Largest sphere in the space between dense packed spheres

In summary, the conversation discussed finding the radius of the largest sized sphere that can fit in the space between four densely packed spheres of unit radius arranged in a tetrahedron. The question was posed and the respondent reminded the asker to provide their own efforts in solving the problem. The conversation was closed as it was deemed a homework type question.
  • #1
iantresman
67
2
If I consider a tetrahedron of four densely packed spheres of unit radius, what it the radius of the largest sized sphere that can fit in the space in between?
FCC_closed_packing_tetrahedron_(4).jpg
 

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  • #2
Well, since this is PF, the inevitable reply is: what did you do so far to find it ?
Did you alredy draw the tetrahedron in the usual manner (lines) ?
 
  • #3
I didn't know where to start, whether drawing a tetrahedron and 2D circles is relevant.
 
  • #4
If you have a better idea, follow that !
 
  • #5
Thread closed, as it is a homework type question.

A reminder: To qualify as homework merely the problem itself is taken into account, not its real life origin, which we cannot know anything about. So if a problem is of numerical nature or involves an otherwise special example, then it's likely homework. We request our users of the homework section to use and fill out the template, which will automatically be inserted there, esp. part 3, which covers own efforts. It helps us a lot in order to solve the obstacles the user might have.

Thank you.
 

1. What is the largest sphere in the space between dense packed spheres?

The largest sphere in the space between dense packed spheres is known as the "void" or "pore". It is a space that is not occupied by any particles and can vary in size depending on the packing density of the spheres.

2. How is the largest sphere in the space between dense packed spheres determined?

The largest sphere in the space between dense packed spheres is determined by measuring the distance between the centers of two adjacent spheres. This distance is equal to the diameter of the largest sphere that can fit in between them.

3. What is the significance of the largest sphere in the space between dense packed spheres?

The largest sphere in the space between dense packed spheres is important in understanding the packing density and arrangement of particles in a material. It can also affect the material's properties such as permeability and porosity.

4. Can the largest sphere in the space between dense packed spheres vary in different materials?

Yes, the largest sphere in the space between dense packed spheres can vary in different materials due to differences in particle size and shape, as well as the packing density of the particles. It can also be affected by external factors such as pressure and temperature.

5. How does the largest sphere in the space between dense packed spheres relate to the concept of close packing?

The concept of close packing refers to the arrangement of particles in a material where there is minimal space between them. The largest sphere in the space between dense packed spheres is an important factor in determining the efficiency of close packing, as it represents the maximum size of particles that can fit in between the packed spheres.

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