X-RAY MICROSCOPY 



with a constant of proportionality of 1.3 X 

 10-^ 



The absohite intensitj^ of production in 

 thick targets in the forward direction has 

 been measured by the writer (1959a) for tar- 

 gets of aliuninuni, copper and gold. The 

 measurements extend from the high energy 

 limit eo down to about 5.4 eo • From these data 

 the absolute efficiency can be estimated by 

 extrapolation to zero energy and integration 

 over the whole energy range. Such an ex- 

 trapolation is subject to some uncertainty 

 but within this limitation the efficiencies in 

 the forward direction were found to be ac- 

 curately proportional to the accelerating 

 voltage, and approximately proportional to 

 the atomic number. The constant of propor- 

 tionaUty was found to be 1.3 X 10^ which is 

 slightly in excess of Compton and Allison's 

 estimate but in good agreement with the 

 calculations of Kirkpatrick and Wiedmann. 



Characteristic Radiation 



When discussing the production of charac- 

 teristic X - radiation by electron bombard- 

 ment it is convenient to define a cross-section 

 Qk,l • • ' ior K ,L- ■ ■ ionization and to ex- 

 press it as a function of the electron energy 

 and of Vk,l--- the K,L-- excitation 

 energy. The problem of finding a suitable 

 expression has been discussed by Worthing- 

 ton and Tomfin (1956) who express Qk in 

 the form 



0.77re2 - log. [4t7/(1.65 -f 2.65 exp (1 - U))], 



where 



U = V /Vk and V is the electron energy. 



The essential aspects of this expression are 

 the inverse relation between Qk and V k^ 

 (implying a strong inverse relation between 

 Qk and Z), and a rapid rise in Q^c as C/ is 

 increased from 1, to a maximum value at 

 U = approximate^ 2.5, followed by a slow 



fall in Qk as U is further increased. Q kV k^ 

 is the same function of U for all elements, and 

 is illustrated in their paper. The actual out- 

 put of x-radiation is obtained by multiplying 

 Q K by w K, the fluorescence yield, and by ad 

 hoc additional terms depending upon geome- 

 try, self-absorption within the target, etc. 



Little absolute data are available for thin 

 targets but the existing information for silver 

 and nickel targets has been summarized and 

 discussed by Worthington and Tomlin 

 (1956), following Massey and Burhop (1952). 

 The experimental and theoretical results do 

 not fit well, although the curves agree in 

 general shape. 



The output from thick targets has been M 

 calculated by Worthington and Tomlin, but 

 direct experimental observation by these 

 authors and by the writer (1959b) on copper, 

 and by Dolby (1960) on aluminum suggest 

 that their calculations yield values which are 

 high by factors of approximately 2 and 4, 

 respectively. 



The experimental data and the theoretical 

 expressions show that the efficiency and the 

 intensity vary with kilovoltage in a some- 

 what complex manner. For the intensity, 

 empirical relations of the form 



/ = kiVo 



Vk)' 



have frequently been observed to be of use 

 over a restricted range of the variables, 

 where q equals, for example, 1.6 (Worthing- 

 ton and Tomlin 1956) or 1.65 (Compton and 

 AlUson 1935). But formulas of wide appli- 

 cability and methods of calculating the ab- 

 solute yields on a systematic basis have yet 

 to be found. 



REFERENCES 



1. Amrehn, H., Z. Phys., 144, 529 (1956). 



2. Amrehn, H., and Kuhlenkampff, H., Z. 



Phys., 140, 452 (1955). 



3. BoHM, K., Physik. Z., 38, 334 (1937). 



4. BoHM, K., Ann. Physik, 33, 315 (1938). 



5. BoRRiES, B. v., "Die Ubermikroscopie", Saen- 



ger: Berlin (1949). 



6. BOTDEN, p. J. M., COMBEE, B., AND HOUT- 



MAN, J., Philips Tech. Rev., 14, 165 (1952). 



660 



