China
Africa
Explore chapters and articles related to this topic
The Structure of Solids
Published in Joseph Datsko, Materials Selection for Design and Manufacturing, 2020
The Burgers vector is the distance, measured in multiples of the lattice parameter, that is needed to close a straight-sided loop around a dislocation by going the same number of lattice distances in all four directions. The term is used to define the size of a dislocation and is designated by the letter b. Figure 2–23 shows an edge and a screw dislocation the size of one Burgers vector. A characteristic of an edge dislocation is that it lies perpendicular to its Burgers vector, whereas a screw dislocation lies parallel to its Burgers vector.
Plastic flow Important regularities
Published in Lev Zuev, Autowave Plasticity, 2020
It is fundamental that strain localization is observed at all scale levels of this process, as was shown above. Even at the lattice scale level [Porubov, 2009], the propagation of elastic waves of sufficiently large amplitude is also accompanied by their localization and the formation of wave features due to the nonlinearity of the elastic medium [Ashcroft, Mermin, 1979]. As for dislocations, already in the first works devoted to their properties [Kontorova, Frenkel, 1938; Reed, 1957] (see also [Brown, Kivshar, 2008]), it was shown that the shift associated with breaking and restoring interatomic bonds is localized on the acting slip planes, while the material between these planes remains elastically deformed. In this case, the shift caused by one dislocation is equivalent to the displacement of one part of the crystal relative to another by the magnitude of the Burgers vector b of the dislocation. It follows from this that plastic deformation at the dislocation scale level is localized.
Structural Description of Materials
Published in Snehanshu Pal, Bankim Chandra Ray, Molecular Dynamics Simulation of Nanostructured Materials, 2020
Snehanshu Pal, Bankim Chandra Ray
The Burgers vector can be defined as a vector of lattice distortion, which arises out of dislocation in a crystal lattice. It is represented as a bold letter “b.” Jan Burgers, a Dutch Physicist, coined this term. The significance of the Burgers vector can only be understood once we compare a dislocation-free crystal with that of a crystal having dislocations. Thereby, the magnitude and direction of the Burgers vector can be visualized clearly in Figure 1.44.
Displacement field due to glide and climb of rectilinear dislocations in gradient elasticity
Published in Philosophical Magazine, 2021
A screw dislocation is visualised as the result of cutting crystal along a half-plane and then sliding one half across the other to a distance of the Burgers vector that is parallel to the edge of the cut, as depicted in Figure 4. As is evident from this figure, the non-vanishing component of the displacement field is , which varies with only x and y: If the cut surface is defined on the half-plane , has the following property In fact, the cut surface is the surface swept by the dislocation and whereby the adjacent atoms on the two sides of the cut are displaced relative to each other. To obtain this discontinuity in an isotropic medium, we can assume that the displacement increases uniformly with the angle θ, The relation for θ in the Cartesian coordinate system is [25] Modern computer languages have specific functions for ; for example, ArcTan[x,y] in Mathematica, atan2 in MATLAB and arctan2 in NumPy library of Python can be applied for this purpose.
Electro-elastic dislocations in piezoelectric materials
Published in Philosophical Magazine, 2020
Eleni Agiasofitou, Markus Lazar
Dislocations in piezoelectric materials can strongly influence the performance and properties of electronic devices. A dislocation in an elastic medium is characterised by the Burgers vector, which represents the jump of the displacement vector. A dislocation in a piezoelectric medium can possess additionally a jump in the electric potential produced in the Volterra process in order to create the dislocation. Studying dislocations in piezoelectric materials, Barnett and Lothe [20] were the first to mention that the jump in the electric potential corresponds to an electric dipole layer along the cut plane. In this work, we use the terminology electro-elastic dislocation to refer to a dislocation in a piezoelectric material, that is characterised by the jump of the displacement vector and the jump of the electric potential along the dislocation surface. Furthermore, the dislocation core may be subjected to a line force and an electric line charge. Barnett and Lothe [20] generalised Stroh's six-dimensional framework to an eight-dimensional framework that includes the Burgers vector and a line charge in order to treat a charged dislocation in piezoelectric insulators. A closed-form solution of an electro-elastic screw dislocation, which suffers a finite discontinuity in the displacement vector and electric potential across the slip plane, and has a line force and an electric line charge along its core, was given by Pak [21] for piezoelectric hexagonal materials. Wang and Pan [22] investigated screw dislocations possessing a Burgers vector and a jump in the electric potential in piezoelectric nanowires. Minagawa [23] studied the stress and electric fields produced by straight dislocations and dislocation loops in a piezoelectric crystal considering only a discontinuity in the displacement vector and neglecting the jump in the electric potential. Electro-elastic dislocations (straight dislocations and dislocation loops) having finite discontinuities in both the displacement vector and the electric potential across the dislocation surface were studied by Nowacki [24], Nowacki and Alshits [25] and Han and Pan [26] for piezoelectrics. The fields produced by an arbitrary three-dimensional dislocation loop in general anisotropic piezoelectric bimaterials have been studied by Han and Pan [27].