Analyse XRD Data to Find Lattice Constant & Crystal Structure

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In summary, the conversation discusses the use of X-Ray Diffraction Data to determine the lattice constant and crystal structure of a material. The peaks are found and d is calculated using the Bragg equation, with n=1 and half of the measured angle. The Miller Indices are then used to index the peaks, and the JCPDS file can be used as a reference for the lattice constants. The conversation also mentions the use of the wave vector, but the speaker is not familiar with it. The conversation concludes with the speaker stating that their work is finished.
  • #1
Phileas.Fogg
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Hello,
I have X-Ray Diffraction Data: Intensity versus angle [tex] 2 \Theta[/tex] and shall find out the lattice constant and even better the crystal structure. The Data is from a [tex]\Theta-\Theta[/tex]Diffractometer. [tex]\lambda = 1,54 \cdot 10^{-10}m[/tex]

I know that I have to find the peaks and can calculate d from the Bragg equation:
[tex] d = n \lambda/2 \sin\theta[/tex]
Is it correct to take half of the measured angle for the equation and to set n=1 in this case?

Moreover my problem is, I don't know how to find out the lattice constant and the structure by calculating d. I don't have any data to compare d with (where do I get this data?).
I know that the material ist Tungsten Carbide or Tungsten-Cobalt with hexagonal crystal structure, but I shouldn't use this information beforehand. What shall I do?

Regards,
Mr. Fogg
 
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  • #2
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  • #3
Hello,
thanks!

Do I also have to convert [tex]2 \Theta[/tex] into Radians when I use the Bragg's Law? In my calculation, I sometimes get a negative d , is that possible?

How do I Index the peaks with Miller Indices?

I don't know, how this equation helps me

[tex] \frac{1}{d_{hkl}^2} = \frac{4}{3} \frac{h^2+hk+k^2}{a^2} + \frac{l^2}{c^2} [/tex]
 
  • #4
Phileas.Fogg said:
Hello,
thanks!

Do I also have to convert [tex]2 \Theta[/tex] into Radians when I use the Bragg's Law? In my calculation, I sometimes get a negative d , is that possible?

no, theta in Bragg’s law is in degrees. it's not possible at all to have d as a negative value



How do I Index the peaks with Miller Indices?

I don't know, how this equation helps me

[tex] \frac{1}{d_{hkl}^2} = \frac{4}{3} \frac{h^2+hk+k^2}{a^2} + \frac{l^2}{c^2} [/tex]

look for the JCPDS file of this compound [it is a reference data that holds both the fixed values of d for all possible peaks of the material, and the corresponding (hkl) planes], use this equation along with Bragg’s law to solve, you know that two equations are needed to solve for two variables [which are the lattice constants a and c. of course you use the value of the measured d at a certain peak, that is a certain plane where it can be identified using the JCPDS card, do this for two peaks then solve], good luck!
 
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  • #5
Thank You,
where can I get the JCPDS file?

When I convert the measured angle [tex] 2 \Theta[/tex] into the z-component of the wave vector with

[tex] q_{z,i} = \frac{4 \pi}{\lambda} \sin(\alpha_i) [/tex]

do I have to halve [tex] 2 \Theta [/tex] ?

Mr. Fogg
 
  • #6
Phileas.Fogg said:
Thank You,
where can I get the JCPDS file?


search the net! look for tungsten carbide (WC) JCPDS powder diffraction file

ps. JCPDS = International Center for Powder Diffraction Data



When I convert the measured angle [tex] 2 \Theta[/tex] into the z-component of the wave vector with

[tex] q_{z,i} = \frac{4 \pi}{\lambda} \sin(\alpha_i) [/tex]

do I have to halve [tex] 2 \Theta [/tex] ?

Mr. Fogg

I don’t quite follow you, what is this for?
 
  • #7
drizzle said:
no, theta in Bragg’s law is in degrees. it's not possible at all to have d as a negative value

One measured peak is for example at [tex] 2 \Theta = 157523,511 [/tex]°. In my calculation

1) Division by 2 gives [tex] \Theta = 78761,756 [/tex] °
2) Converting into radiants (for OpenOffice Calc) gives [tex] \Theta = 1374,652 [/tex]
3) now calculating (with OpenOffice Calc) [tex] \sin(\Theta) = -0,979 [/tex]

So I get a negative d now! What's wrong? Maybe I am too stupid to handle OpenOffice Calc in this case :-p

If I don't convert into radiants, the problem is still present concerning other peaks.

Mr. Fogg
 
  • #8
drizzle said:
I don’t quite follow you, what is this for?

The new wave vector in our experiment is final minus initial wave-vector:

[tex] \vec{q} = \vec{k}_f - \vec{k}_i[/tex]

and it's z-component is

[tex] q_z = 2 k \sin(\alpha_i)[/tex]
 
  • #9
Phileas.Fogg said:
One measured peak is for example at [tex] 2 \Theta = 157523,511 [/tex]°. In my calculation

ehim :biggrin:, I think this is the value of the maximum intensity, right? in any XRD pattern the range of 2theta values is from 0 to 90 or so [and the horizontal axis is the one you look at to get the angle at which the peak occurs ;)]


ps. actually, if you do convert the angle into radians instead of degrees it would give the same result. but B should be converted into radians before calculating the grain size g [as shown in the linked thread]
 
  • #10
:biggrin: :biggrin: :biggrin:

Now I found my mistake.

I didn't replace the dot with a comma in the file, I got. That's why there occurred these incredible angles :smile:

Now I will revise my analysis and keep your help in mind. When a question occurs, I will ask you again.

Thank You!

Mr. Fogg

PS: Do You know what to do with the wave vector?
 
  • #11
Phileas.Fogg said:
:biggrin: :biggrin: :biggrin:

Now I found my mistake.

I didn't replace the dot with a comma in the file, I got. That's why there occurred these incredible angles :smile:

Now I will revise my analysis and keep your help in mind. When a question occurs, I will ask you again.

Thank You!

Mr. Fogg

PS: Do You know what to do with the wave vector?

I’m not really familiar with this, sorry. but I'm sure you'll get the help you need from other PF members...welcome anyways :smile:
 
  • #12
Phileas.Fogg said:
Hello,
thanks!

Do I also have to convert [tex]2 \Theta[/tex] into Radians when I use the Bragg's Law? In my calculation, I sometimes get a negative d , is that possible?

How do I Index the peaks with Miller Indices?

I don't know, how this equation helps me

[tex] \frac{1}{d_{hkl}^2} = \frac{4}{3} \frac{h^2+hk+k^2}{a^2} + \frac{l^2}{c^2} [/tex]

what equation is this called? what are the parameters 'l' and 'c'? how do u find lattice parameter if the cell is not cubic but tetragonal or orthorhombic?
 
  • #13
Hello,
I already finished my work

@ nyxynyx : Do you want to know that, or do you try to help me? Because everything is finished already. I don't need any replies to this thread, but thanks.

Mr. Fogg
 
  • #14
i would like to know that! i believe it has got something to do with the extinction rules but I can't find any tables for extinction rules of tetragonal and orthorhombic
 

FAQ: Analyse XRD Data to Find Lattice Constant & Crystal Structure

How do I prepare my XRD data for analysis?

To prepare your XRD data for analysis, you will first need to collect the data using an X-ray diffraction machine. This involves placing your sample in the machine and recording the diffraction pattern. Once you have collected your data, you will need to correct for background noise and calibrate the data using a known standard, such as silicon or aluminum.

What is the lattice constant and why is it important?

The lattice constant is the distance between repeating units in a crystal structure. It is an important parameter to measure as it can provide information about the size and arrangement of atoms in a crystal, as well as the type of crystal structure present.

How do I determine the lattice constant from XRD data?

To determine the lattice constant from XRD data, you will need to analyze the diffraction peaks using a software program such as Origin or MATLAB. By measuring the angles and intensities of the peaks, you can calculate the lattice constant using Bragg's law, which relates the diffraction angle to the lattice constant.

What crystal structures can be identified using XRD data?

XRD data can be used to identify a variety of crystal structures, including cubic, tetragonal, hexagonal, and orthorhombic structures. It can also be used to identify the presence of amorphous materials or mixed phases.

Are there any limitations to using XRD data for lattice constant and crystal structure analysis?

Yes, there are some limitations to using XRD data for lattice constant and crystal structure analysis. XRD is unable to distinguish between atoms with similar atomic numbers, and it is also unable to provide information about the arrangement of atoms within a crystal lattice. Additionally, the sample must be crystalline and have a regular atomic arrangement for accurate analysis.

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