Total Cross-Sections of U, UO2 and Tho2 for Thermal and Subthermal Neutrons

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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 technique. 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 increase 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 calculations 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 temperature 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 transmission 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 resolution 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 density 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 temperature. 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 temperature 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 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. 4 the increase of the sample temperature gives an increase of

The crystal structure of ThO9 at 20°C is of the CaF_-type as it is for UO, (see fig. 1 b). The lattice constant is a =5. 5997 A. Cd O Table II gives the calculated position of the Bragg edges for ThO^. The discussion of this table and of the low-temperature experimental

results follows exactly the one given for UO?. In a special measurement the slow chopper was used for better statistics in the energy region from 0. 010 eV to 0. 015 eV to look for the mixed-indices reflection (041) at 750 C. However, we could not notice any clear effect due to such a reflection.

ACKNOWLEDGEMENTS

The author wishes to express his thanks to Dr. Erik Johansson and Mr. Erik Jonsson for many discussions and for help in the experiments. He would also like to thank the members of the staff of the reactor Rl for their assistance. - 8 -

REFERENCES

1. JOHANSSON E, LAMPA E and SJÖSTRAND N G, A fast chopper and its use in the measurement of neutron spectra. Arkiv f. Fysik, Jlj$, (I960) 513-531.

2. JACOB C W and WARREN B E, Crystal structure of uranium. J. Am. Chem. Soc., ^9, (1937) 2588-91.

3. KONOBEEVSKY S T et al. , Int. Conf. on the Peaceful Uses of Atomic Energy, Geneva Sept. 1-13, 1958. Vol. 6, Geneve 1958, p. 194-203.

4. PROGRESS IN NUCLEAR ENERGY, Ser. 5, METALLURGY and FUELS, Vol. 1, Oxf. 1961, p. 387.

5. SWANSON H E and FUYAT RUTH K, Standard X-ray diffraction powder patterns. Nat. Bur. Stand. Circ. 539, Vol. 2. Wash. 1953.

6. SWANSON H E and TATGE E, Standard X-ray diffraction powder patterns. Nat. Bur. Stand. Circ. 539, Vol. 1. Wash. 1953.

7. WILLIS B T M, Neutron diffraction studies of the actinide oxides. 1. Proceeding of the Royal Society of London, Ser. A, 274, (1963) 122-134. Table I. Calculated neutron energy and height of Bragg edges in the cross-section for uranium at room temperature.

M barnS hkl Ehkl (eV> xhkl ^Kkl ( )

020 2 0.00238 3.490 X 0.959 = 3.346 0.207 110 4 0.00310 4.667 X 0.948 = 4.424 2. 760

021 4 0.00321 4.429 X 0.946 = 4.189 3.929

002 2 0.00334 2.08 7 X 0. 944 = 1.970 1.970

111 8 0.00394 6.535 X 0.933 = 6.097 2.29 2

022 4 0.00572 1.875 X 0.906 = 1.698 0.105

112 8 0.00644 3.122 X 0.893 = 2.787 1. 739

130 4 0.00786 1.159 X 0.873 = 1.011 0.159

131 8 0.00869 1.995 X 0.861 = 1.717 1.445

040 2 0.00950 0.408 X 0.849 = 0.346 0.265

0 23 4 0.00989 0. 797 X 0. 844 = 0.673 0.631

200 2 0.01005 0.405 X 0.841 = 0.340 0.340

041 4 0.01034 0.739 X 0.838 = 0.619 0.147

113 8 0.01063 1.474 X 0. 833 = 1.227 0.461

132 8 0.01120 1.363 X 0.825 = 1.112 0. 175

220 4 0.01240 0.583 X 0.808 = 0.471 0.029

042 4 0.01285 0.562 X 0. 802 = 0.450 0.345

221 8 0.01326 1.071 X 0.797 = 0.853 0. 800

004 2 0.01337 0.390 X 0. 795 = 0.310 0.310

202 4 0.01339 0.496 X 0. 795 = 0.394 0.394

133 8 0.01538 0.83 5 X 0. 768 = 0.641 0.539 024 4 0.01575 0.413 X 0. 763 = 0.315 0.019

222 8 0.01577 0. 824 X 0.763 = 0.628 0.038

114 8 0.01648 0. 734 X 0. 754 = 0.553 0.345

043 4 0.01703 0.367 X 0. 747 = 0.274 0,065

150 4 0.01736 0.246 X 0. 743 = 0.183 0.178

151 8 0.01820 0.627 X 0. 732 = 0.458 0.012

240 4 0.01955 0.298 X 0. 715 = 0.213 0.163

223 8 0.01995 0. 829 X 0.710 = 0.588 0.551

241 8 0.02039 0. 803 X 0.705 = 0.566 0.134 - 2 W 2 * av ' M x e X hkl 3/2 7r-a-b-c-(h2/a2+k2/b2+ I2

tu c\ v f si-n 2 7T yk J hkl (barns) = X, , 7 J ~ hkl |cos2 2 5T yk Table H.

Calculated neutron energies for the Bragg edges in ThC>2 and UO_ at room temperature, (n = 1, 2, 3 .. .

ThO UO hkl, M 2 2 E (eV) E (eV)

220, 12 0.00522 Th + 2 O 0.00547 U + 2 O 400, 6 0.01042 Th + 2 O 0.01094 U + 2 O 422, 24 0.01564 Th + 2 O 0.01641 u + 2 O h + k + 1 = 4 n 440, 12 0.02086 Th + 2 O 0.02187 u + 2 O 620, 24 0.02607 Th + 2 O 0.02734 u + 2 O 111, 8 0.00196 Th 0.00205 u 311, 24 0.00717 Th 0.00752 u 331, 24 0.01238 Th 0.01299 u h + k + 1 = 4n - 1 511,1 24 0.01760 Th 0.01846 u 333,J 8 531, 48 0.02281 Th 0.02392 u

200, 6 0.00261 Th - 2 O 0.00273 u - 2 O 222, 8 0.00782 Th - 2 O 0.00820 u - 2 O

420, 24 0.01303 Th - 2 O 0.01367 u - 2 O h + k + 1 = 4n- 2 442, \ 24 0.02347 Th - 2 O 0.02461 u - 2 O 600, J 6 Fig. 1 a. Crystal structure of alpha uranium.

3/4 1/4 3/4 1/4 O O rO y.b. Two projections of the structure o of alpha uranium. The fraction 3/4 °1 at the circles gives the height of the atom in terms of a and o

a = 2. 852 A b o o K> o o b = 5.865 A 3/4 1/4 3/4 1/4 o c = 4.945 A o

1 b. Crystal structure m' tne o K ides Thorium-oxide aQ ="^7599*7 A Uranium-oxide a = 5.4682 A o (fluorite-structure at room temperature)

0 1 1/2 o i o o- •O 1/4,3/4 1/4,3/4 O Uranium or Thorium

0 1 1/2 A O 6 Oxygen

1/4,3/4 1/4,3/4 -o -O o i 1/2 o i energyj

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