4-10
* 10-15 m · s / N
AT-cut quartz
Z’
F
X’
F
30
25
20
15
10
5
0
-5
-10
-15
00
100
200
300
400
500
600
700
800
900
Y
Kf (Y)
Y
Force-Frequency Coefficient
   A force applied to a resonator causes lattice deformation that results in a frequency change.  The above curve shows the force-frequency coefficient, KF, as a function of the direction of the applied force.  An AT-cut quartz plate was squeezed, as shown, by a diametrically applied force. The frequency changes were measured as a function of direction of the force with respect to the x’-axis, and KF was calculated using the expression shown above.  The zero crossing is at  = 61o.  However, the the force-frequency coefficient, and it’s zero crossing, also depend on temperature.  For both the AT-cut and the SC-cut, the zero crossing is at a few degrees smaller  angle when, e.g., measured at 80oC vs. 25oC.

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.