Abstract: A method of forming a mixture including a ceramic material into a sheet, sectioning at least a portion of the sheet using a mechanical object and forming at least one shaped abrasive particle from the sheet, such that the at least one shaped abrasive particle can have a two-dimensional shape as viewed in a plane defined by a length and a width of the shaped abrasive particle selected from the group consisting of polygons, ellipsoids, numerals, Greek alphabet characters, Latin alphabet characters, Russian alphabet characters, complex shapes having a combination of polygonal shapes, and a combination thereof.

Abstract: A particulate material having a body including a first phase having at least about 70 wt % alumina for a total weight of the first phase, and a second phase comprising phosphorus, wherein the body includes at least about 0.1 wt % of the second phase for the total weight of the body, and wherein the second phase has an average grain size of not greater than about 1 micron.

Abstract: A method of forming an abrasive article includes depositing a mixture into an opening of a substrate, contacting an exposed surface of the mixture in the opening to a texturing form to form a textured preform, and removing the mixture from the opening and forming an abrasive particle having a textured surface.

Abstract: An abrasive grain is disclosed and may include a body. The body may define a length (l), a height (h), and a width (w). In a particular aspect, the length is greater than or equal to the height and the height is greater than or equal to the width. Further, in a particular aspect, the body may include a primary aspect ratio defined by the ratio of length:height of at least about 2:1. The body may also include an upright orientation probability of at least about 50%.

Abstract: An abrasive article comprising a first group including a plurality of shaped abrasive particles overlying a backing, wherein the plurality of shaped abrasive particles of the first group define a first non-shadowing distribution relative to each other.

Abstract: An abrasive grain is disclosed and may include a body. The body may define a length (l), a height (h), and a width (w). In a particular aspect, the length is greater than or equal to the height and the height is greater than or equal to the width. Further, in a particular aspect, the body may include a primary aspect ratio defined by the ratio of length:height of at least about 2:1. The body may also include an upright orientation probability of at least about 50%.

Abstract: An abrasive article comprising a first group including a plurality of shaped abrasive particles overlying a backing, wherein the plurality of shaped abrasive particles of the first group define a first non-shadowing distribution relative to each other.

Abstract: A method of forming a mixture including a ceramic material into a sheet, sectioning at least a portion of the sheet using a mechanical object and forming at least one shaped abrasive particle from the sheet, such that the at least one shaped abrasive particle can have a two-dimensional shape as viewed in a plane defined by a length and a width of the shaped abrasive particle selected from the group consisting of polygons, ellipsoids, numerals, Greek alphabet characters, Latin alphabet characters, Russian alphabet characters, complex shapes having a combination of polygonal shapes, and a combination thereof.

Abstract: A shaped abrasive particle including a body having a first major surface, a second major surface, and a side surface joined to the first major surface and the second major surface, and the body has at least one partial cut extending from the side surface into the interior of the body.

Abstract: An abrasive particulate material which is made of alumina crystals and a primary additive composition impregnated within the abrasive particulate material, the primary additive composition including a combination of Mg and Ca, wherein Mg and Ca are present in an additive ratio [Mg:Ca] within a range between about 1:1 and about 10:1, and a Ca amount is at least about 0.2 wt % Ca for the total weight of the abrasive particulate material.

Abstract: An abrasive article comprising a first group including a plurality of shaped abrasive particles overlying a backing, wherein the plurality of shaped abrasive particles of the first group define a first non-shadowing distribution relative to each other.

Abstract: An abrasive grain is disclosed and may include a body. The body may define a length (l), a height (h), and a width (w). In a particular aspect, the length is greater than or equal to the height and the height is greater than or equal to the width. Further, in a particular aspect, the body may include a primary aspect ratio defined by the ratio of length:height of at least about 2:1. The body may also include an upright orientation probability of at least about 50%.

Abstract: An abrasive grain is disclosed and may include a body. The body may define a length (l), a height (h), and a width (w). In a particular aspect, the length is greater than or equal to the height and the height is greater than or equal to the width. Further, in a particular aspect, the body may include a primary aspect ratio defined by the ratio of length:height of at least about 2:1. The body may also include an upright orientation probability of at least about 50%.

Abstract: A shaped abrasive particle including a body comprising a first major surface, a second major surface, and a side surface extending between the first major surface and the second major surface, the body comprising a sharpness-shape-strength factor (3SF) within a range between about 0.7 and about 1.7 and a Shape Index within a range between at least about 0.01 and not greater than about 0.49.

Abstract: A particulate material having a body including a first phase having at least about 70 wt % alumina for a total weight of the first phase, and a second phase comprising phosphorus, wherein the body includes at least about 0.1 wt % of the second phase for the total weight of the body, and wherein the second phase has an average grain size of not greater than about 1 micron.

Abstract: A method of forming a shaped abrasive particle including extruding a mixture into a form, applying a dopant material to an exterior surface of the form, and forming a precursor shaped abrasive particle from the form.

Abstract: A particulate material having a body including a first phase having at least about 70 wt % alumina for a total weight of the first phase, and a second phase comprising phosphorus, wherein the body includes at least about 0.1 wt % of the second phase for the total weight of the body, and wherein the second phase has an average grain size of not greater than about 1 micron.

Abstract: An abrasive article includes a shaped abrasive particle including a body having a first height (h1) at a first end of the body defining a corner between an upper surface, a first side surface, and a second side surface, and a second height (h2) at a second end of the body opposite the first end defining an edge between the upper surface and a third side surface, wherein the average difference in height between the first height and the second height is at least about 50 microns. The body also includes a bottom surface defining a bottom area (Ab) and a cross-sectional midpoint area (Am) defining an area of a plane perpendicular to the bottom area and extending through a midpoint of the particle, the body has an area ratio of bottom area to midpoint area (Ab/Am) of not greater than about 6.

Abstract: A particulate material includes an aluminous material and a silica dopant. The particulate material includes crystallite particles with a crystallite particle size of less than about 10 nm. The crystallite particles are stacked together to form primary particles with a primary particle size of less than about 500 nm. The primary particles are agglomerated together to form secondary particles with a secondary particle size of greater than about 1 ?m. The particulate material has a mean pore diameter of not less than 8 nm.

Abstract: A method of forming a shaped abrasive particle includes having a body formed by an additive manufacturing process.