Theory Simulation For Thermodynamic And Solid Solution Properties Of Eare Earth Magnesium Alloys

Mg-based alloys are the lightest structure materials for various application alloys, due to their low density, high specific strength, high specific stiffness, excellent heat conduction and electric conduction, good dimension stability, electromagnetic shielding and easy recovery. However, the strength of Mg alloys is inferior to Al-alloys. The use of Mg-alloys has been limited due to poor high temperature properties. So increasing room and elevated temperature strength of Mg-alloys is a key problem in Mg-alloys materials investigated. The adding of rare earth elements remarkably improves the room and elevated temperature strength of magnesium alloys. In the present thesis, with the analytic embedded atom method (EAM), the thermal, mechanical and solid solution properties of Mg-rare earth alloys are studied at the atomic level. In addition, the brittle and elastic properties are also investigated at the electronic level.The electronic structure, elastic constants and brittle behavior for 10 B2-MgRE (RE=Sc, Y, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er) alloys have been studied by means of the first-principles VASP firstly and systematically. These results are compared with that of ductility alloys YCu. It is proved that the B2-MgRE alloys have brittle behavior from various aspects. For B2-MgRE alloys, the Fermi energy occurs above a peak in the density of states (DOS), the bonding states are full, and the filling of the anti-bonding states is sensitive to deviations in the local structure that affect the Fermi energy. In constant, for ductile YCu the Fermi energy occurs near a minimum in the DOS, and the bonding states are only partially full. Thus, the bonding is relatively insensitive to local distortions. The results indicated that B2-MgRE alloys have brittle behavior due to the indirectional bonding. For all 10 MgRE compounds, shear modulus G_{100}>> G_{110}, indicating that it is easier to shear on {110} plane along [1 10] direction rather than on {100} along [010] direction, showing anisotropy. This phenomenon does not occur for YCu, indicating it is equal to shear on {110} plane along [1 10] direction rather than on {100} along [010] direction, showing isotropy. The Cauchy pressures have positive values for ductile YCu compounds, showing that the bonding is more metallic in character and it has better ductile, which is in good agreement with the experiment, while the Cauchy pressure is negative for MgRE intermetallics, indicating more directional and lower mobility character in the bonding. The B/G ratio of MgRE alloys is less than 1.75, all MgRE compounds are brittle, MgSc the most brittle, and MgHo the least brittle. While for ductile YCu, the B/G ratio is larger than 1.75, showing ductile, which agrees very with the experiment.Molecular dynamics has been performed to study the temperature dependence of lattice constants and cohesive energy for the light rare earth Mg-Pr, Mg-Nd, Mg-Ce alloys. The results are in fairly good agreement with the experimental data. The heat of formations for MgRE, Mg₂RE, Mg₃RE, Mg₄₁RE₅, Mg₁₂RE (RE=Pr, Nd, Ce) compounds agree very with the experimental data, enriching the thermodynamic data of Mg-rare earth alloys. It is predicted that Mg41Nd5 alloy is the most stability phase in the Mg-rich range, and Mg₁₂Nd is metastable phase. The elastic constant for MgRE, Mg₂RE, Mg₃RE, Mg₄₁RE₅, Mg₁₂RE (RE=Pr, Nd, Ce) intermetallic decreases with the temperature increasing, showing thermal softening. The largest contribution comes from the Born term to elastic constants. The fluctuation contribution is negative for all elastic constants. Fluctuation contribution increases as temperature increasing. The melting point for MgPr, Mg₃Pr, MgNd and Mg₃Nd alloys are predicted in terms of two means, a gradual heating and coexisting solid-liquid phase method. The partial pair distribution function presents that there is strong interaction among heterogenic atomic pairs. The vibrational density of states (VDOS) indicated that the VDOS shifts to low frequency with increasing temperature. The partial VDOS at low frequency is originated from rare earth atom, while the VDOS at high frequency is come from Mg, the contribution of rare earth vibrations dominates since it is heavier than Mg. In harmonic approximation, the specific heat obeys T3 law at low temperature, keeps a constant at high temperature. The free energy of alloy decreases as the increasing temperature, while the vibrational entropy of alloy increases, due to disorder state increasing. All those obey classical thermodynamic rules.The dependence of thermodynamic properties and elastic constant on temperature for the binary heavy rare earth Mg-Dy (Ho, Y) alloys are studied. The elastic constants of binary heavy rare earth Mg alloys decrease as increasing temperature. The partial pair distribution function presents also that there is strong interaction among heterogenic atomic pairs, which is similar to that of light rare earth Mg alloys. For comparison, the bulk modulus of heavy rare earth Mg alloys are larger than those of light rare earth Mg alloys, which explains the mechanical properties is improved by the adding heavy rare earth metals from theoretical points of views.The lattice constants, cohesive energy, heat of formation, elastic constants, specific heat, vibrational free energy and vibrational entropy of MgGd, Mg₂Gd and Mg₃Gd alloys are investigated systematically. The results are in good agreement with the experimental data. The temperature dependence of bulk moduli of ordered phases and pure metals Mg and Gd reveals those ordered phases may be strength phases in Mg-Gd system. In fact, there are other strength mechanism in Mg-Gd system, such as solution-hardening and precipitation-hardening, which is different from Mg-Pr system. The partial VDOS presents the partial VDOS at low frequency is originated from rare earth atom, while the VDOS at high frequency is come from Mg atoms, the contribution of rare earth vibrations is dominative since it is heavy than Mg.The solid solution properties for Mg alloys with different rare earth metals are studied. The simulated results reveal that the lattice constants of Mg alloys are larger that that of metal Mg, increase as increasing rare earth composition. For specific rare earth composition, the c/a in Mg-Gd alloy is constant with temperature, restraining the occurrence of non-basal slip and twinning, giving rise to strengthing of Mg-rare earth alloys. The bulk modulus of Mg alloy with different the content of rare earth metals reveal also that the bulk modulus of Mg-rare earth alloys is larger than that of metal Mg, increase as the content of rare earth metals, showing that the adding of rare earth metal can strengthen the strength of Mg alloys, improving the mechanical properties of Mg alloys. For comparison, among the Mg-Gd, Mg-Dy and Mg-Y, the solid solution strength of Mg-Gd is the best, Mg-Y worest. The solid solution properties for ternary Mg-Al-RE (RE=Dy, Gd, Y) alloys are investignated using the molecular dynamics based on EAM. Rear earth and Al will prfer to form RE-Al alloy when Mg matrix contains rare earth and Al elements at the same time. Alloying Gd, Dy, Y and Al gives rise to the variation of the lattice parameters and modulus for Mg alloys. Alloying both Gd and Al strengthen the strength of Mg alloys. The strength of Mg alloys increases with decreasing the content of Al when the composition of Al is higher than that of Gd. This phenomenon may be explained by means of the fact that Al and Gd metals will prefer to form Gd-Al alloy, the additional Al and Mg metals will form Mg₁₇Al₁₂ intermetallics, which is a disadvantage to the strength of Mg-alloys.