Effects Of External Forces On The Electronic And Elastic Properties Of New Superhard Materials ?-Si₃N₄ And T-C₈B₂N₂

A superhard material is a material with a hardness value exceeding 40 GPa when measured by the Vickers hardness test.Superhard materails are widely used in the fields of cutting tools,super-abrasive materials and wear-resistant coatings due to their high incompressibility,high electronic density and bond covalency.The Vickers hardness test is the most popular way to get the hardness of a material.However,this kind of experimental measurement is always accompanied by complex experimental process,expensive equipments and uncontrollable external factors.Therefore,how to get the hardness value of a material in theory is currently the focus of researchers.The?-Si3N4 structure is used as the theoretical prototype for ?-C3N4,which is believed to have a high bulk modulus,surpassing that of diamond.This gives us a driving force to study the properties of ?-Si3N4 theoretically and experimentally.t-C8B2N2 is composed of three light elements,carbon,boron and nitrogen.It has been proved that t-C8B2N2 is a superhard material with a hardness value higher than that of cubic boron nitride(c-BN).In this dissertation,we explored how the properties of ?-Si3N4 and t-C8B2N2 vary with hydrostatic pressure and biaxial strain by first-principles.We mainly force on their electronic and elastic properties,especially their hardness values The main framework of this paper is as follows:In the first chapter,we introduced some major concepts in this work,including what is superhard material,what are the main superhard materials,and computational materials science.We also showed the research status of the two materials,?-Si3N4 and t-C8B2N2.In Chapter 2,we introduced the origin and basic framework of density functional theory(DFT),as well as two primary approximation methods developed for accurate calculation,local density approximation(LDA)and generalized gradient approximation(GGA).In Chapter 3,we focus on the effects of hydrostatic pressure and biaxial strains on the elastic and electronic properties of ?-Si3N4,Which are calculated by first-principles using the generalized gradient approximation(GGA).Our calculation explicitly demonstrates that the variation trend of lattice constants under pressure is basically consistent with the experimental results,showing the accuracy of our results.?-Si3N4 is an indirect band gap semiconductor with a band gap value of 4.21 eV.The energy band structure of ?-Si3N4 can be modulated by external forces.The energy gap increases monotonically with pressure,however,strain-induced changes in band gap are asymmetric and nonlinear.?-Si3N4 undergoes an indirect to direct band gap transition at ?xx=5%,while ?-Si3N4 is always an indirect band gap semiconductor under pressure and compressive strains.Both bulk modulus and Vickers hardness enhance(decrease)with pressure and compressive(tensile)?xx.The evolution of BH/GH ratio indicates that ?-Si3N4 has a better(worse)ductile behavior under pressure and compressive(tensile)?xx.The calculated hardness of ?-Si3N4 is 30.4 GPa,which fails to exceed the critical value of 40 GPa for superhard materials.The 3D plots of Young' s modulus show huge difference in mechanical properties between[0001]direction and a-b plane and the anisotropy becomes larger by using strain engineering.The sound velocities and Debye temperature of ?-Si3N4 are also discussed for the first time.In Chapter 4,we mainly studied the effects of pressure and biaxial strain on the electronic and elastic properties of t-C8B2N2 using local density approximation(LDA)In order to get the structure of t-C8B2N2,we redefined the crystal structure of a cubic diamond to a tetragonal supercell by a transformation of lattice vector,then replaced some of the C atoms with B and N.t-C8B2N2 is an indirect bandgap semiconductor with a bandgap value of 1.75 eV.The bandgap value increases linearly under hydrostatic pressure.An indirect to direct bandgap transition occurs when 3%<?xx<5%All the elastic constants(except C66)and elastic modulus increase(decrease)with increasing pressure and compressive(tensile)?xx.The BH/GH of t-CgB2N2 is 0.994,suggesting that t-CgB2N2 is brittle in nature.However,the different gradient of BH and GH with pressure and biaxial strains gives t-CgB2N2 a better ductile behavior.A set of 3D plots show a larger directional variability in the Young' s modulus E at different pressure and biaxial strains,which is consist with the results of anisotropy factors.The obtained hardness of t-C8B2N2 is 64.7 GPa by using the microscopic theory and enhances under pressure and compressive ?xx.The results can be verified by the analysis of relative bond strength.A conclusion is given in chapter 5.