典型晶体结构特征 – IYATT-yx 的博客

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最近更新于 2024-05-06 08:00

 $\begin{array}{c|} \hline 结构特征 & \ & 结构类型 & \ \\ \hline \ & 面心立方(A1/fcc) & 体心立方(A2/bcc) & 密排六方(A3/hcp) \\ \hline 典型金属材料 & Cu、Ag、Au、Al、Ni、\gamma-Fe & Cr、V、W、\alpha-Fe & Be、Mg、Zn、Cd \\ \hline 点阵常数 & a & a & a,c(\frac{c}{a}\approx1.633) \\ \hline 原子半径R & \frac{\sqrt{2}}{4}a & \frac{\sqrt{3}}{4}a & \frac{a}{2}(\frac{1}{2}\sqrt{\frac{a^2}{3}+\frac{c^2}{4}}) \\ \hline 晶胞原子数 & 6\times\frac{1}{2}+8\times\frac{1}{8}=4 & 8\times\frac{1}{8}+1=2 & 12\times\frac{1}{6}+2\times\frac{1}{2}+3=6 \\ \hline 配位数 & 12 & 8 & 6+6 \\ \hline 致密度k & \frac{4\times\frac{4}{3}\pi\times(\frac{\sqrt{2}}{4}a)^3}{a^3}\approx0.74 & \frac{2\times\frac{4}{3}\pi\times(\frac{\sqrt{3}}{4}a)^3}{a^3}\approx0.68 & \frac{6\times\frac{4}{3}\pi\times(\frac{a}{2})^3}{6\times(\frac{1}{2}\times a\times\frac{\sqrt{3}}{2}a)c}\approx0.74 \\ \hline 密排方向 & <110> & <111> & <11\overline20> \\ \hline 密排方向最小长度 & \frac{\sqrt2}{2}a & \frac{\sqrt3}{2}a & a \\ \hline 密排面 & \{111\} & \{110\} & \{0001\} \\ \hline 密排面间距 & \frac{\sqrt3}{3}a & \frac{\sqrt2}{2}a & \frac{1}{2}c \\ \hline 堆垛方向 & <111> & <110> & <0001> \\ \hline 堆垛方式 & ABCABC & ABAB & ABAB \\ \hline \begin{aligned} &四面体间隙 \\ &(数量、大小\frac{r_B}{r_A}、位置) \end{aligned} & \begin{aligned} &8 \\ &0.225R \\ &(\frac{1}{4},\frac{1}{4},\frac{1}{4}) \end{aligned} & \begin{aligned} &12 \\ &0.291R \\ &(\frac{1}{2},\frac{1}{4},0) \end{aligned} & \begin{aligned} &12 \\ &0.225R \\ &(\frac{2}{3},\frac{1}{3},\frac{7}{8})(0,0,\frac{5}{8}) \end{aligned} \\ \hline \begin{aligned} &八面体间隙 \\ &(数量、大小\frac{r_B}{r_A}、位置) \end{aligned} & \begin{aligned} &4 \\ &0.414R \\ &(\frac{1}{2},\frac{1}{2},\frac{1}{2})(\frac{1}{2},0,0) \end{aligned} & \begin{aligned} &6 \\ &0.154R<100>,0.633R<110> \\ &(\frac{1}{2},\frac{1}{2},0)(\frac{1}{2},0,0) \end{aligned} & \begin{aligned} &6 \\ &0.414R \\ &(\frac{2}{3},\frac{1}{3},\frac{3}{4}) \end{aligned} \\ \hline \end{array}$

图1 fcc 晶体结构