Posted by Steve Simon on February 16, 2014, 3:27 pm, in reply to "Lattices"
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You define a crystal as a lattice times a basis. You define the PLVs to define the lattice. If you have more than one atom in the unit cell, you need a basis as well to give the position of all of the atoms in each unit cell with respect to the reference lattice point positions. So defining the basis does not change the lattice or require you to redefine your PLVs. The new location of atoms are not lattice points. (Atom positions are given by lattice point plus basis vector). A family of lattice plane needs to go through the lattice point position, but not through the atom positions. This might sound a bit confusing in the context of what we said about scattering being the diffraction of the wave from families of lattice planes -- but the point is that if the family of lattice planes makes some diffraction grating that the waves scatter from, then the atoms of a particular type (which are displaced from the lattice point positions by some fixed basis vector) also form a diffraction grating with the same spacing. |
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