About chemical form and binding energy of 14 C in irradiated graphite of uranium-graphite nuclear reactors *

Issues associated with handling irradiated graphite of uranium-graphite nuclear reactors are examined. It is demonstrated that selection of approaches, methods and means for handling irradiated graphite are determined by the form of occurrence and binding energy of long-lived 14C radionuclide with graphite crystalline lattice. The purpose of the present study is the determination of possible chemical compounds in which 14C can be found and assessment of fastness of its binding in the structure of irradiated graphite. Indigent and foreign experience of handling graphite radioactive wastes was analyzed, calculations and measurements were performed. Information was provided on the channels of accumulation of 14C in the structure of reactor graphite and it was demonstrated that the largest quantities of the radionuclide in question are generated according to the reaction 14N(n, p)14C. Here, most part of radioactive carbon is generated on 14N nuclei found in the form of impurities in non-irradiated graphite and in the composition of gas used for purging nuclear reactor in the process of operation. 14C radionuclide generated according to 14N(n, p)14C nuclear reaction is localized in the near subsurface graphite layer (in the near subsurface layer of pores) at the depth of not more than 50 nm. Analysis was performed of possible chemical compounds which may incorporate radioactive carbon. It was established that the form of occurrence is determined by the operational properties of specific graphite element in the reactor core. 14C binding energy in the structure of irradiated graphite was evaluated and depth of its penetration in the structure was calculated. It was established that selective extraction of this radionuclide is possible only under elevated temperatures in weakly oxidizing environment which is explained by the binding energy reaching up to 800 kJ/mole in the process of chemical sorption of 14C on the surface of graphite and depth of its occurrence equal to ~ 70 nm in the course of ion implantation. It was demonstrated that radioactive carbon generated according to 13C(n, γ)14C nuclear reaction is uniformly distributed among graphite elements and possesses binding energy ~477 kJ/mole. Its selective extraction is possible only under the condition of destruction of graphite crystalline lattice and organization of the process of isotopic separation. The obtained results allow recommending the most efficient methods of handling irradiated graphite during decommissioning uranium-graphite reactors.


14
C generated and accumulated along several independent channels under the effects of natural and technogenous factors is one of long-lived radionuclides which are the most widely spread in nature.Interaction of neutron cosmic radiation with light nuclei refers, first of all, to natural factors.The rate of generation of radioactive nuclei of 14 C depends on the neutron flux density and is estimated to be equal to 2.5 atom/(s•cm 2 ).In this case the largest amount of this radionuclide is generated at the height of 12 km above the sea level (Rublevskij et al. 2004).
Nuclear tests and operation of nuclear fuel cycle facilities refer to technogenous factors of generation of 14 C. Here, the latter factor plays the decisive role in the accumulation of this radionuclide.As much as 250 000 tons of radioactive graphite wastes (RW) were accumulated in Russia and abroad during the period of existence of nuclear power industry.Mass of irradiated graphite per one power unit reaches from 800 to 2500 t.Here, specific activity of 14 C in irradiated reactor graphite varies within the range of 10 4 -10 6 Bq/g.Class of graphite RW generated during decommissioning uranium-graphite nuclear reactors is determined by the quantity (activity) of the most long-lived 14 C radionuclide.Cost of final disposal of graphite RW is directly dependent on the RW class and, therefore, on the concentration of radioactive carbon.That is why reduction of cost of handling graphite RW is possible under the condition of successful resolution of the task of selective extraction of 14 C.
Selection of approaches, methods and technical means of handling irradiated graphite is determined, apart from everything else, by the form of occurrence and binding energy of 14 C.However, this issue is the subject of much controversy among both Russian (Kasheev et al. 2013, Bushuev et al. 2015) and foreign (Dunzik-Gougar and Smith 2014) scientists.It is associated with the difference in specific activity, conditions of generation and the nature of distribution of 14 C in irradiated graphite which is predetermined by the difference of physical and chemical properties of non-irradiated graphite, parameters of nuclear reactor operation and history of irradiation.The purpose of the study is the analysis of possible chemical compounds in which 14 C can be found and evaluation of strength of its bonding in the structure of irradiated graphite.

Channals of 14 C accumulation in irradiated graphite
The largest quantities of 14 C are generated in the cores of uranium-graphite nuclear reactors of PUGR (production uranium-graphite reactors), RBMK, AM and AMB types.In this case specific features of operation of graphite stack are the determining factors from the viewpoint of accumulation of 14 C.For the purposes of prevention of oxidation and cooling down of graphite internal volume of the reactor is purged with high-purity nitrogen and nitrogen-helium mixture circulated through independent closed loop under pressure close to atmospheric pressure.Besides the above, penetration of air containing nitrogen into the reactor purging system due to infiltration environment, as well as nitrogen present in the purging mixture because of the impossibility of its complete purification is possible.Because of the operational features the number of independent channels of 14 C accumulation in graphite elements of uranium-graphite reactor (UGR) is different.
The following nuclear reactions can be attributed to the main nuclear reactions resulting in the generation of radioactive carbon: Generation of 14 C from stable 13 C isotope is typical for all types of UGR graphite stacks but, however, the fraction of 14 C generated according to this channel is insignificant.Firstly, maximum possible quantity of this radionuclide is limited by the initial concentration of stable isotope which is equal in natural mixture of isotopes to ~ 1.1 %.Secondly, cross-section of 13 C(n, γ) 14 C reaction amounts to approximately 0.9 mbarn, and, notably, absorption of thermal neutrons predominantly takes place.This results in the uniform generation of 14 C among graphite elements.Calculated value of 14 C generation rate according to the reaction channel under examination here is equal for RBMK-1000 reactor to 1.4•10 10 Bq/day per one graphite stack (Rublevskij et al. 2004).After 43 years of continuous operation of such reactor specific activity of 14 C generated according to 13 C(n, γ) 14 C reaction channel in the graphite stack will be equal to ~ 8•10 4 Bq/g.
The largest quantity of 14 C in reactor graphite is generated according to 14 N(n, p) 14 C reaction because of high value of cross-section of neutron interactions with 14 N nuclei (s = 1800 mbarn).This nuclear reaction is possible because nitrogen is present in the non-irradiated graphite in the form of micro-impurities or is present in the composition of gases in the purging mixture used in the process of operation of nuclear reactor.In the first case microscopic impurities are present in graphite because of the impossibility of complete purification of graphite preforms in the process of their production.Despite long-term calcination in special kilns at temperatures of 2300 -3000°C and processing in aggressive environment (for instance, in chlorine or in difluorochloromethane) (Virgil'ev et al. 2006) concentration of nitrogen in non-irradiated graphite is estimated to be equal to 31 -100 ppm (Sklyar 1984).In the second case 14 C is generated from nitrogen nuclei included in the composition of purging gas.Concentration of radionuclide accumulated according to this reaction is difficult to estimate and varies within wide range of 40 -90% from the total activity of sample of irradiated graphite (Bushuev et al. 2015).It is first of all associated with design features, operatio-nal modes and neutron physics parameters of a separate UGR.
One of the channels of 14 C accumulation in the uranium-graphite nuclear reactor core are nuclear reactions on oxygen nuclei 17 O(n, α) 14 C and 16 O(n, 3p) 14 C for which cross-sections of neutron interactions with nucleus are equal to 240 mbarn and 2.2 mbarn, respectively.Activation of oxygen found in the purge gas, in coolant and in nuclear fuel (for nuclear reactors of RBMK type where ceramic fuel in the form of uranium dioxide UO 2 is used) takes place as a rule.Oxygen can be present in reactor graphite in the form of compounds with carbon penetrating graphite in the process of its production.
In the process of graphitization during production of nuclear graphite carbon atoms having free bonds on the discontinuity boundary can combine with O 2 which is not completely removed during purification.
It is worth mentioning that 14 C can be generated during ternary fission of 235 U and 239 Pu nuclei which can penetrate graphite stack in case of loss of hermiticity of cladding of fuel elements caused by drainage of water from pressure channel and disturbance of heat removal regime.Approximately 9.1•10 -7 and 3.1•10 -7 14 C nuclei are generated in this case per one act of fission of 235 U and 239 Pu, respectively (Frolov et al. 2004).However, concentration of radioactive carbon accumulated according to 235 U(n, f) 14 C and 239 Pu(n, f) 14 C reaction channels does not exceed 0.01% of total activity of 14 C contained in the graphite element.
Thus, nuclear reactions 13 C(n, γ) 14 C, 14 N(n, p) 14 C, 17 O(n, α) 14 C are the main channels of accumulation of 14 C radionuclide in elements of UGR graphite stack.

Determination of form of occurrence of 14 C in irradiated graphite
The question of the form of occurrence of long-lived 14 C radionuclide in irradiated graphite is the most important from the viewpoint of selection of the methods of handling during decommissioning of UGR reactors.It is connected with the fact that carbon can form chemical bond with practically all elements of periodic table.Moreover, it is included in the composition of all organic compounds which are capable to enter biological chains thus representing hazard to human health.14 C radionuclide generated according to 13 C(n, g) 14 C reaction has, probably, strong bond with other atoms of crystalline lattice and is practically immune against selective separation without destruction of graphite crystalline lattice.However, position of 14 C in the lattice in the case of reaction on nuclei of stable isotope 13 C will be determined by the energy of absorbed neutron.This is associated with the fact that fast (damaging) neutrons energy of which amounts, on the average, to 2 MeV are capable to displace atoms from the points of crystalline lattice due to elastic interactions (Trevethan et al. 2013).In this case proba-bility of absorption of such neutron by 13 C nucleus with formation of 14 C nucleus is very low because of relatively small cross-section of the interaction (~ 10 -5 -10 -6 barn).Resonance absorption resulting in the appearance of 14 C in the points of crystalline lattice is the exception.With moderation of neutron the value of interaction cross-section increases which also leads to the accumulation of radioactive carbon isotope.However, energy of moderating neutron may be sufficient for displacing 13 C from the lattice point and for subsequent interacting with it with formation of 14 C (Fig. 1).Here the newly formed radionuclide cannot penetrate the potential barrier and escape metastable state and positions itself in the lattice in the form of interstitions (for instance, in the form of Frenkel pair) retaining certain excess energy as compared with atom in equilibrium state.Therefore, 14 C generated according to 13 C(n, γ) 14 C channel can be situated either in the points of crystalline lattice or in the space between lattice points migrating under the effects of external factors.
Emission of proton by excited 15 N nucleus and creation of 14 C nucleus with recoil energy ~ 41,1 keV take place in case of 14 C formation according to 14 N(n, p) 14 C neutron reaction (Pageot et al. 2016).This energy is sufficient for breaking any chemical bonds and ionization of surrounding gaseous medium.Here, formation of chemically active centers consisting of excited atoms which can enter chemical reactions with deaccelerating recoil nucleus is possible.In the case of presence in the gaseous medium of molecular oxygen or water vapors (because of infiltration from the environment) oxidation reactions with formation of 14 CO or 14 CO 2 are the most probable (Nefedov et al. 1960).However, for formation of such compounds it is necessary, first of all, that 14 C collides with O 2 and H 2 O molecules and, secondly, particles must possess energies larger than the activation energy.Since deaccelerating nucleus forms compounds already at energy of ~ 20 keV then the rate of accumulation of 14 CO or 14 CO 2 will be determined exclusively by the concentration of oxygen (because of increased frequency of molecular collisions).Incipience of carbon-containing compounds more complex than carbon oxides is also possible.For example, results of studies on the determination of form of occurrence of 14 C by selective extraction of different functional groups from the surface of irradiated graphite of NBG-18 and NBG-25 brands are presented in (Vulpius et al. 2013).The radionuclide in question can be found in the following forms: carboxyl group, lactones (organic anhydrides), phenols, carbonyls, anhydrides, ethers, etc.
Results obtained during studies of samples of irradiated graphite using time-of-flight mass-spectrometer demonstrate that 14 C can also be found in the following compounds: 14 C(N), 14 CH(NH), 14 CH 2 (NH 2 ), 14 CC(CN), 14 C-14 C(N 2 ), 14 C-14 CH(N 2 H), 14 CO(NO), 14 CCN. 14C-14 CC(CN 2 ), 14 CCO(CNO), 14 CO 2 (NO 2 ) (LaBrier and Dunzik-Gougar 2015).Analysis of registered peaks is complicated because of the difficulty of identification of 14 C and 14 N in different molecules.Therefore, uncertainty emerges in the establishment of form of occurrence of radioactive carbon in different compounds consisting of oxygen, nitrogen and hydrogen.14 C compounds formed during ternary fission of heavy nuclei according to (n, f) reaction are of interest.Penetrating graphite stack fragments of nuclear fuel enter as the result of effects of multiple factors in chemical interactions with graphite, water vapors and with air.Spilled fuel was irradiated during extended period in the reactor stack which facilitated accumulation of transuranic elements and fission products which contained 14 C.As the result of accidents radioactive carbon can be found in the following forms: UC 2 , UC, U 2 C 3 , PuC 2 , PuC, Pu 2 C 3 (Barbin et al. 2015).However, concentration of such compounds in the graphite stack does not exceed 0.01% of the total quantity of compounds composition of which includes 14 C because of low probability of the process of ternary fission of 235 U and 239 Pu.

Binding energy of 14 C in the structure of irradiated graphite
Question of binding energy of 14 C radionuclide in graphite structural elements is important from the viewpoint of selection of the method for decontamination, re-processing or utilization of irradiated nuclear graphite of UGR reactors.The character of bond of the radionuclide in question will be first of all determined by its chemical form.However, the history of exposure of the selected element of graphite stack and the channels of formation of 14 C in it are of not insignificant importance as well.
14 C radionuclide formed in 13 C(n, g) 14 C nuclear reaction on thermal neutrons and found in the graphite crystalline lattice is rigidly bound with adjoining atoms.Here, every carbon atom forms in the crystalline lattice of irradiated graphite bond with three other atoms and is found in the state of sp 2 -hybridization.Binding energy of 14 C in graphite crystalline lattice is close to binding energy of stable isotopes which amounts on the average to 477 kJ/ mole (Zhou et al. 2006).However, energy of atomic oscillations in the lattice changes in the transformation of 13 C into 14 C and, as the consequence, insignificant change of binding energy of 14 C takes place.
Rupture of chemical bonds between nitrogen atoms because of high recoil energy of the formed radioactive carbon nucleus occurs in the formation of 14 C according to 14 N(n, p) 14 C nuclear reaction.Probably the recoil energy is transformed into the energy of thermal motion of 14 C which is decelerated during its propagation through the purging gas.Compounds containing 14 C thus formed can be held on the surface of irradiated graphite under the effects of Van der Waals forces (Golkarian and Jabbarzadeh 2013).The cause of this is the adsorption of gas of compounds (Fig. 2).Surface of nuclear graphite (including surfaces of pores) is the adsorbent, purging gas or its compounds with 14 C are the adsorbtive and any chemical compound described above is the adsorbate.Quantity of adsorbed 14 C is determined in the simplest case from equation of Langmuir isotherm and is dependent on thermal hydraulic parameters of reactor operation as follows: where a ¥ is the maximum concentration of the substance (maximum adsorption); P is the partial pressure of the gas; K is the adsorption equilibrium constant.
During physical adsorption binding energy of 14 C compounds on the surface of graphite amounts to (4 -72) kJ/ mole and depends on the form of occurrence of the radionuclide.During operation of graphite stack in normal operation mode specific energy of thermal movement of purging gas varies within the range of 3.6 -10 kJ/mole depending on the type of UGR.In extreme or emergency conditions this value can reach 15 kJ/mole.Therefore, part of 14 C compounds adsorbed on the surface of graphite is carried away by purging gas.Only molecules located deeply inside the pores of reactor graphite (as a rule, inside closed pores) where energy of thermal movement of molecules of purging gas does not exceed the binding energy remain on the surface.
Chemisorption characterized with increased binding energy and depth of penetration of 14 C takes place in case of aggravation of adsorption by chemical interaction between compounds containing 14 C and graphite surface.This results in the irreversibility of the sorption process during operation of graphite stack of nuclear reactor and to the change of structure of adsorbate and adsorbent.Following the Zeldovich theory of chemical reaction rate on porous or powder-like substances the depth of penetration of 14 C radionuclide is reversely proportional to the square root of reaction rate constant (Zeldovich 1939) which, in turn, depends on the pressure and temperature.Since graphite works in the reactor at high temperatures, surface chemical reactions impossible under standard conditions take place.Energy of bond between compounds containing 14 C and surface of irradiated graphite varies during chemisorption from 260 to 800 kJ/mole depending on the form of occurrence of the radionuclide (Zeldovich 1939).Depth of contamination of irradiated graphite with radioactive carbon formed from nitrogen used during purging the graphite stack can be determined from the following equation: where D is the effective diffusion coefficient depending on the number and diameter of pores in irradiated graphite; c is the concentration of contaminant at depth x; K r is the rate constant of chemical reaction per unit surface; S is the specific surface per unit volume of porous substance; f(c) is the function of chemical reaction rate dependent on the reaction order.Calculations were performed using equation (2).Taking into account specific features and time of exposure of different graphite elements in the UGR maximum depth of penetration of 14 C formed from nitrogen participating in the purging of graphite stack amounts in replaceable parts to ~ 10 -20 nm and that in graphite blocks is not more than 50 nm.Estimation was performed for chemical compounds represented in the study.
Absolutely different process leading to the accumulation of the radionuclide in question in the near subsurface layer can occur on the surface of irradiated graphite along with adsorption of 14 C compounds formed on nitro-gen nuclei participating in purging graphite stack (Fig. 3).Nuclear reaction with emission of proton and formation of radioactive carbon with recoil energy equal to 40 -60 keV which is implanted in the graphite structure occurs during absorption of neutron by 14 N nucleus (Pageot et al. 2016).
During long time this channel of accumulation was not examined during estimation of quantity and depth of implantation of 14 C in irradiated graphite.However, since recent time it attracts more and more attention because it was proven that up to 80% of radioactive carbon in the near subsurface layer of graphite is formed as the result of implantation (Dunzik-Gougar and Smith 2014).This is especially important for indigenous reactors of PUGR and RBMK types where purging is performed by nitrogen of nitrogen-helium mixture.Depth of implementation of 14 C in the graphite crystalline lattice can be estimated using the following expression (Anischik and Uglov 2003): where N is the density of 14 C atoms per unit volume; E is the energy of 14 C atom; S n is the cross-section of nuclear (elastic) deceleration; S e is the cross-section of inelastic deceleration; R is the depth of implantation.Quantity of 14 C along the depth of irradiated graphite can be estimated using Gaussian function knowing the depth of implantation R and assuming that distribution of implanted ions is symmetrical: where D is the integral flux of 14 C per unit surface of graphite (including pores); E is the energy of 14 C atom; x is the distance from external surface of graphite to the place of implantation; q is the angle between the direction of 14 C implantation and normal to the surface of graphite.Maximum depth of 14 C implantation in the graphite crystalline lattice of UGR reactors of PUGR and RBMK types amounts to 55 -70 nm taking into account the operational features of these reactors and with S e = 585 -730 keV/μm, S n = 10 -15 keV/μm.For foreign reactors of UNGG type this value amounts to ~ 0.9 nm.In this case 14 C is found in the form of defects and interstitions between points and planes of crystalline lattice.

Conclusions
It was demonstrated in the study that long-lived 14 C radionuclide is mainly formed in irradiated graphite according to the following three independent channels: 13 C(n, g) 14 C, 14 N(n, p) 14 C, 17 O(n, a) 14 C.This explains its heterogeneous distribution in the graphite structure.Here, most part of radioactive carbon is formed on14 N nuclei which are present in non-irradiated graphite in the form of microscopic impurities and in the composition of gas used for purging graphite stack in the process of reactor operation. 14C radionuclide formed according to 14 N(n, p) 14 C nuclear reaction is localized in the near subsurface layer of graphite (in the near subsurface layer of pores) at the depth of not more than 50 nm and possesses binding energy with graphite up to 800 kJ/mole which is explained by the processes of adsorption and chemisorption.However, selective extraction of this radionuclide is possible only at elevated temperatures in weakly oxidizing environment.In case of ion implantation 14 C is found at the depth of not more than 70 nm and complete removal of contaminated layer is required for its extraction.Besides that, radioactive carbon formed according to 13 C(n, γ) 14 C nuclear reaction is uniformly distributed over irradiated graphite elements and possesses binding energy equal to ~ 477 kJ/mole.Its selective extraction is possible only after destruction of crystalline lattice and organization of isotope separation process.
Results of experimental studies of processing the surface of irradiated graphite taken from PUGR and RBMK reactor stacks in the environment consisting of argon and oxygen concentration of which was lower than stoichiometric quantity were presented earlier (Pavliuk et al. 2017, Kashcheev et al. 2017, Bespala et al. 2016).Intensive extraction of 14 C from the near subsurface layer occurred without significant loss of mass of the sample at temperature equal to ~ 850°C.This confirms the assumption on the form of occurrence and the character of

Figure 1 .
Figure 1.Layout of formation of 14 C positioned between graphite crystalline lattice planes.

Figure 2 .
Figure 2. Adsorption of 14 C compounds on the surface of irradiated nuclear graphite.

Figure 3 .
Figure 3. Process of ion implantation of 14 C in the crystalline structure of reactor graphite.