Tuesday, January 8, 2019

Pulling Crystals

This was what I thought of pulling silicon crystal,


and the artifacts that it creates.  This is what I thought that would reduce such ringing artifacts,


\(\theta\)  for diamond cubic crystals will be,


\(OA=OC=\cfrac{3}{4}\sqrt{\cfrac{2}{3}}a\)

\(OH=\cfrac{1}{4}\sqrt{\cfrac{2}{3}}a\)

\(\theta=arcsin(\cfrac{OH}{OC})=arcsin(\cfrac{1}{3})=19.47^o\).

where \(C\) is at the first layer and is bonded to the next layer of silicon is at \(O\).  The next pull does not form up the bond along \(OA\), but it is at \(19.47^o\) from \(O\).  Bonds similar to \(CO\) form up else where in the crystal.  After four steps, because \(OH=\cfrac{1}{4}AH\), the atom needed at \(A\) falls into place.  At each step, a sheet of atoms is shifted into place.

Good night...