Geoscience Reference
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of two factors and impairs significantly the intrinsically very favorable thermal
behavior of this material.
Jumas et al. (1987) gave an excellent comparison of piezoelectric properties of
AlPO 4 to quartz [96] . According to them, the coupling coefficients measured with
AT resonators with filter-type response were about 11%. For quartz, the maximum
values were 7.4%, and this permits one to obtain filters with twice the bandwidth.
The electric constant of berlinite is lower by a factor of 1.2
1.35 than the corre-
sponding constant of quartz, but the density is very similar. The frequency constants
fr are lower than those for the corresponding orientation of quartz by a factor
1.1
1.7; for the AT-cuts the factor is 1.15.
The first-, second-, third-, etc. order FTCs of berlinite are mostly dependent on
the TC of the pertinent elastic constants and the dilation coefficient [111] . As the
latter are similar to those of quartz [68] , most of the better thermal behavior
observed with “dry” berlinite, as compared to quartz, results from smaller values of
the TC of elastic constants. For some other constants, similar things may also be
expected. In Figure 5.27 , the results of Poignant are given, indicating a similar
behavior of the TC of C33 for quartz and berlinite [90] . It is also expected that for
other analogues of quartz with similar
phase transition and reduced elastic
constants, similar or better thermal behavior of resonators could be obtained.
This point is of great importance for frequency generation and filtering applica-
tions of resonators, for which it is fundamental to obtain a frequency response free
of unwanted (unharmonic) modes. For identical cut, resonant frequency, and plat-
ing, it can be shown that smaller dimensions of electrodes are required for berlinite
than for quartz to obtain a frequency response without spurious unharmonic modes
(trapping of only one mode).
Shannon and coworkers (1993) [112,113] have studied in detail the dielectric
properties of berlinite with reference to the presence of (OH) 2 . It has been well
established that water in berlinite is found in both macroscopic and microscopic
inclusions. Because crystals are grown from H 3 PO 4 or H 3 PO 4 /HCl solutions, it is
likely that the inclusions also contain this acidic solution and consequently, high
αβ
Table 5.9 Tentative Comparison with Quartz (Thickness Y Rotated Resonators at the
Same Frequency)
Useful coupling coefficient (AT filter trapped resonators)
Enhanced by 1.4 1.5
Shift of oscillators or bandwidth of filters (AT-cut)
Twice
Angular sensitivity (first-order FTC)
Reduced
Thermal stability (higher order FTC)
Better
Q factor propagation losses
Already sufficient (may be
comparable)
Thickness of plates (AT)
Reduced by 1.15
Electrode dimensions (AT)
Reduced by 1.32 (TT)
(Same plating 2D TT of TS)
Reduced by 1.24 (TS)
Nonlinear properties
To be determined
“Dry” berlinite has similar C, E, EPS constants, first-order TC and much reduced higher order TC.
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