NOVELTY - The lithium or lithium-ion electrochemical cell (10) comprises a cathode, an anode, and a non-aqueous lithium-containing electrolyte (14). The anode and the cathode comprise a particulate carbon-containing material, which comprises rounded carbon particles, and is prepared by heating precursor materials in a sealed autogenic pressure reactor at a temperature and for a period of time to dissociate the precursor material into a gaseous component for generating a pressure for components of the dissociated precursor material to combine and form the particulate carbon-containing material.    USE - The lithium or lithium-ion electrochemical cell is useful in a battery (claimed), which is rechargeable lithium-ion battery, useful for powering a portable electronic devices such as cell phones and laptop computers and medical-, space-, aeronautic- and defense-related devices and useful in transportation applications such as hybrid-electric, plug-in hybrid-electric and all-electric vehicles.    ADVANTAGE - The lithium or lithium-ion electrochemical cell improves capacity, energy, life and durability of the battery.    DETAILED DESCRIPTION - The lithium or lithium-ion electrochemical cell (10) comprises a cathode, an anode, and a non-aqueous lithium-containing electrolyte (14). The anode and the cathode comprise a particulate carbon-containing material, which comprises rounded carbon particles, and is prepared by heating precursor materials in a sealed autogenic pressure reactor at a temperature and for a period of time to dissociate the precursor material into a gaseous component for generating a pressure for components of the dissociated precursor material to combine and form the particulate carbon-containing material. The combined amount and the combined chemical composition of each precursor material in the reactor are sufficient to form the particulate carbon-containing material. The carbon-containing material is a stoichiometric, defect or disordered material with respect to composition and atomic, cationic or anionic sites. The reactor is operated under conditions of a minimum working pressure of 100 pounds per square inch and a minimum temperature of 100 degrees C to a maximum working pressure of 800-2000 pounds per square inch and a maximum temperature of 300-800 degrees C. The particulate carbon-containing material is a carbon-coated metal oxide or metal phosphate nanoparticle material comprising particles, and comprises carbon microspheres comprising spherical carbon particles having a size of 1-5 microns in diameter and carbon nanotubes containing a cobalt catalyst. The particulate carbon-containing material is further prepared by reacting solid or liquid, solvent-free titanium carboxylate precursor materials and solvent-free tin alkoxylate precursor materials in an enclosed autogenic pressure reactor in which the precursor materials are dissociated and reacted at elevated temperature for creating self-generated pressure within the reactor. The precursor materials of the carbon-coated metal oxide comprise precursor compounds comprising carbon, oxygen, and elements making up the nanoparticle material. The carbon-coated metal oxide nanoparticle material comprises: titanium dioxide core particles coated with 0.5- 30 wt.% of carbon, and has a size of 5-150 nm, where the titanium dioxide core particles are predominately single phase anatase titanium oxide; and tin dioxide core particles coated with 1-4 nm of carbon, and has a size of 5-20 nm, where the tin dioxide core particles are predominately cassiterite-type tin oxide. The product obtained from the autogenic pressure reactor is heated to reduce the amount of carbon coating the product. The carbon-coated metal phosphate nanoparticle material is prepared by reacting solid, solvent-free precursor materials in an enclosed autogenic pressure reactor in which the precursor materials are dissociated and reacted at elevated temperature for creating self-generated pressure within the reactor. The rounded carbon particles consist of spherical carbon particles, prolate-shaped carbon particles, oblate-shaped carbon particles, carbon nanotubes and/or carbon microspheres. The particulate carbon-containing material is annealed by heating the particles obtained from the autogenic pressure reactor under an inert atmosphere at a temperature of 2400-3000 degrees C. The carbon microspheres are prepared by heating a solvent-free polyethylene terephthalate polymer in an enclosed autogenic pressure reactor in which the polyethylene terephthalate polymer is dissociated and reacted at elevated temperature for creating self-generated pressure within the reactor. The carbon microspheres contain a combination of disordered carbon and graphitic carbon, where a ratio of disordered carbon to graphitic carbon is less than 1. The carbon nanotubes are prepared by heating solvent-free precursor materials comprising low density polyethylene and a cobalt carboxylate compound in an enclosed autogenic pressure reactor in which the precursor materials are dissociated and reacted at elevated temperature for creating self-generated pressure within the reactor. The carbon nanotubes include nanoparticles of titanium dioxide and/or silicon dioxide on the surface of the nanotubes. INDEPENDENT CLAIMS are included for:    (1) a method of fabricating rounded carbon particles suitable for use in an electrochemical cell;    (2) a rounded carbon particles;    (3) a method for fabricating a carbon-coated particulate metal oxide, metal phosphate, metal or metaloid material suitable for use in an electrochemical cell; and    (4) a carbon-coated particulate metal oxide, metal phosphate, metal or metaloid material.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of an electrochemical cell.    Electrochemical cell (10)    Negative electrode (12)    Electrolyte (14)    Positive electrode (16)    Insulating housing. (18)