In my book,its given that Ti-c interstitial compound has higher melting point than that of pure metal Ti.i wanted to know why small atoms like( H,C,N,B) in the vacant spaces in the lattice of transition metals increase their melting point.
That was my line of reasoning: I am reasonably sure about fcc (compare http://www.crystallography.net/5910091.html?cif=5910091). As electronegativity difference is around 1, I expected some ionic character, so smaller radius for Ti (cation) and a larger radius for C (anion). Lousy, but should be pointing in the right direction. And I found a page with ionic radii that seemed to confirm this line of thinking, unfortunately, I don't remember where it was.
I admit I have no idea where is the border between "still an interstitial compound" and "no longer an interstitial compound" - I mean, at some point it is hard to speak about "small atoms sitting in holes", they start to occupy not a hole (which happens when metal atoms stay in almost the same places they occupied before adding the other element), but just a normal place in the lattice (so the metal atoms have to move away to make place for newcomers).
Considering the original question, I would argue as follows: Metals, including Titanium are generally electron deficient materials, i.e. they have much more neighbouring atoms than they can form covalent bonds. The carbon atom delivers electrons which the metal can use to form bonds to it's neighbours thus increasing strongly the cohesion of the metal.