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The Knoop test is used to measure the hardness of a material. It is defined by the impression made in the surface of the material by a weighted diamond of precisely defined geometry, as function of imposed load. The diamond is a elongated pyramid, seven times longer than it is wide, with the faces of the pyramid having angles of 130o on the short axis and 172o on the long axis. Here's a quick diagram showing a diamond tip under a load making an indentation in a material.

    #LOAD##                                     \  |  /
    #######                                      \ | /
    \  |  /               #LOAD##                 \|/
     \ | /                #######                  
      \|/                 \  |  /                <-L->      (L is the length of indentation made)
-----------------    ------\ | /------     ------     ------
*****************    *******\|/*******     *******   *******
*****************    *****************     *****************

This gives a KH value, expressed in units of gigapascals. A 'Knoop hardness number' or KHN can also be given to a material, and is given by the formula :-

HK = P/CpL2

Where P is the load imposed,(kilogrammes), L is the length of the indentation in millimetres and Cp is a correction factor. The exact load used must also be quoted (loads generally range from 0.98 Newtons to 19.6) Newtons; as all values will be relative to this.

This provides a means to readily compare the absolute hardness of materials, unlike the Mohs test, which only tells you A is harder than B in a purely relative way. Other similar 'micro-indentation' tests are Vickers hardness test and the Berkovich hardness test, where the indentors are square and trigonal pyramids respectively. Frederick Knoop developed his test to overcome problems with cracking of the sample being examined when using symmetrical tips. The longer, shallower indentation made stresses the material far less than the deep pits made with, say, a Vickers tip.

This technique is prone to errors; firstly limitations with measurement of the length of the indentation (often only 60-70 microns long) making the percentage error larger with very hard materials because of this. (To be really accurate you'd need to make measurements smaller than the wavelength of light you're using!). Vibration is also a source of error to be eliminated. Also the nature of the material may be such that the experiment is difficult to reproduce (eg if the material cracks) or if the indentation is difficult to observe (eg in transparent materials).
This is where the correction factor in the equation above comes into play; it's possible to underestimate where the tip is when making measurements, particulary when looking at glass and ceramics. The correction factor is usually given by the formula :-
7l/(2NA), where l is the wavelength of light used and NA is the numerical aperture of objective lens on the microscope you're using. There's some confusion of wether or not you should use this correction factor; it depends on the standard you follow and some data books have both corrected and uncorrected values.

The Hardest Materials

1. Diamond, the hardest material known has KH values of 90 GPa for a single crystal, and 50 GPa for polycrystalline states.

2. Cubic BoronNitride. This ceramic has GPa values of 48 GPa single crystal and 32 GPa polycrystalline.

3. Cobalt Tungsten Boride, this has a GPa value of 45.

4. Stishovite, this can be found in nature in meteorite craters, as is a high pressure modification of SiO2, KH= 33 GPa.

As the properties of material change depending on temperature, engineers get very interested in the KH values of substances as they are heated. For example, boron carbide (B4C) is harder than boron nitride above 400 centigrade, and above 1100 C it's even harder than diamond.....

Among the sources used :-
"Hardness Testing of Ceramics" by George D. Quinn of the National Institute of Standards and Technology. August, 1998, Volume 154, Number 2 edition of "Advanced Materials and Processes"
It can be found on the web at :-

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