For binary Fe-C alloy one can find the answer in the equilibrium phase diagram: C atoms are in Fe3C and in metallic matrix: in fcc and bcc lattices they are in octahedral positions.
Thank you for your kind attention Prof.Golovin. As i grasped, the C atoms can be in the positions illustrated with red point in following figure. but, what about the percent of the carbon in the metallic matrix? if we only have three atoms (for example), which positions can be to cause a stable condition (minimum cohesive energy)? do they position in a random manner?
Dear Seyed Mehrdad Zamzamian, you add picture for bcc lattice which is reasonable for room temperature (I do not know from your question at which temperature you are interested). Red points - octahedral positions. Total amount of C in matrix can be calculated at RT can be easily calculated from equilibrium phase diagram - this is typical exercise for students. Under non-equilibrium conditions there is a chance to estimate C content in solid solution by measuring the height of Snoek peak. You can find details in: http://www.springer.com/us/book/9783540687573 or download it from my cite at researchgate. You can also have a look to attached file. Good luck!
I really appreciate the time you spend for answer and for references that you suggested. the method that you have mentioned is a experimental approach, but my goal is to consider metal alloy characteristics using a computational molrcular dynamic code like lammps. in defining a binary alloy like Fe-C. as you mentioned, the C atoms are locate in octahedral positions. Now, my interesting is to know how many C atoms should be define in octahedral positions (figure above for unit cell) in lammps code to have an alloy 97%Fe 3%C. measuring C content in the solid is not desire in this case. the temperature that i am interested in is higher than 400k.
You can use "http://lammps.sandia.gov/doc/compute_voronoi_atom.html". Occupation keyword can be used to find the interstitial atoms and can be visualized in OVITO. Neighbors keyword can be used to find the atom in that interstitial site. Or you can save the PE, KE and stress of all atoms and visualize in OVITO. A-A, B-B and A-B will have different above parameter values and can be identified in OVITO.