The evaluation of the pyrochemistry for the treatment of Gen IV nuclear fuels - Inert matrix chlorination studies in the gas phase or molten chloride salts

The structure of the fuels for the future Gen IV nuclear reactors will be totally different from those of PWR, especially for the GFR concept including a closed cycle. In these reactors, fissile materials (carbides or nitrides of actinides) should be surrounded by an inert matrix. In order to build a reprocessing process scheme, the behavior of the potential inert matrices (silicon carbide, titanium nitride, and zirconium carbide and nitride) was studied by hydro- and pyrometallurgy. This paper deals with the chlorination results at high temperature by pyrometallurgy. For the first time, the reactivity of the matrix towards chlorine gas was assessed in the gas phase. TiN, ZrN and ZrC are very reactive from 400 °C whereas it is necessary to be over 900 °C for SiC to be as fast. In molten chloride melts, the bubbling of chlorine gas is less efficient than in gas phase but it is possible to attack the matrices. Electrochemical methods were also used to dissolve the refractory materials, leading to promising results with TiN, ZrN and ZrC. The massive SiC samples used were not conductive enough to be studied and in this case specific SiC-coated carbon electrodes were used. The key point of these studies was to find a method to separate the matrix compounds from the fissile material in order to link the head to the core of the process (electrochemical separation or liquid-liquid reductive extraction in the case of a pyrochemical reprocessing).     

Application of the theory of random matrices to a reactor-noise problem

The stochastic equation corresponding to a nuclear reactor with random distribution of materials is written in a matrix form, in this way the probability distribution of reactivities is derived as the probability distribution of the higher eigenvalues of random matrices. The theoretical results are illustrated and validated with Monte Carlo simulations based on the diffusion equations and the matrix approach.     

On the neutron scattering transformation matrices

The computations of some neutron elastic transformation matrices with the two recently developed methods, the BRC method (Bersillon et al., 1983) and the BGU method (Ofek et al., 1984), have shown that the present ENDF/B transformation matrices, evaluated with the Amster method, suffer from inaccuracies and have to be used with precautions. On one hand, the BRC method, by which each element of the transformation matrix is expanded into a Taylor series of the inverse mass of the scattering nucleus, is indeed a single precision stable, but it is limited to scattering nuclei with A > 1. On the other hand the BGU method, with which the representation of a matrix element by an integral with Legendre polynomials is converted to a sum of integrals with rational functions, solves the evaluation of the matrix elements in a closed form and it is valid for A < 1 as well, but it suffers from roundoff instability in computing high order matrix elements. Herein, we extend the BGU method and generalize some of the expressions, which reduce the roundoff instability. Hence, better precision is obtained. In particular, a computation of the hydrogen transformation matrix with the BGU method indicates that the high order elements of the ENDF/B-V hydrogen matrix are erroneous. Moreover, since the discrete level inelastic transformation matrices are equivalent to the elastic ones, the BGU method also enables the computation of inelastic transformation matrices for neutron energies close to the threshold of the reaction. In addition, we present here new explicit expressions for some matrix elements, which may facilitate the computation of the transformation matrices.     

Much ado about nothing: response matrices for void regions

Weak form Galerkin approaches are examined for obtaining response matrices for void regions – that is regions where nothing is present. The need arises in spherical harmonics methods based on second-order forms of the neutron transport equation; the methods fail in voids because the cross-section appearing in the equation’s denominator then vanishes. The diffusion approximation, being the lowest-order spherical harmonic method, is first employed as a vehicle for examining response matrices derived from both primal and dual weak forms of the mixed-first-order and second-order transport equations. Those for which discretization results in singular matrix equations as the cross-section goes to zero are rejected. First-order- mixed formulations with modified natural boundary conditions are shown to lead to nonsingular response matrices for voids. The primal method is chosen as the better of the two candidates for generalization from the diffusion to the transport equations, and the transport formulation is presented.     

Measurement of Average Cross Section for 238U(n, 2n)237U Reaction

Accurate solution of the group diffusion equations for PWR cores requires explicit treatment of the non-homogeneous macroscopic parameters within each fuel assembly. It is argued that the response matrix approach is a convenient method to handle this problem provided all matrix elements for the non-homogeneous assemblies can be computed. This so called local problem is solved in this paper by a perturbation algorithm which leads to sensitivity coefficients for the power series expansions of the response matrix elements. A numerical study for 2 representative assemblies of the Indian Point Unit No. 2 (IP2) reactor is carried out and response matrices obtained by the perturbative method are compared with values computed by a finite difference program.     

聚乙烯基炭黑复合PTC材料的研究

研究了以两种不同的高密度聚乙烯为基体炭黑复合材料的电阻正温度系数(PTC)特性与填料浓度、加工工艺及后处理条件的关系，给出了最优化工艺条件。实验结果表明，两种聚乙烯/炭黑复合材料在材料的混炼和后处理工艺、以及室温电阻R0和PTC特性等方面都表现出较大的差异。具有高熔融指数的聚乙烯/炭黑复合体系(PE20／CB)具有良好的易混炼性和材料的均匀性，并且当炭黑含量在18％-26％范围内变化时，材料具有较理想的R0和PTC性能。低熔融指数聚乙烯/炭黑复合体系(PE2／CB)则在材料的稳定性和NTC现象的消除方面胜出一筹。     

A new approach for calculating non-uniform lattices

A new method is proposed for calculating non-uniform LWR lattices. The method is based on some reasonable assumptions. A new fine-mesh algorithm is derived for the global reactor calculation. The balance equation can be considered as the generalization of the finite-difference form of the diffusion equation. Its coefficients are response matrix elements instead of the traditional homogenized macroscopic cross-sections. As not only cell boundary quantities but also cell-averaged reaction rates (including average flux) are connected with each other by response matrices, on solving the balance equation not only is the fine-mesh flux distribution obtained but also the effective cell parameters. The response matrix elements are obtained from cylindricalized cell transport calculations. In the proposed method several transport problems with different boundary conditions are to be solved for each cell type. The cell transport calculations and the global reactor calculation are coupled in a consistent manner.     

Investigation of the incorporation of spent alkali chloride melt in ceramic

Investigations to validate a method of immobilizing high-level wastes from pyroelectrochemical reprocessing of spent nuclear fuel in mineral-like crystal matrices have been conducted. Methods for obtaining and the microstructure, elemental and phase compositions, and chemical stability of a ceramic matrix based on the mineral kosnarite, intended to be used for immobilizing wastes of alkali-metal chloride melts, are studied using inactive model materials, x-ray phase analysis, scanning electron microscopy, x-ray microspectrometry, and leach tests. __________ Translated from Atomnaya énergiya, Vol. 102, No. 3, pp. 178–182, March, 2007.     

Complete modeling of multidimensional noise as a multivariate autoregressive process

A new method for multivariate autoregressive modeling of a vector time series is described, which has an advantage in guaranteeing less-biased estimation in a least-squares sense by ensuring orthogonality between the components of a residual vector. An expression for a multivariate autoregressive model with a zero-lag coefficient matrix is derived theoretically and utilized for the modeling based on a weighted least-squares procedure. Model parameters such as regression matrices and residual matrix are determined recursively for each value of order by using the LWR algorithm. It is shown that the present modeling differs from the ordinary one in estimating open-loop properties, though these modeling are equivalent for closed-loop estimates.     

Iterative solution of the reduced eigenvalue problem

The Guyan method of reducing the stiffness and mass matrices of large linear structures introduces errors in the reduced mass matrix. These errors cannot be completely avoided even if the analysis coordinates are chosen optimally. However, they can be eliminated by iterating on the eigenvectors found from the Guyan reduced matrices. The necessary iteration steps follow directly from the eigenvalue problem. The resulting iteration procedures are presented and applied to two test problems showing that the iterations enable the exact eigensolutions to be extracted. All errors from the Guyan reduced matrices are removed or substantially decreased.     

A kinetic model for the direct response matrix method

ABSTRACT

An accurate analysis model for transient reactor behavior is necessary to keep sufficient safety margins of nuclear power plants to prevent cliff edge effects. In this study, the direct response matrix (DRM) method is applied to the kinetic domain and the transient analysis is enabled based on the transport equation. The kinetic DRM model introduces the time delay to four sub-response matrices. The time delay can be evaluated by a Monte Carlo calculation. The model is evaluated in homogeneous and heterogeneous problems. The Doppler feedback is considered in the heterogeneous problem and the calculation results are compared with the experimental data. The calculation results indicate that the calculation step 1.0E-7 s is sufficient for the model and the model provides results in good agreement with the experimental data. It is concluded that the present model with the DRM method can be used for transient analysis.     

Zirconium alloys matrix as innovative material for composite fuel

A novel class of zirconium alloys is suggested as fuel matrix. They are “deep” ternary or quaternary eutectics having relatively low melting point i.e. from 963 to 1133 K in comparison with pure zirconium and intended for use as a matrix of dispersion high uranium content fuel (CERMET and METMET) particularly for thermal reactors. For fast reactors and MA burning Zr–Ti based alloys are proposed that have resistant metallurgical bonds between fuel and steel cladding. Investigations have been carried out on the structure and properties of the alloys as well as the specific technologies of their fabrication, in particular via induction furnace melting. The alloys may be also produced in the amorphous state as granules and strips. It is shown that thanks to their capillary properties they might be applied in brazing dissimilar materials. Based on novel zirconium matrix alloys high uranium content fuel compositions were produced. They have high thermal conductivity and compatibility as well as 25–50% higher uranium content than for VVER and PWR fuels.Fuel pins are fabricated by capillary impregnation method. The use of dispersion fuel with novel zirconium matrix alloys improves neutronics characteristics of reactor cores and might lead to extension of burn-up, low operating temperatures and serviceability under transient conditions.     

Synthesis of polymeric micro- and nanostructural materials for application in non-linear optics

The present paper describes a new approach developed for the preparation of micro- and nanostructural materials on the basis of polymeric compositions used as a matrix in non-linear optics. This approach consists in filling the pores of poly(ethylene terephthalate) track membranes (PET TM) from polymeric compositions using an impregnation method. It is shown that depending on the concentration of polymeric compositions in the solution it is possible to form a variety of micro- and nanostructural materials (tubules and wires as well as composite membranes) with a wide spectrum of characteristics. The developed method of producing micro- and nanostructural materials provides a possible way for creating polymeric objects with non-linear optic properties which can be used to design electronic micro- and nanodevices and to obtain chemical and optical sensors.     

Young's Moduli of Compact Matrices for HTGR Fuel

Young's moduli of matrices of compacted graphite samples were determined from measured values of ultrasonic-wave propagation through the sample at room temperature. The results were analyzed with particular interest directed to the effects of differences in matrix density and graphite orientation on the propagation velocity, from which the modulus was calculated. The characteristics of the matrices were observed by X-ray diffractometry on the crystallite sizes, and the shapes of the graphite powders constituting the main substance of the compact matrices were scrutinized by scanning electron microscope.

The value of Young's modulus was found to increase with binder content in the matrices constituted uniquely of one kind of graphite material, while in the case of composite matrices embodying a mixture of petroleum coke graphite and natural graphite, the modulus decreased with increasing natural graphite content. The velocity of ultrasonic-wave propagation—from which the value of Young's modulus is derived—depends on the density alone in isotropic matrices prepared from milled isotropic coke graphite, whereas in anisotropic matrices embodying needle coke graphite it depends on graphite orientation as well as on density. The contributions of density (p) and of reflective intensity ratio (IR) to the propagation velocity (V) are expressed ΔV=a (Δo) ⁿ and ΔV=b (ΔIR), where the symbol Δ indicates increment, while a, b and n are constants depending upon the characteristics of the compact matrix.     

Complex behavior in quaternary zirconias for inert matrix fuel: what do these materials look like at the nanometer scale?

Conventional crystallographic analysis of cubic stabilised zirconias (CSZ) over a wide range of stabilisers and stoichiometries has shown O atom displacements along lattice vectors and cation disorder with irreproducible characteristics. However, because diffraction is only sensitive to the average long-range order and biased towards periodic and symmetric distortions, it is essential to supplement it with probes of short-range order that may reveal additional, element-specific details about local ordering. We have performed X-ray Absorption Fine Structure (XAFS) spectroscopy measurements on a series of Er-Y-(U-Ce)-Zr oxides to determine the local environment around each of the cations. Results from these experiments demonstrate that not only are there significant element- and composition-dependent distortions away from the crystallographic structure but also interactions between specific pairs of the metal ions indicative of cooperative behaviour. This suggests that some of the metal ions are not randomly, isomorphically substituted into the lattice but instead have tendencies to form nanometer-scale clusters and networks. In this respect, substantial differences are seen in the influence of Ce and U on the Y-centered distortions, consistent with different roles for these two elements in inert matrix fuel (IMF) matrices. This type of nanometer-scale heterogeneity is typically coupled to the phase stability and other properties of other materials and may therefore be important to these zirconias in their IMF application.     

Ceramic matrices for plutonium disposition

One of the major issues related to the expanded use of nuclear power and the development of advanced nuclear fuel cycles is the fate of plutonium and “minor” actinides. In addition, substantial quantities of plutonium and highly enriched uranium from dismantled nuclear weapons now require disposition. There are two basic strategies for the disposition of the actinides: (1) to “burn” or transmute the actinides using nuclear reactors or accelerators; (2) to “sequester” the actinides in chemically durable, radiation-resistant materials that are suitable for geologic disposal. This paper deals with actinide-bearing materials that support the latter approach. During the past two decades, a considerable amount of research and development has been done in an effort to develop matrices for the immobilization of plutonium and the “minor actinides”, Np, Am and Cm. A variety of waste form materials – oxides, silicates and phosphates – have been developed that have a high capacity for the incorporation of actinides, are chemically durable and, in some cases, resistant to the radiation-induced transformation to the aperiodic state. These waste forms can be selected depending on the composition of the waste stream that contains the actinides, the desired materials' properties of the waste form, and the geochemical and hydrologic conditions of the specific repository. The present state-of-knowledge for these materials is such that now one can design materials for very specific conditions, such as the thermal history and accumulated radiation dose, in a repository.     

Covariances of Evaluated Nuclear Cross Section Data for Th, W and Mn

The EMPIRE code system is a versatile package for nuclear model calculations that is often used for nuclear data evaluation. Its capabilities include random sampling of model parameters, which can be utilised to generate a full covariance matrix of all scattering cross sections, including cross-reaction correlations. The EMPIRE system was used to prepare the prior covariance matrices of reaction cross sections of ²³²Th, ^{180,182,183,184,186}W and ⁵⁵Mn nuclei for incident neutron energies up to 60 MeV. The obtained modelling prior was fed to the GANDR system, which is a package for a global assessment of nuclear data, based on the Generalised Least-Squares method. By introducing experimental data from the EXFOR database into GANDR, the constrained covariance matrices and cross section adjustment functions were obtained. Applying the correction functions on the cross sections and formatting the covariance matrices, the final evaluations in ENDF-6 format including covariances were derived. In the resonance energy range, separate analyses were performed to determine the resonance parameters with their respective covariances. The data files thus obtained were then subjected to detailed testing and validation. Described evaluations with covariances of ²³²Th, ^{180,182,183,184,186}W and ⁵⁵Mn nuclei are included into the ENDF/B-VII.1 library release.     

Overall mechanical properties of fiber-reinforced metal matrix composites for fusion applications

The high-temperature strength and creep properties are among the crucial criteria for the structural materials of plasma facing components (PFC) of fusion reactors, as they will be subjected to severe thermal stresses. The fiber-reinforced metal matrix composites are a potential heat sink material for the PFC application, since the combination of different material properties can lead to versatile performances. In this article, the overall mechanical properties of two model composites based on theoretical predictions are presented. The matrix materials considered were a precipitation hardened CuCrZr alloy and reduced activation martensitic steel `Eurofer'. Continuous SiC fibers were used for the reinforcement. The results demonstrate that yield stress, ultimate tensile strength, work hardening rate and creep resistance could be extensively improved by the fiber reinforcement up to fiber content of 40 vol.%. The influence of the residual stresses on the plastic behavior of the composites is also discussed.     

Transfer matrix approach to earthquake amplification through layered soils

In this paper, the system transfer matrix for layered soil is obtained as the continued product of the transfer matrices for each individual layer. To determine the transfer function for the medium, the Laplace transformation is used to suppress the time variable in the governing equation, and the fact that the continuity of the shearing stress and the displacement (or equivalently of their transforms) must be maintained across each interface, naturally suggests their choice as the components of a state vector. After the problem has been recast into a transfer matrix setting, the continuity of the state vector is automatically assured by continued matrix multiplication.The transfer matrix for a single soil layer is considered first, for which the complex amplification is obtained. The influence of various levels of damping on the amplification is discussed, and it is shown that the response to a harmonic input is easily determined since the complex amplification is precisely the frequency response function. The multilayered medium is considered next, and it is shown that the amplification term is found through the multiplication of layer transfer matrices. Time response can then be obtained by means of a Fourier inversion which is easily accomplished through a fast Fourier transform algorithm. Finally, the problem of a soil layer on semi-infinite rock is considered in the absence of damping. Since the solution of this problem can be readily obtained in closed form, its discussion and interpretation are relatively simple. The fact that the transmission and reflection of waves at the soil-rock interface does not occur is analytically demonstrated, and explained on physical grounds.     

Decay heat production in a TRU burner

The design of new reactors such as ADS has been investigated in many countries during the last years for burning transuranic nuclides (TRUs) contained in spent reactor fuel. To increase the TRU incineration rate, fertile-free dedicated fuels, which may contain a large fraction of minor actinides (MAs), are currently considered. Based on past experience, R&D activities for dedicated fuels in Europe concentrate on fuel forms, in which the oxide actinide phase is mixed with oxide or metal inert matrices. Decay heat in a system with inert matrix fuel (IMF) containing MAs may differ from that in a conventional fast reactor. In this paper, several fast reactor designs with different TRU content are considered and related decay heat values, calculated on the basis JEFF 3.0 and JEFF 3.1 nuclear data libraries, are compared. It is shown that some decay heat components for fuels with MAs may be lower than those for MA-free fuels, but the total decay heat may be significantly higher for cooling times exceeding about 1 min.