The purpose of the present invention is to provide a polishing composition which can polish an object to be polished containing oxygen atoms and silicon atoms at high polishing speed, and can reduce generation of scratches on a surface of the object to be polished. A polishing composition used for polishing an object to be polished containing oxygen atoms and silicon atoms, the polishing composition including: abrasive grains A having an average primary particle size of 3 nm or more and 8 nm or less; abrasive grains B having an average primary particle size of more than 8 nm; and a dispersing medium, wherein a content of the abrasive grains B in the polishing composition is larger than a content of the abrasive grains A in the polishing composition, average silanol group density of the abrasive grains A and the abrasive grains B is 2.0 nm.sup.2 or less, and an aspect ratio of the abrasive grains B is more than 1.3 and 2.0 or less.

A polishing liquid comprising abrasive grains, an additive, and water, wherein the abrasive grains include a hydroxide of a tetravalent metal element, produce absorbance of 1.00 or more for light having a wavelength of 400 nm in a first aqueous dispersion having a content of the abrasive grains adjusted to 1.0 mass %, and produce light transmittance of 50%/cm or more for light having a wavelength of 500 nm in the first aqueous dispersion, and a NO.sub.3.sup. concentration of a second aqueous dispersion obtained by retaining the first aqueous dispersion at 60 C. for 72 hours is 200 ppm or less.

A polishing liquid comprising abrasive grains, an additive, and water, wherein the abrasive grains include a hydroxide of a tetravalent metal element, produce absorbance of 1.00 or more for light having a wavelength of 400 nm in a first aqueous dispersion having a content of the abrasive grains adjusted to 1.0 mass %, and produce light transmittance of 50%/cm or more for light having a wavelength of 500 nm in the first aqueous dispersion, and a NO.sub.3.sup. concentration of a second aqueous dispersion obtained by retaining the first aqueous dispersion at 60 C. for 72 hours is 200 ppm or less.

A polishing agent for chemomechanically polishing a base having a carbon-based material and an insulating material to remove at least a part of the carbon-based material, the carbon-based material having a carbon content of 60 to 95 atm % as measured by X-ray photoelectron spectroscopy, the polishing agent comprising: an abrasive grain comprising silica; an allylamine-based polymer; and water, wherein a mass ratio of a content of the allylamine-based polymer with respect to a content of the abrasive grain is 0.002 to 0.400, and the abrasive grain has a positive charge in the polishing agent.

A polishing agent for chemomechanically polishing a base having a carbon-based material and an insulating material to remove at least a part of the carbon-based material, the carbon-based material having a carbon content of 60 to 95 atm % as measured by X-ray photoelectron spectroscopy, the polishing agent comprising: an abrasive grain comprising silica; an allylamine-based polymer; and water, wherein a mass ratio of a content of the allylamine-based polymer with respect to a content of the abrasive grain is 0.002 to 0.400, and the abrasive grain has a positive charge in the polishing agent.

A machine tool includes one tip arranged on the spindle at a position that faces the table, a cutting edge position storing unit that stores therein multiple measured values that are obtained by performing measurement of the position of the tip at least two times in a state where the spindle is set at at least one phase and the tip is positioned at an identical point, a spindle tilt angle calculating unit that calculates a tilt angle of the spindle with respect to an XY-plane, based on the multiple measured values, and a coordinate system rotation unit that rotates the XY-plane about at least one of X-axis and Y-axis, based on the tilt angle of the spindle calculated by the spindle tilt angle calculating unit.

The present invention provides a method for evaluating a polishing pad by which a life of a polishing pad to polish a wafer is evaluated, the method being characterized in that a quantity of polishing residues deposited on the polishing pad is measured, and the life of the polishing pad is evaluated based on a measurement value provided by the measurement. Consequently, it is possible to provide the method for evaluating a polishing pad and the method for polishing a wafer that enable immediately evaluating the life of the polishing pad and also enable suppressing a reduction in productivity and a yield ratio at the time of polishing the wafer.

A polishing composition capable of suppressing surface defects and reducing haze is provided. The polishing composition includes: abrasives; at least one water-soluble polymer selected from vinyl alcohol-based resins having a 1,2-diol structural unit; a polyalcohol; and an alkali compound. Preferably, the polishing composition further includes a non-ionic surfactant.

A polishing composition that can suppress surface defects and reduce haze is provided. A polishing composition includes: abrasives; at least one water-soluble polymer selected from vinyl alcohol-based resins having a 1,2-diol structural unit; and an alkali compound, where an average particle size of particles in the polishing composition measured by dynamic light scattering is not more than 55 nm. Preferably, the polishing composition further includes a non-ionic surfactant. Preferably, the polishing composition further includes a polyalcohol.

A cerium-based abrasive that achieves a high polishing rate and suppresses the occurrence of surface defects such as scratches and pits and the deposition of the abrasive particles on the polished surface in surface polishing of glass substrates or the like, at low cost with a high production efficiency. The cerium-based abrasive includes a cubic composite rare earth oxide and a composite rare earth oxyfluoride, containing 95.0 to 99.5 mass % of total rare earth elements in terms of oxides, containing 54.5 to 95.0 mass % of cerium in terms of oxide, 4.5 to 45.0 mass % of lanthanum in terms of oxide, and 0.5 to 2.0 mass % of neodymium in terms of oxide relative to the total rare earth elements in terms of oxides, containing 0.5 to 4.0 mass % of fluorine atoms, and containing 0.001 to 0.50 mass % of sodium atoms relative to the total rare earth elements in terms of oxides.