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The disclosure relates to a method for concentrating rare earth elements (REEs) from a coal byproduct. The method includes mixing the coal byproduct input with aluminum phosphate, sulfur and/or other compounds used as an additive; heating the coal byproduct input in air for a period of 3 minutes or longer at a temperature above a liquid starting temperature of the coal byproduct input, forming a molten coal byproduct; cooling the molten coal byproduct at a rate slower than critical glass transition cooling rate of the melt, forming REE phosphate product; heating the coal byproduct input above the liquid starting temperature of the coal byproduct after REE phosphate product is formed; and cooling the coal byproduct input at a rate faster than the critical glass transition cooling rate of the melt, minimizing forming unwanted solids.