First-principles Study Of Mechanical Properties For Transition Metals And Their Carbides And Nitrides

Transition metal carbides and nitrides usually have good properties of large hardness, high melting point and wear resistance. They are used for hard coating and cutting tools widely. In this thesis, a first principles study of the electronic properties and mechanical properties of transition metals, transition metal carbides and nitrides is presented.We can understand the nature of various physical properties of solids by studying their electronic structures. Solids are composed of numerous atoms and each atom has a nucleus and some electrons. If we write the Schrodinger equation of this many-particle system and solve it, we can understand many properties of solid. But there are about 10~29 nuclei and electrons in 1 m3 in the solid. It is not practical to solve the Schrodinger equation of a many-particle system like this directly and we must make some simplifications and approximations. We can separate the electronic motion and the nuclear motion by the adiabatic approximation (Born-Oppenheimer approximation) and simplify the many-electron equation to one-electron equation by Hartree-Fock self-consistent field method. But the correlation interaction between electrons is not included in this method. The more strict description to the simplification from many-electron equation to one-electron equation is the density functional theory (DFT). In the framework of DFT, we can get the detail expressions of the functional of the exchange-correlation interaction by local density approximation (LDA), local spin density approximation (LSDA), generalized gradient approximation (GGA), weighted density approximation (WDA) and so on. Supposing that the solid is an ideal crystal with certain period, the single electron can be considered to move in a periodical potential filed. It is known from Bloch theorem that the solution of one-electron Schrodinger equation in the periodical potential field is the periodical function and the period of the solution is same with the potential. It is difficult to get the accurate expression of the solution of the one-electron Schrodinger equation. The wave function of the electron is usually expanded by one set of basis. Solving the coefficients of the expansion, we can get the solution of the one-electron Schrodinger equation. The usual methods for the expansion are linear combination of atomic orbitals method (LCAO), augmented plane wave method (APW), linear muffin-tin orbitals method (LMTO) and plane wave method (PW).The electronic structure of the solid is mainly decided by the electronic states near the Fermi level. It is difficult in practice to calculate the core state. Pseudopotentials are often used in calculations. In this case, only the few valence electrons are considered and the pseudopotentials of the system can release the strong attraction of the core area to the valence electrons. And the pseudo-system has the same band structure with the real system. There are two kinds of pseudopotentials: empirical pseudopotentials and the first principles pseudopotentials. The empirical pseudopotentials can be obtained by fitting the experimental data. The first principles pseudopotentials have no empirical parameters and they are obtained by solving all-electron Dirac equations. The first principles pseudopotentials are norm-conserving. The wave functions corresponding to the pseudopotentials and the real potentials have the same eigenvalues and the same shape and amplitude outside the atomic core. Moreover, the pseudopotentials vary very slowly in the atomic core. The first principles norm-conserving pseudopotentials can produce the correct charge density distribution and they are suitable for the self-consistent calculations. The first principles pseudopotentials are usually used in the current works of the computational material science.The transition metals concerned in this thesis are in face-centered cubic (fee) and body-centered cubic (bec) structures, and the transition metal carbides and nitrides in rock-salt structure. The plane-wave pseudopotential total-energy scheme is used in the current work. Local-density approximation (LDA) is employed to the density functional theory (DFT). The non-semicore Hartwigsen-Geodecker-Hutter (HGH) relativistic separable dual-space Gaussian pseudopotentials in the context of local-density approximation (LDA) are adopted in the calculations. For the transition metal atom, all d electrons and 4s, 55 or 6s electrons are treated as valence electrons; for the atom of non-metal element, 2s and 2p electrons are treated as valence electrons. The total energy of unit cell, equilibrium lattice constant, bulk modulus, electronic density of states (DOS) and valence electron density distribution are calculated. The total energy of unit cell is obtained by the momentum-space formalism for the total energy of solids, which was derived by J. Ihm, A. Zunger and M. L. Cohen. Fitting E-V relationship with Vinet's equation of state, bulk modulus is obtained. The calculated equilibrium lattice constants and bulk moduli agree with the results of other theoretical works.It is found from the results of the calculations that, for bec transition metals, thepresence of / electrons in the atom core leads larger bulk modulus. For the same transition metal element, the presence of non-metal element in the transition metal carbides and nitrides introduces a different kind of bonding involving hybridized p-d orbitals. The hybridized p-d states mainly contribute to the bonding states and cause that bulk modulus of transition metal carbides or nitrides is larger than the corresponding pure metals. Since the electronegativity of N is stronger than C, more valence electrons are bound around N atom. It is caused that the value of valence electron density distribution at the midpoint of the two nearest metal atoms of the transition nitride is lower than the carbide for the same transition metal element. For the transition metal elements in the same period, the trend of the bulk modulus with the increase of the number of valence electrons for the four sorts of solids concerned in this thesis is same: bulk modulus increases firstly and then decreases. It is related to the occupation of the bonding and anti-bonding states in the solids. When the number of the valence electrons increases, the bonding states whose energy is lower are occupied. The more valence electrons, the more bonding states are occupied. It causes bulk modulus increase. When the bonding states are saturated, the bulk modulus meets the maximum. When the number of valence electrons continues increasing, the anti-bonding states will be occupied. The occupation of the anti-bonding states weakens the strength of the solid. The more anti-bonding states are occupied, the larger this weakening effect would be. It leads bulk modulus decrease. The correlation of bulk modulus of bcc transition metals, fee transition metals, transition metal carbides and nitrides and the value of valence electron density distribution at the midpoint of the two nearest metal atoms is linear with high correlation coefficient. The valence electron density at the midpoint of the two nearest metal atoms in transition metals and their compounds can be used as a parameter to scale bulk modulus.