# Relative occupied volume

1. Feb 14, 2009

### drizzle

hey everyone,
I’m a bit confused, I’m trying to calculate the relative occupied volume of ZnO unit cell, I’ve just calculated that Zn and O atoms occupy about 43.3% of the unit cell, there are 4 atoms per unit cell 2 for each one, although I doubt this value, does it varies or is it a constant value for ZnO, cause I found that Zn and O atoms occupy 40% from an article, the process I did to get this value is as follows:
Lattice constants: a=0.32495 nm, c=0.52069 nm
Ion radiuses: Zn =0.6 Å, O=1.38 Å
Spheres volume: Zn=9.0432E-31 m^3, O=1.10029E-29 m^3
Unit cell volume (Vu)=a^2*c=5.4981E-29 m^3
Total spheres volume (Vt)= 2*V(Zn)+2*V(O)= 2.38144E-29 m^3
The relative occupied V=[(Vt)/(Vu)]*100=43.3%

Another question plz;
I found from some source that lattice constants of ZnO are given as: a = 0.3250 nm, c = 0.5207 nm and the unit cell volume of 47.63*10^-30 m^3. this volume is not calculated from the lattice constants where it is 5.5E-29 m^3, how was the unit cell volume calculated?
Thanks.

2. Feb 14, 2009

### kanato

So, a few things:

What's the crystal structure of ZnO? I didn't think it was tetragonal. a^2*c is only the volume for a tetragonal cell, if it's hexagonal or some other structure where the lattice vectors are not orthogonal, then you need to take that into consideration. That is probably why your volume calculation is different in your last question.

One of your inputs, the ionic radius of Zn has only one significant figure? Your final result, to one significant figure is 40%. If you want more accurate output you should first get more precise input. Typing "ionic radius zinc" into google gives me a value of 0.74 angstroms.

Ionic radii should not be taken too seriously, as in a crystal you will always have some degree of covalent bonding.

Edit: Oh, and if you're going to put numbers from an article, you should provide a reference to the article so other people can look at it. If they used different numbers or a different method, I can't help you figure something like that out without having access to the article.

3. Feb 15, 2009

### drizzle

yes, ZnO exhibits a wurtzite (hexagonal) structure, and its unit cell have 4 atoms as I described, what is the relation to calculate the unit cell volume, if my calculation is not right?

For the other question the values were taken from “Colloquiums tasks for Dielectrics- Solution” you can type it into google, it also has a sketch the unit cell. Thanks