The Structure of Liquids. I.

Finbak, Chr.; Schwarz, Birgit; Melaja, Asko; Kainulainen, Aune; Halonen, Aira; Pulkkinen, Erkki

doi:10.3891/acta.chem.scand.03-1279

Cited by 69 publications

(9 citation statements)

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“…Herein the same definitions of the real‐ and reciprocal‐space scattering functions are used as in our previous work 2 . The real‐space total correlation function is defined by

T^{R} false(r false) = T^{R, 0} false(r false) + \frac{2}{π} \int_{0}^{\infty} Q i^{R} (Q) M (Q) \sin (r Q) d Q,,

where R = N or X denotes the radiation type; i N ( Q ) is the measured distinct 57 neutron scattering, whereas

i^{X} false(Q false) = \frac{i (Q)}{{(\sum_{i = 1}^{n} c_{i} f_{i} (Q))}^{2}},

is the measured distinct X‐ray scattering after division by a sharpening 58 function used to approximately eliminate the X‐ray form factor, f i ( Q ), Q ‐dependence of the scattering 59 . Subscripts i denote elements of the periodic table and c i are atomic fractions.…”

Section: Methodsmentioning

confidence: 99%

Lead silicate glass structure: New insights from diffraction and modeling of probable lone pair locations

et al. 2021

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Structures of binary PbO‐SiO2 glasses have been studied in detail over the compositional range 35 to 80 mol% PbO using high‐resolution neutron diffraction, high‐energy X‐ray diffraction, static 207Pb NMR, and structural modeling. The changes in the local environment of Pb(II) are subtle; it has a low coordination to oxygen (∼3 to 4) plus a stereochemically active electron lone pair and, thus, behaves as a glass network forming (or intermediate) cation over the entire composition range. This conclusion contradicts previous reports that Pb(II) is a network modifier at low concentrations, and is supported by an analysis of lead and alkaline earth silicate glass molar volumes. The Pb‐O peak bond length shortens by 0.04 Å with increasing PbO content, indicating stronger, more covalent bonding, and consistent with an increase in the number of short (≤ 2.70 Å) Pb‐O bonds, from 3.3 to 3.6. This is accompanied by increased axial symmetry of the Pb(II) sites, and is interpreted as a gradual transition toward square pyramidal [PbO4] sites such as those found in crystalline PbO polymorphs. An attendant decrease in the periodicity associated with the first sharp diffraction peak (FSDP) toward that of β‐PbO, accompanied by increases in the correlation lengths associated with the plumbite network (FSDP) and silicate anions (neutron prepeak), provides evidence of increased intermediate‐range order and has implications for the glass forming limit imposed by crystallization. Pb(II) electron lone pairs occupy the natural voids within the silicate network at low PbO contents, while at high PbO contents they aggregate to create voids that form part of the plumbite network, analogous to the open channels in Pb11Si3O17 and the layered structures of α‐ and β‐PbO. Si‐O and Pb‐O bond lengths have been correlated with 29Si and 207Pb NMR chemical shifts, respectively. This is the first time that such correlations have been demonstrated for glasses and attests to the accuracy with which pulsed neutron total scattering can measure average bond lengths.

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“…Herein the same definitions of the real‐ and reciprocal‐space scattering functions are used as in our previous work 2 . The real‐space total correlation function is defined by

T^{R} false(r false) = T^{R, 0} false(r false) + \frac{2}{π} \int_{0}^{\infty} Q i^{R} (Q) M (Q) \sin (r Q) d Q,,

where R = N or X denotes the radiation type; i N ( Q ) is the measured distinct 57 neutron scattering, whereas

i^{X} false(Q false) = \frac{i (Q)}{{(\sum_{i = 1}^{n} c_{i} f_{i} (Q))}^{2}},

Section: Methodsmentioning

confidence: 99%

Lead silicate glass structure: New insights from diffraction and modeling of probable lone pair locations

et al. 2021

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“…is the measured distinct X‐ray scattering after division by a sharpening 40 function used to approximately eliminate the X‐ray form factor ( f i ( Q ) 41 ) Q ‐dependence of the scattering. Subscripts i denote elements of the periodic table and c i are atomic fractions.…”

Section: Methodsmentioning

confidence: 99%

Structural origin of the weak germanate anomaly in lead germanate glass properties

et al. 2021

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Binary PbO–GeO2 glasses have been studied in detail from 5 to 75 mol% PbO using high‐resolution neutron diffraction, high‐energy X‐ray diffraction, 207‐Pb NMR, pycnometry, and thermal analysis. The Ge–O coordination number displays a broad maximum nGeO = 4.14(3) close to 27 mol% PbO. This is smaller than the maximum nGeO = 4.3 reported in CaO–GeO2 glasses but occurs at a similar composition. This structural behavior appears to explain the relatively weak germanate anomaly manifest in lead germanate glasses, for example as a maximum in the measured atom number density and a plateau in the glass transition temperatures. The structural role of Pb(II) is complex. On the one hand, short covalent Pb–O bonds and small Pb–O coordination numbers of ∼3 to 4 indicate glass network former character for Pb(II), associated with a stereochemically active electron lone pair. On the other hand, the presence of some GeO5 or GeO6 units, in addition to the majority GeO4 tetrahedral species, indicates some modifier character of Pb(II) at low PbO contents, giving rise to the observed weak germanate anomaly, as well as elongation and enhanced ionicity of the Pb–O bonds. Overall, the observed structural behavior of Pb(II) in lead germanate glasses appears as intermediate between that observed in lead silicate and lead borate glasses. Despite rapid quenching, at low PbO contents, the glasses studied exhibited nanoscale heterogeneity, evidenced by small‐angle X‐ray scattering consistent with the early stages of spinodal decomposition.

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“…Not only is this data usually the least reliable, but any discontinuity at Smax is increased by sharpening, giving an increased ripple. Finbak (1949) proposed that the electronic RDF, calculated by taking gZ(s) = 1, was more reliable in studies of atomic liquids. With g2(s) constant, sZ(s) decays more rapidly and termination is less of a problem.…”

Section: Electronic Rdfmentioning

confidence: 99%

“…Not only is this data usually the least reliable, but any discontinuity at Smax is increased by sharpening, giving an increased ripple. Finbak (1949) Bjornhaug, EUefsen & Tonnesen (1954).…”

Section: Electronic Rdfmentioning

confidence: 99%

An improved transformation procedure for radial distribution function analysis

Lovell¹,

Mitchell²,

Windle³

1979

Acta Cryst Sect A

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Various methods of reducing the effect of termination error on radial distribution functions are briefly reviewed. A new approach is introduced in which the RDF is calculated by generating the Fourier transform at predetermined points. The resulting sampled transform is relatively free of termination ripple and the spacing of the points reflects the true resolution of the method for the particular, experimentally limited, Smax. The optimum choice of sampling points is determined in relation to special data terminations such as at a zero value of the interference functions or at a peak or trough position. The effectiveness of the sampled transform routine in reducing termination error is demonstrated by applying it to prematurely truncated interference functions derived from scattering data from atactic polystyrene. The advantage of the sampled transform approach to RDF analysis is that it prevents a termination discontinuity in the interference function, such as is often unavoidable even when special care is taken to apply precise corrections to the data, from causing an obscuring ripple on the RDF. In fact, in the extreme, it enables generation of useful RDF's of glassy polymers from data which have been neither corrected nor normalized.

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The Structure of Liquids. I.

Cited by 69 publications

References 0 publications

Lead silicate glass structure: New insights from diffraction and modeling of probable lone pair locations

Lead silicate glass structure: New insights from diffraction and modeling of probable lone pair locations

Structural origin of the weak germanate anomaly in lead germanate glass properties

An improved transformation procedure for radial distribution function analysis

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