MODERATING RATIO PARAMETER EVALUATION FOR DIFFERENT MATERIALS BY MEANS OF MONTE CARLO CALCULATIONS AND REACTIVITY DIRECT MEASUREMENTS

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1 MODERING RIO PRMEER EVLUION FOR DIFFEREN MERIL BY MEN OF MONE CRLO CLCULION ND RECIVIY DIREC MEUREMEN. Borio, M. Cagnazzo, F. Marchetti, P. Pappalardo,. alvini. Laboratorio Energia Nucleare pplicata (L.E.N..) of University of Pavia Pavia, Italy 1. Introduction he aim of this work is to determine moderating properties of different materials, in specific the lowingdown Power (DP) and the Moderating Ratio (MR), defined as DP =ξ MR= ξ where and represent respectively the macroscopic scattering and absorption cross section, and ξ is the average logarithmic energy loss per collision. lowing-down power indicates how rapidly a neutron will slow down in the material, but it does not fully explain the effectiveness of the material as a moderator. In fact, a material can slow down neutrons with high efficiency because of its big, but it can be a poor moderator because it also absorbs neutrons with high probability. hus, the most complete measure of the effectiveness of a moderator is the moderating ratio parameter because it takes into account also the absorption effects: the bigger is the moderating ratio values, the more effectively the material performs as a moderator. he first part of the work consisted in the comparison between the DP and MR parameter evaluated for different materials by means of Monte Carlo simulations and by means of calculations based on their definition formula: these calculations are based on knowledge of material composition and of microscopic cross section σ i (derived from literature). he second part of the work was dedicated to correlate the materials MR values with the measured variation of reactivity induced by the insertion of the materials in the core of RIG Mark II reactor of the University of Pavia. 2. DP and MR determination by means of MCNP Code and by means of definition formula. Calculations from the definition formula and Monte Carlo simulations were performed for the following material: d (g/cm 3 ) H 2 O 1.00 Graphite 1.60 ample 1.90 ample B

2 Where ample and ample B are two perfluoropolyether received from olvay olexis s.p.a. [1] with the following composition: ample : CF 3 O(CF 2 CF(CF 3 )O) n (CF 2 O) m (CF(CF3)O) p CF 3 n=20; m=0.3; p=0.7 ample B: - O(CF 2 O) m (CF 2 CF 2 O) n - n= 81.54; m=76.2, (molar fractions) = CF 3 (0.64); CF 2 Cl (0.21); CF 2 CF 2 Cl (0.15). Monte Carlo simulation were performed by means of MCNP (Monte Carlo N-Particle) code and concerned the evaluation of macroscopic total cross section and of diffusion length L. Considering a mono-directional beam of neutrons of intensity Φ 0, which strikes on a material of thickness x (Fig. 1), every neutron that interacts in the material will be lost from the beam. If Φ ( x) is the intensity of the uncollided neutrons after penetrating the distance x and emerging from the target, the attenuation of neutron beam is given by: Φ = Φ0 e x ince the purpose is to evaluate in correspondence of thermal energy region, the input for the source Φ 0 in MCNP has been a neutron beam whit Maxwell energy spectral distribution at K. he output correspond to the uncollided flux Φ : once fixed the thickness x, can be calculated. x (cm -1 ) Calculation MCNP H 2 O Graphite ample ample B N - ource φ 0 * φ Figure 1 he diffusion length L is a typical parameter for a neutron population at thermal equilibrium in the infinite medium in which diffusion takes place. he relation connecting L with the distance R from the neutron source and with the corresponding flux Φ(R) at that point, in an infinite and homogeneous medium (Fig. 2), is given by: Φ ( R) R = a e R L 178

3 ource φ(r) * R Figure 2 0,1 0, R (cm) Figure 3: exponential fit of Φ ( R) R as function of R. In this case, MCNP calculation is performed placing a neutron isotropic point source in the middle of a sphere of radium R filled whit moderator material (the outside of the sphere is composed of moderator too to take into account the diffusion in an infinite medium). he output of MCNP is the flux Φ (R) : by means of an exponential fit of Φ ( R) R the moderator diffusion length L can be evaluated (Fig. 3). L (cm) H 2 O 2.75 [2] 2.85 [3] Graphite 52.5 [2] - 59 [3] ample ample B Once and L have been evaluated it is possible to calculate the macroscopic scattering ( ) and absorption ( ) cross section by use of following equations: = + 1 L = 3 ; << he results were compared with values reported in literature, when possible, and with those obtained by simple calculation of macroscopic cross section. (cm -1 ) H 2O Graphite [3] ample ample B (cm -1 ) H 2O [3] Graphite 2.73e-4 [3] 2.834e e-4 ample e e-4 ample B e e-3 179

4 Logarimic energy loss per collision ξ has been calculated by definitions: ( 1) ξ = ξ = s ln 1 ξi respectively in the case of a nuclide with atomic number and of a mixture of nuclides. Calculated value of ξ were compared with literature when possible. i ( i ) s ξ calculation ξ literature H 2 O GRPHIE ample ample B Using the obtained value for and, lowing-down Power (DP) and Moderating Ratio (MR) have been calculated for different materials: results are reported in the following tables and mark a common trend and a good agreement between calculation and MCNP simulation. DP H 2 O 1.35 [2] Graphite 0.06 [2] ample ample B MR H 2 O 71 [2] Graphite 192 [2] ample ample B MR determination by reactivity measure. he experimental determination of Moderating Ratio has been performed by measuring the insertion of positive or negative reactivity in the reactor due to the introduction of the materials inside the Central himble of reactor core. In order to avoid reactivity effects due to temperature, measurement has been performed at 15W power. he measure procedure consisted of the following steps: Reactor is brought critical at 15 W power, central thimble is void; 180

5 the position values of control rods are registered; a sample of material X is introduced into the Central himble: the perturbation induces a deviation from steady state, which is associated to an insertion of positive or negative reactivity ρ ; Fixed the HIM e RNIEN control rods positions, critical condition at 15 W is achieved again by inserting or extracting the REGULING control rod the positive of negative reactivity inserted in the core ( ρ X ) as consequence of the introduction of material X, is evaluated using the REGULING rod calibration data. Before to start the measurement an analysis of the four materials was performed looking for contaminant with high absorption cross section. ll samples resulted very clean materials, but, from the analysis certificate, graphite resulted contaminated by less than 0.5 ppm in weight of natural boron. Besides, since graphite was in a micro-particulate state, the density of the sample was considerably low, about 1.03 g. cm -3. For this reasons, the MR parameter for graphite was recalculated by means of the definition formula: the new value estimation was 191. he results of the measurement performed on the samples are reported below: ρ (cents) H 2 O (density = 1.00) 9.22 Graphite (density = 1.03) 7.52 ample (density = 1.90) 9.95 ample B (density = 1.85) 8.74 t this point the goal was to correlate the measured ρ X with the calculated MR. In order to do this it was necessary to think about what parameters of the measure could give a contribution to the variation of reactivity but wouldn t effect the MR value. wo parameters were identified: the total weight of the sample of the material inserted in the reactor core W x and the atomic density per barn of the material itself N x. s result a new parameter of the measure was defined as follow: x ρx = ρ H O 3 W H 3 2 x x 2 W O N N H 2 O and the MR x /MR H2O values of the materials were displayed as a function of the parameter x giving as a result an exponential fit (Fig. 4). he error on the MR evaluation is due to the uncertainties on the microscopic cross section values and on the density values of the materials and, for our calculation, can be estimated about few percent. he error on parameter is mainly due to the accuracy in the indication of the reactor power level and to the uncertainties in the estimation of the REGULING rod reactivity value, of the weight and of the density of the materials. he error on parameter is estimated less than ±2%. 181

6 10 MRx/MRH20 1 0,1 0,85 0,9 0,95 1 1,05 1,1 Figure 4: exponential fit of MR x /MR H2O values of the materials as a function of the parameter x. 4. Conclusions he comparison between the DP and MR parameter evaluated for different materials by means of Monte Carlo simulations and by means of direct calculations based on their definition formula showed a good agreement with errors less that 10%. hus the Monte Carlo code seems to be a good support for the calculation of the moderating parameters, particularly useful when the materials are compound of many elements. he correlation between the values of the MR of different materials with the measured variation of reactivity induced by the insertion of the materials in the reactor core is possible by means of a definition of a new parameter of the measure. his parameter, named, depends from the total weight of the sample inserted in the reactor core and from the atomic density per barn of the material. he MR values of the materials displayed as a function of the parameter give as a result an exponential fit. In order to validate this correlation, though, it will be necessary to perform other measurements using very clean materials with a very well known composition. his will be one of the future activity of LEN. [1] G. Marchionni, G. jroldi, and G. Pezzin, in Comprehensive Polymer cience,.l. ggarwal and. Russo (Eds.), econd upplement, Pergamon, 1996, London, pp [2] K.H.Beckurts and K.Wirtz, Neutron Physics, pringer-verlag, [3] John R. Lamarsh, Introduction to Nuclear Reactor heory, ddison-wesley Publishing Company, Reading, Massachussetts, U...,