There are new peaks on the diffractogram that show this phenomena?

The single shift of 101 means a possible modification of the lattice just in this specific plane. You have to compare the ion radius of the dopant with the titanium. Smaller ions can substitute other atoms in the lattice without evident modification of the structure, however also bigger ions can be replace atoms in the lattice and if the radius is comparable to the original one there is no difference in the XRD. Different situation if a new peak between 30 and 36° appears (in consideration that anatase has tetragonal structure).

You have to consider that if you analyze doped nanoparticles the FWHM of the peaks is very large and it is difficult to say if there is a slight shift or not. Another consideration is about the method of the synthesis and the T/P parameters. Some residues of the precursor used can form different compounds or small amount of the relative oxides.

IMHO because you are analyzing NPs systems it is very difficult to say if there is a shift (if you are not using a Synchrotron X-ray Diffraction) and also you need to be absolutely sure your system have very high purity.

The short answer to the question is: Yes. This has been shown in excess for the substitution of Ca for (smaller) Mg in the calcite lattice due to a contraction of the crystal lattice of calcite. So you'll need to figure out first whether the crystal radii of you dopants are smaller or larger than Ti (or O if they replace O rather than Ti), a larger crystal radius of the dopant will cause a expansion of the crystal lattice and shifts peaks to lower angle and the reverse for smaller crystal radii.

What you'll need to take into account as well, what Enrico Greco is talking about is how much strain the replacement mechanism causes on the structure and the effect on the particle size (both likely resulting in an increase of the FWHM). Also you'll need to take into account that the electron density of your dopants will affect the peak ratios in your diffraction patterns.

Nevertheless, even with a small change in the lattice parameters and a large increase of the FWHM by performing relatively basic Rietveld refinements (e.g. with Topas) you will be able to determine minor changes in the crystal lattice, especially if you use an internal standard like Si to correct for shifts in the diffraction pattern due to minor changes in geometry and position of your sample.

ps. synchrotron radiation is not essential for such analyses, though it definitely can be useful.

Thank you very much to all

The main question is: what does doping means in your case? I commonly use this term in case of a small amount. If you assume a concentration of about 1% of an doped element than this atom appears along all three dimensions in average in each fifth unit cell only (if we exclude the formation of ordered structures). From this you can already imagine that this doping should only result in wider peaks than shift the peak. The peak broadening is an effect of the local loss of translation periodicity of the lattice caused by bigger/smaller atoms. The higher the concentration the closer substituting atoms  and the more probable an effective contraction of the entire lattice becomes. IN case of ordering everything becomes more complicated since then translation periods much bigger than one unit cell occur. The peaks stay narrow and additional peaks appear, mainly visible at clearly lower Bragg angles than observed before.

Peak shift can also have its origin and a misalignment of the sample. The misalignent of the diffractometer (e.g. changing of tube, detector, monochromator etc) can also generate a considerable peak shift. If the concentration of your doping is small (as I expect) I would not assume a peak shift you really observe immediately. Calcite-dolomite is a nice example for a solid solution in mineralogy but I would call the solid solution doping. But this is a question of terms used.

And as Pieter said: Only because Synchrotron is fashion and famous for its brilliance it cannot help when your material bears the observed properties. People also investigat martensite with synchrotron and do not consider that only a negligible part of the observed broadening is caused by the natural width of the radiation used since everything correlates with the loss of the assumed infinte periodicity of the lattice...either the product of small crystals which are far away from being infinite (perfect crystals with an abrupt end, i.e. used for "grain size" determination), or by lattice defects (dislocations, vacances, grain boundaries etc -- which is assumed to b responsible for "strain"....NOT "residual strain". This is something totally different.).   

@ Pieter: He cannot work with an internal standard since he has no powder but a bulk material. Moreover, the internal standard should have a similar linear absorption and grain size as the phase you are investigating. I know, anything is better than nothing but one should keep the required conditions in mind.

Dear prof. Nolze,

thank you very much for your very useful answer. As you correctly supposed i used a small amount of doping agent (from 0.2 to 1 % at.), I'm very grateful for yours and other answers because they solved my doubts.

Thank you very much

Then, as I expected, you should not assume that the observed peak shift has it's primary reason in a simple increase of the lattice parameter. 

I have been also more recently studying the effect of annealing temperature on the XRD peak shift of the dominant Anatase peak in titanium dioxide nano tube an i have somewhat observed an increase in crystallize size with in increase in annealing temperature simultaneous with the d spacing also increasing. I have also observed a general decrease in FWHM with increase in annealing temperature. Is this normal?