When a compound is not reported in JCPDS how can we able to predict the structure. Is the Powder XRD is useless without JCPDS software?
The procedure is straightforward and is something that we teach to our first year undergraduate students when we introduce them to diffraction. I'll describe the old-fashioned paper and pencil method:
First, measure the 2-theta values of the lowest angle diffraction peaks in your pattern and list them in a column. For each, calculate [sin(theta)]^2 and then compute the ratios of successive values of [sin(theta)]^2, and list these as the nearest integer. These are labelled "N" below. For a first example, suppose we have the following 2-theta values and their results:
2-theta sin(theta) [sin(theta)^2 N(ratios of previous column as integers)
25.45 0.2203 0.0485 1
36.30 0.3115 0.0971 2
44.86 0.3815 0.1456 3
52.28 0.4406 0.1941 4
59.02 0.4926 0.2426 5
65.31 0.5396 0.2912 6
77.08 0.6231 0.3882 8
82.73 0.6609 0.4367 9
Since [sin(theta)]^2 is proportional to N, where d=a/sqrt(N) and N= h^2 + k^2 +l^2 the values above correspond to a primitive cubic structure (we can tell this because N=7 is not possible from the sum of three squares). If the result came out as:
2-theta sin(theta) [sin(theta)^2 N(ratios of previous column as integers)
25.45 0.2203 0.0485 1
36.30 0.3115 0.0971 2
44.86 0.3815 0.1456 3
52.28 0.4406 0.1941 4
59.02 0.4926 0.2426 5
65.31 0.5396 0.2912 6
71.30 0.5828 0.3397 7
77.08 0.6231 0.3882 8
82.73 0.6609 0.4367 9
then we would know that this is actually a cubic I structure (body centred, bcc) because 7 is impossible, and actually our results should be correctly listed as:
2-theta sin(theta) [sin(theta)^2 N(ratios of previous column as integers)
25.45 0.2203 0.0485 2
36.30 0.3115 0.0971 4
44.86 0.3815 0.1456 6
52.28 0.4406 0.1941 8
59.02 0.4926 0.2426 10
65.31 0.5396 0.2912 12
71.30 0.5828 0.3397 14
77.08 0.6231 0.3882 16
82.73 0.6609 0.4367 18
and the values of N correspond to the reflections expected from the systematically allowed reflections of the body-centred translational symmetry (h+k+l even, i.e. 110 (N=2), 200 (N=4), 112 (N=6), 220 (N=8) etc.)
Finally, if the results came out as:
2-theta sin(theta) [sin(theta)^2 N(ratios of previous column as integers)
44.86 0.3815 0.1456 3
52.28 0.4406 0.1941 4
77.08 0.6231 0.3882 8
93.87 0.7306 0.5338 11
99.48 0.7631 0.5823 12
we would know that the structure is fcc (cubic F) with only the reflections corresponding to (hkl) all odd or all even present (i.e. 111 (N=3), 200 (N=4), 220 (N=8), 311 (N=11), 222 (N=12) etc.)
Hope this helps!
Dear Ranjith,
In your question, firstly, it is not so pleasing to see the word "useless" for powder XRD. JCPDS or any other software has actually been computed or formed by finding the crystal structures of different compounds by doing manual analysis of XRD patterns. Certainly, for any XRD pattern, a basic analysis is available and this should be something that we must know before even using the JCPDS or any other software. One must know the theoretical knowledge of structure factor, missing reflections for a particular structure, typical h, k, l relation (like for e. g. h, k, l all even or all odd for an FCC structure), relationship between lattice paramater, (hkl) and interplanar spacing, etc. I would suggest you to go through any book (Materials Science and Engg. by Raghavan) to find the basic procedure to compute the type of crystal structure from an experimentally observed XRD pattern.
Hope you will find some useful information in your search.
Sreekanth
The procedure is straightforward and is something that we teach to our first year undergraduate students when we introduce them to diffraction. I'll describe the old-fashioned paper and pencil method:
First, measure the 2-theta values of the lowest angle diffraction peaks in your pattern and list them in a column. For each, calculate [sin(theta)]^2 and then compute the ratios of successive values of [sin(theta)]^2, and list these as the nearest integer. These are labelled "N" below. For a first example, suppose we have the following 2-theta values and their results:
2-theta sin(theta) [sin(theta)^2 N(ratios of previous column as integers)
25.45 0.2203 0.0485 1
36.30 0.3115 0.0971 2
44.86 0.3815 0.1456 3
52.28 0.4406 0.1941 4
59.02 0.4926 0.2426 5
65.31 0.5396 0.2912 6
77.08 0.6231 0.3882 8
82.73 0.6609 0.4367 9
Since [sin(theta)]^2 is proportional to N, where d=a/sqrt(N) and N= h^2 + k^2 +l^2 the values above correspond to a primitive cubic structure (we can tell this because N=7 is not possible from the sum of three squares). If the result came out as:
2-theta sin(theta) [sin(theta)^2 N(ratios of previous column as integers)
25.45 0.2203 0.0485 1
36.30 0.3115 0.0971 2
44.86 0.3815 0.1456 3
52.28 0.4406 0.1941 4
59.02 0.4926 0.2426 5
65.31 0.5396 0.2912 6
71.30 0.5828 0.3397 7
77.08 0.6231 0.3882 8
82.73 0.6609 0.4367 9
then we would know that this is actually a cubic I structure (body centred, bcc) because 7 is impossible, and actually our results should be correctly listed as:
2-theta sin(theta) [sin(theta)^2 N(ratios of previous column as integers)
25.45 0.2203 0.0485 2
36.30 0.3115 0.0971 4
44.86 0.3815 0.1456 6
52.28 0.4406 0.1941 8
59.02 0.4926 0.2426 10
65.31 0.5396 0.2912 12
71.30 0.5828 0.3397 14
77.08 0.6231 0.3882 16
82.73 0.6609 0.4367 18
and the values of N correspond to the reflections expected from the systematically allowed reflections of the body-centred translational symmetry (h+k+l even, i.e. 110 (N=2), 200 (N=4), 112 (N=6), 220 (N=8) etc.)
Finally, if the results came out as:
2-theta sin(theta) [sin(theta)^2 N(ratios of previous column as integers)
44.86 0.3815 0.1456 3
52.28 0.4406 0.1941 4
77.08 0.6231 0.3882 8
93.87 0.7306 0.5338 11
99.48 0.7631 0.5823 12
we would know that the structure is fcc (cubic F) with only the reflections corresponding to (hkl) all odd or all even present (i.e. 111 (N=3), 200 (N=4), 220 (N=8), 311 (N=11), 222 (N=12) etc.)
Hope this helps!
X-ray Diffraction by B.E. Warren is a great book for learning the basic principle of x-ray crystallography. You can get a copy on amazon for less than $10. It's out of date with respect to the instrumentation (mainly the lack of area detectors at the time), but the principles are the same.
A classic textbook that every materials science engineer should have is "Elements of X-ray Diffraction" by Cullity. It is still available with, I believe, updated editions. It will go through the procedures on how to analyze powder diffraction patterns. Used copies should be easily available from Barnes & Noble in the US and through Abes Bookstore in the UK.
U can use a structure solution by difference fourier analysis or by charge flipping method. But first u had to do indexing (DICVOL, ITO, McMaille or TREOR).
U can use some free software such as JANA2006 and GSAS-II, commercial such as HS+ and Topas
Dear Dev,
From your question, i think you know that structure belongs to cubic symmetry. If you know then simply use ratio of h2+k2+l2 or as suggested by Prof Simon Redfern and compare your results: [If your crystal is cubic and just you want to know it is BCC/FCC etc, you can find reference in "Elements of XRD" by B.D.Cullity Book as suggested by Michael Tem
With best wishes
Enough answers that will assist you as a hard working student have been provided. Work through them and you will surely appreciate the good works of our foundation Scientists.
I apologies for my mistake Sreekanth Mandati sir. And I thank you Simon Redfern, Sreekanth Mandati, Volker Klemm, Lawrence Margulies, Charles S. Montross, Michael Tem, Amaresh Raichur, Israel Owinjima Owate for your ideas....
How can I find the structure (FCC or BCC etc) via XRD structure for high entropy alloys?
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