Biomedical Engineering Reference
In-Depth Information
that of interfacial boundary since the relaxation time τ
m
= 1/ω
m
for the
interfacial boundary is much larger than that for the bulk crystal. Hence
when the bulk (grain) resistance (r
g
) is much lower and the resistance in
the equivalent circuit is dominated by grain-boundary resistance (r
gb
),
the arc of grain may be masked in a limited frequency range. However
when r
gb
becomes very high, the corresponding ν
m
will lie outside the
limited frequency range and will only show a part of grain-boundary arc
in the Z*- plot. h e Z*- plot at 443 K shows a semicircle arc (Figure 14.4)
over the frequency range of 100Hz-1MHz, but without the zero intercept
(inset of Figure 14.4).
h is suggests that except for the large arc with a high r
gb
, a small arc with
a low r
g
exists at higher frequency. h e frequency-dependent conductivity
is given by
σ =
ω tan δ.
(14.1)
0
Here σ' is the real part of the conductivity. h e frequency spectra of
the conductivity for present material are shown in Figure 14.5 at dif er-
ent measuring temperatures. h e conductivity shows a dispersion which
shit s to the higher-frequency side with the increase of temperature. It is
seen from Figure 14.5 that σ decreases with decreasing frequency and
becomes independent of frequency at er a certain value. However this
trend is apparently not followed up at temperature 503 K which is close
to T
c
(533 K). Extrapolation of this part towards lower frequency will give
σ
dc
. h e temperature variation of σ
dc
thus obtained follows the Arrhenius
law given by
-1
303K
323K
343K
363K
383K
403K
423K
443K
463K
483K
503K
-2
-3
-4
-5
-6
3
4
5
6
7
8
log
ω
Figure 14.5
Frequency dependent of σ at various temperatures for present material.
