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Lattice energy

by Soilwork
Tags: energy, lattice
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Soilwork
#1
Aug6-06, 10:13 AM
P: 87
I've just come across a problem and the equation within this problem isn't entirely explained in the text. I've searched on the net for this same 'lattice energy' equation, but there have been no results.

Here is the equation:

[tex] E = Aexp^ \frac{-r} { \alpha} - \frac{Me^2} {4 \pi \epsilon_0 r}[/tex]

Here is the question that the equation came from:

The lattice energy, E, per ion of LiF may be written in the form [tex] E = Aexp^ \frac{-r} { \alpha} - \frac{Me^2} {4 \pi \epsilon_0 r}[/tex], where M is the Madelung constant, e is the electronic charge, r is the separation of neighbouring ions and A and [tex]\alpha[/tex] are constants. Calculate E for LiF. (M=1.75, [tex]\alpha[/tex] = 0.02 nm; lattice parameter of LiF = 0.4 nm.

Anyway I was wondering if anyone knew what the first exponential equation was and if they could tell me what the constant A is?? Is it calculated using any of the given values above or something??

EDIT: Well I know that I have to calculate it now, but I have no idea what this constant is called or where it comes from. Thanks anyway guys :)
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Soilwork
#2
Aug7-06, 01:25 PM
P: 87
I have found out what that term is...finally. It is apparently called the Born-Mayer potential.

I get that to find the constant A you need set dE/dr = 0 and solve for A.

This is all fine and I can easily express A analytically, but I cannot obtain a numerical result because I'm not so sure about the separation distance.

We are given the lattice parameter so I thought that I'd need to find the crystal structure of LiF and then express r in terms of the lattice parameter using simple geometry.

I found that LiF is FCC and I can find r in terms of the lattice parameter for this structure...but the catch is I can't do it for an FCC structure where the atoms are not the same size??? I know that I can just look up the radii of the cation and anion and add this to obtain the separation distance, but this defeats the purpose of being given the lattice parameter? I just don't know why we're given the lattice parameter 'cause I can't see how you would use it to calculate r given that Li and F are different sizes.


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