4-13
The force-frequency coefficient, KF (y), is defined by
Maximum KF (AT-cut) = 24.5 x 10-15 m-s/N at y = 0o
Maximum KF (SC-cut) = 14.7 x 10-15 m-s/N at y = 44o
As an example, consider a 5 MHz 3rd overtone, 14 mm diameter resonator. Assuming the presence of diametrical forces only, (1 gram = 9.81 x 10-3 newtons),
              2.9 x 10-8 per gram for an AT-cut resonator
                     1.7 x 10-8 per gram for an SC-cut resonator
       0 at y = 61o for an AT-cut resonator, and at y = 82o for an            SC-cut.
{
F
F
X’
Z’
Y
Mounting Force Induced Frequency Change
   The mounting structure can produce not only in-plane diametric forces but also tangential (torsional) forces, especially in 3 and 4-point mounts, and bending (flexural) forces, e.g., due to clip misalignment and electrode stresses.  These stresses produce frequency shifts, and the changes in these stresses result in frequency aging.


A. Ballato, E. P. EerNisse, and T. Lukaszek, "The Force--Frequency Effect in Doubly Rotated Quartz Resonators," Proc. 31st  Annual Symposium on Frequency Control, pp. 8-16, 1977, AD-A088221.

   E. D. Fletcher and A. J. Douglas, “A Comparison Of The Effects Of Bending Moments On The
   Vibrations Of AT And SC (or TTC) Cuts Of Quartz,” Proc. 33rd  Annual Symposium on
   Frequency Control, pp. 346-350, 1979.