- #1
Jchem
- 28
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Ok I am trying to show the packing efficiency for 3 different types of packing.
1) Hexagonal closest packing (efficiency = 74%)
2) Cubic closest packing - (efficiency = 74%)
3) Body-centered - (efficiency = 68%)
I know the efficiency values because they are in my textbook and all over the internet. I need to come up with these numbers myself.
efficiency = Volume of the spheres/Volume of a box around the spheres.
the spheres in my model have a radius of 3cm, so volume of the spheres is easy... 4/3(pie)r^3 x (number of spheres)
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I'm trying to figure out a way to find the volume of a box around Hexagonal closest packing and cubic closest packing.
_____________________________________________________________
Hexagonal closest packing: 13 balls in total in 3 layers. (see pictures below)
bottom layer: 3 spheres
middle layer: 7 spheres
top layer 3 spheres
_____________________________________________________________
Cubic closest packing : 13 balls in total in 3 layers
bottom layer: 4 balls
middle layer: 5 balls
top layer: 4 balls
______________________________________________________________
I know that the volume of both must be the same since they each have 13 balls and each have the same packing efficiency.
How do I find the volume of a box around these spheres?
:
I've been trying to figure this out for hours so any help at all is appreciated...and sorry for the length of the question
1) Hexagonal closest packing (efficiency = 74%)
2) Cubic closest packing - (efficiency = 74%)
3) Body-centered - (efficiency = 68%)
I know the efficiency values because they are in my textbook and all over the internet. I need to come up with these numbers myself.
efficiency = Volume of the spheres/Volume of a box around the spheres.
the spheres in my model have a radius of 3cm, so volume of the spheres is easy... 4/3(pie)r^3 x (number of spheres)
------------------------------------------------------------------------
I'm trying to figure out a way to find the volume of a box around Hexagonal closest packing and cubic closest packing.
_____________________________________________________________
Hexagonal closest packing: 13 balls in total in 3 layers. (see pictures below)
bottom layer: 3 spheres
middle layer: 7 spheres
top layer 3 spheres
_____________________________________________________________
Cubic closest packing : 13 balls in total in 3 layers
bottom layer: 4 balls
middle layer: 5 balls
top layer: 4 balls
______________________________________________________________
I know that the volume of both must be the same since they each have 13 balls and each have the same packing efficiency.
How do I find the volume of a box around these spheres?
:
I've been trying to figure this out for hours so any help at all is appreciated...and sorry for the length of the question