| The measurement and prediction of liberation spectra for multiphase ores have long attracted mineral engineers and particle scientists since Gaudin's time, but the research in both aspects has progressed rather slowly, chiefly because of the lack of appropriate theories and facilities. In this work, the liberation spectra of pyrite and other ash-forming minerals from coal were successfully measured for the first time using SEM-AIA (scanning electron microscopy coupled with automated image analysis) technique. A liberation model for multiphase ore systems was also developed by means of alternating renewal theory.; In measuring the liberation spectra of pyrite and other ash-forming minerals from coal, comprehensive experimental work was performed. Coal Pittsburgh #8 1997 from Consol, Pittsburgh was chosen as a typical sample for this test. In the first place, image qualities were guaranteed by adopting a series of techniques, one of which was using iodoformed epoxy resin to separate the carbonate phase in coal from the epoxy resin background. In order to generate the kernel function of stereological correction for three-phase ore systems with the measurement of linear liberation spectra for coal, 12 narrow size and narrow density parent coal samples and 56 corresponding progeny samples were carefully prepared. More than 3000 images with good qualities were captured from sectioned samples. Liberation spectra for coal Pittsburgh #8 1997 were successfully measured by means of MMIA—a mineral processing software developed at the Utah Comminution Center. The author also showed how to directly use those experimental data to analyze liberation characteristics of coal without making stereological correction.; On the basis of successfully using the SEM-AIA technique to measure liberation spectra for broken coal particles, the SEM-AIA technique was subsequently adopted to examine the internal structure of unbroken coal. The internal structure of coal was then reasonably simplified, and, accordingly, a liberation model for three-phase ore systems was developed using the alternating renewal theory. Before the model was formulated, a pure mathematics problem, three-state sojourn time distribution, had been solved. In order to have the liberation model solvable, the general analytical solution of n-fold convolution for exponential sum functions was conquered. Finally, the predicted results of liberation spectra for coal Pittsburgh #8 1997, in different particle sizes, were presented and compared with the measured data. |
