An single crystal is one single block where all the symmetry operations of the structure are valid for the whole block. However, this is so for an ideal single crystal only. In real single crystal often consists of mosaic distribution of regions which are slightly misoriented. This mosaic spread reduces the extinction of the ideal perfect crystal and the kinematical  theory is of X-ray diffraction is valid. The polycrystalline material consists of single crystals described above but of very small sizes of the order of micrometers but randomly distributed when there is no preferred orientation. The chemists often produce polycrystalline samples in their lab. There exist several methods to grow single crystals from the polycrystalline substance. Now X-ray diffraction signature of a single crystal is the existence of Bragg spots. They will be only seen in a diffractometer whenever the Bragg condition is satisfied. A polycrystalline substance will however show Debye rings rather than Bragg spots. To interpret diffraction effects from powder or polycrystalline substances we must consider only he magnitude of the momentum transfer viz. |Q| because due to random orientation the information of the vector properties of Q has been lost. For single crystal diffraction however we retain the vector charecter of Q. Q is defined as Q = 4\pi sintheta/lambda. The crystallographer use an another vector s = sintheta/lambda but it is basically the same as Q.

An single crystal is one single block where all the symmetry operations of the structure are valid for the whole block. However, this is so for an ideal single crystal only. In real single crystal often consists of mosaic distribution of regions which are slightly misoriented. This mosaic spread reduces the extinction of the ideal perfect crystal and the kinematical  theory is of X-ray diffraction is valid. The polycrystalline material consists of single crystals described above but of very small sizes of the order of micrometers but randomly distributed when there is no preferred orientation. The chemists often produce polycrystalline samples in their lab. There exist several methods to grow single crystals from the polycrystalline substance. Now X-ray diffraction signature of a single crystal is the existence of Bragg spots. They will be only seen in a diffractometer whenever the Bragg condition is satisfied. A polycrystalline substance will however show Debye rings rather than Bragg spots. To interpret diffraction effects from powder or polycrystalline substances we must consider only he magnitude of the momentum transfer viz. |Q| because due to random orientation the information of the vector properties of Q has been lost. For single crystal diffraction however we retain the vector charecter of Q. Q is defined as Q = 4\pi sintheta/lambda. The crystallographer use an another vector s = sintheta/lambda but it is basically the same as Q.

All the symmetry properties of the structure are present in an ideal single crystal whereas for polycrystalline substances all the symmetry elements are only retained for a single grain which is also a single crystal but very small.

Thank you for clarifying the differences. if yo have any idea about the amorphous and polyamorphous materials also please expalin here.

Amorphous materials do not have long-range crystalline structure but often have short-range correlations which lead to broad humps in the intensity variation X-ray diffraction intensities with Q or scattering angle 2\theta. Short range correlation signifies that in the local structure it has still the some recognizable chemical bonding and cluster formation but they do not repeat regularly to form crystals not even polycrystalline form that are charecterized by sharp Bragg spots or Debye rings. Now a crystal may have polyphorphism meaning it may be crystallized in different crystal structures depending on the growth method and conditions. This happens when these different crystalline structures have almost same energies. Similar situation can happen to an amorophous substance which may have different types of short range order and there may even be transitions between these different polyamorophous phases like in their crystalline analog where the corresponding term is polymprphous phases.

Thank you but small corrections in the term Polymorphism. 

Dear sir,

Suppose i powder a single crystal , can i say that it is polycrystalline??

Yes of course. That way you may get a better quality polycrystalline sample than by other routes. I have myself done this several times. You feel yourself a bit guilty because it is so difficult to grow single crystals.

How to distinguish between single crystal and polycrystal  just by observing XRD pattern? Clarify with XRD pattern. Also which information is revealed from the observation of XRD pattern?

Single crystals will show sharp Bragg spots whereas the polycrystal will show Debye rings in X-ray diffraction provided you diffractometer has a 2D detector. If you have diffractometer with a single detector then polycrystals will give you a lot of peaks whereas a single crystal may not give any opeak at all unless it is oriented.

A polycrystalline material need not always produce isotropic rings. In the case of oriented polymers (fibers, sheets etc), sharp diffraction "peaks" are observed. The sharpness of the peaks (azimuthal width) is a function of the degree of orientation in the polymer.