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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↗

Body of Knowledge (BOK) for Copper Wire Bonds

Copper wire bonds have replaced gold wire bonds in the majority of commercial semiconductor devices for the latest technology nodes. Although economics has been the driving mechanism to lower semiconductor packaging costs for a savings of about 20% by replacing gold wire bonds with copper, copper also has materials property advantages over gold. When compared to gold, copper has approximately: 25% lower electrical resistivity, 30% higher thermal conductivity, 75% higher tensile strength and 45% higher modulus of elasticity. Copper wire bonds on aluminum bond pads are also more mechanically robust over time and elevated temperature due to the slower intermetallic formation rate - approximately 1/100th that of the gold to aluminum intermetallic formation rate. However, there are significant tradeoffs with copper wire bonding - copper has twice the hardness of gold which results in a narrower bonding manufacturing process window and requires that the semiconductor companies design more mechanically rigid bonding pads to prevent cratering to both the bond pad and underlying chip structure. Furthermore, copper is significantly more prone to corrosion issues. The semiconductor packaging industry has responded to this corrosion concern by creating a palladium coated copper bonding wire, which is more corrosion resistant than pure copper bonding wire. Also, the selection of the device molding compound is critical because use of environmentally friendly green compounds can result in internal CTE (Coefficient of Thermal Expansion) mismatches with the copper wire bonds that can eventually lead to device failures during thermal cycling. Despite the difficult problems associated with the changeover to copper bonding wire, there are billions of copper wire bonded devices delivered annually to customers. It is noteworthy that Texas Instruments announced in October of 2014 that they are shipping microcircuits containing copper wire bonds for safety critical automotive applications. An evaluation of copper wire bond technology for applicability to spaceflight hardware may be warranted along with concurrently compiling a comprehensive understanding of the failure mechanisms involved with copper wire bonded semiconductor devices.

Body of Knowledge (BOK)↗

Urethane/Silicone Adhesives for Bonding Flexing Metal Parts

Adhesives that are blends of commercially available urethane and silicone adhesives have been found to be useful for bonding metal parts that flex somewhat during use. These urethane/silicone adhesives are formulated for the specific metal parts to be bonded. The bonds formed by these adhesives have peel and shear strengths greater than those of bonds formed by double-sided tapes and by other adhesives, including epoxies and neat silicones. In addition, unlike the bonds formed by epoxies, the bonds formed by these adhesives retain flexibility. In the initial application for which the urethane/silicone adhesives were devised, there was a need to bond spring rings, which provide longitudinal rigidity for inflatable satellite booms, with the blades that provide the booms axial strength. The problem was to make the bonds withstand the stresses, associated with differences in curvature between the bonded parts, that arose when the booms were deflated and the springs were compressed. In experiments using single adhesives (that is, not the urethane/ silicone blends), the bonds were broken and, in each experiment, it was found that the adhesive bonded well with either the ring or with the blade, but not both. After numerous experiments, the adhesive that bonded best with the rings and the adhesive that bonded best with the blades were identified. These adhesives were then blended and, as expected, the blend bonded well with both the rings and the blades. The two adhesives are Kalex (or equivalent) high-shear-strength urethane and Dow Corning 732 (or equivalent) silicone. The nominal mixture ratio is 5 volume parts of the urethane per 1 volume part of the silicone. Increasing the proportion of silicone makes the bond weaker but more flexible, and decreasing the proportion of silicone makes the bond stronger but more brittle. The urethane/silicone blend must be prepared and used quickly because of the limited working time of the urethane: The precursor of the urethane adhesive is supplied in a two-part form, comprising a resin and a hardener that must be mixed. The resulting urethane adhesive has a working time of 3 to 5 minutes. To prepare the urethane/silicone blend, one must quickly add the silicone to the urethane adhesive and mix it in thoroughly within the working time of the urethane. Once the urethane/silicone blend has been mixed and applied to the bond surfaces, it takes about 2 hours for the adhesive to cure under pressure. However, it takes about 24 hours for the adhesive to reach full strength.

Edwards, Paul D.↗

Thermal Transport and Mechanical Stress Mapping of a Compression Bonded GaN/Diamond Interface for Vertical Power Devices

Bonding diamond to the back side of gallium nitride (GaN) electronics has been shown to improve thermal management in lateral devices; however, engineering challenges remain with the bonding process and characterizing the bond quality for vertical device architectures. Here, in this study, integration of these two materials is achieved by room-temperature compression bonding centimeter-scale GaN and a diamond die via an intermetallic bonding layer of Ti/Au. Recent attempts at GaN/diamond bonding have utilized a modified surface activation bonding (SAB) method, which requires Ar fast atom bombardment immediately followed by bonding within the same tool under ultrahigh vacuum (UHV) conditions. The method presented here does not require a dedicated SAB tool yet still achieves bonding via a room-temperature metal–metal compression process. Imaging of the buried interface and the total bonding area is achieved via transmission electron microscopy (TEM) and confocal acoustic scanning microscopy (C-SAM), respectively. The thermal transport quality of the bond is extracted from spatially resolved frequency-domain thermoreflectance (FDTR) with the bonded areas boasting a thermal boundary conductance of >100 MW/m 2 ·K. Additionally, Raman maps of GaN near the GaN–diamond interface reveal a low level of compressive stress, <80 MPa, in well-bonded regions. FDTR and Raman were coutilized to map these buried interfaces and revealed some poor thermally bonded areas bordered by high-stress regions, highlighting the importance of spatial sampling for a complete picture of bond quality. Overall, this work demonstrates a novel method for thermal management in vertical GaN devices that maintains low intrinsic stresses while boasting high thermal boundary conductances.

Raman↗

Environmental Contributions to Proton Sharing in Protein Low-Barrier Hydrogen Bonds

Hydrogen bonds (H-bonds) are central to biomolecular structure and dynamics. Although H-bonds are typically characterized by well-defined proton positions, proton delocalization has been proposed to play a role in facilitating enzyme catalysis and allostery in some systems. Experimentally locating protons is difficult, hampering the study of proton mobility in H-bonds. We used neutron crystallography, atomic resolution X-ray bond length analysis, and large quantum mechanics/molecular mechanics-Born–Oppenheimer molecular dynamics (QM/MM-BOMD) simulations to comprehensively characterize the shared proton/deuteron in a Glu–Asp low-barrier hydrogen bond (LBHB) in the bacterial protein YajL that is a conventional H-bond in the homologous disease-associated human protein DJ-1. X-ray bond length analysis of protiated and perdeuterated DJ-1 and YajL shows no significant effect of deuteron substitution on these carboxylic acid-carboxylate H-bonds but does reveal an effect at the active site glutamic acid near a cysteine thiolate. Residues in an H-bonded network that might favor LBHB formation in YajL were interrogated by the mutation of homologous residues in DJ-1. A distal DJ-1 substitution increases proton delocalization in the Glu–Asp H-bond, demonstrating that mutations within extended H-bond networks can modulate proton transfer barriers in carboxylic acid-carboxylate H-bonds. In addition, proton mobility in the H-bond is correlated with dimer-spanning motions in the QM/MM-BOMD simulations of YajL and DJ-1. Our results show that proton delocalization can be tuned using combined bioinformatic, structural, and computational information, opening the possibility of using engineered proton delocalization as a probe of H-bonding environments and as a tool to test hypotheses about LBHB function.

Lin, Jiusheng [University of Nebraska, Lincoln, NE↗

Th 2 O – , Th 2 Au – , and Th 2 AuO 1,2 – Anions: Photoelectron Spectroscopic and Computational Characterization of Energetics and Bonding

The observation and characterization of the anions: Th 2 O – , Th 2 Au – , and Th 2 AuO 1,2 – is reported. These species were studied through a synergetic combination of anion photoelectron spectroscopy and ab initio correlated molecular orbital theory calculations at the CCSD(T) level with large correlation-consistent basis sets. To better understand the energetics and bonding in these anions and their corresponding neutrals, a range of smaller diatomic to tetratomic species were studied computationally. Correlated molecular orbital theory calculations at the CCSD(T) level showed that in most of these cases, there are close-lying anions and neutral clusters with different geometries and spin states and are consistent with the experimentally observed spectra. Thus, comparison of experimentally determined and computationally predicted vertical detachment energies and electron affinities for different optimized geometries and spin states shows excellent agreement to within 0.1 eV. The structures for both the neutrals and anions have a significant ionic component to the bonding because of the large electron affinity of the Au atom and modest ionization potentials for Th 2 , Th 2 O, and Th 2 O 2 . The analysis of the bonding for the Th–Th bonds from the molecular orbitals is consistent with this ionic model. The results show that there is a wide variation in the bond distance from 2.7 to 3.5 Å for the Th–Th bonds all of which are less than twice the atomic radius of Th of 3.6 Å. The bond distances encompass bond orders from 4 to 0. Furthermore, there can be different bond orders for the same bond distance depending on the nature of the ionic bonding suggesting that one may not be able to correlate the bond order with the bond distance in these types of clusters. In addition, the presence of an Au atom may provide a unique probe of the bonding in such clusters because of its ability to accept an electron from clusters with modest ionization potentials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗