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An alternative description has been also modeled though not fit to the data. In this model the sample is described as consisting of many individual subsamples in which a single five-layer set of lamellae are placed at different depths ZL from the SiO2 within the Nafion film. Since, in this model, these subsamples are larger than the neutron coherence length in the plane of the sample, the scattering from each subsample will add incoherently; i.e, the intensities will be added, If the individual layers were smaller than the coherence length of the neutron, only the average in-plane composition would contribute to the scattering, Models with narrow distributions of ZL centered away from either interface show a beating pattern of the oscillations, similar to the single sample models discussed in the text, which is also not consistent with the data. Broader distributions do not have such a beating pattern, but the intensity of the oscillations of the summed intensity fall und
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2 within the Nafion film. Since, in this model, these subsamples are larger than the neutron coherence length in the plane of the sample, the scattering from each subsample will add incoherently; i.e., the intensities will be added. (If the individual layers were smaller than the coherence length of the neutron, only the average in-plane composition would contribute to the scattering.) Models with narrow distributions of ZL centered away from either interface show a beating pattern of the oscillations, similar to the single sample models discussed in the text, which is also not consistent with the data. Broader distributions do not have such a beating pattern, but the intensity of the oscillations of the summed intensity fall under an envelope function which includes a broad peak at roughly half the Q value of the high-Q peak, which is not seen in the data, indicating that this model is not as good a fit to the data as one with a single set of lamellae located at the interface or surface of the Nafion film.
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