2. Next nearest neighbor interactions. Consider a monatomic lattice. The potential energy of the crystal system, modeled as a linear chain of atoms is UpE. = 1/(2a)E„1; where n runs over all the atoms in the chain and r, is the net displacement of the n'th atom. (a) Show that if the atom is interacting with p atoms on either side instead of one (as we discussed in class), the the force acting on the n'th atom is given by, F, = -Ea,(um - Un+p); where a, represents the force constant between atoms numbered n and n +p.
2. Next nearest neighbor interactions. Consider a monatomic lattice. The potential energy of the crystal system, modeled as a linear chain of atoms is UpE. = 1/(2a)E„1; where n runs over all the atoms in the chain and r, is the net displacement of the n'th atom. (a) Show that if the atom is interacting with p atoms on either side instead of one (as we discussed in class), the the force acting on the n'th atom is given by, F, = -Ea,(um - Un+p); where a, represents the force constant between atoms numbered n and n +p.
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Transcribed Image Text:2. Next nearest neighbor interactions. Consider a monatomic lattice. The potential
energy of the crystal system, modeled as a linear chain of atoms is UpE. = 1/(2 a)E„r;
where n runs over all the atoms in the chain and r, is the net displacement of the
n'th atom.
(a) Show that if the atom is interacting with p atoms on either side instead of one
(as we discussed in class), the the force acting on the n'th atom is given by,
F, = -Ea,(u, – Un+p);
where a, represents the force constant between atoms numbered n and n + p.
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