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276 CHAPTER 3

            and inserting the expression for   from Eq. (3.29), one obtains





            Thus, by combining Eqs. (3.36) and (3.106)



            The total charge in the ion cloud   is, on the one hand, equal to   [Eq. (3.39)]
            as required by the electroneutrality condition and, on the other hand, the result of
            integrating dq. Thus,






                What lower limit should be used for the integration? In the point-charge model,
            one used a lower limit of zero, meaning that the ion cloud commences from zero (i.e.,
            from the surface of a zero-radius ion) and extends to infinity. However, now the ions
            are taken to be of finite size, and a lower limit of zero is obviously wrong. The lower
            limit should be a distance corresponding to the distance from the ion center at which
            the ionic atmosphere starts (Fig. 3.30).






























                          Fig.  3.30. For  a  finite-sized  ion, the ion  atmos-
                          phere starts at a distance a from the center of the
                          reference ion.
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