Nano Materials by A.K. Bandyopadhyay

By A.K. Bandyopadhyay

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The ‘interaction’ of a moving dipole with an electric field produces ‘changes’ in the electronic energy → and that’s how the ‘degeneracy’ is lifted by the spin-orbit coupling or L – S coupling. 83) since (r × p) is the orbital angular momentum (L). S operates on the electron spin wavefunction. , the ‘spin-orbit’ coupling increases very rapidly with nuclear charge (Z) of the atoms or molecules. Since atomic or molecular wavefunctions are spatially ‘extended’, there is some probability of finding a molecule's electrons on the ‘heavy atoms’ of the solvent.

The electron delocalization is responsible for the ‘external’ heavy atom effect. Finally, by evaluating the expectation values of the operators L and S for atoms, it can be seen that a non-vanishing expectation value results only for open shells. For closed shells, the sum of the angular momentum and spins is zero. In solids, we have ‘open shells’ for transition metals and rare earths. 5 for expectation value). Apart from paramagnetism due to the electrons, we must also consider diamagnetism. The latter results from the induction of ‘eddy’ currents by an external magnetic field.

It should be remembered that the ‘discrete nature of solids’ creating separate ‘allowed’ and ‘forbidden’ energy regions manifest in the observation of sharp resonance-like structures in the optical spectra of solids. Now, let us get into the most important theorem in formulating the ‘band structure’ in solids [7, 8]. 2 The Bloch Theorem In the ‘free electron’ theory → what do we assume ? 87) The physical meaning of k is that it represents the momentum of electron divided by D . In order to get a complete solution of the above wave function with time, we multiply ψ(x) by exp(– iωt), where ω= axis.

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