| 其他摘要 | First-principles method is one of the most important tools in materials modeling, which helps us to understand the properties of materials at the electronic structure level. In the present work, first-principles methods are adopted to investigate pressure induced omega-β phase transformation of IVB metals and the alloying effect of rare earth elements on the properties of Ti alloys.
First, we studied the elastic stabilities of beta-Ti, Zr and Hf and their electronic structures with respect to external pressures. The calculated elastic moduli C′ of beta-Ti, Zr, and Hf at ambient conditions are all negative, indicating that they are elastically unstable according to Born elastic stability criterion. The applying of external pressure hardens, and the critical pressure that ensure the beta pahse satisfing the elastic stability criterion (C′=0) are about 45GPa for Ti, 10.5GPa for Zr, and 7.5 GPa for Hf The moduli C44 of beta-Ti, Zr and Hf are always positive. It is found that C44 of beta-Ti softens under intermediate pressure whereas those of beta-Zr and Hf do not, which may explain the fact that pressure induced direct omega-β phase transition is observed in Zr and Hf but not in Ti. We also calculated the bonding charge density on the (110) plane and density of states (DOS) at various pressures. At low pressures, the bonding charge density of the beta phase of the three metals mainly concentrates at the octahedral interstice whereas charge depletion occurs in between two nearest-neighboring atoms along [111] direction, i.e., there is no bonding between nearest-neighboring atoms, which is responsible for the elastic instability of beta phase. The charge redistribution from the octahedral interstice to the region in between two nearest-neighboring atoms is found with increasing pressure. The pressure induced charge redistribution is more evident for beta-Zr, then for Hf, and the least for Ti, in accordance with the sequence of the critical pressures needed to stabilize them elastically. The DOSs of beta-Ti, Zr and Hf split with increasing pressure, and the Fermi level locates at the valley of the DOS, indicating the stronger binding between the atoms and beta phase more stable at high pressure.
In order to understand the thermal aspect of the omega-beta transition in Ti, Zr, and Hf, we calculated the energy barriers of omega-beta transition at various pressure. In order to do so, the pressure dependent c/a of the omega phase was carefully determined. It is noted that the c/a ratios of omega phases of Ti, Zr and Hf start to decrease drastically with increasing pressure beyond the critical pressure at which the omega-beta transition occurs. Therefore, the drastic decrease of the c/a ratio can be considered as an indicator of the omega-beta transition. At low pressure, the omega phase is more stable than the beta phase, wherat at high pressure the beta phase is more stable than the omega phase. In both cases, there are no enthalpy barrier for the omega-beta transition. However, around the theoretical critical pressure (96 GPa for Ti, 24 GPa for Zr, and 67 GPa for Hf, at which the beta and omega phases are equally stable) for the omega-beta phase transition, we get enthalpy barriers of 22.5 meV for Ti, 19.2 meV for Zr, and 24.5meV for Hf.
In order to understand the alloying effect of the RE elements on the properties of Ti alloys, we calculated the interaction energies between RE atoms and between RE atom and vacancy as well as interstitial impurities such as C, N, and O. The results show that the RE-vacancy and RE-RE interactions are attractive due to the weaker RE-Ti bond than the host Ti-Ti bond. All of the RE atoms investigated in this paper are repulsive to C and N, but attractive to H. RE-O interactions are repulsive for the light RE atoms, though the interactions are very weak for the heavy RE atoms. The mechanism underlying the interactions and their possible influence on the properties of Ti alloys are discussed. |
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