14 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 1 



backed by a metal layer. The system can also be used for the thick- 

 ness determination of a metal coating on a metal substrate, providing 

 the conductivities of the coating and of the metal base differ suffi- 

 ciently (e.g., silver on brass, nickel on steel). 1 The depth of the 

 induced eddy current will depend upon the conductivity of the layer 

 through which the current flows. The effective conductivity of the 

 composite surface layer, and hence the magnitude of the induced 

 eddy current, will depend upon the thickness of the coating. Separate 

 (empirical) calibrations are required for each combination of base 

 metal and coating metal. 



The transfer characteristic is nonlinear. The method is capable of 

 measuring metal coatings as thin as 2 to 3 ju. Hadley 2 has determined 

 the thickness of aluminum films between 50 and 200 m^ by measur- 

 ing the variation of the storage factor Q of a coil brought close to the 

 film. 



See also M. L. Greenough, Electronics, 20, 172 (November, 1947); 

 M. L. Greenough and W. E. Williams, J. Research Natl. Bur. Standards, 46, 5 

 (1951). For other references see A.L.Alexander, P. King, and J. A. Dinger, Ind. 

 Eng. Chemistry, 17, 389 (1945); S. Lipson, Am. Soc. Testing Materials Bull., 

 135, 20 (1945); C. M. Hathaway and E. S. Lee, Mech. Eng., 59, 653 (1937). 



1-13. Capacitive Systems 



The capacitance between two electrodes, 

 Fig. (1-1)12, which belong to a cross-sec- 

 tional area a and which are separated by a 

 small distance d (all linear dimensions in 

 centimeters) is 



a 



Fig. (1-1)12. Capacitive 

 gauge for thickness meas- 

 urement on insulators. 



G mY = 0.08S5e 



(1) 



where e is the dielectric constant of the medium between the plates. 

 Frequently plates of circular shape (radius r) are used, so that for 

 d < r, i.e., neglecting fringe effect, 



C = 0.278e 



d 



(2) 



If the fringe capacitance cannot be neglected, the capacitance can 

 be found from 



C = 0.0885e 





+ r 



In 



I677T 



d 



(3) 



1 A. Brenner and J. Garcia-Rivera, Plating, 40, 1238 (1953). 



2 C. P. Hadley, Rev. Sci. Instr., 27, 176 (1956). 



