Magnesium diboride differs from ordinary metallic superconductors in several important ways, including the failure of conventional models to predict accurately its unusually high transition temperature, the effects of isotope substitution on the critical transition temperature, and its anomalous specific heat. A detailed examination of the energy associated with the formation of charge-carrying pairs, referred to as the 'superconducting energy gap', should clarify why MgB(2) is different. Some early experimental studies have indicated that MgB(2) has multiple gaps, but past theoretical studies have not explained from first principles the origin of these gaps and their effects. Here we report an ab initio calculation of the superconducting gaps in MgB(2) and their effects on measurable quantities. An important feature is that the electronic states dominated by orbitals in the boron plane couple strongly to specific phonon modes, making pair formation favourable. This explains the high transition temperature, the anomalous structure in the specific heat, and the existence of multiple gaps in this material. Our analysis suggests comparable or higher transition temperatures may result in layered materials based on B, C and N with partially filled planar orbitals.

We present a study of the superconducting transition in MgB2 using the ab-initio pseudopotential density functional method and the fully anisotropic Eliashberg equation. Our study shows that the anisotropic Eliashberg equation, constructed with ab-initio calculated momentum-dependent electron-phonon interaction and anharmonic phonon frequencies, yields an average electron-phonon coupling constant λ = 0.61, a transition temperature Tc = 39K, and a boron isotope-effect exponent αB = 0.31 with a reasonable assumption of µ * = 0.12. The calculated values for Tc, λ, and αB are in excellent agreement with transport, specific heat, and isotope effect measurements respectively. The individual values of the electron-phonon coupling λ( k, k ′ ) on the various pieces of the Fermi surface however vary from 0.1 to 2.5. The observed Tc is a result of both the raising effect of anisotropy in the electron-phonon couplings and the lowering effect of anharmonicity in the relevant phonon modes.Although MgB 2 is a readily available sp-bonded material, superconductivity in this material with a transition temperature of T c = 39 K was found only very recently [1]. This relatively high T c has motivated many studies, as has the observation that the detailed superconducting properties of MgB 2 show significant deviations from those calculated using the standard BCS model. The isotope effect exponent for boron α B is reduced substantially from the conventional value for sp metals [2,3], and the average electron-phonon coupling strength λ obtained from specific heat measurement [4,5] seems too small to justify the high T c . In addition, specific heat measurements [4,5], tunneling [6] and photoemission [7] spectra, and point-contact spectroscopy [8,9] show low energy excitations suggesting a secondary gap. Theoretical calculations show that the Fermi surface has several pieces and is very anisotropic [10], and that the electron-phonon coupling is dominated by the in-plane B-B stretching modes (E 2g ) [10][11][12] which have a large anharmonicity [13,14]. The electron-phonon interaction varies strongly on the Fermi surface [14,15], and a twoband model suggests a multigap scenario [14]. However, there has not yet been a quantitative, first-principles calculation of T c including the full variation of the electronphonon interaction on the Fermi surface and the anharmonicity of the phonons to help confirm the phononmediating pairing mechanism for superconductivity in MgB 2 .In this letter, we present T c and isotope-effect exponents for MgB 2 obtained by solving the k and ω dependent Eliashberg equation. It is shown that the anisotropy (i.e., the electronic-state dependence) of the electronphonon interaction on the Fermi surface is strong enough to raise T c to 39K even though the interaction is weakened by the anharmonicity of the phonons as compared to the harmonic case. In addition, it is shown that the anharmonicity of the phonons reduces α B to 0.31. These results show that conventional phonon-mediated electron pairing theory can explai...

Recent indentation experiments indicate that wurtzite BN (w-BN) exhibits surprisingly high hardness that rivals that of diamond. Here we unveil a novel two-stage shear deformation mechanism responsible for this unexpected result. We show by first-principles calculations that large normal compressive pressures under indenters can compel w-BN into a stronger structure through a volume-conserving bond-flipping structural phase transformation during indentation which produces significant enhancement in its strength, propelling it above diamond's. We further demonstrate that the same mechanism also works in lonsdaleite (hexagonal diamond) and produces superior indentation strength that is 58% higher than the corresponding value of diamond, setting a new record.

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Recent experiments claimed successful synthesis of cubic boron-carbonitride compounds BC2N with an extreme hardness second only to diamond. In the present Letter, we examine the ideal strength of cubic BC2N using first-principles calculations. Our results reveal that, despite the large elastic parameters, compositional anisotropy and strain dependent bonding character impose limitation on their strength. Consequently, the hardness of the optimal BC2N structure is predicted to be lower than that of cubic BN, the second hardest material known. The measured extreme hardness of BC2N nanocomposites is most likely due to the nanocrystalline size effect and the bonding to the surrounding amorphous carbon matrix. This may prove to be a general rule useful in the quest for new superhard covalent materials.

We report first-principles calculations of ideal tensile and shear strength for the recently synthesized orthorhombic OsB2 that is a primary example of a new class of ultra-hard materials synthesized by combining small, light, and covalent elements with large, electron-rich transition metals. Our calculations show that the shear strength on the (001) plane is highly anisotropic with a low peak stress of 9.1 GPa in the (001)[010] shear direction but a much higher peak stress of 26.9 GPa in the (001)[100] direction. The strong resistance against (001)[100] shear deformation prevents the indenter from making a deep imprint, giving rise to a high Vickers hardness on the (001) plane, despite the weak shear strength in the (001)[010] shear direction. The calculated peak stress of 26.9 GPa in the (001)[100] shear direction agrees well with the 30 GPa Vickers hardness observed experimentally on the (001) plane in OsB2. However, the weak shear strength (9.1 GPa) in the (001)[010] shear direction severely limits its application as abrasives and cutting tools for ferrous metals as well as scratch-resistance coatings. Our results highlight the importance of understanding atomistic deformation modes under various loading conditions in designing new ultra-hard materials.

Recent experiments reported a substantial strengthening of cubic boron nitride by nanotwinning. This discovery raises fundamental questions about new atomistic mechanisms governing incipient plasticity in nanostructured strong covalent solids. Here we reveal an unusual twin-boundary dominated indentation strain-stiffening mechanism that produces a large strength enhancement at nanometer-scale twinning size where a strength reduction is normally expected due to the reverse Hall-Petch effect. First-principles calculations unveil significantly enhanced indentation shear strength in nanotwinned cubic boron nitride by bond rearrangement at the twin boundary under indentation compression and shear strains that produces especially strong stress response. This remarkable strain-stiffening mechanism offers fundamental insights for understanding the stress response of nanotwinned covalent solids under indentation.

We report on a first-principles study of the structural deformation modes in diamond, cubic boron nitride (c-BN), and cubic BC2N. We show that (i) the diamond C-C bonds remain strong up to the breaking point, leading to the large and nearly identical shear and tensile strength, (ii) c-BN exhibits a shear failure mode different from that in diamond and a significant softening in the B-N bonds at large tensile strains long before the bond breaking, and (iii) cubic BC2N displays a large disparity between the shear and tensile strength, contrary to the expectation for the hybrid of diamond and c-BN. We examine the microscopic bond-breaking processes to elucidate the atomistic mechanisms for the deformation modes and the implications for material strength.