點計metallic crystals packing ef

Packing efficiency =volume of spheres in unit cell / volume of unit cell
= no. of atom in unit cell X(volume of sphere) / (edge length)^3

For simple cubic packing :
Edge length = 2r
no of atom in unit cell = 1
Packing efficiency = (1X(4/3πr^3)/(2r)^3) X 100%
= 52.4%
For body centered cubic :
Edge length = 4r/
圖片參考：http://upload.wikimedia.org/math/1/6/0/160a5b4ac79375bd4c5e13c0f3a95f73.png
3
no of atom in unit cell = 1
Packing efficiency = (2X(4/3πr^3)/(4r/
圖片參考：http://upload.wikimedia.org/math/1/6/0/160a5b4ac79375bd4c5e13c0f3a95f73.png
3)^3) X 100%
= 68%

For face center cubic :
Edge length =
圖片參考：http://upload.wikimedia.org/math/1/6/0/160a5b4ac79375bd4c5e13c0f3a95f73.png
8 X r

no of atom in unit cell = 4
Packing efficiency = (4X(4/3πr^3)/(
圖片參考：http://upload.wikimedia.org/math/1/6/0/160a5b4ac79375bd4c5e13c0f3a95f73.png
8 X r)^3) X 100%
=74%

這只是大約　沒有一定
如果要計算，你只要在晶胞中找　原子／離子的半徑
計算它們所佔的體積，再利用原子數目　丫佛加得羅常數　密度　找晶胞體積
它們所佔的體積／晶胞體積　就是packing efficiency