The whole point of asking this question is that any unit cell for eg. FCC lattice having more than 1 atom per unit cell is an interpenetration of 2 or more sub units and we can't trace the entire lattice using only one translation vector? And only primitive unit cells can be traced using only one translation vector?
The primitive unit cell contains only one LATTICE point, not necessarily only one atom. It should be obvious that for a crystal structure with two different types of atoms, the primitive cell cannot be represented with only one atom. Imagine a BCC arrangement with corners of one atom type and centers of another. The primitive unit cell would be the whole BCC, containing one of each atom.
The primitive unit cell contains only one LATTICE point, not necessarily only one atom. It should be obvious that for a crystal structure with two different types of atoms, the primitive cell cannot be represented with only one atom. Imagine a BCC arrangement with corners of one atom type and centers of another. The primitive unit cell would be the whole BCC, containing one of each atom.
Diamond contais 2 C atoms; GaAs - 1 Ga and 1 As; LiBeF3 - 5 atoms. LiBO2 - 16 atoms; LuPO4 - 24 atoms per a unit cell, respectively.
I'll keep two former sentences in the Michael Foegelle's answer and I'll correct two latter ones (the term BCC being reserved for lattices):
The primitive unit cell contains only one LATTICE point, not necessarily only one atom. It should be obvious that for a crystal structure with two different types of atoms, the primitive cell cannot be represented with only one atom.
Imagine atomic arrangement in a cubic crystal structure with corners of one atom type and centers of another (for example CsCl). The primitive unit cell would be the whole cube, containing one of each atom (one Cs and one Cl).
Another way to think about it is based on its construction. If one draws a plane perpendicular to and bisecting the line joining one lattice point to all the neighboring ones, repeating for all the neighboring lattice points to the same original point, the resulting volume constitutes the primitive unit cell. So yes, the primitive unit cell contains one latttice point per unit cell, but each lattice point can contain more than one atom, callled the basis. For example, Boron contains 57 atoms per unit cell.
So can I say that with each lattice point constituting a primitive unit we may have 1 or more basis atom/s associated.
Yes. You can say that in a primitive unit cell you only have one lattice point, but you may have several basis atoms (the basis of the primitive unit cell). The Wigner-Seitz construction suggested by Campuzano is probably the easiest way to visualize it.
Thanks Vladimir. I'd been bothered by some imprecision in the last statement in my post but hand't gotten around to fixing it. I should also have said that the cubic cell was an example of the primitive unit cell, since it may be possible to find more than one primitive geometry for a given crystal lattice. I'd also left out the term "basis" that Juan Carlos brought up. Heck, I'm doing good remembering any of this since it's been 20 years since I've dealt with any of it! =) Spending my life in the RF world these days and my condensed matter background only loosely touches on it occasionally.
Primitive unit cell contains one lattice point per cell and not one atom. This lattice point can have many atoms depends on the basis of crystal.
Fe - 1, diamond - 2, GaAs - 2, LiBeF3 - 5, LaPO4 hexagonal - 18, LaPO4 monoclinic - 24 atoms per unit cell, recpectively.
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