Transition Metal Borides, Carbides, And Nitrides: First-principles Calculations

Transition metal compounds have been attracting people's attention due to their variety of physical properties. High hardness materials, such as TiN, TaC, Zr3N4, and Hf3N4, have wide application in industry field. Studying the orign of their exotic properties and synthesis of new materials possessing wonderful physical property are of fundamental significance. Recently, ultra-incompressible materials, PtN₂, IrN₂, and OsN₂, were successfully synthesized and draw much attention due to the increased industrial requirement of materials haveing high hardness, thermodynamically stability, and chemical stability. The most intriguing thing is that ReB₂ can be synthesized at ambient pressure, and more over, has a high hardness of 48 GPa, which means that it could be synthesized at relatively low cost and has potential application. In addition, it is a metal, different from the traditional superhard materials, such as diamond, and cubic BN, which are semiconductor. 5d transition metal has high electron density, and thus, is ultra-incompressible. It is interesting to investigate 5d transition metal borides, carbides, and nitrides. Very recently, Ta₂N₃ was synthesized under high presure and temperture with a hardness of about 30 GPa and was expected to have other excellent physical properties. Thermodynamically ground state WN₂ was predicted to have potential high hardness. A material with high hardness generally tends to resist to large tensile and shear strains, therefore, to investigate elastic properities of a material is helpful to underestand its origin of high hardness. However, the structure of a material ia a precondition to underestand its physical properity. In this paper, first-principles calculations were carried out to investigate structures and elastic properities of several 5d transition metal borides, carbides, and nitrides. Using emperical hardness model, we have investigated their hardness and partly explained the origin of their high hardness.Os_0.5W_0.5B₂ was a newly synthesized ternary compound with ReB₂ structure. Its measured hardness is of about 40.4 GPa with a load of 0.49 N. Similar to ReB₂, it is more incompressible in c direction than in other two directions. Calculations show that Re_0.5W_0.5B₂ and Re_0.5Os_0.5B₂ also have high therotical hardness, high shear modulus, and the largest ultra-incompressibility in c direction. The origin of the c-axis ultraincompressibility correlates not only with the strong covalency of B-B and M-B bonds, but also with the local buckled structure of interconnected covalent bonds. We attribute the high shear modulus and high hardness of three ternary compound to their strong B-B bonds and metal-B bonds.TaC, due to its high hardness, high melt point, chemical stability, thermodynamically stability, and resistence to oxidization and corrosion, has a wide application. Calculations on Rs-TaC, Wc-TaC, ZB-TaC, and NiAs-TaC reveal that Rs-TaC has the lowest energy among the four structures and therefore, is the most stable phase. The calculated hardness of Ta-C bond is 41.1GPa, higher than that of Re-B bond in ReB₂. In RS-TaC, the orbits of dxydyzdxz and dx2-y2dz2 in Ta sublattice are degenerated. The incorporation of C atoms into Ta sublattice made the 5d orbit of Ta atom slipt into eg and t2g orbits, with eg orbit moving to lower energy section and some of the t2g electrons forming local peak at about -5 eV. However, the states near the Fermi level are still dominated by t2g electrons. The 2p electrons of C atoms hybridize with eg electrons of Ta atoms, forming strongσbonds, which is responsible for the lower energy of Rs-TaC compared to other three phases, and the wide psudogap near the Fermi level. Therefore, RS-TaC is the most stable phase among the considered ones. The strongσbonds are also responsible for the high shear modulus and high hardness of RS-TaC. The calculations also show that during 0– 80 GPa, RS-TaC is the most stable phase among the four phases.First-principles calculations can not only explain some experimental phenomenon, but also predict crystal structures. The calculations here suggest that cubic OsC and tetragonal Os₂C₃ is semiconductors and two hexagonal OsC₂ may be superhard materials for their high shear moduli. The strong covalent bonds exist not only between Os and C atoms but also between the nearest Os atoms in tetragonal Os₂C₃ and orthogonal Os2C3. Among the considered various stoichiometric osmium carbides, shear modulus increases with the increased carbon content and a sublinear relationship exists between the Debye temperature and shear modulus. Tetragonal ReN₂ and WN₂ are also predicted to be stable phases and have higher shear modulus than all the synthesized 5d transition metal dinitrides. The computed hardness of tetragonal ReN₂ and WN₂ is higher than that of ReB₂. What surprised us most is that the computed hardness of the weakest bond in tetragonal ReN₂ and WN₂ is 50% higher than that in ReB₂. The calculations show tetragonal ReN₂ may be synthesized experimentally.Orthogonal Ta₂N₃ was synthesized very recently. It may have high hardness, special physical properities, and special applications. However, it is unstable at ambient pressure. Calculations indicate that it is stable at high pressures (10– 25 GPa) and could distort to monoclinic structure at ambient pressure. The minor substitution of nitrogen by oxygen in orthorhombic Ta₂N₃ (Ta₁₆N₂₂O₂) could stabilize the orthogonal lattice, and moreover, is thermodynamically favorable and mechanically stable. The calculations suggest that N-vacant Ta₂N₃ (Ta₈N₁₁) is also mechanically stable. Both Ta₁₆N₂₂O₂ and Ta8N11 have high shear moduli, and thus potential high hardness.