Cubic crystals Knoop hardness

Figure 3.7. Knoop hardness anisotropy observed on specific planes of InP and cubic BN crystals. Note that 45° from <110> is equivalent to [100]. Data are represented from Brazen and Brookes. " ...

Table 3.1. Knoop Hardness Results from Cubic Single Crystals...

Figure 3.16 and Tables 3.7 and 3.8 show that the anisotropy is of the same nature as that observed for Knoop indentation hardness measurements in that (110) and <100) are the hard and soft directions, respectively, for crystals which slip on 110 (110), and similar behavior is exhibited by those cubic crystals with 110 <111>, 112 <111), and 123KlH> systems. Again, analogously to the Knoop measurements, the converse is found for 100 (0Tl> and lllKlTo) systems. 

Because this is not a commonly encountered indenter and because of the restricted type of plane that it can usefully investigate, there are very few results from which to draw conclusions. However, for cubic crystals the difference between those having 001 (011) slip systems and the other types is evident in the symmetry of the hardness anisotropy curves as it was in the case of the Knoop indenter and the Vickers diamond. 

It is obvious by now that the mismatch of symmetry between the Knoop indenter and 111 planes is a weakness when exploring hardness anisotropy of such planes. However, since scratch hardness does not suffer from such a mismatch, the resolved shear stress curves for the (111) plane in cubic crystals with the three commonly found slip systems shown in Figure 3.29 may be useful in anisotropy and slip system investigations. Clearly more detailed anisotropy is predicted but the small anisotropy factors implied in the scale-of Figure 3.29 must be remembered. Generally speaking, only the main features of the predicted curves have ever been established and experimental uncertainty makes it unlikely that the fine detail will be found. 

A clear crystallochemical interpretation of hardness anisotropy measurement results, especially for monocrystals, makes it possible to estimate the structural homogeneity of crystal. Button et al. (1979) testing the hardness of cubic sodium tungsten bronzes Na W03 (where 0.4 < x < 0.75) with the Knoop indenter, found the hardness of W03 to rise from 450 to 844 within a highly differentiated hardness anisotropy for various values of the Na+ ion. This variation is the outcome of differences in atomic spacings in crystals. 

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