Copper in this respect is luck one. Since it has very low stacking fault energy dislocations formed during the cold-worked  show extended configuration having stacking fault ribbons  between partial dislocations.  The change in the separation of the   {111} and  {200} reflections  in a deformed and in a well-annealed sample becomes proportional with the stacking fault probability.  This probability is given by the bi-product of  dislocation density  and stacking fault ribbon width.  The ribbon width may be measured by TEM, which independent  of dislocation density for a given material.  Therefore XRD  combined with TEM  is a powerful technique to obtain dislocation density in low stacking fault material such as alpha brass etc.

Hi Rohit, in the paper of T. Ungár you find all information you need:

http://ac.els-cdn.com/S0921509301010255/1-s2.0-S0921509301010255-main.pdf?_tid=d8644144-34ef-11e5-b309-00000aab0f6c&acdnat=1438064223_1e1749a33eaf01e32e8e5c9a3bd2dc73

Article Densities and character of dislocations and size-distributio...

Yes you can calculate from Groma's Variance methods as well as using the modified Wiliamson Hall methods. The care required is that you have record very good x-ray diffraction patterns with small step size and high peak to background ratio. The major difference between the two methods is that Groma's variance based method allow you to calculate dislocation density from individual peak while the Williamson Hall method uses multiple peaks. This difference becomes important when samples have significant texture.

Hi Rohit, tit is difficult to give you a specific  answer with many missing information about the experiments that you have already conducted. I suggest to search for the work by Prof. Tamas Ungar and the work by Dr.M G Glavicic on using XRD line broadening to estimate dislocation density in deformed material. 

I think the most powerful technique to estimate dislocation density even the dislocation cell size without worrying whether one has low or high stacking faults energy is  NMR measurement of peak broadening associated with the nuclear quadruple interaction by relying on the powerful first principle calculations of certain fundamental parameters such as the 'enhancement Factor' associated with the conduction electron charge redistribution around the dislocations etc. This has been done for Copper by Ogurtani and extensively used in the literature to study not only static but also dynamic behavior of dislocations in metals and alloys. SEE:  Some related publication in RG  and also Ph.D. Thesis by Ogurtani available from Harvard Library Cat.

Rohit Mathew The dislocation density is a measure of the number of dislocations in a unit volume of a crystalline material i.e. the length of dislocation lines per unit volume of the crystal (m/m3) Edge dislocation Screw dislocation Dislocations distort a crystal lattice, causing elastic stress around the dislocation line, & hence strain energy. For ultimate strength, dislocations are to be eliminated.

In this video, I have discussed the nature of dislocation density and how to calculate the dislocation density from XRD using origin. In the case you want to further ask about it, please do comment on the specific video, I'll respond to it shortly. I have provided the practice as well as calculations files here. Thanks

https://youtu.be/WyvwytYYSK8

Please check the following article,

T. Ungar, S. Ott, P.G. Sanders, A. Borbely, J.R. Weertman, Dislocations, Grain Size and Planar Faults in Nanostructured Copper Determined by High Resolution X-Ray Diffraction and a New Procedure of Peak Profile Analysis, Acta Mater. Vol. 46 No. 10 (1998) 3693-3699.