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13. Coherent and incoherent states and, consequently, some elastic stress must build up. Thus, there are two limiting cases conceivable: coherent state and incoherent state, as shown schematically in Fig. 13. In the coherent case, since the stress introduced by H atoms depends on H concentration, certain modes of stress and concentration waves build up so as to satisfy the stress-free condition on the surface; in this way, the spinodal decomposition becomes dependent on sample shapes. In the incoherent case, on the other hand, the stress is relaxed on the boundaries of each of the small grains; accordingly, no shape dependence of the spinodal decomposition exists.
It must be borne in mind, however, that even in polycrystalline samples, the spinodal decomposition temperature can be suppressed to some extent ( '" 20 K) due to partially coherent stress relaxation. 46,47] and has been applied to the problem of spinodal decomposition in the Pd-H and Nb-H systems. However, these calculations have been only partially successful so far, the main reason suspected being the inaccuracies in the interaction parameters. But, as long as spinodal decomposition is concerned, its major driving force is no doubt the long-range elastic force, which in turn can be well described by the meanfield theory.
4 (S )( c:: --5 -6 -7 -8 -92~------~3------~-L4---------J5 10 3 /T(K-') Fig. 17. 10 I a05~~--------~--------~------~ 200 300 T (K) 400 500 Fig. 18. Plots of kTinZ. vs. T for the tenninal solubility of the V-H system. 121] bend at higher temperatures can be attributed to a gradual decrease oL1Hso1 v> which can be obtained immediately as a function of temperature by subtracting the T ASso1v term on the graph. 121] that the gradual decrease of AH so1v observed at high temperatures can be explained largely in terms of the interaction between H atoms, as described in Sect.