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Crystals consist of molecules or atoms that repeat regularly throughout real space. Regular repetition is translational periodicity. Therefore, translational periodicity in a crystal means that the electron density \(ρ(\textbf{r})\) at any point \(\textbf{r}\) follows the two equations: \[ρ(\textbf{r} + \textbf{T}) = ρ(\textbf{r}) \nonumber ...
15 lip 2022 · The translational symmetry of an ordered distribution of 3-dimensional objects can be described by many types of lattices, but there is always one of them more suited to the object, ie: the one that best describes the symmetry of the object.
Pure translation symmetry is characteristic of crystal structures, leading to concepts of lattices, unit cells, and crystal systems. Molecules, crystals, and other individual objects have point-group symmetry, while crystal structures, with their combination of translation with other forms of symmetry, are characterized by space groups.
Well, there’s symmetry to help you out! Instead of an infinite number of atoms, you only need to describe the contents of one unit cell, the structural repeating motif... and life could be even easier, if there are symmetry elements present inside the unit cell!
4 kwi 2013 · The molecular symmetry is called the point group of the molecule. A point group can be represented by a set of matrices W. The point group of a crystal is the symmetry group of the bundle of normals on the crystal faces. The set of all translations of a crystal is its translation group.
24 mar 2016 · In order to explain what crystals are and how their structures are described, we need to understand the role of symmetry, for this lies at the heart of crystallography. ‘Symmetry’ explains the different types of symmetry: rotational, mirror or reflection, point, chiral, and translation.
24 lip 2019 · Since a crystal is periodic by translation, a symmetry element such as a rotation axis, mirror plane or inversion centre within a crystal must be repeated at all positions that are equivalent by translation.
