Oh okay - for a question like this you need to find the repeating motif. Unless it is a non periodic crystal (rare), there will be a unit that you can repeat by translation, over and over to build the complete structure.
I couldn't quite see what the repeating motif was for your diagram so looked it up.
So, for quartz, it's a bit more complicated than the region you showed, kind of twisted, this is the motif:
But you've got to take account of the way atoms are shared at the boundaris of the motif and make sure each atom is counted only once - all the external oxygen atoms are counted twice. There are three silicon atoms, and ten oxygen atoms - but eight of the oxygen atoms are on the outside and so are shared when the motif is repeated. The oxygen atoms are shared between two silicon atoms so just need to divide by two, so you have
Silicon: 3 atoms within the motif - not shared between adjacent copies
Oxygen : 2 atoms within the motif not shared
Oxygen: 8 atoms on the edge of the motif shared with adjacent copies of the motif - so have to divide this number by 2.
So you get a total of
3 silicon
2 + 8/2 = 6 oygen
So formula
Si3O6
for the motif.
Generally - you'd expect it to match the chemical formula, here SiO2, so you would expect to have twice as many oxygen as silicon atoms.
More about it here:
Quartz Structure
Quora User's answer is simpler :) - so long as you know that every silicon is joined to four oxygens and every oxygen shares two silicons, you don't need to know the motif or detailed structure.
You know in advance it has to be SiO2.
I couldn't quite see what the repeating motif was for your diagram so looked it up.
So, for quartz, it's a bit more complicated than the region you showed, kind of twisted, this is the motif:
But you've got to take account of the way atoms are shared at the boundaris of the motif and make sure each atom is counted only once - all the external oxygen atoms are counted twice. There are three silicon atoms, and ten oxygen atoms - but eight of the oxygen atoms are on the outside and so are shared when the motif is repeated. The oxygen atoms are shared between two silicon atoms so just need to divide by two, so you have
Silicon: 3 atoms within the motif - not shared between adjacent copies
Oxygen : 2 atoms within the motif not shared
Oxygen: 8 atoms on the edge of the motif shared with adjacent copies of the motif - so have to divide this number by 2.
So you get a total of
3 silicon
2 + 8/2 = 6 oygen
So formula
Si3O6
for the motif.
Generally - you'd expect it to match the chemical formula, here SiO2, so you would expect to have twice as many oxygen as silicon atoms.
More about it here:
Quartz Structure
Quora User's answer is simpler :) - so long as you know that every silicon is joined to four oxygens and every oxygen shares two silicons, you don't need to know the motif or detailed structure.
You know in advance it has to be SiO2.
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Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
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