The reason why doublet peaks occur was already explained perfectly by Vibhor Atreya, so I will just discuss why you may not see the doublets. If you can see two separate peaks or just one peak (that is broadened because it consists actually of two overlapping peaks) depends on two aspects: the separation of the peaks and their broadening.The peak separation, i.e the c/a ratio, mainly depends on the carbon content of the steel (my favorite paper showing this dependence is C.S. Roberts, Journal of Metals 5 (1953), 203, but there are also many others). If the carbon content of your steel is small, you may never see doublets, because the separation is so small that the doublets overlap heavily and form one visible peak. The XRD peak broadening has a number of contributions both from the sample and the diffractometer. For example, very small grain size in the martensite results in significant peak broadening, so that the doublets may be not visible as individual peaks even if the splitting is quite large. Generally, the broader your peaks the more tetragonal distortion (higher c/a ratio) is necessary to oberserve the doublets. The use of radiation consisting of both Kalpha1 and Kalpha2 can also contribute to the "invisibility" of the doublets, since in this case you have actually 4 peaks very close together  on 2theta scale (one doublet from Kalpha1 and Kalpha2 each), which are more likely to overlap such heavily to hide the actual individual peaks in one observable peak profile.

This phenomena is very common. You know that from peak location (theta) you can calculate planar spacing (d) and from that you can get to know the lattice parameter. If the lattice is pure fcc or bcc, it has a cubic structure and all lattice parameters are equal. So the result is one peak corresponding to one value of lattice parameter. Now martensite has bct structure, so there are two different lattice parameters. But the difference between them is very small. So the result is you see two peaks very close to each other.

Or you can say it this way: with slow cooling fcc steel was supposed to convert to bcc (single peak) but fast cooling didn't allow it to do so. So it didn't change into bcc completely but into an intermediate stage bct (two parameter, two close peaks). So ideal condition is single peak, but due to martensite formation, we get two close peaks instead, ie, it splits. I hope it helps.

The reason why doublet peaks occur was already explained perfectly by Vibhor Atreya, so I will just discuss why you may not see the doublets. If you can see two separate peaks or just one peak (that is broadened because it consists actually of two overlapping peaks) depends on two aspects: the separation of the peaks and their broadening.The peak separation, i.e the c/a ratio, mainly depends on the carbon content of the steel (my favorite paper showing this dependence is C.S. Roberts, Journal of Metals 5 (1953), 203, but there are also many others). If the carbon content of your steel is small, you may never see doublets, because the separation is so small that the doublets overlap heavily and form one visible peak. The XRD peak broadening has a number of contributions both from the sample and the diffractometer. For example, very small grain size in the martensite results in significant peak broadening, so that the doublets may be not visible as individual peaks even if the splitting is quite large. Generally, the broader your peaks the more tetragonal distortion (higher c/a ratio) is necessary to oberserve the doublets. The use of radiation consisting of both Kalpha1 and Kalpha2 can also contribute to the "invisibility" of the doublets, since in this case you have actually 4 peaks very close together  on 2theta scale (one doublet from Kalpha1 and Kalpha2 each), which are more likely to overlap such heavily to hide the actual individual peaks in one observable peak profile.

Thank you for responding to the questions. It was helpful, however I find it surprising that most of the research articles when estimating retained austenite content by the method of comparing integrated intensity of peaks of austenite and martensite never show the splitting information of the peaks.

If i have understand correctly from the answers above. The broadened peak of martensite (211) actually consists of (112)/(211) or total fours peak when measuring with Kalpha 1 and Kalpha2.

However in published articles the martensite peak is always labelled as (211) is there a special reason why the splitting information is not labelled, should it be written as (112)/(211) instead. Even though one cannot see the splitting but it is supposed to be there.

Can you please comment on this.

I have performed measurements for medium carbon martensite steel which could have the broadening of (211) peak of martensite up to FWHM of 8. In annealed state the martensite broadening is smaller and i have seen splitting of the (211) which i think is due to use of Kalpha1 and Kalpha2.

I guess by "the method of comparing integrated intensity of peaks" you mean the method as described for example in R.D. Anrell, Journal of The Iron and Steel Institute, October 1968, 1036 or A.K. De et al, Scripta Mater. 50 (2004), 1445. According to this method, the volume fraction of a phase is proportional to the sum over all its peak intensities Ihkl divided by the material scattering factors Rhkl divided by the number of peaks. Although I'm no expert in XRD of martensite, I think that treating the two overlapping doublet peaks as one peak for this quantitative phase analysis is allowed because of the following reason:

Consider the (211) peak: In the cubic case (i.e. when you consider only one peak), this peak has intensity Ic211 and multiplicity m=24. In the tetragonal case, there are It211 with m=16 and It112 with m=8. Now let's assume that all contributions to the material scattering factors Rhkl except the multiplicity are the same for the two doublet peaks (e.g. structure factor, Lorentz polarization factor, etc). This assumption should be approximately true as long as the tetragonal distortion is not too large. With this assumption, R=const * m. Besides, assuming that there is no preferred orientation of the tetragonal c-axis results in It211=2/3 * Ic211 and It112=1/3 * Ic211.

In the sum of the intensities of the martensite phase, you get for (211) in the tetragonal case:

It211 / (const*16) + It112 / (const*8) = (It211 + 2*It112) / (16*const) = (1.5*It211+3*It112) / (24*const) = (1.5* (2/3) * Ic211 + 3*(1/3) * Ic211 ) / (24*const) = (2*Ic211)/(24*const)

Thus, the contribution from the (211) peak to the sum of intensities is doubled in the tetragonal consideration. But you also have 2 peaks instead of 1. If all peaks split up into doublets, you would sum up the doubled intensities and then divide by the doubled number of peaks, resulting in the same result as for the cubic consideration. However, some peaks don't split up (e.g. (222)), some peaks form doublets (e.g. (211)), some triplets (e.g. (310)). In this case, the tetragonal treatment of the peaks changes the weighting of the individual peak intensities for the sum: Peaks, which split up into more peaks, get more weight.

In a texture-free sample this should not affect the resulting volume fractions. If the sample is textured, the different weighting will change the result of this quantitative phase analysis. However, for the textured case the whole method is just an approximation according to my understanding. The accuray of the estimated volume fractions will then mainly depend on the texture and the number of peaks measured.

This explanation just came up from my understanding of this "method of comparing integrated intensity of peaks", but I don't have any publications supporting this consideration. Thus, I'm looking forward to any comments.

Well surely, that was a very detailed answer. Yes, i guessed the same but you took a step a head in proving it with some simple calculations. It would be nice we get some more feedback ... thanks for the reply....

SAE SP-453 - Retained Austenite and Its Measurements by X-Ray Diffraction - The definitive work on austenite measurement.  It presents plenty of theory and basis for the formulae but its focus is very practical.  It is old, but still unsurpassed (to my knowledge)