Angel won a NATO Overseas Research Fellowship and joined Prof. Charles Prewitt's group at the Stony Brook University in 1985 to develop new analysis methods to determine the crystal structures of incommensurate minerals.

At the Geophysical Laboratory staff members Robert Hazen and Larry Finger trained him in high-pressure crystallography.

In 2001 he was appointed research professor in crystallography at Virginia Tech in the US and with Nancy L. Ross founded the Virginia Tech Crystallography Laboratory which performs X-ray diffraction measurements in support of research programs in chemistry, geosciences, physics, and biological sciences,[6][7][8] In 2011, Angel held a Mercator Professorship of the German Research Foundation at the Mineralogisch-Petrographisches Institut [9] of the University of Hamburg in Germany and then moved to Italy to work in the Department of Earth Sciences of the University of Padova (2011–2017).

Angel has developed and established novel methods for single-crystal diffraction,[11][12][13] at extreme conditions in order to characterize and understand the fundamental relationships between the atomic-scale structures and properties of materials.

The software that he has developed for controlling single-crystal X-ray diffractometers,[14] and processing of data[15] is distributed as freeware[16] and is in use by many research groups world-wide.