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All the centered Bravais lattices are redundant in the sense that it is possible to use a primitive cell of smaller volume instead. However, this often means that crystal symmetries are no longer aligned with the cell axes. For the orthorhombic system, you either have 2-fold rotation or screw axis parallel to the cell edges, or mirror planes or glide planes ...


5

Body-centered tetragonal is face-centered cubic only if $c/a=\sqrt2$. If you try your transformation with a $c/a$ value greater/less than $\sqrt2$, your "cube" will have lateral edges that are longer/shorter (resp.) than the basal edge and so really remains tetragonal. You can also read this the other way. If you are presented with a body-...


4

Monoclinic lattices do not have their two oblique axes equal; or in terms of point group symmetry, the $C_\mathrm{2h}$ symmetry characteristic of monoclinic lattices is promoted to $D_\mathrm{2h}$, therefore orthorhombic, when those two axes are equal. Your primitive cell has what would be the two oblique axes of a monoclinic cell equal, therefore retaining ...


4

Don't think of it so much as putting the center mass of an atom on a vertex but as matching the unit cell symmetry to the crystal symmetry. Take the definition from google below, I've bolded key parts: The smallest group of atoms of a substance that has the overall symmetry of a crystal of that substance, and from which the entire lattice can be built up ...


3

The CRC Handbook of Chemistry and Physics contains a dedicated compilation by H. W. King, titled «Crystal Structures and Lattice Parameters of Allotropes of the Elements». In case your research library is closed, you may access some of its editions freely or borrow them with the library card of archive.org. In case of the 97th edition (by 2016), the section ...


2

There are two equivalent ways to define the meaning of the Miller indices: via a point in the reciprocal lattice, or as the inverse intercepts along the lattice vectors. The reflecting plane are parallel to a plane that includes the following three points: $$\frac{\mathbf{a}_1}{h}; \frac{\mathbf{a}_2}{k}; \frac{\mathbf{a}_3}{l}$$ To show that the plane ...


1

In answer to you first question, no if hkl differ, yes if they do not. I try to explain below. In a crystal the unit cell defines the repeating unit. Inside the unit cell the atoms are arranged as they are in the molecular structure with the molecule being at the same angle and position within each of the unit cells. Each atom scatters the x-ray radiation ...


1

The picture is not a lattice, it is a periodic pattern. In a lattice, all lattice points are related by the translational symmetry given by the unit cell vectors. I can take any two lattice points and take the vector between them. Then, when I add that vector to any other lattice points, I should land on another lattice point. This is not the case here. If ...


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