Contribution of the entropy on the thermodynamic equilibrium of vacancies in nickel

Imperfections are not 0 K: free energy of point defects in crystals

Defects determine many important properties and applications of materials, ranging from doping in semiconductors, to conductivity in mixed ionic-electronic conductors used in batteries, to active sites in catalysts. The theoretical description of defect formation in crystals has evolved substantially over the past century. Advances in supercomputing hardware, and the integration of new computational techniques such as machine learning, provide an opportunity to model longer length and time-scales than previously possible. In this Tutorial Review, we cover the description of free energies for defect formation at finite temperatures, including configurational (structural, electronic, spin) and vibrational terms. We discuss challenges in accounting for metastable defect configurations, progress such as machine learning force fields and thermodynamic integration to directly access entropic contributions, and bottlenecks in going beyond the dilute limit of defect formation. Such developments are necessary to support a new era of accurate defect predictions in computational materials chemistry.

The Primary Irradiation Damage of Hydrogen-Accumulated Nickel: An Atomistic Study

Nickel-based alloys have demonstrated significant promise as structural materials for Gen-IV nuclear reactors. However, the understanding of the interaction mechanism between the defects resulting from displacement cascades and solute hydrogen during irradiation remains limited. This study aims to investigate the interaction between irradiation-induced point defects and solute hydrogen on nickel under diverse conditions using molecular dynamics simulations. In particular, the effects of solute hydrogen concentrations, cascade energies, and temperatures are explored. The results show a pronounced correlation between these defects and hydrogen atoms, which form clusters with varying hydrogen concentrations. With increasing the energy of a primary knock-on atom (PKA), the number of surviving self-interstitial atoms (SIAs) also increases. Notably, at low PKA energies, solute hydrogen atoms impede the clustering and formation of SIAs, while at high energies, they promote such clustering. The impact of low simulation temperatures on defects and hydrogen clustering is relatively minor. High temperature has a more obvious effect on the formation of clusters. This atomistic investigation offers valuable insights into the interaction between hydrogen and defects in irradiated environments, thereby informing material design considerations for next-generation nuclear reactors.

One dimensional wormhole corrosion in metals

Corrosion is a ubiquitous failure mode of materials. Often, the progression of localized corrosion is accompanied by the evolution of porosity in materials previously reported to be either three-dimensional or two-dimensional. However, using new tools and analysis techniques, we have realized that a more localized form of corrosion, which we call 1D wormhole corrosion, has previously been miscategorized in some situations. Using electron tomography, we show multiple examples of this 1D and percolating morphology. To understand the origin of this mechanism in a Ni-Cr alloy corroded by molten salt, we combined energy-filtered four-dimensional scanning transmission electron microscopy and ab initio density functional theory calculations to develop a vacancy mapping method with nanometer-resolution, identifying a remarkably high vacancy concentration in the diffusion-induced grain boundary migration zone, up to 100 times the equilibrium value at the melting point. Deciphering the origins of 1D corrosion is an important step towards designing structural materials with enhanced corrosion resistance.

Including state-of-the-art physical understanding of thermal vacancies in Calphad models

A physically sound thermochemical model accounting for explicit thermal vacancies in elements and alloys is presented. The model transfers the latest theoretical understanding of vacancy formation into the Calphad formalism where it can extend currently available thermodynamic databases to cover vacancy concentrations without a complete re-assessment. The parametrization of the model is based on ab initio-calculated enthalpy of vacancy formation and two model parameters describing the excess heat capacity of vacancy formation. Excellent agreement is obtained with temperature-dependent vacancy concentrations and elemental heat capacities while reasonable extrapolation of phase stability to high temperatures is ensured. Extrapolation to multicomponent systems is reasonable and the long-standing Neumann-Kopp related problem in the Calphad community is solved since multicomponent solid solutions will no longer show fingerprints of elemental heat capacity peaks at their melting points. FCC-Ag, FCC-Al and FCC-Cu, FCC-Zn, FCC-Ni, BCC-Ti, and BCC-W are used as a demonstration, along with the Cu-Zn binary system.

Theoretical insights into non-Arrhenius behaviors of thermal vacancies in anharmonic crystals

Vacancies are prevalent point defects in crystals, but their thermal responses are elusive. Herein, we formulate a simple theoretical model to shed light on the vacancy evolution during heating. Vibrational excitations are thoroughly investigated via moment recurrence techniques in quantum statistical mechanics. On that basis, we carry out numerical analyses for Ag, Cu, and Ni with the Sutton-Chen many-body potential. Our results reveal that the well-known Arrhenius law is insufficient to describe the proliferation of vacancies. Specifically, anharmonic effects lead to a strong nonlinearity in the Gibbs energy of vacancy formation. Our physical picture is well supported by previous simulations and experiments.

Enthalpy-entropy compensation of atomic diffusion originates from softening of low frequency phonons

Experimental data accumulated over more than 120 years show not only that diffusion coefficients of impurities ordinarily obey the Arrhenius law in crystalline solids, but also that diffusion pre-exponential factors measured in a same solid increase exponentially with activation energies. This so-called compensation effect has been argued to result from a universal positive linear relationship between entropic contributions and energy barriers to diffusion. However, no physical model of entropy has ever been successfully tested against experimental compensation data. Here, we solve this decades-old problem by demonstrating that atomistically computed harmonic vibrational entropic contributions account for most of compensation effects in silicon and aluminum. We then show that, on average, variations of atomic interactions along diffusion reaction paths simultaneously soften low frequency phonons and stiffen high frequency ones; because relative frequency variations are larger in the lower region of the spectrum, softening generally prevails over stiffening and entropy ubiquitously increases with energy.

Atomistic diffusion in solids determines aging and the transformation of materials. Here, the authors resolve the origin of the ubiquitous enthalpy-entropy compensation effect, showing how it emerges from shifts in the vibrational modes of the materials during activation.

Multiscale analysis of hydrogen-induced softening in f.c.c. nickel single crystals oriented for multiple-slips: elastic screening effect

Hydrogen-deformation interactions and their role in plasticity are well accepted as key features in understanding hydrogen embrittlement. In order to understand the nature of the hydrogen-induced softening process in f.c.c. metals, a substantial effort was made in this study to determine the effect of hydrogen on the tensile stress-strain behavior of nickel single crystal oriented for multiple-slips. It was clearly established that the hydrogen softening process was the result of a shielding of the elastic interactions at different scales. Hydrogen-induced softening was then formalized by a screening factor S of 0.8 ± 0.05 for 7 wppm of hydrogen, which can be incorporated into standard dislocation theory processes. The amplitude of softening suggests that the shielding process is mainly responsible for the stress softening through the formation of vacancy clusters, rather than a direct impact of hydrogen. This effect is expected to be of major importance when revisiting the impact of hydrogen on the processes causing damage to the structural alloys used in engineering.

Anisotropy of hydrogen diffusion in nickel single crystals: the effects of self-stress and hydrogen concentration on diffusion

Hydrogen diffusion has an important role in solute-dependent hydrogen embrittlement in metals and metallic alloys. In spite of extensive studies, the complexity of hydrogen diffusion in solids remains a phenomenon that needs to be clarified. In this paper, we investigate the anisotropy of hydrogen diffusion in pure nickel single crystals using both an experimental approach and a thermodynamic development. As a first approximation, experimental data from electrochemical permeation and thermal desorption spectroscopy are described using the classical Fick's laws and an apparent diffusion tensor. Within a thermodynamic framework, the diffusion equation can be derived from Fick's laws with an apparent diffusion coefficient which contains an added solute content dependent term β. This term is due to the elastic strain field associated with the insertion of solute atoms. For nickel crystals, the dependence of β on the crystallographic orientation arises from the elastic anisotropy. Additionally, our results elucidate the discrepancies between the thermodynamic model and experimental observations of the effect of the solute concentration on the diffusion process. Moreover, this highlights the importance of the impact of hydrogen on vacancy formation and the subsequent consequences on the anisotropy of the apparent diffusion coefficient.