iMechanica - defects in materials
https://www.imechanica.org/taxonomy/term/2811
enGeneral correlations between local electronic structures and solute-defect interactions in bcc refractory metals
https://www.imechanica.org/node/23652
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/11937">alloy design</a></div><div class="field-item odd"><a href="/taxonomy/term/2811">defects in materials</a></div><div class="field-item even"><a href="/taxonomy/term/3987">electronic</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span data-preserver-spaces="true">The interactions between solute atoms and crystalline defects such as vacancies, dislocations, and grain boundaries are essential in determining alloy properties. Here (</span><strong><em><span>Nature Communications</span></em></strong><span>, (2019) 10:4484</span><span data-preserver-spaces="true">) we present a general linear correlation between two descriptors of local electronic structures and the solute-defect interaction energies in binary alloys of body-centered-cubic (bcc) refractory metals (such as W and Ta) with transition-metal substitutional solutes. One electronic descriptor is the bimodality of the </span><em>d</em><span data-preserver-spaces="true">-orbital local density of states for a matrix atom at the substitutional site, and the other is related to the hybridization strength between the valance </span><em>sp-</em><span data-preserver-spaces="true"> and </span><em>d-</em><span data-preserver-spaces="true">bands for the same matrix atom. For a particular pair of solute-matrix elements, this linear correlation is valid independent of types of defects and the locations of substitutional sites. These results provide the possibility to apply local electronic descriptors for quantitative and efficient predictions on the solute-defect interactions and defect properties in alloys.</span></p>
<p><span data-preserver-spaces="true"> </span></p>
<p><span data-preserver-spaces="true"><a href="https://www.nature.com/articles/s41467-019-12452-7">https://www.nature.com/articles/s41467-019-12452-7</a></span></p>
<p><span data-preserver-spaces="true"><a href="http://mse.engin.umich.edu/about/news/newly-discovered-connection-could-help-design-of-nextgen-alloys">http://mse.engin.umich.edu/about/news/newly-discovered-connection-could-help-design-of-nextgen-alloys</a></span></p>
<p><span data-preserver-spaces="true"><a href="https://phys.org/news/2019-10-hard-ceramic-tough-steel-newly.html">https://phys.org/news/2019-10-hard-ceramic-tough-steel-newly.html</a></span></p>
<p> </p>
</div></div></div>Tue, 08 Oct 2019 11:21:25 +0000Liang Qi23652 at https://www.imechanica.orghttps://www.imechanica.org/node/23652#commentshttps://www.imechanica.org/crss/node/23652Enhanced Lithiation in Defective Graphene
https://www.imechanica.org/node/17127
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/671">graphene</a></div><div class="field-item odd"><a href="/taxonomy/term/4465">density functional theory</a></div><div class="field-item even"><a href="/taxonomy/term/8293">VASP</a></div><div class="field-item odd"><a href="/taxonomy/term/8359">Li-ion battery</a></div><div class="field-item even"><a href="/taxonomy/term/2811">defects in materials</a></div><div class="field-item odd"><a href="/taxonomy/term/7045">Vivek Shenoy</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p> </p>
<p><a class="figureLink" title="Full-size image (79 K)" href="http://www.sciencedirect.com/science/article/pii/S0008622314008082#gr3"><img class="imgLazyJSB figure large" src="http://ars.els-cdn.com/content/image/1-s2.0-S0008622314008082-gr3.jpg" alt="Full-size image (79 K)" width="301" height="252" border="0" data-loaded="true" data-thumbeid="1-s2.0-S0008622314008082-gr3.sml" data-fulleid="1-s2.0-S0008622314008082-gr3.jpg" data-thumbheight="164" data-thumbwidth="195" data-fullheight="447" data-fullwidth="533" /></a></p>
<p><span><a class="title" href="http://www.sciencedirect.com/science/article/pii/S0008622314008082" target="_blank">Enhanced lithiation in defective graphene</a></span>
</p><p><span><strong>CARBON</strong> [ <a class="links" href="https://www.academia.edu/8232024/CARBON_Enhanced_Lithiation_in_Defective_Graphene" target="_blank"><strong>PDF</strong> </a>]</span></p>
<p>We performed first-principle calculations based on density functional theory (DFT) to investigate adsorption of lithium (Li) on graphene with divacancy and Stone–Wales defects. Our results confirm that lithiation is not possible in pristine graphene. However, enhanced Li adsorption is observed on defective graphene because of the increased charge transfer between adatom and underlying defective sheet. Because of increased adsorption, the specific capacity is also increased with the increase in defect densities. For the maximum possible divacancy defect density, Li storage capacities of up to ∼1675 mAh/g can be achieved. While for Stone–Wales defects, we find that a maximum capacity of up to ∼1100 mAh/g is possible. Our results provide deeper understanding of Li-defect interactions and will help to create better high-capacity anode materials for Li-ion batteries.</p>
<p><strong><em>* Our previous papers on Li-ion Battery</em> (LIB)</strong></p>
<p><a href="http://imechanica.org/node/16905" target="_blank">Atomistic Mechanism of Phase Boundary Evolution during Initial Lithiation of Crystaline Silicon</a></p>
<p><a href="http://imechanica.org/node/16479" target="_blank">Defect-induced plating of lithium metal within porous graphene networks</a></p>
<p><span><strong><em>* Why Mechanics Community in Lithium Battery Research ? Read Prof. Zhigang Suo's blog :</em></strong></span></p>
<p><a href="http://imechanica.org/node/10622" target="_blank">Lithium batteries--When mechanics meets chemistry</a></p>
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<p>Regards,</p>
<p><a href="http://dibakardatta.com/" target="_blank">Dibakar Datta</a></p>
<p><a href="http://shenoy.seas.upenn.edu/publications.html" target="_blank">Prof. Vivek B Shenoy Lab @ UPenn</a></p>
<p><a href="http://homepages.rpi.edu/~koratn/" target="_blank">Prof. Nikhil Koratker Lab @ RPI</a></p>
<p>-------------------------------------------------</p>
</div></div></div>Mon, 08 Sep 2014 10:59:35 +0000Dibakar Datta17127 at https://www.imechanica.orghttps://www.imechanica.org/node/17127#commentshttps://www.imechanica.org/crss/node/17127TOPOLOGICAL CLASSIFICATION OF DEFECTS
https://www.imechanica.org/node/10416
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/2811">defects in materials</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>When we topologically classify the defects in ordered media, we consider the character of the fundamental group of the associated order parameter space. To construct those groups, we circumscribe the line defects by circles and the point defects by spheres.<br />
My question is what is done for a surface (possibly infinite) defect, say domain walls. My query primary concerns crystal lattices. I want to characterize the essential defects in solid crystals--for dislocation and interstitial/vacancy, it is straightforward. But what to be done in case of grain/phase boundary?</p>
</div></div></div>Wed, 15 Jun 2011 07:16:50 +0000Ayan Roychowdhury10416 at https://www.imechanica.orghttps://www.imechanica.org/node/10416#commentshttps://www.imechanica.org/crss/node/10416Journal Club Theme of Sept. 15 2008: Defects in Solids---Where Mechanics Meets Quantum Mechanics
https://www.imechanica.org/node/3837
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/1269">electronic structure</a></div><div class="field-item odd"><a href="/taxonomy/term/2810">bridging length scales</a></div><div class="field-item even"><a href="/taxonomy/term/2811">defects in materials</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Defects in solids have been studied by the mechanics community for over five decades, some of the earliest works on this topic dating back to Eshelby. Yet, they still remain interesting, challenging, and often spring surprises—one example being the observed hardening behavior in surface dominated structures (as discussed in past journal club themes by Wei Cai and Julia Greer). In this journal theme, I wish to concentrate on the underlying physics behind defect behavior and motivate the need to combine quantum mechanical and mechanics descriptions of materials behavior. Through this discussion, I hope to bring forth: (i) The need to bridge mechanics with quantum mechanics; (ii) The challenges in quantum mechanical calculations; (iii) How the mechanics community can have a great impact.
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<strong>(i) The need to bridge mechanics with quantum mechanics:</strong></p>
<p>Defects play a crucial role in influencing the macroscopic properties of solids—examples include the role of dislocations in plastic deformation, dopants in semiconductor properties, domain walls in ferroelectric properties, and the list goes on. These defects are present in very small concentrations (few parts per million), yet, produce a significant macroscopic effect on the materials behavior through the long-ranged elastic and electrostatic fields they generate. But, the strength and nature of these fields as well as other critical aspects of the defect core are all determined by the electronic structure of the material at the quantum-mechanical length-scale. Hence, there is a wide range of interacting length-scales, from electronic structure to continuum, that need to be resolved to accurately describe defects in materials and their influence on the macroscopic properties of materials. </p>
<p>At this point, I wish to stress the importance of both electronic structure (quantum-mechanical effects) and long-ranged elastic fields by presenting some known results on the energetics of a single vacancy. The vacancy formation energy in aluminum computed from electronic-structure (ab-initio) calculations is about 0.7 eV, of which the contribution of elastic effects (atomic relaxations) is less than 10% of the formation energy, rest is electronic effects (quantum-mechanical effects)! In mechanics, these electronic effects are lumped as the core-energy, which is considered an inconsequential constant, and we deal with only elastic effects. On the other hand, computational materials scientists often work with only core energies as they appear to be the major contribution to the total defect energy. In my opinion, both are equally important and neither can be neglected and I will present some evidence to corroborate this claim. Some recent electronic-structure calculations have been performed to investigate the influence of homogeneous macroscopic strain on the energetics of vacancies (some of which are present in Ho et al. Phys. Chem. Chem. Phys. 2007, 9, 4951), where, in one case atomic relaxations are suppressed and the energetics are solely due to electronic effects and another where atomic relaxations are allowed which contain both electronic effects and elastic interactions with macroscopic fields. In the first case, the vacancy formation energy changed from 0.7 eV at no imposed macroscopic strain to 0.2 eV for 0.15 volumetric strain. This suggests that the defect core energy is very strongly influenced by the macroscopic deformation at the core site, and is not an inconsequential constant! This dependence is quantum-mechanical and there is no obvious way to determine this other than resorting to electronic structure (ab-initio) calculations. On the other hand, in the second case, upon relaxing the atoms and accounting for the elastic effects, the contribution for these elastic effects changed from 10% of the total formation energy at no macroscopic deformation to 50% at 0.15 volumetric strain. These results provide strong evidence that both the core of a defect and the long-ranged elastic fields are equally important in understanding the behavior of defects and these are inherently coupled through the electronic structure of the material. </p>
<p><strong>(ii) The challenges in electronic structure calculations:</strong></p>
<p>The basis of all electronic structure calculations is quantum mechanics which has the mathematical structure of an eigen-value problem. Though the physics behind quantum mechanics has been well-known for almost seven decades, the challenge arises from the computational complexity of the resulting governing equations (Schrodinger’s equation). Unfortunately solutions to the full Schrodinger’s equation are intractable beyond a few electrons (<10) making any meaningful computation of materials properties beyond reach. The direction pursued by the computational physics community in the mid-nineteenth century was beautifully summarized by Paul Dirac: “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of quantum mechanics should be developed, which can lead to an explanation of the main features of the complex atomic systems without too much computation”. These approximate methods are what constitute the electronic structure calculations which are widely used in the present day. The starting point of all electronic structure theories for computing ground-state materials properties is a variational principle, something which is very often seen in mechanics. I have written a brief overview (for readers interested in more details) of various electronic structure calculations and the various approximations involved in arriving at these theories:
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node/3813
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One of the most popular electronic structure theory that is widely used is the density-functional theory (DFT). It has its roots in the seminal work of Kohn, where he rigorously proved that the ground-state properties of a material system are only a function of the electron-density, which has made electronic structure calculations of materials possible. Albeit many theoretical developments in this field and the advent of supercomputing, the computational complexity of these calculations still restricts computational domains to couple of hundred atoms. Thus, historically it was natural to concentrate on periodic properties of materials. DFT has been very successfully in capturing a wide range of bulk properties which include elastic moduli, band-structure, phase transformations, etc. The interest in periodic properties has resulted in the use of a plane-waves as a basis set to compute the variational problem associated with density functional theory. Such a Fourier space formulation has limitations, especially in the context of defects: it requires periodic boundary conditions, thus limiting an investigation to a periodic array of defects. This periodicity restriction in conjunction with the cell-size limitations (200 atoms) arising from the enormous computational cost associated with electronic structure calculations, limits the scope of these studies to very high concentrations of defects that rarely—if ever—are realized in nature. Thus recently, there is an increasing thrust towards using real-space formulations and using finite-element or a wavelet basis, or a finite-difference scheme. The following three articles are good representations of the use of these methods.</p>
<p>1. <a href="http://arxiv.org/abs/cond-mat/9903313">J.E. Pask, B.M. Klein, C.Y. Fong, P.A. Sterne, Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach, Phys. Rev. B. 59 12352 (1999).</a> <br />
2. <a href="http://arxiv.org/abs/cond-mat/9805262">T.A. Arias, Multiresolution analysis of electronic structure: semicardinal and wavelet basis, Rev. Mod. Phys. 71, 267 (1999).</a> <br />
3. <a href="http://www.math.ucsb.edu/~cgarcia/OFDFT/Garcia-Cervera_CommCompPhys_2_p334_2007.pdf">C.J. Garcia-Cevera, An efficient real-space method for orbital-free density functional theory, Comm. Comp. Phys. 2, 334 (2006).<br /></a>
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<br /><strong>(iii) How the mechanics community can have a great impact.</strong></p>
<p>Although the use of real-space formulations seems to provide freedom from periodicity, the computational complexity still restricts calculations to a few hundred atoms. However, an accurate description of defects requires resolution of the electronic structure of the core as well as the long-ranged elastic effects. There have been some multi-scale methods based on embedding schemes that have been proposed which address this problem. One representative article for these methods is the following:</p>
<p>4. <a href="http://arxiv.org/abs/cond-mat/0506006">G. Lu, E. Tadmor, and E.Kaxiras, "From electrons to finite elements: A concurrent multiscale approach for metals" Phys. Rev. B 73, 024108 (2005).<br /></a><br /><br />
The philosophy behind these embedding schemes is to embed a refined electronic structure calculation (inside a small domain) in a coarser atomistic simulation using empirical potentials, which in turn is embedded in a continuum theory. Valuable as these schemes are, they suffer from some notable shortcomings. In some cases, uncontrolled approximations are made such as the assumption of separation of scales, the validity of which can not be asserted. Moreover, these schemes are not seamless and are not solely based on a single electronic structure theory. In particular, they introduce undesirable overlaps between regions of the model governed by heterogeneous and mathematically unrelated theories.</p>
<p>I feel there is tremendous potential for the mechanics community to contribute in the development of multi-scale schemes solely based on electronic structure calculations which are seamless, have controlled approximations, assure the notion of convergence, and provide insights into the behavior of defects. To start the discussion and motivate, let me provide an analogy. The electronic structure of a defect in a material has similar structure to a composite problem with a damage zone. Homogenization techniques and adaptive finite-element basis sets are common solutions to such composite problems! With a little care, I believe it is possible for the mechanics community to make a huge impact in electronic structure calculations of defects. <br />
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</div></div></div>Sun, 14 Sep 2008 21:50:53 +0000Vikram Gavini3837 at https://www.imechanica.orghttps://www.imechanica.org/node/3837#commentshttps://www.imechanica.org/crss/node/3837