NOVELTY - Recovering useful compounds from a byproduct composition produced in a silicon tetrafluoride production process, comprises: calcining a byproduct composition comprising sodium sulfate and aluminum sulfate and forming an oxidized phase mixture; absorbing gaseous sulfur trioxide in a mixture of sulfuric acid and water; cooling the oxidized phase mixture; mixing the cooled solid phase mixture with water; filtering the dissolved product to obtain cake; crystallizing sodium sulfate salt solution; drying the cake to produce alumina solids; and drying the sludge to produce dry sodium sulfate salt.    USE - The method is useful for recovering useful compounds from a byproduct composition (claimed), where the useful compound includes pure silica, silanes, pure silicon for solar cells, silicon nitride for ceramic products and fluorinated carbon-silicon polymers for materials for architectural uses.    ADVANTAGE - The method is economical and environmentally friendly.    DETAILED DESCRIPTION - Recovering useful compounds from a byproduct composition produced in a silicon tetrafluoride production process, comprises: calcining a byproduct composition comprising sodium sulfate and aluminum sulfate and forming an oxidized phase mixture comprising alumina solids, and sodium sulfate and a gaseous phase comprising sulfur trioxide; absorbing the gaseous sulfur trioxide in a mixture of sulfuric acid and water to produce oleum; cooling the oxidized phase mixture to produce a cooled solid phase mixture; mixing the cooled solid phase mixture with water to produce a dissolved product comprising dissolved sodium sulfate and suspended alumina solids; filtering the dissolved product to obtain a cake comprising alumina and a sodium sulfate salt solution; crystallizing the sodium sulfate salt solution to produce steam condensate and a sodium sulfate sludge; drying the cake to produce alumina solids; and drying the sludge to produce a dry sodium sulfate salt. An INDEPENDENT CLAIM is included for a system for recovering alumina and sodium sulfate from a kiln byproduct in a silicon tetrafluoride production process, comprising a hopper for receiving the kiln byproduct, a rotary feeder for transferring the kiln byproduct to a calcination kiln, where the calcination kiln operable to temperatures of 1000 degrees C, a combustor for supplying heat to the calcination kiln, an exchanger for cooling an oxidized product from the calcination kiln and preheating air for the combustor, a product dissolving tank for receiving the cooled oxidized product from the exchanger, a rotary filter for separating suspended particles from an effluent of the product dissolving tank, a crystallizer for recovering sulfate salts from a liquid effluent of the rotary filter, a dryer for drying particulate recovered from the rotary filter and an oleum scrubber for receiving a gaseous product of the calcination kiln.