Page 101 - Materials Chemistry, Second Edition
P. 101

88                                              2 Solid-State Chemistry






                                             +
                                             +

                       E
                                               E a






                                     Extent of the migration (z)
            Figure 2.57. Illustration of the energetics involved for the atomic diffusion of interstitial impurities.



                    N v
             ð30Þ       ¼ e  ðE a =kTÞ ;
                    N T
           where: N v is the number of vacancies; N T , the total number of atoms in the crystal
           lattice; E a , the activation energy for the diffusion process; k, the Boltzmann constant
                                  1
           (1.38   10  23  J atom  1  K ); and T is the temperature (K).

           2.3.6. Physical Properties of Crystals


           Hardness
           Thus far, we have examined the 3-D arrangements of atoms, ions, or molecules
           comprising a crystal lattice. The macroscopic physical properties of crystalline
           materials are directly related to these arrangements. For instance, the overall hard-
           ness of a crystal depends on the nature of the interactions among the discrete
           components of the crystal lattice. Those crystals possessing covalent interactions
           (e.g., diamond) will have a high hardness, whereas those containing only van der
           Waals forces will be soft (e.g., talc). A variety of scales (Table 2.10) may be used to
           assign the relative hardness of a material. The Mohs scale is generated by a
           qualitative assessment of how easily a surface is scratched by harder materials,
           with the hardest material (diamond) given a value of ten. The hardness of a material
           is directly proportional to its tensile strength; depending on which method is used,
           proportionality factors may be calculated. For instance, if the Brinell hardness value
           is known, the tensile strength is simply 500 times that value.
             Tests such as Vickers, Knoop, and Brinell use an indentation technique that
           impinges a hard tip (e.g., diamond) into the sample with a known load (Figure 2.58a).
           After a designated period of time, the load is removed, and the indentation area is
           measured. The hardness, H, is defined as the maximum load, L, divided by the
   96   97   98   99   100   101   102   103   104   105   106