最近更新于 2023-12-10 10:08

\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}

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图1 fcc 晶体结构


图2 bcc 晶体结构

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图3 hcp 晶体结构

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图4 fcc 八面体间隙


图5 fcc 四面体间隙

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图6 bcc 八面体间隙

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图7 bcc 四面体间隙

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图8 hcp 八面体和四面体间隙

作者 IYATT-yx