Empirical Potential Structure Refinement Modeling Research Articles

The structure of molten calcium ferrite under various redox conditions.

Laser-heated melts based on the 43CaO-57Fe2O3-x eutectic, close to the calcium ferrite (CF) composition, were measured with high-energy X-ray diffraction using aerodynamic levitation over a range of redox states controlled by CO/CO2 gas atmospheres. The iron-oxygen coordination number was found to rise from 4.4 ± 0.3 at 15% Fe3+ to 5.3 ± 0.3 at 87% Fe3+. Empirical potential structure refinement modelling was used to obtain the ferric and ferrous partial pair distribution functions. It was found that the Fe2+ iron-oxygen coordination number is consistently approximately 10% higher in CF than in pure iron oxide, while Fe3+ is essentially identical in all but the most oxygen-rich environments (where it is higher in CF compared with FeOx). The model also shows calcium octahedra to be the dominant species across all redox environments, although the population of CaO7 increases with the availability of oxygen at the expense of CaO4 and CaO5. This article is part of the theme issue 'Exploring the length scales, timescales and chemistry of challenging materials (Part 1)'.

Alkali Metal Ion Recognition by 18-Crown-6 in Aqueous Solutions: Evidence from Local Structures

The underlying recognition mechanisms of alkali metal ions by crown ethers in aqueous solutions are yet to be fully understood at the molecular level. We report direct experimental and theoretical evidence for the structure and recognition sequence of alkali metal ions (Li+, Na+, K+, Rb+, and Cs+) by 18-crown-6 in aqueous solutions by wide-angle X-ray scattering combined with an empirical potential structure refinement modeling and ab initio molecular dynamics simulation. Li+, Na+, and K+ are located in the negative potential cavity of 18-crown-6, with Li+ and Na+ deviating from the centroid of 18-crown-6 by 0.95 and 0.35 Å, respectively. Rb+ and Cs+ lie outside the 18-crown-6 ring and deviate from the centroid of 18-crown-6 by 0.05 and 1.35 Å, respectively. The formation of the 18-crown-6/alkali metal ion complexes is dominated by electrostatic attraction between the cations and the oxygen atoms (Oc) of 18-crown-6. Li+, Na+, K+, and Rb+ form the H2O···18-crown-6/cation···H2O "sandwich" hydrates, while water molecules only hydrate with Cs+ of the 18-crown-6/Cs+ complex on the same side of Cs+. Based on the local structure, the recognition sequence of 18-crown-6 for alkali metal ions in an aqueous solution follows K+ > Rb+ >Na+ >Li+, which is completely different from that (Li+ > Na+ > K+ > Rb+ > Cs+) in the gas phase, confirming that the solvation medium seriously affects the cation recognition of crown ethers. This work provides atomic insights into understanding the host-guest recognition and solvation behavior of crown ether/cation complexes.

In situ Raman and X-ray scattering of a single supersaturated aqueous Mg(NO3)2 droplet ultrasonically levitated.

A single liquid droplet in the air generated by ultrasonic levitation provides such analytical advantages as a small sample volume (~ μL) for expensive proteins, container-free condition for deeply supercooling and supersaturation, time-dependent observation, and homogeneous rapid mixing. The investigation of the properties and structure of a droplet at a molecular level is highly needed for understanding the physicochemical behaviors of a droplet and an underlying mechanism of processes in the droplet. We develop in situ Raman and synchrotron X-ray scattering methods of a single liquid droplet of ~ 1mm size ultrasonically levitated. The composition of a supersaturated Mg(NO3)2 droplet and speciation in the droplet are determined by analyzing the nitrate N-O and the water O-H stretching vibrational Raman bands. The X-ray interference function of an supersaturated Mg(NO3)2 droplet is subjected to an empirical potential structure refinement modeling to reveal the ion solvation, association, and solvent water structure. Furthermore, crystallization of Mg(NO3)2⋅nH2O from a saturated droplet is observed and identified.

Structural analysis of hydrazinium trifluoroacetate aqueous solution by X-ray diffraction and empirical potential structure refinement modeling in the temperature range of 25 to −125 °C

X-ray diffraction of a hydrazinium trifluoroacetate ([N2H5]+ [TFA]-) aqueous solution at 14.4 mol% of N2H5TFA is measured in a temperature range from 25 to −125 °C. The solution in a supercooled region exhibits an anomalous temperature behavior of the heat capacity without ice crystallization taken place for neat water. The X-ray interference functions of an N2H5TFA solution are subjected to empirical potential structure refinement (EPSR) modeling to obtain the site-site pair distribution functions, the coordination number distribution, the angle distribution, and the spatial density function (3D structure). The tetrahedral-like network structure as observed for neat water remains for an N2H5TFA aqueous solution, and the structure is enhanced at temperatures below −75 °C, although the solution does not freeze. The enhancement of the tetrahedral-like network structure could be responsible for the anomalous behavior of the heat capacity of the solution at a low temperature. It is consistent with the scenario of the second critical point of neat water where the transition from high-density water to low-density water is considered to take place.

3D local atomic structure evolution in a solidifying Al-0.4Sc dilute alloy melt revealed in operando by synchrotron X-ray total scattering and modelling

Using synchrotron X-ray total scattering and empirical potential structure refinement modelling, we studied systematically in operando condition the disorder-to-order local atomic structure transition in a pure Al and a dilute Al-0.4Sc alloy melt in the temperature range from 690 °C to 657 °C. In the liquid state, icosahedral short-range ordered Sc-centred Al polyhedrons form and most of them with Al coordination number of 10–12. As the melt is cooled to the semisolid state, the most Sc-centred polyhedrons become more connected atom clusters via vertex, edge and face-sharing. These polyhedrons exhibit partially icosahedral and partially face-centred-cubic symmetry. The medium-range ordered Sc-centred clusters with face-sharing are proved to be the “precursors” of the L12 Al3Sc primary phases in the liquid-solid coexisting state.

Structure of an aqueous RbCl solution in the gigapascal pressure range by neutron diffraction combined with empirical potential structure refinement modeling

An aqueous 3 m (=mol/kg) RbCl solution in D2O is measured at 298 K/0.1 MPa, 298 K/1 GPa, 523 K/1 GPa, and 523 K/4 GPa by neutron diffraction. The interference functions are analyzed by an empirical potential structure refinement (EPSR) modeling. The ion hydration and association and hydrogen-bonded water structure as a function of temperature and pressure are revealed in the pair correlation function, coordination number, triangular distribution, and spatial density function (3D structure). The results show that structure parameters are temperature and pressure-dependent. The second hydration layer of Rb+ and Cl− becomes evident under elevated pressure and temperature conditions. The average oxygen coordination number of Rb+ in the first hydration layer increases from 6.3 ± 1.7 at ambient pressure to 8.9 ± 2.3 at 4 GPa with decreasing coordination distance of 0.290 nm to 0.288 nm. The average oxygen coordination number of Cl− in the first hydration shell increases from 5.9 ± 1.5 at ambient pressure to 9.1 ± 2.1 at 4 GPa, and the corresponding coordination distance decreases from 0.322 nm to 0.314 nm with increasing pressure. The orientation of the water dipole in the first solvation shell of Rb+ and a central water molecule is sensitive to pressure, but that in the first solvation shell of Cl- does not change very much regardless of the thermodynamic condition. The number of contact-ion pairs Rb+-Cl− decreases with elevated temperature and increases with elevated pressure. Water molecules are closely packed, and the tetrahedral hydrogen-bonded network of water molecules no longer exists in extreme conditions.

Structure of soda-lime-aluminosilicate glasses as revealed by in-situ synchrotron powder diffraction experiments

The atomic structure of a soda-lime-aluminosilicate network glass that underwent two different thermal treatments has been investigated by in-situ Synchrotron Powder Diffraction experiments in the 30–1000 ∘C temperature range. First Sharp Diffraction Peak analysis has been initially performed to investigate intermediate range order characteristics: it provided information on volume variations upon heating and cooling, and final relaxation level as a function of the different thermal treatment. Pair Distribution Function analysis has been performed by Empirical Potential Structure Refinement modeling: it pointed out the short range order peculiarities of the samples. In particular, the thermal expansion behaviour of different atomic pairs has been revealed, together with a wide range of structural features like coordination numbers and polymerization degree. The present work well describes the multiple over temperature phenomenology of the investigated composition and discloses how the local range behaves independently from the thermal history of the sample.

The structure of aqueous solutions of hexafluoro-iso-propanol studied by neutron diffraction with hydrogen/deuterium isotope substitution and empirical potential structure refinement modeling.

Neutron diffraction measurements of H/D isotopic substitution are made at room temperature for seven H/D substituted hexafluoro-iso-propanol (HFIP; 1,1,1,3,3,3-hexafluoro-2-propanol)-water mixtures at 0.1, 0.2, and 0.4 HFIP mole fraction (xHFIP). The eight partial structure factors except for the H(CH)-H(CH) pair obtained are subjected to an empirical potential structure refinement (EPSR) method to derive all site-site pair correlation functions. It is found that with increasing HFIP concentration the ice-like network of water disappears between xHFIP = 0.1 and 0.2, followed by the formation of a chain-like water structure embedded in an intrinsic structure of HFIP evolved at xHFIP = 0.4. The hydroxyl group of HFIP forms hydrogen bonds with the surrounding water molecules at all HFIP mole fractions investigated. There is no evidence that the water structure is well defined around the CF3 groups of HFIP, but water molecules surround tangentially the CF3 groups of HFIP.

Dihydrogen Bonds in Aqueous NaBD4 Solution by Neutron and X-ray Diffraction.

Neutron diffraction, X-ray diffraction, and empirical potential structure refinement modeling were employed to study the structure of alkaline aqueous NaBD4 solutions at different NaBD4 concentrations and temperatures. In 1.0 mol·dm-3 NaBD4 aqueous solutions, about 5.6 ± 1.6 water molecules bond to BD4- via tetrahedral edges or tetrahedral corners without a very specific hydration geometry; that is, each hydrogen atom of BD4- bonds to 2.2 ± 1.0 water molecules through dihydrogen bonds with the D(B)···D(W) distance of 1.95 Å. The number of dihydrogen bonds decreases with increasing concentration and increases with temperature. Dihydrogen bonding is a predominantly electrostatic interaction which shows relatively lower directionality and saturability in comparison with the regular hydrogen bonds between water molecules. The water orientation around BD4- shows that the proportion of tetrahedral-edge dihydrogen bonds increases with temperature and decreases with concentration.

Solution structure of propane and propene dissolved in the ionic liquid 1-butyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}imide from neutron diffraction with H/D substitution and empirical potential structure refinement modelling

Neutron scattering combined with H/D-isotopic substitution, fitting the experimental data using the Empirical Potential Structure Refinement (EPSR) method has been used to investigate the liquid structure of 1-butyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}imide () and solutions of propane (0.15 mol fraction) and propene (0.23 mol fraction) dissolved in the ionic liquid dissolved after pressurising at 6 bar. Both strong cation-anion and cation-cation correlations are observed in the first coordination shell with anions and cations occupying mutually exclusive positions around the imidazolium cation, consistent with previous models derived from molecular dynamics simulation. No significant changes in the neutron scattering data were observed after dissolution of either propane and propene suggesting that the primary coulombic structure of the ionic liquid is preserved. Modelling the data with EPSR reveals subtle differences in the cation-hydrocarbon correlations, with propene associated with all three imidazolium ring C-H positions whereas propane exhibits less association with the C(2)-H ring position and has a greater level of correlation with the terminal group of the cation butyl-chain.

Hydrogen bonding and clusters in supercritical methanol–water mixture by neutron diffraction with H/D substitution combined with empirical potential structure refinement modelling

ABSTRACTNeutron diffraction measurements of H/D isotopic substitution have been performed for seven H/D substituted methanol-water mixtures of 0.3 mol fraction of methanol (xM) under the supercritical (618 K, 100 MPa) and ambient (298 K, 0.1 MPa) conditions. The seven structure factors obtained were subjected to an empirical potential structure refinement (EPSR) modelling to derive all site-site pair correlation functions, coordination number distributions, spatial density functions, and cluster distributions. Water has a four coordinated structure in the first coordination shell under both ambient and supercritical conditions; however, the spatial density distribution of water molecules in the second coordination shell is delocalised under the supercritical condition. The mean coordination number of all atomic pairs with hydrophilic interactions decreases in the supercritical state. On the other hand, the mean coordination number of interactions between the hydrophobic part of methanol and water molecule is less sensitive to temperature. In the supercritical condition, water clusters with a wide size distribution are generated in a methanol-water mixture as well as in pure water. Since the critical temperature of a methanol-water mixture is lower than that of pure water, it can be concluded that the addition of methanol can generate fragment water clusters at a lower temperature.

Role of short range order on crystallization of tectosilicate glasses: A diffraction study

The relationship between glass structure and crystallization behavior has remained elusive, though a general solution would have broad applications. In this work, three-component glasses were studied in the system MTSixO2x+2, where M = Na, Li, or Ca, T = Al, B, or Fe, and x = 1, 2, and 3. These glasses, selected to systematically explore network and modifier substitutions, included mineralogically important silicate chemistries (i.e., albite, jadeite, carnegieite, nepheline, anorthite, eucryptite, spodumene, aegirine, reedmergnerite, malinkoite). Glasses were interrogated using neutrons and synchrotron X-rays, and empirical potential structure refinement (EPSR) modeling was performed to compare the average glass structures to the analogous crystalline references. Through EPSR modeling, it was shown that similarity in the coordination number of the non-network cations in glass systems (i.e., alkali and alkaline earth) predicts which glasses easily crystallize an isochemical phase during cooling from melt. Average coordination number of the M and T type cations of glass versus isochemical crystal is proposed as a metric to predict crystallization. This metric is compared to other proposed metrics such as normalized temperatures, change in density, fragility, and thermodynamic parameters. This the first study to employ EPSR modeling to relate crystallization propensity of isochemical crystals to network modifier short-range order.

Structure of Aqueous Trehalose Solution by Neutron Diffraction and Structural Modeling.

The molecular structure of an aqueous solution of the disaccharide trehalose (C12H22O11) has been studied by neutron diffraction and empirical potential structure refinement modeling. Six different isotope compositions with 33 wt % trehalose (corresponding to 38 water molecules per trehalose molecule) were measured to ensure that water-water, trehalose-water, and trehalose-trehalose correlations were accurately determined. In fact, this is the first neutron diffraction study of an aqueous trehalose solution in which also the nonexchangeable hydrogen atoms in trehalose are deuterated. With this approach, it was possible to determine that (1) there is a substantial hydrogen bonding between trehalose and water (∼11 hydrogen bonds per trehalose molecule), which is in contrast to previous neutron diffraction studies, and (2) there is no tendency of clustering of trehalose, in contrast to what is generally observed by molecular dynamics simulations and experimentally found for other disaccharides. Thus, the results give the structural picture that trehalose prefers to interact with water and participate in a hydrogen-bonded network. This strong network character of the solution might be one of the key reasons for its extraordinary stabilization effect on biological materials.

A Neutron Diffraction Study of the Electrochemical Double Layer Capacitor Electrolyte Tetrapropylammonium Bromide in Acetonitrile.

Neutron diffraction with isotopic substitution has been used to characterize the bulk liquid structure of the technologically relevant electrolyte solution, 1 M tetrapropylammonium bromide (TPA Br) in acetonitrile (acn), and of pure deuterated acetonitrile. Empirical potential structure refinement modeling procedures have been used to extract detailed structural information about solvent-solvent, solvent-ion, and ion-ion correlations. Analysis of the refined data shows the expected local dipolar conformation of acn in the pure solvent. This short-range dipolar ordering is also present within the solutions of TPA Br in acn, and it affects how the solvent orders itself around the ions. The solvation numbers of the TPA cations and the bromide anions are deduced, 8 and 5, respectively, as are the orientations of the solvent molecules that surround the ions. Evidence for ion association is also presented, with nearly two-thirds of the ions in the system being in associated pairs or clusters.

ラマン散乱，X線回折，及びEmpirical Potential Structure Refinementモデリングによる亜臨界硝酸マグネシウム水溶液の三次元構造の可視化

常温常圧から40 MPa，350℃ までの1 mol dm－3硝酸マグネシウム水溶液のラマン散乱測定を行った．温度が上昇するにつれて，1050 cm－1のN－O対称伸縮振動バンド（n1）は低波数側へシフトした．一方，2540 cm－1の水のOD対称伸縮振動バンドは，温度上昇とともに高波数側へシフトした．いずれのバンドにも200℃ 付近に屈折点が観測され，NO3－イオンの水和と溶媒の水の構造変化が起こることが示唆された．40 MPa，常温から210℃ までの硝酸マグネシウム水溶液についてX線回折測定を行った．得られた構造因子を基に二体ポテンシャルを修正する，empirical potential structure refinement（EPSR）モデリングにより，溶媒水とイオン水和及びイオン対の三次元構造を可視化した．溶媒水の第一配位殻では温度上昇伴う構造変化は見られなかった．しかし，第二水和殻は平均配位数が25℃，0.1 MPaで10.5から，210℃，40 MPaで8.5へ減少した．Mg2＋イオンは，25℃，0.1 MPaで6個の水分子が八面体構造で配位しているが，210℃，40 MPaでは平均1個のNO3－イオンが第一水和殻に侵入してMg2＋とイオン対を形成した．NO3－イオンの平均配位数は，25℃，40 MPa下では11.2であり，210℃，40 MPaでは9.8へ減少した．NO3－イオンは，Mg2＋イオンに単座配位し，Mg2＋－ON－Nの角度は約150°であった．

Solvation of Inorganic Nitrate Salts in Protic Ionic Liquids

The bulk nanostructure of several inorganic salt solutions in protic ionic liquids is elucidated using neutron diffraction and empirical potential structure refinement modeling. The protic ionic liquids studied are ethylammonium nitrate (EAN) and ethanolammonium nitrate (EtAN), which are mixed with either LiNO3, Mg(NO3)2, Ca(NO3)2, or Al(NO3)3 at 1:10 or 1:30 solute:solvent mol:mol ratios. The models show inorganic metal ions are solvated within the polar domains of the nanostructure and can induce significant differences in bulk solvent nanostructure from that of the pure ionic liquids. For EtAN, the uncharged groups aggregate and form an apolar domain in spite of the cation’s reduced amphiphilicity because the trans rotamer is favored when an inorganic salt is added.

Neutron and X-ray diffraction and empirical potential structure refinement modelling of magnesium stabilised amorphous calcium carbonate

Amorphous calcium carbonate (ACC) plays a key role in biomineralisation processes in sea organisms. Neutron and X-ray diffraction have been performed for a sample of magnesium-stabilised ACC, which was prepared with a Mg:Ca ratio of 0.05:1 and 0.25 H2O molecules per molecule of CO3. The empirical potential structure refinement method has been used to make a model of magnesium-stabilised ACC and the results revealed a fair agreement with the experimental diffraction data. The model has well-defined CO3 and H2O molecules. The average coordination number of Ca is 7.4 and is composed of 6.8 oxygen atoms from CO3 molecules and 0.6 oxygen atoms from H2O molecules. The average CaO bond length is 2.40Å. The distribution of Ca in the model is homogeneous with a uniformly distributed Ca-rich network and no evidence of the Ca-poor channels as previously reported for a reverse Monte Carlo model of ACC.

The temperature dependent structure of liquid 1-propanol as studied by neutron diffraction and EPSR simulations

The structure of liquid 1-propanol is investigated as a function of temperature using neutron diffraction together with Empirical Potential Structure Refinement modelling. The combined diffraction and computer modelling analysis demonstrates that propanol molecules form hydrogen bonded clusters with a relatively wide size distribution, which broadens at lower temperatures. We find that the cluster size distribution is well described by a recently proposed statistical model for branched H-bonded networks [P. Sillrén, J. Bielecki, J. Mattsson, L. Börjesson, and A. Matic, J. Chem. Phys. 136, 094514 (2012)]. The average cluster size increases from ~3 to 7 molecules, whilst the standard deviation of the size distribution increases from 3.3 to 8.5 as the temperature is decreased from 293 to 155 K. The clusters are slightly branched, with a higher degree of branching towards lower temperatures. An analysis of the cluster gyration tensor (R(mn)) reveals an average elongated ellipsoidal shape with axes having proportions 1:1.4:1.9. We find that the average radius of gyration has a cluster size dependence consistent with that of fractal clusters, R(g) ∝ n(1/D), with a fractal dimension D ≈ 2.20, which is close to D = 2.00 expected for an ideal random walk or D = 2.11 expected for reaction limited aggregation. The characteristic angles between the H-bonded OH-groups that constitute the clusters show only a weak temperature dependence with O-H···O angles becoming more narrowly distributed around 180° at lower temperatures.

Structure of water from ambient to 4 GPa revealed by energy-dispersive X-ray diffraction combined with empirical potential structure refinement modeling

X-ray diffraction measurements in an energy-dispersive mode have been made on water under various thermodynamic conditions of 298K/30MPa, 473K/30MPa and 573K/30MPa on a laboratory X-ray diffractometer. All the X-ray structure factors as well as those of water already measured at 298K/1GPa, 473K/0.35GPa and 486K/4GPa by using synchrotron X-ray radiation were subjected to empirical potential structure refinement (EPSR) modeling to reveal the detailed hydrogen bonding features in terms of partial pair correlation function, coordination number and three-dimensional spatial density function as a function of temperature and pressure. It has been shown to what extent the tetrahedral hydrogen-bonded network of water is perturbed by pressure and temperature. Structural characteristics of liquid water are discussed in connection with unique properties and functions of water under extreme conditions.

Nature and distribution of iron sites in a sodium silicate glass investigated by neutron diffraction and EPSR simulation

Abstract The short and medium range structure of a NaFeSi2O6 (NFS) glass has been investigated by high-resolution neutron diffraction with Fe isotopic substitution, combined with Empirical Potential Structure Refinement (EPSR) simulations. The majority (∼60%) of Fe is 4-coordinated ([4]Fe) and corresponds only to ferric iron, Fe3+, with a distance d [ 4 ] Fe 3 + - O = 1.87 ± 0.01 A. This is at variance with the 3D-structure predicted by glass stoichiometry. The existence of a majority of [4]Fe3+ sites illustrates a glass structure that differs from the structure of crystalline NaFeSi2O6, which contains only octahedral Fe3+. The EPSR modeling of glass structure shows that [4]Fe3+ is randomly distributed in the silicate network and shares corner with silicate tetrahedra. The network-forming behavior of [4]Fe3+, coupled with the presence of Na+ ions acting as charge-compensators, is at the origin of peculiar physical properties of Fe-bearing glasses, such as the increase of the elastic modulus of sodium silicate glasses with increasing Fe-concentration. Our data provide also direct evidence for 5-coordinated Fe, with an average distance d [ 5 ] Fe - O = 2.01 ± 0.01 A. This second Fe population concerns both Fe2+ and Fe3+. 5-Coordinated Fe atoms tend to segregate by sharing mainly edges. The direct structural evidence of the dual role of ferric iron in NFS glass provides support for understanding the peculiar properties of NFS glass, such as magnetic, optical, electronic or thermodynamic properties.