![]() ![]() Together, the four are known as the basic rigid motions of the plane, which, in view of the fact that there are no others, is really a stupid nomenclature. It can be shown that there are only four plane isometries: translation, reflection, rotation and glide reflection. A projection of an orthorhombic lattice on the lattice plane (001) is given in. Isometry, also called rigid motion, is a transformation (of the plane in our case) that preserves distances. The importance of the glide reflection lies in the fact that it is one of the four isometries of the plane. If the translation part is trivial, the glide reflection becomes a common reflection and inherits all its properties.Īll these properties are implied by the definition of the glide reflection being a product of reflection and translation. Unless the translation part of a glide reflection it trivial (defined by a 0 vector), the glide reflection has neither fixed points, nor fixed lines, save the axis of reflection itself. Reflection maps parallel lines onto parallel lines. Reflection is isometry: a glide reflection preserves distances. Glide reflection changes the orientation: if a polygon is traversed clockwise, its image is traversed counterclockwise, and vice versa. ![]() The following observations are noteworthy: If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet. This applet requires Sun's Java VM 2 which your browser may perceive as a popup. One can easily verify that the same result is obtained by first reflecting and then translating the image. points and horizontal glide reflections which lie midway between lattice. The order of the two constituent transforms (translation and reflection) is not important. glide reflection G and a perpendicular translation Tt is a glide reflection G at. In Figure 3557d, the dark bands indicate that the electron beam is either parallel to a glide plane or vertical to a screw axis in the crystal, and the black crosses refer to forbidden reflections.Glide reflection is a composite transformation which is a translation followed by a reflection in line parallel to the direction of translation. For a screw axis or glide plane, if the projection of the unit cell in the beam direction has a symmetry, then the forbidden reflections would not be fully forbidden but would obviously be very weak. The odd order reflections in the direction of the axis will be forbidden if the glide plane is parallel to the electron beam. At Bragg condition, a horizontal twofold axis or twofold screw axis in the ZOLZ along g presents a mirror line of symmetry onto disk g, and this line runs normal to g, and a horizontal mirror plane or glide plane leads to a centric distribution of intensity in every CBED disk. The lattice parameters are a = 0.34 nm, and c = 1.137 nm.Ī vertical glide plane results in a mirror line in the CBED pattern. Electron diffraction pattern obtained from Zr 41Ti 14Cu 12.5Ni 10Be 22.5 in zone axis. Due to the absence of ZOLZ/FOLZ periodicity difference, we can know that there is no glide plane perpendicular to the direction.įigure 3557c. The electron diffraction pattern in Figure 3557c shows both ZOLZ and FOLZ reflections obtained from Zr 41Ti 14Cu 12.5Ni 10Be 22.5 in zone axis. Reflection conditions due to the existence of glide planes. In an upcoming section, theres a description of the 17 wallpaper groups, that is, the symmetry. ![]() But if it has a 60° rotation or a 120° rotation, the lattice must be hexagonal. If it has a 90° rotation, then the lattice must be square. Iii) Crystal planes and orientation relationships. If a pattern has a reflection as a symmetry, then its lattice has to be rhombic, rectangular, or square. With stereographic projections, we can easily visualize crystallographic features: For a given sense vector that points in one direction along the dislocation, the Burgers vector is invariant. When it is curved some parts can be a screw dislocation and some parts an edge dislocation. The line is not necessary to be straight. This extinction may occur, for instance, in the presence of a screw-axis or a glide planes because the multiple scattering contributions cancel each other even in the dynamical scattering regime due to destructive interference between contributions with opposite phase.Ī glide dislocation is generally a line boundary between the slipped and unslipped portions of the glide (slip) plane. Gjönnes-Moodie extinction is a type of dynamical extinctions in some electron diffraction patterns. ![]()
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