Amorphous interference function

Inspection of Eq. 7 reveals that the molecular interference function, s(x), can be derived from the ratio of the total cross-section to the fitted IAM function, when the first square bracketed factor has been accounted for. A widely used model of the liquid state assumes that the molecules in liquids and amorphous materials may be described by a hard-sphere (HS) radial distribution function (RDF). This correctly predicts the exclusion property of the intermolecular force at intermolecular separations below some critical dimension, identified with the sphere diameter in the HS model. The packing fraction, 17, is proportional for a monatomic species to the bulk density, p. The variation of r(x) on 17 is reproduced in Fig. 14, taken from the work of Pavlyukhin [29],... 

Fig. 26. Reduced interference functions F(Q) reproduced from the data obtained by Cargill III (1975) for the amorphous alloys Gdo.36 o.64...

Fig. 28. Model and experimenlal interference functions for amorphous GdQ,gCo0j2 (after Cargill III, 1981b). The dashed line is the experimental result for F(Q). Results are shown for both relaxed and unrelaxed 800 atom models with = 1.1. Gaussian broatiening of the model distribution functions was adjusted to yield approximately the same near neighbour peak widths as those observed experimentally. The model interference functions are also affected by this broadening.

Cargill and Kirkpatrick (1976) found qualitative agreement to exist between binary DRP distribution and experimental distribution functions for amorphous Gd, COj alloys when requiring the tetrahedral perfection to be sufficiently high (k = l.l). The model and experimental distribution functions and interference functions F Q)= for amorphous GdjgCo82 are compared in fig. 28. No... 

Fig, 117. Interference functions for amorphous LajjAl25Ni2o samples in as-quenched and annealed (51 OK, 300s) states. 

The ordinary RDF and the environmental RDF around Ni for the amorphous samples are shown in figs. I18a,b (Inoue et al. 1991b) i 4iere the solid and dotted curves correspond to the as-quenched sample and that annealed in the supercooled liquid region, respectively. As expected from the interference function in fig. 117, the ordinary RDFs for both of the samples in fig. 118a are almost identical. The first peak at about 0.36 run in the total RDF has a shoulder at 0.28 run. For convenience, this shoulder and peak are labeled r and r2, respectively. The first peak in the environmental RDF around Ni has a single peak at r and there is no peak at r-i-... 

FIGURE 1.6 Interference function I s) versus 2 sin6/X A" (a) for an amorphous film of silicon (b) for an amorphous film of silica. (Adapted from P. Chaudhari, J.R Graczyk, and... 

Interference Functions /(s) of Amorphous (as Deposited) Carbon Films Compared to Graphite Peak... 

In this chapter we present results of neutron diffraction and conputer simulation studies on hydrogenated and deuterated CuxTi. x(0.35 < x < 0.67) amorphous alloys. Ihe first part will serve as an illustration of the above considerations and presents the evolution of the interference functions and pair-correlation functions as a function of alloy composition and hydrogen or deuterium content -. In the second part we will use these eiqperlmental results to build up a computer model of these alloys. The last part will present the thermal evolution of a Cuq 50 TIq 50 Hq 5 amorphous alloy as followed by large-angle and small-angle neutron scattering ... 

Interference between X-rays scattered at different atomic centres occurs in exactly the same way as for an atom. The scattered amplitude becomes a function of an atomic distribution function. In an amorphous fluid, a gas or non-crystalline solid the function is spherically symmetrical and the scattering independent of sample orientation. It only depends on the radial distribution of scattering centres (atoms). 

Top for an assumed dielectric function e = 1.5 + i 0.5. The scattering efficiency shows for x > 1 the oscillations due to interference effects typical for particles with diameters of the order of a few wavelengths. Bottom for optical constants of amorphous MgFeSiCVt (from the Jena databases) dust grains with a = 0.1 p.m. The absorption efficiency shows the two strong silicate features around k = 9.7 p.m and k = 18 p.m. 

Scattered waves from neighbouring atoms interfere in exactly the same way and unless the atoms are ordered as in a crystal, the total diffraction pattern is a function of the radial distribution of scattering density (atoms) only. This is the mechanism whereby diffraction patterns arise during gas-phase electron diffraction, scattering by amorphous materials, and diffraction... 

Interference and radial distribution functions for Fe8oPi3C7 amorphous alloys are shown in Fig. 6.16 (Note compositions in amorphous alloys are usually given as atom percentages). 

Given the long-chain nature of polymer molecules, it is obvious that the process of crystallization involves extensive molecular translation from the high degree of disorder characteristic of the melt to the highly ordered state. Also, this must occur in a time that is short relative to the time required for crystallization. Consequently, the degree of crystallinity in most polymers is a function of the rate of crystallization. After rapid crystallization, the amorphous content of the polymer sample is increased. On the other hand, if a molten polymer is crystallized slowly, the crystals develop in a more perfect manner and tend to exclude impurities that could interfere with the ordering process. 

Laridjani and Sadoc (1981) studied amorphous Gd-Y alloys in the composition range 10 to 90 at% Y by X-ray diffraction. The amorphous alloys were prepared by sputtering onto an aluminum substrate at 78 K under argon pressure. Uniform foils having a thickness of 5 to 10pm were obtained. A chemical short-range order was indicated by the interference and radial distribution function. These authors found that the radial distribution function could be accounted for by a mixture of tetrahedra and octahedra. At low concentrations of Y in Gd or Gd in Y there were four tetrahedra for one octahedra, but the number of tetrahedra increased as the concentration approached an equiatomic mixture of yttrium and gadolinium. 

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