By Andrew N. Cleland
This textual content presents an creation, on the point of a complicated pupil in engineering or physics, to the sphere of nanomechanics and nanomechanical units. It offers a unified dialogue of stable mechanics, with notation in step with smooth conference. A dialogue of electric transducer purposes is integrated, overlaying such subject matters as piezoresistance and piezoelecticity. The textual content features a dialogue of basic and spurious resources of noise, and the way those resources impact either the amplitude and part of a mechanical resonator. a short dialogue of nonlinearity in mechanical structures is given. established functions of those units, in addition to an creation to fabrication options, also are mentioned; a primer on optical in addition to electron beam lithography is given in concise chapters. The textual content concludes with an summary of power destiny applied sciences, together with a dialogue of carbon nanotubes and different molecular assemblies.
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Additional resources for Foundations of Nanomechanics: From Solid-State Theory to Device Applications
Two- and Three-Dimensional Lattices In this chapter we move from the one-dimensional atomic chain to two- and three-dimensional systems. We introduce the concept of the crystal lattice and the corresponding concept of the reciprocallattice; we then work out the formalism for calculating the normal modes in a three-dimensional infinite solid, with abrief discussion of how this can also be applied to finite objects. We conclude our discussion by discussing the quantized excitations of the vibrational normal mo des of the solid, known as phonons.
For a normal mode in the optical band, by contrast, the two atoms move in opposite directions, so U n and V n have opposite signs. 3 o -n/4ro n/4ro q Fig. 19. The eigenfrequency solutions w±(q) for the two mass linear chain. 7. closer to one atom than its neighbor, the optical band motion will couple to the electrie field in an electromagnetic wave, through the induced dipole moment. The upper frequency band is therefore optieally active; this is the origin of the terminology. 5 Quantum Mechanics and Thermodynamics of the Linear Chain We now begin a treatment of the quantum mechanieal properties of our atomic chain.
3 Fixed Boundary Conditions We have treated the problem of the N atom chain using periodic boundary conditions. 3 An N-mer Moleeule: The N Atom Linear Chain 21 ..... o-rtlro Fig. 12. Phase velocity (dotted line) and group velo city (solid line) for the N atom chain. using more "realistie" boundary eonditions; we will therefore briefly treat the problem of fixed boundary eonditions, where we eonneet atoms 1 and N by springs to fixed, rigid supports, shown in Fig. 13. ~ ... ~ n= 1 2 N Fig. 13. Fixed boundary conditions for a chain with N atoms.