#### 期刊菜单

Fe-X (X = Si, Cr, Mn, Ni)二元合金结构和弹性性质的第一性原理计算
First-Principles Study on Structure and Elastic Properties of Fe-X (X = Si, Cr, Mn, Ni) Binary Alloy
DOI: 10.12677/MS.2017.76080, PDF, HTML, XML, 下载: 2,210  浏览: 5,078

Abstract: The effects of alloying element such as Si, Cr, Mn and Ni on the structure and elastic properties of face centered cubic Fe were investigated by the method of the first-principles based on density functional theory. The results showed that the alloying elements (Si, Cr, Mn, Ni) were all increased the lattice constant of face centered cubic Fe, and thus increased the cell volume. After adding the alloying elements, the all binary alloy systems meet the mechanical stability conditions. The elastic constants of C11, C12, and C44 were increased almost all, the elastic moduli were increased also and the Poisson’s ratio was changed little as a whole.

1. 引言

2. 计算方法和模型

Voigt模型中，体模量Bv和剪切模量Gv与弹性常数的关系为：

${B}_{V}=\frac{1}{3}\left({C}_{11}+2{C}_{12}\right)$ (1)

${G}_{V}=\frac{1}{15}\left({C}_{11}-{C}_{12}+3{C}_{44}\right)$ (2)

${B}_{R}=\frac{1}{3{S}_{11}+6{S}_{12}}$ (3)

${G}_{R}=15{\left[4\left({S}_{11}-{S}_{12}\right)+3{S}_{44}\right]}^{-1}$ (4)

${B}_{V}={B}_{R}=\frac{1}{3}\left({C}_{11}+2{C}_{12}\right)$ (5)

${G}_{R}=\frac{15\left({C}_{11}-{C}_{12}\right){C}_{44}}{4{C}_{44}+3\left({C}_{11}-{C}_{12}\right)}$ (6)

Hill模型的体模量B和剪切模量G可以通过将Voigt和Reuss模型的计算结果进行平均值简化得到，即：

$B=\frac{1}{2}\left({B}_{V}+{B}_{R}\right)$ (7)

$G=\frac{1}{2}\left({G}_{V}+{G}_{R}\right)$ (8)

$E=\frac{9BG}{3B+G}$ (9)

$v=\frac{3B-2G}{2\left(3B+G\right)}$ (10)

3. 结果与讨论

3.1. 晶体结构

3.2. 弹性性质

(a) (b)

Figure 1. The unit cell structure of Fe32(a) and Fe31Si(b)

Table 1. The lattice parameter of Fe and Fe-X(X = Si, Cr, Mn, Ni) binary alloy

Table 2. The calculated elastic constants of Fe and Fe-X(X = Si, Cr, M, Ni) binary alloy

Table 3. Calculated bulk, shear and Young’s modulus and Poisson coefficient for Fe and Fe-X(X = Si, Cr, Mn, Ni) binary alloy

4. 结论

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