Wigner Energy Research Articles

Applicability of abrasive waterjet cutting to irradiated graphite decommissioning

Characterization, dismantling and pre-disposal management of irradiated graphite (i-graphite) have an important role in safe decommissioning of several nuclear facilities which used this material as moderator and reflector. In addition to common radiation protection issues, easily volatizing long-lived radionuclides and stored Wigner energy could be released during imprudent retrieval and processing of i-graphite. With this regard, among all cutting technologies, abrasive waterjet (AWJ) can successfully achieve all of the thermo-mechanical and radiation protection objectives. In this work, factorial experiments were designed and systematically conducted to characterize the AWJ processing parameters and the machining capability. Moreover, the limitation of dust production and secondary waste generation has been addressed since they are important aspects for radiation protection and radioactive waste management.The promising results obtained on non-irradiated nuclear graphite blocks demonstrate the applicability of AWJ as a valid technology for optimizing the retrieval, storage, and disposal of such radioactive waste. These activities would benefit from the points of view of safety, management, and costs.

The Wigner energy and defects evolution of graphite in neutron-irradiation and annealing

The annealing process of nuclear graphite accompanying the release of Wigner energy was studied in this research. IG-110U and ETP-10 graphite were irradiated at 200 °C by neutrons with low-dose (1.38 × 1019 n/cm2) and high-dose (1.92 × 1020 n/cm2), respectively. Their Wigner energy release at 100–550 °C was measured based on a high-precision differential scanning calorimeter. Characteristics of Wigner energy release spectrum were investigated. The activation energy of the energy release peak (170–230 °C) for low-dose graphite was 1.48 eV, which was related to the decomposition of interstitial clusters and the behaviour of subsequent interstitial pairs. Furthermore, a comprehensive analysis of Wigner energy release combined with thermal conductivity and multi-scale structural parameters during the neutron irradiation and annealing process is given.

Neutron irradiation induced magnetization and persistent defects at high temperatures in graphite

Structural as well as magnetization studies have been carried out on graphite samples irradiated by neutrons for over 50 years in the CIRUS research reactor at Trombay, India. Neutron diffraction studies reveal that the defects in irradiated graphite samples are not well annealed and remain significant up to high temperatures much greater than 653 K where the Wigner energy is completely released. We infer that the remnant defects may be intralayer Frenkel defects, which do not store large energy, unlike the interlayer Frenkel defects that store the Wigner energy. Magnetization studies on the irradiated graphite show ferromagnetic behavior that persists up to \ensuremath{\sim}850 K and a large additional paramagnetic contribution. Ab initio calculations based on the spin-polarized density-functional theory show that the magnetism in defected graphite is essentially confined to a single twofold-coordinated carbon atom that is located around a vacancy in the hexagonal layer.

Wigner energy in irradiated graphite: A first-principles study

First-principles calculations were performed to examine the defect-induced energy storage in graphite. The accumulation of energy resulting from inducing defects in graphite is a well-known phenomenon. Given the recent interest in exploiting this process for energy-storing purposes, more careful investigation is necessary. Some of the earliest studies of damaged graphite, and the stored energy associated with that, were motivated by the associated technological issues in nuclear reactor operation. A large number of excited state defects, for example Frenkel pairs, can be generated in graphite through bombardment of high-energy neutrons. The sudden release of this energy (also called Wigner energy) poses a serious concern to the safe operation of nuclear reactors. At the same time, controlled defect generation in graphite using neutron/ion irradiation might represent a potential energy storage mechanism. In recently published papers, the design of an integrated energy system that couples a nuclear reactor with a Wigner effect-based energy storing system was proposed. To accurately estimate the performance that can be achieved in terms of stored energy density through defect generation, density functional theory (DFT) based first-principles calculations were performed. In this work, stored energy accumulation was modeled in two ways - by Frenkel pair accumulation and overlapping collision cascade methods. The former was done with ab initio molecular dynamics (AIMD) simulations, and the latter was done with combined classical molecular dynamics (MD) and AIMD simulations. The agreement between the calculated and experimental results for how stored energy changes with dosage suggests that this model could be useful for the on-going research into damaged graphite as an energy storage medium.

Uncertainty analysis for the nuclear liquid drop model and implications for the symmetry energy coefficients

Background: Despite its age, the nuclear liquid drop (LD) model, plus the microscopic corrections, still plays an important role in nuclear mass studies. Especially, the LD model readily correlate the finite nucleus and the nuclear matter through the symmetry energy term.Purpose: To systematically analyze the model uncertainty of the LD mass formula and check the corresponding symmetry energy coefficients.Method: The Monte Carlo bootstrap approach, based on the nonparametric sampling, is applied to determine the statistical uncertainties of the parameter set in two popular LD formulas. The dependence between these parameters is also quantified via the correlation coefficients.Results: The least required proportion of the experimental mass data is fixed for the fitting process of the LD formula. After the statistical deviation is determined for each parameter in the LD formula, the model uncertainty is evaluated as illustrated for one heavy isotopic chain. The Pearson coefficients between each two parameters involved in the LD mass formula are tabulated and figured plus the detailed discussions on the surface and volume symmetry energy coefficients.Conclusion: The uncertainties of the fitted parameters and the LD model itself are smooth, leading to a relatively stable extrapolation. It is necessary to include the Wigner energy term in the LD model when yielding the reasonable symmetry energy coefficients.

Analysis of Heat Release Processes inside Storage Facilities Containing Irradiated Nuclear Graphite

The article is dedicated to the safety assessment of mixed storage of irradiated graphite and other types of radioactive waste accumulated during the operation of uranium-graphite reactors. The analysis of heat release processes inside storages containing irradiated nuclear graphite, representing a potential hazard due to the possible heating and, accordingly, the release of long-lived radionuclides during oxidation was carried out. The following factors were considered as the main factors that can lead to an increase in the temperature inside the storage facility: corrosion of metallic radioactive waste, the presence of fuel fragments, and also the random exposure of irradiated graphite to local sources of thermal energy (spark, etc.). It was noted in the work that the combined or separate influence of some factors can lead to an increase in the temperature of the onset of the initiation of Wigner energy release in graphite radwaste (Tin ≈ 90–100°C for the “Worst-case” graphite). The model of heat generation in the storage was developed based on the analysis of the features of graphite radioactive waste storage and Wigner energy release. The layered location of different types of waste (graphite and aluminum) and the local character of the distribution of heat sources were adopted in this model. The greatest heating is achieved if graphite radioactive waste is located near the concrete walls of the storage facility, as well as in direct contact with irradiated aluminum radioactive waste, which was shown in this paper.

The Wigner Energy and Defects Evolution of Graphite in Neutron-Irradiation and Annealing

The Wigner Energy and Defects Evolution of Graphite in Neutron-Irradiation and Annealing

A simple alternative to the relativistic Breit\u2013Wigner distribution

First, we discuss the conditions under which the non-relativistic and relativistic types of the Breit–Wigner energy distributions are obtained. Then, upon insisting on the correct normalization of the energy distribution, we introduce a Flatté-like relativistic distribution -denominated as Sill distribution- that (i) contains left-threshold effects, (ii) is properly normalized for any decay width, (iii) can be obtained as an appropriate limit in which the decay width is a constant, (iv) is easily generalized to the multi-channel case (v) as well as to a convoluted form in case of a decay chain and - last but not least - (vi) is simple to deal with. We compare the Sill distribution to spectral functions derived within specific QFT models and show that it fairs well in concrete examples that involve a fit to experimental data for the rho , a_1(1260), and K^*(982) mesons as well as the varDelta (1232) baryon. We also present a study of the f_2(1270) which has more than one possible decay channels. Finally, we discuss the limitations of the Sill distribution using the a_0(980)-a_0(1450) and the K_0^*(700)-K_0^*(1430) resonances as examples.

Precision mass measurement of lightweight self-conjugate nucleus 80Zr

Protons and neutrons in the atomic nucleus move in shells analogous to the electronic shell structures of atoms. The nuclear shell structure varies as a result of changes in the nuclear mean field with the number of neutrons N and protons Z, and these variations can be probed by measuring the mass differences between nuclei. The N = Z = 40 self-conjugate nucleus 80Zr is of particular interest, as its proton and neutron shell structures are expected to be very similar, and its ground state is highly deformed. Here we provide evidence for the existence of a deformed double-shell closure in 80Zr through high-precision Penning trap mass measurements of 80–83Zr. Our mass values show that 80Zr is substantially lighter, and thus more strongly bound than predicted. This can be attributed to the deformed shell closure at N = Z = 40 and the large Wigner energy. A statistical Bayesian-model mixing analysis employing several global nuclear mass models demonstrates difficulties with reproducing the observed mass anomaly using current theory. High-precision mass measurements of exotic zirconium nuclei are reported, and reveal a double-shell closure for the deformed nucleus 80Zr, which is more strongly bound than previously thought.

Integration of a Wigner effect-based energy storage system with an advanced nuclear reactor

In this work, an innovative energy storage concept based on the purposeful creation of defects in crystalline material by neutron irradiation is presented. Lattice defects are generated when heavy particles collide with the atoms in acrystal structure, i.e., if the incoming particles have enough energy, recoil atoms are displaced from their initial lattice sites. Most of the displaced atoms will eventually combine with nearby vacancies, but some of them will come to rest in non-ideal locations. The energy held by displaced atoms is called Wigner energy. Lattice defects can migrate and form clusters, and the Wigner energy can be released from these groupings if sufficient activation energy is provided. In the nuclear industry, this effect is well-known since it represented an issue for graphite-moderated reactors. This work presents the conceptual design of an engineering system that exploits this physical process to store the energy of neutrons in advanced reactor concepts. In the first part of the paper, the theoretical performance of an energy storage system based on the Wigner effect is described. Given the lattice properties and the compatibility with the harsh reactor environment, graphite was selected as the candidate material for the irradiation targets. Both experimental data and molecular dynamics simulations confirmed that this system can achieve performance comparable with state-of-the-art batteries in terms of stored energy density. In the second part of the paper, the engineering challenges of this innovative technology and the proposed solutions are described. After defining the optimal irradiation conditions, the different steps of the operation of the proposed energy system (from energy storing to energy harvesting) were defined. Finally, the integration of this concept with advanced reactor designs, i.e., a Sodium-cooled Fast Reactor and a Molten Salt-cooled Reactor, was investigated and the corresponding performance was evaluated.

Np-Pair Correlations in the Isovector Pairing Model

A diagonalization scheme for the shell model mean-field plus isovector pairing Hamiltonian in the O(5) tensor product basis of the quasi-spin SUΛ(2) ⊗ SUI(2) chain is proposed. The advantage of the diagonalization scheme lies in the fact that not only can the isospin-conserved, charge-independent isovector pairing interaction be analyzed, but also the isospin symmetry breaking cases. More importantly, the number operator of the np-pairs can be realized in this neutron and proton quasi-spin basis, with which the np-pair occupation number and its fluctuation at the J = 0+ ground state of the model can be evaluated. As examples of the application, binding energies and low-lying J = 0+ excited states of the even–even and odd–odd N∼Z ds-shell nuclei are fit in the model with the charge-independent approximation, from which the neutron–proton pairing contribution to the binding energy in the ds-shell nuclei is estimated. It is observed that the decrease in the double binding-energy difference for the odd–odd nuclei is mainly due to the symmetry energy and Wigner energy contribution to the binding energy that alter the pairing staggering patten. The np-pair amplitudes in the np-pair stripping or picking-up process of these N = Z nuclei are also calculated.

Study of irradiated graphite-bakelite paste

Abstract The article is devoted to the study of irradiated graphite-bakelite paste formed during the restoration of graphite stack and the operation of uranium-graphite reactors. It was shown that irradiation of graphite-bakelite paste in the reactor leads to the formation of long-lived radionuclides and the accumulation of Wigner energy. The studies of graphite-bakelite paste extracted from the graphite stack of one of the UGR with a closed primary loop showed that the samples of graphite-bakelite paste are contaminated unevenly with 137Cs, 154Eu, 60Co, and 241Am radionuclides (fission and activation products and actinides). From the results of experiments on leaching of radionuclides from graphite-bakelite paste, it can be seen that radionuclides 241Am and 137Cs are more subjected to leaching. The estimation of the stored energy in the selected samples shows that the heat release begins at a temperature of 600–650 ◦C. The largest amount of stored energy is released at a temperature of 750 ◦C. Moreover, the magnitude of this quantity does not exceed 1–6 J/g. It was also shown that the development of the concept and program for decommissioning of UGR, the stack of which was restored using graphite-bakelite paste, requires additional studies to determine the potential danger of irradiated graphite-bakelite paste.

Heat transfer of hexagonal boron nitride (h-BN) compound up to 1 MeV neutron energy: Kinetics of the release of wigner energy

In the present work, hexagonal boron nitride (h-BN) samples were irradiated by using high fluxes neutron irradiation. The neutron irradiation of the samples was carried out at the room temperature up to 1015 n/cm2 neutron flux with up to 1 MeV neutron energy at the IBR-2 M pulsed reactor in the Joint Institute for Nuclear Research, Dubna, Russia. The hexagonal boron nitride (h-BN) heat transfers changes with a differential mechanism under high flux neutron irradiation. The heat transfer depends on the transfer energy of the neutron. In the DSC curves for unirradiated and irradiated hexagonal boron nitride samples are seen phase transitions at the high temperature. However, the mechanism of the heat transfer flow rate functions for hexagonal boron nitride is more complex at the 300 ≤ T ≤ 1400 K temperature range. On the other hand, the Wigner energy of irradiated boron nitride samples was calculated for each of the irradiation fluxes. The Wigner energy increased up to 373 J/g with increasing neutron flux. The results have revealed that it has been observed a change in the rate of release of Wigner energy from 400 K to 1300 K. The surface morphology of hexagonal boron nitride under different fast neutron irradiation doses is investigated. The swelling was observed in the surface dynamics of the materials with an increased dose of irradiation.

Isospin dependence of the nuclear binding energy * *Supported by the National Key R&DProgram of China (2018YFA0404403),and the National Natural Science Foundation of China(12075169, 11605122, 11875188)

In this paper, we study the symmetry energy and the Wigner energy in the binding energy formula for atomic nuclei. We simultaneously extract the symmetry energy and Wigner energy coefficients using the double difference of "experimental" symmetry-Wigner energies, based on the binding energy data of nuclei with . Our study of the triple difference formula and the "experimental" symmetry-Wigner energy suggests that the macroscopic isospin dependence of binding energies is explained well by the symmetry energy and the Wigner energy, and further consideration of the term in the binding energy formula does not substantially improve the calculation result.

On the importance of np-pairs in the isovector pairing model

It is shown that the isovector np-pair number operator can be realized in the O(5) quasi-spin basis. The computation of the isovector np-pair number is demonstrated for even-even and odd-odd ds-shell nuclei described by the charge-independent mean field plus isovector pairing model restricted within the O(5) seniority-zero subspace, thereby binding energies and low-lying excited states of these ds-shell nuclei are fit, along with estimates for the isovector neutron-proton pairing contributions. For reasonable neutron-proton pairing strengths the isovector np-pairing energy contribution to the total binding energy in odd-odd N = Z nuclei is systematically larger than that in the even-even nuclei. In sum, the results suggest that the isovector np-pairing mode is favored in odd-odd N = Z nuclei; and additionally, a decrease in the double binding-energy difference for odd-odd nuclei is primarily due to the symmetry and Wigner energy contributions to the binding energy.

Potential energy models of excited compound nucleus

Potential energy is important ingredient in static and dynamical investigations of a nuclear fission process. The calculation of surface, nuclear, Coulomb, rotational, curvature, congruence, and Wigner energy functionals is presented for large variety of nuclear shapes generated by a {c,h,α} parametrization. Using these functionals one can calculate the potential energy in several macroscopic models of the liquid-drop type. A numerical code which calculates all these quantities is made available. Program summaryProgram Title: FRM_epotCPC Library link to program files:http://dx.doi.org/10.17632/h7r43t7dnh.1Licensing provisions: CC BY NC 3.0Programming language: C++Nature of problem: The shape dependence of the surface, nuclear, Coulomb, rotational, curvature, congruence, and Wigner energy functionals together with the moments of inertia for rotation, center-of-mass distance between nascent fragments are calculated for deformed shapes of the fissioning compound nucleus. These functionals allow to calculate the potential energy in several macroscopic models of the liquid-drop type for a large variety of nuclear shapes.Solution method: The shape of the fissioning nucleus is described by the {c,h,α} parametrization. This parametrization determines the axially symmetric shapes in cylindrical coordinates. The potential energy functionals are calculated using numerical integration procedure as a function of the three shape parameters. Using these functionals one can generate potential energy of the nucleus in four different versions of the liquid-drop model. All subroutines, which define the nuclear shape are separated from the code, which calculates the potential energy functionals. Thus, the program could be easily adopted for any other shape parametrization in case if it is given in cylindrical coordinates.

Defect topology and annihilation by cooperative movement of atoms in neutron-irradiated graphite

Graphite has been used as neutron moderator or reflector in many nuclear reactors. The irradiation of graphite in a nuclear reactor results in a complex population of defects. Heating of the irradiated graphite at high temperatures results in annihilation of the defects with release of an unusually large energy, called the Wigner energy. From various experiments on highly irradiated graphite samples from CIRUS reactor at Trombay and ab-initio simulations, we have for the first time identified various 2-, 3- and 4-coordinated topological structures in defected graphite, and provided microscopic mechanism of defect annihilation on heating and release of the Wigner energy. The annihilation process involves cascading cooperative movement of atoms in two steps involving an intermediate structure. Our work provides new insights in understanding of the defect topologies and annihilation in graphite which is of considerable importance to wider areas of graphitic materials including graphene and carbon nanotubes.

Combustion of a Dust/Gas Mixture Consisting of Particles of Irradiated Nuclear Graphite

The paper describes the problem of the formation of dust/gas mixtures during the work related to the dismantling of graphite stack during the decommissioning of a uranium-graphite reactor. The amount of stored energy in the irradiated graphite elements of the reactor was experimentally determined. The influence of the Wigner energy release process on the combustion of a dust/gas mixture consisting of particles of irradiated nuclear graphite is shown.

Metastable interlayer Frenkel pair defects in black phosphorus

The low formation energy of atomic vacancies in black phosphorus allows it to serve as an ideal prototypical system for exploring the dynamics of interlayer interstitial-vacancy (I-V) pairs (i.e. Frenkel defects) which account for Wigner energy release. Based on a few-layer model of black phosphorus, we conduct discrete geometry analysis and investigate the structural dynamics of intimate interlayer Frenkel pairs from first-principles calculations. We reveal a highly metastable I-V pair state driven by anisotropic dipole-like strain fields which can build strong connections between neighbouring layers. In the 2D limit (monolayer), the intimate I-V pair exhibits a relatively low formation energy of 1.54 eV and is energetically favoured over its isolated constituents by up to 1.68 eV. The barrier for annihilation of the Frenkel pair is 1.46 eV in the bilayer, which is remarkably higher than that of similar defects in graphite. The findings reported in this work suggest that there exist rich bridging pathways in black phosphorus, leading to stable dimensional reduction and structural condensation on exposure to moderate electron excitation or thermal annealing. This study paves the way for creating novel dimensional-hybrid polymorphs of phosphorus via the introduction of such metastable interlayer I-V pair defects.

Fully Ceramic Microencapsulated fuel in prismatic high-temperature gas-cooled reactors: Sensitivity of reactor behavior during design basis accidents to fuel properties and the potential impact of the SiC defect annealing process

We conducted reactor performance calculations to assess the potential design basis accident performance of HTGR fuel designs. Three Fully Ceramic Microencapsulated (FCM) fueled HTGR designs were developed in a previous work (Lu et al., 2018). The maximum fuel temperature in the cores fueled by these three FCM fuels was predicted to be higher than that in the reference 350-MWt mHTGR core in both normal operating conditions and during representative design basis accidents (Lu and Brown, 2019). To better understand the potential safety margins in mHTGR design basis accidents, we performed thermal-hydraulics sensitivity studies to investigate how maximum fuel temperature varies considering various parameters, e.g. thermal properties, within the ranges corresponding to the differences between the FCM-fueled prismatic mHTGR cores and the reference core with conventional fuel compacts. We found that the difference in the steady-state axial power distribution contributed the most to the difference in the maximum fuel temperature, in both normal operation and design basis accidents.Experimental data suggested that the annealing process of irradiation defects in SiC would be rapid at mHTGR relevant fuel temperatures. The bounding potential impact of the SiC annealing on the maximum fuel temperature was analyzed considering both the thermal conductivity recovery and the Wigner energy release due to the annealing of SiC. We found that the defect annealing process in SiC would at most increase the peak maximum fuel temperature of an FCM-fueled core by 40 K in loss of forced cooling accidents and by 10 K in a control rod withdrawal accident. Additional experiments on the SiC defect annealing kinetics and Wigner energy release in more relevant conditions are needed.