Introduction to Biosensor Technology - Sensor Technology in Neuroscience - page 20

piezoelectric effect. Historically, the Curie brothers are universally credited with
the discovery of piezoelectricity as a result of their pioneering work on crystals
at the Laboratory of Mineralogy at the Sorbonne in Paris. Lord Kelvin 66
subsequently worked on a thermodynamic theory of the effect and also late in
the 19th century another giant of the scientific world, Lord Rayleigh, 67 showed
that surface waves could be instigated in elastic solids. This work was the
genesis of surface-launched waves in piezoelectric materials discussed briefly in
this text. In 1895 Marie Sklodowska married her supervisor Pierre Curie and in
their work on the discovery of radium produced what was termed a 'quartz
electric balance' as stated in her fascinating thesis. 68 Although there have been a
number of claims as to the initiation use of piezoelectric devices as chemical
sensors, it is certain that the work described in this thesis is genuinely the first.
Any description of the piezoelectric effect must begin with the concept of
viscoelasticity displayed by certain crystals and solids. The application of a
stress on a viscoelastic medium can be described by a generalized tensor form of
Hooke's famous equation:

d n 4 t 3 n g | 1

d n 3 .

T ij ¼ c ijkl S kl þ Z ijkl S kl ð 1 : 3 Þ

where T ij and S kl represent the stress and strain tensors, respectively. The
coecients c ijkl and Z ijkl are, respectively, the fourth-rank elastic coecient
tensor and the fourth-rank viscoelastic coecient tensor. In order to derive the
wave equations connected to the piezoelectric phenomenon it is necessary to
couple eqn (1.4) to those of electromagnetism. However, not all solids display
the phenomenon so we digress briefly to outline the crystals that do indeed yield
the effect.
The devices used in biosensing have in common the deformation caused in a
piezoelectric crystal by the application of an electric field. The origin of this
effect lies in the interaction between electric charge and elastic restoring forces
in the crystal. All importantly the phenomenon cannot take place in a crystal
possessing central symmetry. The piezoelectric point groups exhibiting this
property with full Hermann-Maugin notation are presented in Table 1.3. Note
that there is at least one piezoelectric crystal in each crystallographic system. In
order to maximize the coupling of electrical and mechanical affects it is
conventional for practitioners to use particular slices of crystals or cuts. For
example, with respect to the major piezoelectric material, quartz, these are AT-,
ST- and BT-cuts, etc. For interested readers the Institute of Electrical and
Electronics Engineers (IEEE) notation for the various slices is given in ref. 69.
It is now possible to proceed to the coupling of Maxwell's famous laws of
electromagnetism with eqn (1.5). From this combination, following certain
assumptions, the important equations known as the classical piezoelectric
constitutive relationships can be expressed

T ij ¼ c ijkl S kl þ Z ijkl S kl þ e ijk E k ð 1 : 4 Þ

D i ¼ e ik E k þ e ikl S kl ð 1 : 5 Þ