Heterogeneity versus homogeneity effects in neutron absorbers used in transport packages

Abstract

Many fissile material transport packages incorporate boron as a neutron poison [predominantly as a boron–metal matrix composite (MMC)] to maintain criticality safety. The MMC contains a prespecified proportion of Boron ‘homogeneously’ distributed throughout the metal matrix. Uncertainty arises as to the meaning of ‘homogeneous’, in the context of providing the neutron absorbing properties assumed in the safety case for a package and the potential effect on criticality. During criticality analyses, it is usual for homogeneous materials to be assumed as uniform, without irregularities, with equal properties in all directions, at the atomic level. Since the boronated materials are ‘alloys’, the constituents are not chemically combined but finely mixed, with the boron particles, of various sizes, viewable via a microscope. This signifies that at the atomic level, the material is not homogeneous, but a heterogeneous mixture with size and distribution of boron within the MMC being not strictly uniform.

Depending on variation in boron size and distribution, the neutron absorption capability of the MMC could be reduced, with consequential reduction in criticality safety margins. During the recent manufacture of a MOX fuel transport package, which included a boron carbide (B₄C)–aluminium alloy, material quality tests were performed to examine the structure of the material. Although the tests confirmed the size and distribution of B₄C within the MMC to be such that it could be classified as ‘homogeneous’, supporting calculations were completed to determine potential effects on criticality of a heterogeneous versus homogeneous neutron absorbing material. To determine the change in neutron absorbing properties of the MMC due to atomic versus microscopic assumptions, the Monte Carlo neutronics code MONK was used to extensively examine the effects of a heterogeneous MMC with a boron particulate of various sizes and proportions compared to a homogeneous boron distribution within the material. The paper presents, from a criticality viewpoint, the effects of heterogeneity versus homogeneity for boronated poisons in a particular fissile material transport package. It also emphasises the benefits of the utilisation of software/computing developments during the calculational process, which enable wide ranging surveys over many variables to be completed quickly and efficiently.     

硼酸盐晶须增强聚乙烯复合材料及其热中子屏蔽性能研究

以硼酸镁(Mg2B2O5)和硼酸铝(Al4B2O9)晶须作为中子吸收体与高密度聚乙烯(HDPE)复合,制备了硼酸盐晶须/HDPE复合材料。讨论了影响材料力学性能及屏蔽性能的因素,并与常用的碳化硼(B4C)屏蔽材料进行了对比。实验结果表明:3种复合材料对热中子的屏蔽效果为B4CMg2B2O5Al4B2O9,复合材料对热中子的屏蔽率均随吸收体含量和材料厚度的增加而增大,当硼酸镁晶须/HDPE复合材料的厚度为15.76mm时,材料对热中子的屏蔽率可达86.58%。晶须/HDPE复合材料的拉伸强度随晶须含量的增加而增大,当硼酸镁晶须的含量为9.1%时,复合材料的拉伸强度可达24.39 MPa,和碳化硼/HDPE复合材料相比,硼酸盐晶须更能增强HDPE基屏蔽材料的力学性能。     

Manufacturing of Porous Boron Steels Potentially Useful as Nuclear Materials

B₄C is a good neutron absorber, commonly used together with light materials in panels. The objective of this work is to manufacture high boron steels, using B₄C additions, through mechanical alloying and sintering, to get a material potentially useful for nuclear waste management. The porosity of the material can help to the removal of helium bubbles. Iron and B₄C powders were mechanically alloyed for different times, following the process studying apparent density, morphology (SEM) and structure (XRD).

Powder was uniaxially compacted and sintered at different conditions. Specimens were analysed by SEM and physical and mechanical properties were evaluated (density, dimensional change and bending strength).

Microstructures are very different and therefore, they have different properties depending on sintering temperature. Although boride formation always takes place, only ferritic areas were found at 600°C, meanwhile ferritic and perlitic areas appeared at 900°C, and both of them disappeared at l,200°C.     

Neutron absorber coatings for criticality control in annular tanks employed in spent fuel reprocessing

Computational analysis has been carried out to evaluate the effectiveness of neutron absorber coatings for criticality control in an annular tank used in fast reactor spent fuel reprocessing unit. The effect of composition, thickness and coating configuration for a given tank design and fuel solution concentration was evaluated on the basis of the multiplication factor (k_eff) calculated using the Monte Carlo N-Particle (MCNP) code. The neutron absorbers considered for the study were pure boron carbide (B₄C), B₄C/Ni–Cr combination and colmonoy. The effect of enriched boron was also analyzed. The results show that the coatings can enhance the storage capacity up to 30% for the annular tank studied.     

Study on B4C decoupler with burn-up reduction aiming at 1-MW pulsed neutron source

In pulsed neutron sources, a neutron absorber called decoupler, which is characterized by a decoupling energy (Ed), is attached to the moderator to sharpen the neutron pulses for achieving good neutron energy resolutions. Cadmium and boron carbide (B₄C) are widely used as the decoupler materials. However, it is difficult to use B₄C in MW-class spallation neutron sources owing to high burn-up, which decreases Ed and increases helium gas swelling due to neutron absorption. To solve these issues concerning a B₄C decoupler, we introduce the concept of pre-decoupler to reduce neutron absorption in the B₄C decoupler, which is sandwiched by appropriate neutron absorption materials. Then, we study impacts of the pre-decouplers on B₄C decoupler in terms of burn-up by performing simplified model calculations. It is shown that neutron absorption in B₄C is reduced by 60% by using a Cd pre-decoupler without neutron intensity penalty. Moreover, helium gas swelling in B₄C is restrained to be one-third of the value when not using the pre-decoupler.     

Uncertainty analysis in Monte Carlo criticality computations

Uncertainty analysis is imperative for nuclear criticality risk assessments when using Monte Carlo neutron transport methods to predict the effective neutron multiplication factor (k_eff) for fissionable material systems. For the validation of Monte Carlo codes for criticality computations against benchmark experiments, code accuracy and precision are measured by both the computational bias and uncertainty in the bias. The uncertainty in the bias accounts for known or quantified experimental, computational and model uncertainties. For the application of Monte Carlo codes for criticality analysis of fissionable material systems, an administrative margin of subcriticality must be imposed to provide additional assurance of subcriticality for any unknown or unquantified uncertainties. Because of a substantial impact of the administrative margin of subcriticality on economics and safety of nuclear fuel cycle operations, recently increasing interests in reducing the administrative margin of subcriticality make the uncertainty analysis in criticality safety computations more risk-significant. This paper provides an overview of two most popular k_eff uncertainty analysis methods for Monte Carlo criticality computations: (1) sampling-based methods, and (2) analytical methods. Examples are given to demonstrate their usage in the k_eff uncertainty analysis due to uncertainties in both neutronic and non-neutronic parameters of fissionable material systems.     

Monte Carlo simulation of a conceptual thermal column in the Syrian miniature neutron source reactor using MCNP-4C

Based on probabilistic approach, the MCNP-4C code has been used effectively to simulate the Syrian MNSR reactor core and all its surrounding components in three dimensions, including a preliminary conceptual design of a thermal column to be installed later. For verification and validation purposes, reactor calculations include: criticality and control rod worth. Values of these parameters are 1.00517 and 6.54 mk, respectively. The thermal column is to be installed in the water of the reactor pool. Optimal conditions for this thermal column were tested using the already developed model. Optimization focused on the most suitable position for placement of the column in the water pool, dimensions, and material. The aim was to have a thermal neutron flux of 1 × 10⁹ n cm⁻² s⁻¹ in the center of thermal column, and resonant and fast neutron fluxes to be as low as possible as well.     

Enhancement of dispersion and adhesion of B4C particles in epoxy resin using direct ultrasonic excitation

Enhancement of the mechanical properties of the B₄C/epoxy composites, which is used as a neutron shield for spent nuclear fuel cask, was achieved by direct ultrasonic dispersion of the B₄C particles in the hardener using an immersed horn, while those prepared without direct ultrasonic dispersion showed insufficient adhesion as well as some agglomerates in the epoxy resin. Degrees of agglomeration and adhesion were analyzed by means of the SEM images and the FTIR peaks belong to C-C stretching mode of the hardener ring, which was lowered and flattened by van der Waals interaction between the B₄C particles and the hardener ring substituent. The tensile strength of the B₄C/epoxy composites prepared by direct ultrasonic dispersion was maintained (or increased) compared to that for the neat epoxy matrix, while those prepared without ultrasonic dispersion were degraded significantly. Consequently, direct ultrasonic dispersion process developed in this investigation could achieve uniform dispersion as well as strong adhesion of the B₄C particles in/with the epoxy matrix enhancing the material properties without any chemical treatment resulting unwanted impurities.     

Finite element spherical harmonics (PN) solutions of the three-dimensional Takeda benchmark problems

A set of multi-group eigenvalue (K_eff) benchmark problems in three-dimensional homogenised reactor core configurations have been solved using the deterministic finite element transport theory code EVENT and the Monte Carlo code MCNP4C. The principal aim of this work is to qualify numerical methods and algorithms implemented in EVENT. The benchmark problems were compiled and published by the Nuclear Data Agency (OECD/NEACRP) and represent three-dimensional realistic reactor cores which provide a framework in which computer codes employing different numerical methods can be tested. This is an important step that ought to be taken (in our view) before any code system can be confidently applied to sensitive problems in nuclear criticality and reactor core calculations. This paper presents EVENT diffusion theory (P₁) approximation to the neutron transport equation and spherical harmonics transport theory solutions (P₃–P₉) to three benchmark problems with comparison against the widely used and accepted Monte Carlo code MCNP4C. In most cases, discrete ordinates transport theory (S_N) solutions which are already available and published have also been presented. The effective multiplication factors (K_eff) obtained from transport theory EVENT calculations using an adequate spatial mesh and spherical harmonics approximation to represent the angular flux for all benchmark problems have been estimated within 0.1% (100 pcm) of the MCNP4C predictions. All EVENT predictions were within the three standard deviation uncertainty of the MCNP4C predictions. Regionwise and pointwise multi-group neutron scalar fluxes have also been calculated using the EVENT code and compared against MCNP4C predictions with satisfactory agreements. As a result of this study, it is shown that multi-group reactor core/criticality problems can be accurately solved using the three-dimensional deterministic finite element spherical harmonics code EVENT.     

Thermoluminescent Response to Fast Neutrons of Mixture of CaSO4: Tm and Polyethylene

This report is dealing with the basic mechanism for fast neutron dosimeter. It was based on the principle that the protons produced by elastic scattering between fast neutrons and hydrogen atoms in polyethylene powder will excite their neighbor thermo-luminescent material CaSO₄: Tm powder. The mathematical formulation was according to Takenaga's approach. The optimum mixing weight ratio of polyethylene to CaSO₄: Tm was found to be 2:1. In this study the total experimental error for fast neutron dose determination was about 12%.     

Fabrication and Thermal Conductivity of Boron Carbide/Copper Cermet

Studies on fabrication and thermal conductivity of B₄C/Cu cermet were made to obtain high performance neutron absorber materials for Liquid Metal-cooled Fast Breeder Reactor (LMFBR). A mixed powder of B₄C and Cu was mechanically blended at high speed thereby a coating layer of Cu was formed on the surface of B₄C powder. Then the B₄C powder with Cu coating was hot pressed at temperatures from 950 to 1,050°C to form a B₄C cermet. A high density B₄C/CU cermet with 70 vol% of B₄C and relative density higher than 90% was successfully fabricated. In spite of the low volume fraction of Cu. the B₄C/Cu cermet exhibited high thermal conductivity which originated from the existence of continuous metallic phase Cu in B₄C/Cu cermet.     

中子吸收材料累积中子注量研究

中子注量可作为加速辐照实验的辐照指标。为了通过加速辐照的方式检验中子吸收材料的中子吸收性能,计算了中子吸收材料贮存不同时间下的中子注量。通过对乏燃料组件初始富集度、燃耗深度以及乏池温度、可溶硼浓度的研究,得到中子吸收材料在乏池贮存时中子注量的包络值,同时计算得到不同贮存时间材料¹⁰B的消耗量。结果表明,材料的中子吸收性能在贮存10～60 a的情况下并无明显变化。本文结果可为检验材料的中子吸收性能提供支持。     

Infinite multiplication factor of low-enriched UO2–concrete system

The possibility of criticality of fuel debris in a form of uranium dioxide (UO₂)–concrete mixture is evaluated by calculating the infinite multiplication factor (k _∞) for a study of criticality control on the fuel debris generated through the molten core concrete interaction in a severe accident of a light water reactor. The infinite multiplication factor can be greater than unity, which means that handling of the mixture is subject to criticality control. This paper shows that concrete provides efficient neutron moderation and points out the necessity of further investigations on the criticality of UO₂–concrete system for actual handling of fuel debris.     

Life Time Estimation for Cladding Tube Cracking Caused by Absorber Swelling of PWR RCCA Rodlets

Intergranular cracks of cladding tubes had been observed at the tips of the rodlets of PWR rod cluster control assemblies (RCCAs). Because RCCAs are important core components, an investigation was carried out to estimate their service life time.

(1) As it is essential to know the effect of slumping of the neutron absorber for the life time estimation, tests on absorber material were carried out. Both the dynamic and static stresses of the absorber are sufficiently small compared with its mechanical characteristics and it is concluded that slumping does not occur.

(2) The crack was initiated at the inner surface of the cladding tubes and Sipush et al. obtained an intergranular fracture surface in tensile tests of similar material at a very slow strain rate in an argon gas atmosphere. Therefore the mechanism of the intergranular crack of the cladding tube is not IASCC but irradiation assisted cracking (IAC) caused by an increase in hoop strain due to the swelling of the absorber and a decrease in elongation due to neutron irradiation.

(3) The crack initiation limit of cylindrical shells made of low ductile material and subjected to internal pressure is determined in relation to the uniform strain of the material and is in accordance with that of the RCCA rodlets in an actual plant.

From the above investigation, the method of estimating the life time and countermeasures for its extension are obtained.     

The thermal neutron diffusion cooling coefficient in polyethylene

The diffusion cooling coefficient C for thermal neutrons in polyethylene at 20°C has been determined theoretically. Granada's Synthetic Model of the scattering law has been applied to describe the interaction of neutrons with polyethylene. Two approximations of the neutron energy distribution in finite homogeneous systems have been used. The result of the calculation using a rough approximation is C_B=2160 cm⁴ s⁻¹. According to a more advanced formalism which follows Nelkin's analysis of the neutron pulse decay in a finite medium, applying the diffusion theory with transport correction, the value obtained is C=2916 cm⁴ s⁻¹.     

Neutron Irradiation Effect on Isotopically Tailored 11B4C

The present investigation was carried out to elucidate the effects of neutron irradiation on the dimensional change and thermal conductivity of isotopically tailored ¹¹B₄C. The specimens used in the present investigation are 99% ¹¹B-enriched ¹¹B₄C, 91% ¹⁰B-enriched ¹⁰B₄C, and β-SiC. ¹⁰B₄C was sampled from an irradiated material used as a neutron absorber in a “JOYO” MK-II control rod. The ¹¹B₄C and SiC specimens were irradiated in the experimental fast reactor “JOYO” to fluences of 1:94 × 10²⁶ n/m² (E > 0:1 MeV) at 530°C and 3:12 × 10²⁶ n/m² (E > 0:1 MeV) for ¹⁰B₄C, with a ¹⁰B burnup of 47:3 × 10²⁶ cap/m³. Measurements on changes in dimensions and thermal conductivity, as well as postirradiation annealing up to 1400°C, were carried out. The results of such measurements indicated that the changes in the dimensions and thermal conductivity of neutron-irradiated ¹¹B₄C were substantially smaller than those of ¹⁰B₄C and SiC. Postirradiation annealing measurements for ¹¹B₄C showed that the thermal conductivity was almost completely recovered at 1400°C. The changes in thermal conductivity by annealing were analyzed in terms ofphonon scattering theory. The onset of recovery of the thermal conductivity of ¹¹B₄C agreed well withirradiation temperature; however, the recovery of length did not coincide with irradiation temperature.     

Buckling analysis of a cylindrical shell,under neutron radiation environment

This research investigates the buckling of a cylindrical shell in the neutron radiation environment, subjected to combined static and periodic axial forces. Radiation induced porosity in elastic materials affects the thermal, electrical and mechanical properties of the materials. In this study, the data based technique was used to determine the volume fraction porosity, P, of shell material. A least-squares fit of the Young's module data yielded the estimated Young's modulus. The shell assumed made of iron irradiated in the range of 2–15e?7 dPa/s at 345–650 °C and theoretical formulations are presented based on the classical shell theory (CST). The research deals with the problem theoretically; keeping in mind that one means of generating relevant design data is to investigate prototype structures. A parametric study is followed and the stability of shell is discussed. It is concluded that both temperature and neutron induced swelling have significant effects on the buckling load.     

Spherical Harmonics Solutions of Multi-Dimensional Neutron Transport Equation by Finite Fourier Transformation

A method of solution of a monoenergetic neutron transport equation in P_L approximation is presented for x-y and x-y-z geometries using the finite Fourier transformation. A reactor system is assumed to consist of multiregions in each of which the nuclear cross sections are spatially constant. Since the unknown functions of this method are the spherical harmonics components of the neutron angular flux at the material boundaries alone, the three- and two-dimensional equations are reduced to two- and one-dimensional equations, respectively. The present approach therefore gives fewer unknowns than in the usual series expansion method or in the finite difference method. Some numerical examples are shown for the criticality problem.     

Anisotropic Diffusion Effect on Criticality of Plate Lattice Fast Assembly

The neutron diffusion in plate lattice is generally somewhat anisotropic. In case of usual plate cells for the mockup of LMFBR composition, the diffusion coefficient for parallel direction to lattice plate, based on Benoist's theory, proves to be larger by 2～4% than that for perpendicular direction, which is considered to affect the criticality of plate lattice fast assembly.

A practical treatment of the anisotropic diffusion effect on criticality has been proposed, in which, like the transport correction, the anisotropic diffusion effect is treated as a correction term to be applied to the conventional isotropic diffusion calculation. The method is applied to actual plate lattice critical assemblies, already built in FCA, ZPR or ZEBRA. The anisotropy correction on criticality turns out to amount to the order of -0.2～-0.4%Δ k/k for the normal plate lattice-core. The amount of anisotropy correction is further enhanced in case of an assembly consisting of plate lattice-blanket or sodium-voided core. The anisotropic diffusion effect on criticality is, therefore, important for the analysis of criticality of plate lattice assembly, and should be corrected in addition to the conventional heterogeneity effect. The present method, based on the perturbation theory, is practical and useful.