Redlack, Austin2017-09-072017-09-071972-11-011972-11http://hdl.handle.net/10012/12332This thesis is written in two parts. In Part One, we develop a new method for evaluating three dimensional lattice summations and apply it to the evaluation of the electrostatic potential of a finite ionic crystal. We then compare our expression with those obtained using infinite crystals. Some of the effects which are not obtainable using an infinite crystal are: i. the electrostatic potential depends on the shape of the sample when a dipole or quadrupole moment is present, and 2. the electrostatic potential at the surface of a crystal changes rapidly near the surface. In Part Two, we use the method developed in Part One to evaluate the electrostatic potential in a deformed crystal and use the resulting expression to define the macroscopic electric field and the electric displacement field. For the case of uniform fields, the expressions for these fields reduce to those in common use.enDoctoral Thesis