By Joseph Kestin

ISBN-10: 0124053505

ISBN-13: 9780124053502

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**Sample text**

Thus we come to the conclusion that the force of interaction between two elementary, electrically neutral particles must depend on their distance, varying from strong repulsion at short distance to very weak attraction at very large distance. It follows that the repulsive force must decrease to zero for a particular distance, become attractive, pass through a position of maximum attraction, and decay to zero as the distance is increased. Rather than represent the variation of the force F(r) itself with distance r, it is more convenient to express it with the aid of a potential φ(τ) which describes the energy stored by two particles in terms of the distance r between their centers.

10. 5b) in the text. 11. 4), and compute (a) the magnitude of the maximum force, F, of attraction; (b) the separation between the atoms at the point where the attractive force is a maximum. 42 Ä. 12. The Mdfse potential for intermolecular forces is <£(r) = e[e- 2 ( c / r o ) ( r - d ) - 2e- ( c / r <» ( r - d >]. (a) Derive an expression for the force, and show that d=rm. 13. The Stockmeyer potential, where μα and μύ are dipole moments and gißa,θ0,φ„ — φα) = 2 cos θα cos 6h — sin θα sin 6b cos („ — φα), represents the superposition of the Lennard-Jones potential and the interaction of two point dipoles whose orientations with respect to their connecting axis are given by the angles Θ and φ.

It is worth noting that each translational and rotational degree of freedom contributes one quadratic term in the equation for energy, whereas each vibrational degree of freedom contributes two such terms. 8. THE MECHANICAL MODEL FOR A PERFECT CRYSTAL A perfect crystal is pictured as an assembly of vibrating atoms, each attached to a definite point in a regular lattice. Atoms of a given chemical species are considered indistinguishable from each other. For many purposes it is necessary to admit the possibility that atoms (and electrons) perform slow, t Readers not familiar with these expressions may consult, for example, A.