Alexander received his DPhil in Engineering Science from Merton College, University of Oxford, in 1995. He then held a Junior Research Fellowship at Fitzwilliam College, Cambridge. In 1999, he returned to Oxford to lead his own research group in the Department of Engineering Science, focusing on the study of materials structure and processes using optical, electron, ion, neutron, and X-ray beams. He is now an Emeritus Professor of the Department.