The eld of Materials Science is concerned with, e.g., properties and performance of materials. An important class of materials are crystalline materials that usually contain \dislocations" { a line-like defect type. Dislocation decisively determine many important materials properties. Over the past decades, signi cant e ort was put into understanding dislocation behavior across di erent length scales both with experimental characterization techniques as well as with simulations. However, for describing such dislocation structures there is still a lack of a common standard to represent and to connect dislocation domain knowledge across di erent but related communities. An ontology o ers a common foundation to enable knowledge representation and data interoperability, which are important components to establish a \digital twin". This paper outlines the rst steps towards the design of an ontology in the dislocation domain and shows a connection with the already existing ontologies in the materials science and engineering domain.
Dislocation { one-dimensional lattice defects in crystalline materials { are
responsible for plastic deformation of, e.g., metals or semiconductors, and play
an important role concerning mechanical properties such as the hardening
behavior. Since the dislocation had been postulated in the 1930s by Orowan [
During the past years, data-driven approaches made new methods and tools
for analyzing and understanding the evolution of dislocation systems possible
[4{6]. Similarly, the whole eld of Materials Science and Engineering (MSE), a
parent domain of the specialized domain of dislocations, is currently also
undergoing almost disruptive change. This change brings simulations and experiments
together, enabled by data-driven/data science approaches, and ultimately makes
the digital transformation in the eld of MSE possible [7{9]. One of the key
enabler of the digital transformation is the Digital Twin (DT) [
In this work, rst steps towards formalizing the knowledge of dislocations together with the relevant details concerning the crystallography are introduced. Emphasis is put on representing the dislocation geometry, utilizing semantic formalization using an ontology. We start by designing and modeling a formal de nition of crystalline materials in terms of the underlying crystallography including slip plane and slip direction. The former is the plane to which the motion of the dislocation is generally constrained, the latter is the direction along which plastic deformation takes place. Those should be explicitly described along with the idealization of dislocation as a mathematical line and other required details of crystalline materials.
The paper is organized as follows. Section 2 presents related work of materials science domain ontologies and points out the existing gaps. Section 3 describes the physical aspects of dislocations along with the proposed ontology. Finally, Section 4 concludes and sketches the envisioned future work. 2
Over the past three decades, a number of groups were involved with explicit
conceptualization of the knowledge of their own MSE domains by means of
ontologies. One of the earliest materials ontology is the Plinius ontology [
Another ongoing e ort to establish semantic standards that apply at the
highest possible level of abstraction, under which all conceivable domain ontologies
can be subsumed and interoperated, is the European Materials and Modelling
Ontology (EMMO)1 developed by the European Materials Modelling Council
(EMMC)2. It provides a common semantic framework for describing materials,
models, and data with the possibility of extension and adaptation to other
domains. For instance, the authors in [
Apart from work related to EMMO, e orts also have been made to represent
the domain knowledge of crystal structures. The authors of MatONTO [
Recent development work concerning the Materials Design Ontology (MDO)
[
2 https://emmc.eu 3 https://www.iucr.org/ ontologies in terms of the representation of crystalline defects. Therefore, in this work, the rst steps towards ontology design of dislocations in crystalline materials are taken. For this, the terms from MDO will be connected and reused, especially these terms that describe the crystal structure, e.g., the atom entity and the lattice to enable data interoperability between domains.
Description of the Physical Domain and Ontology Design 3.1
Representation of Crystalline Materials and Line Defects
Before the ontology is designed, the most relevant concepts and notions for
crystalline materials and line defect are now described. This is by far not a
complete introduction; for more information the reader is referred to, e.g., [
Crystalline materials are characterized by a periodic arrangement of the constituent atoms (see Fig. 1, left for an example). The representation of crystal structures consists of the lattice together with a motif : the lattice is a mathematical concept of an in nite, repeating arrangement of points in a space (3D), in a plane (2D), or on a line (1D), in which all points have the same surrounding and coincide with atom positions. The motif (or base) consists of an arrangement of chemical species which in the real crystal can be atoms, ions, or molecules. One can now identify a smallest pattern of atoms which upon repetition along all spatial directions would again cover the whole structure: this pattern is the unit cell, shown as the black parallelepiped in Fig. 1. The edge lengths of this cell de ne the three lattice parameters. As shown in Fig. 2, to fully characterize the unit cell altogether six parameters are needed: three lengths, (a; b; c) and three angles ( ; ; ). Based on these parameters, unit cells are often classi ed into a crystal system. There are seven distinct crystal systems, often ordered according to the increasing symmetry: cubic, tetragonal, orthorhombic, hexagonal, trigonal, triclinic, and monoclinic. E.g., the cubic structure has a = b = c; = = = 90 and the monoclinic structure has a 6= b 6= c; = = 90 ; 6= 90 .
Based on these de nitions one can now de ne lattice points, lattice directions, and lattice planes as shown in Fig. 3: the lattice consists of a set of lattice points (which are the points where atoms or molecules are located), a lattice direction or lattice vector is a vector connecting two lattice points, and a lattice plane, forms an in nitely stretched plane (characterized through a plane normal) that cuts through lattice points such that again a regular arrangement of lattice points in the plane occurs. Real crystalline materials generally don't have perfect order of atoms { at least not everywhere. Typically, a piece of material contains a large number of crystalline defects where the local order of the crystal structure is destroyed. Such a defect might be a point defect (e.g., a missing atom) or a line defect/dislocation (a strongly localized, tube-like region of disorder, which contains in the center the highly disordered dislocation core). While in general the notion of \defect" has a somewhat negative connotation, it is exactly this deviation from the perfect structure that result in important, e.g., electrical, mechanical, or thermal properties. In the following the one-dimensional defect type is considered; other defects will be discussed in a follow up publication.
In the context of plastic deformation, a dislocation is de ned as the boundary of a slipped area within which atoms are displaced by the size of an elementary unit translation given by the so-called Burgers vector. Yet, the question arises on which granularity level a dislocation should be de ned? One can de ne it in terms of displaced atoms, or { as will be done in the following { one can take a mesoscopic view where individual atoms are no longer visible and the tube-like defect \region" is in fact reduced to a mathematical line. The motion of this line through the crystalline material is constraint to a speci c crystallographic plane. Details of the motion are determined by details from the atomic scale which is why the full crystallographic information still is required, even though the \defect region" is now idealized as mathematical line. These two di erent levels of detail requires particular attention when it comes to designing the dislocation ontology.
The motion of the dislocation is constrained to a speci c crystallographic plane, called the slip plane. Within the slip plane, there are speci c slip directions along which plastic deformation occurs, given by the so-called Burgers vector. A slip system is then de ned as the set of slip planes with the same unit normal vector and the same slip direction is de ned. Thus, the slip system is fully determined by the unit normal vector and the slip direction or the Burgers vector (where the latter is not a unit vector).
On the mesoscale, the mathematical dislocation object as shown in Fig. 4 is a directed curve that has a start point and an end point. The local line orientation changes along the line while the Burgers vector is constant for each point of the line. Lastly, since the dislocation is a directed curve it has a line sense which unlike the local line orientation is a property of the whole line.
start end dislocation line local line direction Burgers vector
Ontology Design The ontology design of dislocations in crystalline materials begins with the conceptualization of the crystal structure, followed by that of dislocations in crystalline materials. For this, the Crystal Structure module and the Dislocation module are developed. As shown in Fig. 5, the classes from MDO4:Lattice and MDO:Occupancy de ning the lattice concept and the motif concept as an arrangement of chemical species in the crystal structure, respectively, are connected and reused.
The MDO contains only the class MDO:Lattice but does not contain any terms such as lattice point, lattice direction, and lattice plane. These will be added in our ontology. The MDO:Lattice class is re ned such that each lattice individual consists furthermore of a UnitCell which is de ned through the six lattice parameters (LatticeParameterLength and LatticeParameterAngle).
Given that the dislocation moves on a preferred plane, the slip plane, the slip plane concept needs to be described rst. As shown in Fig. 5, CrystalStructure has the SlipPlane (a subclass of LatticePlane) and SlipSystem. Furthermore, on the SlipPlane there are speci c directions called SlipDirection along which plastic slip happens and which is a subclass of the LatticeDirection. Finally, each CrystalStructure individual has a SlipSystem consisting of normal direction (SlipPlaneNormal) and SlipDirection of the respective slip plane. The dislocation module as shown in Fig. 6, represents the Dislocation LatticePoint
hasLatticePoint hasLatticePoint LatticeParameterAngle hasLatticeParameterAngle
hasUnitCell UnitCell hasLatticeParameterLength hasLatticePoint
LatticePlane hasLatticePlane
LatticeDirection hasLatticeDirection rdfs:subClassOf hasLatticeDirection MDO:Lattice hasLattice
SlipPlane hasSlipPlane CrystalStructure hasOccupancy rdfs:subClassOf
hasSlipDirection hasSlipPlaneNormal
hasSlipSystem hasCrystalStructure
SlipDirection
consistsOf SlipPlaneNormal consistsOf SlipSystem LatticeParameterLength
MDO:Occupancy
CrystallineMaterial as subclass of a CrystallineDefect from which all crystalline defects (zerodimensional up to three-dimensional defects) are derived. The Dislocation relates to BurgersVector and LineSense. Furthermore, since the dislocation only moves on a preferred type of plane, a relation between the Dislocation and its SlipPlane is de ned. The CrystallineMaterial together with the SlipPlane are the link to the crystal structure module.
LineSense
CrystallineDefect In this paper, steps towards an ontology design of dislocations in crystalline materials are presented. This has been done by developing a modular ontology of crystal structure and dislocation where common classes from the MDO have been reused and adapted. Future work will focus on the re nement of the above introduced concepts, so that further aspects and concepts from the materials science domain are included. Examples of this extension are the di erential geometrical representation of dislocations as curved lines, consideration of the Bravais lattice but also other types of defects (e.g., point defects, grain boundaries). In addition, to extend the interoperability between domain ontologies especially within the MSE community, ontology alignment into EMMO also would be a very worthwhile undertaking. 5
AI and SS acknowledge nancial support from the European Research Council through the ERC Grant Agreement No. 759419 MuDiLingo ("A Multiscale Dislocation Language for Data-Driven Materials Science") and Helmholtz Metadata Collaboration (HMC) within the Hub Information at the Forschungszentrum Julich.