Determination of Stored Energy in LiF Irradiated in a Reactor Using a Colorimeter
Abstract Generated abstract
This paper investigates the energy stored in radiation induced defects in LiF crystals irradiated in a reactor, using differential thermal annealing in a high temperature vacuum calorimeter. The authors measure stored energy release spectra for irradiation times from 0.5 to 5 hours and find annealing maxima that shift from about 310°C to 370°C with increasing irradiation duration, with release ceasing near 500°C. Stored energy increases with irradiation time but tends toward saturation at about 97 J/g after 5 hours, while its fraction of absorbed energy decreases. Using reported concentrations of F and M centers, the study estimates that near saturation M centers account for almost half of the stored energy, with about 15 eV released per M center.
Full Text
DETERMINATION BY CALORIMETER OF THE ENERGY STORED IN LiF UNDER IRRADIATION IN A REACTOR
E. K. ZAVADOVSKAYA, N. M. TIMOSHENKO
(Presented by the seminar of the laboratory EnELIS, Research Institute of PhTT)
The number and type of defects arising in a solid when it interacts with radiation can be determined by studying a number of properties (optical, mechanical, electrical). However, none of these research methods makes it possible to carry out an energetic estimate of the disturbances created by radiation. As is known, radiation disturbances increase the potential energy of a system; in other words, under irradiation energy is stored in defects.
The study of stored energy in a solid, in combination with other methods (especially optical and electrical ones), makes it possible to obtain broader information about the type of defects, their stability, behavior during annealing, etc. Therefore, undoubtedly, the energetic assessment of radiation disturbances is of both scientific and theoretical interest. The most convenient and expedient method for determining stored energy in a solid is the calorimetric method.
In our investigations, measurement of the stored energy was carried out by the method of differential thermal annealing in a high-temperature vacuum calorimeter [1]. LiF was chosen as the material for investigation for the following reasons:
- Irradiation with thermal neutrons is accompanied by the nuclear reaction
\[ \mathrm{Li}^{6} + n = \mathrm{He}^{4} + \mathrm{H}^{3} + 4.8\ \mathrm{MeV}. \]
The decay products transfer to the crystal 4.8 MeV of kinetic energy, creating in it a large number of defects.
- Defects in LiF are distinguished by high stability.
LiF crystals were irradiated in the IRT-2000 reactor of the Institute of Nuclear Physics of the Academy of Sciences of the Uzbek SSR with a mixed flux of fast and thermal neutrons and \(\gamma\)-rays. At the irradiation site the fast-neutron flux was \(nv = 1 \cdot 10^{11}\) neutrons/\(\mathrm{cm}^{2}\cdot\mathrm{s}\); the thermal-neutron flux was \(nv = 1.6 \cdot 10^{13}\) neutrons/\(\mathrm{cm}^{2}\cdot\mathrm{s}\).
Annealing of the disturbances induced during irradiation in the reactor is accompanied by the release of energy stored in defects. In the spectrum of stored-energy release of an LiF crystal irradiated for 5 hours (Fig. 1, curve 4), there is a clearly expressed maximum at \(t^\circ = 370^\circ\mathrm{C}\). In addition to this maximum, there are weakly resolved peaks at temperatures of \(220^\circ\mathrm{C}\), \(270^\circ\mathrm{C}\), and \(420^\circ\mathrm{C}\).
For a crystal irradiated in the reactor for 0.5 h (curve 1), a clearly pronounced maximum is observed at a temperature of 310°C. Increasing the irradiation time is accompanied by a shift of this maximum toward the region of higher temperatures. Thus, upon irradiation for 1 h, in addition to the maximum at 310°C, a maximum appears at 350°C, which with more prolonged irradiation changes into a maximum at 370°C.
Fig. 1. Spectra of the release of stored energy in LiF crystals upon irradiation in a reactor for: 1—0.5 h; 2—1 h; 3—2 h; 4—5 h
The shift of the maxima toward the region of higher temperatures with increasing irradiation duration is evidently due either to an increase in the concentration of defects (and consequently to a delay in their annealing at the given heating rate), or to an increase in the concentration of the products of the nuclear reaction—helium and tritium—which may in some way affect the stability of the defects, or to the simultaneous presence of these two processes.
The intense release of stored energy at a temperature of 370°C indicates that, at this temperature, intensive annealing occurs of defects in LiF crystals produced by irradiation in the reactor. Further heating is accompanied by a decrease in the stored energy and, consequently, by a decrease in the defect concentration. The cessation of the release of stored energy at a temperature of 500°C indicates that, upon heating to this temperature, all defects induced in LiF by irradiation in the reactor are completely annealed.
Figure 2 shows the dependence of the stored energy in LiF crystals on the irradiation time in the reactor. The stored energy increases with increasing duration of irradiation in the reactor. The intensive growth of stored energy at short irradiation durations is replaced by a tendency toward saturation upon irradiation for 5 h (total
thermal-neutron fluence \(2.65 \cdot 10^{17}\) neutrons/\(\text{cm}^2\)). Upon reaching saturation, the stored energy in LiF crystals is \(97\ \text{J/g}\).
The calculation of the energy absorbed by the crystal under irradiation with thermal neutrons made it possible to estimate the fraction of stored energy relative to the absorbed energy. When irradiated in the reactor for 5 hours, the energy absorbed by the crystal is \(6.6 \cdot 10^4\ \text{J/g}\), while \(97\ \text{J/g}\) is stored. The stored energy amounts to \(0.145\%\) of the absorbed energy. When irradiated for 0.5 hour, the stored energy amounts to \(0.90\%\) of the absorbed energy. In other
Fig. 2. Dependence of stored energy in LiF on irradiation time in the reactor
words, as the duration of irradiation in the reactor increases, the magnitude of the stored energy increases, but the fraction of stored energy relative to the absorbed energy decreases.
The increase in stored energy is due to an increase in the concentration of defects; the saturation of the stored energy after 5 hours of irradiation indicates that the limiting concentration of defects has been reached in LiF and that a dynamic equilibrium has been established between two processes—defect generation and their radiation annealing.
The results of measurements of stored energy made it possible to carry out calculations and estimate the contribution made by individual types of defects (namely, \(F\)- and \(M\)-centers) to the total value of the stored energy. In the calculations we proceeded from the following assumptions [3]:
a) energy storage occurs only at \(F\)- and \(M\)-centers,
b) the energy released upon destruction of an \(F\)-center is equal to \(10\ \text{eV}\).
One can write:
\[ E = E_F + E_M, \tag{1} \]
where \(E\) is the energy stored in defects and determined experimentally;
\(E_F\) and \(E_M\) are the energies stored respectively at \(F\)- and \(M\)-centers.
Knowing the number of \(F\)- and \(M\)-centers formed in the crystal upon irradiation with the corresponding flux of thermal neutrons [2], we can determine the energy stored at the \(F\)-centers:
\[ E_F=e_F\cdot N_F=10\cdot N_F\;(\text{eV}), \tag{2} \]
where \(e_F\) is the energy released upon destruction of an \(F\)-center (we assumed that \(e_F=10\) eV);
\(N_F\) is the total number of \(F\)-centers accumulated in \(1\ \text{cm}^3\) at the given flux of thermal neutrons.
From (2) and (1) one can obtain that
\[ E_M=E-E_F=E-10_F N. \tag{3} \]
Knowing the concentration of \(M\)-centers, one can calculate the energy released upon destruction of one \(M\)-center.
\[ e_M=\frac{E_M}{N_M}=\frac{E-10N_F}{N_M}\;(\text{eV}). \tag{4} \]
From the results of the experiment we carried out, it follows that, for two-hour irradiation (the thermal-neutron flux is \(0.96\cdot 10^7\)), the stored energy is:
\[ E=87\ \text{J/g}=1.25\cdot 10^{21}\ \text{eV/cm}^3. \]
According to [2], the concentration of defects in LiF is as follows:
\[ N_F=6.5\cdot 10^{19}\ \text{cm}^{-3},\quad N_M=4\cdot 10^{19}\ \text{cm}^{-3}. \]
Then
\[ E_F=6.5\cdot 10^{19}\cdot 10=6.5\cdot 10^{20}\ \text{eV}, \]
\[ E_M=1.25\cdot 10^{21}-0.65\cdot 10^{21}=6\cdot 10^{20}\ \text{eV/cm}^3. \]
The energy per one \(M\)-center is:
\[ e_M=\frac{E_M}{N_M}=\frac{6\cdot 10^{20}}{4\cdot 10^{19}}=15\;(\text{eV}). \]
Let us calculate the fraction of the energy falling on the \(M\)-centers:
\[ \frac{E_M}{E}=\frac{6\cdot 10^{20}}{1.21\cdot 10^{21}}=0.48. \]
Thus, for LiF crystals under irradiation in a reactor, when the stored energy reaches saturation, the energy stored at the \(M\)-centers amounts to almost one half of all the energy stored by the crystal.
The results of calculating the stored energy for other doses are in good agreement with the experimental results.
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