“…62 In Figure 6, we obtain a good agreement with experimental data for the Fe-H system with the vacancy formation energy 1.7 eV, 60 divacancy formation energy 3.4 eV, and the H binding energies from Ref. 61.…”
Hydrogen induced vacancy formation in metals and metal alloys has been of great interest during the past couple of decades. The main reason for this phenomenon, often referred to as the superabundant vacancy formation, is the lowering of vacancy formation energy due to the trapping of hydrogen. By means of thermodynamics, we study the equilibrium vacancy formation in fcc metals (Pd, Ni, Co, and Fe) in correlation with the H amounts. The results of this study are compared and found to be in good agreement with experiments. For the accurate description of the total energy of the metal–hydrogen system, we take into account the binding energies of each trapped impurity, the vibrational entropy of defects, and the thermodynamics of divacancy formation. We demonstrate the effect of vacancy formation energy, the hydrogen binding, and the divacancy binding energy on the total equilibrium vacancy concentration. We show that the divacancy fraction gives the major contribution to the total vacancy fraction at high H fractions and cannot be neglected when studying superabundant vacancies. Our results lead to a novel conclusion that at high hydrogen fractions, superabundant vacancy formation takes place regardless of the binding energy between vacancies and hydrogen. We also propose the reason of superabundant vacancy formation mainly in the fcc phase. The equations obtained within this work can be used for any metal–impurity system, if the impurity occupies an interstitial site in the lattice.
“…62 In Figure 6, we obtain a good agreement with experimental data for the Fe-H system with the vacancy formation energy 1.7 eV, 60 divacancy formation energy 3.4 eV, and the H binding energies from Ref. 61.…”
Hydrogen induced vacancy formation in metals and metal alloys has been of great interest during the past couple of decades. The main reason for this phenomenon, often referred to as the superabundant vacancy formation, is the lowering of vacancy formation energy due to the trapping of hydrogen. By means of thermodynamics, we study the equilibrium vacancy formation in fcc metals (Pd, Ni, Co, and Fe) in correlation with the H amounts. The results of this study are compared and found to be in good agreement with experiments. For the accurate description of the total energy of the metal–hydrogen system, we take into account the binding energies of each trapped impurity, the vibrational entropy of defects, and the thermodynamics of divacancy formation. We demonstrate the effect of vacancy formation energy, the hydrogen binding, and the divacancy binding energy on the total equilibrium vacancy concentration. We show that the divacancy fraction gives the major contribution to the total vacancy fraction at high H fractions and cannot be neglected when studying superabundant vacancies. Our results lead to a novel conclusion that at high hydrogen fractions, superabundant vacancy formation takes place regardless of the binding energy between vacancies and hydrogen. We also propose the reason of superabundant vacancy formation mainly in the fcc phase. The equations obtained within this work can be used for any metal–impurity system, if the impurity occupies an interstitial site in the lattice.
“…A complete description about the present statistical model will be given elsewhere [17]. The similar statistical model has been proposed for formation of the vacancy-hydrogen complexes in alpha iron [18]. In the present model, an equilibrium equation for a fractional abundance of the vacancy-hydrogen complex ≡…”
Section: Statistical Thermodynamics Model Of Super-saturated Hydrogen...mentioning
Tungsten is a prime candidate as the divertor material of the ITER and DEMO reactors, which would be exposed to unprecedentedly high-flux plasmas as well as neutrons. For a better characterization of radiation damages in the tungsten under the divertor condition, we examine influences of super-saturated hydrogen on vacancies in the tungsten. The present calculations based on density functional theories (DFT) reveal unusual phenomena predicted at super-saturated hydrogen concentration: 1) Strongly enhanced vacancy concentration with the super-saturated hydrogen concentration is predicted by a thermodynamics model assuming multiplehydrogen trapping, i.e., hydrogen clusters formation, in the vacancies; and 2) DFT molecular dynamics revealed that hydrogen clusters can prevent a vacancy from recombining with the neighboring crowdion-type selfinterstitial-atom. This suggests that neutron damage effects will be increased in the presence of the hydrogen clusters.
“…Thus, these interstitial atoms prefer to stick with a vacancy. This explains the experimental observation of vacancy and interstitial atom complexes [14,25]. The charge density difference analysis of an N atom in Fe with a vacancy was performed in order to understand the bonding mechanism shown in figure 1 as the N atom in particular has high exothermic dissolution energies in Fe with a vacancy.…”
The diffusion mechanism of point defects within α-Fe with a single vacancy is investigated using the density functional theory. Calculation reveals that H has a slight effect towards Fe diffusion to a vacancy. He has a strong binding with a vacancy; therefore, Fe diffusion is unlikely to happen. The diffusion of C and N from a vacancy has a high barrier. However, Fe diffusion to a vacancy decreases if the C and N diffuse from a vacancy. Thus, the effect of interstitial atoms within α-Fe with a single vacancy towards diffusion and a possible diffusion pathway is discussed.
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