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The relationship between lateral force, normal force and normal displacement has been investigated. Surfaces of diverse materials were nanoscratched at constant rate. Nanoindents with cube corner, Berkovich or cono-spherical indenter indicate proportionality of (normal force) ~ (normal displacement) 3/2  up to considerable forces, sometimes approaching the 10 mN range, but phase transformations under pressure may change the slope. This differs from the varying Meyer exponents reported at forces higher by two to three magnitudes when applied to Vickers indenters. Nanoscratching on diverse materials consistently reveals proportionality of (lateral force) ~ (normal force) 3/2 . This relationship is valid for amorphous (fused quartz) and crystalline materials such as silicon, silica, strontium titanate and the polar molecular crystals of thiohydantoin and nin-hydrin with hydrogen bonds, or pure van-der-Waals crystals of tetraphenylethylene. Anisotropies of the crystals and the type of destruction (breaking covalent bonds, or hydrogen bonds, or van-der-Waals interactions; abrasion, or molecular movements) do not affect the obviously universal relationship but only the proportionality factor with the dimension μN –0.5  which describes materials response to the scratching action for the particular crystal face and anisotropic direction. The new quantitative relationship is usable for the calculation of scratch work and of other quantities related to the lateral force on the basis of the new empirical constants. Both new relationships from nanoindents and nanoscratches are unified in the (lateral force) ~ (normal displacement) 9/4  relationship and experimentally verified.

Nanoscratching on surfaces: the relationships between lateral force, normal force and normal displacement