I took XRD of my compound, It has three peaks. I have to calculate the hkl values for them. I calculated the 'd' for Bragg's Equation for all three peaks. I do not know the lattice parameter(a) of my compound. How could I calculate with out knowing (a). Please help.
Thank you
since d=a/sqrt(h2+k2+l2) and d=λ/2/sin(ϴ)
h2+k2+l2= [ 2a/λ*sin(ϴ) ]2
since 2a/λ is constant
(h12+k12+l12) / (h22+k22+l22)=sin(ϴ1) / sin(ϴ2)
Don't forget the scale in your diffraction pattern is 2ϴ, i.e. you have to half the angle.
Dear Vadiraj
Before going to answer your question, I want to ask you a doubt. How do you know that the material has cubic structure?
Let’s assume that the material has cubic symmetry then hkl values can be calculated in following steps
(1) First calculate ‘d’ by using the equation 2d sinϴ = λ
(2) Use Full prof software, which is freely available to calculate the lattice parameter ‘a’. Good fitting will again confirm the cubic structure.
(3) By using combination of ‘d’ and ‘a’, hkl values can be calculated.
since d=a/sqrt(h2+k2+l2) and d=λ/2/sin(ϴ)
h2+k2+l2= [ 2a/λ*sin(ϴ) ]2
since 2a/λ is constant
(h12+k12+l12) / (h22+k22+l22)=sin(ϴ1) / sin(ϴ2)
Don't forget the scale in your diffraction pattern is 2ϴ, i.e. you have to half the angle.
Dear Vadiraj,
Go for MATCH 2 softwere, you can easily match your XRD pattern by giving the starting materials for your sample and then easily obtained the lattice parameter and (h k l) too,
Regards,
Priyanath
How to calculate hkl value from powder xrd data using any software is available???
please tell me.
Dear Vadiraj K T I am showing basic calculation steps to calculate (h k l) values.
Ex- X-ray diffraction of copper (crystal structure; face center cubic FCC): Wavelength of X-ray is 0.154 nm. For Cu first peak at 43.2o degree, now (h k l) ?
λ = 2d sin(θ) --------Eq(1)
where λ = wavelength of X-rays
d = interplaner spacing
2 θ =43.2o
θ = 43.2o/2
From equation (1), we can calculate (d) value.
d=0.209 nm
dhkl = a/(h2+k2+l2)1/2 ---------Eq(2)
For copper (FCC)
a = 2r/21/2 --------- Eq(3)
where r = atomic radius = 0.128 nm (for Cu)
Now from Eq(3), we can calculate (a)
a = 0.362 nm
From Eq(2)
(h2+k2+l2)1/2 = 1.732
(h2+k2+l2) = 3 = 12+12+12= (111)
FCC- principle diffraction planes
Ex- (111), (200), (220)
Now if you don't know (a) valve then consider 2a/λ = as a constant. And with the help of two peaks of XRD you can calculate (h k l) values.
dear Alok Bhadauria , thank you for the calculation. i have a doubt. if I get (h2+k2+l2) = 0 can I assume hkl as (000) and for (h2+k2+l2) = 2, hkl (110)?
if you give guide me to a reference literature it would be helpful. thank you
Dear bogeshwaran, h2+k2+l2=0 means that is origin. For any materials (Crystal structure: FCC, BCC or HCP,) (hkl) can not (000), because, that is belong to an origin. And for h2+k2+l2=2, there is only one possibility that is {110}. You are right.
Thank you Mr.Alok, if h2+k2+l2=1 can I assume it as (100) or is there any concept to be followed while writing the (hkl) values?
Next doubt is, if I get h2+k2+l2=0 then is my experimentation wrong? or is the sample not a crystal? or is there any other inference
Bogeshwaran Karunanithi please follow this below link, you will get basic idea about calculating the hkl. https://www.unf.edu/~michael.lufaso/chem4627/ch2_solid_state.pdf
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