why you say they are arbitrary? The 2theta plotting is just convenient: several machines operate with fixed source and therefore the measured angle (the one of the detector) is 2theta with respect to the incident beam. As for the intensity why you say it is arbitrary? "counts" is the most common unit of measurement as the detecing circuit usualy counts the number of pulses (related to the number of detected photons). Of course you can arbitrarily choose your time to plotting in "counts" does not give you an abosulte scaling. You can however rescale your pattern and plot it in electron units (the rescale is necessary e.g. when you deal with the PDF method)
why you say they are arbitrary? The 2theta plotting is just convenient: several machines operate with fixed source and therefore the measured angle (the one of the detector) is 2theta with respect to the incident beam. As for the intensity why you say it is arbitrary? "counts" is the most common unit of measurement as the detecing circuit usualy counts the number of pulses (related to the number of detected photons). Of course you can arbitrarily choose your time to plotting in "counts" does not give you an abosulte scaling. You can however rescale your pattern and plot it in electron units (the rescale is necessary e.g. when you deal with the PDF method)
To determine the lattice parameter for every each of the spectrum XRD's it is easier to use the MATHCAD software e.g 110, 110...so the two theta it just from machine same from the answer given before. The important here is how to get the lattice parameter before it was plotting using the MS excel.
Intensity of XRD peaks also depends on the orientation of crystallites, crystallite size and texture and hence the intensity is expressed in arbitrary units. The most intense peak is 100 and others are normalized with respect to the most intense one.
Matteo's answer - as usual - is accurate and informative. The theta scale comes from the Bragg equation and is related to the plane spacing; as Matteo says, the 2 is included because of the design of (older?) diffractometers. If you're not clear on the geometry of diffraction and diffractometers, I recommend finding a good textbook before you go much further - my favourite is 'The Basics of Crystallography and Diffraction' by Christopher Hammond, but plenty of others will be just as good.
(Note that you may occasionally see diffraction data plotted with s on the horizontal axis. This is used in more accurate calculations of, for example, crystallinity of polymers, but is beyond the scope of this discussion!)
The raw intensity data is measured in counts, corresponding roughly to individual diffraction events. This is heavily dependent on the source, the detector, the instrumental design, sample preparation and a host of other factors and so is not terribly useful in itself. As Dr. Parthasarathy notes, it is common to normalise by the intensity of the largest peak, so that comparisons may be made between measurements collected under different conditions.
For more quantitative calculations, it is also possible to include a reference material and scale the intensity by that of one of its peaks. The reference intensity ratio (RIR) method for quantitatively determining sample composition takes this approach.
Note that strictly speaking, we should talk of the AREA of diffraction peaks. In comparing peak HEIGHTS, we are tacitly assuming that they have the same full width at half maximum. This turns out not to be a bad assumption, but can cause inaccuracies if peaks are broad.
.. last not least it is not a bad idea for many purposes to scale the Y-axis to a count rate (i.e. counts/s) because then you may easily compare data sets measured with the same setup, but different scan speed, or different degree of crystallization in a series of samples, etc.
@Philip: thanks for the nice words. Yes I completely agree that "Intensity" when talking about a single peak MUST be the integrated one. Just notice that the peaks become naturally broadened at high angle due to the nonlinear scaling between reciprocal and 2theta space...
@Dirk: rescaling is good ONLY for plotting purposes! Never analyse the data in cps (counts per second)!!!! In fact most software use the intensity to extract the information on the variance associated to each measurement point.. as the value is related to the square root of the counts, changing the intensity artificially changes the weight.
@ Matteo: Of course you are right, rescaling to count rates is only for visualization, never for fitting - absolutely correct!
@ At all: Have a nice week-end
Very frequently in papers two or more patterns are plotted together with a vertical shift in one or more of them to allow visualization of similarities and differences. Other times two or more patterns are nomalized or rescaled to have the maximum intensity in the same value, again to improve visualizaition of details. In both situations individual intensities of the patterns are arbitrary numbers, not the relative intensities though that relate to the diffraction intensities.
In these two cases the use of "Intensity (arb. units)" in the Y axis of the plot is clearly justified. It would be useful, though, to have the information on the processing the data suffered before ending in the figure, so readers can relate the figure to the original data. This is mostly important in situations where the absence of extra peaks or phases is intended to be shown in small figures with undetermined background or data noise.
Since the absolute measured intensity in a pattern depends on the selection of experimental conditions (optics, count time, source intensity, etc) additionally to the scattering power of the sample then it is acceptable to rescale patterns for visualization purposes, but only for that purpose since the absolute value of the intensity is related to the standard uncertainty and therefore the noise in the pattern is not rescaled with the intensity. I agree with previous comments that Rietveld or other type of analysis should be performed on raw data (unless proper care is taken to indicate the true standard uncertainty of each observed intensity value that will differ from the square root of the intensity if any rescaling is applied).
Maybe we should start asking the publishers (through editorial or referee work) to include the raw data that supports figures or conclusions of a publication in some form (suplementary material for example) so the reader can judge for himself if the conclusions of the authors are correct.
Dear Bamadev Das,
what was the purpose of the XRD spectra you have seen that caused your question?
My guess is they were not very useful addition to the article, they were inserted there only to make the said article look "more scientific". That's sad truth. Well, sometimes they are attached to convince the reader that the samples under investigation were free from foreign phases, just pure and uniform. Arbitrary units in intensity scale are just fine then, even if the scale itself is logarithmic.
@Leo: I always ask the authors to submit their data when the results are doubtful or something strange seems to happen... and as ICDD member, you know the huge problems related to real data ...
@Marek, I totally agree with you when you say that sometimes diffraction data are just thrown in to show that another measurement has been done (or cause "everybody shows something like this"). Unfortunately in most cases the only thing you can see is the noise or the age of the tube :D
Normallly, its unit is count. When we plot them compared together, we have to normalized XRD intensity.
Why it is plotted with two theta? Because, diffraction line diffracted with 2 theta degree compared with the incident line.
Muhammad, could you share the source of "Lins(counts)" expression? Is it a paper? Please share the citation or a picture of the pattern or something that does not infringe copyright law and I guess many of us will be able to interprete it and help you.
Leopoldo suescun, sorry typo --it is Lin (counts) NOT lins--what lin meaning?
Maybe the natural logarithm of intensity? Show me the graph and I'll try to figure out.
Each peaks in a XRD pattern are related to another peaks of that material in some proportionality. Thus one should calculate the relative intensity of all peaks considering the major peak as 100%.
On recording XRD form different machines or with different settings the counts will change according to various factors. Hence the above method can be used to analyze a material. Counts generally refers the number of reflections arised due to the crystal planes.
Definition
Powder X-ray Diffraction (XRD) is one of the primary techniques used by mineralogists and solid state chemists to examine the physico-chemical make-up of unknown solids. This data is represented in a collection of single-phase X-ray powder diffraction patterns for the three most intense D values in the form of tables of interplanar spacings (D), relative intensities (I/Io), and mineral name.
The XRD technique takes a sample of the material and places a powdered sample in a holder, then the sample is illuminated with x-rays of a fixed wave-length and the intensity of the reflected radiation is recorded using a goniometer. This data is then analyzed for the reflection angle to calculate the inter-atomic spacing (D value in Angstrom units - 10-8cm). The intensity(I) is measured to discriminate (using I ratios) the various D spacings and the results are to identify possible matches.
Results are commonly presented as peak positions at 2θ and X-ray counts (intensity) in the form of a table or an x-y plot
Sharin Bin Ab Ghani, cps refers to counts per second, the intensity is scaled by the time used to collect it in every step. cts refers to counts.
If you want to represent two diffraction patterns that were collected in the same instrument with the same geometry but different counting time you may want to scale them to cps, however scaling them in any other form will be fine if you explicitly declare the scaling procedure.
For Rietveld refinement you don´t want a pattern in cps unless you explicitly calculate the standard uncertainty for each intensity and add it to the data file.
I hope this helped.
Leo
Thanks Leo, really appreciate it. One more thing, can we convert the cts to cps? How to do that?
If you know the time per step for data collection you should be able to calculate cts from cps by multiplying cps*(time/step). If you don´t have that information then you´ll have to guess it. Since the cts are natural numbers and the pattern was probably collected with constant time/step if you check the intensity values you will find fractions that suggest if time is 2, 3, 4, 5, etc... If you cannot find this and want to share the data please send it privately and I´ll try to find it.
Good luck
Leo
Any body have JCPDS card for Ti, Al, V, Ni, Mo, Sn elements
if possible Plz post here, it will helpful to find the elements and hkl values to me
Thanks in Advance
why 2theta? the image here can give you an answer.
However, it depends on what you would like to communicate based on your data.
Some authors presented d-spacing / theta instead of 2 theta.
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