| Abstract: | We studied, and performed research for our Ph.D. degrees in the area of gas electron diffraction. Our mentor was Lawrence Brockway. a pioneer in this subject. At that time, research in gas electron diffraction was in its early stages of development. In 1941, the distinguished Peter Debye wrote a theoretical paper concerning gas electron diffraction which challenged ones capability to develop the necessary experimental equipment and to further advance the theoretical developments so as to greatly extend the science of gas electron diffraction. We carried these thoughts in mind when we joined the Naval Research Laboratory, where the opportunity to design and produce excellent equipment was readily available. In the course of pursuing this research area, one of the findings was the existence of non-negativity as a condition for the results of a diffraction experiment for gaseous substances. When we became interested in the field of crystal structure determination, the familiarity with non-negativity which was needed in the study of gases, led to a search for the necessary and sufficient condition for a Fourier series to be non-negative. The search was successful and has played an important part in crystal structure determination. Some early applications to complicated structures are described. |
