The coloring oxides are responsible for the color.
These are all oxides from the transition elements in the Mendeleev table.
A transition elements is any element whose atom has an incomplete d sub-shell, or which can give rise to cations with an incomplete d sub-shell. You can locate most of them on a Mendeleev table that shows also the atomic electronic structure. (complete d shell contain 10 electrons) Practically, they include all columns from the Mendeleev table that include these elements: Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu. Cupper is an exemple of an element that has a complete atomic d shell but that is incomplete when combined in a molecule. The color of copper oxides is well known.
Electrons from the d orbitals are responsible for the color of these oxides. Indeed, the d - d absorption mechanism is the origin of the colours of the transition metal compounds. These electron transitions have an moderate energy cost and fall in the visible spectrum.
Finally, I should stress that the actual color is determined by the actual electronic environment of the coloring atom within the molecule (oxide typically). Therefore, the color and blackness of coloring oxides will depend very much on the degree of oxidation.
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Generally speaking, my experience is that fly ash from lignite or subbituminous coals is lighter in color (buff to tan) and that fly ash from bituminous coal is darker in color (gray). A gray color can be attributed to the presence of unburned carbon in fly ash which is more common in fly ash from bituminous coal. In ash without any carbon present, the color is likely due to the presence of iron compounds and the oxidation state of those. When iron +3 compounds are present, the ash would likely have a brown color relating to the tan or buff color of fly ash from low-rank coal. If the iron is present as +2, the color would be bluish gray to gray. The gray would change to brown when the ash was heated in the presence of air.
Thank you for your inquiry.