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

In summary, the lattice parameters c and a of Hexagonal ZnO can be calculated using the Miller indices and lattice spacing measurements from X-ray diffraction data. The equations used to determine these parameters take into account the hexagonal crystal structure and the angle between the crystal axis and the X-ray beam. These calculations are important for understanding the structural properties of Hexagonal ZnO, which plays a crucial role in its applications in various fields such as optoelectronics, catalysis, and sensors.
  • #1
thola
1
0
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)
 
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  • #2
thola said:
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)


How do I calculate the lattice parameters (a,b,c) from hkl ( miller indices) of XRD pattern?
 
  • #3
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
read said:
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.

Sorry, A=(1/a)*2/sqrt(3), of course.
 
  • #5
Calculations of lattice parameters (a,b,c) from hkl

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

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


theivasanthi said:
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?

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

Dear Read,
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


theivasanthi said:
Dear Read,
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.

This method is powder indexing. There are many free programs, e.g. in http://www.ccp14.ac.uk/solution/indexing/ . I would recommend to start with DICVOL.
 

1. How do you determine the lattice parameter c of Hexagonal ZnO?

The lattice parameter c of Hexagonal ZnO can be determined by using X-ray diffraction (XRD) techniques. XRD involves exposing a crystal to X-rays and measuring the angles at which the X-rays are diffracted. These measurements can then be used to calculate the lattice parameters of the crystal.

2. What is the significance of the lattice parameters c and a in Hexagonal ZnO?

The lattice parameters c and a are important in determining the crystal structure and properties of Hexagonal ZnO. These parameters can provide information about the arrangement of atoms in the crystal lattice and can affect the physical, chemical, and electronic properties of the material.

3. Is there a specific formula for calculating the lattice parameters c and a of Hexagonal ZnO?

Yes, the lattice parameters c and a can be calculated using the following formula: c = (2/3)*sqrt(3)*dhkl and a = dhkl, where dhkl is the interplanar spacing and (hkl) represents the Miller indices of the crystal planes.

4. Can the lattice parameters c and a of Hexagonal ZnO be measured using other techniques besides XRD?

Yes, the lattice parameters c and a can also be measured using techniques such as transmission electron microscopy (TEM) and scanning electron microscopy (SEM). These techniques involve imaging the crystal structure at a nanoscale level and can provide accurate measurements of the lattice parameters.

5. How do defects or impurities in the crystal affect the lattice parameters c and a of Hexagonal ZnO?

Defects or impurities in the crystal lattice of Hexagonal ZnO can cause distortions in the crystal structure, resulting in changes in the lattice parameters c and a. This can affect the properties of the material, such as its conductivity and mechanical strength, and can also impact the performance of devices made from Hexagonal ZnO.

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