Radial distribution function amorphous alloys

In amorphous solids there is a considerable disorder and it is impossible to give a description of their structure comparable to that applicable to crystals. In a crystal indeed the identification of all the atoms in the unit cell, at least in principle, is possible with a precise determination of their coordinates. For a glass, only a statistical description may be obtained to this end different experimental techniques are useful and often complementary to each other. Especially important are the methods based on diffraction experiments only these will be briefly mentioned here. The diffraction pattern of an amorphous alloy does not show sharp diffraction peaks as for crystalline materials but only a few broadened peaks. Much more limited information can thus be extracted and only a statistical description of the structure may be obtained. The so-called radial distribution function is defined as ... 

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). 

The maximum information that can be obtained from X-ray diagrams of amorphous alloys is much more limited. In the simplest case of an amorphous material, composed of a single atomic sjjecies only, it would lead to the knowledge of the so-called radial distribution function (RDF), which provides only spherically averaged information on atomic position correlations. For a given atom at the origin the radial distribution function is defined as... 

Fig. 25. Schematic representation of partial radial distribution functions and total radial distribution function for an amorphous alloy compo.sed of the elements A and B.

Fig. 27. First maximum in the radial distribution functions of the amorphous alloys Gdo.3sFeo.64 and Gdo.jgCoo gj. The curves and the Gaussian fits were drawn by Cargill III (1975) using his experimental data.

A substantial amount of effort has been spent on finding model descriptions of the atomic scale structure of amorphous alloys. Such three-dimensional models have attempted to provide concrete though idealized pictures of the arrangements of the atoms that go beyond the information that can usually be obtained from experimental radial distribution functions. The most prominent among them are microcrystalline and cluster models, and models based on the dense random packing of hard spheres (DRPHS). 

Fig. 83. The environmental radial distribution function (RDF) for Ni (solid) and the ordinary RDF (dotted) of amorphous MgsoNijoLajo alloy.

The atomic sizes of the constituent elements in the ternary R-Al-M amorphous alloys differ significantly. Therefore, the interpretation of the total radial distribution function (RDf) obtained by the ordinary X-ray diffraction method is complicated, and it is extremely hard to obtain structural parameters for each independent pair of elements. By using the anomalous X-ray scattering (AXS) method with which the structural environment around a particular constituent element can be determined, it is expected that this difference is observed and the structural environment around Ni in the amorphous La55Al25Ni2o alloy is estimated in as-quenched, annealed (in the supercooled liquid region) and crystallized states. From these systematic AXS measurements, the structural changes due to crystallization were discussed. 

Fig. 5. Radial distribution function G(r) for amorphous Zr Rh and two Zr RhH alloys, one produced by liquid quenching and then hydrided (orig. amorphous). The other made by SSR (orig. cryst.). ...

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. 

Brequel, H., Soraru, G. D., Schiffini, L., Enzo, S. (2000). Radial distribution function of amorphous silicon oxycarhide compounds. Metastable, Mechanically Alloyed and Nanocrystalline Materials, Pts 1 and 2, 343-3,677-682. 

In section 5 the structure or atomic arrangement associated with amorphous alloys is defined in terms of the pair correlation functions and the radial distribution... 

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