TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: The solid-liquid separation is performed in plate frame filter, centrifugal filter, or microporous filter. The decompressing and distilling step is performed at 80-100 degrees C and 50-100 mTorr to obtain filtrate with water content of 6-8 wt.%; or at 60-90 degrees C and 20-60 mTorr to obtain filtrate with water content of less than wt.%. The flotation step is performed using flotation liquid with specific gravity of 2.35-2.9 for 1-5 times, and flotation liquid with specific gravity of 2.35 to 2.5. The ultrasonic vibration auxiliary flotation is performed for 20-60 minutes, and standing for 20-240 minutes. The method also comprises removing iron using 5-40% hydrofluoric acid and/or 5-60% mixed acid of nitric acid for 5-120 minutes; and etching silicon ingot using 5-30 wt.% hydrochloric acid solution for 5-240 minutes or by 5-50 wt.% of sodium hydroxide and/or potassium hydroxide for 5-240 minutes. The etching step can be performed using mixed acid comprising hydrochloric acid, hydrofluoric acid, nitric acid or sulfuric acid for 10-240 minutes. The silicon powder is heated and melted at 1420-1800 degrees C using plasma gas source consisting of nitrogen, hydrogen, argon gas, helium gas, oxygen gas, and/or steam; and refining for 5-240 minutes. The method further comprises vacuum refining silicon ingot at 1414-2000 degrees C, 0.00001-10 Torr for 0.5-24 hours. The solidification of silicon ingot is performed in unidirectional solidification furnace at 1-40 mm/hour. Preferred Component: The additive is aerosol silicon dioxide. The ratio of new and old dispersion liquids is (1:0)-(1:1). The new and old silicon carbides have mixing ratio of (1:0)-(1:4).    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Component: The additive is organic acid salt, alkyl sulfonate, polyacrylic acid, hydroxyl cellulose, or carboxyl cellulose.    TECHNOLOGY FOCUS - POLYMERS - Preferred Component: The additive can be alkyl sulfonate, polyacrylic acid, hydroxyl cellulose, or carboxyl cellulose. The flotation liquid is tetrabromoethane, methyl bromide, dibromomethane, ethanol, chloroform, carbon tetrachloride, benzene, and/or ether.