SURFACE LAYERS OF CRYSTALS 137 



The explanation of the higher intensity of reflection from the disturbed 

 surface lies in the fact that the rays of the incident X-ray beam, coUimated 

 by a pair of slits, are not perfectly parallel, but diverge, meeting the cr}'stal 

 plate at various angles, whose range, depending on the geometry of the slits, 

 is usually about 15 to 25 minutes of arc. If the surface regiln of the cr>'stal 

 plate is undisturbed only a very small part of the incident beam will meet the 

 crystal at the Bragg angle for X-ray reflection. If, however, some of the 

 quartz has been disturbed it will have a variety of orientations with respect 

 to the main crystal structure and the various disturbed bits of quartz will be 

 at the Bragg angle for the various divergent rays of the incident X-ray beam. 

 In this way more of the incident beam is reflected by a disturbed crj'stal 

 surface than by an undisturbed crystal surface. The disturbed material 

 measured by this technique differs in orientation from that of the main plate 

 by not more than a few minutes so that even this disturbed material uses 

 only a small sector of the divergent incident beam. Surface particles mis- 

 oriented by larger angles are not numerous enough to reflect X-rays into the 

 ionization chamber with measurable intensity. 



An alternative interpretation of the higher intensity of reflection from the 

 disturbed material should be mentioned although it has little practical signif- 

 icance. Consideration of the Bragg equation, n\ = 2d sin 6, will show that 

 a range of d values would make it possible for a range of 6 values to satisfy 

 the equation. If, therefore, there were some variability in the spacing, d, 

 between the atomic planes from which the X-rays were being reflected, re- 

 flection would take place over a corresponding range of angles of incidence.^ 

 Such variability in d spacing would be a result of lattice distortion. It would 

 generally be accompanied by misorientation and therefore its consideration 

 as a phenomenon distinct from misorientation becomes rather academic. 

 The disturbance will therefore be spoken of as misorientation although it 

 probably also involves small changes in d spacing. 



Measurable lattice distortion can be produced by other means than surface 

 working. The reflection-intensity of an etched plate is increased three or 

 four times if the plate is strained by bending during the reflection of the X- 

 ray beam. When the pressure on the plate is released the reflection-intensity 

 resumes its former value. The distortion produced by unequal pressures on 

 the plate results in the heterogeneity of orientation which makes possible the 

 use of a larger part of the incident beam, resulting in higher reflection-inten- 

 sity. When lapped plates are similarly deformed the increase in reflection-in- 

 tensity is less since some heterogeneity of orientation already exists. As 

 would be expected, the efi'ect of the deformation is progressively less with 



^ Consideration of the known compressibility and tensile strength of quartz indicates 

 that the maximum change in d spacing which could be obtained would be of the order of 

 0.1%. For small values of 6 the change in 6 for this d change would also be 0.1%, increas- 

 ing, with larger d values to about 0.2% at = 70°. 



