Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “INTERSTITIALS”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20

Limitations of the TG-43 formalism for skin high-dose-rate brachytherapy dose calculations

Purpose: In skin high-dose-rate (HDR) brachytherapy, sources are located outside, in contact with, or implanted at some depth below the skin surface. Most treatment planning systems use the TG-43 formalism, which is based on single-source dose superposition within an infinite water medium without accounting for the true geometry in which conditions for scattered radiation are altered by the presence of air. The purpose of this study is to evaluate the dosimetric limitations of the TG-43 formalism in HDR skin brachytherapy and the potential clinical impact. Methods: Dose rate distributions of typical configurations used in skin brachytherapy were obtained: a 5 cm × 5 cm superficial mould; a source inside a catheter located at the skin surface with and without backscatter bolus; and a typical interstitial implant consisting of an HDR source in a catheter located at a depth of 0.5 cm. Commercially available HDR{sup 60}Co and {sup 192}Ir sources and a hypothetical {sup 169}Yb source were considered. The Geant4 Monte Carlo radiation transport code was used to estimate dose rate distributions for the configurations considered. These results were then compared to those obtained with the TG-43 dose calculation formalism. In particular, the influence of adding bolus material over the implant was studied. Results: For a 5 cm × 5 cm{sup 192}Ir superficial mould and 0.5 cm prescription depth, dose differences in comparison to the TG-43 method were about −3%. When the source was positioned at the skin surface, dose differences were smaller than −1% for {sup 60}Co and {sup 192}Ir, yet −3% for {sup 169}Yb. For the interstitial implant, dose differences at the skin surface were −7% for {sup 60}Co, −0.6% for {sup 192}Ir, and −2.5% for {sup 169}Yb. Conclusions: This study indicates the following: (i) for the superficial mould, no bolus is needed; (ii) when the source is in contact with the skin surface, no bolus is needed for either {sup 60}Co and {sup 192}Ir. For lower energy radionuclides like {sup 169}Yb, bolus may be needed; and (iii) for the interstitial case, at least a 0.1 cm bolus is advised for {sup 60}Co to avoid underdosing superficial target layers. For {sup 192}Ir and {sup 169}Yb, no bolus is needed. For those cases where no bolus is needed, its use might be detrimental as the lack of radiation scatter may be beneficial to the patient, although the 2% tolerance for dose calculation accuracy recommended in the AAPM TG-56 report is not fulfilled.

61 RADIATION PROTECTION AND DOSIMETRY↗

Electronic characterization of defects in narrow gap semiconductors

We use a Green's function technique to calculate the position of deep defects in narrow gap semiconductors. We consider substitutional (including antisite), vacancy, and interstitial (self and foreign) deep defects. We also use perturbation theory to look at the effect of nonparabolic bands on shallow defect energies and find nonparabolicity can increase the binding by 10 percent or so. We consider mercury cadmium telluride (MCT), mercury zinc telluride (MZT), and mercury zinc selenide (MZS). For substitutional and interstitial defects we look at the situation with and without relaxation. For substitutional impurities in MCT, MZT, and MZS, we consider x (the concentration of Cd or Zn) in the range 0.1 less than x less than 0.3 and also consider appropriate x so E(sub g) = 0.1 eV for each of the three compounds. We consider several cation site s-like deep levels and anion site p-like levels. For E(sub g) = 0.1 eV, we also consider the effects of relaxation. Similar comments apply to the interstitial deep levels whereas no relaxation is considered for the ideal vacancy model. Relaxation effects can be greater for the interstitial than the substitutional cases. Specific results are given in figures and tables and comparison to experiment is made in a limited number of cases. We find, for example, that I, Se, S, Rn, and N are possible cation site, s-like deep levels in MCT and Zn and Mg are for anion site, p-like levels (both levels for substitutional cases). The corresponding cation and anion site levels for interstitial deep defects are (Au, Ag, Hg, Cd, Cu, Zn) and (N, Ar, O, F). For the substitutional cases we have some examples of relaxation moving the levels into the band gap, whereas for the interstitial case we have examples where relaxation moves it out of the band gap. Future work involves calculating the effects of charge state interaction and seeing the effect of relaxation on vacancy levels.

Patterson, James D.↗

Blind Leak Detection for Closed Systems

The current inspection technique for locating interstitial leaking in the Space Shuttle Main Engine nozzles is the application of a liquid leak check solution in the openings where the interstitials space between the tubing and the structural jacket vent out the aft end of the nozzle, while its cooling tubes are pressurized to 25 psig with Helium. When a leak is found, it is classified, and if the leak is severe enough the suspect tube is cut open so that a boroscope can be inserted to find the leak point. Since the boroscope can only cover a finite tube length and since it is impossible to identify which tube (to the right or left of the identified interstitial) is leaking, many extra and undesired repairs have been made to fix just one leak. In certain instances when the interstitials are interlinked by poor braze bonding, many interstitials will show indications of leaking from a single source. What is desired is a technique that can identify the leak source so that a single repair can be performed. Dr, Samuel Russell and James Walker, both with NASA/MSFC have developed a thermographic inspection system that addresses a single repair approach. They have teamed with Boeing/Rocketdyne to repackage the inspection processes to be suitable to address full scale Shuttle development and flight hardware and implement the process at NASA centers. The methods and results presented address the thermographic identification of interstitial leaks in the Space Shuttle Main Engine nozzles. A highly sensitive digital infrared camera (capable of detecting a delta temperature difference of 0.025 C) is used to record the cooling effects associated with a leak source, such as a crack or pinhole, hidden within the nozzle wall by observing the inner hot wall surface as the nozzle is pressurized, These images are enhanced by digitally subtracting a thermal reference image taken before pressurization. The method provides a non-intrusive way of locating the tube that is leaking and the exact leak source position to within a very small axial distance. Many of the factors that influence the inspectability of the nozzle are addressed; including pressure rate, peak pressure, gas type, ambient temperature and surface preparation. Other applications for this thermographic inspection system are the Reinforced-Carbon-Carbon (RCC) leading edge of the Space Shuttle orbiter and braze joint integrity.

Oelgoetz, Peter↗

On the mobility of defect clusters and their effect on microstructure evolution in fcc Ni under irradiation

Here, µs-scale molecular dynamics studies of vacancy and interstitial clusters in fcc Ni revealed three- and one- dimensional (3-D and 1-D) modes of the cluster motion. The 1-D mobility of interstitial defects is known to enhance swelling rate. The theoretical analysis performed here suggests two novel mechanism by which the 3-D mobile clusters affect microstructure evolution under irradiation. First, the mobility of vacancy clusters hinders nucleation of stable voids due to recombination with interstitial-type loops and edge dislocations. Second, the capture efficiency of dislocations is higher for 3-D mobile vacancy and interstitial clusters than single defects, with the combined effect depending on relative fractions of clustered vacancies and interstitials produced in cascades. The observed differences in radiation damage of most fcc and bcc metals is attributed to the difference in cascade-produced vacancy defects: immobile SFTs and loops in fcc metals and mobile clusters in bcc metals. In this context, fcc Ni is similar to bcc metals due to its high stacking fault energy.

36 MATERIALS SCIENCE↗

Nitrogen diffusion in hafnia and the impact of nitridation on oxygen and hydrogen diffusion: A first-principles study

Using first-principles simulations, we have computed incorporation energies and diffusion barriers of ammonia, the nitrogen molecule and atomic nitrogen in monoclinic hafnia (m-HfO{sub 2}). Our calculations show that ammonia is likely to dissociate into an NH{sub 2} molecular unit, whereas the nitrogen molecule remains as a molecule either in the interstitial space or at an oxygen lattice site. The lowest energy pathway for the diffusion of atomic nitrogen interstitials consists of the hopping of the nitrogen interstitial between neighboring three-coordinated lattice oxygen atoms that share a single Hf atom, and the barrier for such hops is determined by a switching mechanism. The substitutional nitrogen atom shows a preference for diffusion through the doubly positive oxygen vacancy-mediated mechanism. Furthermore, we have investigated the impact of nitrogen atoms on the diffusion barriers of oxygen and hydrogen interstitials in m-HfO{sub 2}. Our results show that nitrogen incorporation has a significant impact on the barriers for oxygen and hydrogen diffusion: nitrogen atoms attract oxygen and hydrogen interstitials diffusing in the vicinity, thereby slowing down (reducing) their diffusion (diffusion length)

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

First-principles study of inert gas incorporation and migration in zirconium nitride

Uranium-Molybdenum alloy based fuels are the most promising fuel for the future high performance research reactors using low enriched uranium (LEU). However, when used in dispersion with aluminum, significant amount of interaction products form at the interface between the UMo fuel particle and the surrounding Al during in-pile tests which leads to non-acceptable swelling. To reduce the swelling in U-Mo/Al dispersion fuel at high burnups, different diffusion barrier coatings, e.g., ZrN, were deposited on the U-Mo particles to avoid the interaction between fuel particles and the Al matrix. These diffusion barrier coatings are very effective in reducing the formation of interaction layer and therefore the fuel swelling. So far, ZrN is selected as the candidate coating material for the European Dispersion Fuel program due to the superior thermophysical properties of ZrN. The thermodynamic and kinetic stability of ZrN coating with respect to Al and U-Mo has been studied by the current authors using density functional theory calculations. So far there are very few studies of the diffusion behaviors of inert gases in ZrN. A recent publication on irradiated (Pu,Zr)N reveals that the majority of fission-induced Xe is retained in the material, while He is release to the fuel pin to a large extent. This raises the questions on the underlying differences of inert gas behavior in nitride fuel. Therefore, the purpose of this study is to understand the incorporation and migration behavior of inert gases He, Kr and Xe in ZrN using density functional theory (DFT) based first-principles calculations. Using density-functional theory calculations we provided a systematic study of the incorporation and migration of fission gases in ZrN. We investigated the formation energies of several defects (vacancies, interstitials, divacancies, Frenkel pairs, and Schottky defects) and the incorporation energies of inert gases in these defects. Results show that the formation energies of point defects are strongly affected by the chemical potentials of N and Zr species. The energetically most favorable incorporation site for fission gases is found to be the first nearest neighbor Schottky defect, in which the fission gas atom sits at somewhere between the Zr and N vacancies. The predicted solution energies of rare gases, i.e, He, Kr and Xe, in ZrN, is almost linearly dependent on the atom size of inert gases. We compared the solution energy Xe in ZrN with several other nuclear materials with the same B1 structure (MX), e.g., TiN, UN and UC. The solution energies of Xe in MX are closely related to the size of vacancy sites. The potential migration mechanisms of Xe in ZrN include interstitial and vacancy-assisted diffusion. The calculations show that vacancies essentially act as Xe trapping sites. The migration behavior of Xe in N and Zr divacancy and Schottky defects were compared with that through tetrahedral interstitials. It is found that the migration barrier is much lower with the interstitial mechanism than those with the vacancy mechanism. Therefore, at low temperatures Xe diffusion in ZrN is mostly through the interstitial mechanism or existing grain boundaries while at high temperature volume diffusion could be preferred, i.e., diffusion with Zr and N vacancies. (authors)

36 MATERIALS SCIENCE↗

Effect of alloying elements on defect evolution in Ni-20X binary alloys

The effect of alloying elements on radiation-induced microstructural evolution in Ni and Ni-20X (X = Fe, Cr, Mn and Pd) binary alloys was investigated using ion irradiation and cross-sectional transmission electron microscopy. The three-dimensional migration mode is identified to be the dominating migration mechanism for interstitial clusters in these binary alloys, contrary to the one-dimensional mode that dominates in the well-studied dilute alloys. The results reveal that: (1) the average size of defect clusters decreases as the solute atomic volume size factor increases. Smaller void size in Ni-20Cr is attributed to faster vacancy mobility in the near surface region, and weaker vacancy binding energy beyond the irradiation peak than Ni-20Fe. The smaller voids observed in Ni-20Mn and Ni-20Pd beyond the damage peak are due to the stronger Mn/Pd-vacancy binding effect of largely oversized solute atoms. (2) Oversized solutes can act as strong trapping sites for interstitials. The larger the solute atomic volume factor, the stronger the trapping force. This leads to a more significantly sluggish interstitial migration and smaller dislocation loop size. The average dislocation loop size in Ni-20Fe was four times larger than Ni-20Pd (atomic volume factor being 10.6% and 41.3%) but an order of magnitude lower in density. The smaller dislocation loop size in Ni-20Cr is attributed to stronger interstitial binding of Cr-Ni. In conclusion, overall, the alloying effect on defects is more significant in concentrated binary alloys than in dilute binary alloys, due to the concentration difference of alloying atoms and the interstitial dominant migration mechanisms in the main irradiated region.

36 MATERIALS SCIENCE↗

Upregulation of Interleukin-33 in obstructive renal injury

Interstitial fibrosis and loss of parenchymal tubular cells are the common outcomes of progressive renal diseases. Pro-inflammatory cytokines have been known contributing to the damage of tubular cells and fibrosis responses after renal injury. Interleukin (IL)-33 is a tissue-derived nucleus alarmin that drives inflammatory responses. The regulation and function of IL-33 in renal injury, however, is not well understood. To investigate the involvement of cytokines in the pathogenesis of renal injury and fibrosis, we performed the mouse renal injury model induced by unilateral urinary obstruction (UUO) and analyze the differentially upregulated genes between the obstructed and the contralateral unobstructed kidneys using RNA sequencing (RNAseq). Our RNAseq data identified IL33 and its receptor ST2 were upregulated in the UUO kidney. Quantitative analysis confirmed that transcripts of IL33 and ST2 were upregulated in the obstructed kidneys. Immunofluorescent staining revealed that IL-33 was upregulated in Vimentin- and alpha-SMA-positive interstitial cells. By using genetically knockout mice, deletion of IL33 reduced UUO-induced renal fibrosis. Moreover, in combination with BrdU labeling technique, we observed that the numbers of proliferating tubular epithelial cells were increased in the UUO kidneys from IL33-or ST2-deficient mice compared to wild type mice. Collectively, our study demonstrated the upregulation of IL-33/ST2 signaling in the obstructed kidney may promote tubular cell injury and interstitial fibrosis. IL-33 may serve as a biomarker to detect renal injury and that IL-33/ST2 signaling may represent a novel target for treating renal diseases. -- Highlights: •Interleukin (IL)-33 was upregulated in obstructed kidneys. •Interstitial myofibroblasts expressed IL-33 after UUO-induced renal injury. •Deficiency of IL33 reduced interstitial fibrosis and promoted tubular cell proliferation.

60 APPLIED LIFE SCIENCES↗

Ab initio study of point defects near stacking faults in 3C-SiC

Interactions between point defects and stacking faults in 3C-SiC are studied using an ab initio method based on density functional theory. The results show that the discontinuity of the stacking sequence considerably affects the configurations and behavior of intrinsic defects, especially in the case of silicon interstitials. The existence of an intrinsic stacking fault (missing a C-Si bilayer) shortens the distance between the tetrahedral-center site and its second-nearest-neighboring silicon layer, making the tetrahedral silicon interstitial unstable. Instead of a tetrahedral configuration with four C neighbors, a pyramid-like interstitial structure with a defect state within the band gap becomes a stable configuration. In addition, orientation rotation occurs in the split interstitials that has diverse effects on the energy landscape of silicon and carbon split interstitials in the stacking fault region. Moreover, our analyses of ionic relaxation and electronic structure of vacancies show that the built-in strain field, owing to the existence of the stacking fault, makes the local environment around vacancies more complex than that in the bulk.

36 MATERIALS SCIENCE↗

Asymmetry of radiation damage properties in Al-Ti nanolayers

Molecular dynamics (MD) simulations were employed with empirical potentials to study the effects of multilayer interfaces and interface spacing in Al-Ti nanolayers. Several model interfaces derived from stacking of close-packed layers or face-centered cubic \{100\} layers were investigated. The simulations reveal significant and important asymmetries in defect production with $\sim$60\% of vacancies created in Al layers compared to Ti layers within the Al-Ti multilayer system. The asymmetry in the creation of interstitials is even more pronounced. The asymmetries cause an imbalance in the ratio of vacancies and interstitials in films of dissimilar materials leading to $>$90\% of the surviving interstitials located in the Al layers. While in the close-packed nanolayers the interstitials migrate to the atomic layers adjacent to the interface of the Al layers, in the \{100\} nanolayers the interstitials migrate to the center of the Al layers and away from the interfaces. The degree of asymmetry and defect ratio imbalance increases as the layer spacing decreases in the multilayer films. Underlying physical processes are discussed including the interfacial strain fields and the individual elemental layer stopping power in nanolayered systems. In addition, experimental work was performed on low-dose (10$^{16}$ atoms/cm$^2$) helium (He) irradiation on Al/Ti nanolayers (5 nm per film), resulting in He bubble formation $\sim$1 nm in diameter in the Ti film near the interface. The correlation between the preferential flux of displaced atoms from Ti films to Al films during the defect production that is revealed in the simulations and the morphology and location of He bubbles from the experiments is discussed.

Al-Ti interatomic potential↗

Architecture-Guided Fluid Flow Directs Renal Biomineralization

Nephrocalcinosis often begins on a calcium phosphate deposit, at the tip of the medullo-papillary complex (MPC) known as Randall’s plaque (RP). Contextualizing proximally observed biominerals within the MPC has led us to postulate a mechanobiological switch that can trigger interstitial biomineralization at the MPC tip, remote from the intratubular biominerals. Micro X-ray computed tomography scans of human MPCs correlated with transmission and scanning electron micrographs, and X-ray energy dispersive spectrometry demonstrated novel findings about anatomically-specific biominerals. An abundance of proximal intratubular biominerals were associated with emergence of distal interstitial RP. The fundamental architecture of the MPC and mineral densities at the proximal and distal locations of the MPC differed markedly. A predominance of plate-like minerals or radially oriented plate-like crystallites within spheroidal minerals in the proximal intratubular locations, and core-shell type crystallites within spheroidal minerals in distal interstitial locations were observed. Based on the MPC anatomic location of structure-specific biominerals, a biological switch within the mineral-free zone occurring between the proximal and distal locations is postulated. The “on” and “off” switch is dependent on changes in the pressure differential resulting from changes in tubule diameters; the “Venturi effect” changes the “circumferential strain” and culminates in interstitial crystal deposits in the distal tubule wall in response to proximal tubular obstruction. These distal interstitial mineralizations can emerge into the collecting system of the kidney linking nephrocalcinosis with nephrolithiasis.

59 BASIC BIOLOGICAL SCIENCES↗

Average structure and local configuration of excess oxygen in UO2+x

Determination of the local configuration of interacting defects in a crystalline, periodic solid is problematic because defects typically do not have a long-range periodicity. Uranium dioxide, the primary fuel for fission reactors, exists in hyperstoichiometric form, UO2+x. Those excess oxygen atoms occur as interstitial defects, and these defects are not random but rather partially ordered. The widely-accepted model to date, the Willis cluster based on neutron diffraction, cannot be reconciled with the first-principles molecular dynamics simulations present here. We demonstrate that the Willis cluster is a fair representation of the numerical ratio of different interstitial O atoms; however, the model does not represent the actual local configuration. The simulations show that the average structure of UO2+x involves a combination of defect structures including split di-interstitial, di-interstitial, mono-interstitial, and the Willis cluster, and the latter is a transition state that provides for the fast diffusion of the defect cluster. The results provide new insights in differentiating the average structure from the local configuration of defects in a solid and the transport properties of UO2+x.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The multiple roles of small-angle tilt grain boundaries in annihilating radiation damage in SiC

Lattice defects generated by radiation damage can diffuse to grain boundaries (GBs) and be annihilated at GBs. However, the precise role of GBs in annihilating the segregated defects remains unclear. Here, we employed multi-scale models to determine how interstitials are annihilated at small-angle tilt GBs (STGBs) in SiC. First of all, we found the pipe diffusion of interstitials in STGBs is slower than bulk diffusion. This is because the increased interatomic distance at dislocation cores raises the migration barrier of interstitial dumbbells. Furthermore, we found both the annihilation of interstitials at jogs and jog nucleation from clusters are diffusion-controlled and can occur under off-stoichiometric interstitial fluxes. Finally, a dislocation line model is developed to predict the role of STGBs in annihilating radiation damage. This model includes defect flux to GBs, pipe diffusion in STGBs, and the interaction of defects with jogs. The model predicts the role of STGBs in annihilating defects depends on the rate of defects segregation to and diffusion along STGBs. STGBs mainly serve as diffusion channel for defects to reach other sinks when defect diffusivity is high at boundaries. As a result, when defect diffusivity is low, most of the defects segregated to STGBs are annihilated by dislocation climb.

36 MATERIALS SCIENCE↗

Thermoelectric properties of bromine filled CoSb 3 skutterudite

Historically, the improved thermoelectric performance of skutterudite compounds has largely been driven by the incorporation of electropositive donors on interstitial sites. These 'rattlers' serve to optimize both electronic and thermal properties by tuning the carrier concentration and scattering phonons. In this work, we show that interstitial bromine can be incorporated into CoSb3 and assess the impact on electronic and thermal transport. In contrast to prior high pressure syntheses with iodine, interstitial bromine incorporation is achieved at ambient pressure. Transport properties are stable up to at least 375 degrees C. Bromine serves as an electronegative acceptor and can induce degenerate (>5 x 1019 cm-3) hole densities. In contrast to other p-type skutterudite compositions, bromine preserves the intrinsically high hole mobility of CoSb3 while significantly reducing the lattice thermal conductivity. The development of a stable p-type dopant for the interstitial filler site enables the development of skutterudites with both donor and acceptor interstitials to maximize phonon scattering while maintaining the high mobility of CoSb3.

36 MATERIALS SCIENCE↗

Low-energy pathways lead to self-healing defects in CsPbBr 3

Self-regulation of free charge carriers in perovskites via Schottky defect formation has been posited as the origin of the well-known defect-tolerance of metal halide perovskite materials. Understanding the mechanisms of self-regulation promises to lead to the fabrication of better performing solar cell materials with higher efficiencies. We investigate many such mechanisms here for CsPbBr 3 , a popular representative of a more commercially viable all-inorganic metal halide perovskite. We investigate different atomic-level mechanisms and pathways of the diffusion and recombination of neutral and charged interstitials and vacancies (Schottky pairs) in CsPbBr 3 . We use nudged elastic band calculations and ab initio-derived pseudopotentials within quantum ESPRESSO to determine energies of formation and migration and hence the activation energies for these defects. While halide vacancies are known to exhibit low formation energies, the migration of interstitials is less studied. Our calculations uncover interstitial defect pathways capable of producing an activation energy at, or below, the single experimental value of 0.53 eV observed for the slow, temperature-dependent recovery of light-induced conductivity in bulk CsPbBr 3 . Our work reveals the existence of a low-energy diffusion pathway involving a concerted “domino effect” of interstitials, with the net result that interstitials can diffuse more readily over longer distances than expected. This observation suggests that defect self-healing can be promoted if the “domino effect” strategy can be engaged.

14 SOLAR ENERGY↗

Analysis of defects in In 2 O 3 :H synthesized in presence of water vapor and hydrogen gas mixture

Using hybrid functional-based density functional theory calculations, we analyze the structure and kinetics of defects formed in two competing synthesis routes to prepare hydrogen-doped In 2 O 3 films, using a hydrogen and oxygen gas mixture vs synthesis in the presence of water vapor. For both of these synthesis routes, we find that H + is the dominant defect species: when the Fermi level is close to the conduction band, H + has a lower formation energy than other intrinsic or extrinsic defects. Our results also suggest that water molecules spontaneously split into H + (which occupies octahedral voids) and OH – interstitials (which occupies vacant oxygen lattice sites or oxygen vacancies). From the analysis of the binding energies between these different defects, we conclude that these defects do not cluster and are most likely to stay spatially distributed throughout the films. In addition, the sum of formation energies of an oxygen (i.e., O$^{2–}_i$) and a H + interstitial is close to the formation energy of a OH – interstitial, meaning that water molecules are completely split into 2H + and O$^{2–}_i$ at the synthesis conditions. Further, in the presence of H 2 + O 2 gas mixture, oxygen interstitials occupy oxygen vacancies while hydrogen interstitials occupy vacant oxygen lattice sites and form bonds with lattice oxygens. Our analysis of the defect equilibria suggests that the hydrogen content in films synthesized in the presence of water vapor is higher than films synthesized in the presence of a hydrogen gas mixture. At high dopant concentrations, a hydrogen bond network is formed in the system and this leads to large distortions in the lattice.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗