PPT – Lecture 3: More on Structures, Miller Indeces, Stereographic Projection PowerPoint Presentation – ID:3384893

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. Some compound structures that derive from fcc with insterstitial sites filled:TiN (NaCl structure)N at octahedral sites,as many as atomsTiH2 (CaF2 structure)H at tetrahedral sites,twice as many as atomsTiH (ZnS, zinc blende)H only in every other tetrahedral site,related to diamondTi alone is hcp. The size of atoms varies amazingly little, given the large increase in the number of electrons. Especially true for the meals used in typical alloys.Notice the small sizes of H, B, C, N. Defining the size of atoms is not trivial, they are not rigid balls. The atom-atom distance depends on the character of the bond. The elementary vectors of translation, i.e. the edges of the elementary cell, define the unit vectors of our coordinate system. Directions and planes are defined in this coordinate system. It is identical to the ordinary rectangular coordinate system with identical scales only for cubic structures. Usually we are interested in directions where u, v, w are small integers. Standard notation for a direction: [u v w] Some planes of the [0 0 1] zone(A zone is the set of all planes that are parallel to the given direction.Weiss zone law: hu + kv + lw =0) Complications with the hcp structureIn the ideal case, lattice parameters a and c are related:a = edge of hexagon = diameter of atoms c = twice the distance between layersThe red tetrahedron is regular, thusc/a = 1.62 for Mg, Co, 1.86 for Zn, 1.58 for Ti In order to reflect symmetry in the basal plane, rather than (h k l) Miller indeces defined with two primitive vectors in the basal plane, the four-index Miller-Bravais notation is used: In order to represent a direction (or the normal of a plane) in a stereographic projection, intersect the reference sphere with the direction (P) then project P from the “South pole” of the sphere onto the equatorial plane. [0 0 1] direction points up. The intersection of directions with the sphere are projected to the equatorial plane from the [0 0 -1] point, the upper hemisphere is imaged. The more detailed standard [0 0 1] projection of a cubic lattice.Every type of direction appears in the shaded triangle, the rest relates by symmetry operations. Pole figure of rolled aluminum. The sample is looked at from the normal direction, the rolling direction (RD) and the transverse direction (TD) are the vertical and horizontal axis. Shade shows he probability of the indicated direction pointing in the given direction. Source.


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