For powder X-ray diffraction planes with the same d-spacing will indeed be coincident in the pattern, and in the absence of strain or preferred orientation will be indistinguishable. But in a single crystal diffraction experiment you are able to isolate individual diffraction peaks which will now be distributed across 3D reciprocal space, which is what becomes folded down into 1D (d-spacing if 2theta) for powder diffraction.

For powder X-ray diffraction planes with the same d-spacing will indeed be coincident in the pattern, and in the absence of strain or preferred orientation will be indistinguishable. But in a single crystal diffraction experiment you are able to isolate individual diffraction peaks which will now be distributed across 3D reciprocal space, which is what becomes folded down into 1D (d-spacing if 2theta) for powder diffraction.

Agree with Dr. Redfern’s answer. By the way, in PXRD, this is related to a multiplicity factor and does have an influence on the peak intensity.

The magnitude of the reciprocal lattice vector K(hkl) = 2pi/d(hkl), which is the same for all these planes. Therefore we cannot distinguish the reciprocal lattice vectors normal to these planes except by their orientations. In a typical powder diffraction experiment, however, all orientations are randomly distributed and equally likely. Therefore it is not possible to distinguish these planes from such an experiment. Further, symmetry of the crystal would take you from one plane to another by an appropriate rotation, which cannot be realized in a powder diffraction experiment due to the equal likelihood of all orientations.

I have a little confusion and any explanation is highly appreciated in this regard.

If the d-spacing values of 100, 010 and 001 planes are same then we can say the system is either cubic or rhombohedral depending on the whether the angle is orthogonal or not.

In cubic or orthogonal lattiice, to my understanding (100), (010) and (001) are exactly same planes. they are NO different than each other either in physical or in chemical nature. if the planes are different from each other chemically, then by the law of thermodynamics the lattice can not be cubic or isotropic and should show anisotropic (e.g. triclinic, tetrahedral) strain. This will result into splitting of peaks.

Is there any other explanation for differenciation between (100), (010) and (001) planes except to facilitate a mathemetical (or more precisely geometrical) framework?

Please let me know and if possible please give me an example of such a crystal.

All the three planes are non degenerate that's why can not be separated in XRD. But if you do the degeneracy among them by someway, like preferred crystal growth in some particular direction or any type of interaction (physical or chemical) with some foreign substances or the matrix, then it may be differentiated in XRD.

Biplab Roy you need them. How would you then describe the plane (111) without 3 base vector?

Well guys you cannot have everything from powder diffraction. If the sample is cubic and not of such a space group like Pa3, where there is no four-fold symmetry then you do not miss much. But if your sample is pseudocubic then you will never be able to determine the structure correctly. The same applies to all other pseudosymmetric cases viz. pseudotetragonal, pseudoorthorhomic etc. etc. In these cases you need to have single crystals and careful experiments on single crystals will tell you more of the structure that you cannot have from powders. The situatio is even more critical for magnetic structure determination because in the magnetically ordered phase the crystal transform sometimes to low symmetry structure due to the magnetoelastic effect.

So better learn to grow single crystals!