Thermodynamics of impurity-enhanced vacancy formation in metals

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.

Element Effects on High-Entropy Alloy Vacancy and Heterogeneous Lattice Distortion Subjected to Quasi-equilibrium Heating

“…The CoCrFeMnNi alloy was only measured up to 1,273 K because of greater volatilization of Mn. Per Bukonte et al .’s derivation 32 , the Gibbs free-energy change per mole in a metallic system subjected to vacancy formation iswhere ΔG , ΔH , ΔS conf , and ΔS vib are the Gibbs free energy change at temperature T , the formation enthalpy of vacancy, the configurational entropy of vacancy, and the vibrational entropy of vacancy, respectively.…”

“…Since there are size differences among the vacancies and different elements in HEAs, divacancy may form in alloys subjected to heating. Bukonte et al .’s thermodynamics derivations 32 focus on the effect of divacancy. In their derivations 32 , the total entropy term ΔS consists of the vibrational entropy ΔS vib and the configurational entropy ΔS conf .…”

“…Bukonte et al .’s thermodynamics derivations 32 focus on the effect of divacancy. In their derivations 32 , the total entropy term ΔS consists of the vibrational entropy ΔS vib and the configurational entropy ΔS conf . The vibrational (or thermal) entropy describes random vibrational motion in a defective crystal.…”

Grand canonical approach to modeling hydrogen trapping at vacancies in α−Fe

“…The lowering of vacancy formation energy by hydrogen trapping is the origin of the superabundant vacancy effect discovered by Fukai andŌkuma [13]. Trapping by vacancies and the superabundant vacancy effect have been investigated by many authors since, for a wide range of metals [14][15][16][17][18][19][20][21][22]. This formation energy lowering was described by Kirchhheim [15,16] as a 'defactant' effect, by analogy with Gibbs' original theory of surfactants.…”

Thermodynamic analysis of the interaction between metal vacancies and hydrogen in bulk Cu

“…Even higher molar fractions for fcc Fe have been reported by Nazarov et al 22 However, Fe, Ni, and Pd have a much higher H solubility compared to Cu. 23 Furthermore, vacancies in these metals reach molar fractions of 10 −3 , 24 whereas in Cu, vacancy molar fractions are estimated to be one order of magnitude lower, even at high temperatures near the melting point. 25 Experimental studies for ECD Cu have revealed H molar fractions of around 10 −4 near the melting temperature of Cu under extreme H partial pressures exceeding 10 kbar (1 GPa).…”