X-RAYS A.\J) ORIf.XTATloy OF OVART/. CRYSTALS 



31,? 



the saw blade being parallel to V and Z. The crystal is then turned through 

 angle .Ii clockwise as seen from above about a vertical axis, then through 

 angle A2 counterclockwise about the original direction of the X axis. A 

 slib is cut of thickness t and this slab laved down by rotating it 90° clock- 

 wise about the original .V axis direction. It is then rotated through angle 

 Az clockwise about a vertical axis and two cuts are made, separated by a 

 width iv (length C being cut last). The rotation through the .I3 angle begins 

 with the linear edge of the reference level of the slab lying parallel to the saw. 

 The components of the plate edges I\ , P2 , P-i (length, thickness, and 

 width, respectively) on the A', Y, and Z coordinates after rotation through 

 the angle .li are given by the following matrix (See Section 5 of "The 

 Mathematics of the Physical Properties of Crystals" by"W. L. Bond, Bell 

 System Technical Journal, \'^olume XXII, No. 1): 



A' component Y component Z component 



/ cos Ai sin Ai 0\ of Pi 



r' = ( —sin Ai cos Ai 1 of P2 



1/ of P3 



(3.6) 



its of the plate edges on the A', Y, Z coordinates after 

 angles Ai and -4? are: 



The components y,L i.iv, ^LCL^^^ v-^ig^o 

 rotation through angles Ai and -42 are: 



/l \ / cos Ai sin Ai 



cos 



.42 — sin /I2 |( — sin ^1 cos .4i 











(3.7) 



\0 sin .42 cos -42/ . 



X component Y component Z component 



(cos Ai sin Ai \ of Pi 



— sin .4 1 cos -4 2 cos -4 1 cos ^2 -sin ^2 1 of P2. 



— sin A I sin .42 cos Ai sin .42 cos .42/ of P3 



The components of the plate edges on the .Y, F, Z coordinates after 

 rotation through angles .4i , .42 and .43 are: 



cos .4i sin .4i \ 



— sin .4i cos .42 cos y4i cos .42 — sin/12) 



— sin .4i sin .42 cos .4i sin /1 2 cos A^/ 



Z component 

 cos .4 2 sin .43] of Pi 



r'" = 



cos .43 sin /i3 

 1 

 — sin .43 cos .43 



I' component 



cos -4i cos .43 sin Ai cos Az 



— sin .4i sin .42 sin .43 -|- cos .4 1 sin ^2 sin .43 



— sin .4i cos .42 cos .4i cos .42 



— cos Ai sin Az —sin Ai sin Az 



— sin Ai sin A2 cos .43 + cos Ai sin .42 cos .43 



— sin .42 of P2 



cos Ai cos .43 1 of P3 



J •■(3.8) 



