Are these really carbon nanospheres ? How were they obtained ? Were they pyrolysed at high temperature enough to get "pure" carbon ? It is strange that nothing appears in XRD, as even vitreous carbon presents a well known diffusion pattern, with broad but very clear bands. Hence my questions about their preparation ... If not heated enough, they are not true carbon spheres (e.g. hydrothermal "carbon" is such, and requires additional pyrolysis at 900°C for being called "carbon").
If your material is amorphous or nanocrystalline you will still get peaks in XRD, but they will be extremely broad. Using PDF analysis you can fully characterize the short and medium range order of an amorphous phase and determine the crystal structure of nano-crystalline phases. I hope I have cleared up the misleading comments you have received here.