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QUESTION 3 The 'holes' or voids in between the close-packed solid spheres in packing arrangements such as hcp or ccp (fcc) are of two different types. (Confirm this by making up a few close packed layers using polystyrene balls). a) Use appropriate sketches to show the difference between a tetrahedral and an octahedral void in a cubic close packed lattice. b) Show that the largest sphere that can fit into an octahedral hole in any close packed lattice has a radius r = (2$^{\frac{1}{2}}$ - 1) = 0.414R, where R is the radius of the identical spheres composing the lattice. (Hint: Make a model of the 'octahedral hole' using six polystyrene spheres). c) Derive a similar formula for a tetrahedral hole. d) Using the formulae above, suggest which atoms or ions could fit into an octahedral or tetrahedral hole in (i) aluminum (ii) gold.

          QUESTION 3
The 'holes' or voids in between the close-packed solid spheres in packing arrangements such as hcp or ccp
(fcc) are of two different types. (Confirm this by making up a few close packed layers using polystyrene balls).
a) Use appropriate sketches to show the difference between a tetrahedral and an octahedral void in a
cubic close packed lattice.
b) Show that the largest sphere that can fit into an octahedral hole in any close packed lattice has a radius
r = (2$^{\frac{1}{2}}$ - 1) = 0.414R, where R is the radius of the identical spheres composing the lattice. (Hint: Make a
model of the 'octahedral hole' using six polystyrene spheres).
c) Derive a similar formula for a tetrahedral hole.
d) Using the formulae above, suggest which atoms or ions could fit into an octahedral or tetrahedral hole
in (i) aluminum (ii) gold.

QUESTION 3
The 'holes' or voids in between the close-packed solid spheres in packing arrangements such as hcp or ccp
(fcc) are of two different types. (Confirm this by making up a few close packed layers using polystyrene balls).
a) Use appropriate sketches to show the difference between a tetrahedral and an octahedral void in a
cubic close packed lattice.
b) Show that the largest sphere that can fit into an octahedral hole in any close packed lattice has a radius
r = (2^(1)/(2) - 1) = 0.414R, where R is the radius of the identical spheres composing the lattice. (Hint: Make a
model of the 'octahedral hole' using six polystyrene spheres).
c) Derive a similar formula for a tetrahedral hole.
d) Using the formulae above, suggest which atoms or ions could fit into an octahedral or tetrahedral hole
in (i) aluminum (ii) gold.

Added by Brittany C.

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