X-RAVS AND ORIENTATION OF QUARTZ CRYSTALS 



299 



3.5 The Naming of Atomic Planes in Crystals 



It is convenient to be able to refer to any atomic plane in a crystal by 

 some symbol that uniquely defines its orientation. The symbols com- 

 monly used for this purpose are known as Miller indices (or Bravais-Miller 

 indices for the hexagonal system) and are the reciprocals of the intercepts 

 of the atomic plane on a set of crystallographic axes chosen in accordance 

 with the symmetry of the crystal. In quartz this set of axes is as shown in 

 Fig. 3.4: a vertical axis c and three horizontal axes at 120° ai , a2 , a^ . 



Measurement of the interfacial angles of thousands of quartz crystals 

 has shown that the natural faces have intercepts on the crystallographic 



+C 



Hg. 3.4 — Hexagonal crystallographic axes 



axes that are integral multiples of a fixed distance, which is the same in 

 the case of all three a axes and different in the case of the c axis. This 

 fixed distance along the c axis is found to be 1.09997 times the fixed dis- 

 tance along the a axes. Therefore, the "unit length" of each of the a 

 axes is said to be 1; that of the c axis 1.09997 and a face that cuts the c 

 axis at 1.09997a from the origin is said to have the c intercept of 1. (This 

 unit axial length is different for different substances but the same for all 

 crystals of the same substance.) For example, the front cap face in figure 

 3.5 has the axial intercepts 1, co , —1, 1, naming the axes in the order 

 fli , (12, as, c. The indices for this face are written (lOll) (general form 

 hkil). The front vertical face has the intercepts 1, x, — 1, co and the 



