In this model, reaction 3 is faster than reaction 4, if atomic sulfur accumulates. Atomic sulfur has not been found in colloidal or powder suspension systems containing a sacrificial electron donor, so that there seems to be a direct involvement of the host Nafion. Finally, since the S/Cd ratio for the irradiated cubic CdS sample approaches that for CdS powder after a short period of Ar+ bombardment, the atomic sulfur layer appears to be, at most, a few monolayers thick. As indicated in Table

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... , the surface of the cubic CdS film soaked in Na2S solution without irradiation is covered with excess S2ion of Na2S. Surface sulfate species is also present. The data indicate that the S2ion of Na2S or H2S is strongly adsorbed on the CdS-Nafion surface and is oxidized to sulfate (Figures 4 and 6) without irradiation. Conclusions conclusions: is small. On the basis of the results reported here, we draw the following (1) The concentration of surface cation exchange sites in Nafion 1985,89, 52-57 (2) The small CdS particles at the surface of the hexagonal CdS films are subject to dissolution in boiling water, whereas the large CdS particles at the surface of the cubic CdS fdms are stable in boiling water. (3) After extensive washing, the surface of films containing cubic CdS remains dominated by sulfide ions of CdS, whereas the surface of films containing the hexagonal form are altered, leaving surface sulfate associated with the Nafion and Cd2+ associated with cation exchange sites. (4) Adsorbed sulfide ions on Nafion and CdS-Nafion are oxidized to sulfate ions at 300 K in the presence of oxygen. (5) The gray-blue deposit formed on cubic CdS-Nafion surfaces under irradiation is identified as atomic sulfur. Acknowledgment. Algorithms for finding local minima, maxima, and saddle points on surfaces, starting from an arbitrary point, are presented. These algorithms are based on making a local approximation to the surface in the form of a rational function constructed from the local first and second derivatives of the surface. All parameters of these algorithms required for stepping across the surface are determined in nonarbitrary ways. The convergence of these procedures to the desired stationary point is shown to be quadratic. Applications for stationary-point searches on two model surfaces are also given for illustrative purposes.