adam1
Mar9-08, 02:57 PM
U(x,y)=Asin(pi*x/Lx) + Bcos(pi*y/Ly) where A,B,Lx,Ly are positive
1 Locate all the stationary points (i.e. minima, maxima and transition states
(TS)) for this potential.
a. What is the periodicity of U(x,y) along the two directions?
b. Derive the TS barriers that an atom diffusing on the surface would
have to surmount during a “jump” between two minima as a function
of A and B.
c. Using information about the shape of U(x,y), propose possible
analytical curves separating the basin of attraction of adjacent minima.
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
1 Locate all the stationary points (i.e. minima, maxima and transition states
(TS)) for this potential.
a. What is the periodicity of U(x,y) along the two directions?
b. Derive the TS barriers that an atom diffusing on the surface would
have to surmount during a “jump” between two minima as a function
of A and B.
c. Using information about the shape of U(x,y), propose possible
analytical curves separating the basin of attraction of adjacent minima.
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution