Papers by Keyword: Hydrogen Diffusion

Abstract: The purpose of this work is developing of the statistical model of hydrogen diffusion in the crystal lattice of BCC metals with an estimate of the contribution of quantum effects and deviations from the Arrhenius equation. The values of the statistical model calculations of H diffusion coefficients in Fe, V, Nb and Ta are in good agreement with the experimental data. The statistical model can also explain deviations from the Arrhenius equation at temperatures 300-500 K in Fe and Nb. The downward deviation of the diffusion coefficient at 300K can be explained by the fact that the statistical model does not consider the tunneling effect at temperatures below 300K. It was suggested that thermally activated fast tunnelling transition of hydrogen atoms through the potential barrier at temperatures below 500 K provides an almost free movement of H atoms in the α-Fe and V. Using the statistical model allows for the prediction of the diffusion coefficient for H in BCC metals at intermediate temperatures.

Abstract: In this work, the strategy for numerical solutions in transport processes is investigated. Permeation problems can be solved analytically or numerically by means of the Finite Difference Method (FDM), while choosing the Euler forward explicit or Euler backwards implicit formalism. The first method is the easiest and most commonly used, while the Euler backwards implicit is not yet well established and needs further development. Hereafter, a possible solution of the Crank-Nicolson algorithm is presented, which makes use of matrix multiplication and inversion, instead of the step-by-step FDM formalism. If one considers the one-dimensional diffusion case, the concentration of the elements can be expressed as a time dependent vector, which also contains the boundary conditions. The numerically stable matrix inversion is performed by the Branch and Bound (B&B) algorithm [2]. Furthermore, the paper will investigate, whether a larger time step can be used for speeding up the simulations. The stability range is investigated by eigenvalue estimation of the Euler forward and Euler backward. In addition, a third solver is considered, referred to as Combined Solver, that is made up of the last two ones. Finally, the Crank-Nicolson solver [9] is investigated. All these results are compared with the analytical solution. The solver stability is analyzed by means of the Steady State Eigenvector (SSEV), a mathematical entity which was developed ad hoc in the present work. In addition, the obtained results will be compared with the analytical solution by Daynes [6,7].

Abstract: The goal of this paper is to introduce an analytical approach for the inversion of nxn solver matrices, which are typically used in Finite Difference Method approximations. In the present case, they are used to solve the Diffusion Equation numerically, since in many physics and engineering fields, partial differential equations cannot be solved analytically. The method presented in this work is primarily formulated for cylindrical coordinates, which are often used in Gas Release Experiments as those described in [8]. However, it is possible to introduce a generalized method, which also allows solutions for Cartesian solvers. The advantage of having the explicit inverse is considerable, since the computational effort is reduced. In this paper we also carry out an investigation on the eigenvalues of the backward and forward solver matrix in order to determine an optimal range for the discretization parameters.

Abstract: Here we report on the results of our theoretical study of hydrogen localization and motion in disordered bcc Ti-V-Cr alloys. The calculations have been carried out within a DFT supercell approach for a certain composition, namely Ti_0.33V_0.27Cr_0.4 for H/M = 1/32. It was found that hydrogen is localized in highly distorted tetrahedral sites formed by different metal species. H atoms are displaced towards titanium. The estimation of the hydrogen diffusion parameters provides the activation energy value of 0.126 eV and the diffusion coefficient at 294 K equal to 1.9 10^-10 m/s² that is in good agreement with available experimental data.

Abstract: Samples of partly desorbed MgH₂ have been studied by the X-ray diffraction method. All samples contained two phases (Mg and MgH₂) and were stable at ambient condition for several months. After fast quenching in liquid nitrogen the samples became unstable and transformed after several days into Mg. The rate of decomposition depends on the amount ratio of Mg and MgH₂ phases in the sample. Destabilization of the hydride phase observed in quenched samples can be explained on the basis of different diffusion of disordered and ordered hydrogen atoms.

Abstract: Samples of desorbed NdRh₃-based hydrides have been investigated by the X-ray diffraction method. X-ray data analysis showed that the samples contain two phases with hexagonal and cubic lattices. It was revealed that proportion of these phases in the samples depends on the rate of heating before the hydrogen desorption. At high rates of the heating in the desorbed samples amount of the phase with cubic lattice increased. This behaviour of the hydrogen in hydrides can be explained by the difference in the diffusion of disordered and ordered hydrogen atoms.

Abstract: The effect of hydrogen on the mechanical properties of disordered and ordered (Fe,Ni)₃V alloys has been investigated. The diffusion behaviors of hydrogen in the disordered and ordered (Fe,Ni)₃V alloys were reported. The results showed that the depth of intergranular (IG) fracture on a surface of tensile fracture of (Fe,Ni)₃V alloy increased linearly with increasing pre-charging temperature at the same pre-charging time. An apparent hydrogen diffusion coefficient was calculated by the time lag method. The apparent hydrogen diffusion coefficient in the disordered (Fe,Ni)₃V alloy was greater than that in the ordered (Fe,Ni)₃V alloy. The relationship between the apparent hydrogen diffusion coefficient and pre-charging temperature in (Fe,Ni)₃V alloy agreed with Arrhenius equation. The activation energies of apparent hydrogen diffusion in the disordered and ordered (Fe,Ni)₃V alloys were 34.6 kJ/mol and 42.2 kJ/mo1, respectively.

Abstract: In a global study of titanium alloys behavior in specific aqueous solution (embrittlement, corrosion and corrosion under stresses), the present work focuses on hydrogen diffusion into the metal and the consequences on its microstructure. Two ways of hydrogen charging were used to investigate this issue (gaseous and cathodic charging). The final aim is to determine a fitted method to create an identified microstructure and then to perform accelerated aging tests of titanium U-Bend samples into an autoclave with a specific environment. Hydrogen absorption and formation of titanium hydride have been studied by SEM analyses and by X-ray diffraction methods.

Abstract: The results of ab initio calculations of diffusion barriers for a hydrogen atom in zirconium α phase have been presented. The potential barrier and length of the jumps have been obtained for all possible directions of hydrogen diffusion. Also the influence of local lattice distortion caused by the presence of impurity on the height and shape of the barriers has been studied in this work.

Abstract: Hydrogen diffusion within a metal or alloy is conditioned by the stress-strain state therein. For that reason it is feasible to consider that hydrogen diffuses in the material obeying a Fick type diffusion law including an additional term to account for the effect of the stress state represented by the hydrostatic stress. In this paper the hydrogen transport by diffusion in metals is modelled in notched specimens where loading generates a triaxiality stress state. To this end, two different approaches of stress-assisted hydrogen diffusion, one-dimensional (1D) and two-dimensional (2D), were compared in the vicinity of the notch tip in four notched specimens with diverse triaxiality level at two different loading rates. The obtained results show that the 2D approach predicts lower values of hydrogen concentration than the 1D approach, so that a loss of directionality of hydrogen diffusion, depending on both notch geometry parameters (radius and depth) and loading rate, appears when a 2D approach is considered.