Neutron Correlation Functions Research Articles

The structure of sodium silicate glass from neutron diffraction and modeling of oxygen‐oxygen correlations

AbstractIt is shown that modeling the first oxygen‐oxygen peak in the neutron correlation function of a glass enables structural information about other correlations to be obtained, and the method is illustrated by application to a sodium silicate glass. The first O–O coordination number can be calculated from network theory, and sodium silicate crystal structures show that the mean O–O distance can be calculated from the Si–O distance, despite the distortion of the SiO4 tetrahedra. Modeling the O–O peak for a sodium silicate glass allows the Na‐O bond length distribution to be determined. For a binary glass with 42.5 mol% Na2O, it is found that the Na–O coordination number is 4.8(2) with an average bond length of 2.45 Å, and the Na–O bond lengths are more widely distributed than in sodium silicate crystal structures. Sodium ions are bonded mostly to non‐bridging oxygens (NBOs), and the Na–NBO coordination number may be four as in crystals. Sodium ions are also bonded to a smaller number of bridging oxygens (BOs). Contrary to previous reports, it is not concluded that Na–NBO bonds are shorter than Na–BO bonds, but instead that the Na–BO distribution is relatively narrow, whilst the Na–NBO distribution extends to both shorter and longer distance. The broad distribution of Na–O bond lengths arises from a relatively broad distribution of Na–NBO bond valences, subject to the overall requirement of charge balance.

Neutron Diffraction and Raman Studies of the Incorporation of Sulfate in Silicate Glasses.

The oxidation state, coordination, and local environment of sulfur in alkali silicate (R2O–SiO2; R = Na, Li) and alkali/alkaline-earth silicate (Na2O–MO–SiO2; M = Ca, Ba) glasses have been investigated using neutron diffraction and Raman spectroscopy. With analyses of both the individual total neutron correlation functions and suitable doped–undoped differences, the S–O bonds and (O–O)S correlations were clearly isolated from the other overlapping correlations due to Si–O and (O–O)Si distances in the SiO4 tetrahedra and the modifier–oxygen (R–O and M–O) distances. Clear evidence was obtained that the sulfur is present as SO42– groups, confirmed by the observation in the Raman spectra of the symmetric S–O stretch mode of SO42– groups. The modifier–oxygen bond length distributions were deconvoluted from the neutron correlation functions by fitting. The Na–O and Li–O bond length distributions were clearly asymmetric, whereas no evidence was obtained for asymmetry of the Ca–O and Ba–O distributions. A consideration of the bonding shows that the oxygen atoms in the SO42– groups do not participate in the silicate network and as such constitute a third type of oxygen, “non-network oxygen”, in addition to the bridging and non-bridging oxygens that are bonded to silicon atoms. Thus, each individual sulfate group is surrounded by a shell of modifier and is not connected directly to the silicate network. The addition of SO3 to the glass leads to a conversion of oxygen atoms within the silicate network from non-bridging to bridging so that there is repolymerization of the silicate network. There is evidence that SO3 doping leads to changes in the form of the distribution of Na–O bond lengths with a reduction in the fitted short-bond coordination number and an increase in the fitted long-bond coordination number, and this is consistent with repolymerization of the silicate network. In contrast, there is no evidence that SO3 doping leads to a change in the distribution of Li–O bond lengths with a total Li–O coordination number consistently in excess of 4.

Neutron scattering length determination by means of total scattering

A new method for the measurement of bound coherent neutron scattering lengths is reported. It is shown that a relative measurement of the neutron scattering length, {\overline b}, of an element can be made by analysis of the neutron correlation function of a suitable oxide crystal powder. For this analysis, it is essential to take into account the average density contribution to the correlation function, as well as the contributions arising from distances between atoms in the crystal. The method is demonstrated and verified by analysis of the neutron correlation function for the corundum form of Al2O3, yielding a value {\overline b} = 3.44 (1) fm for Al, in good agreement with the literature. The method is then applied to the isotopes of iridium, for which the values of the scattering lengths were unknown, and which are difficult to investigate by other methods owing to the large cross sections for the absorption of neutrons. The neutron correlation function of a sample of Sr2IrO4 enriched in 193Ir is used to determine values {\overline b} = 9.71 (18) fm and {\overline b} = 12.1 (9) fm for 193Ir and 191Ir, respectively, and these are consistent with the tabulated scattering length and cross sections of natural Ir. These values are of potential application for obtaining improved neutron diffraction results on iridates by the use of samples enriched in 193Ir, so that the severe absorption problems associated with 191Ir are avoided. Rietveld refinement of the neutron diffraction pattern of isotopically enriched Sr2IrO4 is used to yield a similar result for Ir. However, in practice the Rietveld result is shown to be less reliable because of correlation between the parameters of the fit.

Alkali environments in tellurite glasses

Neutron diffraction measurements are reported for five binary alkali tellurite glasses, xM2O·(100−x)TeO2 (containing 10 and 20mol% K2O, 10 and 19mol% Na2O, and 20mol% 7Li2O), together with 23Na MAS NMR measurements for the sodium containing glasses. Differences between neutron correlation functions are used to extract information about the local environments of lithium and sodium. The Na–O bond length is 2.37(1) Å and the average Na–O coordination number, nNaO, decreases from 5.2(2) for x=10mol% Na2O to 4.6(1) for x=19mol% Na2O. The average Li–O coordination number, nLiO, is 3.9(1) for the glass with x=20mol% Li2O and the Li–O bond length is 2.078(2) Å. As x increases from 10 to 19mol% Na2O, the 23Na MAS NMR peak moves downfield, confirming an earlier report of a correlation of peak position with sodium coordination number. The close agreement of the maximum in the Te–O bond distribution for sodium and potassium tellurite glasses of the same composition, coupled with the extraction of reasonable alkali coordination numbers using isostoichiometric differences, gives strong evidence that the tellurium environment in alkali tellurites is independent of the size of the modifier cation used.

Correlating structure with non-linear optical properties in xAs40Se60·(1-x)As40S60 glasses.

A series of xAs40Se60·(100 - x)As40S60 glasses, where x = 0, 25, 33, 50, 67, 75 and 100 mol% As40Se60, has been studied using neutron and X-ray total scattering, Raman spectroscopy and (77)Se MAS-NMR. The results are presented with measurements of non-linear refractive indices, n2, and densities. There is no evidence for the formation of homopolar bonds in these glasses, but neutron correlation functions suggest that there is a non-random distribution of sulfur and selenium atoms in sulfur-rich glasses. The average number of sulfur atoms at a distance of 3-4 Å from a selenium atom, nSeS, deviates from a linear variation with x in glasses containing <50 mol% As40Se60; n2 for these glasses also varies non-linearly with x. Importantly, a direct comparison of n2 and nSeS gives a linear correlation, suggesting that n2 may be related to the distribution of chalcogen atoms in the glasses.

Symmetry energy from QCD sum rules

We review the recent attempts to calculate the nuclear symmetry energy from QCD sum rules. Calculating the difference between the proton and neutron correlation function in an isospin asymmetric nuclear matter within the QCD sum rule approach, the potential part of the nuclear symmetry energy can be expressed in terms of local operators. We find that the scalar (vector) self-energy part gives negative (positive) contribution to the nuclear symmetry energy, consistent with the results from relativistic mean-field theories. Moreover, the magnitudes are consistent with phenomenological estimates. In terms of the operators, we find that an important contribution to self-energies contributing to the symmetry energy comes from the twist-4 matrix elements, whose leading density dependence can be extracted from deep inelastic scattering experiments. Our result also extends an early success of the QCD sum rule method in understanding the symmetric nuclear matter in terms of QCD variables to the asymmetric nuclear matter case.

Structural studies of lead aluminate glasses

Lead aluminate melts were quenched rapidly with a roller quencher and bulk glasses were formed over a composition range from 72.5 to 80.0 mol% PbO. Pulsed neutron diffraction, 27Al MAS NMR and Raman spectroscopy were used to study the structure of a series of these glasses. The results show that in the glasses the aluminium is four coordinated by oxygen across the compositional range, with a bond length of about 1.76 Å. The Pb–O peak in the neutron correlation function is asymmetric, and it can be modelled in terms of two bond lengths of ∼2.25 Å and ∼2.47 Å, with the majority of the coordination at the shorter distance. There is evidence that most or all of the lead ions are on asymmetric sites, coordinated by three oxygens in a trigonal pyramid arrangement. Both the neutron diffraction and Raman results indicate that the Pb–O bond lengths become shorter with increasing lead content.

분자동력학법에 의한(62-x)CaO·38Al2O3·xBaO 유리의 구조 분석

Molecular dynamics simulation (MD) of (62-x)CaOㆍ38Al₂O₃ㆍxBaO glasses has been carried out using empirical potentials with the covalent term. The simulations closely reproduce the total neutron correlation functions of glass with 5 mol% BaO and physical properties of these glasses such as elastic constants. For these glasses, aluminum is tetrahedrally coordinated by oxygen, but there is a part of fivefold and six-fold coordination of aluminum. There are no major changes to the mid-range structure of glass, as barium is substituted for calcium. To predict the barium coordination number, we have used the bond valence (BV) theory and also compared the results of simulation with Bond valence. The coordination number for oxygen around barium atoms is close to 8 and the average distance of barium and oxygen is nearly 2.80 A. The viscosity of these glasses increases with the content of barium oxide substituted for calcium oxide.

Vibrational spectra of vitreous germania from first-principles

We report on a first-principles investigation of the structural and vibrational properties of vitreous germania $(v\text{\ensuremath{-}}\mathrm{Ge}{\mathrm{O}}_{2})$. Our work focuses on a periodic model structure of 168 atoms, but three smaller models are also studied for comparison. We first carry out a detailed structural analysis both in real and reciprocal spaces. Our study comprises the partial pair correlation functions, the angular distributions, the total neutron correlation function, the neutron and $x$-ray total structure factors, and the Faber-Ziman and Bhatia-Thornthon partial structure factors. We find overall good agreement with available experimental data. We then obtain the vibrational frequencies and eigenmodes. We analyze the vibrational density of states in terms of Ge and O motions, and further in terms of rocking, bending, and stretching contributions. The inelastic neutron spectrum is found to differ only marginally from the vibrational density of states. Using a methodology based on the application of finite electric fields, we derive dynamical Born charge tensors and Raman coupling tensors. For the infrared spectra, we calculate the real and imaginary parts of the dielectric function, including the high-frequency and static dielectric constants. The Raman spectra are shown to be sensitive to the medium-range structure and support an average Ge-O-Ge angle of 135\ifmmode^\circ\else\textdegree\fi{}. We identify the shoulder ${X}_{2}$ as a signature of breathing O vibrations in three-membered rings. Four-membered rings are found to contribute to the main Raman peak. We advance an interpretation for the shoulder ${X}_{1}$ in terms of delocalized bond-bending modes. We derive bond polarizability parameters from the calculated Raman coupling tensors and demonstrate their level of reliability in reproducing the spectra. The calculated vibrational spectra all show good agreement with the respective experimental spectra.

Molecular dynamics simulations of calcium aluminate glasses

Molecular dynamics simulations of a series of calcium aluminate glasses have been carried out using empirical potentials with a covalent term. The simulations closely reproduce the total neutron correlation function of glasses with 30 and 38 mol% Al 2O 3 and physical properties such as elastic constants. For compositions close to the eutectic 37 mol% Al 2O 3, aluminum is tetrahedrally coordinated by oxygen, but the proportion of five-fold and six-fold coordination and also edge-sharing tetrahedra gradually increases with increasing Al 2O 3 content. The coordination number for oxygen around calcium atoms is close to 6 and this involves a larger coordination at a shorter, well-defined distance, followed by a smaller coordination with a broader range of distances. When the Al 2O 3 content decreases, the calcium aluminate structure becomes depolymerised and the average ring size increases. Also reported is an X-ray photoelectron spectroscopy measurement on a glass sample with 38 mol% Al 2O 3, which shows that 38.6 ± 0.9% of the oxygens are non-bridging, in excellent agreement with the simulations.

Structure of tellurite glasses—effects ofK2O orP2O5 additions studied by diffraction

Neutron and x-ray diffraction experiments of high resolving power with neutronsfrom a spallation source and high-energy photons from a synchrotron have beenperformed on compositional series of binary tellurite glasses with additions ofK2O orP2O5 (max. 16 or 32 mol%). Since the P–O bond lengths do not interfere with the Te–Opeaks the Te–O and O–O correlations are approximated by Gaussian fitting of thex-ray and neutron correlation functions up to lengths of 0.28 nm. In the case ofK2O–TeO2 glasses reasonable assumptions are made for the K–O first-neighbour peaks. Te–O and O–Ocoordination numbers are four and five for the glasses of compositions close to pureTeO2 which indicates formation of a three-dimensional network of corner-connectedTeO4 trigonal bipyramids. The tellurite network groups areTeO4 andTeO3 unitsin K2O–TeO2 glassesand TeO4 and TeO5 units in P2O5–TeO2 glasses. Additional Te–O neighbours found at0.23 nm<r<0.26 nmfor K2O–TeO2 glasses suggest theexistence of TeO3+1 unitsand those found at 0.23 nm<r<0.29 nm for the P2O5–TeO2 glasses indicate theexistence of distorted TeO6 polyhedra. Tellurite networks are flexible to form the appropriate coordinationenvironments for quite different ions or groups of opposite charge such asK+ ions and(PO4/2)− tetrahedra wherechange of the TeOn network units provides the needed number of oxygen neighbours.

The use of crystallographic data in interpreting the correlation function for complex glasses

The interpretation of the total correlation function, T(r), for a complex glass is extremely difficult without complementary information, even in the case of the peaks at low r arising from the basic structural units. For example, in alkali borosilicate glasses, there are no less than 10 possible structural units, viz. SiØ4, SiØ3O−, SiØ2O22-, SiØO33-, SiO44-, BØ4-, BØ3, BØ2O−, BØO22- and BO33-, where Ø represents a bridging and O− a (negatively charged) non-bridging oxygen atom. All of these structural units have slightly different bond lengths and, in addition, the borate structural unit parameters change when they are incorporated into the various superstructural units arising from the borate component. The present paper discusses the role of crystallographic information in the analysis of the correlation functions for complex glasses and a summary is presented of accurate crystallographic data for alkali borates, silicates and borosilicates, which are employed to establish optimum bond lengths and angles for the various structural units within the glasses, and the detailed geometry of the borate superstructural units. These parameters form the basis for a more comprehensive interpretation of the neutron correlation functions for a number of glasses from the sodium borosilicate system.

Pulsed neutron diffraction from GeS 2-based sulphide glasses

Pulsed neutron diffraction has been used to investigate the structure of stoichiometric 5(GeS 2)·(As 2S 3) glass. The high real-space resolution reveals chemical disorder in the form of homopolar bonds that cannot be clearly observed by any other direct structural probe. The sulphur–sulphur peak in the neutron correlation function is markedly less reliable than the cation–cation peak for quantifying the chemical disorder. For 5(GeS 2)·(As 2S 3) glass, the cation–cation coordination number, n XX, is 0.24 and this implies a sulphur–sulphur coordination number, n SS, of 0.13.

The structure of vapour-deposited arsenic sulphides

High resolution X-ray and neutron correlation functions have been obtained for arsenic sulphide bulk glass and vapour-deposited films by making measurements to high momentum transfers. These data are compared with a vatiety of models and it is concluded that the structure of the films is dominated by the presence of As 4S 4 molecules in the vapour phase, which results in more As-As bonds than the minimum required by stoichoimetry. The extent to which these As 4S 4 molecules polymerise in the as-deposited film is unclear, but depends strongly on preparation conditions.