Strain induced band gap deformations of hydrogenated/fluorinated graphene and hexagonal BN sheet have been investigated using first principles density functional calculations. Within harmonic approximation, the deformation is found to be higher for hydrogenated systems than for the fluorinated systems. Interestingly, our calculated band gap deformation for hydrogenated/fluorinated graphene and BN sheets are positive, while those for pristine graphene and BN sheet are found to be negative. This is due to the strong overlap between nearest neighbor {pi} orbitals in the pristine sheets, that is absent in the passivated systems. We also estimate the intrinsic strength of these materials under harmonic uniaxial strain, and find that the in-plane stiffness of fluorinated and hydrogenated graphene are close, but larger in magnitude as compared to those of fluorinated and hydrogenated BN sheet.
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