578 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



therefore reveal the action of pairing. Experiments of this sort have been 

 performed and will also be described in this paper. 



The reduction in the diffusivity of a donor such as lithium may be 

 desirable in certain places. 



(F) Direct Transport 



Diffusion studies suffer from the. defect that ion pairing produces a 

 concentration dependent diffusivity. (See Appendix B). For this resaon 

 a very desirable measurement would involve determining the amount of 

 a mobile donor like lithium transported by an electric field through a 

 uniformly saturated specimen of semiconductor. This flux, together with 

 information concerning the level of saturation, should provide a direct 

 measure of the mobility of lithium under homogeneous conditions. 

 Formula (7.15) or its refinement (7.25) could then be applied directly 

 to the results. 



The above list is by no means complete, for there are still other tech- 

 niques available for measurement, for example nuclear and paramagnetic 

 resonance. Enough has been given however to indicate the ^^dde range 

 of phenomena which ion pairing in solids can affect. In liquids, only A 

 and F are of any consequence. It is important to realize that not only do 

 these phenomena serve as tools for the study of ion pairing, but that ion 

 pairing, when properly understood, can serve as a tool for the study of 

 the phenomena themselves. 



IX. PAIRING CALCULATIONS 



The evaluation of fi according to (7.14) presents somewhat of a prob- 

 lem because the integral must be arrived at numerically. Fortunately, 

 the literature contains tables of the integral in what amounts to di- 

 mensionless form. The transformation 



^ = q'/KkTr (9.1) 



is introduced and then fi is shown to be given by 



U = 4Tr[q^/KkTf Q(a) (9.2) 



where 



a = q-/KkTa (9.3) 



and logio Q((x) is tabulated in Table III. 



In a specimen in which the numbers of donors and acceptors are im- 



