Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов. Читать онлайн. Newlib. NEWLIB.NET

Автор: Группа авторов
Издательство: John Wiley & Sons Limited
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Жанр произведения: Техническая литература
Год издания: 0
isbn: 9781118799499
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an ab initio simulation (solid black line) and a simulation with an effective force field (solid blue line), after [17]. Symbols: Data from two neutron scattering experiments [22].

      (13)equation

      where p runs over all the eigenmodes, and images is the so‐called oscillator strength which is defined as

      (14)equation

      Here, e I,k(ωp) is the part of the eigenvector e(ωp) that contains the three components of particle I, and the quantity ZI,jk is the Born effective charge tensor defined as:

      (15)equation

      where e is the elementary charge, i.e. ZI,ij is an effective charge that connects the strength of an external electric field ℰ to the force F I on particle I.

      These quantities allow to obtain immediately the real and imaginary parts of the dielectric function ɛ(ω) = ɛ1(ω) + 2(ω) [24]:

      (16)equation

      (17)equation

      Closely related to ɛ(ω) is the absorption spectra α(ω) which is given by

      (18)equation

      Graphs depict the (a)–(c): Infrared spectra for amorphous SiO2 as obtained from ab initio simulations (solid lines) and from experiments (dotted lines). (d) and (e): Infrared spectra for a sodium borosilicate glass as obtained from ab initio calculations and compared to experimental data for pure SiO2 and B2O3 glasses, as well as for a sodium borosilicate glass with a similar composition. Graphs depict the (a)–(c): Infrared spectra for amorphous SiO2 as obtained from ab initio simulations (solid lines) and from experiments (dotted lines). (d) and (e): Infrared spectra for a sodium borosilicate glass as obtained from ab initio calculations and compared to experimental data for pure SiO2 and B2O3 glasses, as well as for a sodium borosilicate glass with a similar composition.

      At high frequencies one finds two bands. The first one, ranging from 850 to 1200 cm−1, can be assigned to oxygen stretching modes of Si─O bonds. That this band lies at lower frequencies than for silica (sharp peak at around 1070 cm−1) is consistent with earlier results showing that the presence of non‐bridging oxygen atoms shifts the band to lower frequencies [19]. The second band extends between 1200 and 1600 cm−1, and is due to the motions of oxygen atoms belonging to [3]B, in agreement with the fact that B2O3, which has mainly [3]B units, shows a very pronounced peak in this frequency range. Regarding absorption, good agreement is again found between the spectrum of NBS and the ab initio calculations made for a closely related composition (Figure 5d and e). The main deviation is found at high frequency where a peak is absent in the experimental spectrum but present in the simulation, since the latter overestimated the concentration of [3]B units because of the high quenching rate [6].

      Finally, we mention that DFT‐based methods have also been proposed in order to compute Raman and hyper‐Raman spectra for periodic solids [25, 26]. These approaches have been used to calculate the corresponding spectra for the main oxide network‐formers, i.e. SiO2, B2O3, or GeO2, with a good a very good agreement to experimental data [12, 13, 18].

      Regarding the peak positions, the agreement between the ab initio simulations and the experimental spectra is remarkably good (Figure 6a). For lithium silicates, slight discrepancies are found for the peak intensities but they are likely due to the modest size and high quenching rates of the simulated samples. In fact, one can handle this problem by determining how the concentrations of the various structural units depend on the cooling rate (or on the temperature of the liquid) and then adjusting them to the actual experimental conditions [6].

Graphs depict the application of ab initio simulations to NMR spectroscopy. (a) Si magic angle spinning spectra of calcium metasilicate, lithium tetrasilicate, and sodium tetrasilicate glasses. (b) Dependence of the Si isotropic chemical shifts on the Si–O–T angle calculated for different Q(n) species in 43 Na2O–57 SiO2, 22.5 Na2O–77.5 SiO2, NS4, and LS4 glasses. Solid lines: linear fits to the data.