X-RAVS AND ORIENTATION OF {H'ARTZ CRYSTALS 333 



From (vS.48) we see that the order of application of ei , ^2 , ^3 is immaterial. 



If the desired transformation is r° (i.e., with zero errors) ( = r'", equation 

 3.9 for the NT plate), and the actual one is r, we can consider that r° is 

 made up from the desired rotations .li , Ai , A^ and the ;■ is made up of the 

 rotations Ai = .4° + Ai , .I2 = .I? + Ao , .I3 = .^s + A3 ; or alternatively r 

 is made from the transformation r° followed by the transformation e so that 



(3.49) 



whence 



tan Ai = 



(er°)2i r°i — CiTu + 63^11 



— sin A2 = {er°)2z = r°n — eir^ + e^ru (3.50) 



{er°)n r°z — ^3^23 + e^rtz 



tan Az = 



{er°)z2 r%z - eor^ + 61^23 



where ier°)-n is the term in row 2, column 1 of the matrix er°; r?3 is the term 

 in row 2, column 3 of the matrix r° (equation 3.9), etc. 



From our unfinished example of the A^T plate we have e^ = .0087, €2 = 

 -.0018, C3 = whence 



— tan Ai = 



-.64279 + .0087 X .766 + -.6361 



-.10662 - .0087 X .08946 + .1074 



whence Ai = 99^36' 

 -sin A2 = -.75852 - .0087 X .6365 + = -.7649 



whence .1, = 49°49' 

 -.13917 - - .0018 X .6365 -.1403 



tan A3 = 



.63653 + .0018 X .1392 - .0087 X .7585 .6302 



whence Az = -12°33' 



In starting work on a new cut of crystal one may have difficulty in finding 

 the indices of the Laue spots. The easiest method is to photograph a 

 crystal that has been carefully cut at measured angles from known planes 

 (for instance natural faces). For example, from the angles laid off in the 

 shop an NT plate such as that described should be sufficiently accurate 

 that when P2 is located on the atomic plane chart. Fig. 3.7, and several 

 nearby planes of small indices are computed on the P axes, there should he 

 no doubt as to which spots correspond to these locations. 



From a few of these spots one can find many others by "zonal" relations. 

 A zone is a family of atomic planes all of which are parallel to one line called 

 the zonal axis. Just as there are indices of a plane there are zonal indices. 



