First-principles Study On The Phase Transition,mechanical Properties And Electronic Structures Of TMN_x(TM=Ti,Zr;x=0.5,1,2)

Metal nitrides are widely used in mechanical,chemical and aerospace industry,due to their special physical and chemical properties?high melting point,high hardness,corrosion resistance,superconductivity,photoluminescence,etc.?.They also have potential application in the field of catalysis and energy.Titanium nitrogen compounds and zirconium nitrogen compounds belong to group IVB compounds.They are a kind of ceramic material with special properties,which not only have the excellent characteristics of transition metals,but also have the performance of covalent compounds.That is why they have been given much attention.This paper studies the stability,phase transition,mechanical and electrical properties of six different crystal phases of TiN and ZrN using the first-principles method.The results show that the B1 phase is the most stable structure in both at T=0 K and P=0 GPa.The following results are obtained by calculating the relationship between the relative enthalpy values and the pressures.The phase change pressures of B1 to B2,B1 to P6₃/mmc,B2 to WC,B3 to WZ for the TiN structure are 340 GPa,274 GPa,164 GPa and 122 GPa;the phase transition pressures of B1 to B2,B1 to NiAs,B2 to WC,B3 to WZ for the ZrN structure are 209 GPa,138 GPa,92 GPa and185 GPa,respectively.It is showed that all structures satisfy the mechanical stability conditions according to analyzing mechanical and electrical properties,and they are all metallic.In addition,we also systematically study the mechanical and electrical properties of three different components for Ti-N system and Zr-N system.It is found that the hardness gradually increases,the material changes from ductility to brittleness with the increase of N content in the same substance by calculating the second-order elastic constant,and all structures show obvious anisotropy.By comparing different substances in a specific component,the hardness of the titanium nitrogen compounds is greater than that of the zirconium nitrogen compounds.However,the ratio of bulk elastic modulus?B?to shear modulus?G?shows that the toughness of the zirconium nitrogen compounds is better than that of titanium nitrogen compounds.Electronic property analysis indicate that all structures are metallic and the density of states are mainly distributed in three energy ranges,each of which is contributed by different electrons.The order is N 2s,N 2p and Ti/Zr 3d/4d electrons.We also calculated the electronic properties of TiN₂,the results show that TiN₂ is a Dirac semimetal,and there are two cones?D1,D2?near the Fermi level,which belong to the first kind and second kind Dirac cones separately.The cones are protected by symmetry,and they maintain stability under the influence of SOC.