Have a look at:

http://en.wikipedia.org/wiki/Vegard%27s_law

http://en.wikipedia.org/wiki/Amagat%27s_law

I'm afraid not much more can be said in your 'easy' case.  Maybe you should play with sum of (partial) volumes assumed as third powers of lattice constants?  That's purely 'geometrical' approach and its results (if any) may be far from physical reality, even if you have a single lattice constant for each composition.