Her research group pioneered applications of direct imaging techniques for atomic-scale structures on surfaces. She worked closely with theorists to design experiments to address theoretical and conceptual questions important to the fields of catalysis, thin film growth and nano-electronics. She has published over 200 academic articles, which have been cited over 8000 times. Her most widely cited work includes at least four areas of fundamental research (see Selected Publications below); structure-transport relationships in graphene, surface morphology and step fluctuations, electronic interactions with surface defects, and adsorbate-interactions. In parallel with her academic career, Williams has worked extensively in providing technical advice to the U.S. government, primarily through the Departments of Energy and Defense. As a result of her experience, in 2009 she was asked to lead a study on issues of verification of nuclear testing, which was one of the concerns cited in the Senate decision not to ratify the treaty in 1999. The resulting report, reviews the verification capabilities in the US and at the Comprehensive Nuclear Test-Ban Organization (CTBTO), and shows that detection capability advanced significantly over the years after the 1999 U.S. decision not to ratify. The report places the state-of-the art detection capability in the context of different types of proliferation threats, and thus provides a valuable context for decision makers. The report also emphasizes the importance of sustaining and continuing to advance technical capabilities for verification, both in the U.S. and at the CTBTO. Williams is the vice-chair of JASON, an independent group of scientists offering advice to the US government on key science and technology issues. At BP, Williams worked in Group Technology, where she was responsible for assurance of technology programs, and strategic research and program development. Early in her tenure, she set up the initial advisory structure for BP's Gulf of Mexico Research Initiative Within the company, she advocated for increased implementation of advanced computational approaches in molecular chemistry, fluid dynamics, and distributed sensing and ‘big data’ analysis. She also led a strategic multi-university research program on natural resource constraints in the context of energy (the Energy Sustainability Challenge). In addition to the extensive University research publications that resulted from the program, the ESC team also created three reference booklets on energy-resource issues, “The ESC Materials Handbook", “Water in the Energy Industry,”  and “Biomass in the Energy Industry”. Williams has spoken widely about the need for advances in Science and Technology to sustainably supply the energy the world needs.