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At least 235 records · Page 13

Quantitative three-dimensional imaging of chemical short-range order via machine learning enhanced atom probe tomography

Abstract Chemical short-range order (CSRO) refers to atoms of specific elements self-organising within a disordered crystalline matrix to form particular atomic neighbourhoods. CSRO is typically characterized indirectly, using volume-averaged or through projection microscopy techniques that fail to capture the three-dimensional atomistic architectures. Here, we present a machine-learning enhanced approach to break the inherent resolution limits of atom probe tomography enabling three-dimensional imaging of multiple CSROs. We showcase our approach by addressing a long-standing question encountered in body-centred-cubic Fe-Al alloys that see anomalous property changes upon heat treatment. We use it to evidence non-statistical B 2 -CSRO instead of the generally-expected D0 3 -CSRO. We introduce quantitative correlations among annealing temperature, CSRO, and nano-hardness and electrical resistivity. Our approach is further validated on modified D0 3 -CSRO detected in Fe-Ga. The proposed strategy can be generally employed to investigate short/medium/long-range ordering phenomena in different materials and help design future high-performance materials.

36 MATERIALS SCIENCE↗

Medium-independent hydrogen atom binding isotherms of nickel oxide electrodes

Adsorption and transfer of hydrogen atoms at solid/solution interfaces are fundamental to heterogeneous catalysis for chemical energy transformations and other processes. Reported here are electrochemical and spectroelectrochemical measurements of the thermodynamics of H-atom binding to nickel oxide electrodes, both the average and the distribution of NiO–H bond dissociation free energies (BDFEs). These are perhaps the first measurements of binding isotherms at non-metal electrodes. Remarkably, both the BDFEs and the non-Langmuirian isotherms are the same in water, acetonitrile, and dimethylformamide, and with different buffers and proton activities. Such medium independence of the BDFEs and isotherms has not been previously reported for any binary material. The medium independence supports the common use of computed hydrogen binding energies as intrinsic descriptors of surface reactivity, while the broadened isotherms add a level of complexity to such analyses. Furthermore, this work demonstrates the capability to derive key thermodynamic parameters at chemically reactive solid-liquid interfaces.

13 HYDRO ENERGY↗

Numerical simulations of the seasonal/latitudinal variations of atomic oxygen and nitric oxide in the lower thermosphere and mesosphere

A 2-Dimensional zonally-averaged thermospheric model and the global University College London (UCL) thermospheric model have been used to investigate the seasonal, solar activity and geomagnetic variation of atomic oxygen and nitric oxide. The 2-dimensional model includes detailed oxygen and nitrogen chemistry, with appropriate completion of the energy equation, by adding the thermal infrared cooling by O and NO. This solution includes solar and auroral production of odd nitrogen compounds and metastable species. This model has been used for three investigations; firstly, to study the interactions between atmospheric dynamics and minor species transport and density; secondly, to examine the seasonal variations of atomic oxygen and nitric oxide within the upper mesosphere and thermosphere and their response to solar and geomagnetic activity variations; thirdly, to study the factor of 7 to 8 peak nitric oxide density increase as solar F sub 10.7 cm flux increases from 70 to 240 reported from the Solar Mesospheric Explorer. Auroral production of NO is shown to be the dominant source at high latitudes, generating peak NO densities a factor of 10 greater than typical number densities at low latitudes. At low latitudes, the predicted variation of the peak NO density, near 110 km, with the solar F sub 10.7 cm flux is rather smaller than is observed. This is most likely due to an overestimate of the soft X-ray flux at low solar activity, for times of extremely low support number, as occurred in June 1986. As observed on pressure levels, the variation of O density is small. The global circulation during solstice and periods of elevated geomagnetic activity causes depletion of O in regions of upwelling, and enhancements in regions of downwelling.

Rees, D.↗

Implementation of Active Sites in DSMC to Capture Pitting of Oxidizing Carbon Materials

In this work we demonstrate a newly developed capability to capture pitting of carbon fibers in DSMC simulations, specifically using the Stochastic PArallel Rarefied-gas Time-accurate Analyzer (SPARTA) code. State-of-the-art reactive surface models in DSMC compute collision dependent carbon consumption rates (usually through desorption of CO) based on a set of surface reactions that has been derived from molecular beam experiments. The reactivity on each carbon surface element is constant in those models, such that the carbon surface recedes uniformly as a result of ablation. However, it is well known that in reality the carbon surface has locally different reaction rates due to the presence of defects at the atomic scale. These defective sites have a much higher reactivity than the average sites (2-3 orders of magnitude) and are first to react during ablation leading to its removal. This causes all the neighboring atoms to be defective and increase their reactivity, thus leading to the localized carbon removal around these ”active” sites. In this manner, these highly reactive defective sites serve as nucleation sites for the formation and growth of etch pits with potentially detrimental effects on the structural integrity. Recently a detailed surface chemistry framework was developed in SPARTA, capable of incorporating various reaction mechanisms such as adsorption, desorption, Eley-Rideal (ER) and Langmuir-Hinshelwood (LH) mechanisms. Within this framework, we have implemented the capability of a single surface having multiple site sets with different reactivities. Using this feature, we can simulate the presence of active sites on carbon surfaces, whose reactivity is much greater than an average site as a result of defects. We have implemented the active site fraction as a property of surface elements within SPARTA, which is directly proportional to the local reactivity of each surface element. By introducing an initial distribution of the active site fraction across the carbon surface, and propagating it in a manner that mimics the evolution of real reacting carbon surfaces, we are able to capture the formation and growth of etch pits as a result of surface consumption reactions such as oxidation.

DSMC↗

Evaluation of Oxygen Interactions with Materials 3: Mission and induced environments

The Evaluation of Oxygen Interactions with Materials 3 (EOIM-3) flight experiment was developed to obtain benchmark atomic oxygen/material reactivity data. The experiment was conducted during Space Shuttle mission 46 (STS-46), which flew July 31 to August 7, 1992. Quantitative interpretation of the materials reactivity measurements requires a complete and accurate definition of the space environment exposure, including the thermal history of the payload, the solar ultraviolet exposure, the atomic oxygen fluence, and any spacecraft outgassing contamination effects. The thermal history of the payload was measured using twelve thermocouple sensors placed behind selected samples and on the EOIM-3 payload structure. The solar ultraviolet exposure history of the EOIM-3 payload was determined by analysis of the as-flown orbit and vehicle attitude combined with daily average solar ultraviolet and vacuum ultraviolet (UV/VUV) fluxes. The atomic oxygen fluence was assessed in three different ways. First, the O-atom fluence was calculated using a program that incorporates the MSIS-86 atmospheric model, the as-flown Space Shuttle trajectory, and solar activity parameters. Second, the oxygen atom fluence was estimated directly from Kapton film erosion. Third, ambient oxygen atom measurements were made using the quadrupole mass spectrometer on the EOIM-3 payload. Our best estimate of the oxygen atom fluence as of this writing is 2.3 +/- 0.3 x 10(exp 20) atoms/sq cm. Finally, results of post-flight X-ray photoelectron spectroscopy (XPS) surface analyses of selected samples indicate low levels of contamination on the payload surface.

Koontz, Steven L.↗

HydraGNN_Predictive_GFM_2024 - Ensemble of predictive graph foundation models for ground state atomistic materials modeling

We provide the ensemble of fifteen pre-trained graph foundation models (GFMs) for atomistic materials modeling applications. Each one of the fifteen GFMs has been trained on five open-source datasets that (once aggregated) amount to over 154 million atomistic structures, which cover over two-thirds of the natural elements of the periodic table and that comprises a broad set of organic and inorganic compounds. This vast set of atomistic structures comprises ground state configurations that are dynamically stable (i.e., equilibrated structures with atomic forces approximately close to zero values) as well as dynamically unstable structures (i.e., non-equilibrium structures with non-negligible non-zero values of atomic forces). The ensemble of datasets aggregated does NOT include excited states. The datasets have been curated to remove atomistic structures with spectral norm of the force tensor above 100 eV/angstrom. Moreover, a linear term of the energy was computed for each dataset using a linear regression model that uses the chemical concentration of each natural element as regressor. The linear term predicted by the linear regression model has been subtracted from each original energy value to perform a re-alignment of the energy values across different electronic structures approximation theories performed to generate the diverse multi-source, multi-fidelity datasets. The folder "ADIOS_files" contains the set of pre-processed datasets in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used for the development and training of GFMs in this work. The "ADIOS_files" directory contains 6 sub-directories named as follows: - ANI1x-v3.bp - MPTrj-v3.bp - OC2020-20M-v3.bp - OC2020-v3.bp - OC2022-v3.bp - qm7x-v3.bp Each sub-directory contains the pre-processed datasets converted in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used to the development, training, and performance testing of the ensemble go predictive graph foundation models. Each GFM was developed using HydraGNN (https://github.com/ORNL/HydraGNN) as underlying graph neural network (GNN) architecture. The multi-task learning (MTL) capability of HydraGNN was used to simultaneously train the GFMs on labeled values for direct predictions of energy (a total system property of an atomistic structure that measures the chemical stability) and atomic forces (an atomic level property of an atomistic structure that measures the dynamical stability). The hyper parameters of the GFM have been tuned using scalable hyperparameter optimization (HPO) algorithms implemented in the software DeepHyper (https://github.com/deephyper/deephyper). The pre-training of each HPO trial was performed using distributed data parallelism (DDP) to scale the training across 128 compute nodes of the exascale OLCF supercomputer Frontier. Each HPO trial was trained only for 10 epochs and an early stopping was performed to avoid wasting significant computational resources on GNN architectures that were clearly underperforming. For each HPO trial, the 'omnistat' tool developed by (AMD Research - Advanced Micro Device) was used to measure the total energy consumption in kWh. The ensemble of GFMs was obtained by selecting the fifteen best performing HPO trials. Four models have been selected for their clear advantage in accuracy, and these are the GFMs with IDs 229, 156, 147, 260. Additional eleven models have been selected based on judicious balance between accuracy and energy consumption needed for training, and these are the GFMs with IDs 165, 78, 137, 1, 175, 171, 181, 67, 179, 167, 351. Each selected GFM of the ensemble was continued to cumulate a total of at most 30 epochs. In some cases, the total number of epochs actually performed was les than 30 due to two combined factors: (1) the size of the GFM (i.e., the number of model parameters to train) and (2) the total wall-clock time for which the computational resources could be allocated on OLCF-Frontier. The "Ensemble_of_models" directory contains 15 sub-directories named as follows: - gfm_0.229 - gfm_0.156 - gfm_0.147 - gfm_0.260 - gfm_0.165 - gfm_0.78 - gfm_0.137 - gfm_0.1 - gfm_0.175 - gfm_0.171 - gfm_0.181 - gfm_0.67 - gfm_0.179 - gfm_0.167 - gfm_0.351 Each one of these sub-directories refers to one of the fifteen HPO trials that have been selected to continue the pre-training with at most 30 epochs. With each sub-directory associated with a specific HPO trial, the following files can be found: - config.json: file for argument parsing to develop and train an HydraGNN architecture - gfm_0.ID_epoch_N.pk: file with model parameters for HPO ID trial after N epochs of training The ensemble of fifteen GFM architectures was used for (1) ensemble averaging to stabilize the predictions of energy and atomic forces after pre-training for post-processing analysis and (2) ensemble uncertainty quantification (UQ). The code used to develop, pre-train, and load the pre-trained models for post-processing analysis is available on the ORNL-GitHub at the following link: https://github.com/ORNL/HydraGNN/tree/Predictive_GFM_2024

36 MATERIALS SCIENCE↗

Accurate Prediction of Voltage of Battery Electrode Materials Using Attention-Based Graph Neural Networks

Performing first-principles calculations to discover electrodes’ properties in the large chemical space is a challenging task. While machine learning (ML) has been applied to effectively accelerate those discoveries, most of the applied methods ignore the materials’ spatial information and only use predefined features: based only on chemical compositions. Here, we propose two attention-based graph convolutional neural network techniques to learn the average voltage of electrodes. Our proposed methods, which combine both atomic composition and atomic coordinates in 3D-space, improve the accuracy in voltage prediction significantly when compared to composition-based ML models. The first model directly learns the chemical reaction of electrodes and metal ions to predict their average voltage, whereas the second model combines electrodes’ ML predicted formation energy (E form ) to compute their average voltage. Our E form -based model demonstrates improved accuracy in transferability from our subset of learned Li ions to Na ions. Moreover, we predicted the theoretical voltage of 10 Na x MPO 4 F (M = Ti, Cr, Fe, Cu, Mn, Co, and Ni) fluorophosphate battery frameworks, which are unavailable in the Material Project database. It could be shown that we can expect average voltages higher than 3.1 V from those Na battery frameworks except from the NaTiPO 4 F and TiPO 4 F pair of electrodes, which offer an average voltage of 1.32 V.

25 ENERGY STORAGE↗

Attosecond Time Delay Trends across the Isoelectronic Noble Gas Sequence

The analysis and measurement of Wigner time delays can provide detailed information about the electronic environment within and around atomic and molecular systems, with one the key differences being the lack of a long-range potential after a halogen ion undergoes photoionization. In this work, we use relativistic random-phase approximation to calculate the average Wigner delay from the highest occupied subshells of the atomic pairings (2p, 2s in Fluorine, Neon), (3p, 3s in Chlorine, Argon), (4p, 4s, 3d, in Bromine, Krypton), and (5p, 5s, 4d in Iodine, Xenon). The qualitative behaviors of the Wigner delays between the isoelectronic pairings were found to be similar in nature, with the only large differences occurring at photoelectron energies less than 20 eV and around Cooper minima. Interestingly, the relative shift in Wigner time delays between negatively charged halogens and noble gases decreases as atomic mass increases. All atomic pairings show large differences at low energies, with noble gas atoms showing large positive Wigner delays, while negatively charged halogen ions show negative delays. The implications for photoionization studies in halide-containing molecules is also discussed.

Grafstrom, Brock↗

Observational constraints on the multiphase nature of outflows using large spectroscopic surveys at z ∼ 0

ABSTRACT Mass outflow rates and loading factors are typically used to infer the quenching potential of galactic-scale outflows. However, these generally rely on observations of a single gas phase that can severely underestimate the total ejected gas mass. To address this, we use observations of high mass (≥1010 M⊙), normal star-forming galaxies at z ∼ 0 from the MaNGA, xCOLD GASS, xGASS, and ALFALFA surveys and a stacking of Na d, Hα, CO(1–0), and H i 21 cm tracers with the aim of placing constraints on an average, total mass outflow rate, and loading factor. We find detections of outflows in both neutral and ionized gas tracers, with no detections in stacks of molecular or atomic gas emission. Modelling of the outflow components reveals velocities of |vNa d| = 131 km s−1 and |vHα| = 439 km s−1 and outflow rates of $\dot{M}_{\rm {Na\,\small{D}}}$ = 7.55 M⊙ yr−1 and $\dot{M}_{\text{H}\alpha }$ = 0.10 M⊙ yr−1 for neutral and ionized gas, respectively. Assuming a molecular/atomic outflow velocity of 200 km s−1, we derive upper limits of $\dot{M}_{\text{CO}}\lt 19.43$ M⊙ yr−1 and $\dot{M}_{\rm {H\,\small {I}}}\lt $ 26.72 M⊙ yr−1 for the molecular and atomic gas, respectively. Combining the detections and upper limits, we find average total outflow rates of $\dot{M}_{\text{tot}}\lesssim$27 M⊙ yr−1 and a loading factor of ηtot ≲ 6.39, with molecular gas likely contributing ≲72 per cent of the total mass outflow rate, and neutral and ionized gas contributing ∼28 and <1 per cent, respectively. Our results suggest that, to first order, a degree of quenching via ejective feedback could occur in normal galaxies when considering all gas phases, even in the absence of an active galactic nucleus.

Roberts-Borsani, G. W.↗

Feasibility study of oxygen-dispensing emitters for thermionic converters, phase 1

A metal/ceramic Marchuk tube was used to measure work functions of oxygen-doped tantalum, to determine applicability of the material to plasma-mode thermionic converters. Oxygen-doped tantalum was shown to increase in work function monotonically with oxygen doping in the range 0.1 to 0.3 atomic percent. Oxygenated test emitters were run at an average temperature of 2165 K and a T/T sub Cs ratio -5.8 to observe the influence of oxygen depletion. Bare work function decreased with outgassing of oxygen. Projections were made based on outgassing kinetics and area/volume ratios to calculate the longevity of oxygen doping in a practical converter. Calculations indicated that the program goal of 10,000 hr could be achieved at 1800 K with an initial oxygen doping of 1 atomic percent and a practical emitter area/volume ratio.

Desteese, J. G.↗

Synthesis and Characterization of Pt‐Ag Icosahedral Nanocages with Enhanced Catalytic Activity toward Oxygen Reduction

Abstract There is an urgent need to develop cost‐effective electrocatalysts based on Pt for a broad spectrum of applications, including those vital to the operation of fuel cells. Hollowing out the interior of Pt nanocrystals offers a simple and viable strategy for maximizing the utilization efficiency of this precious metal while enhancing the electrocatalytic performance. Herein, we report the synthesis and electrocatalytic evaluation of Pt−Ag icosahedral nanocages with an average wall thickness of 1.6 nm. The Pt atoms are coated on the surface of Ag icosahedral seeds, leading to the formation of Ag@Pt nL core‐shell icosahedral nanocrystals with tunable shell thicknesses. The core‐shell nanocrystals are then converted to icosahedral nanocages by selectively etching away the Ag in the core. The as‐obtained nanocages with a composition of Pt 4.5 Ag exhibit an almost 3‐fold enhancement in specific activity toward oxygen reduction relative to the commercial Pt/C in acid media.

Wang, Wenxia↗

Codesigning Alloy Compositions of CdSe y Te 1− y Absorbers and Mg x Zn 1− x O Contacts to Increase Solar Cell Efficiency

Thin‐film solar cells such as CdTe are a major commercial photovoltaic technology, with more than 25 GW installed worldwide and levelized costs of electricity competitive with fossil fuels. Further progress may result from integrating CdSe y Te 1− y absorbers with Mg x Zn 1− x O contacts, but the device efficiency is difficult to maximize due to coupled dependence on chemical composition of both alloys. Herein, a high‐throughput approach is demonstrated to codesign chemical compositions in alloyed Mg x Zn 1− x O/CdSe y Te 1− y thin‐film solar cells, using combinatorial libraries of PV devices with orthogonal composition gradients in CdSe y Te 1− y absorbers and Mg x Zn 1− x O contacts. It is found that the solar cell performance is a strong and coupled function of both elemental compositions, with efficiency up to 17.7% ( V OC = 836 mV, fill factor = 69%, J SC = 30.6 mA cm −2 ) at atomic compositions of Mg/(Mg + Zn) ≈18% and average Se/(Se + Te) ≈4%. These performance trends among >100 devices are explained by >100 ns lifetime of photoexcited charge carriers at the Mg x Zn 1− x O/CdSe y Te 1− y interface where strong Se accumulation is also observed. This study reports the optimal compositions of the commercially relevant Mg x Zn 1− x O/CdSe y Te 1− y solar cells and demonstrates a general approach to codesigning performance of alloyed thin‐film solar cells and other optoelectronic devices.

14 SOLAR ENERGY↗

Machine-learning-guided descriptor selection for predicting corrosion resistance in multi-principal element alloys

More than $270 billion is spent on combatting corrosion annually in the USA alone. As such, we present a machine-learning (ML) approach to down select corrosion-resistant alloys. Our focus is on a non-traditional class of alloys called multi-principal element alloys (MPEAs). Given the vast search space due to the variety of compositions and descriptors to be considered, and based upon existing corrosion data for MPEAs, we demonstrate descriptor optimization to predict corrosion resistance of any given MPEA. Our ML model with descriptor optimization predicts the corrosion resistance of a given MPEA in the presence of an aqueous environment by down selecting two environmental descriptors (pH of the medium and halide concentration), one chemical composition descriptor (atomic % of element with minimum reduction potential), and two atomic descriptors (difference in lattice constant (Δa) and average reduction potential). Our findings show that, while it is possible to down select corrosion-resistant MPEAs by using ML from a large search space, a larger dataset and higher quality data are needed to accurately predict the corrosion rate of MPEAs. This study shows both the promise and the perils of ML when applied to a complex chemical phenomenon like corrosion of alloys.

36 MATERIALS SCIENCE↗

Ultrafast lattice disordering can be accelerated by electronic collisional forces

In the prevalent picture of ultrafast structural phase transitions, the atomic motion occurs in a slowly varying potential energy surface determined adiabatically by the fast electrons. However, this ignores non-conservative forces caused by electron-lattice collisions, which can significantly influence atomic motion. Most ultrafast techniques only probe the average structure and are less sensitive to random displacements, and therefore do not detect the role played by non-conservative forces in phase transitions. Here we show that the lattice dynamics of the prototypical insulator-to-metal transition of VO 2 cannot be described by a potential energy alone. We use the sample temperature to control the preexisting lattice disorder before ultrafast photoexcitation across the phase transition and our ultrafast diffuse scattering experiments show that the fluctuations characteristic of the rutile metal develop equally fast (120 fs) at initial temperatures of 100 K and 300 K. This indicates that additional non-conservative forces are responsible for the increased lattice disorder. In conclusion, these results highlight the need for more sophisticated descriptions of ultrafast phenomena beyond the Born-Oppenheimer approximation as well as ultrafast probes of spatial fluctuations beyond the average unit cell measured by diffraction.

36 MATERIALS SCIENCE↗

Physics of Ultra-High Energy Density Relativistic Plasmas from Ordered Nanostructures

This award funded a four-year program at Colorado State University on the physics of ultra-high energy density plasmas generated by focusing femtosecond, >1021 Wcm-2 laser pulses onto ordered nanowire arrays. We used the ALEPH petawatt-class Ti:Sa laser with its high contrast 400 nm second harmonic beamline to irradiate arrays of Ni and TiO2 nanowires made by template assisted electrodeposition and atomic layer deposition over a wide range of average densities. We met two of the three original project goals: radial ion acceleration via doppler shifted K shell emission, and time and spectrally resolved K shell measurements. The main experimental advance was integrating the Lawrence Livermore National Laboratory (LLNL) TREX ultrafast x-ray streak camera with a suite of spherically bent quartz Bragg crystal spectrometers built using Princeton Plasma Physics Laboratory (PPPL) methodology. This is the first TREX-on-bent-quartz setup fielded at a femtosecond, >1021 Wcm-2 facility. It is now a permanent diagnostic at ALEPH and is offered to the LaserNetUS user community. The program produced three peer reviewed journal articles that acknowledge this award. The platform will continue at the upgraded CSU ATLAS facility, where the ALEPH laser is being upgraded to 2 PW.

Hollinger, Reed [Colorado State University]↗

Combining machine-learned and empirical force fields with the parareal algorithm: application to the diffusion of atomistic defects

We numerically investigate an adaptive version of the parareal algorithm in the context of molecular dynamics. This adaptive variant has been originally introduced in [1]. We focus here on test cases of physical interest where the dynamics of the system is modelled by the Langevin equation and is simulated using the molecular dynamics software LAMMPS. In this work, the parareal algorithm uses a family of machine-learning spectral neighbor analysis potentials (SNAP) as fine, reference, potentials and embedded-atom method potentials (EAM) as coarse potentials. We consider a self-interstitial atom in a tungsten lattice and compute the average residence time of the system in metastable states. Our numerical results demonstrate significant computational gains using the adaptive parareal algorithm in comparison to a sequential integration of the Langevin dynamics. We also identify a large regime of numerical parameters for which statistical accuracy is reached without being a consequence of trajectorial accuracy.

36 MATERIALS SCIENCE↗

A survey of local interstellar hydrogen from OAO-2 observations of Lyman alpha absorption

The Wisconsin far ultraviolet spectrometer aboard OAO-2 observed the wavelength region near 1216 A for 69 stars of spectral type B2 or earlier. From the strength of the observed interstellar L sub alpha absorption, atomic hydrogen column densities were derived over distances averaging 300 pc away from the sun. The OAO data were compared to synthetic ultraviolet spectra, originally derived from earlier higher resolution rocket observations, which were computer processed to simulate the effects of absorption by different amounts of hydrogen followed by the instrumental blending.

Savage, B. D.↗

X-ray investigation of molten crystal hydrates H2SO4(nH2O) and HNO3(nH2O)

Integral analysis of the intensity of the electron density distribution curve in molten crystal hydrates provided by X-ray analysis, permits the following conclusions on the structure of the complex SO and NO ions, and the short-range order in the structure of the solution. The SO4 ion in the solution has a tetrahedral structure with an S to O distance equal to 1.5 A. For the NO3 in the solution, a planar triangular shape is probable, with an N to O distance equal to 1.2 A. Preferential distances between each of the oxygens of the SO ion and the nearest molecules of water proved near to the corresponding distances in solid crystal hydrates. For an (H2SO4)(H2O) solution, the average number of water molecules surrounding each oxygen atom of the SO4 (--) ion was on the order of 1.3 molecules. Hence the preferential distances between the water molecules and the oxygen atoms of the SO ion, and the preference of their mutual position, correspond to the fixed position of these same elements of the structure in the solid crystal hydrate.

Romanova, A. V.↗