SPECIFYING QUARTZ CRYSTAL ORIENTATION 229 



crystals we mark the negative end of the electric axis as positive we can 

 treat it exactly as though it were a right-handed crystal. 



The first plates used were x and y piezoids (squeezing solids). For 

 these simply described cuts one does not need to know the quartz "handed- 

 ness." These crystals had large frequency temperature coefficients. 

 But when Lack, Willard and Fair brought out the low temperature coeffi- 

 cient AT plate, its more complicated orientation required the right-left 

 differentiation. The AT, the subsequent BT, CT, DT, etc., were thought 

 of as y-cuts rotated through various angles about the edge that coincided 

 with X. For example, the AT was a +35|° cut, or was a y plate rotated 

 35j° about .v; the BT was a —49° cut. Their orientations are illustrated 

 in Fig. 2.6. 



As more complicated orientations were designed to give even better 

 temperature coefficients at extreme frequencies the description became more 

 difficult, requiring the specification of two or three angles. Many schemes 

 for specification have been devised but the Institute of Radio Engineers is 

 recommending the adoption of a system we shall call the I.R.E. system. 



The crystal designer has the problem: "How shall I orient the length, 

 width and thickness of a piezoid with respect to the x, y and z axes so as to 

 give the required electrical properties? He thinks in terms of fixed x, y 

 and z axes, variable piezoid edge directions. The crystal cutter has the 

 converse problem. "How shall I orient the :v, y and z axes of the crystal 

 so that fixed saws will give the required surfaces?" For this reason the 

 most convenient orientation angles from the designer's viewpoint may 

 not be the simplest from the cutter's viewpoint. Also the translation 

 from one set to the other may not be simple. 



The early methods of orientation specification were somewhat chaotic. 

 There was no overall plan of what angles were to be specified and from 

 what axes they were to be measured. Each group of crystals was a law 

 unto itself. 



The I.R.E. Orientation Angles 



The relations between the x, y and z axes of the crystal and the length, 

 width and thickness of the piezoid are given in Fig. 2.7. 



The position of Fig. 2.7 may be considered as a result of turning the piezoid 

 through the successive angles ((>, d, \{/ starting from an initial position length 

 parallel to x, width parallel to y and thickness parallel to z as in Fig. 2.8. 

 First the crystal is turned through angle (f> about z in the direction shown 

 in Fig. 2.7. Then it is lowered through angle 6 about an axis parallel to the 

 width direction, again in the direction shown in Fig. 2.7. Finally it is skewed 

 through an angle \l/ about an axis parallel with the thickness direction in 

 the sense shown in Fig. 2.7. 



