From what I was reading, Silicon has a FCC unit cell but they also said that the Silicon atoms form a tetrahedron at 109 degrees from each other. Then they said that the tetrahedron is formed by overlapping of two FCC unit cells ane starting at (0,0,0) and the other starting at (a/4,a/4,a/4) where a is the FCC unit cell dimension. Now, aren't the claims themselves contradictory on the face of it? If I have an FCC unit cell, shouldn't my next cell start at (a,0,0), (0,a,0) and the likes…?? Isn't that the meaning of a unit cell? Shouldn't a lattice be a vectorial repetition of the dimensions of a unit cell? In this case, if I assumed the FCC as my basis vectors, would that get violated if I intended to represent my chrystal lattice with that?
[Physics] Crystal structure of Silicon
crystalssemiconductor-physics
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Don't listen anyone. It is possible, but I have to admit - hard. Otherwise, how were first mono-crystals grown?
Initially, you may buy 'pure' silicon (pure for chemical reactions, not electronics). First of all you need to make a rod. To do that you'll need form out of material which can withstand 1600C (hard part, can't name ones at the moment), and heat Si in it using induction heating.
Induction heating might be the hardest part - but there are lots of guides around. Induction heater able to melt metal is 100% doable at home.
Once you have Si rod - you need to purify it using 'zone melting' using your induction heater. Will take ages, so you might want to make motorized thing which will move rod or heater for several days/weeks.
After that your rod is polycrystalline - which is already ok for solar cells.
For Czochralski process you may reuse again your induction heater, but the hardest part is getting clean 'form' for molten Si, as silicon is ultrapure and very easy to contaminate.
Alternatively, you may get mono-crystalline or large-grain polycrystalline Si right out of your zone heating station if you would do slow pass at the end and add seed crystal. But this might be tricky a little.
If your rod in thin enough (1-3cm) you may cut it using diamond disks, sold in usual shops. Thicker rods will require larger disks (which are not easy /cheap to buy) or 'diamond wire'.
Whole process is quite complex, but will give you lots of experience working with tough things. Dealing with silicon is much harder than Steel ;-)
PS. If you would do everything except getting seed crystals, I can send you some.
The silicon lattice has a diamond structure where each Si atom has four nearest neighbors connected by a covalent bond forming tetrahedra that are periodic in space as can be seen in the picture. Thus one tetrahedron represents a possible primitive unit cell of the crystal whose translational repetition generates the crystal lattice.
Each tetrahedron contains two Si atoms, one in the center and a quarter on each corner of the tetrahedron. However, different unit cells can be used to describe the same crystal lattice. It is easier to visualize the diamond lattice by the depicted conventional (not primitive) cubic unit cell with side length $a$. It can be seen that this corresponds to two interpenetrating face centered cubic Bravais point lattices that are displaced with respect to each other by a quarter of the cube's diagonal.
From the perspective of crystal structure, the Si atoms belonging to these two sub-lattices are different, although they are chemically identical. It can be seen in the picture that a corner atom has a nearest neighbor in one direction of the diagonal but not in the other direction. Thus the crystal needs two Si atoms per primitive unit cell whose choice is not unique. One possible primitive unit cell is, as you suspected, the tetrahedron. Possible basis vectors for this primitive unit cells of the face centered lattice are the translations from one corner of the conventional cubic unit cell to its adjacent quadratic face centers.
See, e.g., Ashcroft and Mermin, 1976, Chapter 4.
Best Answer
There are two separate issues here.
Firstly the smallest possible unit cell for a crystal is called the primitive unit cell. However in many cases this is an awkward shape and it's easier to use a bigger unit cell that contains more than one primitive unit cell. The FCC unit cell is one of these non-primitive (I'm not sure what the actual term is) unit cells.
Secondly even the primitive unit cell does not necessarily contain just a single atom. The corners of the primitive cell are marked by atoms that have the same environment, but the silicon structure contains two different environments for the silicon. Have a look at this picture of the silicon structure:
If you look at the atom I've outlined in red and the atom I've outlined in green you'll see they are in different environments. If you look at the upper two bonds you'll see that for the red atom the V formed by the bonds projects out of the screen. For the green atom the V lies in the plane of the screen. In effect you get the red atom by rotating the green atom 90ยบ about a vertical axis.
So even the primitive cell contains two silicon atoms, and the compound FCC cell contains four primitive cells. Despite this, every silicon atom is indeed at the centre of a tetrahedron.