Input: | Output: |
![]() |
![]() |
This analysis modifier identifies all dislocations in a crystal, determines their Burgers vectors, and outputs a line representation of the dislocation defects. The modifier implements the so-called Dislocation Extraction Algorithm (DXA), a unique computational method developed by the author of OVITO. The original DXA method has been described in the paper
The current implementation in OVITO follows a newer, more general approach, which has been described in a follow-up paper:
Please cite the latter reference when using the Dislocation analysis modifier. A short overview over how the DXA works can be found at the end of this page.
The DXA transforms the original atomistic representation of a dislocated crystal into a line-based representation of the dislocation network. It determines the true Burgers vector of each dislocation segment and identifies dislocation junctions. The algorithm can recognize partial dislocations and also certain secondary grain boundary dislocations (e.g. twinning dislocations).
Note that, even though the implementation of the DXA in OVITO is highly optimized, the algorithm is computationally expensive and requires sufficient working memory. The minimum memory requirement is 1 kilobyte per input atom! Thus, to analyze a dataset containing 1 million atoms, at least 1 GB of free memory must be available. Otherwise your operating system may start swapping data to disk and become unresponsive.
This parameter specifies the lattice type of the input crystal. Currently, simple crystal stuctures such as FCC, HCP, BCC, and diamond are supported. The DXA ignores the chemical atom types. Thus, a zinc blende structure, for example, can simply be treated as a cubic diamond crystal.
The selected input crystal type tells OVITO how to identify the local coordination structure of each atom and how to compute the local crystal orientation. The selected crystal type also determines how the computed Burgers vectors are represented (three-component notation for crystals with cubic symmetry, four-component notation for hexagonal crystals).
Furthermore, for each available crystal type, OVITO defines a set of dislocation classes into which the extracted dislocation lines are grouped. Dislocations with a Burgers vector that does not belong to any of the predefined families are assigned to the category "Other". Currently, the list of dislocation classes is hardcoded and cannot be changed by the user. Please contact the developer if you think that a new dislocation class should be added for a certain crystal type.
This sets the maximum length of trial Burgers circuits, which are constructed by the DXA to discover dislocations in the crystal. The maximum circuit length is specified in terms of the number of atom-to-atom steps. Dislocations whose core is too wide to be enclosed by a circuit of the given maximum length will not be found by the algorithm.
The default value for this parameter is 14, which is sufficient to discover all typical lattice dislocations in the types of crystals supported by the modifier.
Once the DXA has discovered a dislocation segment and constructed a Burgers circuit around its dislocation core, the algorithm advances the circuit along the dislocation to generate a line presentation of the segment. The thickness of the core may vary along the dislocation (e.g. it becomes wider close to a dislocation junction). This is why the circuit has a certain amount of elasticity, which is set by the stretchability parameter. A value of 9 (the default), for example, allows the circuit to expand to a length that is nine steps longer than the limit set by the trial circuit length parameter above.
This option enables an additional algorithm step which enhances the identification of dislocations in some situations. The DXA then tries to reconstruct the mapping of the physical crystal to an ideal crystal from available information on the surrounding atoms. The goal of this step is to further extend the good crystal region and reduce the bad region around defect cores as far as possible. As a result, dislocations can now be found that have very wide cores or which are located in highly distorted crystal regions. For example, it may become possible in certain cases to extract the complete (primary) dislocation content of a grain boundary with this option, even if the dislocation cores overlap.
However, the reconstruction step may have side effects: The automated algorithm may report spurious dislocations in highly distorted regions of a crystal (i.e. containing a very dense accumulation of defects), which a human would not consider proper dislocations. For example very short segments, sometimes even shorter than their core diameter. Furthermore, as another side effect, the location and shape of regular dislocations reported by the algorithm may be less accurate if this option is enabled. The reason is that the Burgers circuit constructed by the algorithm will no longer enclose the original, extended core of a dislocation, but an artificially shrinked version. However, the computed Burgers vector will not be affected by this.
Please use this option only if you have experience in manually identifying dislocations in atomistic simulations so you can verify the output of the algorithm if necessary.
Tells the analysis modifier to display the so-called interface mesh, a closed manifold which separates the good crystal region from the bad crystal region. This is a geometric structure computed internally by the algorithm, which is normally not of interest. In other words this option is only for debugging purposes and allows to follow the intermediate stages of the algorithm.
This option restricts the analysis to the subset of currently selected atoms. When activate, unselected atoms will be ignored (as if they did not exist) and will be assigned the structure type "Other". This option can be useful if you want to identify dislocations in a crystal with a structure not supported by the modifier, but which has a sublattice that is supported (and you do not want to delete atoms belonging to the other sublattice(s) for some reason).
The raw dislocation lines generated by the DXA are typically noisy (due to the atomistic nature of the dislocation cores) and need to be post-processed to produce smooth dislocation curves. This parameter controls the number of iterations of the smoothing algorithm to perform.
The raw dislocation lines generated by the DXA consist of a very dense sequence of points. To produce smooth lines, the number of points is reduced in a post-processing step. This parameter controls the desired distance between successive points along a dislocation line. The distance is only an approximate number and is measured in multiples of the interatomic spacing in the underlying crystal.
The raw defect mesh generated by the DXA contains atomically sharp steps and needs to be post-processed to produce a smooth surface. This parameter controls the number of iterations of the smoothing algorithm to perform.
After analyzing the atomistic input crystal, the modifier produces serveral pieces of output:
The dislocation segments identified by the DXA are output as continuous lines. Each dislocation segment has a starting point and an endpoint. The two define the orientation of the dislocation line (the line sense). Each end may be part of a junction, where it is connected to other dislocation segments, or it may be a dangling end. Dislocations that merge into a crystal's surface or into other extended defects have dangling ends. If a dislocation is a loop, its starting point forms a 2-junction with its endpoint. Dislocation loops need not be loop-shaped; they can also be infinite lines, going through a periodic boundary of the simulation cell.
In addition to this geometric information, each dislocation segment has two additional properties: The ID of the crystallite cluster it is embedded in (see below) and its Burgers vector. The Burgers vector computed for a segment is its true Burgers vector, i.e. a vector in the ideal reference crystal frame.
As part of the dislocation identification process, the DXA divides the input crystal into a so-called good and a bad region. Within the good crystal region the algorithm was able to map atoms to a perfect reference state. This part of space includes atoms that are in a perfect crystalline environment (which may be subject to slight elastic distortions), stacking faults, and coherent grain boundaries. The bad crystal region, in contrast, comprises those parts where the atomic arrangement does not resemble a perfect crystal (or any of the planar defects mentioned above). The cores of dislocations belong to the bad crystal region as well as other, unidentified defects, the outer surfaces, and voids within the crystal.
The DXA constructs the dividing surface which separates the good from the bad crystal region. This interface mesh is a two-dimensional manifold that encloses the dislocation cores and all other defects in the crystal (except stacking faults and certain grain boundaries, which have been classified as being part of the good region). This intermediate geometric data structure allows the DXA to effectively find dislocation lines by applying the Burgers circuit construction. Those parts of the interface mesh which are associated with dislocations will subsequently be removed. The remaining parts, which enclose non-dislocation defects, form the so-called defect mesh. It is a triangulated mesh, which is output by the DXA analysis modifier, and which represents the bad crystal regions that have not been classified as dislocations.
As part of the DXA a structure identification is performed, in which the local environment of each atom is analyzed to identify
atoms that form a perfect crystal lattice. This information is output by the modifier as a new particle property
named Structure type
. The atomic structure identification is based on the common neighbor analysis method,
and the results are very similar to what you would get by applying the Common Neighbor Analysis
or the Identify Diamond Structure modifier.
Note that the list of structure types the algorithm looks for depends on the selected input crystal type. For example, if the selected input crystal type is "FCC", then the DXA will only look for atoms in FCC and HCP arrangements. The latter form stacking faults and coherent twin boundaries and are therefore important for the identification of partial dislocations in the FCC lattice.
After the atomic structure identification step is completed, the DXA combines atoms into clusters. A cluster is a contiguous crystallite consisting of atoms of the same structural type (e.g. "FCC"). Atoms that are part of an FCC stacking fault, for instance, are grouped into an HCP cluster. Another example: An FCC bicrystal with a coherent twin boundary gets divided into three clusters: Two FCC clusters for the grains and one HCP cluster that comprises the atoms of the boundary core.
Each cluster created by the algorithm has a unique ID (a positive integer), and the modifier outputs the assignments of atoms to clusters as
a new particle property named Cluster
, containing the ID of the cluster the atom belongs to.
Atoms with an undentified coordination structure are not part of any cluster, which is indicated by the special value 0.
The atomic clusters form an abstract adjacency graph, which is built up by the algorithm. For example, a bicrystal with two grains separated by a grain boundary can be described in terms of a graph with three nodes (the three atomic clusters) and two edges connecting both grains with the grain boundary cluster. Each cluster establishes a local lattice coordinate system, and the true Burgers vector computed by the DXA for a dislocation embedded in a crystal cluster is expressed in this coordinate frame. A graph edge connecting two adjacent cluster carries information about their crystallographic orientation relationship. This orientation relationship, which is described in terms of a transformation matrix, can be used to rotate vectors from the lattice coordinate frame of one grain to other grain. Ultimately, this abstract description of a polycrystalline microstructure enables the identification of dislocations (which can involve Burgers circuits that cross grain boundaries and stacking faults).
Even though the cluster graph is generated by the DXA modifier as an intermediate data structure, OVITO currently provides no means for the user to access or visualize this output data. Future versions of the program may come with a user interface that allows to inspect the generated cluster graph.
Note that you can position the mouse cursor over an extracted dislocation line in the viewports to let OVITO display its properties in the status bar of the main window.
What follows is a brief summary of the Dislocation Extraction Algorithm (DXA). If you are interested in more details, please have a look at this paper.
![]() |
Burgers circuit method to detect and identify a dislocation. A closed circuit around the dislocation is translated from (a) the dislocated crystal to (b) the perfect reference crystal. The closure failure is called the Burgers vector of the dislocation. |
The fundamental concept underlying the DXA is the Burgers circuit construction [Frank1951], which is the canonical method already proposed in the 1950s to discriminate dislocations from other crystal defects and to determine their Burgers vectors. In the formulation employed here, a Burgers circuit C is a path in the dislocated crystal consisting of a sequence of atom-to-atom steps (line elements Δx), as shown in the figure.
We assume that there exists a mapping Δx→ Δx' that translates each line element of the path to a corresponding image, Δx', in a perfect crystal lattice. Summing these transformed line elements algebraically along the associated path, C', gives the true Burgers vector of the dislocation enclosed by C:
The Burgers vector b is the closure failure of the path after transferring it to the perfect reference crystal. Notably, the resulting vector b stays the same if we change the original circuit C, as long as it still encloses the same dislocation. On the other hand, if b=0, we know that the Burgers circuit did not enclose any defect with dislocation character (deliberately ignoring the possibility that the circuit encloses multiple dislocations whose Burgers vectors cancel).
Typically the Burger circuit construction is performed by hand to analyze two-dimensional crystal images obtained from high-resolution microscopy or atomistic computer simulations. Human intuition and cognitive capabilities are required to spot irregularities in the crystal lattice which are potential dislocation defects and to map path steps in elastically distorted crystal regions to the ideal lattice. Automating these tasks poses a particular challenge when developing a dislocation identification algorithm. First of all, an efficient strategy is needed that guides the construction of Burgers circuits, given that there is no a priori knowledge of the dislocation positions, because it clearly is not feasible to enumerate all possible circuits in a crystal to find the contained dislocations.
![]() |
(a) Delaunay tessellation of a dislocated crystal. Defect core atoms as identified by a structural characterization technique are shown in a darker color. (b) Colored arrows indicate the computed mapping of tessellation edges to corresponding ideal lattice vectors. Bad tessellation elements, for which the mapping to the perfect reference lattice cannot be determined, have been marked with a gray color. (c) Color legend for the eight different ideal lattice vectors appearing in (b). |
Within the DXA framework, this problem is addressed by using the Delaunay tessellation of the dislocated input crystal (figure a). The edges of this tessellation define the set of elementary atom-to-atom steps from which Burgers circuits will be constructed. Before generating any circuits, the algorithm first tries to map each edge of the Delaunay tessellation to a corresponding vector in the perfect reference crystal (figure b). This is done with the help of the Common Neighbor Analysis (CNA) method, which finds atoms that form a perfect (but elastically strained) crystal lattice. Delaunay edges connecting a crystalline atom with one of its neighbors are mapped to the corresponding ideal lattice vectors by the algorithm.
Within the cores of dislocations, the atomic arrangement deviates considerably from a perfect crystal. Hence, the CNA will classify these core atoms as non-crystalline atoms. All tessellation edges adjacent to such atoms will be marked as "bad" by the algorithm, effectively excluding them from any Burgers circuits to be constructed. This corresponds to the original principle formulated by F. C. Frank, which states that a valid Burgers circuit must not pass through so-called bad crystal. Good crystal regions, in contrast, are defined as those parts where the mapping to the perfect reference crystal is nonambiguous. In fact, the DXA also divides space into good and bad regions in this spirit as shown in figure (b). Those Delaunay elements (triangles in 2D, tetrahedra in 3D systems) that are adjacent to one or more bad edges, which could not be mapped to an ideal lattice vector, are themselves marked as bad elements, while all others are considered good volume elements.
Now it is time to think about how to efficiently construct trial Burgers circuits to find and classify the dislocations in the crystal. As mentioned above, the total number of possible circuits in a three-dimensional crystal is prohibitively large, and we need to find a way to considerably reduce the search space. The solution is provided by the aforementioned partitioning into good and bad regions, which defines a boundary surface separating the two regions. In three-dimensional systems this boundary is called the interface mesh and is constituted by those triangular Delaunay facets having a good tetrahedral element on one side and a bad element on the other.
![]() |
Illustration of the line sweeping phase of the DXA. After constructing the interface mesh enclosing the defect core atoms, the algorithm uses a Burgers circuit on the interface mesh to sweep the dislocation line. While the Burgers circuit is being advanced in a step-wise fashion, triangle by triangle, a continuous line representation of the dislocation defect is produced. |
The interface mesh, which is depicted in this figure, is a two-dimensional manifold that encloses all defects in the crystal (including non-dislocation defects and even free surfaces of the crystal). Constructing trial Burgers circuits on this triangulated surface is sufficient to discover all dislocations. Moreover, this approach helps to ensure that the generated Burgers circuits enclose only single dislocation lines. Trial circuits generated by the DXA on the interface mesh are closed sequences of tessellation edges, and their Burgers vectors are computed from the equation above by summing the respective ideal lattice vectors, which were determined in the first algorithm step. All possible trial circuits up to some prescribed maximum length (modifier parameter Trial circuit length) can be efficiently enumerated using a recursive search algorithm.
The algorithm enumerates all possible circuits on the interface mesh in order of increasing length until one with a non-zero Burgers vector is encountered. This seed circuit is subsequently used to discover the rest of the dislocation line. This happens by advancing the circuit on the interface mesh and sweeping along the dislocation line as indicated in the figure. During this sweeping phase, a one-dimensional line representation of the dislocation is generated by computing the new center of mass of the circuit each time it advances along the boundary of the dislocation core. Here, a circuit can be pictured as a rubber band tightly wrapped around the dislocation's core. As the circuit moves along the dislocation segment, it may need to locally expand to sweep over wider sections of the core, e.g. kinks or jogs. To prevent the circuit from sweeping past dislocation junctions or interfaces, a hard limit is imposed on the maximum circuit length (modifier parameter Circuit stretchability).