Annealing bulk stress

The establishment of a defined annealing bulk stress takes place as described in the part above on annealing. 

Annealing Bulk Stresses. As described in Subsect. 4.2.3, the annealing bulk stresses are established according to the rate cooling process. To reduce the probability of rupture, efforts are already made to produce compressive stresses on the surface of the blank during the annealing process. 

As shown in Table 4.2, the asymmetric temperature distributions in the thickness direction in a flat disc and a meniscus lead to very different stresses after cooling under otherwise equal boundary conditions. In particular, the compressive stress in the y direction on the bottom is very strongly reduced in the meniscus in comparison with the flat disc. This means that the possibility to compensate for tensile stresses at the surface, which are caused by the crystal layer (see the following paragraph) or the support system, by annealing bulk stresses is significantly less with a meniscus-shaped disc than with a flat disc (called the meniscus effect in the following). 

Between 7 and 470 K a is found to increase with temperature. This increase is reversible and corresponds well with that of bulk silicon [Ko4]. If PS is annealed in nitrogen at higher temperatures (600 °C), hydrogen desorption takes place, which changes the condition of the inner surface drastically. At these temperatures an irreversible increase in a is observed for micro PS. A similar increase in a after annealing is found for meso PS. Changes that affect the core of the crystallites, e.g. stress effects [Ko4], as well as surface-related effects like the formation of surface states [Ko5, BalO], are proposed to be responsible for the observed increase of a with T. 

In one dimensional diffusion experiments (e.g., starting with a thin film source of A on a B crystal surface) one often finds an exponential decrease in the A concentration at the far tail of the concentration profile. This behavior has been attributed to pipe diffusion along dislocation lines running perpendicular to the surface. Models have been introduced which assume a (constant) pipe radius, rp, inside which Dl = p-D, b and p denoting here bulk and dislocation respectively. P values of 103 have been obtained in this way. It is difficult to assess the validity of these observations. The model considerably simplifies the real situation. During diffusion annealing, the structure of the dislocation networks is likely to change because of self-stress (see Chapter 14) and chemical interactions. 

The volume decrease accompanying formation of intermetallic compounds produces a bulk dilation stress over the whole thickness of growing layers. Thermal expansion of the couple constituents during heating up as well as their contraction during cooling down in the course of successive anneals of the same couple produces a shear stress. These inevitably lead to the rupture of Ni-Zn and Co-Zn diffusion couples, with the latter effect being most disastrous. 

Another motivation for measurement of the microhardness of materials is the correlation of microhardness with other mechanical properties. For example, the microhardness value for a pyramid indenter producing plastic flow is approximately three times the yield stress, i.e. // 3T (Tabor, 1951). This is the basic relation between indentation microhardness and bulk properties. It is, however, only applicable to an ideally plastic solid showing no elastic strains. The correlation between H and Y is given in Fig. 1.1 for linear polyethylene (PE) and poly(ethylene terephthalate) (PET) samples with different morphologies. The lower hardness values of 30-45 MPa obtained for melt-crystallized PE materials fall below the /// T cu 3 value, which may be related to a lower stiff-compliant ratio for these lamellar structures (BaM Calleja, 1985b). PE annealed at ca 130 °C... 

The relaxation process may lead either to a decrease in residual stress or an increase in elastic properties, or both, with incubation time. However, independent of the actual interpretation, these results support the hypothesis that the chains in the films, which were initially out of equilibrium, tend to equilibrate during annealing. As shown above, this relaxation process was documented by dewetting. Interestingly, relaxations were much faster than according to bulk reptation at 125°C for the high molecular weight PS used here (Trep 2 x 10 s) [43, 104, 163, 164],... 

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