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First Principles Predicting Enhanced Ductility of Boride Carbide Through Magnesium Microalloying Bin Tang,1+ Yi He,1+ William A

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First Principles Predicting Enhanced Ductility of Boride Carbide Through Magnesium Microalloying Bin Tang,1+ Yi He,1+ William A First Principles Predicting Enhanced Ductility of Boride Carbide through Magnesium Microalloying Bin Tang,1+ Yi He,1+ William A. Goddard III,2 and Qi An3* 1State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 611731, China 2Materials and Process Simulation Center, California Institute of Technology, Pasadena, California 91125, United States 3Department of Chemical and Materials Engineering, University of Nevada-Reno, Reno, Nevada 89557, United States *Corresponding author-Email: [email protected] +B.T and Y.H. contributed equally to this work. Abstract: The low fracture toughness of strong covalent solids prevents them from wide engineering applications. Microalloying metal elements into covalent solids may lead to a significant improvement on mechanical properties and drastically changes on the chemical bonding. To illustrate these effects we employed density functional theory (DFT) to examine the bonding characteristic and mechanical failure of recent synthesized magnesium boride carbide (Mg3B50C8) that is formed by adding Mg into boron carbide (B4C). We found that Mg3B50C8 has more metallic bonding charterer than B4C, but the atomic structure still satisfies Wade’s rules. The metallic bonding significantly affects the failure mechanisms of Mg3B50C8 compared to B4C. In Mg3B50C8, the B12 icosahedral clusters are rotated accommodated to the extensive shear strain without deconstruction. In addition, the critical failure strength of Mg3B50C8 is slightly higher than that of B4C under indentation stress conditions. Our results suggested that the ductility of Mg3B50C8 is drastically enhanced compared to B4C while the hardness is slightly higher than B4C. Keywords: Mg3B50C8, DFT, chemical bonding, mechanical failure 1 1. Introduction Boron carbide (B4C) and related superstrong ceramics, such as boron suboxide (B6O) and boron subphosphide (B12P2), have been widely used as cutting tools, body armors and in many other industrial applications because of such excellent physical properties as good corrosion resistance, low density, high strength, and high 1-11 temperature stability. However, B4C and related superhard covalent solids are too brittle under high pressure and hypervelocity impact because of the amorphous shear band formation.8,9,11,12. Many approaches have been suggested and examined to enhance the ductility of B4C and related materials by suppressing the amorphous shear band formation.10,13-16. Particularly, previous density functional theory (DFT) studies have suggested that doping Si into B4C can significantly enhance the ductility by suppressing the deconstruction of icosahedral clusters.10,16. This was validated by very recent experiment indicating that adding ~1.5at% Si into B4C exhibits the mitigation of the amorphous shear band formation.14 Another DFT study showed that making co-crystal of B4C and B6O can suppress the failure mechanism of B4C, improving its ductility.13 In addition, the recent study combining transmission electron microscopy experiments and reactive force field (reaxFF) reactive molecular dynamics simulations indicated that decreasing the grain size to nanoscale in B4C facilitates the grain boundaries (GBs) sliding, enhancing the ductility of 15 polycrystalline B4C. Recently, adding metals into B4C has been very attractive because this may drastically change its mechanical, electronic and optical properties. Particularly, the 2 mechanical properties of B4C could be enhanced by dopants that can be divided into active doping and inactive doping according to their capability to reacting with B4C. The active elements mainly include the Si, Ti, Al, etc,17-22 while the inactive elements are Cu, Ag, and Au.23-26 Among active elements, the Si can react with carbon atoms in B4C at high temperature to form stable silicon carbide (SiC). But the free carbon in B4C is limited, leading to some of the silicon atoms directly inserting into the crystal 10,14,20 lattice of B4C. In addition, Ti can react with B and C atoms to form stable 27,28 hardening material TiB2, TiB and TiC. Al can also react with some mounts of B4C to form Al-BC compounds.29-31 The main strengthening mechanism of these approaches is that the densification can be promoted through the liquid-phase sintering, the boosted reaction between the additives and B4C, and the reinforced metal boride phases. Adding metal elements to B4C may significantly affect such mechanical properties as elasticity, plasticity, stiffness, hardness, fracture toughness, etc. Therefore, it has been attracted for experimental and theoretical studies on the mechanical properties of metal doped B4C. Particularly, adding magnesium (Mg) to B4C results in the formation of Mg3B50C8 whose microhardness (Vickers (HV) of 32.0 32 33 GPa) is higher than that of B4C (Vickers of 30.0 GPa) . In addition, adding Li to B4C forming LiB13C2 (r-LiB13C2) whose crystal structure can be derived directly from 34 the boron very rich boron carbide (B13C2) as a simple atomic filling. However, it remains unknown how the doped metal elements affect the intrinsic deformation and failure mechanisms, which could play an important role in determining the strength 3 and ductility of these superhard ceramics. Beside mechanical properties, adding metal elements may significantly affect the chemical bonding and electronic properties of B4C. Doping metal elements in semiconductors would normally cause metal elements to lose their electrons and become positive ions. B4C is a high temperature P-type semiconductor material and the doped metal elements may affect the bonding character and the carriers, resulting in the changes of the electronic properties. Therefore, it is essential to explore how the metallic dopants affect the chemical bonding of B4C. In this Article, we carried out DFT simulations at the Perdew-Burke-Ernzer-hof (PBE) functional level35 to examine the bonding characteristic and shear induced failure mechanism of Mg3B50C8. We found that the chemical bonding in Mg3B50C8 still satisfies the Wade’s rule in which 26 electrons are required to stabilize the B12 36 icosahedron. More interesting, the failure mechanism of Mg3B50C8 is significantly different compared to B4C. The icosahedron in Mg3B50C8 has not been deconstructed under ideal shear deformation up to 0.833 shear strain. While in B4C, icosahedra are disintegrated at 0.348 shear strain, leading to the amorphous shear band formation.9 Under biaxial shear deformation mimicking the indentation stress conditions, icosahedra in Mg3B50C8 are deconstructed at 0.227 shear strain, which arises from the interaction of C-B-C chain and icosahedral clusters under highly compressive stress conditions. 2. Computational Methodology The mechanical properties and chemical bonding properties of Mg3B50C8 were 4 investigated using periodic DFT approach implemented in VASP package.37-39 The Perdew-Burke-Ernzerhof (PBE) functional was employed to describe electronic exchange and correlation interaction. The projector augmented wave (PAW) method was used to generate the pseudopotential that accounts for the core-valence interactions.40 The 2p63s2, 2s22p1, and 2s22p2 electrons were treated as valence electrons for Mg, B, and C, respectively. The tetrahedron method with Blöchl correction was applied to account for the electron partial occupancies.41 For the convergence of DFT simulation, the plane wave cutoff, the energy convergence for self-consistent field (SCF), and force convergence on each atom were set to 500 eV, 10−5 eV and 10−2 eV/Å, respectively. The elastic properties of Mg3B50C8 were investigated by deriving the elastic 42,43 constant, bulk modulus (B) and shear modulus (G). The elastic constant Cij were computed from the stress-strain relationship which was obtained by distorting the equilibrium lattice configuration along various directions. Then, the stiffness constant Sij was derived through the inverse relation between stiffness constant Sij and elastic -1 constant Cij, which is Sij = (Cij) . Finally, the isotropic polycrystalline elastic moduli (B and G) were computed from stiffness constant and elastic constant by calculating the arithmetic mean of Voigt and Reuss bounds.44 To examine the mechanical response and failure mechanism of Mg3B50C8, we first applied ideal shear deformation by imposing the shear strain on a particular slip system while allowing full structural relaxation along other five strain components. Then we applied biaxial shear deformation to mimic the complex stress conditions in 5 Vickers indentation experiments. Beneath an indenter, the shear stress (σxz) and the normal compressive stress (σzz) satisfy the condition of σzz = σxz × tan Φ where Φ is the centerline-to-face angle of the indenter (Φ = 68° for Vickers indenter).45 To determine the most plausible slip system for Mg3B50C8, we selected 5 slip systems including (100)[001], (100)[010], (010)[001], (001)[1̅1̅0] and (001)[1̅00] for the ideal shear deformation. Two slip systems with the lowest ideal shear strength will be considered further for the biaxial shear deformation. The residual stresses after relaxing were less than 0.5 GPa for both ideal shear and biaxial shear deformation. For the shear deformation, we used the supercell containing 61 atoms for (100)[001], (100)[010], and (010)[001] slip systems, and a supercell with 122 atoms for (001)[1̅00] and (001)[1̅1̅0] slip systems in which the unit cell is replicated twice along [1̅00] and [1̅1̅0] directions, respectively. The supercell with
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