Unformatted text preview: particle in a solid or liquid oscillates in three dimensions about the equilibrium position. The equilibrium separation is: a) 1σ, When there are many ,articles, the phasσs,, l, g) od) 3particles depends on their total translational b)1.12σp c)1.2 e ( f those σ 4) The force vanishes a) at one value of r, b) at two values of r Near equilibrium separation, the motion looks like a regular mass-spring T or F
M. Chertok, Physics 7A 6 Near Equilibrium M. Chertok, Physics 7A 7 Particle Model, (ii)
For system of many particles, phase (s,l,g) depends on Etot
High energy: particles unbound -- gas Average separation is much greater than r0 Low energy: particles bound -- solid or liquid Average separation ~ r0 M. Chertok, Physics 7A 8 Bound or free?
e en ship
Potential Energy (in units of well depth, ") Pair-wise or Atom-Atom Potential
(as modeled with the Lennard-Jones Potential)
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Pair-wise Potential (as modeled with the Lennard-Jones Potential) Etot = 0.4ε hat . tion um Etot = -0.25ε Etot = -0.6ε rticle -1.2 distance between centers of atoms, r (in units of particle diameter, ! )
M. Chertok, Physics 7A 9 Particle Model, (iii)
Graph is 1-D. However, every particle interacts with all its nearby neighbors.
Result is 3-D PE for a given particle. Its minimum deﬁnes equilibrium position of particle in solid or liquid. “single parti...
View Full Document