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At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Study of Protein Dynamics via Neutron Spin Echo Spectroscopy

Most human body proteins' activity and functionality are related to configurational changes of entire subdomains within the protein crystal structure. The crystal structures build the basis for any calculation that describes the structure or dynamics of a protein, most of the time with strong geometrical restrictions. However, these restrictions from the crystal structure are not present in the solution. The structure of the proteins in the solution may differ from the crystal due to rearrangements of loops or subdomains on the pico to nanosecond time scale (i.e., the internal protein dynamics time regime). This study describes how slow motions on timescales of several tens of nanoseconds can be accessed using neutron scattering. In particular, the dynamical characterization of two major human proteins, an intrinsically disordered protein that lacks a well-defined secondary structure and a classical antibody protein, is addressed by neutron spin echo spectroscopy (NSE) combined with a wide range of laboratory characterization methods. Further insights into protein domain dynamics were achieved using mathematical modeling to describe the experimental neutron data and determine the crossover between combined diffusive and internal protein motions. The extraction of the internal dynamic contribution to the intermediate scattering function obtained from NSE, including the timescale of the various movements, allows further vision into the mechanical properties of single proteins and the softness of proteins in their nearly natural environment in the crowded protein solution.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Unravelling the sintering temperature-induced phase transformations in Ba(Fe 0.7 Ta 0.3 )O 3-δ ceramics

This work reports on the fundamental details of the crystal structure and phase transformations in Ba(Fe 0.7 Ta 0.3 )O 3-δ , the best known temperature-independent oxygen-sensing ceramic material for applications in extreme environments. Ba(Fe 0.7 Ta 0.3 )O 3-δ ceramics were synthesized using conventional solid-state ceramic reaction under variable sintering temperatures (T s = 1200–1350 °C). Combined X-ray diffraction (XRD) and high-resolution transmission electron microscopy (TEM) measurements revealed the T s -induced phase transformations and their origin in Ba(Fe 0.7 Ta 0.3 )O 3-δ . Associated with phase transformations, pseudo-cubic (PC) reflections, such as {200} PC , {211} PC , and {220} PC , exhibited distinct anomalies with increasing T s . At T s = 1200 °C, Ba(Fe 0.7 Ta 0.3 )O 3-δ stabilized in mixed orthorhombic + rhombohedral phases (Amm2 + R3m). With increasing T s (≥1250 °C), Ba(Fe 0.7 Ta 0.3 )O 3-δ ceramics stabilized in tetragonal/rhombohedral [P4mm + R3m] mixed phases, while variations in the quantity of the respective phases were observed. Because both structure and crystal chemistry play key roles in achieving enhanced performance in chemical sensing and catalytic converters, detailed understanding of the phase transformations and crystal structure of Ba(Fe 0.7 Ta 0.3 )O 3-δ ceramics, as derived in this work, will be useful to develop chemical sensors with optimum performance for high-temperature and corrosive environments.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Structure prediction of porous organic crystals

In this work, we explore the possibility of applying automated crystal structure prediction to reproduce the experimentally identified metastable porous polymorphs. Using our recently developed High-Throughput Organic Crystal Structure Prediction ( HTOCSP ) framework, we conducted a systematic study on five representative organic crystalline systems including hydrogen-bonded frameworks (HOFs), featured by the presence of significant porosity, in conjunction with different choices of energy models from classical, machine learning force fields, tight binding to density functional theory. Our results suggest that the current structure generation framework, with careful selection of symmetry conditions, is likely to generate rather complex and abundant metastable crystal candidates for porous crystals. In conjunction with the recent advance in universal machine learning force fields, it becomes possible to identify experimental structures as the energetically favorable candidates from a simple energy versus density analysis, thus paving the way for computational design of complex porous materials with the target systems prior to the experimental synthesis and characterization.

36 MATERIALS SCIENCE↗
DOE OSTI2023

High absorption photovoltaic material and methods of making the same

A high absorption photovoltaic material and method of making the material for use in a solar cell are disclosed. The photovoltaic material includes a surface modified with a layer of repeating photonic crystal structures. The photonic crystal structures are approximately inverse conically shaped and have a curved sidewall that has an approximately Gaussian shape. The photonic crystal structures generally have a high vertical depth and sidewall angle. The structures also have a gradient refractive index profile and exhibit the parallel-to-interface refraction light trapping effect. An anti-reflective coating is disposed over the photonic crystal structure layer. The photovoltaic material exhibits near unity light absorption over a broad range of visible and near infrared wavelengths and incidence angles, even at reduced thicknesses. The photovoltaic structures are formed via a combined photolithography and reactive-ion etching method at low power with a gas mixture having a high ratio of an etchant component to a passivation component.

Kuang, Ping↗
DOE OSTI2020

3D Morphology of Bimodal Porous Copper with Nano-Sized and Micron-Sized Pores to Enhance Transport Properties for Functional Applications

Multiscale porous metals with multiscale porosity from nanometer to micrometer have a high specific surface area and high effective diffusivity for ion transport, thereby enhancing functionalities and extending the applications of porous metals. Herein, the Cu–Fe–Al ternary system was selected as the precursor alloy to construct multiscale, bimodal porous copper by the chemical dealloying method. The effect of the phase composition and initial microstructure of precursor alloys (Al x Fe 75– x Cu 25 , x = 10–60) on the three-dimensional (3D) morphology of multiscale porous metals was systematically investigated, with a goal to precisely control the multiscale porous structure. The four crystal structure phases (body-centered cubic (BCC), face-centered cubic (FCC), CsCl type (B2), and monoclinic) in precursor alloys were analyzed by synchrotron X-ray diffraction refinement. The 3D morphology, feature size distribution, and tortuosity of four representative porous Cu after dealloying Al x Fe 75– x Cu 25 ( x = 10, 30, 50, and 60) precursor alloys were directly visualized and quantified via advanced synchrotron X-ray nanotomography. The relationship between the phases/crystal structures of precursor alloys and their corresponding porous morphology was established: the micron-sized pores in bimodal porous Cu are formed by dissolving the CuFeAl phase with BCC and monoclinic crystal structures, and the nano-sized pores are formed by dealloying the CuFeAl phase with FCC and B2 crystal structures. The size of the nanoporous structure depends on the ratio between the more noble and more active components in the precursor alloy, while the size of the microporous structure depends on the corresponding phase size in the precursor alloy. The tortuosity results showed that the multiscale porous structure with both nanoporosity and microporosity exhibits lower tortuosity, which will enhance transport properties for functional applications.

25 ENERGY STORAGE↗
DOE OSTI2021

Cation and anion topotactic transformations in cobaltite thin films leading to Ruddlesden-Popper phases.

Topotactic transformations involve structural changes between related crystal structures due to a loss or gain of material while retaining a crystallographic relationship. The perovskite oxide La0.7Sr0.3CoO3 (LSCO) is an ideal system for investigating phase transformations due to its high oxygen vacancy conductivity, relatively low oxygen vacancy formation energy, and strong coupling of the magnetic and electronic properties to the oxygen stoichiometry. While the transition between cobaltite perovskite and brownmillerite (BM) phases has been widely reported, further reduction beyond the BM phase lacks systematic studies. In this paper, we study the evolution of the physical properties of LSCO thin films upon exposure to highly reducing environments. We observe the rarely reported crystalline Ruddlesden-Popper phase, which involves the loss of both oxygen anions and cobalt cations upon annealing where the cobalt is found as isolated Co ions or Co nanoparticles. First-principles calculations confirm that the concurrent loss of oxygen and cobalt ions is thermodynamically possible through an intermediary BM phase. The strong correlation of the magnetic and electronic properties to the crystal structure highlights the potential of utilizing ion migration as a basis for emerging applications such as neuromorphic computing.

Chiu, I-Ting↗
DOE OSTI2022

Synthesis of dysprosium oxychloride (DyOCl)

Dysprosium oxychloride, DyOCl, was synthesized using a simple dehydration method with DyCl3·6H2O. X-ray powder diffraction data was used to determine the crystal structure. The DyOCl compound is isostructural to the matlockite (PbFCl) crystal structure and crystallizes in the tetragonal P4/nmm (#129) space group. The crystal structure contains the alternating cationic layers of (DyO)n and anionic layers of nCl– along the c-axis. The structural data including unit cell, volume, and density of DyOCl were compared to other REOCl data from Inorganic Crystal Structure Database (ICSD) and our previous study on TbOCl. Fourier-transform infrared spectroscopy (FTIR) was performed, and the vibrations of DyOCl possibly from Dy–O and Dy–Cl were observed at 543 and 744 cm-1. Scanning electron microscopy analysis (SEM) showed irregularly shaped crystals.

Chong, Saehwa↗
DOE OSTI2025

Role of the Mobile Active Site Flap in IMP Dehydrogenase Inhibitor Binding

Inosine 5′-monophosphate dehydrogenase (IMPDH) is a promising antibiotic target. This enzyme catalyzes the NAD-dependent oxidation of inosine 5′-monophosphate (IMP) to xanthosine 5′-monophosphate (XMP), which is the rate-limiting step in guanine nucleotide biosynthesis. Bacterial IMPDH-specific inhibitors have been developed that bind to the NAD + site. These inhibitors display varied affinities to different bacterial IMPDHs that are not easily rationalized by X-ray crystal structures of enzyme–inhibitor complexes. Inspection of X-ray crystal structures of 25 enzyme–inhibitor complexes, including 10 newly described, suggested that a mobile active site flap may be a structural determinant of inhibitor potency. Saturation transfer difference NMR experiments also suggested that the flap may contact the inhibitors to varying extents in different IMPDHs. Flap residue Leu413 contacted some inhibitors but was not structured in the crystal structures of other inhibitor complexes. The substitution of Leu413 with Phe or Ala in Bacillus anthracis IMPDH had inhibitor-selective effects, suggesting residue 413 could be a structural determinant of affinity. Curiously, the Ala substitution increased the potency of most inhibitors, even those that contacted Leu413 in the crystal structures. Presteady-state and steady-state kinetics experiments showed that the Leu413Ala substitution had comparable effects on inhibitor binding to the noncovalent E·IMP complex and the covalent intermediate E-XMP*, suggesting that the flap had similar interactions in both complexes. These results demonstrate that contacts do not necessarily indicate favorable interactions, and poorly structured mobile regions should not be discounted when assessing binding determinants.

Conformation↗
DOE OSTI2026

A New Nitrogen-Rich Energetic Material with So Many Tautomers

A new nitrogen-rich triazolo-triazole compound, (3-(6-methyl-1H-[1,2,4]triazolo[4,3-b][1,2,4]triazol-3-yl)-1H-1,2,4-triazol-5-amine), TTT1, has been prepared, and its acid–base and tautomeric behavior has been investigated. In the pH range of 0.3–12, TTT1 can accept up to two protons, forming a monocation and a dication, and can deliver one proton, forming a monoanion. The tautomeric behavior is particularly rich for the monocation, for which computational analysis predicts four different tautomers in a narrow energy range of 2 kcal/mol. Two of these tautomers (2H-7H-8H and 3H-7H-8H) have been isolated in salts of the monocation with suitable counterions (chloride, bromide, perchlorate). Surprisingly, the most stable predicted tautomer, 1H-3H-7H, has not been found in the four crystallized salts of the monocation. The energetic perchlorate salt of the monocation (3H-7H-8H tautomer) shows good thermal stability and good stability to impact, friction, and electric discharge. The packing of this compound shows the formation of H-bonded dimers with interactions between N8–H···N1. The crystal structure of this energetic salt was studied experimentally up to 2.8 GPa; no phase change or decomposition was observed.

Chemical structure↗
DOE OSTI2022

Machine Learning-Guided Discovery of Ternary Compounds Containing La, P, and Group 14 Elements

In this work, we integrate a deep machine learning (ML) method with first-principles calculations to efficiently search for the energetically favorable ternary compounds. Using La–Si–P as a prototype system, we demonstrate that ML-guided first-principles calculations can efficiently explore crystal structures and their relative energetic stabilities, thus greatly accelerate the pace of material discovery. A number of new La–Si–P ternary compounds with formation energies less than 30 meV/atom above the known ternary convex hull are discovered. Among them, the formation energies of La 5 SiP 3 and La 2 SiP phases are only 2 and 10 meV/atom, respectively, above the convex hull. These two compounds are dynamically stable with no imaginary phonon modes. Moreover, by replacing Si with heavier-group 14 elements in the eight lowest-energy La–Si–P structures from our ML-guided predictions, a number of low-energy La–X–P phases (X = Ge, Sn, Pb) are predicted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Ethane and methane at high pressures: Structure and stability

We have performed a combined experimental and theoretical study of ethane and methane at high pressures of up to 120 GPa at 300 K using x-ray diffraction and Raman spectroscopies and the USPEX ab initio evolutionary structural search algorithm, respectively. For ethane, we have determined the crystallization point, for room temperature, at 2.7 GPa and also the low pressure crystal structure (phase A). This crystal structure is orientationally disordered (plastic phase) and deviates from the known crystal structures for ethane at low temperatures. Moreover, a pressure induced phase transition has been identified, for the first time, at 13.6 GPa to a monoclinic phase B, the structure of which is solved based on good agreement with the experimental results and theoretical predictions. For methane, our x-ray diffraction measurements are in agreement with the previously reported high-pressure structures and equation of state (EOS). Finally, we have determined the EOSs of ethane and methane, which provides a solid basis for the discussion of their relative stability at high pressures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Competition of magnetocrystalline anisotropy of uranium layers and zigzag chains in UNi 0.34 Ge 2 single crystals

Structural and thermodynamic properties of single-crystalline UNi 1-x Ge 2 with x = 0.66 have been investigated by measuring magnetization, specific heat, and thermal expansion over a wide range of temperatures and magnetic fields. The measurements revealed the emergence of a long-range antiferromagnetic ordering of uranium magnetic moments below the Néel temperature T N = 45.5 (1) K and the existence of two easy axes in the studied compound, namely b and c, which correspond to the planes of the uranium zig-zag chains. A magnetic field applied along these two crystallographic directions induces in the system a first-order metamagnetic phase transition (from antiferromagnetic to field-polarized paramagnetism), and the width of the magnetic hysteresis associated with that transition reaches as much as 40 kOe at the lowest temperatures. A magnetic phase diagram developed from the experimental data showed that the metastable region associated with that magnetic hysteresis forms a funnel that narrows toward the N´eel point in a zero magnetic field. The four-layer Ising model has successfully predicted the colinear antiferromagnetic structure in UNi 0.34 Ge 2 (known from earlier reports), its magnetic phase diagram, and temperature and field variations of its magnetization. Moreover, it suggests that the first-order phase transition extends down to zero magnetic field, although it is barely detectable in the experiments performed in low magnetic fields. According to this model, the second-order phase transition occurs in the compound only in zero field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

CASM — A software package for first-principles based study of multicomponent crystalline solids

CASM is a software package that enables first-principles based studies of crystalline materials. It has been designed to treat coupled chemical, mechanical, vibrational, and magnetic degrees of freedom to determine ground state and finite temperature properties of crystals. The symmetry of the underlying parent crystal structure is used to enumerate perturbations of the parent crystal structure and generate derivative structures which can be input to first-principles calculations in order to explore the ground state energy landscape. CASM algorithmically constructs cluster expansions that fully couple discrete and continuous degrees of freedom, and generates highly efficient code to evaluate the cluster expansion basis functions. Widely used machine learning methods are integrated for fitting expansion coefficients to first-principle calculations. The fully parameterized cluster expansions can be combined with (kinetic) Monte Carlo methods to calculate finite temperature thermodynamic and kinetic properties. CASM Alloy Manager identifies distinct parent crystal structures in an alloy system, creating individual projects for each, and integrating the results. The integrated infrastructure facilitates the linkage between first-principles statistical mechanics predictions with higher length scale computational methods, such as phase field simulations. In conclusion, CASM projects are designed to be easy to share in repositories, to re-use, and to extend to include additional chemical species or types of degrees of freedom.

36 MATERIALS SCIENCE↗
DOE OSTI2022

ORNL_AISD_NiNb

This dataset describes the nickel-niobium solid solution binary alloy, where the two constituent elements nickel (Ni) and niobium (Nb) are randomly placed on an underlying crystal lattice. This dataset for nickel-niobium (Ni-Nb) alloys available includes the formation energy and bulk modulus for each crystal structure. Each atomic sample has a disordered phase which is obtained starting from an initial regular crystal structure of type body-centered cubic (BCC), face-centered cubic (FCC), or hexagonal compact packed (HCP). The geometry optimization ensures that all the alloy samples reached the equilibrium with negative formation energy. We perform geometry optimizations using the LAMMPS simulation package [1], a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. We utilized the embedded atom model (EAM) potential for Ni and Nb developed in a previous study [2]. The potential could describe behaviors of the liquid and solid phases of Ni-Nb alloy. The structural factors and angular distributions of three atoms are well-matched with X-ray and ab initio-based molecular dynamics data. We prepared the three different crystals with different initial lattice parameters (3.52 Ã… for FCC, 3.32 Ã… for BCC, and 3.5 Ã… for HCP). We performed energy minimization in two steps. Firstly, we minimized the structures with an isotropic unit cell to minimize the side effects from our arbitrary lattice parameters for all other compositions. Then, we applied geometry optimization with a triclinic (non-orthogonal) unit cell to fully minimize the stress components to calculate the elastic constants. In this procedure, we chose 10,000 as the maximum number of allowable steps aimed at obtaining fully relaxed atomic geometries. The dataset consists of three sets of crystal structures. The first set contains 46,086 irregular crystal structures, each of them with 54 atoms, obtained through optimization starting from a regular BCC crystal structure. The second set contains 24,543 irregular crystal structures, each of them with 32 atoms, obtained through optimization starting from a regular FCC crystal structure. The third set contains 39,303 irregular crystal structures, each of them with 48 atoms, obtained through optimization starting from a regular HCP crystal structure. The atomic configurations within each set span the possible compositional range. The three sets have been unified in a global dataset, which is extremely heterogeneous in terms of crystal structures, lattice volumes, and atomic configurations. Organization of files inside the dataset: the dataset contains three subdirectories called • BCC_opt • FCC_opt • HCP_opt based on the type of initial regular structure used to start the geometry optimization. Inside each of these folders, every atomic structure is identified by a string “A_B_Câ€, where A denotes the number of Nb in the system, B denotes index of structure with a given Nb number, and C denotes the total number of structures generated with a given Nb number. For each optimized crystal structure identified by the unique string of characters “A_B_Câ€, three files are provided: • A_B_C_opt.xyz: The optimized geometries in xyz format • A_B_C_opt.cfg: The optimized geometries in cfg format. It includes cell information and atomic energy, and forces calculated from LAMMPS. • A_B_C.elastic: Raw data of 21 elastic constants from LAMMPS output. • A_B_C.bulk: Calculated upper and lower bounds of bulk modulus and averaged one based on Voigt-Reuss-Hill approach from *.elastic. References: [1] A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in 't Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, and S. J. Plimpton. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comp. Phys. Comm., 271:108171, 2022. [2] Y Zhang, R Ashcraft, MI Mendelev, CZ Wang, and KF Kelton. Experimental and molecular dynamics simulation study of structure of liquid and amorphous ni62nb38 alloy. The Journal of chemical physics, 145(20):204505, 2016.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The influence of the 6s 2 configuration of Bi 3+ on the structures of A′BiNb 2 O 7 (A′ = Rb, Na, Li) layered perovskite oxides

Solid state compounds which exhibit non-centrosymmetric crystal structures are of great interest due to the physical properties they can exhibit. Here, the ‘hybrid improper’ mechanism – in which two non-polar distortion modes couple to, and stabilize, a further polar distortion mode, yielding an acentric crystal structure – offers opportunities to prepare a range of novel non-centrosymmetric solids, but examples of compounds exhibiting acentric crystal structures stabilized by this mechanism are still relatively rare. Here we describe a series of bismuth-containing layered perovskite oxide phases, RbBiNb 2 O 7 , LiBiNb 2 O 7 and NaBiNb 2 O 7 , which have structural frameworks compatible with hybrid-improper ferroelectricity, but also contain Bi 3+ cations which are often observed to stabilize acentric crystal structures due to their 6s 2 electronic configurations. Neutron powder diffraction analysis reveals that RbBiNb 2 O 7 and LiBiNb 2 O 7 adopt polar crystal structures (space groups I2cm and B2cm respectively), compatible with stabilization by a trilinear coupling of non-polar and polar modes. The Bi 3+ cations present are observed to enhance the magnitude of the polar distortions of these phases, but are not the primary driver for the acentric structure, as evidenced by the observation that replacing the Bi 3+ cations with Nd 3+ cations does not change the structural symmetry of the compounds. In contrast the non-centrosymmetric, but non-polar structure of NaBiNb 2 O 7 (space group P2 1 2 1 2 1 ) differs significantly from the centrosymmetric structure of NaNdNb 2 O 7 , which is attributed to a second-order Jahn-Teller distortion associated with the presence of the Bi3+ cations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Comparing the structures and photophysical properties of two charge transfer co-crystals

Organic co-crystals have emerged as a promising class of semiconductors for next-generation optoelectronic devices due to their unique photophysical properties. This paper presents a joint experimental-theoretical study comparing the crystal structure, spectroscopy, and electronic structure of two charge transfer co-crystals. Reported herein is a novel co-crystal Npe:TCNQ, formed from 4-(1-naphthylvinyl)pyridine (Npe) and 7,7,8,8-tetracyanoquinodimethane (TCNQ) via molecular self-assembly. This work also presents a revised study of the co-crystal composed of Npe and 1,2,4,5-tetracyanobenzene (TCNB) molecules, Npe:TCNB, herein reported with a higher-symmetry (monoclinic) crystal structure than previously published. Npe:TCNB and Npe:TCNQ dimer clusters are used as theoretical model systems for the co-crystals; the geometries of the dimers are compared to geometries of the extended solids, which are computed with periodic boundary conditions density functional theory. UV-Vis absorption spectra of the dimers are computed with time-dependent density functional theory and compared to experimental UV-Vis diffuse reflectance spectra. Both Npe:TCNB and Npe:TCNQ are found to exhibit neutral character in the S 0 state and ionic character in the S 1 state. In conclusion, the high degree of charge transfer in the S 1 state of both Npe:TCNB and Npe:TCNQ is rationalized by analyzing the changes in orbital localization associated with the S 1 transitions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Pauling’s rules for oxide-based minerals: A re-examination based on quantum mechanical constraints and modern applications of bond-valence theory to Earth materials

Since their introduction in 1929, Pauling’s five rules have been used by scientists from many disciplines to rationalize and predict stable arrangements of atoms and coordination polyhedra in crystalline solids; amorphous materials such as silicate glasses and melts; nanomaterials, poorly crystalline solids; aqueous cation and anion complexes; and sorption complexes at mineral-aqueous solution interfaces. The predictive power of these simple yet powerful rules was challenged recently by George et al. (2020), who performed a statistical analysis of the performance of Pauling’s five rules for about 5000 oxide crystal structures. They concluded that only 13% of the oxides satisfy the last four rules simultaneously and that the second rule has the most exceptions. They also found that Pauling’s first rule is satisfied for only 66% of the coordination environments tested and concluded that no simple rule linking ionic radius to coordination environment will be predictive due to the variable quality of univalent radii. We address these concerns and discuss quantum mechanical calculations that complement Pauling’s rules, particularly his first (radius sum and radius ratio rule) and second (electrostatic valence rule) rules. We also present a more realistic view of the bonded radii of atoms, derived by determining the local minimum in the electron density distribution measured along trajectories between bonded atoms known as bond paths, i.e., the bond critical point (rc). Electron density at the bond critical point is a quantum mechanical observable that correlates well with Pauling bond strength. Moreover, a metal atom in a polyhedron has as many bonded radii as it has bonded interactions, resulting in metal and O atoms that may not be spherical. O atoms, for example, are not spherical in many oxide-based crystal structures. Instead, the electron density of a bonded oxygen is often highly distorted or polarized, with its bonded radius decreasing systematically from ~1.38 Å when bonded to highly electropositive atoms like sodium to 0.64 Å when bonded to highly electronegative atoms like nitrogen. Bonded radii determined for metal atoms match the Shannon (1976) radii for more electropositive atoms, but the match decreases systematically as the electronegativities of the M atoms increase. As a result, significant departures from the radius ratio rule in the analysis by George et al. (2020) is not surprising. We offer a modified, more fundamental version of Pauling’s first rule and demonstrate that the second rule has a one-to-one connection between the electron density accumulated between the bonded atoms at the bond critical point and the Pauling bond strength of the bonded interaction. Pauling’s second rule implicitly assumes that bond strength is invariant with bond length for a given pair of bonded atoms. Many studies have since shown that this is not the case, and Brown and Shannon (1973) developed an equation and a set of parameters to describe the relation between bond length and bond strength, now redefined as bond valence to avoid confusion with Pauling bond-strength. Brown (1980) used the valence-sum rule, together with the path rule and the valence-matching principle, as the three axioms of bond-valence theory (BVT), a powerful method for understanding many otherwise elusive aspects of crystals and also their participation in dynamic processes. We show how a priori bond-valence calculations can predict unstrained bond-lengths and how bond-valence mapping can locate low-Z atoms in a crystal structure (e.g., Li) or examine possible diffusion pathways for atoms through crystal structures. In addition, we briefly discuss Pauling’s third, fourth, and fifth rules, the first two of which concern the sharing of polyhedron elements (edges and faces) and the common instability associated with structures in which a polyhedron shares an edge or face with another polyhedron and contains high-valence cations. The olivine [α-(MgxFe1–x)2SiO4] crystal structure is used to illustrate the distortions from hexagonal close-packing of O atoms caused by metal-metal repulsion across shared polyhedron edges. We conclude by discussing several applications of BVT to Earth materials, including the use of BVT to: (1) locate H+ ions in crystal structures, including the location of protons in the crystal structures of nominally anhydrous minerals in Earth’s mantle; (2) determine how strongly bonded (usually anionic) structural units interact with weakly bonded (usually cationic) interstitial complexes in complex uranyl-oxide and uranyl-oxysalt minerals using the valence-matching principle; (3) calculate Lewis acid strengths of cations and Lewis base strengths of anions; (4) determine how (H2O) groups can function as bond-valence transformers by dividing one bond into two bonds of half the bond valence; (5) help characterize products of sorption reactions of aqueous cations (e.g., Co2+ and Pb2+) and oxyanions [e.g., selenate (Se6+O4)2- and selenite (Se4+O3)2-] at mineral-aqueous solution interfaces and the important role of protons in these reactions; and (6) help characterize the local coordination environments of highly charged cations (e.g., Zr4+, Ti4+, U4+, U5+, and U6+) in silicate glasses and melts.

Geochemistry & Geophysics↗