Radial Distribution Function Curves Research Articles

Anomalous X-ray Scattering Study of GeO2Glass

Abstract The anomalous X-ray scattering (AXS) technique was applied to a structural study of GeO2 glass, using synchrotron radiation and a new goniometer system. The environmental radial distribution function (RDF) was determined from intensity measurements at the Ge K absorption edge and compared with the ordinary RDF curve estimated from the. X-ray scattering intensity by Mo K α radiation. By combining the environmental and ordinary RDFs of the GeO2 glass it has been confirmed that the fundamental local unit structure is a GeO4 tetrahedron and that these tetrahedra are joined at their corners to form a network structure. The capability of the AXS technique has been approved as a relatively new tool for the structural characterization of disordered materials.

An X-Ray Diffraction Investigation of the Coordination Structure of Mn(II) Ions in Highly Concentrated Aqueous MnBr2 and MnCl2 Solutions

Abstract The solute structures of highly concentrated aqueous 5.087 and 2.744 mol dm−3 MnBr2, and 4.744 and 2.732 mol dm−3 MnCl2 solutions were determined by the analysis of the radial-distribution function curves of X-ray diffraction experiments. Mixed-ligand aquahalogenomanganese(II) complexes were found to be present in these solutions, holding a distorted octahedral geometry. The interatomic distances of the aquabromo complex are 2.178–2.184 Å for Mn–OH2 and 2.596–2.643 Å for Mn–Br; those of the aquachloro complex are 2.183–2.185 Å for Mn–OH2 and 2.492–2.496 Å for Mn–Cl. The interatomic distances of Mn–OH2 are shorter than those of the MnBr2·4H2O and MnCl2·4H2O crystals and are consistent with those of the Mn(OH2)6(NO3)2 crystal. The length of the Mn–Cl bond here determined is practically the same as that within the MnCl2·4H2O crystal, but the Mn–Br bond found is shorter than that within the MnBr2·4H2O crystal. The average coordination number of the Mn–Br contact per Mn(II) increased from 1.104 to 1.212 with an increase in the Br/Mn ratio from 2.076 to 3.269, while the number of the Mn–Cl contact per Mn(II) increased from 1.259 to 1.501 with an increase in the Cl/Mn ratio from 2.000 to 3.352. In all solutions, the aquamonohalogeno and aquadihalogeno complexes exist as the main species, but the aquadihalogeno complex is more dominant in the MnCl2 solution than in the MnBr2 solution.

Structural analysis of CaSiO 3 glass by X-ray diffraction and Raman spectroscopy

The short-range structure of CaSiO 3 glass was studied by a combination of radial distribution analysis with an intensity comparison method on the basis of X-ray diffraction data. Three main peaks appeared at 1.64, 2.43 and 3.64 Å in the radial distribution function curve. The Raman bands were observed at 367, 642, 878 and 972 cm −1 and the Raman spectrum was found to be similar to that observed in pyroxenes: single chains consisting of SiO 4 tetrahedra are linked by calcium ions laterally. The calcium ion is surrounded by six oxygen atoms at an average distance of 2.34 Å and the remainder CaO pairs at a distance of 2.54 Å. The calculated intensity curve based on this model was in good agreement with the observed one.

Structure of Glasses and Melts in the Na<sub>2</sub>O-SiO<sub>2</sub>-TiO<sub>2</sub> System

In order to elucidate the influence of TiO2 on the structure of sodium silicate glasses and melts, a MD (molecular dynamics) simulation using the ionic pair potential function, Born-Mayer-Huggins form, has been performed for 0.25Na2O⋅0.47SiO2⋅0.28TiO2 glass and the corresponding melt. The calculation pair correlation functions were in good agreement with a RDF (radial distribution function) curve obtained from the previous structural analysis by TOF (time-of-flight) pulsed neutron scattering. The computer-simulated configuration for the glass indicated that most of Ti ions were in 4-fold coordination, whilst the remainder were 6-fold coordination. The frequency spectrum of the glass obtained from MD simulation was in good agreement with the Raman spectra measured on glasses in the Na2O-SiO2-TiO2 system. As a result, the weak Raman band near 700cm-1 can be assigned to Ti ion in 6-fold coordination, and the strong Raman band near 900cm-1 reflects a Ti-O stretching band, which is characteristic of TiO4 tetrahedra corner-linked with SiO4 tetrahedra. The Raman spectra for glasses and melts in Na2O-SiO2-TiO2 system were measured by the high temperature Raman spectroscopic technique. A slight difference in the obtained Raman spectra was observed between the glasses and the corresponding melts, implying that the structure of glass should be similar to that of the corresponding melt.

Short-range structures of barium, lead, and strontium meta-fluorozirconate glasses

X-ray radial distribution analysis has been performed on Ba, Pb, and Sr metafluorozirconate glasses using MoK α radiation. No reliable scattering intensity measurement could be made of the SrZrF 6 glass owing to appreciable amounts of specimen fluorescence. The BaZrF 6 and PbZrF 6 glasses gave radial distribution function curves with very similar features, which showed peaks at about 2.20, 2.80, and 4.50Å and at about 2.15, 2.60, and 4.30Å, respectively. The radial distribution functions can be satisfactorily interpreted on the basis of the crystal structures of β-BaZrF 6 and α-PbZrF 6, respectively. It is proposed that the basic structures of the BaZrF 6 and PbZrF 6 glasses consist of edge-shared ZrF 8-dodecahedra chains, ionically linked by Ba and Pb ions. The same model would be applicable to the SrZrF 6 glass, judging by the previous Raman spectroscopic and differential analysis studies.

Structure analysis of MgSiO 3 glass

The structure of MgSiO 3 glass was investigated by a combination of radial distribution function (RDF) analysis with an intensity comparison method on the basis of X-ray diffraction data. There appeared five peaks at 1.63, 2.08, 2.58, 3.25 and 4.2 Å in the RDF curve. The short range structure was found to be similar to that observed in pyroxenes: single chains composed of SiO 4 tetrahedra are linked by Mg 2+ ions laterally. The Mg 2+ ion is surrounded by six oxygen atoms on average, four of which form MgO pairs with an average distance of 2.08 Å and the remainder Mg O pairs of 2.5 Å which contribute to the formation of the third peak at 2.58 Å in the RDF curve together with the OO pairs (2.66 Å) in SiO 4 tetrahedra. The calculated intensity curve based on this model was in good agreement with the observed one.

Hydrogen and deuterium atoms in amorphous ZrNi alloys

The local environment of hydrogen and deuterium atoms dissolved in amorphous alloys with the composition ZrNi and Zr 2Ni was studied using neutron inelastic scattering and neutron diffraction techniques. The frequency distribution functions exhibit a broad peak at about 130 meV. Interatomic DNi and DZr correlations are observed in the radial distribution function curves at correlation lengths of 1.7 Å and 2.1 Å respectively for both alloy compositions. It is concluded that the majority of hydrogen and deuterium atoms in the amorphous alloys are trapped at holes in the tetrahedra which consist of three or four zirconium atoms. The maximum hydrogen content per metal atom can be explained by assuming a statistical configuration of the metal atoms.

Structural Analysis of Metadickite

The structure of metadickite, which was a dehydration phase of a dickite from Shokozan mine, Hiroshima, Japan calcined at 600°C for 24 h, was investigated by X‐ray radial distribution function (RDF) analysis and the correlation method. The RDF curve showed the coordination numbers of both Si and Al atoms to be four and the structural regularity was observed up to ∼0.8 nm. Several structural models for metadickite were examined by the correlation method and the most likely model is considered to be the arrangement built up of SiO4 tet‐rahedral sheets, similar to the original dickite, and an adjacent edge‐shared AlO4 tetrahedral chain, with a 6‐4‐4 type oxygen atom distribution.

Effect of radiation on the structure of natural rubber

Abstract The effects of radiation-induced crosslinking on the physical arrangement of macromolecules in molten state natural rubber (NR) were examined. Three NR samples with doses of 0, 300, and 550 Mrad were studied based on differential radial distribution function (DRDF) curves derived from wide-angle x-ray scattering data. The resultant DRDF curves for all samples show the presence of intermolecular peaks at ∽5, 10, and 15 a. The appearance of such periodic intermolecular peaks suggests the presence of locally aligned chain segments, to the extent of ∽15a, in both uncrosslinked and crosslinked NR. The 5-a periodicity observed is the average chain-to-chain distance between more or less parallel molecules. The high-energy radiation causes a decrease in the area of these DRDF peaks for NR irradiated to higher than 300 Mrad. This result suggests a corresponding radiation-induced destruction of the intermolecular organization.

Infra-red spectra of crystalline phases and related glasses in the TeO2-V2O5-Me2O system

The crystal line phases Me2O·V2O5·2TeO2 (Me=Li, Na, K, Cs, Ag) and their glasses are studied with the aid of infra-red spectroscopy. The radial distribution function (RDF) curves of two glasses, Na2O·V2O5·2TeO2 and Cs2O·V2O5·2TeO2, are obtained by an X-ray diffraction study. An attempt is made to identify the main bands in the infra-red spectra of the crystalline compounds and the glasses. The absorption bands in the 970 to 880 cm−1 range are assigned to the stretching modes of the VO2 isolated groups. A trend is observed towards a shift of the high-frequency band by the replacement of an alkaline ion with another in the order Ag+, Cu+, Li+, Na+, K+, Rb+, Cs+, which is explained by their different polarizing ability. With the aid of X-ray diffraction studies it is shown that the basic structure units in the glasses studied are the VO4 and TeO4 groups.

The structure of amorphous aluminium phosphate by radial distribution functions derived from X-ray diffraction

An investigation of the molecular structure of amorphous aluminium phosphate, prepared from a recently discovered complex (AlPO4 · HCl · 4C2H5OH), has been carried out using radial distribution function (RDF) techniques. Studies were made on two samples, one prepared by decomposing the solid complex and the other from powder produced by evaporating to dryness a solution of the complex in methanol and then decomposing and grinding the solid obtained. RDF curves were obtained from both samples, and were found to closely resemble that previously reported for vitreous silica. The short range order in both samples is similar to that in vitreous silica, with aluminium and phosphorous atoms occupying positions in aluminium phosphate similar to the positions of silicon atoms in silica. This structure is consistent with the crystal chemistry of aluminium phosphate. It is possible to assign all the peaks in the RDF plots out to values of r∼5 A to known inter-atomic distances. The peak at 1.6 A represents the Al-O and Al-P bond lengths, and is broader than the corresponding Si-O peak in vitreous silica, as the Al-O and P-O bonds are respectively slightly longer (Al-O) and shorter (P-O) than the equivalent Si-O bonds. Subsequent peaks result from the O-O distances (∼ 2.6 A); the Al-Al, Al-P and P-P distances (∼ 3.1A); the Al-second O and P-second O distances (∼ 4.2 A), and O-second O, Al-second Al, P-second P and Al-second P distances (∼ 5.0 A). The sample prepared from the methanolic solution shows some small additional peaks in the region 4 to 5 A, indicating more order in the second neighbour distances. Analysis of the P-O and Al-O peak area indicates that both P and Al atoms are co-ordinated to four network oxygen atoms at a distance ∼ 1.6A, and that absorbed water also co-ordinates to one or both atoms with a P-O and/or Al-O distance of ∼ 1.6 A.

Statistical Mechanical Calculation of the Radial Distribution Function for a Water-like Fluid

Abstract The radial distribution function (RDF) for a water-like system, which has the fundamental characteristics of water, is calculated using the graph-theoretical technique developed by Andersen and Chandler. An interaction potential devised to simulate the hydrogen bond is regarded as a perturbation of the pair interaction between the two molecules of a reference system which consists of hard spheres each having a point dipole at each center. The effect of the hydrogen bond-like potential on the distribution of the molecules is shown explicitly. The results show a tetrahedral coordination similar to that in water. The resulting RDF has qualitatively reproduced the features observed in the experimental RDF curve for water.

Structure of evaporated films of arsenic trisulphide

The diffraction of 100 KV electrons by evaporated films of arsenic tri- sulphide was measured and the reduced radial distribution function obtained by Fourier analysis. Considerable ordering is present for radii up to about 8 Å, but there is a rapid decrease in order for larger atomic separations. The position and area of the first peak in the radial distribution function (RDF) shows that the vitreous structure is built up on the same triangular coordination that occurs in the crystal lattice. The positions of the peaks in the RDF curve are compared with the interatomic distances in single crystals. It is concluded that the vitreous structure can be considered as a considerably distorted and slightly expanded crystal lattice. The vitreous density, calculated from the structure obtained from this RDF analysis, agrees with the observed density.

Radial distribution function of amorphous Ni [sbnd]Pt [sbnd]P alloys

Accurate X-ray diffraction measurements were made upon five amorphous alloys having the composition (Ni x Pt 100− x ) 75 P 25 with 20 ⩽ x ⩽ 60, which were obtained by rapid quenching from the liquid state. The shapes of the interference function a( K), and of the atomic radial distribution function (RDF) curves are strikingly similar to those observed for metallic liquids. Contrary to what was observed in previously studied amorphous metallic alloys, there is no shoulder on the high angle side of the second peak of a( K) and the RDF does not have a double peak beyond the first maximum. The ratio of second to first near-neighbor atomic distances is 1.86±0.02, a value which is larger than that (∼1.7) observed for previously known amorphous foils. The first coordination number is close to 12. On the basis of these and further experimental studies on the first band of various amorphous metallic alloys, it is concluded that the present alloys possess a higher degree of disorder than that found in any of the existing amorphous metallic materials. The degree of disorder is comparable to that present in fused silica. The factors contributing towards successful synthesis of these alloys are discussed.

Kinematic theory of diffraction by matter of any kind and the theory of liquids

Abstract An expression for the intensity function scattered coherently by an arbitrarily distorted lattice has been derived which degenerates under well-defined conditions to the well-known formulae valid for crystals, liquids and gases or amorphous substances. A new method for the analysis of the radial distribution function (RDF) of simple liquids has been suggested. RDF curves for liquid argon near the triple point have been analysed to obtain the distance statistics of neighbours and their coordination numbers. Using the first-neighbour statistics an expression for the partition function for matter of any kind and, in particular, for simple liquids has been deduced.