ARTICLES BY BELL SYSTEM AUTHORS 291 



Designing for Air Purity. A. M. Hanfmann.^ Heating & Ventilating, V. 

 47, pp. 59-64, Jan., 1950. 



Reciprocity Pressure Response Formula Which Includes the Effect of the 

 Chamber Load on the Motion of the Transducer Diaphragms, f M. S. Hawley.^ 

 Acoustical Soc. Am., Jl., V. 22, pp. 56-58, Jan., 1950. 



Abstract — In order to reduce the effects of wave motion in the coupling 

 chamber to permit reciprocity pressure response measurements to higher 

 frequencies, only two of the three transducers involved are coupled at a 

 time to the chamber. Given for these conditions is a derivation of the pres- 

 sure response formula which includes the effect of the chamber load on the 

 motion of the transducer diaphragms. 



Theory of the "Forbidden" (222) Electron Reflection in the Diamond Struc- 

 ture.i R. D. Heidenreich.i Phys. Rev., V. 77, pp. 271-283, Jan. 15, 1950. 



Abstract — The dynamical or wave mechanical theory of electron diffrac- 

 tion is extended to include several diffracted beams. In the Brillouin zone 

 scheme this is equivalent to terminating the incident crystal wave vector 

 at or near a zone edge or corner. The problem is then one of determining the 

 energy levels and wave functions in the neighborhood of a corner. The solu- 

 tion of the Schrodinger equation near a zone corner is a linear combination 

 of Bloch functions in which the wave vectors are determined by the boundary 

 conditions and the requirement that the total energy be fixed. This leads to 

 a multipUcity of wave vectors for each diffracted beam giving rise to inter- 

 ference phenomena and is an essential feature of the dynamical theory. 



At a Brillouin zone edge formed by boundaries associated with reciprocal 

 lattice points S and O the orthogonality of the unperturbed wave functions 

 in conjunction with the periodic potential requires that another recipro- 

 cal lattice point X be included in the calculation. The indices of X must be 

 such that (X1X2X3) = (S1S2S3) — (gig2g3) • The perturbation at the zone edge 

 results in non-zero amplitude coefficients Cg, Cs and Cj for the diffracted 

 waves irrespective of whether or not the structure factor for X , s or g van- 

 ishes. This is the basis of the explanation of the (222) reflection and since it 

 arises through perturbation at a Brillouin zone edge or corner the term 

 I "perturbation reflection" is advanced to replace the commonly used "for- 

 bidden reflection." 

 ! The octahedron formed by the (222) Brillouin zone boundaries exhibits 

 j an array of lines due to intersections with other boundaries to form edges. 

 I This array of lines is called a "perturbation grid" and the condition for the 

 j occurrence of a (222) reflection is simply that the incident wave vector 

 I terminate on or near a grid line. Numerical intensity calculations are pre- 



t A reprint of this article may be obtained on request to the editor of the B. S.T.J. 

 1 B.T.L. 

 2W. E. Co. 



