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Chapter 5Effect of Strain on the Electronic andMagnetic Properties of Defects in CarbonNanostructuresThis chapter contains a study of the structural, electronic and magnetic properties of severaldefects in carbon nanostructures under an external applied strain. We will address how thepresence of strain can be used to modify the electronic and structural properties of vacanciesand substitutional metals in carbon nanostructures, and how the interplay between magnetismand mechanical perturbations can play an important role in this class of systems. The chapteris divided as follows:Sec. 5.1 considers monovacancies in a graphene sheet. We find that the applied straincan modify the properties of a monovacancy, so that the defect could show a very rich spinand geometric phase diagram. Stretching increases the size of the spin moment in differentphases while compression reduces or even kills the magnetic signal. The transition to nonmagneticsolution is linked to changes in the global structure of graphene that are associatedwith the formation of long range ripples. For compressions slightly greater than 3%, thisrippling leads to the formation of a heavily reconstructed vacancy structure at saddle pointpositions that consists of two twisted hexagons and pentagons. We propose that the control ofdefect-induced magnetism in graphenic structures is feasible by mechanical deformations.Sec. 5.2 shows that substitutional metallic impurities in carbon nanotubes can display adifferent magnetic behaviour from that observed in a flat graphene monolayer. We use Nidopants as an example and we demonstrate that the intrinsic curvature already present in theSWCNT’s can be used to switch on the magnetism of Ni substitutionals. Ni substitutionalsare non-magnetic in flat graphene. A strong dependence of the spin moment on the impuritydistribution, tube metallicity and diameter of the nanotube is also observed. A simple modeltaking account the curvature-induced anisotropy of the hopping between Ni and the first threeC neighbours is presented and qualitatively explains all features observed in the ab initiocalculations.Finally, Sec. 5.3 focus on calculations on the effect of uniaxial strain applied to Ni dopedgraphene. We show that besides the curvature, the application of a uniaxial strain can also beused to induce and control the magnitude of spin moment in a practical way. In a short rangeof applied strain the spin moment changes from zero at equilibrium up to 1.9 µ B at ∼7.0%strain. This strong variation can be traced back to modifications of the local structure of the105
Chapter 5. Effect of Strain on the Electronic and Magnetic Properties of Defects in Carbon106Nanostructuresdefect. These structural changes can be related to those of the unreconstructed carbon vacancyin graphene under strain which presents strong similarities with Ni substitutionals impurities.The chapter ends with the conclusions in Sec. 5.4.5.1 A general spin-strain phase diagram for a monovacancyin grapheneIn this section we study the effect of isotropic strain on the electronic structure of vacanciesin graphene. The interplay between global and local structures reflects directly in the simultaneousobservation of new types of spin solutions, defect reconstruction and corrugation onthe whole system. The 2D-character of graphene combined with its intrinsic rippled geometryprovide the necessary framework for this new kind of effects. We focus on carbon monovacancy,and find that it shows a rich structural and spin phase diagram as a function of strain.5.1.1 Structure versus strainWe start taking a look at Figure 5.1 which illustrates the relaxed geometry of one of our modelsof a free-standing defective graphene layer under a 1.2 % isotropic compression. Whileunder tension the layer remains perfectly flat, and small compression produces the spontaneousrippling of graphene with a characteristic deformation around the vacancy. At zerostrain, the monovacancy tends to undergo a Jahn-Teller–like distortion that lowers its energyby ∼200 meV: atoms of type 1 (see the inset of Fig. 5.1) reconstruct to form a pentagon withthe neighboring atoms, while atom 2 is left with the dangling bond responsible for the spinpolarization. Although we herein consider a non-planar structure under strain, our findingsat low compressions are similar to results previously obtained for flat graphene [42, 121].However, atom 2 in our rippled structure is progressively lifted from the graphene surface byas much as ∼1.0 Å for strains slightly below 3%, just before the occurrence of a strong vacancyreconstruction. The data of Figure 5.1B reveal a particularly striking result. In contrastto 2D vacancy, for which previous authors invariably described a ’pentagon-goggles’ structure,our own calculations show that the vacancy is strongly reconstructed under rippling. Forcompressive strains greater than 3%, an altogether new defect structure is produced consistingof two heavily distorted hexagons and pentagons and resembling the transition states for themovement of a planar monovacancy. We shall now focus on the description of this region oftransition for compression of up to 2.8%.Figure 5.2A shows the maximum amplitude of the rippling h as a function of strain fordefective graphene (shown by the solid symbols). We removed the defects from each rippledstructure by adding carbon atoms to the vacancy sites and relaxing the structure. Weobtained rippled pristine graphene with maximum amplitudes as shown in Figure 5.2A (opensymbols). The amplitudes and the topographic patterns (insets in Figure 5.2A) show littledifference between pristine or defective graphene, particularly for compressive strains greaterthan ∼1%. It seems that even for large supercells, the main determinant to observe ripples isthe applied strain. However, the structural patterns that occurs in defective graphene define apreferential direction and break the up-down symmetry that exits perpendicular to the layer.This preferential direction and the symmetry breaking are explained by the presence of the
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42 Chapter 1. Introductiontions and
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44 Chapter 2. Electronic Structure
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Page 133 and 134: 132 Appendix A. PublicationsAlso se
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Page 141 and 142: 140 Bibliography[14] H. W. Lee and
Page 143 and 144: 142 Bibliography[44] A. J. Stone an
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Page 147 and 148: 146 Bibliography[102] G. Kresse and
Page 149 and 150: 148 Bibliography[128] R. K. Saini,
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