Abstract
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.
Highlights
The interaction of metals with hydrogen impurities has been broadly studied for technological and scientific purposes
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
Summary
The interaction of metals with hydrogen impurities has been broadly studied for technological and scientific purposes. Near the melting point of metals, the equilibrium vacancy fractions range from about 10À4 to 10À3 while due to the presence of large amounts of H this fraction can increase up to 0.1–0.3. The commonly used assumption to calculate the divacancy concentration as a square of monovacancies is largely overestimating the total vacancy concentration when interstitial H is present and, should not be used when studying SAV formation. We present a more accurate way to study SAVs. By the means of thermodynamics combined with already established material characteristics, we calculate the formation of each vacancy/vacancy complex taking into account the binding energies for multiple H to vacancies. The results from the thermodynamics calculations are compared with the experimental study of Fukai et al., where SAVs are found to be created in Co-H, Ni-H, Pd-H, and Fe-H systems
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