What are lattice points ? How many lattice points are there in one cell of simple cubic , bcc , fcc .
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There are different types of lattices. A lattice point is a point in any of these lattices. Lattices are used to describe highly ordered systems such as crystals and some supersolids. I am unsure whether lattices can only describe periodic systems (see quasicrystals). However, I will be assuming that we are talking about periodic lattices. I will also be assuming that we are dealing with crystals.
Crystal Lattice
The crystal lattice is used to describe the lattice of a real crystal. A lattice point in a crystal lattice represents the position of a sodium ion or a chloride ion.
Bravais Lattice
Bravais lattices are more mathematical and abstract than crystal lattices. They are pretty much the same as crystal lattices. Unlike the crystal lattice, however, lattice points in the Bravais lattice no longer represent a position of a particular atom. Instead a lattice point represents a position in which an atom can be placed. In other words, a lattice point in a Bravais lattice is a point, which is equal and indistinguishable from any other another point. What matters in a Bravais lattice are not the points themselves, but how they are arranged (i.e. symmetry).
Reciprocal Lattice
The Reciprocal Lattice is the Fourier Transform of either the crystal lattice or a Bravais Lattice. More often than not, it is used to refer to the Fourier Transform of the Bravais Lattice. More of that is explained in physics SE. However, I personally think that this video explains it better. A lattice point here can represent an atom or a point, depending on the context.
Finally, as mentioned by other posts, these points can be vacant. Hope that helps.
Crystal Lattice
The crystal lattice is used to describe the lattice of a real crystal. A lattice point in a crystal lattice represents the position of a sodium ion or a chloride ion.
Bravais Lattice
Bravais lattices are more mathematical and abstract than crystal lattices. They are pretty much the same as crystal lattices. Unlike the crystal lattice, however, lattice points in the Bravais lattice no longer represent a position of a particular atom. Instead a lattice point represents a position in which an atom can be placed. In other words, a lattice point in a Bravais lattice is a point, which is equal and indistinguishable from any other another point. What matters in a Bravais lattice are not the points themselves, but how they are arranged (i.e. symmetry).
Reciprocal Lattice
The Reciprocal Lattice is the Fourier Transform of either the crystal lattice or a Bravais Lattice. More often than not, it is used to refer to the Fourier Transform of the Bravais Lattice. More of that is explained in physics SE. However, I personally think that this video explains it better. A lattice point here can represent an atom or a point, depending on the context.
Finally, as mentioned by other posts, these points can be vacant. Hope that helps.
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