RU2472181C1 - Method of measuring fluence of slow neutrons using monocrystalline silicon - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: method involves measuring resistivity of monocrystalline silicon before and after irradiation, irradiation with an unknown neutron fluence, annealing radiation defects in silicon after each irradiation, wherein the silicon is irradiated in a cadmium screen with thickness of 0.5-1.5 mm and without a cadmium screen; cadmium ratio is calculated based on changes in specific conductance R_cd = (σ - σ₀)/( σ_Cd - σ_0,cd), where σ_0,cd, σ₀ denote specific conductance before irradiation in the cadmium screen and without the cadmium screen, σ_cd, σ denote corresponding specific conductance of cadmium in the cadmium screen and without the cadmium screen after irradiation and annealing, and the absolute effective fluence of slow neutrons

is determined, where e, µ_p denote charge and mobility of electrons in silicon monocrystals, χ_t denotes the self-screening coefficient of slow neutrons in a silicon disc, Σ_t denotes the macroscopic reaction cross-section of radiation capture of slow neutrons of silicon-30, F_Cd is a compensation factor which takes into account absorption of epithermal neutrons in cadmium.

EFFECT: change in absolute values of fluence of slow neutrons without additional calibration, independence of measurement results from the neutron spectrum.

Description

The invention relates to the field of radiation technology, as well as to the operation of nuclear installations and accelerators.

Known methods for measuring the fluence of thermal neutrons using ionization chambers and proportional counters [Lomakin SS, Petrov VI, Samoilov PS Neutron radiometry by the activation method. M .: Atomizdat, 1975, 208 p.]. Their advantage is that information on the neutron flux density is continuously output, which allows you to control the neutron fluence directly during irradiation. Their disadvantages: a) significant burn-out of a neutron-sensitive element, which depends on the neutron spectrum; b) increased requirements for thermal and radiation resistance of insulators; c) the relative complexity of the design; d) the need to calibrate these detectors to measure the absolute values of the flux density (fluence) of thermal neutrons using other, more universal methods, for example, activation ones.

There is also a method of measuring neutron fluence with a semiconductor detector, which includes calibrating the detector, measuring the electrical resistance of the detector before irradiation, irradiating with an unknown neutron fluence, measuring the electrical resistance of the detector after irradiation [a.c. No. 934402, published 07.06.82, BI No. 21]. In this case, n-type silicon is used as a detector. The main disadvantage of this method is associated with a significant dispersion of the initial parameters, even for the same type of serial production devices. Therefore, each such device requires individual calibration, after which the restoration of the initial parameters during high-temperature annealing is often impossible due to the destruction of the internal structure of the devices. In addition, to measure the absolute values of the flux density of thermal neutrons, their calibration is also required.

Among all the known methods, the most universal methods for determining the thermal neutron flux density in both relative and absolute units without additional calibration are activation methods [Kramer-Ageev EA, Troshin VS, Tikhonov EG Activation methods of neutron spectrometry. M .: Atomizdat, 1976, 232 p.]. They are often used to calibrate other, simpler methods of measuring neutron fluence. However, these methods are laborious and require special equipment. In addition, when samples are irradiated, they cannot always be used as tracking detectors for two reasons. Firstly, due to the fact that the activity of the detector after irradiation does not depend on the fluence during the entire exposure time, but only on the fluence in recent times, equal to 5-10 half-lives. Secondly, it is not always possible to determine the neutron fluence when the neutron flux changes during the irradiation, for example, due to reactor shutdowns during prolonged irradiation. To a lesser extent, this applies to a cobalt detector, which has a long half-life (5.28 years). However, due to the long half-life after irradiation, its disposal as a radioactive material is required.

Closest to the claimed is a method of measuring the fluence of thermal neutrons with monocrystalline silicon [RU No. 2379713, published January 10, 2010, BI No. 2], including measuring the electrical resistivity (USE) of monocrystalline silicon before and after irradiation, irradiation with an unknown fluence neutrons, annealing of radiation defects in silicon after each exposure.

When silicon is irradiated with thermal neutrons, phosphorus is formed due to the (n, γ) reaction

The concentration of transmutation nuclei of phosphorus N _{p is} proportional to the fluence f of thermal neutrons

where Σ is the macroscopic cross section of reaction (1). Phosphorus in monocrystalline silicon is a donor impurity; therefore, in n-type silicon it increases conductivity (conductivity, by definition, is the inverse of resistance), and in p-type silicon it decreases. In this method, there is a linear relationship between the change in electrical conductivity (usp) and the neutron fluence. Moreover, the coefficient of proportionality is the same for any initial c.u.s. Annealing of silicon after irradiation is necessary in order to remove radiation defects that affect the change in the energy factor In this way, the flux of thermal neutrons can be measured in a wide range of values, from 10 ¹⁵ to 10 ¹⁸ cm ^-2 , and detectors using this method can be used as tracking detectors during irradiation of samples. In addition, physical information (c.u.s.), unlike, for example, the activation method, is stored indefinitely, which allows one to double-check the obtained measurement result of thermal neutron fluence at any time. The disadvantage of this method is that to measure the absolute values of the thermal neutron fluence, it needs to be calibrated using other, more universal methods, for example, activation ones.

The technical result of the invention is: 1) the use of single-crystal silicon for measuring the absolute values of the flux of thermal neutrons without any additional calibration; 2) the independence of the measurement results from the neutron spectrum. At the same time, all the advantages of the prototype are preserved.

This is achieved by the fact that in the known method for measuring the thermal neutron fluence with monocrystalline silicon, including measuring the electrical resistivity of single crystal silicon before and after irradiation, irradiating with an unknown neutron fluence, annealing radiation defects in silicon after each irradiation, characterized in that the irradiation of silicon is carried out in cadmium screen thickness of 0.5-1.5 mm and without a cadmium screen, calculate the cadmium ratio for changes in specific electrical conductivities

where σ _{0, Cd} , σ ₀ are the specific electrical conductivities before and after irradiation in a cadmium screen, σ _Cd , σ are the corresponding electrical conductivities of silicon in and without a cadmium screen after irradiation and annealing, and the absolute effective thermal neutron fluence is determined

where e, μ _n is the electron charge and mobility in silicon single crystals, χ _t is the thermal neutron self-screening coefficient in the silicon washer, ∑ _t is the macroscopic cross section of the radiation capture of thermal neutrons by silicon-30, F _Cd is the correction coefficient taking into account the absorption of epithermal neutrons in cadmium.

To measure the absolute values of the thermal neutron fluence, it is proposed to irradiate silicon in the cadmium screen and without it, as is done in the activation method, using its experience using the cadmium difference method. With regard to silicon, the essence of the method is as follows. One can imagine the concentration of phosphorus-31 generated during the irradiation of silicon without a cadmium filter in the form of two components: generated by thermal (C _t ) and epithermal (C _nt ) neutrons

We have shown [Varlachev V.A., Emets E.G. Solodovnikov E.S. // Izv. universities. Physics. - 2009. - No. 11/2. - S.409-412], that C is linearly associated with a change in the economic coefficient:

where σ ₀ , σ is the.e.p. silicon before and after irradiation, e, µ _n are the charge and mobility of electrons, respectively. It should be noted that the measurement of σ is carried out after annealing of radiation defects, thereby excluding the effect of radiation defects from fast neutrons on the change in the electron beam At present, it is customary to use cadmium-113 as an absorber because of the large absorption cross section in the thermal region and its rapid decrease in the epithermal region. However, the cadmium absorption cross section is not a step function. Therefore, in the activation method of the cadmium difference, the concept of the boundary absorption energy in cadmium E _{Cd is} introduced, which depends on the thickness and shape of the filter. It is believed that neutrons with energies below E _{Cd are} completely absorbed by the filter, and above this energy they are not absorbed. The resulting error (1-4%) is compensated by the cadmium correction F _Cd . In this approximation, when silicon is irradiated in a cadmium filter

where F _Cd is a correction factor that takes into account the absorption of epithermal neutrons in cadmium. The concentration of phosphorus-31 (C _Cd ) is determined by the values of.e. silicon before (σ _{0, Cd} ) and after (σ _Cd ) irradiation:

For reactor neutron fields formed in the presence of good moderators (water, graphite, beryllium, etc.), the spectrum of thermal neutrons is approximately described by the Maxwell distribution. In this case, when using a detector whose reaction cross section in the thermal region of the spectrum varies according to the law 1 / v (v is the neutron velocity)

where C _t is the concentration of phosphorus-31 generated by thermal neutrons; Ф _eff - effective thermal neutron fluence; ∑ _t is the macroscopic cross section of the reaction at a neutron energy corresponding to a certain effective temperature T _eff different from the temperature of the medium T ₀ ; g _t is the Westcott factor, which takes into account the difference in the dependence of the cross section of thermal neutrons of the (n, γ) reaction on silicon-31 from the 1 / v law, χ _t is the self-screening coefficient of thermal neutrons. According to [Evaluated nuclear reaction libraries (ENDF). IAEA Nuclear Data Service, www-nds.iaea.org] the cross section of the (n, γ) reaction on silicon-30 in the thermal region strictly follows the law 1 / v, that is, g _t = 1. Due to neutron leakage and absorption, T _eff > T ₀ , i.e. not all neutrons achieve thermodynamic equilibrium with the environment. In particular [Tarnovsky GB, Yaryna V.P. Taking into account the influence of cadmium screens in neutron activation measurements. // Abstracts of the 3rd All-Union. Meetings on metrology of neutron radiation at reactors and accelerators, M., ed. TSNIIatominform, 1982, p.77], with

where is the average logarithmic loss of energy

∑ _a , ∑ _s are the macroscopic absorption and scattering cross sections of the moderator; k is the Boltzmann constant; A is the mass number of moderator cores

For example, for a beryllium moderator T _eff = 1.0066 T ₀ , i.e. T _eff > T _{0 by} about 2K.

From the expressions (5, 7, 9)

Then, taking into account expression (6, 8), we obtain the effective fluence of thermal neutrons, which irradiated silicon without a cadmium filter

Where

there is a cadmium ratio, which is determined by the measured values of It is easy to switch from the effective thermal neutron fluence to the average (during the irradiation time τ) value of the effective thermal neutron flux density (φ _eff ). By definition, φ _eff = Φ _eff / τ. Moreover, φ _eff is the product of the bulk density of neutrons with energies below the boundary energy of cadmium and the velocity of neutrons with energy kT _eff .

We define the values of F _Cd , χ _t and Е _Cd for silicon. Typically, F _{Cd is} assumed to be 1.01-1.04 [Experimental methods of neutron research: Textbook. A manual for universities / E.A. Kramer-Ageev, V.N. Lavrenchik, V.T. Samosadny, V.P. Protasov. - M .: Energoatomizdat, 1990. - 272 p.]. Therefore, with an error of up to 2%, one can take F _Cd = 1.02.

The self-shielding coefficient χ _{t of} thermal neutrons (the ratio of the number of neutrons emitted from a silicon washer to the number of neutrons emitted into silicon) in an isotropic neutron field was determined by calculations. The calculations were performed by the Monte Carlo method by direct modeling of neutron trajectories in natural silicon. The history of the neutron ended either in its absorption or in the escape from silicon. Variable parameters were the radius and thickness of the washer. For each variant 10 ⁷ neutron stories were played out. The calculation results are shown in the table. Effective optical thicknesses, i.e. average values of segments in a silicon wafer along the path of neutron entry into it.

Self-shielding coefficient (χ _t ) and effective optical thickness d _{eff of a} silicon wafer of radius r and thickness d for thermal neutrons. r, cm 0.5 0.6 0.7 d cm 0.4 0.5 0.6 0.4 0.5 0.6 0.4 0.5 0.6 χ _t 0,996 0,995 0,995 0,996 0,995 0,994 0,995 0,995 0,994 d _eff cm 0.583 0.657 0.717 0.634 0.720 0.793 0.677 0.774 0.859 r, cm 0.8 0.9 1,0 d cm 0.4 0.5 0.6 0.4 0.5 0.6 0.4 0.5 0.6 χ _t 0,995 0,994 0,994 0,995 0,994 0,993 0,995 0,994 0,993 d _eff cm 0.7145 0.821 0.917 0.747 0.863 0.967 0.777 0.902 1.013 r, cm 1,1 1,2 1.3 d cm 0.4 0.5 0.6 0.4 0.5 0.6 0.4 0.5 0.6 χ _t 0,994 0,994 0,993 0,994 0,993 0,993 0,994 0,993 0,992 d _eff cm 0.803 0.936 1,054 0.828 0.966 1,092 0.850 0,994 1,126

V.P. Yaryna and G. B. Tarnovsky [Tarnovsky G. B., Yaryna V. P. Taking into account the influence of cadmium screens in neutron activation measurements. // Abstracts of the 3rd All-Union. Meetings on metrology of neutron radiation at reactors and accelerators, M., ed. TSNIIatominform, 1982, p.77] proposed an empirical formula for calculating the E _{Cd of a} cadmium cylindrical filter placed in an isotropic field:

where h and d are the height and diameter of the cylindrical filter in mm. For example, in the standard set of AKN-T detectors there is a filter with a diameter of 15 mm, a height of 10 mm and a wall thickness of 1 mm. When using this filter, E _Cd = 0.55 eV.

The possibility of implementing the method is confirmed by the following experiments conducted on a research reactor of the IRT-T type with a capacity of 6 MW in Tomsk. The experiments were carried out using the neutron-transmutation technology of silicon existing since 1984, based on the horizontal experimental channel HES-4. There is an annealing furnace for radiation defects of the SUZN1.6 type, installations for measuring the electrical resistivity by the 4-probe method, the lifetime of minority charge carriers, such as conductivity, machines for cutting and grinding ingots, a chemical site for preparing silicon for irradiation and its deactivation. Using this technology, single-crystal silicon washers were prepared. The electrical resistivity was measured using the 4-probe method. The error in measuring the average resistivity at the end of the washer did not exceed 3%. Resistance was measured before and after irradiation and annealing of radiation defects at a temperature of 800 ° C for 2 hours. The thermal neutron fluence was continuously monitored using standard KtV-4 fission chambers used in the technology of neutron transmutation doping of silicon.

The cadmium ratios for silicon R _Cd (Si) and for gold R _Cd (Au) were determined as described. For this, silicon samples, in and without a cadmium cylindrical pencil case, were located on the axis of the GES-4 channel symmetrically with respect to the center of the reactor core. A cylindrical pencil case with a height of 10 mm, a diameter of 15 mm and a wall thickness of 1 mm was used. The distance between the samples was 15 cm. Irradiation was carried out for 4 hours at a reactor power of 6 mW. The initial resistance of the sample irradiated in a Cd filter is 857 Ohm · cm, and without a filter - 772 Ohm · cm. Final resistance - 593.5 Ohm · cm and 99.5 Ohm · cm, respectively. It follows that R _Cd (Si) = 16.9, Φ = 2.14 · 10 ¹⁷ cm ^-2 and φ = 1.49 · 10 ¹³ cm ^-2 s ^-1 . The temperature of the water tank in the reactor pool is 42 ° C, which corresponds to the temperature of the medium T _eff = 315 K, and kT _eff = 0.0292 eV. At this energy, the macroscopic cross section of the reaction is 1.66 · 10 ^-4 cm ^-1 . Gold detectors in the same cadmium pencil case and without it were irradiated at a power of 100 keV for 10 minutes. They were located exactly like the samples of silicon. The cadmium ratio for gold was 4.36, and the effective thermal neutron flux density, reduced to a reactor power of 6 meV, was 1.44 · 10 ¹³ cm ^-2 s ^-1 .

A useful result is that the detector allows you to determine the absolute values of the thermal neutron flux density for any reactor neutron spectrum. In this case, no calibration is required using other methods, such as activation. Each single crystal can be used repeatedly, including as an tracking detector for monitoring the thermal neutron fluence in the range 10 ¹⁵ -10 ¹⁸ cm ^-2 .

Claims (1)

A method for measuring thermal neutron fluence with monocrystalline silicon, including measuring the electrical resistivity of monocrystalline silicon before and after irradiation, irradiating with an unknown neutron fluence, annealing radiation defects in silicon after each irradiation, characterized in that the irradiation of silicon is carried out in a 0.5-1 cadmium screen 5 mm and without a cadmium screen, the cadmium ratio is calculated from changes in the specific electrical conductivities
R _Cd = (σ-σ ₀ ) / (σ _Cd- σ _{0, Cd} ),
where σ _{0, Cd} , σ ₀ - specific electrical conductivity before irradiation in the cadmium screen and without it; σ _Cd , σ are the corresponding electrical conductivities of silicon in the cadmium screen and without it after irradiation and annealing, and determine the absolute effective fluence of thermal neutrons

where e, µ _n is the charge and mobility of electrons in silicon single crystals; χ _t is the coefficient of self-screening of thermal neutrons in the silicon washer; Σ _{t is the} macroscopic section of the reaction of radiation capture of thermal neutrons by silicon-30; F _Cd is a correction factor that takes into account the absorption of epithermal neutrons in cadmium.