TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Condition: The ultrasonic vibrations are within 10-100 preferably 20 or 40-50 kHz. The mixture is subjected to ultrasonic vibrations at 300-350 degreesK and 10-25 MPa.The method involves changing an oxidation state of the metal or metalloid species, using an oxidizing agent consisting of hydrogen peroxide. The mixture is subjected to ultrasonic vibrations in a supercritical fluid extraction vessel and the supercritical fluid extraction vessel contains inert material. The inert material defines a porous medium, which is packed beads.Preferred Component: The supercritical fluid includes argon, carbon dioxide, xenon, nitrous oxide, sulfur hexafluoride, water and/or ammonia. The extractant comprises inorganic acid. It comprises Lewis acid consisting of nitric acid, hydrochloric acid, sulfuric acid, phosphoric acid, perchloric acid, hydrofluoric acid or water. The mixture is a microemulsion.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Component: The supercritical fluid includes pentane, butane, propane, diethyl ether, dichlorodifluoromethane, trifluoromethane, isopropanol, ethanol and/or methanol. The extractant can be organic acid. It comprises 4,4-trifluoro-1-(2-thienyl)-1,3-butanedione. It comprises a chelating agent consisting of tri-n-butylphosphate, tri-n-octylphosphate, lower alkyl phosphates, lower trialkyl phosphates, lower alkyl tri-substituted phosphates, triphenylphosphate, acetylacetone, trifluoroacetylacetone, hexafluoroacetylacetone, thenoyltrifluoroacetone, 4,4-trifluoro-1(2-thienyl)-1,3-butanedione, heptafluorobutanoylpivaloylmethane, water, tri-n-butylphosphine oxide, triphenylphosphine oxide, bis(trifluoroethyl)dithiocarbamate, diethyldithiocarbamate, crown ethers and/or crown ether substituted hydroxamic acid derivatives.    TECHNOLOGY FOCUS - METALLURGY - Preferred Material: The metal species include uranium, platinum, or palladium in either a ground oxidation state or positive oxidation state. The metalloid species include thallium, lanthanum, europium, lutetium, neodymium, copper, iron, nickel, cobalt, bismuth, mercury, zinc, arsenic, antimony, uranium, platinum or palladium.Preferred Composition: At least 70% of the metal or metalloid species are extracted from the material.