Critical Boron Concentration Research Articles

Thorium-based mixed oxide fuel in a pressurized water reactor: A beginning of life feasibility analysis with MCNP

Thorium is an asset the nuclear industry does not use, and plutonium is a liability that much of the world would like to be rid of. By incorporating a thorium–plutonium mixed oxide fuel (Th-MOX) into the fuel cycle, pressurized water reactors could provide a means for the United States to address both of these issues – but only if key reactor safety parameters are not affected.The feasibility of utilizing Th-MOX fuel in a pressurized water reactor is examined under steady-state, beginning of life conditions. With a three-dimensional MCNP model of a Westinghouse-type 17×17 PWR, many possibilities for replacing one-third of the UO2 assemblies with Th-MOX assemblies were considered. The excess reactivity, critical boron concentration, and centerline axial and radial flux profiles for several configurations and compositions of a one-third Th-MOX core were compared to a 100% UO2 core. A blanket-type arrangement of 5.5wt% PuO2 was determined to be the best candidate for further analysis. Therefore, this configuration was compared to a 100% UO2 core using the following parameters: delayed neutron fraction (βeff), temperature coefficient, shutdown margin (SDM), and axial and radial nuclear hot channel factors (FZN and FRN).The one-third Th-MOX configuration showed an undesirable reduction in βeff from 0.00716±4.60E−07 for the 100% UO2 configuration to 0.00607±4.30E−07. The reduction in βeff would perhaps be ameliorated by the one-third Th-MOX configuration’s temperature coefficient of reactivity, which at −2.05±0.02pcm°F−1 is more favorable than the corresponding value of −1.42±0.02pcm°F−1 for the 100% UO2 configuration. The SDM of the one-third Th-MOX configuration is estimated to be 4079±7pcm, which is 28% lower than value of the 100% UO2 configuration. The FZN for the two cores were virtually identical. However, FRN for the one-third Th-MOX configuration (1.67±0.28) was 20% higher than the corresponding value for the 100% UO2 configuration (1.39±0.23).These preliminary results are encouraging. However, additional investigations are required to study the impact of thermal fluid feedback and the effect of burnup and poison buildup.

Critical boron-doping levels for generation of dislocations in synthetic diamond

Defects induced by boron doping in diamond layers were studied by transmission electron microscopy. The existence of a critical boron doping level above which defects are generated is reported. This level is found to be dependent on the CH4/H2 molar ratios and on growth directions. The critical boron concentration lied in the 6.5–17.0 × 1020at/cm3 range in the ⟨111⟩ direction and at 3.2 × 1021 at/cm3 for the ⟨001⟩ one. Strain related effects induced by the doping are shown not to be responsible. From the location of dislocations and their Burger vectors, a model is proposed, together with their generation mechanism.

A systematic core design method for reduction of critical boron concentration in APR 1400 with gadolinia-bearing assembly

A systematic core design method is developed to design Gd-bearing fuel assembly having two types of Gd rods, low-wt%-Gd rod and high-wt%-Gd rod. The purpose of the method is to lower the critical boron concentration (CBC) of a preliminary core loading pattern, and consequently to achieve more negative or less positive moderator temperature coefficient (MTC). The proposed core design method is a process of solving a non-linear programming problem stated with a system of equations. In this method, both the ratio of the number of low-wt%-Gd rod to the number of high-wt%-Gd rod (r) and the assembly average Gd wt% (w) are the solution variables of the system of equations. The target function is the amount of soluble boron concentration reduction, ΔCBC, which is correlated with the reactivity change, ΔkFA, per Gd-bearing fuel assembly by a quadratic reactivity equation. The coefficients of the quadratic equations are calculated prior to the determination of Gd-bearing fuel assembly pattern, using the least square method. The constraints required to determine (r,w) are physically realizable Gd rods pattern, Δki close to ΔkFA derived from ΔCBC, etc. An objective function, minf∑i(ΔkFA-Δki), enables a final loading pattern to reach a target CBC. This design methodology is applied to APR 1400. Total six cases with various target CBCs are investigated to validate the proposed method. CASMO-3/MASTER calculations with new design assemblies produce lower CBCs at BOC than target CBCs keeping maximum pin power below the safety limit, and thus show more negative MTC.

Practical numerical reactor employing direct whole core neutron transport and subchannel thermal/hydraulic solvers

The development and verification of a practical numerical reactor formed by integrating a subchannel thermal/hydraulic solver into the nTRACER direct whole core transport code developed at Seoul National University are presented. In order to accomplish high-fidelity and practicality needed for the applications to routine design analyses of power reactors, the accuracy and the parallel computing efficiency of the direct whole core transport methods, which are characterized by the planar MOC solution based three-dimensional calculation method, the subgroup method for resonance treatment under non-uniform conditions and the Krylov subspace based depletion method, are improved and realistic modeling features such as axial spacer grid modeling and burnup-dependent gap conductance are implemented. The accuracy of the nTRACER neutronics calculations is first verified by comparing its solution with the reference Monte Carlo solutions for a group of benchmark problems. Then the core follow calculation results of the practical numerical reactor for two pressurized water reactors are compared with the measured data such as the critical boron concentration and radial power distributions.From these performance examinations, it is demonstrated that accurate and detailed direct simulations of power reactors is practically realizable without any prior calculations or adjustments before the core calculation.

Influence of Boron on transformation behavior during continuous cooling of low alloyed steels

The phase transformation behavior during continuous cooling of low-carbon (LC) Boron-treated steels was studied. Furthermore, the influence of combining Boron with Nb or Ti or V on transformation kinetics was investigated. Additions of Boron to LC steels have a strong influence on the ferrite transformation. By adding 30 ppm Boron to a Boron-free reference alloy the suppressing effect on the ferrite transformation is most pronounced, whereas 10 ppm Boron has almost no effect and 50 ppm Boron the same effect as 30 ppm Boron. Thereby the critical Boron concentration for transformation kinetics in this alloying concept is 30 ppm. The combination of Boron with Ti shifts the phase fields to shorter times and increase the ferrite start temperature, whereas the combination of B+V and B+Nb only affects the ferrite start temperature. Hardness values are mostly influenced by the presence of Boron and strongly depend on the cooling rate.

Effects of various spacer grid modeling on the neutronic parameters of the VVER-1000 reactor

The main objective of this paper is to study the effects of various spacer grid models on the neutronic parameters of a VVER-1000 reactor. Specifically, the data of the nuclear power plant at the Bushehr site, which is of a VVER-1000 type, will be studied. Three models, representing the spacer grids along the fuel assemblies are presented. These three models are the homogeneous and the heterogeneous local spacer grid models and the shroud spacer grid model. In the homogeneous and the heterogeneous models, the spacer grids are considered at their actual locations in the axial direction. The only difference between the two models is that in the homogeneous model, the spacer grids are homogenized with the coolant while in the heterogeneous model, the spacer grids are modeled around the fuel cells at their exact axial positions. In the shroud model, the spacer grids are modeled in the shroud region containing the coolant and are not necessarily placed at their appropriate axial positions. The aforementioned models and the core geometry are modeled in 3-D hexagonal geometry and solved by the CITATION code. The required cross sections are obtained from the WIMS code using the associated ENDF/B-7 based library. The visual FORTRAN programming 90 is used for analysis of the whole calculation process and provides a sophisticated link between the WIMS and the CITATION codes during core cycle burnup. The core excess reactivity and the critical boron concentration of the reactor are calculated at normal operating state. In addition, the changes in the critical boron concentration and power peaking factors during the first core cycle, for the homogeneous and shroud models are also predicted. The core calculation analysis is done for the core with fully withdrawn control rods. As will be shown, the heterogeneous model, which is a close representation of the actual case, provides a more accurate result than the homogeneous and the shroud models. However, the heterogeneous model is complicated as compared to the other two models. Therefore, the choice of which model to use depends on the accuracy required by the user.

On the use of the Serpent Monte Carlo code for few-group cross section generation

Serpent is a recently developed 3D continuous-energy Monte Carlo (MC) reactor physics burnup calculation code. Serpent is specifically designed for lattice physics applications including generation of homogenized few-group constants for full-core core simulators. Currently in Serpent, the few-group constants are obtained from the infinite-lattice calculations with zero neutron current at the outer boundary. In this study, in order to account for the non-physical infinite-lattice approximation, B1 methodology, routinely used by deterministic lattice transport codes, was considered for generation of leakage-corrected few-group cross sections in the Serpent code. A preliminary assessment of the applicability of the B1 methodology for generation of few-group constants in the Serpent code was carried out according to the following steps. Initially, the two-group constants generated by Serpent were compared with those calculated by Helios deterministic lattice transport code. Then, a 3D analysis of a Pressurized Water Reactor (PWR) core was performed by the nodal diffusion code DYN3D employing two-group cross section sets generated by Serpent and Helios. At this stage thermal–hydraulic (T-H) feedback was neglected. The DYN3D results were compared with those obtained from the 3D full core Serpent MC calculations. Finally, the full core DYN3D calculations were repeated taking into account T-H feedback and assuming Hot Full Power (HFP) conditions. The B1 two-group cross sections and diffusion coefficients generated by the Serpent and Helios codes agree within less than 2.5%. The results of the DYN3D calculations with the Serpent B1 cross section sets agree very well with those of the Serpent full core MC calculations. The relative difference in k eff is below 300 pcm. The maximum and root mean square (RMS) difference in the radial power distribution is 2.7% and 1.1% respectively. The results of the DYN3D full core calculations with T-H feedback obtained with Helios and Serpent generated cross section libraries show an excellent agreement as well. The estimated critical boron concentration agrees within 5 ppm. The maximum and RMS difference in the core radial power peaking factors is 0.8% and 0.4% respectively. In this study, a Matlab script was used for calculation of the leakage-corrected few-group cross sections, however, the B1 methodology has recently been implemented directly in the Serpent code.

Pu recycling in a full Th-MOX PWR core. Part I: Steady state analysis

Current practice of Pu recycling in existing Light Water Reactors (LWRs) in the form of U–Pu mixed oxide fuel (MOX) is not efficient due to continuous Pu production from U-238. The use of Th–Pu mixed oxide (TOX) fuel will considerably improve Pu consumption rates because virtually no new Pu is generated from thorium. In this study, the feasibility of Pu recycling in a typical pressurized water reactor (PWR) fully loaded with TOX fuel is investigated. Detailed 3-dimensional 100% TOX and 100% MOX PWR core designs are developed. The full MOX core is considered for comparison purposes. The design stages included determination of Pu loading required to achieve 18-month fuel cycle assuming three-batch fuel management scheme, selection of poison materials, development of the core loading pattern, optimization of burnable poison loadings, evaluation of critical boron concentration requirements, estimation of reactivity coefficients, core kinetic parameters, and shutdown margin. The performance of the MOX and TOX cores under steady-state condition and during selected reactivity initiated accidents (RIAs) is compared with that of the actual uranium oxide (UOX) PWR core. Part I of this paper describes the full TOX and MOX PWR core designs and reports the results of steady state analysis. The TOX core requires a slightly higher initial Pu loading than the MOX core to achieve the target fuel cycle length. However, the TOX core exhibits superior Pu incineration capabilities. The significantly degraded worth of control materials in Pu cores is partially addressed by the use of enriched soluble boron and B 4C as a control rod absorbing material. Wet annular burnable absorber (WABA) rods are used to flatten radial power distribution. The temperature reactivity coefficients of the TOX core were found to be always negative. The TOX core has a slightly reduced, as compared to UOX core, but still sufficient shutdown margin. In the TOX core β eff is smaller by about a factor of two in comparison to the UOX core and even lower than that of the MOX core. The combination of small β eff and reduced control materials worth may potentially deteriorate the performance under RIA conditions and requires an additional examination. The behavior of the considered cores during the most limiting RIAs, such as rod ejection, main steam line break, and boron dilution, is further investigated and reported in Part II of the paper.

Superconductor-to-insulator transition in boron-doped diamond films grown using chemical vapor deposition

The critical concentration of superconductor-to-insulator transition in boron-doped diamond is determined in two ways, namely, the actual doping concentration of boron and the Hall carrier concentration. Hall carrier concentrations in (111) and (001) films exceed the actual doping concentration owing to the distortion of the Fermi surface. The high critical boron concentration in (110) films is owing to the effect of the high concentration of interstitial boron atoms. A boron concentration of $3\ifmmode\times\else\texttimes\fi{}{10}^{20}\text{ }{\text{cm}}^{\ensuremath{-}3}$ in substitutional site is required for inducing superconductivity in diamond.

Metal–insulator transition and superconductivity in highly boron‐doped nanocrystalline diamond films

AbstractThe low temperature electronic transport of highly boron‐doped nanocrystalline diamond films is studied down to 300 mK. The films show superconducting properties with critical temperatures Tc up to 2.1 K. The metal–insulator and superconducting transitions are driven by the dopant concentration and greatly influenced by the granularity in this system, as compared to highly boron‐doped single crystal diamond. The critical boron concentration for the metal–insulator transition lies in the range from 2.3 × 1020 up to 2.9 × 1020 cm−3, as determined from transport measurements at low temperatures. Insulating nanocrystalline samples follow an Efros–Shklovskii (ES) type of temperature dependence for the conductivity up to room temperature, in contrast to Mott variable range hopping (VRH) in the case of insulating single crystal diamond close to the metal–insulator transition. The electronic transport in the metallic samples not only depends on the properties of the grains (highly boron‐doped single crystal diamond), but also on the intergranular coupling between the grains. The Josephson coupling between the grains plays an important role for the superconductivity in this system, leading to a superconducting transition with global phase coherence at sufficiently low temperatures. Metallic nanocrystalline samples show similarities to highly boron‐doped single crystal diamond. However, metallic samples close to the metal–insulator transition show a richer behavior. In particular, a peak was observed in the low‐temperature magnetoresistance measurements for samples close to the transition, which can be explained by corrections to the conductance arising from superconducting fluctuations.

Electronic and optical properties of boron-doped nanocrystalline diamond films

We report on the electronic and optical properties of boron-doped nanocrystalline diamond (NCD) thin films grown on quartz substrates by ${\text{CH}}_{4}/{\text{H}}_{2}$ plasma chemical vapor deposition. Diamond thin films with a thickness below 350 nm and with boron concentration ranging from ${10}^{17}$ to ${10}^{21}\text{ }{\text{cm}}^{\ensuremath{-}3}$ have been investigated. UV Raman spectroscopy and atomic force microscopy have been used to assess the quality and morphology of the diamond films. Hall-effect measurements confirmed the expected $p$-type conductivity. At room temperature, the conductivity varies from $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\text{ }{\ensuremath{\Omega}}^{\ensuremath{-}1}\text{ }{\text{cm}}^{\ensuremath{-}1}$ for a nonintentionally doped film up to $76\text{ }{\ensuremath{\Omega}}^{\ensuremath{-}1}\text{ }{\text{cm}}^{\ensuremath{-}1}$ for a heavily $B$-doped film. Increasing the doping level results in a higher carrier concentration while the mobility decreases from 1.8 down to $0.2\text{ }{\text{cm}}^{2}\text{ }{\text{V}}^{\ensuremath{-}1}\text{ }{\text{s}}^{\ensuremath{-}1}$. For NCD films with low boron concentration, the conductivity strongly depends on temperature. However, the conductivity and the carrier concentration are no longer temperature dependent for films with the highest boron doping and the NCD films exhibit metallic properties. Highly doped films show superconducting properties with critical temperatures up to 2 K. The critical boron concentration for the metal-insulator transition is in the range from $2\ifmmode\times\else\texttimes\fi{}{10}^{20}$ up to $3\ifmmode\times\else\texttimes\fi{}{10}^{20}\text{ }{\text{cm}}^{\ensuremath{-}3}$. We discuss different transport mechanisms to explain the influence of the grain boundaries and boron doping on the electronic properties of NCD films. Valence-band transport dominates at low boron concentration and high temperatures, whereas hopping between boron acceptors is the dominant transport mechanism for boron-doping concentration close to the Mott transition. Grain boundaries strongly reduce the mobility for low and very high doping levels. However, at intermediate doping levels where hopping transport is important, grain boundaries have a less pronounced effect on the mobility. The influence of boron and the effect of grain boundaries on the optoelectronic properties of the NCD films are examined using spectrally resolved photocurrent measurements and photothermal deflection spectroscopy. Major differences occur in the low energy range, between 0.5 and 1.0 eV, where both boron impurities and the $s{p}^{2}$ carbon phase in the grain boundaries govern the optical absorption.

Core physics analysis of 100% MOX core in IRIS

International Reactor Innovative and Secure (IRIS) is an advanced small-to-medium-size (1000MWt) Pressurized Water Reactor (PWR), targeting deployment around 2015. Its reference core design is based on the current Westinghouse UO2 fuel with less than 5% 235U, and the analysis has been previously completed confirming good performance for that case. The full MOX fuel core is currently under evaluation as one of the alternatives for the second wave of IRIS reactors. A full 3-D neutronic analysis has been performed to examine main core performance and safety parameters, such as critical boron concentration, peaking factors, discharge burnup, reactivity coefficients, shut-down margin, etc. In addition, the basis to perform load follow maneuvers via the Westinghouse innovative strategy MSHIM has been established. The enhanced moderation of the IRIS fuel lattice facilitates MOX core design, and all the obtained results are within the operational and safety limits considered thus confirming viability of this option from the reactor physics standpoint.

A neutron balance approach in critical parameter determination

The determination of a critical parameter, process known also as criticality or eigenvalue search, is one of the major functionalities in neutronics codes. The determination of the critical boron concentration or the critical control rod position are two examples. Classical procedures used to solve this problem are based on the iterative Newton–Raphson method where the value of the parameter is changed until the eigenvalue matches the target. We present here a different approach where an equation, derived from the neutron balance, is set and the critical parameter is the unknown. Solving this equation is equivalent to solve an eigenvalue problem where the critical parameter is the eigenvalue. It is also shown that this approach can be seen as an application of inverse perturbation theory. This method reduces considerably the computation time in situations where changes on the critical parameter make a high distortion on the flux distribution, as it is the case of the control rods. Some numerical examples illustrate the performances and the gain in stability in cases of simultaneous control of criticality and axial offset of the power distribution. The application to the determination of the critical uranium enrichment in a transport code is also presented. The simplicity of the method makes its implementation in fuel bundle lattice and reactor codes very easy.

Development of Hybrid Core Calculation System using Two-dimensional Full-Core Heterogeneous Transport Calculation and Three-dimensional Advanced Nodal Calculation

This paper presents a description of the Hybrid Core Calculation System which is based on a very rigorous but practical method utilizing best estimate core design calculations and taking advantage of the recent remarkable progress of computers. The basic idea of this system is to generate the correction factors for assembly-homogenized cross sections, discontinuity factors, etc. by comparing the CASMO-4 and SIMULATE-3 2-D full-core calculation results under the consistent calculation condition and applying them to the SIMULATE-3 3-D calculation. The CASMO-4 2-D heterogeneous core calculation is performed for each depletion step using the core conditions previously determined by ordinary SIMULATE-3 core calculations. This avoids time-consuming iterative calculations of the critical boron concentration search and the thermal hydraulic feedback. These calculations are instead performed in the final SIMULATE-3 3-D calculation using the previously determined correction factors. The Hybrid Core Calculation System was verified using data from a commercial PWR for several cycles, and it was demonstrated that the accuracy of core calculation is improved.

Nível crítico de boro em cenoura cultivada em um solo sob cerrado

Realizou-se em campo um experimento em um Latossolo Vermelho, distrófico argiloso, sob regime isohipertérmico, para avaliar a resposta da cenoura (Daucus carota) cv. Alvorada à adubação com boro. O delineamento experimental consistiu de blocos casualizados com seis tratamentos (0; 1,7; 3,4; 5,1; 6,8 e 10,2 kg B ha-1) com quatro repetições. O extrator utilizado para a determinação de boro no solo e na matéria seca das folhas foi a Azometina-H. A produção máxima de raízes comercializáveis de cenoura foi de 50,6 t ha-1, obtida com o teor estimado de 0,55 mg kg-1 de boro no solo. O nível crítico de boro no solo, associado a 90% da produção máxima comercializável estimada de cenoura foi de 0,45 mg kg-1. Numa primeira aproximação, os níveis de B (mg kg-1) no solo foram assim classificados: baixo (<0,30); médio (0,31-0,44), adequado (0,45-0,55) e alto (>0,55 mg kg-1 B), e para efeito de diagnose foliar com base nos teores na matéria seca das folhas em: baixo (<24,1), médio (2534,9), adequado (3551,9) e alto (>51,9 mg B kg-1).

Development and verification of the code system for three dimensional hexagonal PWR core fuel management calculation

A three-dimensional hexagonal PWR core fuel management code package TPFAP-H/CSIM-H has been developed. A two-dimensional transport code for hexagonal assembly based on the transmission probability and response matrix method is developed and implemented to modify and reform the existing PWR square assembly code TPFAP to the TPFAP-H which has the capability of hexagonal assembly calculation, keeping all the original functions of TPFAP. Based on the advanced 3D hexagonal diffusion nodal code, the hexagonal PWR core fuel management code CSIM-H is developed. Both codes have been linked together to form the code package TPFAP-H/CSIM-H, which considers the all feedbacks of burnup, power distribution, moderator density and control rod insertion, ... etc. The verification and validation of the code system has been examined through the IAEA WWER-1000 type PWR reactor Kalinin NPP benchmark problem. The numerical results are in good agreement with measurements and close to those of other international institutes. The errors of critical boron concentration and power distribution are all within the permissible limits of engineering requirement.

Advanced PWR Core Calculation Based on Multi-group Nodal-transport Method in Three-dimensional Pin-by-Pin Geometry

A parallel production code, SCOPE2, has been developed for advanced calculations in the reactor core design of PWRs. In SCOPE2, the multi-group diffusion and/or SP3 transport equations are solved by the Red/Black iterative method within the framework of the finite difference method or the advanced nodal method without non-linear iterations. The effects due to pin-cell homogenization are taken into account by using the SPH factors. In this paper, calculation methods needed for fast computation are derived including efficient response matrix formulation of the nodal-SP3 method, an analytic solution of the flux moments in the nodal-SP3 transport equations, and coarse-group coarse-mesh diffusion acceleration method. It was found that the present pin-by-pin nodal-SP3 method was more accurate than the finite difference SP3 method with a small additional computational cost in the same meshing scheme. Tracking calculations of a commercial PWR plant by SCOPE2 revealed that the present model accurately predicted the power distribution and critical boron concentration. A set of depletion calculations in a typical design scheme can be completed within a few hours running on a PC-cluster (16 processors) for the full-core geometry of a 3-loop PWR with 340×3407times;26 meshes based on the 9-group pin-by-pin nodal-SP3 method.

Advanced PWR Core Calculation Based on Multi-group Nodal-transport Method in Three-dimensional Pin-by-Pin Geometry

A parallel production code, SCOPE2, has been developed for advanced calculations in the reactor core design of PWRs. In SCOPE2, the multi-group diffusion and/or SP3 transport equations are solved by the Red/Black iterative method within the framework of the finite difference method or the advanced nodal method without non-linear iterations. The effects due to pin-cell homogenization are taken into account by using the SPH factors. In this paper, calculation methods needed for fast computation are derived including efficient response matrix formulation of the nodal-SP3 method, an analytic solution of the flux moments in the nodal-SP3 transport equations, and coarse-group coarse-mesh diffusion acceleration method. It was found that the present pin-by-pin nodal-SP3 method was more accurate than the finite difference SP3 method with a small additional computational cost in the same meshing scheme. Tracking calculations of a commercial PWR plant by SCOPE2 revealed that the present model accurately predicted the power distribution and critical boron concentration. A set of depletion calculations in a typical design scheme can be completed within a few hours running on a PC-cluster (16 processors) for the full-core geometry of a 3-loop PWR with 340×3407times;26 meshes based on the 9-group pin-by-pin nodal-SP3 method.

Optimized gadolinia concepts for advanced in-core fuel management in PWRs

Utilities operating LWRs require fuel assemblies and in-core fuel management service, which ensure safe, flexible and cost-effective production of electricity. Because the reliability of the fuel has always been the most important requirement, advanced measures to minimize fuel cycle costs are receiving increasing attention in the light of the pressure on costs within the deregulated power generation markets. The role of in-core fuel management in supporting the goal to minimize fuel cycle costs consists in the development of more demanding core loading strategies, i.e. in the first place, more advanced low leakage loading patterns. A prerequisite for this type of loading pattern is the use of an optimized burnable absorber design. Gadolinia (Gd) as integrated burnable absorber is a very effective means for limiting the critical boron concentration and power peaking factors. Current development efforts for optimizing Gd-fuel are focused on the reduction of the inherent penalties of today's Gd-FA designs, i.e. reduced average fuel assembly (FA) enrichment and heavy metal content, as well as the residual reactivity binding. The most effective way to overcome these drawbacks is the reduction of the Gd 2O 3 concentration to values of ≈2 w/o, for which, according to recent measurements of the heat conductivity of modern Gd-fuels, the reduction of the fissile content in the Gd-rods is no longer necessary. Various feasibility studies have been performed to evaluate the consequences of FA designs with low Gd-concentrations (low-Gd designs) for Siemens PWRs and non-Siemens PWRs, for which more restrictive boundary conditions with respect to critical boron concentration and peaking factors have to be fulfilled. These studies, as well as operation experience of reactor cycles using low Gd-FA reload designs, confirm that the in-core fuel management can handle the different Gd burnout characteristics without problems. The economical benefits of low-Gd designs compared to conventional Gd designs are comparable to those achievable by distinctly more costly and complex alternatives, like the use of enriched gadolinia.

Computer simulation of local structure and magnetic properties of amorphous Co–B alloys

Static relaxation simulation and a systematic analysis of the local atomic structure have been performed to investigate the microstructure of amorphous Co–B alloys with pair Pak–Doyama-like potentials for all the bonds in systems. Calculations show the existence of large vacancy-like cavities in the amorphous state. The Monte Carlo method and the Ising model have been used to simulate the magnetic properties of fcc Co, amorphous Co and Co–B alloys. The temperature dependence of magnetization, local magnetization distribution and critical boron concentration for the onset of spontaneous magnetic order have been investigated and presented.