# 原子堆積因子

${\displaystyle \mathrm {APF} ={\frac {N_{\mathrm {atoms} }V_{\mathrm {atom} }}{V_{\mathrm {crystal} }}}}$

## 例子

${\displaystyle a={\frac {4r}{\sqrt {3}}}.}$

${\displaystyle \mathrm {APF} ={\frac {N_{\mathrm {atoms} }V_{\mathrm {atom} }}{V_{\mathrm {crystal} }}}}$
${\displaystyle ={\frac {2(4/3)\pi r^{3}}{(4r/{\sqrt {3}})^{3}}}}$
${\displaystyle ={\frac {\pi {\sqrt {3}}}{8}}}$
${\displaystyle \approx 0.68.\,\!}$

${\displaystyle a=2\times r}$
${\displaystyle c=({\sqrt {\frac {2}{3}}})(4r).}$

${\displaystyle \mathrm {APF} ={\frac {N_{\mathrm {atoms} }V_{\mathrm {atom} }}{V_{\mathrm {crystal} }}}}$
${\displaystyle ={\frac {6(4/3)\pi r^{3}}{[(3{\sqrt {3}})/2](a^{2})(c)}}}$
${\displaystyle ={\frac {6(4/3)\pi r^{3}}{[(3{\sqrt {3}})/2](2r)^{2}({\sqrt {\frac {2}{3}}})(4r)}}}$
${\displaystyle ={\frac {6(4/3)\pi r^{3}}{[(3{\sqrt {3}})/2]({\sqrt {\frac {2}{3}}})(16r^{3})}}}$
${\displaystyle ={\frac {\pi }{\sqrt {18}}}}$
${\displaystyle \approx 0.74.\,\!}$

## 参考文献

1. Schaffer, Saxena, Antolovich, Sanders, and Warner. The Science and Design of Engineering Materials Second Edition. New York: WCB/McGraw-Hill. 1999: 81–88.
2. Callister, W. Materials Science and Engineering Sixth Edition. San Francisco: John Wiley and Sons. 2002: 105–114.