModifier (Python API)