Structure and Thermodynamical Properties of Zirconium Hydrides from First-Principle

Abstract

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 .

Kinetic Model of Incipient Hydride Formation in Zr Clad under Dynamic Oxide Growth Conditions

“…which is simply a coagulation rate for two species -H and Zr-in the proportions indicated by the exponents of ρ Zr and N H . ∆E δ is the formation energy of a molecule of δ hydride (≈ 0.52 eV at 350 • C according to Blomqvist et al [88]) and p(x) represents the thermodynamic probability for this reaction to occur, which can be directly extracted from the Zr-H phase diagram using the lever rule:…”

Formation and characterization of hydride blisters in Zircaloy-4 cladding tubes

“…First, the crystallographic Figure 11: (a) Nanohardness measurements with a 10mN load on two profiles on a 217 µm deep blister on the radial circumferential plane, (b) evolution of the hardness of the hydrided zirconium as a function of the hydrogen content from [31,66,67,68,69,70], (c) elastic modulus measured from the nanohardness measurements considering a ν=0.3 Poisson ratio and (d) evolution of the elastic modulus of the hydrided zirconium as a function of the hydrogen content from [31,65,68,71,72,73,74].…”

New Zirconium Hydrogen Second Nearest Neighbor Modified Embedded Atom Method (MEAM) Potential For Simulation of Stacking Fault Energy Along the <0110> Path Of The Hexagonal Closely Packed Lattice Basal Plane

“…For the equilibrium volume V 0 = 2987.6452Å 3 and the slope k = dP dV V 0 = −0.030463, from Fig.3.4, bulk modulus is B = 91GPa. Compared to the DFT results [39] in Table 3.8 there is a big difference in the bulk modulus values. The bulk modulus is now calculated from the elastic constants from Table 3.8.…”

“…The bulk modulus is now calculated from the elastic constants from Table 3.8. J.Blomqvist et.al [39] have almost the same results in terms of lattice constants from first principles and use the same unit cell, but elastic constants and bulk modulus do not match.…”

“…This is an approximation, because in reality hydrogen atoms move inside the fcc box and randomly occupy the six out of eight available tetragonal positions. This model of the δ hydride ZrH 1.5 was used in many papers ( [39], [13], [8]) and the approximation about randomness was not treated in more detail. There is a slight difference between c and a lattice constants calculated by the MEAM, Table 3.7, and they match closely DFT results in [39] and [8].…”