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Chapter 2 / Atomic Structure and Interatomic Bonding

Chapter 2 / Atomic Structure and Interatomic Bonding

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Force F<br />

Attraction<br />

Repulsion<br />

Attraction Repulsion<br />

Potential energy E<br />

+<br />

0<br />

+<br />

0<br />

E 0<br />

r 0<br />

2.5 <strong>Bonding</strong> Forces <strong>and</strong> Energies ● 19<br />

which is also a function of the interatomic separation, as also plotted in Figure<br />

2.8a. When FA <strong>and</strong> FR balance, or become equal, there is no net force; that is,<br />

FA FR 0 (2.3)<br />

Then a state of equilibrium exists. The centers of the two atoms will remain separated<br />

by the equilibrium spacing r0, as indicated in Figure 2.8a. For many atoms, r0 is<br />

approximately 0.3 nm (3 A˚ ). Once in this position, the two atoms will counteract<br />

any attempt to separate them by an attractive force, or to push them together by<br />

a repulsive action.<br />

Sometimes it is more convenient to work with the potential energies between<br />

two atoms instead of forces. Mathematically, energy (E) <strong>and</strong> force (F) are related as<br />

Or, for atomic systems,<br />

Attractive force F A<br />

Repulsive force F R<br />

Net force F N<br />

(a)<br />

Repulsive energy E R<br />

Net energy E N<br />

Attractive energy E A<br />

(b)<br />

<strong>Interatomic</strong> separation r<br />

<strong>Interatomic</strong> separation r<br />

EN r<br />

<br />

r<br />

E Fdr (2.4)<br />

<br />

F N dr (2.5)<br />

FA dr r<br />

FR dr (2.6)<br />

EA ER (2.7)<br />

in which EN, EA, <strong>and</strong> ER are respectively the net, attractive, <strong>and</strong> repulsive energies<br />

for two isolated <strong>and</strong> adjacent atoms.<br />

<br />

FIGURE 2.8 (a) The<br />

dependence of repulsive,<br />

attractive, <strong>and</strong> net forces on<br />

interatomic separation for<br />

two isolated atoms. (b) The<br />

dependence of repulsive,<br />

attractive, <strong>and</strong> net potential<br />

energies on interatomic<br />

separation for two isolated<br />

atoms.

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