The mineral matter in the eight reference North American coal samples of the Argonne Premium Coal series has been investigated on a quantitative basis using X-ray diffraction (XRD) techniques. X-ray diffraction data obtained from electronic low-temperature (oxygen-plasma) ash (LTA) residues, from ashes produced by heating the coals in air at 370 degreesC, and also from the raw coals themselves, were evaluated using an interactive data processing system (SIROQUANT (TM)) based on Rietveld interpretation methods. The results from the three types of material (LTA, 370 degreesC ash and raw coal) were compared for each sample. This allowed the components present in the raw coals in crystalline form to be recognised separately from mineral artifacts produced, particularly in the low-rank coals, from interaction of organically associated elements (Ca, S, etc.) during the two ashing processes. After the allowance for the production of any artifacts, the quantitative mineral assemblages identified from XRD of the raw coals were found to be consistent, even for coals having a relatively low ash percentage (around 5%), with the results obtained from the respective mineral concentrates prepared by the ashing methods. The effects of heating the coal to 370 degreesC could also be distinguished, relative to the raw coal or the LTA, through changes in components such as pyrite and the clay minerals. Although some areas of uncertainty exist, particularly with magnesium in the low-rank coals, the calculated chemical compositions of the coal ash derived from the mineral mixtures identified for each coal were also found to be consistent with the results of direct chemical analysis of the respective coal ash materials.