Theoretical cleavage strength

It is first useful to establish the maximum strength expeeted from a material, based on the strength of the atomic bonding. Consider two planes of atoms being pulled apart by a tensile stress o-as shown in Fig. 8.1. From consideration of the interatomic potential, the stress is expected to increase initially as a function of the interplanar spacing d. At some point, however, the stress will pass 

In order to determine A, one recognizes that the material will be elastic at low stresses. For this situation sinx x and, using Hooke s Law, one can write 

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The quantity Oc is called the theoretical cleavage strength (we will use the terms fracture and cleavage interchangeably here) and it is the maximum stress required to separate, or cleave, the planes. Since cleavage occurs at an interplanar separation of X = k 12, the work per unit area required to separate planes, also known as the strain energy, is the area under the curve in Figure 5.37 up to that point,... 

Suggest a typical value for the theoretical cleavage strength of a crystalline oxide. 

The calculation of the theoretical strength in Chap. 3 is based on the proper shear stress for ductile ceramics, some at RT, but the vast majority at high temperatures. For non-ductile materials, the normal stress, <7, rather than the shear stress, T, is applicable. Applying a tensile stress normal to the planes, which separates two atomic planes, the theoretical cleavage stress may be evaluated in the same way as described in Sect. 3.3.3, but instead of considering the shear stress a normal stress is considered. One can derive an equation similar to Eqs. (3.17-3.18) in terms of the theoretical cleavage stress as ... 

The calculation results described above account well for the experimental facts that these two metal thiolate complexes could react with H2 reversibly under mild conditions. We proposed that the difference in the bond strength of the M-H bond (Ir-H is stronger than Rh-H at the similar environment) may be responsible for different H2 activation mechanisms of these two metal thiolate complexes. To conclude, our theoretical study shows that the combination of the transition metals and the M-S (thiolate) bond may facilitate the H—H bond cleavage under mild conditions. 

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