Nanocrystals with dimensions of 1–10 nm are of increasing importance in technological applications. The calculation of the Madelung constant for a particular structure type requires the summation of an infinite series of terms, and this method is not applicable to a crystal of nanometre dimensions. Discuss how the concept of a Madelung factor, A*, may be used to describe the total ionic interactions in nanocrystals. How does A* vary as a function of nanocrystal size for 

(a) The NaCl structure type 

(b) The CsCl structure type? How might the properties of a nanocrystal differ from the bulk solid as a result? See M.D. Baker and A.D. Baker, J. Chem. Educ., 2010, 87, 280.