GaAs has a fe Bravais lattice with two atoms in the basis. The lattice constant
ID: 698626 • Letter: G
Question
GaAs has a fe Bravais lattice with two atoms in the basis. The lattice constant is a 5.65 A M:P-43 a-5.434i b-5.434A -5.434 -90.000 90.000. Y-90.000 Some data for the phonon frequencies of the acoustic and optical phonons are TO (r) 50.4101 (x) 45.4101 uLO(P) 53.7 x 1012 uTA (L) 11.7 x 1012 TA(X) 14.810L OLA (X) 42.7×1012 uro (L) 49.3.1012 uro (X) 47.5× 1012 (L) 44.9. 10-2 ACL) 39.3-10 UTO(L) 49.3 10 (a) Sketch the phonon dispersion relation for GaAs along X-T-L (b) How could the phonon dispersion relation be measured experimentally? (c) How could you determine the speed of sound from the dispersion relation? Sketch the phonon density of states that corresponds to the dispersion curve that you have drawn.Explanation / Answer
(b)- When we using direct observation of the dispersion relation for lattice vibrations. It is not practicable for the reason that sound waves of properly high frequencies are not available. and the methods of observing the dispersion relation of lattice vibrations, a specific example
(1) Neutron Inelastic Scattering
(2) Electron Energy Loss Spectroscopy (EELS)
(3) Inelastic Atom Scattering
Neutron Inelastic Scattering- The neutron energy which is in the form of forged vibrations in the same range and the wavelength is the same as the crystal trap, it can be uncontrolled by bulk phones. By analyzing the energy and direction of the dispersed neutron, the phonon dispersion relationship is obtained. Neutron is suited for large scale studies due to its very small cross section so that they can penetrate deep into the crystal bulk.
Electron Energy Loss Spectroscopy (EELS)- ELS and the atomic unbalanced scarcity are currently employed to study the spread of the phones of the surface. It covers the field of energy transfer to about 30-50 MW of nuclear measurement, Which with a resolution of 0.5-1am, while increasing the EELS measurement to 500 MW, although it has a very low resolution of 7meV. Due to the high kinetic energy of electrons (~ 200EV) and their small cross section ~ 5A2, depth of entry into EELS experiments, there are about 2-3 surface layers and the accuracy of the experiment suffers from many scattering events.
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