Your toothpaste and a glacier both work as abrasives
An abrasive does not strictly need to be harder than what it wears down. Any two solids rubbed together long enough will erode each other: soft shoe soles hollow out stone steps over centuries, and glaciers grind whole valleys. Industry simply speeds the process up with tiny, sharp, very hard grains.
An abrasive shapes or finishes a surface by rubbing away part of it through friction. Finishing often means polishing to a mirror shine, but it can also mean deliberately roughening, as with satin, matte or beaded textures. The same principle lies behind grinding, honing, lapping, sanding, sharpening, drilling and cutting, which is why abrasives vary so widely in chemistry and shape. A file, by contrast, is not an abrasive: its teeth cut like a saw's. The exception is the diamond file, a metal rod coated in diamond powder.
Most abrasives are hard minerals, 7 or above on the Mohs scale, or synthetic stones that may match natural minerals exactly but cannot be called minerals because they were made rather than formed. Diamond is both mined and manufactured, and corundum, though found in nature, now usually comes from bauxite. Engineers treat the Mohs scale warily, since its steps are arbitrary and uneven. At the soft end, calcium carbonate serves as the polishing agent in toothpaste.
The working particles, called grit, range from grains around 2 millimetres across down to about 0.001 millimetres. Their jagged edges and points shrink the contact area, concentrating pressure so that bits of the workpiece break away, while the grains themselves gradually blunt or pull loose. Speed of wear depends on the hardness gap, grain size, pressing force and how firmly grains are held to their backing or matrix, which controls when fresh ones are exposed.
A common problem is loading, when debris and spent grit clog the gaps between grains, cutting efficiency and raising friction. Lubricants and coolants help by flushing away the metal shavings known as swarf, carrying off heat and allowing a finer finish. Natural sharpening stones were long thought superior, but synthetic abrasives are closing the gap, partly because impurities in mined stone can weaken it.
Source: Abrasive
