On the Description of Structural Distribution and Diffusion of Radioactive Elements in the System "Glassy Nuclear Magma-Water"

State of radioactive and nuclear safety of the object \Shelter" is analysed. Dynamics of active particles in glassy nuclear magma is suggested to be investigated with the aid diiusion equations taking into account radioactive transformations. The simplest model for the system \glassy nuclear magma{water" is formulated and therefore density prooles of active particles are evaluated.


Introduction
During the last 5 years a large number of investigations was made on the Chornobyl's problem, some of the results were published 1-9], but the vast majority are in the archive les [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].All of them point to the cardinal changes of the melted fuel masses -nuclear magma.Nuclear magma -glassy composite, which is formed from the melt of CaO, MgO, Al 2 O 3 ,Fe 2 O 3 , ZrO 2 , SiO 2 , H 2 O and up to 18% of UO 2 is destroyed, transforming into nuclear dust.One of the important factors of destroying is decreasing temperature of nuclear fuel containing masses, that caused active interaction of water with the nuclear magma 18,15].
Could such changes be predicted?There are many reasons to say -yes.The majority of experiments and investigations concerned processes on the surface of nuclear magma 23].Obviously, investigations of processes inside magma were not possible due to the technical reasons.But if properly formulated, a complex of theoretical investigations of physico-chemical processes inside magma with the purpose of prognosis of the change of its status versus time in great degree could be able to predict those interior processes, consequences of which we observe now.
These investigations are very important now, because nuclear magma inside the object \Shelter" is substantially non-equilibrium system.A clear description and prognosis of processes within the object "Shelter" based on these invesigations will make possible to take appropriate technical decisions and stabilize the state of the object.
Below we will outline the aspects of the safety problem of the object state.This will be done in the sense which investigations should be carried out in order to construct the model of the processes within the object "Shelter" and, thus to be able to e ciently deal with the problem of safety of the "Object".
Summarizing the results of previous investigations, we can say that inside the object \Shelter" are running non-reversible processes with the increasing tendency of nuclear fuel yield to the water basins inside the object.This is one of the factors of nuclear danger inside the premises of the object.The problem of water interaction with fragments of the destroyed active core of reactor, nuclear magma and nuclear dust is extremely important because: c I.R.Yukhnovskii, M.V. Water interaction with nuclear magma causes substantial increase of neutron e ective breeding coe cient K e , and as a result -local self-keeping nuclear chain reactions are possible.Due to the complicated processes of radiolysis the eventual yield of the radioactive materials is observed, what in turn causes uncontrolled transfer of radioactive materials inside the object and beyond its margins.When nuclear magma is destroyed radioactive dust is produced (containing uranium, plutonium, americium) -a one more factor of ecological danger of the object.Processes of destruction of glassy nuclear magma are very complicated.In the rst hand it is necessary to say that glassy nuclear magma, which consists on 30-60% from SiO 2 is non-equilibrium amorphous media with large relaxation times, and thus, the external factors, in particularly water can rapidly alter the state of the media.Even in 1986, when the nuclear magma was formed, it was possible to state that it was steadily destroyed versus time.This was due to the active processes of induced radioactive decay of 235 U, 239 Pu, 241 Pu, products of which are hydrogen, tritium, inert gases -neon, crypton, xenon and the whole range of fragments -unstable elements; these by neutron irradiation transform to the stable isotopes and radioactive elements with the large half-lives (more then 10 5 years).Process of radioactive decay of nuclei of 235 U, 239 Pu, 241 Pu or -, -nuclear transformations are accompanied by a substantial yields of energy.This causes intensive processes of energy transfer in the media, and thus non-homogeneous change of temperature.Besides, products of radioactive decays are practically non-homogeneous incorporations in the structure of glassy nuclear magma and according to the theory of dislocations in solid bodies, can cause the substantial structural transformations, recrystallization 26].Even more complicated processes are connected with the gaseous products of decay -hydrogen, tritium, helium, neon, crypton, xenon.Due to the small solvability of inert gases, inside the material of fuel elements, for example UO 2 , the excess gas is produced and forms gaseous cavities.The formation and growth of these cavities lead to the swelling of the material.The amount of gas, accumulated in the irradiated media -glassy nuclear magma -could be substantial, what causes deformation and destroys the media.Swelling processes depend from the di erent simultaneously running processestemperature changes, conditions and intensity of irradiation and properties of the material.The growth of the gaseous pores is a very important factor of the swelling processes.Experimental investigations 4] point to the substantial porouosity of glassy nuclear magma.Process of formation of pores is possible due to gas atoms di usion in the various defects, cracks, dislocations, di usion of hydrogen to metals, etc.As a result of the macroscopic di usion due to the temperature uctuations gaseous pores may be joined, what leads to even the larger-scaled deformations of material.
The investigations made in 1989-1991 15,17,19] showed that glassy masses of nuclear magma in the object are loosing their rmness.Obviously, this is a result of non-reversible physico-chemical processes in nuclear magma.
The decrease of temperature on the surface of glassy masses in the average to 40-60 0 C, the existance of a large amount of pores and cracks in nuclear magma caused its active interaction with water, which gets inside through the numerous holes in the cover and walls of the object, due to the condensation from air on the inner walls of the object and irrigation of nuclear dust.Water penetrates to cracks and holes in nuclear magma, where process of its radiolysis takes place.This process and its consequences are described in details in Appendices A, B.
Brie y, this causes rapid yield of radioactive material from glassy nuclear magma masses to the water basins of the object, and eventually, the substantial change of concentration versus time of radioactive material inside water basins of the object.
Water penetrates into cracks, pores in nuclear magma wherein it undergoes radiolysis because of -, -decays and -radiation.Radiolysis products, water molecules at the interface \nuclear magma{ water" take part in complicated hydration 27,28] of uranium UO 2 , plutonium PuO 2 and other oxides of active elements.
Intensive leaching of uranium from nuclear magma and outlet into reservoirs inside the object \Shelter" occurs.Experimental studies 15,18,22] point to signi cant time variation of uranium concentration in \Shelter" reservoirs.
We can see that the ratio of cesium, strontium, plutonium and uranium in water eventually grows.Table 1 15] presents the minimal and maximal relative amount of radionuclides for the few years period.Table 2 15,18] demonstrates the mass ratio of uranium in the water probes within the object according to the di erent methods of measurements: laserluminiscent, spectrofotometric, X-ray uorescent.Isotopic composition of uranium was investigated using alpha-spectroscopic and mass-spectroscopic measurements.Generally speaking, all measurements point to the tendecious increase of uranium concentration in the water cavities of the object.All of these minerals have one very signi cant feature -they are good solutants (in water).So, we have to say that we meet with the non-reversible process of increasing migration of nuclear fuel from nuclear magma to the water cavities inside the object.This is one of the most important factors of nuclear danger of the object.
Aqueous solutions of the radioactive elements salts inside the object are interacting with the di erent construction materials: concrete and glassy masses of nuclear fuel.It is clear, that the character of such interaction depends very much on the state of the aquateaus solutions.The presence of uranium, plutonium, americium, curium in aquateaus solutions and also their interaction with the fuel-containing masses leads to the intensive processes of water radiolysis as a result of -anddecays and -radiation.In the process of radiolysis chemically active radicals are formed: hydrated electrons and ions H + , groups OH ?, molecular compounds H 2 , HO 2 , H 2 O 2 , what largely de nes the character of interaction of aquateaus solutions with the di erent materials inside the object.
We can namely point the following four base types of interaction of water with the nuclear fuel.The rst -interaction of water with the fragments of the reactor's active zone.The second -water penetration through holes, cracks and pores inside the nuclear magma.Nuclear magma is very non-homogeneous porous glassy media.Water, getting to the pores, actively interact with the nuclear magma destroying it.The third -the masses of nuclear magma, partly covered by water, which level changes seasonly.The fourth -interaction of water with the nuclear dust.
The particular attention should be paid to the interaction of the aquateaus solutions with the glassy masses of the nuclear fuel.And here we have to give the answer what is the role of the products of radiolysis of water in the process of destroying of these masses, what is the character of their interaction and investigate their in uence on the processes of di usion of uranium, plutonium from nuclear magma into the water solutions.The other important question is how the products of radiolysis in uence on the chemical reactions where possible reactants are the ions of uranyl UO 2+  2 , plutonyl PuO 2+ 2 , and other complexes containing radioactive elements.

Structural distribution functions and di usion of particles in the system \nuclear magma{water"
We are going to treat interaction of nuclear magma with water by the mean of model two-phase system \nuclear magma{water".Nuclear magma was formed as the result of high temperature melting and gradual solidi cation of nuclear fuel along with boron, dolomite, lead, sand, clay combinations which were thrown to the reactor to lower the temperature and terminate active nuclear processes.The global problem of nuclear fuel deconcentration was solving.It resulted in glassy inhomogeneous solid medium in the form of avalanches containing a number of highly active nuclides: U, Pu, Cs, Ce, Am, Cm, Zr, Sb and their isotopes.Reasoning from the chemical content of probes 1-5] nuclear magma is argued to be a multicomponent glass 29,30] in structure with inherent ionic bond -Si-O-Si-,-O-Si-O-, -Ca-O-, -Al-O-Al-, and belong to sital-like glass: Studies of the percentage composition variations for components of the glass 29] show if there is more than 40% SiO 2 glass structure reveals crystalline character.It should be noted that stability of such a glass depends on the presence of OH ?complexes; perhaps glassy nuclear magma contains those complexes.The increase of OH ?content brings glassy medium stability down 29].Taking into account the chemical content of lling materials: dolomite, boron carbonate, natrium phosphate, polymerizing liquids{one could assume the formation of aluminium phosphate glass to be a contender for active wastes matrix materials 31] in chemical content: NaNO 3 , CsNO 3 , SrO, Al 2 O 3 , Fe 2 O 3 , AlPO 4 , H 3 PO 4 , Na 2 SO 4 , NaCl, NiO, Cr 2 O 3 , UO 2 , ZrO 2 , (NH 4 ) 2 MoO 4 .As was shown in experimental papers 4] till 60% SiO 2 enters into the magma composition.Sophisticated chemical treatment as to iron, nickel, zirconium, niobium, uranium probes extracted from \elephant leg" nuclear magma was carried out in papers 1,4].In particular, X-ray analysis of \elephant leg" samples indicated the presence of UO 2 -phase, small amounts of the minerals minessotait (Fe 2:4 Mg 0:4 )(Si 3:95 Al 0:95 )(OH) 2:72 and diopside (SiO 3 ) 2 as well as possibility of (UZr)O 2 combinations since molar ratio of uranium to zirconium is close to unity (0.99-1.2) and also new combination{chornobylite (UZr)SiO 4 .Paper 4] presents the scheme of Cnornobyl glassy avalanches formation after which maximal temperature had ranged up to 2800 0 C. When analysing a glassy medium it is important to ascertain the nature of bonds between its basic components; these are oxides with ionic bond in nuclear magma case.
We emphasize here that melts of glassy systems di er from metalic and salt ones in that transition from solid to uid isn't accompanied by covalent bonds breaking between atoms e.g.Si-O, Al-O, B-O, P-O, i.e. in complexes creating glass \lattice".As this take place dominant in uence of covalent bonds causes glass polymeric structure being designed with polyvalent radicals (SiO 3 ) 2n? n for silicates, (BO 2 ) (n?1)? n for boronides, (PO 3 ) n? n for phosphates.Besides that a glassy structure is known to arise in the only case if the viscisity of a melt increases from several poises to 10 14 and higher.Such a great glass viscosity may be attained only for the melts containing a certain quantity of oxides{glassformers.These are oxides with covalent interatomic bonds.
So nuclear magma is a silicate matrix lled by impurities di erent in chemical content 4] including till 18% UO 2 uranium oxide.Mainly ionic bonds are available between impurities and the silicate matrix thus those impurities might be regarded as ionic clusters (e.g.uranyl ion UO 2+  2 ) inside the silicate matrix.In connection with it nuclear magma can be represented as the system of interacting ionic clusters with polyvalent radicals (SiO 3 ) 2n? n creating polymeric glass structure.Summarizing everything we can consider the system \nuclear magma{water" as a statistical model of interaction between ionic clusters and water solution.It is clear that advancing a model one should require it to describe physical and chemical processes occuring in the object \Shelter" in the most realistic manner.
What basic processes are needed to be treated when investigating nuclear, physical and chemical transformations in the system \nuclear magma{water"?The category of necessary questions includes the following: 1. Di usion of ionic clusters incorporating active elements or isolated ions in the silicate matrix with taking account of coulombic, dipole and resonant kinds of interaction; 2. Di usion of active elements ions from nuclear magma surface to water.Investigation of the interaction between water and nuclear magma taking into consideration both radiolysis because of -, -decays, -radiation and chemical reactions.The di usion of active elements (in ionic form) from nuclear magma surface to water is a ected by both the transport of ions or ionic clusters in the very matrixs and water radiolysis with chemical reactions occuring in it.It is apparent that basic processes leading to the di usion from the silicate matrix to water take place rst of all in the near-surface layer of the system \nuclear magma{water".Water radiolysis has an speci cal e ect on them in particular products of radiolysis: both radicals, especially hydrogen ions H + or OH ? and molecular products: H 2 O ! e ?aq ,H + aq , OH ?aq , HO 2 , H 2 , H 2 O 2 ; index \aq" stands for hydrated ions.To a great extent the above radiolysis products destroy the silicate matrix increasing the probability of active elements out ow from that into water in ionic form.
When describing the disruption of the silicate matrix an important question is to elucidate destructive mechanisms rst of all for magma surface undergoing interaction with water.Interplay of a water solution with a glassy surface is accompanied by a set of interconnected physical and chemical processes: ion-exchange interdi usion, di usion of ions H + or H 3 O + , hydrolysis of the network silicon{ oxygen and its corrosion, formation of pores and crackes.According to the paper 44] they may be sketchy described with the aid of chemical rections.
Ion-exchange di usion can be schematized by the reaction L + + SiO ?M + SiO ?L + +M + (1) wherein L + is e.g.H 3 O + or H + , M + {ions of metals.As a result of the reaction (1) having equilibrium point to be shifted in fact entirely towards the right promoting hydrated complexes SiOH OH, leaching and formation of the rst hydrated layer occurs, which interact afterwards with glassy surface according to the reaction: SiO ?M + + SiOH SiOH+ SiO ?M + (2) In this manner the ion-exchange layer is formed with inherent interdi usion of ions H + and M + .Interaction of water molecules with a silicate surface can be described by chemical reactions SiO ?M + +H 2 O SiOH+OH ?+M + (3) which result in outlet of metal ions into the solution while hydroxide complexes OH ?take part in further reactions of the depolymerization of silicon-oxygen network.
Si{O{Si +OH ?SiO ?+ SiOH (4) SiO ?+ SiOH+H 2 O 2 SiOH+OH ? and so on (5) Reactions of this kind can proceed from glassy magma surface to an alkali active solution (pH=9 11 for reservoirs of the object \Shelter").Apart from reactions 3 water molecules are able to destroy the silicon-oxygen network due to interaction between oxygen ions of water and Si atoms and at the same time H + ions with oxygen atoms of silicon-oxygen network Si{O{H Si{O{Si +H{OH!Si{O Si +H OH! Si{O{H+ Si{OH; (6) A set of reactions (3{6) represents the hydrolysis and depolymerization of the silicon-oxygen network.It brings about the formation of hydrated complexes =Si(OH) 2 , {Si(OH) 3 , Si(OH) 4 , Si(OH) 2? 6 which pass to the solution.In such a manner the corrosion of silicon-oxygen network occurs being enhanced by hydrogen ions H + , hydrated complexes OH ?, which arise additionally as a result of radiolysis, hydrolysis and hydration of uranium UO 2 , plutonium PuO 2 and other oxides 39{43].
For the description of interplay of a water solution with glassy nuclear magma according to reactions (1)-( 6) we need to formulate a physical model to base on it researches into structural functions, their di usion from one phase to another and reaction constants.The prelude of any microscopic treatment is the structural information in the form of density pro les and higher distribution functions.The most accepted way lies in the use of Ornstein-Zernike equation modi ed for inhomogeneous uids.But it needs a certain closure.Most of known closures don't enable to obtain an analytical solution.Moreover the more e cient closure relation is the more tedious numerical computations should be carried out.So we prefer BGY method and the matter is in the following.
Active elements will be supposed to be present in water in small amounts.Within this model active elements particles (UO 2+  2 , Cs + , Sr 2+ )are considered as charged hard spheres having the overall charge to be compensated according to the electroneutrality condition by negative OH ?-groups in continuous medium with the dielectric constant " = 81 (water).
Active water solutions inside the object \Shelter" contact mostly with nuclear magma, concrete, clay and numerous constructive materials.To predict the destroyment and investigate the di usion of active particles it is necessary to know the structure of a solution near these materials.The problem reduces to the treatment of the solution model near a hard wall outlined above, which is along with solvent a continuous medium with the dielectric constant " = 1 15 (glass-like medium, clay, concrete).In this approach pro les are a ected by both structural ordering caused by own sizes and the presence of surface and electrostatic images to be most pronounced at small distances.However their consecutive consideration is fairly intricate problem.To this end we used the rst equation of BGYchain modi ed to describe image charges.These latter are assumed to be ctitious charged particles inside the wall (glass-like medium, clay, concrete, volume V 0 ), which have charges "p?"s "p+"s Z i e and sizes i , wherein Z i e , i are charges and sizes of particles in the solution (volume V ).If to apply the method given in 37] we arrive at the following equation: df a (z 1 ) dz 1 + dU a 1 (z 1 ) dz 1 f a (z 1 ) with r 12 {distance between particles, r 0 12 {that between the rst particle and the image of the second one.It is evident that potential consists of the bulk part dependent on r 12 and the surface one.The problem of bulk screened potential evaluation for arbitrary amount of ions having distinct sizes and valences is solved in 38].We make use of the result for small concentrations in view of that the potential of an inhomogeneous system is expressed through bulk ones as is seen from (8).Thus U a 1 (z 1 ) = " p ? " s " p + " s (Z a 1 e)

Table 2 .
Mass ratio of uranium in water, mg/l.The so-called yellow spots were investigated by the means of electronic spec-troscopy, X-ray phase and X-ray spectral analysis.As a result, it was cleared up that yellow spots are the needle-like crystals of the uranium minerals with the main phases such as: epiyantynite UO 3 2H 2 O, studtite UO 3 16CO 3 1.91H 2 O, two modications of UO 4 4H 2 O, retzerfordine UO 2 CO 3 , and unnamed phases NaUO 2 (CO 3 ) 3 , and also NaU(CO 3 ) 2 2H 2 O 2,3].
38,39] sphere potentials, Coulomb interaction between particles and between particles and images respectively; c , 0 c the density of species c particles and their images.It is easily seen that the second integral term takes into account image e ects on equal terms.But at small concentrations integral terms are minor (pair correlation isn't essential) so ionic distribution near the surface is determined by the potential U a 1 (z 1 ) that is advantageous to use as screened potential.The problem of point particles screened potential near a hard wall has rigorous analytical solution38,39].In the case of ion-ion interaction the result is as follows: National Academy of Sciences in 1995.Chornobyl, 1995, 33p.(in Ukrainian).44] Belustin A.A. Concentration distribution for ions in surface layers of alkali silicate glasses processed with water solutions.// Phys.Chem. of Glass, 1981, vol.7, No 1, p. 257-277 (in Russian).PRO OPIS STRUKTURNOGO ROZPOD LU TA DIFUZ RAD OAKTIVNIH ELEMENT V U SISTEM \SKLOPOD BNA DERNA MAGMA { VODA" .R. hnovs~ki , M.V.Tokarquk, .P.Omel n, .M.Sov' k, R. .elem Proanal zovano stan rad ac no ta derno bezpeki ob' ktu \Ukritt ".Dinam ku rad oaktivnih qastinok u sklopod bn dern magm proponu t~s dosl diti z dopomogo r vn n~difuz , kotr vrahovu-t~procesi rad oaktivnih peretvoren~.Sformul~ovano na prost xu model~sistemi \sklopod bna derna magma { voda" provedeno rozrahunok prof l v gustini rad oaktivnih qastinok.