Physics:Berkovich tip

From HandWiki
A Berkovich tip with 'a' denoting the half angle.
A black-and-white image showing a glossy, triangular pyramid 30° off-axis from a vertical view.
A Scanning electron microscope image of a Berkovich tip used in a Nanoindenter

A Berkovich tip is a type of nanoindenter tip used for testing the indentation hardness of a material. It is a three-sided pyramid which is geometrically self-similar. The popular Berkovich now has a very flat profile, with a total included angle of 142.3 degrees and a half angle of 65.27 degrees, measured from the axis to one of the pyramid flats. This Berkovich tip has the same projected area-to-depth ratio as a Vickers indenter. The original tip shape was invented by Russian scientist E.S. Berkovich in the USSR c. 1950, which has a half angle of 65.03 degrees.[1][2]

As it is three sided, it is easier to grind these tips to a sharp point and so is more readily employed for nanoindentation tests. It is typically used to measure bulk materials and films greater than 100 nanometres (3.9×10−6 in) thick.


  1. E.S. Berkovich, "Three-Faceted Diamond Pyramid for Micro-hardness Testing," Zavodskaya Laboratoria, Vol. 16 #3, 1950, p 345-347 (in Russian). Translated into English and published in Industrial Diamond Review, Vol. 11 No. 127, June 1951, p 129-132.
  2. M.M. Khrushchov & E.S. Berkovich, "Methods of Determining the Hardness of Very Hard Materials: The Hardness of Diamond," Zavodskaya Laboratoria, 1950 (2), p 193 -196 (in Russian). Translated into English by W.G.C and published in Industrial Diamond Review, Vol. 11, Feb 1951, p 42-49 (in English).