Abstract
The equilibrium relationships derived for coherent equilibrium given in Chap. 7 and the conclusions derived from a general review of the origin of hysteresis in first-order phase transformations given in Chap. 6 are assessed here to provide a first attempt at a new semi-quantitative interpretation of the zirconium–hydrogen phase relationships. Numerical estimates are made to determine the stability conditions for the zirconium–hydrogen system on the basis of the coherent phase relationships derived for the polymorphic coherent transformation case given in Chap. 7. A complete quantitative assessment of the foregoing new concepts and their consequences to DHC, however, still remains to be completed. The theoretical assessment is followed by a comprehensive examination of most of the available data for the solvus in zirconium–hydrogen systems. This review has led to some reinterpretation of the meaning and physical significance of some of the solvus data as it applies to DHC.
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Notes
- 1.
In the following specific application of the theory the β phase refers to the δ-hydride phase in the Zr–H system.
- 2.
On theoretical grounds, there is the possibility that this could be the case for the Zr–H system since it is observed (see Chap. 3) that hydride precipitates form long, thin platelets and these shapes are the results of hydride formation by an invariant plane strain transformation for which almost all of the volumetric transformation strain would be directed in the platelet normal direction. For this extreme anisotropy of the transformation strain, using an expression given by Puls [35] for an aspect ratio of 0.1, the elastic accommodation energy is reduced by a factor of ~6.5 compared to the value obtained for a hydride precipitate of the same shape but with transformation strains assuming hydride formation occurred by a pure lattice strain transformation.
- 3.
It could, however, be reduced to zero if all the stresses resulting from the misfit strains of the precipitates are relieved through diffusion of the atoms of the underlying lattice structure with respect to which the misfit strains are imposed.
- 4.
Similarly dilatometry or electrical resistivity techniques use the inflection point as representing the TSS temperature.
- 5.
This effect can also be seen in plots of the derivative of Young’s modulus versus temperature [31].
- 6.
Strictly speaking, TSSDI is not a terminal solvus and should more properly be labeled SSDI.
- 7.
In the paper by Cann et al. [5] \( r_{H}^{\beta /\alpha } \left( {\text{Nb}} \right) \) is given as 2.76; it is not clear which of the two values is the correct one.
- 8.
The review of Cann’s results in Chap. 4 suggests that the change in TSSD should be somewhat less than what Cann estimates since he assumed that the partitioning of the hydrogen to the β phase would be reduced both by the decrease in the measured partitioning ratio and (erroneously, it appears) the reduction in the volume fraction of the beta phase.
- 9.
In a subsequent paper they state that the maximum temperature used was 500 °C with a hold time of 5 min. However, this maximum temperature could not have been used by the authors for specimens with hydrogen content close to and up to the maximum value of 542 wppm, since the dissolution temperature for the maximum hydrogen content is above 500 °C.
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Puls, M.P. (2012). Experimental Results and Theoretical Interpretations of Solvus Relationships in the Zr–H System. In: The Effect of Hydrogen and Hydrides on the Integrity of Zirconium Alloy Components. Engineering Materials. Springer, London. https://doi.org/10.1007/978-1-4471-4195-2_8
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