A Theory of Matter and Electricity by Birkhoff G.D. PDF

By Birkhoff G.D.

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A natural way to make use of the piezoelectric phenomenon is in electro-mechanical resonators and transducers, like microphones and pressure sensors. The constitutive relations for piezoelectric materials are more complicated than for ordinary anisotropic materials because the mechanical stresses and strains themselves are second-order tensors, and hence their relations with electric field and flux density have to be presented by third-order tensors [18]. The relation between the electric field as a cause and the mechanical strain as an effect may also contain nonlinear terms.

A quantitative model for the orientation polarisation can be calculated by assuming the molecules to be randomly oriented. An external electric field tends to orient the permanent dipoles, but on the other hand their thermal motion is a force that tries to preserve the randomness. This situation is formally similar to the magnetic field and response to it in paramagnetic materials. The resulting polarisability 22 Electromagnetic mixing formulas and applications is linear for small field amplitudes and inversely proportional to the temperature, as was shown by Langevin and Debye.

For the high-order terms in these expansions, the relations contain tensors of increasing rank. The magnetic effects are, however, characterised by the fact that time reversal inverts the magnetic field and magnetic moment, which is not the case for electric field and electric moment. This fact can be used if we need to consider which types of solid state crystals can theoretically exhibit such effects, because the symmetry of their structure is reflected in their property tensors [12]. 3 Other polarisation effects Electric polarisation phenomena, in addition to magnetic effects, can also be more complicated than linear isotropic or anisotropic responses.

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A Theory of Matter and Electricity by Birkhoff G.D.


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