Liquid Structure

Project staff

Current research activities:

  • Determination of the microscopic structure of disordered materials using diffraction methods and computer modelling (primarily Reverse Monte Carlo, RMC). Systems studied include:
    • Covalent glasses, such as simple oxide glasses, multi-component borosilicate based glasses and chalcogenide glasses.
    • Metallic glasses (amorphous metallic alloys).
    • Simple molecular liquids.
    • Aqueous solutions.
  • Atomic and magnetic structure of nano- and microcrystalline oxide materials.
  • Residual stress and texture investigations, using high resolution neutron diffraction.
  • Development of the Reverse Monte Carlo method of structural modelling.


  • PSD two-axis neutron diffractometer with position sensitive detectors.
  • MTEST neutron diffractometer.
  • NRAD neutron radiography station, in cooperation with the KFKI Atomic Energy Research Institute.

Recent results

( 2019 2018 2017)

Results in 2020

Solvent-separated anion pairs in concentrated solutions. — Hydrogen bonding to chloride ions in various aqueous environments has been discussed many times over the past more than 5 decades. Still, the possible role of such anion-to-water type hydrogen bonds (HB) in networks of HB-s has not been investigated in any detail. Here, computer models of concentrated aqueous LiCl solutions are considered and usual HB network characteristics, such as distributions of cluster sizes and of cyclic entities, are computed for the models by (1) taking and (2) not taking chloride ions into account. During the analysis of hydrogen bonded rings, a significant amount of ‘solvent separated anion pairs’ (see Fig.1) have been detected at high LiCl concentrations. It is demonstrated that including the halide anions into the network does make the interpretation of structural details significantly more meaningful than when considering water molecules only. Finally, simulated structures generated by ‘good’ and ‘bad’ potential sets have been compared on the basis of the tools developed here, and it is shown that the novel concept (1) is, indeed, helpful from this respect, too.

Figure 1. Snapshot of a simulated particle configuration with a very high LiCl concentration of 19.55 mol/kg. A 5-membered ring is in the front, with 2 Cl- ions and 3 water molecules; the two anions are separated by a water molecule, i.e., the anions are `solvent-separated`.

Temperature-dependent structure of alcohol—water liquid mixtures. — Our group is in the midst of a long-term systematic investigation in this field; as a first step, experimental and simulated results have been published for methanol-water mixtures. Experimentally, these mixtures have been investigated by high-energy synchrotron X-ray and neutron diffraction at low temperatures. It was thus possible to report the first complete sets of both X-ray and neutron weighted total scattering structure factors over the entire composition range (at 12 different methanol concentrations (xM) from 10 to 100 mol%) and at temperatures from ambient down to the freezing points of the mixtures. The new diffraction data may later be used as reference in future theoretical and simulation studies. Measured data were interpreted by molecular dynamics simulations, in which the all atom OPLS/AA force field model for methanol was combined with both the SPC/E and TIP4P/2005 water potentials. Both combinations provide at least semi-quantitative agreement with measured diffraction data. As a general trend, the average number of hydrogen bonds increases upon cooling. However, the number of hydrogen bonds between methanol molecules slightly decreases with lowering temperatures in the concentration range between ca. 30 and 60 mol % alcohol content. The same is valid for water-water hydrogen bonds above 70 mol % of methanol content, from room temperature down to 193 K.

Short range order and topology of Ge-Ga-Te glasses. — Due to their broad infrared transmission window glassy tellurides are extensively used in various fields of IR optics. The general strategy to find tellurides with excellent glass forming ability is to alloy the prototype Ge-Te system with a third component. Glasses with Ge-X-Te (X = Ga, As, Se, I, Ag, AgI) composition often possess a broad supercooled liquid region that makes it possible to shape bulk infrared lenses or draw fibers transmitting up to at least 18 μm. Structural background of glass forming of GexGaxTe100-2x (x = 7.5, 10, 12.5, 14.3) glasses was investigated by diffraction techniques and EXAFS . Models were obtained by fitting experimental datasets simultaneously in the framework of the reverse Monte Carlo simulation technique. It was shown that Ga and Ge atoms are mostly fourfold coordinated while NTe, the average coordination number of Te increases with Ga content (NTe = 2.35 ± 0.1 for x = 14.3). The majority of Ge/Ga atoms are linked to other Ge/Ga atoms via one or two common Te neighbors forming corner and edge sharing tetrahedra.

Figure 2. Part of the model of the Ge7.5Ga7.5Te85 glass obtained by RMC simulation. The Ge, Ga and Te atoms are represented by magenta, blue and grey balls, respectively. Two corner sharing tetrahedra are marked with orange, a short chain of Te atoms is highlighted by red

Results in 2019

Short range order and topology of Ge-Te glasses. — Detailed knowledge of the structure of binary Ge-Te glasses is useful in the structural investigations of more complex telluride glasses used in infrared optics or information technology. A thorough experimental study may also inspire theoreticians by providing them with reliable structural models. The structure of GexTe100-x (x = 14.5, 18.7, 23.6) glasses prepared by twin roller quenching technique was investigated by neutron diffraction, X-ray diffraction and Ge-K-edge X-ray absorption spectroscopy measurements. Large scale structural models were obtained for each composition by fitting the experimental datasets in the framework of the reverse Monte Carlo technique . It was found that the majority of Ge and Te atoms satisfy the 8-N rule. Simulation results indicate that Ge-Ge bonding is not significant for x = 14.5 and 18.7. The shape and position of the first peak of the Ge-Ge partial pair correlation function evidence the presence of corner sharing tetrahedra already in compositions (x = 14.5 and 18.7) where ’sharing’ of a Te atom by two Ge atoms could be avoided due to the low concentration of Ge (see Fig. 1).

Figure 1. Decompo­sition of the first peak of gGeGe(r) of Ge18.7Te81.3 to contri­butions from corner sharing (CS) tet­rahedra, edge sharing (ES) tet­rahedra and topolo­gically distant Ge-Ge pairs.

Structure and dy­namics of isopropa­nol-water liquid mix­tures. — Series of molecular dynamics simulations for 2-propanol−water mixtures, as a function of temperature (between freezing and room temperature) and composition (molar fraction of isopropanol, xip:  0, 0.5, 0.1, and 0.2), have been performed for temperatures reported in the only available experimental structure study. It is shown that, when the all-atom optimized potentials for liquid simulations (OPLS) interatomic potentials for the alcohol are combined with the TIP4P/2005 water model, near-quantitative agreement with measured X-ray data, in the reciprocal space, can be achieved . Such an agreement justifies detailed investigations of structural, energetic, and dynamic properties on the basis of simulation trajectories. Here, the focus was placed on characteristics related to hydrogen bonds (HB): cluster-, and in particular, ring formation, energy distributions, and lifetimes of HB-s have been scrutinized for the entire system, as well as for the water and isopropanol subsystems. It is demonstrated that, similar to ethanol−water mixtures, the occurrence of 5-membered-hydrogen-bonded rings are significant, particularly at higher alcohol concentrations. Concerning HB energetics, an intriguing double maximum appears on the alcohol−alcohol HB energy distribution function. HB lifetimes have been found significantly longer in the mixtures than they are in pure liquids. As seen in Figure 2a, the local order of water molecules in the first shell is clearly a tetrahedral one. If we plot the energy distribution function on this surface (first shell), an attractive interaction between −3.0 and −6.0 kcal/mol is found. On the other hand, the first shell around O atoms of 2-propanol molecules appears in the H-bond donor and acceptor directions, but the structure of the second shell is not much ordered (Figure 2b). Concerning Figure 2c,d, the typical tetrahedral spatial distribution of neighbors (in the 1st and 2nd shells) around water molecules is clearly preserved also at a lower temperature (at 258 K).

Figure 2. (a) First and second shells of the space density distribution (SDD) for water around water at 298 K. (Water−water energy distribution function (EDF) is represented by the color scale only in the case of the First shell). (b) First and second shells of the SDD for 2-propanol around 2-propanol at 298 K. (2-Propanol−2-propanol EDF is represented by the color scale only in the case of the First shell.) (c) second shell of the SDD for water around water at 298 K (water−water EDF is represented by color coding). (d) second shell of the SDD for water around water at 258 K (water−water EDF is represented by color coding). All results are shown for xip = 0.2.

Results in 2018

Understanding disordered structures. — Our research group is involved in the investigation of short range order of liquids, amorphous materials and disordered crystals. We combine experimental data, such as X-ray and neutron diffraction structure factors and EXAFS spectra, with computer modeling tools, such as Reverse Monte Carlo (RMC) and molecular dynamics (MD) simulations. As a result of such a modelling approach, large configurations (typically tens of thousands of atoms) are provided that are energetically reasonable and consistent (within errors) with experimental data. These configurations are then subjected to various geometrical analyses, so that specific questions concerning the structure of a material may be answered. The group is also responsible for the maintenance and operation of the MTEST neutron diffractometer installed at the 10 MW Budapest Research Reactor. Below we provide some selected results from the year 2018.

Covalent glasses. — Short-range order of As40-xCuxTe60 (x = 0, 10, 20, 25, 30) glasses has been studied by neutron- and X-ray diffraction, combined with extended X-ray absorption fine structure (EXAFS) measurements at the K-edges of all components. Large-scale structural models have been generated by fitting the experimental datasets simultaneously in the framework of the reverse Monte Carlo simulation technique. These simulations revealed that there are about 3 As or Te atoms around As and 2 As or Te atoms around Te. Both As and Te possess Cu neighbors.

Figure 1. Comparison of As-Cu and Cu-Cu partial pair correlation functions (left) and As K-edge EXAFS fits (right) of glassy As20Cu20Te60 obtained with and without As-Cu bonds

The presence of Cu-As bonds was proven by dedicated simulation runs. In Fig. 1, we compare the Cu-Cu and Cu-As partial pair correlation functions and the As20Cu20Te60 As K-edge fits obtained with and without Cu-As bonds. Two observations can be made here: i) the fit quality worsens upon eliminating Cu-As bonding, ii) a secondary Cu-Cu peak appears in the Cu-Cu partial pair correlation function to compensate for the lack of the Cu-As peak. This secondary Cu-Cu peak is necessary to maintain at least the Cu K-edge EXAFS fit quality. The presence of As-Cu bonds was verified by dedicated simulation runs. The Cu-Te bond length is 2.57±0.02Å while the Cu-As distance is as high as 2.86±0.04Å. The results further showed that besides As and Te, Cu atoms also bind to Cu. The total coordination number of Cu is significantly higher than 4 for x = 25 and 30.

Temperature-dependent structure and dynamics of ethanol-water mixtures at low alcohol contents. — By making use of literature X-ray diffraction data, extensive molecular dynamics computer simulations have been conducted for ethanol-water liquid mixtures in the water-rich side of the composition range, with 10, 20 and 30 mol% of the alcohol, at temperatures between room temperature and the experimental freezing point of the given mixture. All-atom type (OPLS) interatomic potentials have been assumed for ethanol, in combination with two kinds of rigid water models (SPC/E and TIP4P/2005). Both combinations have provided excellent reproductions of the experimental X-ray total structure factors at each temperature; this provided a strong basis for further structural analyses. Beyond partial radial distribution functions, various descriptors of hydrogen-bonded assemblies, as well as of the hydrogen-bonded network have been determined from the simulated particle configurations. A clear tendency was observed towards that an increasing proportion of water molecules participate in hydrogen bonding with exactly 2 donor and 2 acceptor sites as the temperature decreases. Concerning larger assemblies held together by hydrogen bonding, the main focus was put on the properties of cyclic entities: it was found that, similarly to methanol-water mixtures, the number of hydrogen-bonded rings has increased with decreasing temperature. However, for ethanol-water mixtures the dominance of not the six-, but of the five-fold rings could be observed (see Fig. 2).

Figure 2. Temperature dependence of hydrogen bond ring size distribu­tion in water-20 mol% ethanol mixture

Starting from the molecular dynamics simulations mentioned above, we took a closer look at the time-dependent behavior of molecules. Temperature-dependent hydrogen bond energetics and dynamical features, such as the diffusion coefficient and reorientational times, have been determined for ethanol-water mixtures with 10, 20 and 30 mol % of ethanol. Concerning pairwise interaction energies between molecules, it was found that water-water interactions become stronger, while ethanol-ethanol ones become significantly weaker in the mixtures, than the corresponding values characteristic to the pure substances. Concerning the diffusion processes, for all concentrations the activation barrier of water and ethanol molecule becomes very similar to each other. Reorientational motions of water and ethanol become slower as ethanol concentration is increasing. Characteristic reorientational times of water in the mixtures are substantially longer than these values in the pure substance. On the other hand, for ethanol this change is only moderate. Reorientational motions of water (especially the ones related to the H-bonded interaction) become very similar for those of ethanol in the mixtures.

The structure of the simplest liquid aldehydes. — Although aliphatic aldehydes (a.k.a. alkanals, compounds with chain-end –CHO groups) constitute an essential group of organic substances, structural studies of them are scarce. Synchrotron X-ray diffraction experiments and molecular dynamics simulations have been performed on simple aliphatic aldehydes in the liquid state, from propanal to nonanal. The performance of the OPLS all-atom interaction potential model for aldehydes has been assessed via direct comparison of simulated and experimental total scattering structure factors. In general, MD results reproduce the experimental data at least semi-quantitatively. However, a slight mismatch can be observed between the two datasets in terms of the position of the main diffraction maxima. Partial radial distribution functions (PRDF) have also been calculated from the simulation results. Clear differences could be detected between the various O-H partial radial distribution functions, depending on whether the H atom is attached to the carbon atom that is doubly bonded to the oxygen atom of the aldehyde group or not. Based on the 3 different O-H PRDF-s, as well as on the various H-H PRDF-s, it may be suggested that neighboring molecules turn toward each other (somewhat) preferentially by their aldehyde ends. From gOO(r) and gC’C’(r), and from intermolecular angular correlations it may be discerned that no (or at most, extremely weak) orientational correlations are present between neighboring aldehyde groups.

As a follow-up of the above series of experiments, the total scattering structure factors of pure liquid n-pentanol, pentanal, and 5 of their mixtures have been determined by high-energy synchrotron X-ray diffraction experiments. For the interpretation of the measured data, molecular dynamics computer simulations were performed, utilizing ‘all-atom’ type force fields. The diffraction signals, in general, resemble each other over most of the monitored scattering variable (Q) range above 1 Å-1, but the absolute values of the intensities of the small-angle scattering maximum (‘pre-peak’, ‘first sharp diffraction peak’) around 0.6 Å-1 change in an unexpected fashion, non-linearly with the composition. MD simulations are not able to reproduce this low-Q behavior; on the other hand, they do reproduce the experimental diffraction data above 1 Å-1 rather accurately. Partial radial distribution functions are calculated based on the atomic coordinates in the simulated configurations. Inspection of the various O-O and O-H partial radial distribution functions clearly shows that both the alcoholic and the aldehydic oxygens form hydrogen bonds with the hydrogen atoms of the alcoholic OH-group.

Aqueous salt solutions. — Highly concentrated aqueous lithium chloride solutions have been investigated by classical molecular dynamics (MD) and reverse Monte Carlo (RMC) simulations. At first, MD calculations have been carried out by applying twenty-nine combinations of ion-water interaction models at four salt concentrations. The structural predictions of the different models have been compared, the contributions of different structural motifs to the partial pair correlation functions (PPCF) have been determined. Particle configurations obtained from MD simulations have been further refined using the RMC method to get better agreement with experimental X-ray and neutron diffraction data. The PPCFs calculated from MD simulations have been fitted together with the experimental structure factors to construct structural models that are as consistent as possible with both the experimental results and the results of the MD simulations. The MD models have been validated according to the quality of the fits. Although none of the tested MD models can describe the structure perfectly at the highest investigated concentration, their comparison made it possible to determine the main structural properties of that solution as well. It was found that four nearest neighbors (oxygen atoms and chloride ions together) are around a lithium ion at each concentration while in the surroundings of the chloride ion, hydrogen atom pairs are replaced by one lithium ion as the concentration increases. While in pure liquid water four water molecules can be found around a central water molecule, near the solubility limit nearly all water molecules are connected to two chloride ions (via their hydrogen atoms) and one lithium ion (by their oxygen atoms).

Results in 2017

Metallic glasses. — The structure of glassy Cu47.5Zr47.5Ag5 has been investigated by neutron diffraction with isotopic substitution, X-ray diffraction as well as with Cu and Ag K-edge extended X-ray absorption spectroscopy (EXAFS) measurements. Experimental datasets have been fitted simultaneously with the reverse Monte Carlo simulation technique. Nearest-neighbor distances and coordination numbers have been determined and compared with those of glassy Cu50Zr50 and Cu47.5Zr47.5Al5. It has been found that the Cu-Cu coordination number drops upon adding Al or Ag to Cu50Zr50. Both Ag and Al prefers Zr to Cu. The total coordination number of Ag is 13.9±0.6 while that of Al is 10.2±1.0, suggesting that, in spite of their similar molar volumes, the effective size of Ag and Al in the Cu-Zr matrix is quite different. This is reflected both by the comparison of Zr-Al and Zr-Ag partial pair distribution functions and the Zr-X-Zr (X=Al, Ag) cosine distributions (see Fig. 1.)

Figure 1. Effective size difference of Al and Ag atoms in the Cu-Zr host matrix as reflected by the position of the first peak of Zr-Al and Zr-Ag partial pair distribution functions (a) and by the Zr-Al-Zr and Zr-Ag-Zr cosine distributions (b)

Alcohol-water mixtures. — Our efforts concerning the structure of alcohol-water liquid mixtures have been extended to the study of the temperature dependence of the structure of aqueous solutions of methanol. The evolution of the structure of liquid water-methanol mixtures as a function of temperature has been studied by molecular dynamics simulations, with a focus on hydrogen bonding. The combination of the OPLS-AA (all atom) potential model of methanol and the widely used SPC/E water model has provided excellent agreement with measured X-ray diffraction data over the temperature range between 298 and 213 K, for mixtures with methanol molar fractions of 0.2, 0.3 and 0.4. Hydrogen bonds have been identified via a combined geometric/energetic, as well as via a purely geometric definition. The number of recognizable hydrogen bonded ring structures in some cases doubles while lowering the temperature from 298 to 213 K; the number of sixfold rings increases most significantly. An evolution towards the structure of hexagonal ice, that contains only sixfold hydrogen bonded rings, has thus been detected on cooling water-methanol mixtures. For a picture of typical hydrogen-bonded ring structures, see Figure 2.

Figure 2. Hydrogen-bonded ring structures in methanol/water mixtures (Red: O atoms; light grey: H atoms; dark grey: C atoms. Dashed lines represent hydrogen bonds between molecules.)

Liquid chalcogenides. — The short-range order in the liquid state of GeTe, a prototypical phase-change material employed in data storage devices, has been investigated by X-ray and neutron diffraction in the temperature range from 1197 to 998 K. We have also measured the dynamic viscosity from 1273 to 953 K, which is 55 K below the solidification point, using an oscillating-cup viscometer. The measurements have been complemented with ab-initio molecular dynamics (AIMD) simulations based on density functional theory (DFT). Compatibility of the AIMD-DFT models with the diffraction data has been proven by simultaneous fitting of all datasets in the frame of the reverse Monte-Carlo simulation technique. It has been shown that octahedral order dominates in liquid GeTe, although tetrahedral structures are also present. The temperature dependences of the structural parameters, dynamic viscosity and electronic properties extracted from the AIMD models have been analyzed and discussed. We have shown that GeTe keeps its semiconductor nature in the liquid and supercooled liquid state. Its viscosity obeys the Arrhenius law with a small activation energy of the order of 0.3 eV, which is indicative of a highly fragile liquid.

Aqueous salt solutions. — Aqueous lithium chloride solutions up to very high concentrations have been investigated in classical molecular dynamics simulations. Various force fields based on the 12-6 Lennard-Jones model parametrized for non-polarizable water solvent molecules (SPC/E, TIP4P, TIP4PEw) have been inspected. Twenty-nine combinations of ion-water interaction models have been examined at four different salt concentrations.

Densities, static dielectric constants and self-diffusion coefficients have been calculated (see, e.g., Figure 3). Results derived from the different force fields scatter over a wide range of values. Neutron and X-ray weighted structure factors have also been calcu­lated from the radial distribution func­tions and compared with experimental data. It has  been found that the agreement between calculated and experimental curves is rather poor for several investigated potential models, even though some of them were pre­viously applied in computer simula­tions.

Figure 3. Convergence of the static dielectric constant (ε) for three selected models (Pl, HS-g and Li-IOD-S) at the concentration m = 19.55 mol/kg. The curve is converged for the Pl model, still slightly evolving for the Li-IOD-S model, and definitely not converged even at 8 ns, for the HS-g model.