Lattice Structures, how to identify number of Spheres in Unit Cell

[whitesniper001]

Just going through lattice structures, was finding it hard to identify the number of spheres in unit cell, the two which I struggled with were:

 

• I know that this lattice represents a compound such as ZnS
• The coordination number is 4:4 for both white and black spheres.
• The number of white spheres (face centred cubic lattice) in the unit cell is: (1/8 x 8) + (1/2 x 6) = 4
• The black spheres (tetrahedral holes) I am having problems with, my guess is: 1 x 4 = 4

The reason I calculated it to be 4 is because only half the tetrahedral holes are filled, normally for a structure like Na_​2​O there are 8 white spheres inside and they are all counted as entirely inside. So if there are 8 white spheres and they are counted as (1 x 8), would the same logic then apply if there are only 4 white spheres?

 

My question is, have I calculated the unit cells for the black spheres right if not where have I gone wrong?

 

 

The second lattice I was really struggling with was:

• I know the coordination number is 6:6

 

How do I calculate the number of unit cells in the above lattice? It is the most complicated one I have come across so far.

Edited May 3, 2016 by whitesniper001

[studiot]

Wow what resources are available today.

This stuff is mind bending on first reading.

 

 

You are correct with your first example and you seem to have picked up the rules for numbers of atoms per cell.

 

1) An atom lying totally within a unit cell belongs to that cell only and contributes one.

 

2) An atom lying on the face of the cell belongs to two cells equally and counts as one half.

 

3) An atom lying on an edge is common to four unit cells and therefore contributes one quarter.

 

4) An atom at a corner is common to eight unit cells and therefore counts one eighth.

 

 

Your second example is of the Nickel Arsenide (NiAs) structure with repeating ABABAB etc units.

 

The unit cell is discussed in this powerpoint, page 8,9

 

http://homepages.abdn.ac.uk/j.skakle/pages/y3-2002/3lec6.ppt

 

and again in this pdf from page 46.

 

http://www.chem.uci.edu/~lawm/253%202.pdf

 

You can also play with these interactive sites.

 

http://www.chemtube3d.com/solidstate/_sync(NiAs).htm

 

http://www.chemtube3d.com/solidstate/_NiAs(final).htm

[whitesniper001]

Cheers again, looked through all the files presented.

[studiot]

I seem to remember that the book you mentioned was general chemistry.

From university level you need more area specific books for different topics within the subject.

With all the modern web resources, perhaps you students don't use books these days but here is a brief bibliography.

 

Chemistry a structural view

 

Stranks et al

 

Cambridge University Press

 

Chenical Binding and Structure

 

Spice

 

Pergamon

 

Solid State Chemistry

 

Smart and Moore

 

Chapman and Hall

 

and the grandady of them all

 

Structural Inorganic Chemistry

 

Wells

 

Oxford University Press

Edited May 4, 2016 by studiot

[whitesniper001]

Cheers for the books presented will try to get a hold of some of them. You are right I hardly do use books mostly its based off watching youtube videos, going through articles and lecture notes.