Geoscience Reference
In-Depth Information
by dividing the thickness of the layer grown on the seed, (h
1
2
h
o
)/2, by the run
duration t, and is expressed in mm per day. A much more precise procedure is to
determine R
c
as a function of weight increment provided the surface area does not
change during the run, R
c
5
2.65 g/cm
3
is the density of
quartz. The growth rate increases with the run duration, the increment being rela-
tively faster during the early hours and days
[27]
. The growth rate depends upon
various factors like growth temperature, experimental pressure (% fill), impurities
concentration, presence of defects, seed orientation, solvent/mineralizer, and % of
baffle opening. It has also been known for some time that, qualitatively, acoustic Q
is inversely proportional to the growth rate and directly related to chemical impuri-
ties which will be discussed separately. The internal friction (inverse of mechanical Q)
is dependent on growth rate of synthetic quartz crystals. This was first demonstrated
by Brown
[28]
. Chakraborty (1977)
[29]
has studied the dependence of mechanical Q
on the growth rate of quartz crystals using different mineralizers and concludes that
the inverse relationship (exponential) between mechanical Q and growth rate is inde-
pendent of the nature of the solvent in which the crystals have been grown. Thus, the
mechanical Q is dependent not only on growth rate but also upon various other opera-
tional variables. For example, for growth on surface normal to (0001) (basal plane
growth) or on samples 5
from (0001) (
(P
t
2
P
o
)/2S
t
δ
, where
δ
5
10
6
)
can be grown at rates below 20 mil/day (0.5 mm/day), while even in the presence of
Li
1
, Q's above 10
6
have ordinarily not been obtained at growth rates much above
60 mil/day (1.5 mm/day). Techniques for obtaining high Q at high rates have obvious
economic importance. In particular, rates above 100 mil/day (2.5 mm/day) with
Q's
5
X-cut surface), high Q quartz (Q
1
.
10
6
would provide significant savings in both capital and operating expenses in
commercial quartz growth
[30]
.
.
5.2.2 Seed Effect
The seed plays a predominant role in the quality of the resulting crystal. For higher
frequency applications, a smaller X-axis dimension is needed. Material with growth
along the Z-axis (Z-growth material) is desired for resonators as it has been shown
that this material is about an order of magnitude lower in aluminum concentration
[31]
. The thickness of the seed is usually between 1 and 2 mm. Until recently, it
was necessary to use natural seeds for the preparation of low dislocation crystals.
This is an extremely tedious process since only a small portion of natural crystal is
of sufficient quality for seed use, resulting in a complicated selection process. The
seeds must also be of sufficient size for useful crystal growth. Christie et al. (1983)
[32]
have reported that small seeds can be fastened together to make longer seeds,
but this has not always been successful. Most seeds used today are fabricated from
synthetic quartz crystals. This is a much simpler process since the seeds can be cut
parallel from the original seed. Most crystals grown from synthetic seeds, however,
contain a large number of dislocations of the order of several hundred per square
centimeters. This results in the formation of etch channels in the resonator, which
weaken it mechanically and cause problem when electronic devices are deposited
on the surface
[33]
. The studies of Armington and Larkin (1985)
[34]
have shown
