(a) Derive the vibrational dispersion relation for a one-dimensional diatomic-spring model with
all springs the same and two different (alternating) masses m_(1) and m_(2). Show your working.
(b) Sketch (or plot in python maybe?) your result.
(c) Provide expressions for the frequencies at wavevectors k=(0,+-(pi )/(a)).
(d) Describe the lattice motion at k=0 and k=(pi )/(a).
(e) Why is k confined to the range +-(pi )/(a) ? Why don't we use larger values of k ?
(f) Show that, with appropriate changes, your model reduces to the monoatomic case.
1. (a) Derive the vibrational dispersion relation for a one-dimensional diatomic-spring model with all springs the same and two different (alternating) masses m1 and m2. Show your working
(b) Sketch (or plot in python maybe?) your result.
(c) Provide expressions for the frequencies at wavevectors k = (0, ) (d) Describe the lattice motion at k = 0 and k =
(e) Why is k confined to the range ? Why don't we use larger values of k?
(f) Show that, with appropriate changes, your model reduces to the monoatomic case.