# How do you calculate the lattice parameters c and a of Hexagonal ZnO

1. Jul 9, 2008

### thola

How do you calculate lattice parameters c and a of Hexagonal ZnO ? if you are given the wavelength= 1.5406 nm, diffraction angle= 48 and the miller indexes (102)

2. Nov 15, 2010

### theivasanthi

How do I calculate the lattice parameters (a,b,c) from hkl ( miller indices) of XRD pattern?

3. Nov 16, 2010

Bragg low: 2*d*sin(theta)=lambda

distance in reciprocal space (1/d)^2=(h^2+k^2+h*k)*A^2+l*C^2, where A and C reciprocal basis vectors, A=a*2/sqrt(3), C=1/c.

So, you need at least two reflections. This is quite elementary and can be found in any introductory textbook on crystallography/diffraction. Just google... and http://www.xtal.iqfr.csic.es/Cristalografia/index-en.html

4. Nov 16, 2010

Sorry, A=(1/a)*2/sqrt(3), of course.

5. Nov 19, 2010

### theivasanthi

Calculations of lattice parameters (a,b,c) from hkl

It is said that; 1) if a and c are known, it is possible to calculate the peak position (Theta is the half value of the peak position) 2) if the peak position is known it is possible to calculate the lattice parameter.

How do I calculate the lattice parameters (a,b,c) from hkl ( miller indices) of XRD pattern? or How do I calculate a,b,c from peak position? How do I calculate a,b,c from any other method?

6. Nov 19, 2010

Re: Calculations of lattice parameters (a,b,c) from hkl

This is a textbook problem. You have to calculate d(h,k,l), and then to calculate \theta using Bragg law for each h,k,l. You will finally get a set of equations with unknown parameters a, b, c, \alpha, \beta and \gamma, in general. In simple cases one can determine a,b,c by trivial math, like for (100) reflection in case \alpha=\beta=\gamma=90grad.

For formulas you look in any textbook or in Google, e.g.
http://www.xtal.iqfr.csic.es/Cristalografia/index-en.html section "Direct & reciprocal lattices"

7. Nov 21, 2010

### theivasanthi

lattice parameters (a,b,c) Calculations of unknown structure

I have XRD pattern of Jackfruit powder. There are 5 peaks in that XRD. I have calculated d(h,k,l) and \theta for each h,k,l. I do not know structure whether it is fcc or bcc or hexagonal etc. Now, How do I calculate a,b,c? Is there any method or equations to calculate a,b,c for an unknown structure?

T.Theivasanthi.

8. Nov 21, 2010