Exploring the phase space of TM-Si-B2 materials by DFT based methods

Abstract

The transition metal diborides are a class of refractory compounds, which appeal through their high temperature stability, coupled with remarkable hardness, making them a big objective in current research on ultra-high temperature ceramics, as thin films and in their bulk form. The oxidation resistance and fracture toughness of such films are however lacking, and several alloying routes have been proposed, in order to enhance these properties. Here, the formation of solid solutions with silicon stands out, leading to ternary diboride compounds, which has been the topic of several experimental studies. However, a theoretical description of such alloys is still rarely researched.With the help of Density Functional Theory, the structural and energetical properties of Si alloyed group IV transition metal diborides, namely Ti-Si-B2, Zr-Si-B2, and Hf-Si-B2 system were inspected. A clear preference of Si to be positioned on the B sublattice, was found for all systems investigated. Through a detailed study on the structural integrity of the alloy phases, a finite solubility of silicon was found for AlB2-type structured compounds, leading to a solubility limit of 24 at. %, 27 at. % and 25 at. % Si in Ti(Si,B)2, Zr(Si,B)2 and Hf(Si,B)2, for alloying on the preferred boron sublattice. A statistical study revealed a scattering in structural properties and formation energies of relaxed cells, that were generated by an SQS approach, while scattering ranges of up to 20 meV/atom were observed.By analyzing simulated X-ray diffraction patterns in combination to Radial Distribution Functions, an in depth characterization of the atomic movements found a clustering of Si atoms to be the main reason for a loss of AlB2-type symmetry in the alloyed compounds.The properties of chemical bonding were inspected via their Crystal Orbital Hamilton Populations, revealing an anti-bonding nature of the Si-B and Si-Si interaction, while the interaction of the transition metals with silicon were thoroughly bonding. Therefore the structural destabilization of AlB2-type compounds was found to originate from the inability of the latter states to weight up anti-bonding interactions. From the simulated elastic properties, a decrease of the Young's, bulk and shear modulus, with respect to increased amount of silicon in the compounds under investigation, was observed. This was accompanied by a clear trend for increasing ductility.An investigation on the impact of boron and metal vacancies in the Si alloyed diborides, revealed a structural instability of AlB2-type compounds, with respect to metal vacancies. A diminishing influence of both metal and boron vacancies on the energies of formation, as well as a developing preference for boron vacancies, was discovered for increasing contents of silicon.