Question

Lithium adopts a BCC structure at room temperature with a lattice parameter equal to 3.51 Å.  

a).Find the Li-Li pairs corresponds to the 3 shortest distances. Assume the correlation is between a Li at (x,y,z) and the Li at the origin, i.e. (0, 0, 0). For example, the shortest Li-Li pair (also known as Li-Li correlation) is given by the Li at (0,0,0) and the Li at (0.5, 0.5, 0.5). Your answer should only show the cooridinates of the Li with which the Li at the origin is in pair/correlated.

b).On a pair distribution function graph, i.e. g(r) vs. r, what are the first three peak positions (in Å)?

c).Do the same for Cu, which adopts an FCC structure with a lattice parameter of 3.61Å.

Answer 1

Hi dear,

For the reference, a bcc structure is attached below:

Answer (a) The three closest atoms to an atom at A (0,0,0) would be:

Lithium at B which is (a/2, a/2, a/2)

Lithium at D which is (a, 0, 0)

and Lithium at E which is (a, a, 0)

Here a = 3.51 angstrom hence, Li (B) = (1.755, 1.755, 1.755)

Li (D) = (3.51,0,0) and Li (E) = (3.51,3.51,0)

(b) The first three peaks on g(r) vs r plot would be the distance of atom A to the three distinct shortest atoms (of distinct distances : mind) . Hence,

First peak should appear at distance between A and B, which is = (3*1.755²)^1/2 = 3.039 angstrm

Second peak should appear at distance between A and D, which is = a = 3.51 angstrom

Third peak should appear at distance between A and E which is = (2*3.51²)^1/2 = 4.964 angstrom

(c) In case of FCC of Cu, (see the structure attached below: )

The first peak should appear due to atom B of Cu at face center which has coordinates (a/2, a/2, 0) and distance = a*2^1/2 / 2 = a/2^1/2 = 2.55 angstrom

The second peak should appear due to atom C of Cu at corner which has coordinates (a, 0, 0) and distance = a = 3.61 angstrom

The third peak should appear due to atom D of Cu at the digonal vertex which has coordinates (a, a, 0) and distance = a*2^1/2 = 5.10 angstrom

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