Biomedical Engineering Reference
In-Depth Information
Table 1.3 Piezoelectric point groups.
Crystal system
Hermann-Maugin notation
Cubic
23
43m
d
n
4
t
3
n
g
|
1
Tetragonal
4mm
42m
422
4
4
Orthorhombic
222
2mm
m
Monoclinic
m
2
d
n
3
.
Triclinic
1
6
62m
6
6mm
622
Hexagonal
Rhombohedral
3
3m
Here E
k
is the applied electric field, e
ikl
is the third-rank piezoelectric coecient
tensor, e
ik
is the second-rank dielectric strain coecient tensor and D
i
is the
electric displacement. (The superscript E recognizes that the elastic and
viscoelastic coecients are being held under a constant field E
i
.) The latter
parameter is connected to the concept of induced dipoles and polarization,
which will be very familiar to the physical chemist. The last task in the
development of an overall examination of the piezoelectric effect and device
characteristics is to take account of the fact that it is more often than not the
case that E
i
is allowed to oscillate. This in turn leads to a set of wave equations
(described in more detail in ref. 70) which link together the applied electric field
and actual instigated particle displacement in a time-dependent form.
Knowledge of the parameters incorporated in these equations allows rigorous
solutions, which in turn, leads to the crucial possibility to quantify the response
of various devices in biosensor applications.
Finally we introduce the nature of the movement instigated in the various
acoustic wave devices and the role of the phenomenon of resonance. Movement
of particles in a piezoelectric crystal caused by an oscillating electric-field
induced stress, restored by elastic forces, leads to standing or travelling waves in
the material. The actual displacement (termed 'polarization') is of three
types—linear, elliptical and circular. The various devices to be discussed
subsequently possess waves with shear or compressional character in operation
