In previous issues, we have examined the simpler configurations of Bravais lattices we must now add the “bricks” or the constituent matter (atoms/ions/molecules). With the indicated choice of the primitive cell, we see that this symmetry is not locally conserved, in the sense that the unit cell does not exhibit this symmetry.įigure 5: Hexagonal pattern (Source: Introduction to Solid State Physics 2) Silicon carbide and gallium nitride An example is shown in Figure 2, where we have a 2D lattice with an evident hexagonal symmetry. In general, it follows a non-conservation of the symmetry of the lattice at the single-cell level. 1,2 Wigner-Seitz cellĪs stated above, the primitive cell can be chosen in several distinct ways. There are 14 symmetry groups and, therefore, 14 Bravais lattices, which in turn give rise to 230 crystal structures. By adding the identical transformation n → n ′ = n, the set of such transformations assumes the algebraic group structure, called the symmetry group of the Bravais lattice. Then we have the inversion n → n ′ = − n, and the mirror reflection with respect to an assigned plane. For the rotations, the corresponding symmetries are denoted, for example, with C 6, C 9 regarding the rotations of 60 ˚ and 90 ˚ and their integer multiples. More precisely, a generic vector n of the lattice is transformed into a vector n ′ marked out by the same node. In addition to translational symmetry, there can be rotational symmetries with respect to certain axes. Let’s consider, for example, a 2D lattice, as in Figure 1, where we see that it is possible to choose these vectors in several distinct ways. Assigning a lattice does not mean uniquely determining the vectors of the fundamental translations.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |