Although not detectable using Energy Dispersive Spectroscopy (EDS), the presence of Hydrogen can be detected by the formation of hydride and hydroxide crystallographic structures as show in this example.
Kyanite - Al2SiO5
Andalusite - Al2SiO5
Sillimanite - Al2SiO5
Muscovite - KAl2(AlSi3O10)(F, OH)2
Quartz - SiO2
Chlorite - (Fe, Mg, Al)6(Si, Al)4O10(OH)8
Rutile - TiO2
Hematite - Fe2O3
Zircon - ZrSiO4