FCC Crystal Problem: Nearest Neighbors, Bond Angles & Packing Fraction

In summary, the conversation discussed calculating the number of nearest neighbours in a FCC structure, determining the angle between the bonds, and calculating the packing fraction. The individual was confused and asked for help finding information on packing fraction. Another individual provided a formula for calculating the packing fraction, but suggested double-checking the math.
  • #1
mikehibbert
37
0

Homework Statement



Write down the number of nearest neighbours in a FCC structure, calculate the angle between the bonds and the packing fraction.

Homework Equations



Literally don't know where to start!

The Attempt at a Solution



Very confused at the moment. Tried to look up packing fraction in my Solid State texbook - but it isn't there?! Is there another name for it? Can someone point me in the right direction please? :)
 
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  • #3
ok - could someone validate my answer please?

i got 4 atoms in one crystal,

the volume of one atom: ( pi * (2^(3/2)) * (a^3) ) / 48

the volume of the crystal is a^3

giving a packing fraction of 0.236?
 
  • #4
Check your math.
 

Related to FCC Crystal Problem: Nearest Neighbors, Bond Angles & Packing Fraction

1. What is an FCC crystal?

An FCC (face-centered cubic) crystal is a type of crystal structure in which the lattice points are arranged in a cubic pattern with additional points located in the centers of each face of the cube. This results in a dense and symmetrical arrangement of atoms or molecules.

2. What are nearest neighbors in an FCC crystal?

In an FCC crystal, the nearest neighbors are the atoms or molecules that are closest to a specific point in the lattice. For each lattice point, there are 12 nearest neighbors located at the corners of the cube and 6 on the faces of the cube.

3. How are bond angles determined in an FCC crystal?

The bond angles in an FCC crystal are determined by the arrangement of nearest neighbors. In an FCC lattice, the angles between atoms or molecules are all equal and measure 90 degrees.

4. What is packing fraction in relation to an FCC crystal?

Packing fraction is a measure of how efficiently the atoms or molecules are packed in a crystal structure. For an FCC crystal, the packing fraction is 0.74, meaning that 74% of the available space is occupied by the atoms or molecules.

5. How does the FCC crystal structure compare to other crystal structures?

The FCC crystal structure is one of the most common and densely packed crystal structures. It is similar to the HCP (hexagonal close-packed) structure, but differs in the arrangement of the additional points on the faces of the cube. The BCC (body-centered cubic) structure is less dense and has fewer nearest neighbors compared to the FCC structure.

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