金属Cu和Fe晶格结构与热力学性质的第一性原理计算
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摘要
在第一性原理的基础上,利用密度泛函理论及其微扰理论,采用广义梯度近似(GGA)和TM赝势的方法。研究了过渡金属Cu的声子谱和态密度,以及其在298.15K下熵,格林艾森参数,等体热容等热力学函数并与实验值作了对比与分析。通过分析金属铜的能量最优路径与晶格振动之间的关系,提出了固体-液体之间的相变机理,以及直接导出过渡金属的熔化温度Tm静力学方法。与实验结果相比,本文的熔化温度压力曲线比分子动力学的模拟结果更接近实验值。
利用一般梯度近似(GGA)和修改后的TM赝势的第一性原理计算方法。研究了过渡金属铁不同晶相结构下(δ-bcc、γ-fcc、α-bcc、ε-hcp)的电子能带结构和态密度,以及各晶相在298.15K下的热容,熵等热力学函数并与实验值作了相应的对比与分析。(1)计算了多晶相金属Fe的在γ-fcc晶相下的能量变化曲线,并直接用静力学方法导出γ-Fe的熔化温度与压强(0～200GPa)的关系。与金刚石压砧实验的结果相比符合的很好。(2)通过分析金属铁δ-bcc相结构下的能量的最优路径与晶格振动之间的关系,提出了固体-液体之间的相变机理。计算表明了δ-Fe的温度与压强曲线在1～5.2GPa中必须考虑体积功对系统总能的影响。(3)在计算多晶相金属Fe能量变化曲线过程中必须考虑亚壳层电子3s23P6对最外层价电子的影响。
Based on the first-principles, employing the density functional theory and it's perturbation theory, and the methods of generalized gradient approximation (GGA) and TM pseudo-potential. This thesis studies the phonon spectrum and density of states for the transition metal Cu, and its thermodynamic functions such as entropy, Gruneisen parameter and in the condition of298.15K and compares it with that of the experimental data as well. By analyzing the relationship between the energy optimization path and lattice vibration of Cu, this paper presents the phase transition mechanism as per the nature of solid-liquid phase and introduces the static method to derive the melting temperature of transition metals. Compared with that of the experiment, the melting temperature pressure curve in this paper is more favorable than the result of molecular dynamic simulation.
By employing the first-principles of generalized gradient approximation (GGA) and the modified TM pseudo-potential this thesis furthermore analyzes the electronic band structure and density of states for the transition metal Fe in different crystalline structures(8-bcc、γ-fcc、α-bcc、ε-hcp), and its thermodynamic functions such as heat capacity and entropy in the condition of298.15K and compares it with that of the experimental data as well.(1) The energy curves of this polycrystalline phase Fe in the condition of y-fcc crystalline phase is calculated. The relationship between the melting temperature and pressure (0-200GPa) of y-Fe is derived by static method, which fits well compared with that of the diamond anvil cell.(2) By analyzing the relationship between the energy optimization path and lattice vibration of Fe in the condition of8-bcc phase, this paper proposes the phase transition mechanism for the nature of solid-liquid phase. The calculation indicates that the impact of volume to the total energy system should be taken into consideration when the temperature and pressure of δ-Fe is1~5.2GPa.(3) In the calculation of the energy curves of polycrystalline phase Fe, the impact of the inner shell electron on the outermost shell3s23P6should also be taken into consideration.
利用一般梯度近似(GGA)和修改后的TM赝势的第一性原理计算方法。研究了过渡金属铁不同晶相结构下(δ-bcc、γ-fcc、α-bcc、ε-hcp)的电子能带结构和态密度,以及各晶相在298.15K下的热容,熵等热力学函数并与实验值作了相应的对比与分析。(1)计算了多晶相金属Fe的在γ-fcc晶相下的能量变化曲线,并直接用静力学方法导出γ-Fe的熔化温度与压强(0～200GPa)的关系。与金刚石压砧实验的结果相比符合的很好。(2)通过分析金属铁δ-bcc相结构下的能量的最优路径与晶格振动之间的关系,提出了固体-液体之间的相变机理。计算表明了δ-Fe的温度与压强曲线在1～5.2GPa中必须考虑体积功对系统总能的影响。(3)在计算多晶相金属Fe能量变化曲线过程中必须考虑亚壳层电子3s23P6对最外层价电子的影响。
Based on the first-principles, employing the density functional theory and it's perturbation theory, and the methods of generalized gradient approximation (GGA) and TM pseudo-potential. This thesis studies the phonon spectrum and density of states for the transition metal Cu, and its thermodynamic functions such as entropy, Gruneisen parameter and in the condition of298.15K and compares it with that of the experimental data as well. By analyzing the relationship between the energy optimization path and lattice vibration of Cu, this paper presents the phase transition mechanism as per the nature of solid-liquid phase and introduces the static method to derive the melting temperature of transition metals. Compared with that of the experiment, the melting temperature pressure curve in this paper is more favorable than the result of molecular dynamic simulation.
By employing the first-principles of generalized gradient approximation (GGA) and the modified TM pseudo-potential this thesis furthermore analyzes the electronic band structure and density of states for the transition metal Fe in different crystalline structures(8-bcc、γ-fcc、α-bcc、ε-hcp), and its thermodynamic functions such as heat capacity and entropy in the condition of298.15K and compares it with that of the experimental data as well.(1) The energy curves of this polycrystalline phase Fe in the condition of y-fcc crystalline phase is calculated. The relationship between the melting temperature and pressure (0-200GPa) of y-Fe is derived by static method, which fits well compared with that of the diamond anvil cell.(2) By analyzing the relationship between the energy optimization path and lattice vibration of Fe in the condition of8-bcc phase, this paper proposes the phase transition mechanism for the nature of solid-liquid phase. The calculation indicates that the impact of volume to the total energy system should be taken into consideration when the temperature and pressure of δ-Fe is1~5.2GPa.(3) In the calculation of the energy curves of polycrystalline phase Fe, the impact of the inner shell electron on the outermost shell3s23P6should also be taken into consideration.
引文
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[16]H. Eshet, R. Z. Khaliullin, T. D.Kuhne, J. Behler, M. Parrinello 2010 Phys. Rev. B 81 184107
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[34]O. L. Anderson, D. G. Isaaak, V. E. Nelson (2003) The high-pressure melting temperature of hexagonal close-packed iron determined from thermal physicas. Journal of Physics and Chemistry of Solids.64, 2125-2131
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[38]A.B.Belonoshko, R.Ahuja, and B. Johansson (2000) Quasi-Ab Initio Molecular Dynamic Study of Fe Melting, Physical Review Letters, 84,3638-3641
[39]D. Alfe, G. Kresse, M. J. Gillan. (2000) Structure and dynamics of liquid iron under Earth's core conditions, Physical Review B 61,132-142
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