First principles calculation of single‐crystal elastic constants of titanium tetraboride (Ti3B4) and experimental validation

Abstract The nine independent single‐crystal elastic constants of a new ceramic, titanium tetraboride (Ti 3 B 4 ), have been determined by first principles calculations, and the data were validated experimentally through nanoindentation testing. The independent elastic constants, which are specific to the crystal structure, are important for the fundamental characterization of mechanical and physical properties of the group of hard compounds such as the transition metal borides. The elastic constants of Ti 3 B 4 were determined from crystal strain energies that were calculated by applying specific deformations within WIEN 2k platform utilizing full‐potential linear augmented plane wave ( FLAPW ) and generalized gradient approximation ( GGA ). The WIEN 2K package is based on all‐electron calculations, and hence is considered as the most accurate for first principles calculations. It has been found that the polycrystalline elastic moduli, determined as the Voigt‐Reuss‐Hill averages of the independent elastic constants, are quite impressive ( E = 492 GP a, G = 217 GP a, B = 224 GP a, ν = 0.13) placing the tetraboride very close to the well‐known titanium diboride ( E = 570 GP a, G = 254 GP a, B = 249 GP a, ν = 0.12). The strong B‐B chains were found to be largely responsible for the high values of elastic stiffness constants, in particular the c 33 describing stiffness in the [001] direction. The electron charge densities were found to be accumulated to a higher degree along the B‐B bonds, resulting in strengthening of the B‐B chains in the lattice. The promising data motivated the first experimental synthesis of Ti 3 B 4 in a bulk form, which is also described in this work. To validate the elastic constants determined from first principles, elastic moduli were determined by nanoindentations in multiple grains of a polycrystalline Ti 3 B 4 , synthesized by electric field‐activated reaction sintering. The range of elastic moduli determined from nanoindentation was found to agree well with the range determined by computation. The calculations and experiments demonstrate that Ti 3 B 4 has the potential to be one of the leading structural ceramics.