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# Role of the defect-core in mechanics

Through this post I wish to share some recent results that provide new insights into the role of a defect-core in mechanics. Below is the abstract of the work, and the references and links to the preprints of articles. I look forward to your comments and suggestions.

Abstract:

Electronic structure calculations at macroscopic scales are employed to investigate the crucial role of a defect-core in the energetics of vacancies in aluminum. We find that vacancy core-energy is significantly influenced by the state of deformation at the vacancy-core, especially volumetric strains. Insights from the core electronic structure and computed displacement fields show that this dependence on volumetric strains is closely related to the changing nature of the core-structure under volumetric deformations. These results are in sharp contrast to mechanics descriptions based on elastic interactions that often consider defect core-energies as an inconsequential constant. Calculations suggest that the variation in core-energies with changing macroscopic deformations is quantitatively more significant than the corresponding variation in relaxation energies associated with elastic fields. Upon studying the influence of various macroscopic deformations, which include volumetric, uniaxial, biaxial and shear deformations, on the formation energies of vacancies, we show that volumetric deformations play a dominant role in governing the energetics of these defects. Further, by plotting formation energies of vacancies and di-vacancies against the volumetric strain corresponding to any macroscopic deformation, we find that all variations in the formation energies collapse on to a universal curve. This suggests a universal role of volumetric strains in the energetics of vacancies. Implications of these results in the context of dynamic failure in metals due to spalling are analyzed.

References:

1. V. Gavini, Role of macroscopic deformations in energetics of vacancies in aluminum, Phys. Rev. Lett. 101 205503 (2008). preprint

2. V. Gavini, Role of the defect-core in energetics of vacancies, Proc. R. Soc. A (to appear, 2009). preprint

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## Comments

## Re. Modeling vacancies with DFT

1. Neat!

2. Not yet finished reading, but still, pretty neat (to the extent that I read it).

Someday I plan to eat your intellectual bandwidth by asking you some dumb questions regarding the things kinetic in DFT and squaring off DFT with (what else) MD.

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Hmm... For the time being though, I just got diverted from your papers worrying why K-S could at all work out a variational form---what is it about QM which allowed them to do it... (At a deeper, conceptual sort of a level) ... Never mind...

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All in all, a good read.

## Some questions on Vikram's paper on point defects

Dear Vikram,

Interesting work. This has motivated me to look at similar problems for ferroelectric domain walls. A few questions:

1) On page 10, you mention that when a macroscopic strain is prescribed you first homogeneously deform the perfect crystal and then relax the point defect in the deformed crystal. This is clear in the case of volumetric strains. In the case of uniaxial strains (let say x direction), do you allow relaxation in the other two directions or the crystal is constrained to remain undeformed in y and z directions?

2) In terms of your atomistic calculations, how do you impose a uniform macroscopic strain? Do you impose boundary displacements on some computational cell?

3) In Figure 4, are your displacements with respect to the stress-free bulk or the homogeneously deformed bulk?

4) In the same figure, why don't you use the same magnitude for compressive and tensile stresses? I see -0.36 and 0.33. Why?

Regards,

Arash

## Re: Arash's questions

Dear Arash,

1 & 2. The deformations are introduced through Dirichlet boundary conditions on the displacements on a very large computational cell. The cell was chosen to be large enough to make sure the energies are converged with respect to the cell-size. Thus, in the case of a uniaxial deformation in the x direction, the crystal is constrained in the other two directions.

3. The displacements indicated are with respect to the homogeneously deformed bulk. These decay to zero at the boundary.

4. The simulations that were performed and the data that was collected for volumetric deformations was done through changing the lattice spacing in steps. The strains were computed in the post-processing. The plots in figure 4 were depicting the displacement fields at the extreme ends of the range of volumetric deformations that were chosen. I performed the simulations up to 0.33 volumetric strain because at this strain the formation energy of a mono-vacancy is clearly negative (figure 2). I chose a similar range on the compressive end (but since I collected the data in increments of lattice spacing the range is not identical). In all the simulations conducted, I controlled the deformations but not the stresses (hence figure 4 reflects the same), as thermodynamic quantity I was computing was formation energies (but not enthalpies). As I indicated in the conclusions, computing formation enthalpies (where the stress is the controlling variable) is interesting in itself. I am not sure if you had something else in mind when you asked this question.

Please let me know if these responses clarify your question.

Regards,

Vikram

## Re Re: Arash's questions

Hi Vikram,

Thanks for your response. These clarify my questions. I'll talk to you in more detail shortly about domain walls.

Regards,

Arash