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Register a new userThe continuum elastic and atomistic viewpoints on the formation volume and strain energy of a point defect
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We discuss the roles of continuum linear elasticity and atomistic calculations in determining the formation volume and the strain energy of formation of a point defect in a crystal. Our considerations bear special relevance to defect formation under stress. The elasticity treatment is based on the Greens function solution for a center of contraction or expansion in an anisotropic solid. It makes possible the precise definition of a formation volume tensor and leads to an extension of Eshelbys result for the work done by an external stress during the transformation of a continuum inclusion (Proc. Roy. Soc. Lond. Ser. A, 241 (1226) 376, 1957). Parameters necessary for a complete continuum calculation of elastic fields around a point defect are obtained by comparing with an atomistic solution in the far field. However, an elasticity result makes it possible to test the validity of the formation volume that is obtained via atomistic calculations under various boundary conditions. It also yields the correction term for formation volume calculated under these boundary conditions. Using two types of boundary conditions commonly employed in atomistic calculations, a comparison is also made of the strain energies of formation predicted by continuum elasticity and atomistic calculations. The limitations of the continuum linear elastic treatment are revealed by comparing with atomistic calculations of the formation volume and strain energies of small crystals enclosing point defects.
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During plastic deformation of crystalline materials, point defects such as vacancies and interstitials are generated by jogs on moving dislocations. A detailed model for jog formation and transport during plastic deformation was developed within the vector density-based continuum dislocation dynamics framework (Lin and El-Azab, 2020; Xia and El-Azab, 2015). As a part of this model, point defect generation associated with jog transport was formulated in terms of the volume change due to the non-conservative motion of jogs. Balance equations for the vacancies and interstitials including their rate of generation due to jog transport were also formulated. A two-way coupling between point defects and dislocation dynamics was then completed by including the stress contributed by the eigen-strain of point defects. A jog drag stress was further introduced into the mobility law of dislocations to account for the energy dissipation during point defects generation. A number of test problems and a fully coupled simulation of dislocation dynamics and point defect generation and diffusion were performed. The results show that there is an asymmetry of vacancy and interstitial generation due to the different formation energies of the two types of defects. The results also show that a higher hardening rate and a higher dislocation density are obtained when the point defect generation mechanism is coupled to dislocation dynamics.
Oxygen vacancy formation energy is an important quantity for enabling fast oxygen diffusion and oxygen catalysis in technologies like solid oxide fuel cells. Both previous literature in various systems and our calculations in LaMnO3, La0.75Sr0.25MnO3, LaFeO3, and La0.75Sr0.25FeO3, show mixed results for the direction and magnitude of the change in vacancy formation energy with strain. This paper develops a model to make sense of the different trend shapes in vacancy formation energy versus strain. We model strain effects using a set of consistent ab initio calculations, and demonstrate that our calculated results may be simply explained in terms of vacancy formation volume and changes in elastic constants between the bulk and defected states. A positive vacancy formation volume contributes to decreased vacancy formation energy under tensile strain, and an increase in elastic constants contributes to increases in vacancy formation energy with compressive and tensile strains, and vice versa. The vacancy formation volume dominates the linear portion of the vacancy formation energy strain response, while its curvature is governed by the vacancy-induced change in elastic constants. We show results sensitive to B-site cation, A-site doping, tilt system, and vacancy placement, which contributions may be averaged under thermally averaged conditions. In general, vacancy formation energies for most systems calculated here decreased with tensile strain, with about a 30-100 meV/% strain decrease with biaxial strain for those systems which showed a decrease in vacancy formation energy. Experimental verification is necessary to confirm the model outside of calculation.
The mechanical responses of single crystalline Body-Centered Cubic (BCC) metals, such as molybdenum (Mo), outperform other metals at high temperatures, so much so that they are considered as excellent candidates for applications under extreme conditions, such as the divertor of fusion reactors. The excellent thermomechanical stability of molybdenum at high temperatures (400-1000$^{rm o}$C) has also been detected through nanoindentation, pointing towards connections to emergent local dislocation mechanisms related to defect nucleation. In this work, we carry out a computational study of the effects of high temperature on the mechanical deformation properties of single crystalline Mo under nanoindentation. Molecular dynamics (MD) simulations of spherical nanoindentation are performed at two indenter tip diameters and crystalline sample orientations [100], [110], and [111], for the temperature range of 10-1000K. We investigate how the increase of temperature influences the nanoindentation process, modifying dislocation densities, mechanisms, atomic displacements and also, hardness, in agreement with reported experimental measurements. Our results suggest that the characteristic formation and high-temperature stability of [001] dislocation junctions in Mo during nanoindentation, in contrast to other BCC metals, may be the cause of the persistent thermomechanical stability of Mo.
The effect of elastic strain on catalytic activity of platinum (Pt) towards oxygen reduction reaction (ORR) is investigated through de-alloyed Pt-Cu thin films; stress evolution in the de-alloyed layer and the mass of the Cu removed are measured in real-time during electrochemical de-alloying of (111)-textured thin-film PtCu (1:1, atom %) electrodes. In situ stress measurements are made using the cantilever-deflection method and nano-gravimetric measurements are made using an electrochemical quartz crystal nanobalance. Upon de-alloying via successive voltammetric sweeps between -0.05 and 1.15 V vs. standard hydrogen electrode, compressive stress develops in the de-alloyed Pt layer at the surface of thin-film PtCu electrodes. The de-alloyed films also exhibit enhanced catalytic activity towards ORR compared to polycrystalline Pt. In situ nanogravimetric measurements reveal that the mass of de-alloyed Cu is approximately 210 +/- 46 ng/cm2, which corresponds to a de-alloyed layer thickness of 1.2 +/- 0.3 monolayers or 0.16 +/- 0.04 nm. The average biaxial stress in the de-alloyed layer is estimated to be 4.95 +/- 1.3 GPa, which corresponds to an elastic strain of 1.47 +/- 0.4%. In addition, density functional theory calculations have been carried out on biaxially strained Pt (111) surface to characterize the effect of strain on its ORR activity; the predicted shift in the limiting potentials due to elastic strain is found to be in good agreement with the experimental shift in the cyclic voltammograms for the dealloyed PtCu thin film electrodes.
Here, we report a study on the radiation resistance enhancement of Gd2Zr2O7 nanograin ceramics, in which amorphization, cell volume expansion and multi-stage helium (He) bubble formation are investigated and discussed. Gd2Zr2O7 ceramics with a series of grain sizes (55-221 nm) were synthesized and irradiated by 190 keV He ion beam up to a fluence of 5x10^17 ions/cm2. Both the degree of post irradiation cell volume expansion and the amorphization fraction appear to be size dependent. As the average grain size evolves from 55 to 221 nm, the degree of post irradiation cell volume expansion increases from 0.56 to 1.02 %, and the amorphization fraction increases from 6.8 to 11.1 %. Additionally, the threshold He concentrations (at. %) of bubbles at different formation stages and locations, including (1) bubbles at grain boundary, (2) bubble-chains and (3) ribbon-like bubbles within the grain, are all found to be much higher in the nanograin ceramic (55 nm) compared with that of the submicron sample (221 nm). We conclude that grain boundary plays a critical role in minimizing the structural defects, and inhibiting the multi-stage He bubble formation process.
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