Forces Between Atoms

Forces Between Atoms is the eighth lecture within the Properties of Matter section of PH1011. It covers forces between molecules, equilibrium separation and dissociation energy, Young's modulus and elastic energy.

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Atomic Forces and Potentials
In a simplistic model all atoms should repel one another due to their electron clouds - leaving all substances gaseous. However this is not true, and furthermore solids will resist both compression and extension, suggesting that the atoms exist in an equilibrium position. The balance is between a short range repulsive force (which prevents them from merging entirely) and a long range attractive force (which prevents them from drifting apart, and is caused by dipoles). These forces can be expressed graphically as seen in the image.

Additionally, the potential energy of the system can be found through integration of the force - giving a diagram V(r) = -∫F.dr. The distance from 0 to the minima on the x axis is the equilibrium separation; on the y axis it is the input energy required to split the two atoms. For neutral molecules, the potential is given as V(r) = A/r12 - B/r6, A and B being constants affecting the potential's shape.

Stress and Strain
The elasticity of objects is determined by their ability to regain their original shape after deformation. This can be examined though stress (σ) and strain (ε). Stress is the deformng force, given by F/A (Nm-2 or Pa) and strain is the unit deformation given by Δl/l (no units). Graphing the results finds that objects can be stressed to a certain point and regain elasticity, but after the yield point will be permanently deformed or eventually rupture.

Young's Modulus
Young's Modulus is the relation between stress and strain, and is given by E=σ/ε. The scale of the modulus in specific materials gives an indication of their specific atomic bond strengths.


 * Example: Calculate the extension of a 1m beam (E=200x109) with yield strength 250x106 Pa at its yield point.
 * E=stress/strain => strain = 250x106 Pa/200x109
 * = 1.25x10-3.
 * ε = Δl/l => Δl = 1 x 1.25x10-3 = 1.25mm

Over very small deformations, the stored elastic energy is given by ∫Fdl and the stored energy per volume is given by ∫σdε. These can be integrated down to '1/2EA/l(Δl)2 and 1/2Eε2 respectively.

Summary
Molecules are held in equilibrium by a combination of a short-distance repulsive force and a long distance attractive force. The potential energy required to break this bond can be found by taking the negative integral of the force by extension. Stress is a deforming force and strain is the unit deformation, and the two are related through Young's modulus. For very small deformations simle linear relations can be used.