Objective: The following experiments may be performed with the help of this setup:
Lattice Dynamics Kit
Study of the dispersion relation for the mono-atomic lattice-Comparison with theory.
Determination of the cut-off frequency of the mono-atomic lattice.
Study of the dispersion relation for the di-atomic lattice – ‘acoustical mode’ and ‘optical mode’ energy gap. Comparison with theory. Theory: Lattice dynamics is an essential component of any postgraduate course in Physics, Engineering Physics, Electronic Engineering and Material Science. In particular it is essential for understanding the interaction of electromagnetic waves and crystalline solids. In present setup, mono-atomic and diatomic lattices are stimulated using the transmission line having ten identical sections of LC resonant circuit. The dispersion relation for electrical analogue of the mono-atomic lattice is
and dispersion relation for electrical analogue of diatomic lattice is
With the help of the simple and user friendly setup the phase difference between the input and output wave is measured at different frequencies and tabulated as given below: Then a graph of the experimental value and the theoretical value is plotted and compared. Lattice Dynamics Kit consists of the following parts:
It consists of an Audio oscillator with amplitude control and facility to vary the frequency from 0.9 KHz to 90 KHz. It has built in powersupply and output stage to match the impedance of simulated lattice. Another part of Lattice Dynamic Kit consists of transmission line, which simulates one- dimensional mono-atomic and di-atomic lattices. The only additional equipment needed is a General purpose C.R.O