Volume of a solid at absolute zero

you can use a Gruneisen second order approximation for the zero-pressure equation of state [Vocadlo L, Knight K S, Price G D and Wood I G 2002 Phys. Chem. Miner. 29 132]. In order to apply this equation you must have at least some unit cell volume values at different temperatures, you must know the Debye temperature and the bulk modulus value of your compound. By fitting the experimental volume data (you have some free parameters in the fitting) you can extrapolate the unit cell volume at the lowest temperature.

This holds if you don't have structural transition in the inspeected thermal range, otherwise you have to consider only the volume data of the low-temperature phase.