A broad set of ashes originating from national and international sources of hard coal, brown coal, and biomass is investigated under different ashing temperatures (815 degrees C and 450/550 degrees C) as well as oxidizing and reducing atmosphere conditions. In this computational study the mineral phase composition is estimated and the respective masses are not taken into account, since these approaches have been regularly less successful. The resulting mineral phases are assigned to main mineral groups and related to the experimentally determined ash fusion temperatures. On the one hand this relation is based on network theoretical considerations for the liquid slag and on the other it combines those with the fusion behavior of the residual solid mineral phases. Lowest ash fusion temperatures are addressed to the presence of low temperature melting mixtures of several mineral phases, which formed a very fragile network. Finally, the effects of different ashing temperatures and atmosphere conditions on the resulting mineral phases and respective ash fusion temperatures are studied. (C) 2015 Elsevier Ltd. All rights reserved.