[orgo814]

Here are a few problems from the book I could use guidance in:

1. What is the chemical formula of the compound a portion of whose unit cell is shown in Figure P12.6?
The diagram is in the textbook but its basically a cube with four yellow corner atoms (there are obviously 4 more corner atoms but they're not significant). Then, there's a cube inside of that with 4 red corner atoms and 4 blue corner atoms. My question is...
Normally, any atoms inside a unit cell, when not on the face of the cell, is considered as one (corner atoms are 1/8 and face 1/2). But, these interior corner atoms are on a cube inside another cube. Would I consider these as a whole or would I have to multiply them by 1/8?

2. How many of the large spheres and how many of the small ones are assignable to the unit cell in the figure?
The figure is a face centered cubic cell. The "small" ones include the corner atoms on the cube and face atoms on the cube. The blue ones are just interior atoms. Would the answer be all of the red ones and none of the blue because the red ones are necessary for a face centered cubic cell?

3(last but not least). When amorphous red phosphorous is heated at high pressure it is transformed into the allotrope black phosphorous, which can exist in one of several forms. One form consists of six membered rings of phosphorous atoms. Why are the six atom rings in black phosphorous puckered, whereas the six atom rings in graphite are planar? (different arrangement of atoms)

So..  some main questions to get out of this. Are interior atoms in a unit cell (that aren't face or corner atoms) not assignable to unit cells? And, with the cube within another cube, do I count the atoms on the corners of the inner cube as corner atoms (multiplying amount of corner atoms as 1/8) or just count them as a whole because theyre inside and not face or corner atoms of the exterior. Thank you, I know these are challenging questions so I appreciate any help I can get!