Page 102 - Materials Chemistry, Second Edition
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89
            2.3. The Crystalline State

                                    Table 2.10. Hardness Scales
            Solid                     Mohs              Vickers           Knoop
            Talc                       1                  27              N/A
            Graphite                   1.5                37              N/A
            Gypsum                     2                  61              N/A
            Fingernail                 2.5               102              117
            Calcite                    3                 157              169
            Fluorite                   4                 315              327
            Apatite                    5                 535              564
            Knife blade                5.5               669              705
            Feldspar                   6                 817              839
            Pyrex glass                6.5               982              929
            Quartz                     7                1,161             N/A
            Topaz/Porcelain            8                1,567             N/A
            Sapphire/Corundum          9                2,035             N/A
            Diamond                   10                N/A               N/A
            N/A indicates the hardness value is above/below the acceptable range of the particular hardness scale.
            Values were obtained from the conversion site: http://www.efunda.com/units/hardness/convert_hardness.
            cfm?HD¼HM&Cat¼Steel#ConvInto.

            residual indentation area, A r (Eq. 31). The coefficient, F, varies depending on which
            indentation method is used. This value (14.229 for Knoop and 1.854 for Vickers) is
            related to the geometry of the pyramidal probe, which will affect the penetration depth
            under the same load. Since a spherical probe is used for the Brinell test, a more
            complex formula is used to calculate the hardness (Eq. 32), where D is the diameter of
            the spherical indentor, and D i is the diameter of the indentor impression (both in mm):

                            L
              ð31Þ   H=F
                            A r
                                  L
              ð32Þ   H=  p        p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
                                      2
                          DD        D   D i  2
                         2
            Quite often, an indentation is so small that it is difficult to resolve with a normal light
            microscope. To circumvent these problems, software is now capable of monitoring
            the load and displacement of the probe during the measurement, and relating this to
            the contact area. Such an analysis without the need for visual confirmation is
            necessary for nanoindentation techniques for thin films and other surface hardness
            applications. As its name implies, the hardness of a material is evaluated by the
            depth and symmetry of the cavity created from controlled perforation of a surface
            with a nanosized tip (Figure 2.58b). It should be pointed out that although we have
            discussed crystalline solids in great detail thus far, hardness measurements are also
            easily performed on amorphous solids such as glasses.


            Cleavage and fracturing
            The intermolecular forces in a crystal lattice are often not homogeneous in all
            directions. If the solid consists of strong interactions among neighbors in specific
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