A polishing composition including a colloidal silica containing colloidal silica particles, a pH adjusting agent, and a chelating agent provides a substrate that has a surface having a high flatness, low defects and a low surface roughness with low cost and high productivity, and a substrate having high surface quality suitable as a substrate for mask blanks such as a glass substrate containing SiO.sub.2 as a main component, particularly, as a substrate for mask blanks used in EUVL.

An object of the present invention is to provide a nanobubble-containing inorganic oxide fine particle dispersion having excellent concentration stability in a process used as an abrasive. The object is achieved by the nanobubble-containing inorganic oxide fine particle dispersion including: inorganic oxide fine particles having an average particle size of 1 to 500 nm and containing fine particles containing Ce; and nanobubbles having an average cell size of 50 to 500 nm and being at least one non-oxidizing gas selected from a group consisting of N.sub.2 and H.sub.2.

A slurry for polishing surfaces or substrates that at least partially comprise ruthenium and copper, wherein the slurry includes an alkali hydroxide, oxygenated halogen compound, and a halogen alkyl benzotriazole. The slurry may further include abrasive, acid(s), and, optionally, an alkoxylated alcohol. With these components, the slurry exhibits a high ruthenium to copper removal rate ratio.

An object of the present invention is to provide a silica particle, a silica sol containing the silica particle, and a polishing composition containing the silica sol, which prevent secondary aggregation, have excellent dispersion stability, and are suitable for polishing. The present invention relates to a silica particle in which an average value of a circularity coefficient measured by a field-emission scanning electron microscope is 0.90 or more, and a standard deviation of the circularity coefficient is 0.05 or less.

A polishing liquid for polishing a surface to be polished containing cobalt, the polishing liquid containing abrasive grains, at least one sugar component selected from the group consisting of a sugar alcohol, a sugar alcohol derivative, and a polysaccharide, an acid component, and water, in which a pH of the polishing liquid is more than 8.0.

A polishing composition having silica-based abrasive grains and a polishing method. A polishing composition having silica particles, wherein on the basis of a colloidal silica dispersion of the silica particles, the dispersion has an Rsp of 0.15 to 0.7 as measured using pulse NMR, and the colloidal silica particles have a shape coefficient SF1 of 1.20 to 1.80, wherein Rsp is calculated based on equation (1):

Rsp=(Rav−Rb)/(Rb)  (1) (wherein Rsp is an index that indicates water affinity; Rav is an inverse of a relaxation time of the colloidal silica dispersion; and Rb is an inverse of a relaxation time of a blank aqueous solution obtained by removing the silica particles from the colloidal silica dispersion), and the shape coefficient SF1 is calculated based on equation (2):

SF1=(area of a circle whose diameter is a maximum diameter of the particle)/(projected area)  (2).

A polishing composition that can not only achieve high polishing speed, but also can improve the surface smoothness (surface quality) of a polished substrate and reduce defects is provided. That is, provided is a polishing composition comprising silica particles and a water soluble polymer, wherein the contained silica particles satisfy the following requirements (a) to (c): (a) the primary particle diameter based on the specific surface area is 5 to 300 nm; (b) the coefficient of variation in the particle diameter is 10% or less; and (c) the Sears number Y is 10.0 to 12.0.

A slurry containing abrasive grains and a liquid medium, in which the abrasive grains include first particles and second particles in contact with the first particles, the first particles contain cerium oxide, the second particles contain a cerium compound, and in a case where a content of the abrasive grains is 2.0% by mass, a BET specific surface area of a solid phase obtained when the slurry is subjected to centrifugal separation for 30 minutes at a centrifugal acceleration of 1.1×10.sup.4 G is 24 m.sup.2/g or more.

A polishing liquid containing abrasive grains, a hydroxy acid, a polyol, and a liquid medium, in which a zeta potential of the abrasive grains is positive, and the hydroxy acid has one carboxyl group and one to three hydroxyl groups.

One aspect of the present invention provides a polishing method including polishing a sliding part of a machine device by producing fullerene-aggregated particles by making the sliding part slide while a polishing-agent composition containing fullerenes and a solvent of the fullerenes is applied to the sliding part.