Total Cross-Sections of U, UO2 and Tho2 for Thermal and Subthermal Neutrons
Total Page:16
File Type:pdf, Size:1020Kb
AF-999 UDC 539.125.5.164.078 CM CN CN UJ Total Cross-Sections of U, UO2 and ThO2 for Thermal and Subthermal Neutrons S. F. Beshai AKTIEBOLAGET ATOMENERGI STOCKHOLM, SWEDEN 1966 A.E-222 TOTAL CROSS-SECTIONS OF U, UO AND ThO. 2 ~2 FOR THERMAL AND SUB THERMAL NEUTRONS Samir F. Beshai SUMMARY The total neutron cross-sections of U, UO_ and ThO~ have been measured from 0.0045 eV to 0.028 eV, using the time-of-flight techni- que. The samples were measured at 20 C. ThO? was also measured at 750 C. The neutron source was the reactor Rl, Stockholm. The experimental results presented as graphs in the report show in detail the influence of Bragg scattering. The results further show that the increase of the temperature for the ThO? sample gives an in- crease in the cross-section. The work also contains some calculations of the position in energy of Bragg edges for the three materials. These calculations show a very good agreement with the experiments. For uranium metal some cal- culations have been carried out also for the height (o*ifvi) of the edges. The agreement with the experiments is reasonable. * IAEA-fellow from Atomic Energy Establishment, United Arab Republic. Printed and distributed in March 1966 LIST OF CONTENTS Page 1. Introduction 3 2. Experimental equipment 3 3. Measurements and results 4 3.1 Uranium 4 3.2 Uranium oxide 6 3. 3 Thorium oxide 6 Acknowledgements 7 References 8 Tables Figures - 3 - 1. INTRODUCTION Work has been started at the reactor Rl on the measurement of the total cross-section of U, UO_, Th and ThO,, for thermal and subthermal neutrons. These measurements are carried out with time-of-flight technique for micro-crystalline (or almost micro- crystalline) samples from 20 C to 800 C. The work at high tem- perature especially will produce some new results. The experiment has some connection with reactor physics, because) besides the absorption» the scattering cross-section will enter in the build-up of fuel element spectra. " Furthermore, from a pure physics viewpoint it is interesting and instructive to study the effect on the cross-section of various Bragg reflections. This report deals with measurements on U, UO, and ThO.,. Some calculations of the position and height of various Bragg edges are also included. 2. EXPERIMENTAL EQUIPMENT Most of the measurements were carried out with a fast chopper, the properties of which are described in [l] « Some experiments with a slow chopper (Fermi-type) have also been made, in order to improve the statistics. We have, however, found some difficulty in using this chopper. This is because the trans- mission of epithermal neutrons gives a background with maxima and minima as a function of time-of-flight. One can do the measurements only in the minimum part of the background, i.e. , one can only cover a narrow energy region in each run. Furthermore, the speed of the rotor must be constant all over the measuring time - otherwise the chosen proper position for a measurement will be shifted towards the maximum part of the background, which, of course, will give a wrong value of the total neutron cross-section. The sample holder is made of stainless steel and can be put in- side a tube made of the same material. The heating is done electri- cally, by means of a coil around the tube. The arrangement - 4 - is such» that the temperature of the sample will be constant within - 10 C. The maximum temperature is about 900 C. 3. MEASUREMENTS AND RESULTS The measurements were carried out in the energy range from 0. 0045 eV to 0. 028 eV. Calibration of the energy scale was made by using the (110) Bragg edge in the cross-section for iron. The neutron energy for this edge is 0. 00499 eV. All three of the materials were measured at 20 C. ThO2 was also measured at 750 C. The experimental results have not been corrected for the reso- lution of the chopper. This resolution has the half-width A E = 0. 294 E \|E eV and is approximately shown as a triangle on the diagrams. 3. 1 Uranium A cast piece of U metal, with the thickness 25 mm and the den- sity 18. 7 g/cm , was used for the transmission measurements. A microphotography of one of the surfaces of the sample showed a grain size varying from about 5 fi- to 300 JUL. So far the cross-section has been measured only at room tem- perature. Preliminary tests at 900 C at the metallurgical laboratory with uranium-metal wrapped in zircaloy and placed in a steel con- tainer, were not successful. Renewed tests are going on and maybe later one can measure the total neutron cross-section of uranium at high temperature to study the effects of the phase transformation from a to (3 and from [3 to v . The results for the cross-section measurements at room tem- perature are given in fig. 2. The experimental points have been joined by a curve drawn by eye. The errors indicated are statistical. Other errors are small (in a rough estimation - 1 %) except for possible effects of the resolution. Below, the experimental results will be compared with some calculated results. It is known that the crystal structure of tf-uranium is orthorohom bic with the lattice constants ' : - 5 - a = 2. 852 A b '=5. 865 A and c = 4. 945 A (see fig. la). There are 4 atoms per unit cell. These four atoms have the following coordinates: (0,y, 1/4) ; (0,7.3/4) ; (1/2, 1/2+y, 1/4) ; (1/2, 1/2-y, 3/4). Bragg reflections appear only for h + k = even and the structure factor reduces to two simple expressions: £ = odd F = 4 & sin 2 IT yk i = even F = 4 aTT cos 2 w yk The parameter y is given as 0. 105 - 0.005 in [2] . We have used this value in the present calculation- The scattering amplitude "12 aTJ was chosen as 0.85 " 10 cm. All possible planes (h, k, l) of reflections below 0.02 eV are listed in Table I. Also listed are the heights of the Bragg edges per atom after correction for the Debye- Waller factor. The Debye-temperature was chosen as 144 K. This value was obtained from the discussion in [4] , page 387, using the resistivity in uranium at room temperature equal to 30 10 ohm cm. One can compare the heights of Bragg edges in fig. 2 with the calculated values in Table I. Take,for instance, the measured edge around 0.0134 eV. It is about 1. 5 b in height and corresponds to the sum of the edges for indices (221), (004) and (202). According to Table I the calculated height is 1.504 b. For other edges the agreement is also reasonable - the statistics does not allow any more precise statement. In a more justified comparison between experiment and theory one must also take into account the effect of the resolution. From the measurements of or. (E) in fig. 2 one can make an estimate of the parameter y . The planes of reflections with Miller indices (130) and (132) give a very low height of the edges. This means that cos 6 IT y must be close to zero. If cos 6 7T yis exactly zero one gets y = 0. 083. The edges for Miller indices (220) and (024) + (222) are also low according to fig. 2 and the structure factor must be close to zero. If cos 4 ft y = 0 , one gets y = 0. 125. We have not tried to make a - 6 - better estimate of y from our measurements. However, it it likely that the correct value must be somewhere between 0.083 and 0.125. [2] gives y = 0.105 - 0.005. 3. 2 Uranium oxide A sintered piece of micro-crystalline UO_ (grain size < 10 \x), 3 of thickness 34 mm and of density 10.1 g/cra » was used for the total neutron cross-section measurements. Fig. 3 gives the total neutron cross-section per molecule of UO~ measured at 20 C. The measurement at 750 C was not successful, because after the measuring time when we examined the sample, we found that it had been transformed into fine powder, making the effective sample thickness uncertain. The calculated positions of the Bragg edges are given in Table II. These calculations were made for the crystal structure of UO9 at 20 C, 5 which is of GaF^-type as shown in fig. 1 b. The lattice constant is a = 5. 4682 A. o There are three types of reflections: U + 2 O, U or U-2 O. The plus-sign means that the structure factor contains (aTT + 2 a,J where the a:s are scattering amplitudes. One can see from fig. 3 that the (U + 2 O) reflections for (220) and (422) are strong. This is a con- sequence of the fact that a,, and a~ have the same sign. 3. 3 Thorium oxide The sample consisted of ceramic microcrystalline thorium oxide disks with the thickness 22. 5 mm and the density 8. 71 g/cm . Fig. 4 gives the total neutron cross-section per molecule of ThO2. The solid curve gives <? (E) at 20°C> and the dotted curve gives er (E) at 750 C. The thermal expansion of the sample was taken into account in the determination of the total neutron cross- section at 750 C. As is evident from fig.