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At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Exploring the transition from continuous turbulence fluctuations to bursting ELMs in high SOL density regimes

BOUT++ turbulence simulations of the DIII-D reveal that the density profile between the separatrix and pedestal plays a crucial role in the dynamics of edge localized modes (ELMs) and edge plasma turbulent transport. Nonlinear simulations demonstrate that small ELMs in the DIII-D hybrid scenario under high SOL density conditions are predominantly driven by local ballooning modes near the separatrix, stabilizing global instabilities while enhancing localized pressure fluctuations. A key control parameters for ELM dynamics is the separatrix-to-pedestal density ratio, n e,sep /n e,ped . A high ratio indicates a shallow gradient, favoring small ELMs, while a lower ratio signals a steep gradient, which increases the likelihood of large ELMs. Comprehensive parameter scans, including n e,sep /n e,ped , density gradient profiles near the separatrix, and resistivity, reveal the critical role of these parameters in shaping transitions between turbulence-driven transport and ELM bursting. The scans demonstrate that in high SOL density regimes, small ELMs can result from either global resistive MHD instabilities or local ballooning modes near the separatrix, depending on the steepness of the separatrix density gradient. These findings also highlight the transition from continuous turbulence to small ELMs. The post-crash peak in pressure fluctuations, δP rms serves as a critical metric for identifying transition from continuous turbulence fluctuations to ELM bursting. Larger δP rms values correlate with ELM bursts driven by local or global instabilities, whereas smaller values indicate turbulence-dominated transport. Drift-Alfvén and resistive ballooning turbulence enhance the entrainment of fluctuations from the pedestal to the SOL, contributing to the complex interplay of dynamics in this regime. These findings emphasize the importance of separatrix density shaping and pedestal gradient control for optimizing ELM behavior in ITER and future fusion devices.

Li, Nami [Lawrence Livermore National Laboratory (↗
DOE OSTI2025

CryoTEN: efficiently enhancing cryo-EM density maps using transformers

Abstract Motivation Cryogenic electron microscopy (cryo-EM) is a core experimental technique used to determine the structure of macromolecules such as proteins. However, the effectiveness of cryo-EM is often hindered by the noise and missing density values in cryo-EM density maps caused by experimental conditions such as low contrast and conformational heterogeneity. Although various global and local map-sharpening techniques are widely employed to improve cryo-EM density maps, it is still challenging to efficiently improve their quality for building better protein structures from them. Results In this study, we introduce CryoTEN—a 3D UNETR++ style transformer to improve cryo-EM maps effectively. CryoTEN is trained using a diverse set of 1295 cryo-EM maps as inputs and their corresponding simulated maps generated from known protein structures as targets. An independent test set containing 150 maps is used to evaluate CryoTEN, and the results demonstrate that it can robustly enhance the quality of cryo-EM density maps. In addition, automatic de novo protein structure modeling shows that protein structures built from the density maps processed by CryoTEN have substantially better quality than those built from the original maps. Compared to the existing state-of-the-art deep learning methods for enhancing cryo-EM density maps, CryoTEN ranks second in improving the quality of density maps, while running >10 times faster and requiring much less GPU memory than them. Availability and implementation The source code and data are freely available at https://github.com/jianlin-cheng/cryoten.

Biochemistry & Molecular Biology↗
DOE OSTI2019

X-ray Studies of the Transformation from High-to Low-density Amorphous Water

Here we report about the structural evolution during the conversion from high-density amorphous ices at ambient pressure to the low-density state. Using high-energy X-ray diffraction we have monitored the transformation by following in reciprocal space the structure factor SOO(Q) and derive in real space the pair distribution function gOO(r). Heating equilibrated high-density amorphous ice (eHDA) at a fast rate (4 K/min), the transition to the low-density form occurs very rapidly, while domains of both high- and low-density coexist. On the other hand, the transition in the case of unannealed HDA (uHDA) and very-high-density amorphous ice (VHDA) is more complex and of continuous nature. The direct comparison of eHDA and uHDA indicates that the molecular structure of uHDA contains a larger amount of tetrahedral motives. The different crystallization behavior of the derived low-density amorphous (LDA) states is interpreted as emanating from an increased tetrahedral coordination present in uHDA.

amorphous ice↗
DOE OSTI2025

Unified nonparametric equation-of-state inference from the neutron-star crust to perturbative-QCD densities

Perturbative quantum chromodynamics (pQCD), while valid only at densities exceeding those found in the cores of neutron stars, could provide constraints on the dense-matter equation of state (EOS). Here, in this work, we examine the impact of pQCD information on the inference of the EOS using a nonparametric framework based on Gaussian processes (GPs). We examine the application of pQCD constraints through a ``pQCD likelihood,'' and verify the findings of previous works; namely, a softening of the EOS at the central densities of the most massive neutron stars and a reduction in the maximum neutron-star mass. Although the pQCD likelihood can be easily integrated into existing EOS inference frameworks, this approach requires an arbitrary selection of the density at which the constraints are applied. The EOS behavior is also treated differently on either side of the chosen density. To mitigate these issues, we extend the EOS model to higher densities, thereby constructing a ``unified'' description of the EOS from the neutron-star crust to densities relevant for pQCD. In this approach the pQCD constraints effectively become part of the prior. Since the EOS is unconstrained by any calculation or data between the densities applicable to neutron stars and pQCD, we argue for maximum modeling flexibility in that regime. We compare the unified EOS with the traditional pQCD likelihood, and although we confirm the EOS softening, we do not see a reduction in the maximum neutron-star mass or any impact on macroscopic observables. Though residual model dependence cannot be ruled out, we find that pQCD suggests the speed of sound in the densest neutron-star cores has already started decreasing toward the asymptotic limit; we find that the speed of sound squared at the center of the most massive neutron star has an upper bound of $\sim 0.5$ at the 90% level.

equations of state of nuclear matter↗
DOE OSTI2017

Phosphorus allotropes: Stability of black versus red phosphorus re-examined by means of the van der Waals inclusive density functional method

We evaluate the energetic stabilities of white, red, and black allotropes of phosphorus using density functional theory (DFT) and hybrid functional methods, van der Waals (vdW) corrections (DFT+vdW and hybrid+vdW), vdW density functionals, and random phase approximation (RPA). In this work, we find that stability of black phosphorus over red-V (i.e., the violet form) is not ubiquitous among these methods, and the calculated enthalpies for the reaction phosphorus (red-V)→ phosphorus (black) are scattered between –20 and 40 meV/atom. With local density and generalized gradient approximations, and hybrid functionals, mean absolute errors (MAEs) in densities of P allotropes relative to experiments are found to be around 10%–25%, whereas with vdW-inclusive methods, MAEs in densities drop below ~5%. While the inconsistency among the density functional methods could not shed light on the stability puzzle of black versus red phosphorus, comparison of their accuracy in predicting densities and the supplementary RPA results on relative stabilities indicate that opposite to the common belief, black and red phosphorus are almost degenerate, or the red-V (violet) form of phosphorus might even be the ground state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Vortices in low-density neutron matter and cold Fermi gases

Cold gas experiments can be tuned to achieve strongly-interacting regimes such as that of low-density neutron matter found in neutron-stars' crusts. We report T=0 diffusion Monte Carlo results (i) for the ground state of both spin-1/2 fermions with short-range interactions and low-density neutron matter in a cylindrical container, and (ii) properties of these systems with a vortex line excitation. We calculate the equation of state for cold atoms and low-density neutron matter in the bulk systems, and we contrast it to our results in the cylindrical container. We compute the vortex line excitation energy for different interaction strengths, and we find agreement between cold gases and neutron matter for very low densities. We also calculate density profiles, which allow us to determine the density depletion at the vortex core, which depends strongly on the short-ranged interaction in cold atomic gases, but it is of ≈25% for neutron matter in the density regimes studied in this work. Our results can be used to constrain neutron matter properties by using measurements from cold Fermi gases experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Auxiliary function approach for determining symmetry energy at suprasaturation densities

Nuclear symmetry energy E sym (ρ) at density ρ is normally expanded or simply parameterized as a function of χ = (ρ – ρ 0 )/3ρ 0 in the form of Esym(ρ) ≈ S + Lχ + 2 –1 K sym χ 2 + 6 –1 J sym χ 3 + … using its magnitude S, slope L, curvature K sym and skewness J sym at the saturation density ρ0 of nuclear matter. Much progress has been made in recent years in constraining especially the S and L parameters using various terrestrial experiments and astrophysical observations. Furthermore, such kind of expansions/parameterizations do not converge at supra-saturation densities where χ is not small enough, hindering an accurate determination of high-density E sym (ρ) even if its characteristic parameters at ρ0 are all well determined by experiments/observations. By expanding the E sym (ρ) in terms of a properly chosen auxiliary function Π sym (χ,Θ sym ) with a parameter Θsym fixed accurately by an experimental E sym (ρ r ) value at a reference density ρr, we show that the shortcomings of the χ-expansion can be completely removed or significantly reduced in determining the high-density behavior of E sym (ρ). In particular, using two significantly different auxiliary functions, we show that the new approach effectively incorporates higher χ-order contributions and converges to the same E sym (ρ) much faster than the conventional χ-expansion at densities ≲3ρ 0 . Several quantitative demonstrations using Monte Carlo simulations are given.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Nuclear energy density optimization: Shell structure

Nuclear density functional theory is the only microscopical theory that can be applied throughout the entire nuclear landscape. Its key ingredient is the energy density functional. Here, we propose a new parametrization UNEDF 2 of the Skyrme energy density functional. The functional optimization is carried out using the POUNDERS optimization algorithm within the framework of the Skyrme Hartree-Fock-Bogoliubov theory. Compared to the previous parametrization UNEDF 1, restrictions on the tensor term of the energy density have been lifted, yielding a very general form of the energy density functional up to second order in derivatives of the one-body density matrix. In order to impose constraints on all the parameters of the functional, selected data on single-particle splittings in spherical doubly-magic nuclei have been included into the experimental dataset. The agreement with both bulk and spectroscopic nuclear properties achieved by the resulting UNEDF 2 parametrization is comparable with UNEDF 1. While there is a small improvement on single-particle spectra and binding energies of closed shell nuclei, the reproduction of fission barriers and fission isomer excitation energies has degraded. As compared to previous UNEDF parametrizations, the parameter confidence interval for UNEDF 2 is narrower. In particular, our results overlap well with those obtained in previous systematic studies of the spin-orbit and tensor terms. UNEDF 2 can be viewed as an all-around Skyrme EDF that performs reasonably well for both global nuclear properties and shell structure. However, after adding new data aiming to better constrain the nuclear functional, its quality has improved only marginally. These results suggest that the standard Skyrme energy density has reached its limits, and significant changes to the form of the functional are needed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Higher-order nonequilibrium term: Effective power density quantifying evolution towards or away from local thermodynamic equilibrium

A common approach to assess the nature of energy conversion in a classical fluid or plasma is to compare power densities of the various possible energy conversion mechanisms. A leading research area is quantifying energy conversion for systems that are not in local thermodynamic equilibrium (LTE), as is common in a number of fluid and plasma systems. Here we introduce the “higher-order nonequilibrium term” (HORNET) effective power density, which quantifies the rate of change of departure of a phase space density from LTE. It has dimensions of power density, which allows for quantitative comparisons with standard power densities. We employ particle-in-cell simulations to calculate HORNET during two processes, magnetic reconnection and decaying kinetic turbulence in collisionless magnetized plasmas, that inherently produce non-LTE effects. We investigate the spatial variation of HORNET and the time evolution of its spatial average. By comparing HORNET with power densities describing changes to the internal energy (pressure dilatation, Pi − D , and divergence of the vector heat flux density), we find that HORNET can be a significant fraction of these other measures (8% and 35% for electrons and ions, respectively, for reconnection; up to 67% for both electrons and ions for turbulence), meaning evolution of the system towards or away from LTE can be dynamically important. Applications to numerous plasma phenomena are discussed. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

First-principles equation-of-state table of silicon and its effects on high-energy-density plasma simulations

Using density-functional theory–based molecular-dynamics simulations, we have investigated the equation of state for silicon in a wide range of plasma density and temperature conditions of ρ=0.001–500g/cm 3 and T=2000–10 8 K. With these calculations, we have established a first-principles equation-of-state (FPEOS) table of silicon for high-energy-density (HED) plasma simulations. When compared with the widely used SESAME-EOS model (Table 3810), we find that the FPEOS-predicted Hugoniot is ~20% softer; for off-Hugoniot plasma conditions, the pressure and internal energy in FPEOS are lower than those of SESAME EOS for temperatures above T ≈ 1–10 eV (depending on density), while the former becomes higher in the low- T regime. The pressure difference between FPEOS and SESAME 3810 can reach to ~50%, especially in the warm-dense-matter regime. Implementing the FPEOS table of silicon into our hydrocodes, we have studied its effects on Si-target implosions. When compared with the one-dimensional radiation-hydrodynamics simulation using the SESAME 3810 EOS model, the FPEOS simulation showed that (1) the shock speed in silicon is ~10% slower; (2) the peak density of an in-flight Si shell during implosion is ~20% higher than the SESAME 3810 simulation; (3) the maximum density reached in the FPEOS simulation is ~40% higher at the peak compression; and (4) the final areal density and neutron yield are, respectively, ~30% and ~70% higher predicted by FPEOS versus the traditional simulation using SESAME 3810. All of these features can be attributed to the larger compressibility of silicon predicted by FPEOS. Furthermore, these results indicate that an accurate EOS table, like the FPEOS presented here, could be essential for the precise design of targets for HED experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Accuracy of ab initio electron correlation and electron densities in vanadium dioxide

Here, diffusion quantum Monte Carlo results are used as a reference to analyze properties related to phase stability and magnetism in vanadium dioxide computed with various formulations of density functional theory. We introduce metrics related to energetics, electron densities and spin densities that give us insight on both local and global variations in the antiferromagnetic M1 and R phases. Importantly, these metrics can address contributions arising from the challenging description of the 3d orbital physics in this material. We observe that the best description of energetics between the structural phases does not correspond to the best accuracy in the charge density, which is consistent with observations made recently by Medvedev et~al. in the context of isolated atoms. However, we do find evidence that an accurate spin density connects to correct energetic ordering of different magnetic states in VO$_2$, although local, semilocal, and meta-GGA functionals tend to erroneously favor demagnetization of the vanadium sites. The recently developed SCAN functional stands out as remaining nearly balanced in terms of magnetization across the M1-R transition and correctly predicting the ground state crystal structure. In addition to ranking current density functionals, our reference energies and densities serve as important benchmarks for future functional development.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Nanoscale mapping of the electron density at Al grain boundaries and correlation with grain-boundary energy

Grain-boundary (GB) structures and energies are often calculated and have revealed correlations between the GB energy and change in electron density at the GB. In this work, the plasmon peak in valence electron energy-loss spectroscopy (VEELS) was used to determine the variation in electron density across four well-characterized GBs in Al, spanning a range of known GB energies. The results show that the plasmon energy is lower at the GB than in the adjacent grains due to a decrease in electron density, and the GB energy increases proportional to the density decrease. The decrease in electron density also extends further into adjacent grains with increasing GB energy, extending beyond the geometric changes, or physical width, revealed by electron microscopy. Plasmon damping also increases with increasing GB energy, indicative of increasing disruption of the electron density with increasing GB energy. These results demonstrate that VEELS can be a valuable tool for detecting small electron density changes at GBs, and this change clearly influences, and is correlated to, the GB energy.

36 MATERIALS SCIENCE↗
DOE OSTI2015

SU-E-J-72: Dosimetric Study of Cone-Beam CT-Based Radiation Treatment Planning Using a Patient-Specific Stepwise CT-Density Table

Purpose: To assess dose calculation accuracy of cone-beam CT (CBCT) based treatment plans using a patient-specific stepwise CT-density conversion table in comparison to conventional CT-based treatment plans. Methods: Unlike CT-based treatment planning which use fixed CT-density table, this study used patient-specific CT-density table to minimize the errors in reconstructed mass densities due to the effects of CBCT Hounsfield unit (HU) uncertainties. The patient-specific CT-density table was a stepwise function which maps HUs to only 6 classes of materials with different mass densities: air (0.00121g/cm3), lung (0.26g/cm3), adipose (0.95g/cm3), tissue (1.05 g/cm3), cartilage/bone (1.6g/cm3), and other (3g/cm3). HU thresholds to define different materials were adjusted for each CBCT via best match with the known tissue types in these images. Dose distributions were compared between CT-based plans and CBCT-based plans (IMRT/VMAT) for four types of treatment sites: head and neck (HN), lung, pancreas, and pelvis. For dosimetric comparison, PTV mean dose in both plans were compared. A gamma analysis was also performed to directly compare dosimetry in the two plans. Results: Compared to CT-based plans, the differences for PTV mean dose were 0.1% for pelvis, 1.1% for pancreas, 1.8% for lung, and −2.5% for HN in CBCT-based plans. The gamma passing rate was 99.8% for pelvis, 99.6% for pancreas, and 99.3% for lung with 3%/3mm criteria, and 80.5% for head and neck with 5%/3mm criteria. Different dosimetry accuracy level was observed: 1% for pelvis, 3% for lung and pancreas, and 5% for head and neck. Conclusion: By converting CBCT data to 6 classes of materials for dose calculation, 3% of dose calculation accuracy can be achieved for anatomical sites studied here, except HN which had a 5% accuracy. CBCT-based treatment planning using a patient-specific stepwise CT-density table can facilitate the evaluation of dosimetry changes resulting from variation in patient anatomy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-T-136: Breath Hold Lung Phantom Study in Using CT Density Versus Relative Stopping Power Ratio for Proton Pencil Beam Scanning System

Purpose: To evaluate mass density effects of CT conversion table and its variation in current treatment planning system of spot scanning proton beam using an IROC proton lung phantom for this study. Methods: A proton lung phantom study was acquired to Imaging and Radiation Oncology Core Houston (IROC) Quality Assurance Center. Inside the lung phantom, GAF Chromic films and couples of thermal luminescent dosimeter (TLD) capsules embedded in specified PTV and adjacent structures to monitor delivered dosage and 3D dose distribution profiles. Various material such as cork (Lung), blue water (heart), Techron HPV (ribs) and organic material of balsa wood and cork as dosimetry inserts within phantom of solid water (soft tissue). Relative stopping power (RLSP) values were provided. Our treatment planning system (TPS) doesn’t require SP instead relative density was converted relative to water. However lung phantom was irradiated by planning with density override and the results were compared with IROC measurements. The second attempt was conducted without density override and compared with IROC’s. Results: The higher passing rate of imaging and measurement results of the lung phantom irradiation met the criteria by IROC without density override. The film at coronal plane was found to be shift due to inclined cylinder insertion. The converted CT density worked as expected to correlate relative stopping power. Conclusion: The proton lung phantom provided by IROC is a useful tool to qualify our commissioned proton pencil beam delivery with TPS within reliable confidence. The relative mass stopping power ratios of materials were converted from the relative physical density relative to water and the results were satisfied.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Significant DBSCAN+: Statistically Robust Density-based Clustering

Cluster detection is important and widely used in a variety of applications, including public health, public safety, transportation, and so on. Given a collection of data points, we aim to detect density-connected spatial clusters with varying geometric shapes and densities, under the constraint that the clusters are statistically significant. The problem is challenging, because many societal applications and domain science studies have low tolerance for spurious results, and clusters may have arbitrary shapes and varying densities. As a classical topic in data mining and learning, a myriad of techniques have been developed to detect clusters with both varying shapes and densities (e.g., density-based, hierarchical, spectral, or deep clustering methods). However, the vast majority of these techniques do not consider statistical rigor and are susceptible to detecting spurious clusters formed as a result of natural randomness. On the other hand, scan statistic approaches explicitly control the rate of spurious results, but they typically assume a single “hotspot” of over-density and many rely on further assumptions such as a tessellated input space. To unite the strengths of both lines of work, we propose a statistically robust formulation of a multi-scale DBSCAN, namely Significant DBSCAN+, to identify significant clusters that are density connected. As we will show, incorporation of statistical rigor is a powerful mechanism that allows the new Significant DBSCAN+ to outperform state-of-the-art clustering techniques in various scenarios. We also propose computational enhancements to speed-up the proposed approach. Experiment results show that Significant DBSCAN+ can simultaneously improve the success rate of true cluster detection (e.g., 10–20% increases in absolute F1 scores) and substantially reduce the rate of spurious results (e.g., from thousands/hundreds of spurious detections to none or just a few across 100 datasets), and the acceleration methods can improve the efficiency for both clustered and non-clustered data.

Computer Science↗
DOE OSTI2019

Does Breast Density Increase the Risk of Re-excision for Women with Breast Cancer Having Breast-Conservation Therapy?

Background: Women with dense breasts may have less-accurate preoperative evaluation of extent of disease, potentially affecting the achievement of negative margins. The goal of this study is to examine the association between breast density and re-excision rates in women having breast-conserving surgery for invasive breast cancer. Patients and Methods: Women with stage I/II invasive breast cancer treated with breast-conserving surgery between 1/1/2014 and 10/31/2014 were included. Breast density was assessed by two radiologists. The association between breast density and re-excision was examined using logistic regression. Results: Seven hundred and one women were included. Overall, 106 (15.1%) women had at least one re-excision. Younger age at diagnosis was associated with increased breast density (p < 0.001). On univariable analysis, increased breast density was associated with significantly increased odds of re-excision (odds ratio [OR] 1.38, 95% confidence interval [CI] 1.04–1.83), as was multifocal disease, human epidermal growth factor receptor 2 (HER2) positive status, and extensive intraductal component (EIC) (all p < 0.05). On multivariable analysis, breast density remained significantly associated with increased odds of re-excision (OR 1.37, 95% CI 1.00–1.86), as did multifocality and EIC. HER2 positive status was not significantly associated with re-excision on multivariable analysis. Conclusions: Women with dense breasts are more likely to need additional surgery (re-excision after breast-conserving surgery), but increased breast density did not adversely affect disease-free survival in our study. Our findings support the need for further study in developing techniques that can help decrease re-excisions for women with dense breasts who undergo breast-conserving surgery.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2021

A representation-independent electronic charge density database for crystalline materials

In addition to being the core quantity in density functional theory, the charge density can be used in many tertiary analyses in materials sciences from bonding to assigning charge to specific atoms. The charge density is data-rich since it contains information about all the electrons in the system. With increasing utilization of machine-learning tools in materials sciences, a data-rich object like the charge density can be utilized in a wide range of applications. The database presented here provides a modern and user-friendly interface for a large and continuously updated collection of charge densities as part of the Materials Project. In addition to the charge density data, we provide the theory and code for changing the representation of the charge density which should enable more advanced machine-learning studies for the broader community.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Insights into the crystal chemistry of Earth materials rendered by electron density distributions: Pauling's rules revisited

Pauling's first two rules are examined in terms of the accumulation of the electron density between bonded pairs of atoms for a relatively large number of oxide and silicate crystals and siloxane molecules. The distribution of the electron density shows that the radius of the oxygen atom is not fixed, but that it actually decreases systematically from ~1.40 Å to ~ 0.65 Å as the polarizing power and the electronegativity of the bonded metal atoms increase and the distribution of the O atom is progressively polarized and contracted along the bond vectors by the impact of the bonded interactions. The contractions result in an aspherical oxygen atom that displays as many different bonded “radii” as it has bonded interactions. The bonded radii for the metal atoms match the Shannon and Prewitt ionic radii for the more electropositive atoms like potassium and sodium, but they are systematically larger for the more electronegative atoms like aluminum, silicon and phosphorous. Pauling's first rule is based on the assumption that the radius of the oxide anion is fixed and that the radii of the cations are such that radius sum of the spherical oxide anion and a cation necessarily equals the separation between the cation-anion bonded pair with the coordination number of the cation being determined by the ratio of the radii of the cation and anion. In the case of the bonded radii, the sum of the bonded radii for the metal atoms and the oxide anion necessarily equals the bond lengths by virtue of the way that the bonded radii were determined in the partitioning of the electron density along the bond path into metal and O atom parts. But, the radius ratio for the O and M atoms is an unsatisfactory rule for determining the coordination number of the metal atom inasmuch as a bonded O atom is not, in general, spherical, and its size varies substantially along its bonded directions. But by counting the number of bond paths that radiate from a bonded atom, the coordination number of the atom is determined uniquely independent of the asphericity and sizes of the atom. A power law connection established between the bond lengths and bond strengths for crystals and molecules is mirrored by a comparable power law connection between bond length and the accumulation of the electron density between bonded pairs of atoms, a connection that is consistent with Pauling's electroneutrality postulate that the charges of the atoms in an oxide are negligibly small. The connection indicates that a one-to-one correspondence exists between the accumulation between a pair of bonded atoms and the Pauling bond strength for M-O bonded interaction for all atoms of the periodic table. The connection provides a common basis for understanding the success of the manifold applications that have been made with the bond valence theory model together with the modeling of crystal structures, chemical zoning, leaching and cation transport in batteries and the like. We believe that the wide spread applications of the model in mineralogy and material science owes much of its success to the direct connection between bond strength and the quantum mechanical observable, the electron density distribution. Comparable power law expressions established for the bonded interactions for both crystals and molecules support Pauling's assertion that his second rule has significance for molecules as well as for crystals. A simple expression is found that provides a one to one connection between the accumulation of the electron density between bonded M and O atoms and the Pauling bond strength for all M atoms of the periodic table with ~ 95 % of the variation of the bond strength being explained in terms of a linear dependence on the accumulated electron density. Compelling evidence is presented that supports the argument that the Si-O bonded interactions for tiny siloxane molecules and silicate crystals are chemically equivalent.

Environmental Molecular Sciences Laboratory↗