“…3 for the sake of comparison. It can be observed that for pure Zr the present DE values of the FCC and BCC structures as a reference of the HCP structure are 38 and 75 meV/atom, respectively, which agrees well with the corresponding calculated values of 40 and 78 meV/atom [12]. One could also notice from It is of importance to reveal the intrinsic mechanism of the effect of H on structural stability of Zr, and the electronic structures of various ZrH x phases are therefore calculated in the present study.…”
“…3 for the sake of comparison. It can be observed that for pure Zr the present DE values of the FCC and BCC structures as a reference of the HCP structure are 38 and 75 meV/atom, respectively, which agrees well with the corresponding calculated values of 40 and 78 meV/atom [12]. One could also notice from It is of importance to reveal the intrinsic mechanism of the effect of H on structural stability of Zr, and the electronic structures of various ZrH x phases are therefore calculated in the present study.…”
“…This contrasts greatly with Zhu et al 16 , who claimed that the δ-hydride is by far the most stable hydride, by nearly 8 eV more than the other phases. It is, however, difficult to understand that result, since the "convex hull" presented was not actually convex, and the magnitude of this number is out of line with other results 15,26,40,43 .…”
The thermodynamics of H/α-Zr solid solution and zirconium hydride phases were studied using density functional theory. Disorder in ζ, γ and δ hydrides and solid solutions were modelled using a statistically significant number of randomly generated structures in combination with special quasirandom structures and solid solutions with a range of concentrations. This is used in conjunction with a calculation of thermodynamic parameters of the system, including the temperature dependent sensible enthalpy, configurational entropy and vibrational entropy of the different crystals in the system, developed from phonon density of states. It was found that precipitation of hydrides is not thermodynamically favourable for Zr-H solid solutions containing less than 300 ppm H, suggesting that a mechanism must cause local concentration of H atoms to a greater amount than found globally in experimental samples containing hydrides. Temperature drives the reaction in the direction of solution, primarily due to entropic effects. Generally, γ hydride is the most stable phase, although it is very close in energy to the δ-phase. The sensible enthalpy of precipitation assists in stabilising HCP hydrides, and the configurational entropy change during precipitation favours FCC hydrides. None of the thermodynamic contributions are found to be negligible in driving precipitation.arXiv:1401.5637v1 [cond-mat.mtrl-sci] 22 Jan 2014 2
“…When comparing verious groups' results it is worth noticing that (a) Zr is notoriusly difficult to model and (b) all of the above cited works, except the last one, use a pseudo potential approach, which is generally considered less accurate than projector based and all-electron methods, such as PAW, FP-LAPW and FP-LMTO. In a recent paper Udagawa et al even presented an analysis of plane defect in Zr-H systems by computing γ-surfaces and surface energy in these systems using DFT-methods [13]. There still exists some gaps and some cases where published elastic coefficients do not match from one group to another.…”
Zirconium alloys are used as nuclear fuel cladding material due to their mechanical and corrosion resistant properties together with their favorable cross-section for neutron scattering. At running conditions, however, there will be an increase of hydrogen in the vicinity of the cladding surface at the water side of the fuel. The hydrogen will diffuse into the cladding material and at certain conditions, such as lower temperatures and external load, hydrides will precipitate out in the material and cause well known embrittlement, blistering and other unwanted effects. Using phase-field methods it is now possible to model precipitation build-up in metals, for example as a function of hydrogen concentration, temperature and external load, but the technique relies on input of parameters, such as the formation energy of the hydrides and matrix. To that end, we have computed, using the density functional theory (DFT) code GPAW, the latent heat of fusion as well as solved the crystal structure for three zirconium hydride polymorphs: δ-ZrH 1.6 , γ-ZrH, and -ZrH 2 .
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