- #1

- 1,026

- 0

## Homework Statement

Consider two different two-dimensional arrangements, (a) and (b), of four atoms (just four!) defined as follows:

(a) in which the centres of the four atoms form a square of side [tex] a_0 [/tex]

(b) in which the centres of the atoms form an equilateral diamond shape with angles 60° and 120°, and with the length of the side being [tex]b_0[/tex]

If the inter-atomic interaction potential is of the Lennard-Jones form [tex]U(r) = 4\epsilon [(\frac{\sigma}{r})^{12} - (\frac{\sigma}{r})^6][/tex]

and you neglect next nearest neighbours, calculate:

(i) the nearest neighbour distances [tex]a_0[/tex] and [tex]b_0[/tex], respectively

(ii) the cohesive energy per atom of each arrangement

Hence deduce which of the two arrangements would be favoured energetically at very low temperature. Would taking the next nearest neighbours change this conclusion?

## Homework Equations

Lennerd-Jones Equation given

## The Attempt at a Solution

Hi,

I am not quite sure what to do for this question.

For the first part, I am thinking that the atoms are joined together, so a0 would be one atomic diameter, for B0), it would require some trigonometry to get the length

Does this make sense?

Thanks,

TFM