Coring Diagram

The alpha (for instance) starts to solidify with composition 1 (in the diagram). The next layer of alpha to solidify will be of composition 2 and, if cooling is rapid diffusion will not have time to occur and the central "core" of composition 1 will remain. This process continues with many layers of differing composition alpha forming.

Further Reading:
Materials Science and Engineering; W.D. Callister Page 257