You know there is ⅛ of an atom on each of the 8 corners of the rhombohedron, which adds to one full atom with a spherical radius of. There is no simple answer for the simple tetragonal APF, because the answer changes depending on the a/c ratio. If you wanted to describe the simple tetrahedral crystal with math, you would describe the cell with the vectors: This close-packed direction would therefore have a length of 2r. The close-packed direction is along the short edge(s) of the tetragon, so either a and b, or c. The tetragon is defined as a parallepiped with two sides (a and b) equal and a third side (c) of different length. If the tetragon is elongated so that a=bc, there will be 2 true nearest-neighbors. However, the true depiction depends on whether the cube is elongated or compressed. Simple cubic has 6 nearest-neighbors, so if the distortion is very small, you might consider that all 6 bonds are still the same length, giving CN = 6. You can imagine taking a cube and elongating it, or shrinking it, along one direction. The simple tetragonal unit cell is a distortion of the simple cubic unit cell. However, there are still materials made of multiple kinds of atoms that have a primitive tetragonal Bravais lattice, such as AuCu. Simple Tetragonal Atomic Packing FactorĬommon Examples of Simple Tetragonal Materials.Common Examples of Simple Tetragonal Materials.Simple tetragonal has 1 atom per unit cell, lattice constant a = 2R (ac), Coordination Number CN = 6 (4 or 2), and Atomic Packing Factor APF < 52%. Pure materials never take this crystal structure, and it exists only mathematically. The simple tetragonal unit cell can be imagined as a cube that is slightly taller or shorter in one direction, with an atom on each corner. There is no prototype or Strukturbericht for simple tetragonal. The simple tetragonal unit cell would belong to space group #123 or P4/mmm, with Pearson symbol tP1. There are “primitive tetragonal” crystals, which exist with multiple atoms that overall display primitive tetragonal symmetry. If this structure were to exist, it would be a rectangular prism with an atom on each corner. If you are new to materials science and don’t know what something means, you can check out my articles on the FCC, BCC, or HCP crystals, which explain terminology more slowly.Īs far as I know, there are no real-world materials that exhibit a simple tetragonal unit cell. If you’re searching for information about simple tetragonal crystal cells, I’m assuming you’re a somewhat advanced student in materials science, so I’ll give you the facts quickly and with little explanation. Alright, now we’re getting to the less-common crystal structures.
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