Faber-Ziman

There is an equivalent relationship between the partial structure functions, SapiQ) and the total structure function, S Q). In the Faber-Ziman scheme, the weighting is chosen such that each partial structure factor, Sa iQ), has the same property of the total structure factor that as Q go, So,p(Q)= 1- This means that we can define the Fourier couple between S iQ) and Ga (r) in the same way as for the total structure function, i.e. ... 

Concentration as well as temperature dependences of p in both the amorphous [5.86-89] and the liquid state [5.90-92] are understood in the framework of the diffraction or extended Faber-Ziman model [5.90, 92, 93]. Experimentally determined total as well as model partial-structure functions have been successfully applied. Disregarding inelastic-scattering effects and extensions of... 

D. T. Bowron, J. L. Finney, A. Hallbrucker, I. Kohl, T. Loerting, E. Mayer, and A. K. Soper, The local and intermediate range structures of the five amorphous ices at 80K and ambient pressure A Faber-Ziman and Bhatia-Thornton analysis, J. Chem. Phys. 125, 194502 (2006). 

The matrix of the relative weighting factors shown in Fig. 6.1 was inverted (as described in Sect. 3.2.3) in order to determine the Faber-Ziman (FZ) partial structure factors ... 

Fig. 6.8 The Faber-Ziman partial structure factors and partial pair correlation functions for Feg5Ni35. The black lines in the partial structure factors are spline fits to the data. The black lines in the partial pair correlation functions are Lorch modified Fourier transforms of the same data. The poorer conditioning of the FZ matrix results in noisier partial structure factors than for the BT formalism. Despite this there appears to be relatively little difference between the Ni-Ni, Fe-Fe, and Ni-Fe partial structure factors, suggesting that the mixing is close to that of an ideal liquid. The very sharp peak observed in SniNii ) [with corresponding dip in appears to...

Fig. 1.1 The Faber-Ziman Sap k) a, /3 = M, X) and Bhatia-Thornton Su k) (/, / = N, C) partial structure factors for liquid and glassy ZnCl2. The points with vertical (black) error bars are the measured functions in (a) and (c) for the liquid at 332(5) °C [ 16] and in (b) and (d) for the glass at 25(1) °C [15, 16]. The solid (red) curves are the Fourier backtransforms of the corresponding partial pair-distribution functions after the unphysical oscillations at r-values smaller than the distance of closest approach between the centres of two atoms are set to the calculated Unlit at r = 0. The broken (green) curves in (a) are from the polarisable ion model of Sharma and Wilson [63] for the Uquid at 327 °C...

Fig. 1.2 The Faber-Ziman partial structure factors Sap(k) and partial pair-distribution functions gafi (r) (a, /S = M, X) as calculated for models using two different values for the anion polarisability ax [61]. The curves in (a) and (b) correspond to a rigid ion model (RIM) with ax = 0, while the curves in (c) and (d) correspond to a polarisable ion model (PIM) with ax = 20 au. The introduction of anion polarisability leads to the appearance of an FSDP in S mm (k) at kpsop 1.2 A and to an alignment of the principal peaks in aU three Safi(k) functions atkpp 2 A. The alignment of the principal peaks in (c) arises from in-phase large-r oscillations in the ga r) functions shown in (d)...

The Faber-Ziman Sapik) and corresponding gap(r) functions are shown in Figs. 1.5, 1.6 and 1.7, and the Bhatia-Thornton Sjjik) functions are shown in... 

Ashcroft-Langreth functions may be converted easily into the Faber-Ziman form [68]. The simulated total scattering functions are obtained directly from the weighted combination of the Faber-Ziman partial structure factors. 

Fig. 12.1 Faber-Ziman partial structure factors for liquid GeSc2. Calculations for PW (solid blue line) and LDA (solid red line shifted downwards by —2) FPMD models from [12] ate compeired to the experiment (cyan dots with error bars) from [13]...

Fig. 12.11 Color online) The Faber-Ziman partial structure factors FZaeGeik) (top panel), FZaex(k) middlepanel) and FZxx k) bottom panel). From left to right, for the amorphous GeS4 solid black lines) and GeSe4 solid orange lines) models...

Unfortunately, in the case of B2O3 only the (neutron and X-ray) total stracture factors have been measured and no partials are available. We provide however in Fig. 14.12 a comparison of the neutron weighted Faber-Ziman partials obtained from our models. It is seen that the differences are very tiny and essentially limited to a small frequency shift in the B-B partial. Clearly, a quantitative assessment of / is unlikely to be made from these measurements. 

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