Abstract Estimating the case fatality ratio (CFR) for COVID-19 is an important aspect of public health. However, calculating CFR accurately is problematic early in a novel disease outbreak, due to uncertainties regarding the time course of disease and difficulties in diagnosis and reporting of cases. In this work, we present a simple method for calculating the CFR using only public case and death data over time by exploiting the correspondence between the time distributions of cases and deaths. The time-shifted distribution (TSD) analysis generates two parameters of interest: the delay time between reporting of cases and deaths and the CFR. These parameters converge reliably over time once the exponential growth phase has finished. Analysis is performed for early COVID-19 outbreaks in many countries, and we discuss corrections to CFR values using excess-death and seroprevalence data to estimate the infection fatality ratio (IFR). While CFR values range from 0.2% to 20% in different countries, estimates for IFR are mostly around 0.5–0.8% for countries that experienced moderate outbreaks and 1–3% for severe outbreaks. The simplicity and transparency of TSD analysis enhance its usefulness in characterizing a new disease as well as the state of the health and reporting systems.

The chemical durabilities of two Pu-doped pyrochlore samples were studied by Single-Pass-Flow-Through (SPFT) tests at 70°C. The dissolution of pyrochlore is incongruent with preferential releases of Ca and Gd over Ti, close to stoichiometric releases of U and Ti, and lower releases of Hf and Pu than Ti. Altered pyrochlore and polymorphs of TiO 2 (brookite and probably anatase) have been identified on the surface of the leached sample and the principal secondary phase is an unknown polymorph of TiO 2 containing Hf and varying amounts of Gd and Pu. These surface alteration phases are consistent with reported studies of natural samples. The releases of U, Gd, Ca and Ti into solution follow linear kinetics, whereas the releases of Pu and Hf exhibit non-linear behavior. The presence of ∼5% PuO 2 and trace amounts of glass does not appear to have an effect on the overall durability of the material. Further, the low Pu release rate and the similar kinetics for Pu and Hf releases limit the possibility of nuclear criticality under repository conditions. Overall, this study provides useful information on the lower bounds of durabilities of the materials.

Radiation damage effects in ceramics, e.g., nuclear waste forms, transmutation targets, and inert matrix fuels, may have important implications for the physical and chemical stability of these materials as the cumulative radiation dose increases over time. A key aspect of scientific research in this area is the ability to understand the fundamental damage mechanisms through the combination of experimental and atomistic modelling techniques. In this paper, we review some of the lessons learned from the significant body of data now available for pyrochlore-defect fluorite based materials, followed by an illustration of the advantages of working on simple compounds with well established interatomic potentials. We conclude the paper with a description of radiation damage processes in the La x Sr 1-1.5x TiO 3 defect perovskites, a system that includes phase transformations, short-range order effects, and complex defect behavior.

Thin crystals of rutile, brookite, and anatase were irradiated in-situ with 1.0 MeV Kr using the IVEM-TANDEM facility. Synthetic rutile and cassisterite (SnO2, rutile structure) remained crystalline up to 5 × 1015 ion cm-2 at 50 K. Natural brookite and anatase with low impurity levels became amorphous at 8.1 ± 1.8 × 1014 and 2.3 ± 0.2 × 1014 ions cm-2, respectively, at 50 K. Irradiation at higher temperature revealed Tc = 170 K for brookite and 242 K for anatase. Natural rutile with about 2 wt% impurities became amorphous at 9.4 ± 1.8 × 1014 ions cm-2 at 50 K and has a Tc = 207 K. The available data reveal both a structural effect in the polymorphs with low levels of chemical impurities and a chemical effect in natural rutile specimens containing up to about 1.7 wt% impurities.

Molecular dynamics simulations are used to study amorphisation resistance in the rutile, brookite and anatase polymorphs of titania. As an alternative to the traditional large-scale cascade calculation, small thermal spike simulations are used to quantify recrystallisation on the picosecond scale. In agreement with experiment, the thermal spikes in rutile recover completely (within 5 ps), remain largely intact in anatase, while brookite exhibits intermediate behaviour. Analysis of the annealing response shows that the thermal spike approach captures much of the cascade physics at a fraction of the computational cost, and in doing so provide insight into the radiation response process.

The mode and energy of simple defect incorporation in SrTiO3 (vacancies and interstitials) is quantified using computer simulation techniques with an empirical partial charge model of interatomic forces, as well as using density functional theory calculations. Oxygen and strontium interstitials form split-interstitial configurations whereas titanium interstitials occupy channel positions. Defect migration energies and paths are also considered; interstitials are more mobile than vacancies, with a low predicted oxygen interstitial migration energy of around 0.3eV. We also calculate the threshold displacement energy (Ed) for each atom type in SrTiO3 perovskite using molecular dynamics simulations, by introducing a primary knock-on atom with a range of energies (20–250eV) in principal crystallographic directions at 300K. We find that all atom types are most easily displaced via direct replacement sequences on their own sublattices, which are extensive for Sr atoms due to focusson processes acting along channels. The weighted average threshold displacement energies (for use in TRIM-type calculations) are 50eV for oxygen, 70eV for strontium and 140eV for titanium atoms. These computed energies for O and Sr are comparable to experimentally-derived values in perovskites, whereas the Ed for Ti is much higher; it is expected that the value reported here is more accurate due to experimental difficulties in distinguishing different types of defects.

Sr1-3x/2LaxTiO3 perovskites exhibit large variations in radiation resistance and A-site vacancy ordering, depending on x and thermal history. In this study we use a combination of ab initio and classical simulation techniques to characterize the energetics of A-site vacancy and cation interactions. We find that the A-site interactions follow intuitive electrostatic arguments at low concentrations of defects, promoting association of La ions with vacancies and dissociation of vacancy-vacancy pairs. However, when long-range A-site ordering is present, the defect interactions are inverted due to strain forces arising from cooperative atomic relaxations. To study the regime of partial ordering between these two extremes we use Monte Carlo simulations combined with lattice energy minimization. These show that in highly disordered configurations electrostatic defect interactions dominate, making it difficult for the thermodynamically stable (strain-stabilized) long-range order to nucleate. To quantify the critical nucleation volume we consider the balance of electrostatic and strain forces as a function of the size of the ordered region. These results provide a useful framework for understanding A-site ordering in experimental Sr1-3x/2LaxTiO3 samples, as well as shedding light on the implications of intrinsic defect ordering for radiation resistance.

Threshold displacement energies are determined for Ti and O in rutile TiO2 using molecular dynamics simulations with an empirical model. The simulations involve the introduction of a primary knock-on atom (PKA) with a range of energies (30–150 eV) in various crystallographic directions at 160 K. We observe the formation of stable Frenkel defects, as well as defect recovery via low-energy interstitial migration mechanisms. The latter causes significant statistical variation between simulation outcomes, which leads to the definition of a defect formation probability. This probability is characterized as a function of PKA energy in order to define the threshold displacement energy and compare with experimental results. Using a probability of 10%, the average threshold displacement energy is around 40 eV for oxygen (comparable to experiment) and 105 eV for titanium. Using a probability of 50%, the values are 65 eV and 130 eV respectively, which may be more appropriate for use in TRIM calculations. In addition, we run a parallel set of calculations using a second empirical model, finding that the detailed results are highly model-dependent, particularly the oxygen defect structures and energies, which are compared to new ab initio data.

Atomistic simulation of radiation damage in oxides is a relatively new field compared to similar work in metals and semiconductors, and presents new challenges. We describe the development of a simplified empirical model for the (Sr1−3x/2Lax)TiO3 perovskite system, which contains partially-ordered cation vacancies and has interesting radiation resistance properties. Pair potential parameters are fitted to a range of experimental and new ab initio data, and the resulting model accurately reproduces important properties of the system, including local cation ordering effects.

The study of solid-state ionic systems hinges on the calculation of electrostatic forces between charged ions. Recently, empirical models incorporating variable-charge schemes have been developed for titanium oxides and other ionic solids, combining the charge equilibration scheme with short-range Morse-stretch potentials (MS-Q models). This study considers the most recent MS-Q model for titanium oxides [V. Swamy and J. D. Gale, Phys. Rev. B 62, 5406 (2000)] and explores the contribution of the variable-charge scheme to the computed interatomic forces and crystalline properties. This work shows that the successes and failures of this and other published MS-Q models are due almost entirely to the Morse-stretch potential, with little to no contribution from electrostatic forces between the variable charges. This limits the transferability of such models and calls into question their functional form. Efforts to improve the MS-Q scheme by increasing the charge magnitudes and changing the description of the electrostatic forces do not improve the transferability. Such models require further development before they can compete in performance with well-established fixed-charge empirical models.

The dissolution of synthetic brannerite in aqueous media at 40 and 90 °C under atmospheric redox conditions has been studied. At 40 °C, the presence of phthalate as a buffer component in the pH range of 2–6 has little effect on uranium release from brannerite. Bicarbonate increases uranium release and enhances the dissolution of brannerite. Compared to UO2, brannerite is more resistant to dissolution in bicarbonate solutions. In under-saturated conditions at 90 °C, the dissolution of brannerite is incongruent (preferential release of uranium) at pH 2 and nearly congruent at pH 11. TEM examinations reveal a polymorph of TiO2 (pH 2 specimen) and a fibrous Ti-rich material (pH 11 specimen) as secondary phases. XPS analyses indicate the existence of U(V) and U(VI) species on the surfaces of specimens both before and after leaching, and U(VI) was the dominant component on the specimen leached in the pH 11 solution.

SummaryThe aqueous dissolution of synthetic brannerite (UTi2O6) in an open atmosphere has been investigated. Previous data in the literature have been combined with new experimental work, dealing with the release of uranium from brannerite as a function of solution pH and aqueous carbonate species, in oxygenated solutions. From these data we have developed a conceptual model for uranium release from brannerite consisting of two reaction steps: oxidation of surface uranium(IV) atoms, and subsequent detachment of U(VI) atoms into solution, which is catalysed by surface coordination with protons (acidic media) or carbonate species (alkaline media in equilibrium with the atmosphere). A kinetic rate law is derived for this simple reaction mechanism and fitted to experimental data. The resulting predictive equation for uranium release qualitatively describes the pH-dependent behaviour observed in experiment, and quantitatively gives an upper limit for uranium release from brannerite over a range of conditions and experiment types.

We have used classical molecular dynamic simulations to model the long-lived structural effects of ultraviolet irradiation on amorphous silica. We present evidence that the observed densification arises as a result of the local melting generated by the radiation followed by rapid cooling. We examine physical factors that influence the sign and magnitude of this density change.

The dissolution of synthetic brannerite is incongruent and pH dependent with a minimum in the dissolution rate at near pH 8. Preferential release of U leaves TiO2 on the surface with different morphologies; smooth uniform layers in acidic media and nano-spherule agglomerations in alkaline media. The measured apparent activation energies at pH 5.6 to 9.8 suggest surface reaction-controlled dissolution mechanisms. A natural brannerite sample is amorphous and has shown very little alteration over geological time; under laboratory test conditions the U release is less than an order of magnitude more than in synthetic brannerite.

Using classical dynamics simulations, we model the long-lived structural effect of ultraviolet irradiation on amorphous silica. We find a significant increase in density of a model of amorphous silica following localized energy deposition, in agreement with experimental observation. We present evidence that this densification arises as a result of the rapid local cooling that follows irradiation. Similar high density forms of amorphous silica are found following fast quenches of bulk samples. In support of this proposal we demonstrate that very rapidly quenched silica undergoes dilation, rather than compaction, on irradiation.

This paper presents experimental studies on the kinetics of U release from near single-phase zirconolite, pyrochlore, brannerite and pyrochlore-rich titanate ceramic materials. The dissolution tests were conducted at 20–75°C with initial pHs from 2 to 12, and flow rates from 10 to 80 ml d−1 in the open atmosphere. The U releases from these titanate materials are controlled by initial fast process and then followed by linear kinetics. The close-to-stoichiometric U release from zirconolite and pyrochlore-rich materials and preferential U release from brannerite are consistent with the alterations observed for the natural samples. The rate constants for U releases were determined and the effects of pH and temperature were examined. For each material, the U release vs. pH exhibits a V-shape with a minimum near pH 8. The measured activation energies suggest surface reaction controlled dissolution mechanism. Pyrochlore-rich materials and zirconolite demonstrated higher chemical durability and more resistance to aqueous attack than brannerite. However, impurities and minor brannerite inclusions do not appear to have a detrimental effect on U releases from pyrochlore-rich multi-phase ceramics.

Brannerite, as a minor phase, exists in the pyrochlore-rich titanate ceramic formulations designed for immobilization of surplus weapons Pu. The dissolution of synthetic brannerite was studied at 90°C using static tests in pH 4 solution, deionized water and Finnsjön synthetic groundwater. After 140 days the normalized U release rates into a pH 4 solution and deionized water reach similar values, ~10−2 g m−2 d−1, and are about 2 orders of magnitude higher than those in Finnsjön synthetic groundwater. The normalized Ti release rate into Finnsjön synthetic groundwater is about an order of magnitude higher than those in pH 4 solution and deionized water. The dissolution of brannerite is incongruent in the pH 4 solution and deionized water (preferential release of U over Ti), and nearly congruent in Finnsjön synthetic groundwater. SEM observations of the samples after 140 days in pH 4 solution and deionized water revealed minor surface alteration, in the form of a thin surface layer, probably TiO2, as a result of preferential releases of U in both cases.