Atomistic study of hydrogen embrittlement of grain boundaries in nickel: II. Decohesion

Atomistic simulations of bicrystal samples containing a grain boundary are used to examine the effect of hydrogen atoms on the nucleation of intergranular cracks in Ni. Specifically, the theoretical strength is obtained by rigid separation of the two crystals above and below the GB and the yield strength (point of dislocation emission) is obtained by standard tension testing normal to the GB. These strengths are computed in pure Ni and Ni with H segregated to the grain boundaries under conditions typical of H embrittlement in Ni, and in artificially highly-H-saturated states. In all GBs studied here, the theoretical strength sigma(y) is not significantly reduced by the presence of the hydrogen atoms. Similarly, with the exception of the Ni Sigma 27(115) boundary, the yield strength sigma(y) is not significantly altered by the presence of segregated H atoms. In all cases, the theoretical strengths are similar to 25 GPa and the yield strengths are similar to 10 GPa, so that (i) the theoretical strength is always well above the yield strength, with or without H, and (ii) both strengths are far above the bulk plastic flow stress, sigma(B)(y) of Ni and Ni alloys. Significant reductions in fracture energy (25%-45%) are only achieved for some of the artificially high-H-segregation cases and then only when all the H around the GB is allow to diffuse locally to the fracture surface, which corresponds to unlikely out-of-equilibrium segregation plus local kinetics. Complementing recent work showing that H does not change the ability of GB cracks to emit dislocations and blunt, the present work indicates that equilibrium segregation of hydrogen atoms to GBs has little effect on lowering the GB strength and energy, and so does not significantly facilitate nucleation of intergranular cracks

Effect of Sn on generalized stacking fault energy surfaces in zirconium and its hydrides

Hydrogen embrittlement in Zr alloy fuel cladding is a primary safety concern for water based nuclear reactors. Here we investigated the stabilisation of planar defects within the forming hydrides by Sn, the primary alloying element of Zircaloy-4 used in the cladding. In order to explain formation of hydrides and planar defects observed in our experiments, we performed atomic-scale ab initio calculations focusing on the solute interactions with generalized stacking faults in hcp $\alpha$-Zr and fcc zirconium hydrides. Our calculations showed that an increase in Sn concentration leads to a stabilisation of stacking faults in both $\alpha$-Zr and hydride phases. However, the solution enthalpy of Sn is lower in the $\alpha$-Zr as compared to the other hydride phases indicative of two competing processes of Sn depletion/enrichment at the Zr hydride/matrix interface. This is corroborated by experimental findings, where Sn is repelled by hydrides and is mostly found trapped at interfaces and planar defects indicative of stacking faults inside the hydride phases. Our systematic investigation enables us to understand the presence and distribution of solutes in the hydride phases, which provides a deeper insight into the microstructural evolution of such alloy's properties during its service lifetime.Comment: 17 pages, 8 figure

Softening and hardening of yield stress by hydrogen–solute interactions

Hydrogen atoms have a wide variety of effects on the mechanical performance of metals, and the underlying mechanisms associated with effects on plastic flow and embrittlement remain to be discovered or validated. Here, the reduction in the plastic flow stress (softening) due to hydrogen atoms in solute-strengthened metals, previously proposed by Sofronis et al. is demonstrated at the atomistic level. Glide of an edge dislocation through a field of solutes in a nickel matrix, both in the absence of hydrogen and in the presence of H bound to the solutes, is modelled. The 'solutes' here are represented by vacancies, enabling use of accurate binary Ni-H interatomic potentials. Since vacancies have a misfit strain tensor in the Ni matrix and also bind hydrogen atoms, they are excellent surrogates for study of the general phenomenon. The binding of H to the solute (vacancy) reduces the misfit volume to nearly zero but also creates a non-zero tetragonal distortion. Solute strengthening theory is used to establish the connection between strength and solute/hydrogen concentration and misfit strain tensor. Simulations show that when a dislocation moves through a field of random vacancy 'solutes', the glide stress is reduced (softening) when H is bound to the solutes. Trends in the simulations are consistent with theory predictions. Trends of softening or hardening by H in metal alloys can thus be made by computing the misfit strain tensor for a desired solute in the chosen matrix with and without bound hydrogen atoms. Pursuing this, density functional theory calculations of the interaction of H with carbon and sulphur solutes in a Ni matrix are presented. These solutes/impurities do not bind with H and the complexes have larger misfit strains, indicative of H-induced strengthening rather than softening for these cases. Nonetheless, H/solute interactions are the only mechanism, to date, that shows nanoscale evidence of plastic softening due to hydrogen associated with the hydrogen-enhanced localised plasticity concept in fcc metals

Accuracy of working length determination with root ZX apex locator and radiography: An in vivo and ex vivo study

The purpose of this study was to clinically compare working length (WL) determination with root ZX apex locator and radiography, and then compare them with direct visualization method ex vivo. A total of 75 maxillary central and lateral incisors were selected. Working length determination was carried out using radiographic and electronic apex locator methods. Subsequently, the tooth under study was extracted and actual working length was determined directly under a stereomicroscope. Data were analyzed by Wilcoxon signed-rank, Spearman’s correlation coefficient and intra-class correlation tests. All the statistical analyses were set with a significance level of α = 0.05. The absolute measurement errors of the two methods were compared using Wilcoxon signed test, exhibiting no statistically significant difference in measurement errors between the two methods. Descriptive evaluation revealed that in 72% (n = 54) of the specimens, both methods had errors in the same direction and in 28% (n = 21) of the specimens, the two methods had errors in opposite directions. Intra-class correlation coefficient test demonstrated a high degree of agreement between the two methods. In conclusion, this study did not show any difference between radiography, root ZX and direct visualization in WL determination.Key words: Working length, electronic apex locator, root ZX, radiography

Tailoring negative pressure by crystal defects: Crack induced hydride formation in Al alloys

Climate change motivates the search for non-carbon-emitting energy generation and storage solutions. Metal hydrides show promising characteristics for this purpose. They can be further stabilized by tailoring the negative pressure of microstructural and structural defects. Using systematic ab initio and atomistic simulations, we demonstrate that an enhancement in the formation of hydrides at the negatively pressurized crack tip region is feasible by increasing the mechanical tensile load on the specimen. The theoretical predictions have been used to reassess and interpret atom probe tomography experiments for a high-strength 7XXX-aluminium alloy that show a substantial enhancement of hydrogen concentration at structural defects near a stress-corrosion crack tip. These results contain important implications for enhancing the capability of metals as H-storage materials.Comment: 22 pages, 9 figure

Hydrogen–vacancy–dislocation interactions in α-Fe

Atomistic simulations of the interactions between dislocations, hydrogen atoms, and vacancies are studied to assess the viability of a recently proposed mechanism for the formation of nanoscale voids in Fe-based steels in the presence of hydrogen. Quantum-mechanics/molecular-mechanics method calculations confirm molecular statics simulations based on embedded atom method (EAM) potential showing that individual vacancies on the compressive side of an edge dislocation can be transported with the dislocation as it glides. Molecular dynamics simulations based on EAM potential then show, however, that vacancy clusters in the glide plane of an approaching dislocation are annihilated or reduced in size by the creation of a double-jog/climb process that is driven by the huge reduction in energy accompanying vacancy annihilation. The effectiveness of annihilation/reduction processes is not reduced by the presence of hydrogen in the vacancy clusters because typical V-H cluster binding energies are much lower than the vacancy formation energy, except at very high hydrogen content in the cluster. Analysis of a range of configurations indicates that hydrogen plays no special role in stabilizing nanovoids against jog formation processes that shrink voids. Experimental observations of nanovoids on the fracture surfaces of steels must be due to as-yet undetermined processes

Implied volatility of basket options at extreme strikes

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function