Hardening mechanisms in multilayers

In summary it is clear that the effects of coherency stresses are very far from understood, although experiments suggest that in intrinsically strong materials their effect is relatively small. This has led to the consideration of other possibilities, in particular the effects of elastic inhomogeneity. 

The importance of such effects was deduced from the data shown in Fig. 8.2 from the elegant experiments of Barnett and co-workers (Chu and Barnett, 1995). In the TiN/VN multilayers the two layers are both elastically strained with respect to one another and have different elastic moduli, that of TiN being greater than that of VN, which is similar to that of NbN. Shinn and Barnett (1994) have used this to study the effects of elastic modulus mismatch. As shown in Fig. 8.2, systems where there was a difference in elastic modulus showed a substantial increase in hardness. Where there was no difference in elastic modulus little or no hardening was observed, whilst hardening was obtained in a TiN/Vo.6Nb0.4N system where there was a modulus mismatch but no lattice mismatch (Mirkarimi et al., 1990 Hubbard et al., 1992). 

The situation of a screw dislocation moving towards an atomically sharp interface separating two isotropic layers, A and B, with shear moduli GA and Gb respectively but the same Burgers vector, was analysed by Koehler 

2 The variation in hardness theoretically predicted for the TiN/NbN multilayers compared with data for the isostructural nitrides shown in Fig. 8.1(a). The predictions are based on the ideas of an increment of hardness arising from the elastic mismatch across the layers, equation (8.6), shown as the horizontal dashed line, and for the lateral flow of material within the interlayers, equations (8.10-8.12), shown as the dashed line increasing as the wavelength decreases. In the isostructural multilayers, the upper limit to the increase in hardness should occur when the stress is high enough to drive dislocation motion across the layers. In the nonisostructural, this condition does not apply, or is substantially modified. The lines shown assume that the hardness of monolithic TiN and NbN is 25 GPa and that the layer thicknesses are equal. Other data are given in Table 8.1. 

As might be expected, the magnitude of the force on the dislocation increases as the dislocation gets closer to the interface. The force is repulsive when the dislocation is moving towards the stiffer layer, and attractive when it is moving towards the more compliant layer. 

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