(a)
Interpretation:
The three dimensional structure of one unit cell of the alkali metal fulleride superconductor
Concept introduction:
Unit cell is defined as the smaller group of atoms having overall crystal symmetry from which one can build the whole lattice in repetition order in 3D form.
(b)
Interpretation:
The number of
Concept introduction:
The shape of the tetrahedral holes is triangular. When 2 tetrahedral holes combine from different layers, an octahedral hole is formed. Thus, due to alignment of tetrahedral holes of first and second order align together, an octahedral hole is formed.
(c)
Interpretation:
The fractional coordinates needs to be determined for all the octahedral and tetrahedral holes in the unit cell.
Concept introduction:
Fractional coordinates are defined as fractions of edge length of the unit cell. For example, at the center of the cell, the fractional coordinate of a hole is
(d)
Interpretation:
The radii of the octahedral and tetrahedral holes needs to be calculated assuming the
Concept introduction:
The face diagonal in the unit cell can be represented as follows:
The length of a face diagonal is
Now, along the body diagonal there are 2 spheres touching the tetrahedral holes of radius r thus,
Here, rt is radius of the tetrahedral hole.
Or,
On rearranging,
Here, R is radius of the sphere.
Similarly, an octahedral hole can be represented as follows:
Here, radius of sphere is R and that of an octahedral hole is
Or,
Or,
Here, R is radius of the sphere.
(e)
Interpretation:
The ion from the given ions that will fit into the octahedral and tetrahedral holes needs to be determined. The ion that will only fit if the framework of
Concept introduction:
The shape of the tetrahedral holes is triangular. When 2 tetrahedral holes combine from different layers, an octahedral hole is formed. Thus, due to alignment of tetrahedral holes of first and second order align together, an octahedral hole is formed.
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