Amorphous second neighbor

Correlation functions hoo(R) for the amorphous deposit prepared and studied at 77 K are shown in Fig. 7b together with the curve for polycrystalline ice Ih. As in the crystalline phase, the nearest-neighbor oxygen-oxygen correlations in H20(as) occur in an exceptionally narrow band centered at 2.76 A, with rms-deviation 0.114 A. The distance ratio for second and first neighbors indicates tetrahedral coordination on the average, but the second neighbor peak near... 

The reduced RDF of a-Si H shown in Fig. 2.11 (Schulke 1981) has sharp structure at small interatomic distances, progressively less well-defined peaks at larger distances, and is featureless beyond about 10 A. This reflects the common property of all covalent amorphous semiconductors, that there is a high degree of short range order at the first and second neighbor distances, but then the spatial correlations decrease rapidly. 

Figure 11. X-ray diffraction patterns and EXAFS radial structure functions of two poorly-ciystallized compounds. Both ferrihydrite and silicate glass look amorphous through XRD, but the former is as well short-range ordered as feroxyhite, whereas the latter is disordered even at the local scale. Ge02 is used as the EXAFS example instead of Si02 to better match the second-neighbor scattering factors for the Fe oxides.

The interpretation of diffraction data on amorphous polymers is currently a subject of debate. Ovchinnikov et al. (31,34) interpreted their electron diffraction data to show considerable order in the bulk amorphous state, even for polyethylene. Miller and co-workers (3536) found that spacings increase with the size of the side groups, supporting the idea of local order in amorphous polymers. Fischer et al. (32), on the other hand, found that little or no order fits their data best. Schubach et al. (37) take an intermediate position, finding that they were able to characterize first- and second-neighbor spacings for polystyrene and polycarbonate, but no further. 

Figure 12.5. The radial distribution function for crystalline and amorphous Si. The curves show the quantity G(r) = g(r)/(47tr dr), that is, the radial distribution function defined in Eq.(12.19) divided by the volume of the elementary spherical shell (47rr dr) at each value of r. The thick solid line corresponds to a model of the amorphous solid, the thin shaded lines to the crystalline solid. The atomic positions in the crystalline solid are randomized with an amplitude of 0.02 A, so that G(r) has finite peaks rather than 5-functions at the various neighbor distances the peaks corresponding to the first, second and third neighbor distances are evident, centered at r = 2.35, 3.84 and 4.50 A, respectively. The values of G(r) for the crystal have been divided by a factor of 10 to bring them on the same scale as the values for the amorphous model. In the results for the amorphous model, the first neighbor peak is clear (centered also at 2.35 A), but the second neighbor peak has been considerably broadened and there is no discernible third neighbor peak.

In 1911, Einstein proposed a model for heat conduction in amorphous solids. In this model, he assumed that all the atoms vibrate as harmonic oscillators at the same frequency co . In addition, he also assumed that a particular oscillator (or atom) is coupled to only first, second, and third nearest neighbors. Hence, the vibrational energy of the oscillator can only be transferred to these atoms. A further assumption was that the phases of these oscillators were uncorrelated and were completely random. Using these assumptions, he derived the thermal conductivity to be... 

The structural properties of a second, apparently amorphous phase (all) of the molecular glass former triphenyl phosphite were studied by means of multidimensional solid-state NMR spectroscopy and X-ray diffraction. Phase all was prepared by annealing the supercooled liquid in the temperature range 210 K < T < 230 K. In addition to ID H and P spectra and Ti data, P radio-frequency-driven spin-diffusion exchange spectroscopy were used to analyse the arrangement of neighboring TPP molecules on both a local and intermediate scale. ... 

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