EFFECT OF OPERATING PARAMETERS ON FORMATION PROCESS OF DEFECTS IN MODERATOR BLOCK IN GRAPHITE REACTORS

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1 Jr of Indusrial Polluion Conrol 32(2)(2016) pp wwwiconrolpolluioncom Research EFFECT OF OPERATING PARAMETERS ON FORMATION PROCESS OF A MOCHALOV, A NAYMUSHIN *, V NESTEROV, S SAVANYUK AND I SHAMANIN Naional Research Tomsk Polyechnic Universiy (TPU), , Tomsk, Russian Federaion (Received 6 July, 2016; acceped 09 Augus, 2016) Key words: Graphie reacor, Wigner energy, Irradiaion emperaure, Irradiaion ime, Energy deerminaion ABSTRACT Analyical scheme of defec formaion process was designed, describing emporal dynamics of number of aoms in laice nodes as well as poin and complex defecs According o his scheme, a sysem of differenial equaions was made Analysis of soluion of he equaion sysem and experimenal daa on sored energy (Wigner energy) for indusrial graphie reacors allowed o deermine he dependence of consan recombinaion of poin defecs on irradiaion emperaure Calculaed and experimenal asympoes of Wigner energy dependence on irradiaion ime of graphie were compared INTRODUCTION Exension of lifeime of operaing graphie reacors and reacor decommissioning are of grea imporance nowadays Solving hese problems requires correc esimaions of reacor graphie life-ime as well as energy sored in i (Wigner energy) Neuron irradiaion of graphie alers is properies because of damaging is laice srucure During moderaion process neuron energy is ransferred o aoms of carbon which can be dislocaed in he laice relaive o he iniial locaion Many of hese shifed (primary knocked ou) aoms having high kineic energy can induce displacemen of oher aoms, slow down, ec For example, neuron wih 1 MeV energy can induce up o 900 aom displacemens losing is energy ill he energy of hermal neuron To displace an aom in graphie laice i is required abou 25 ev of energy Many displaced aoms immediaely reurn on vacan places A large number of aoms occupy inermediae posiion This can be individual aoms as well as groups of aoms They have significan impac on numerous properies of he maerial and his significance depends on dose and emperaure of irradiaion (Virgilev, 2001) Temperaure one of he main facors affecing he degree of radiaion damage in maerials srucure (Glushkov e al, 1985; Baybakov e al, 2015; Neserov e al, 2013; Avdohin e al, 2013) Neuron bombardmen leads o formaion of poin defecs, he fae of which is deermined by emperaure condiions Migraion of defecs o sinks, annihilaion of Frankel pairs, formaion of complexes and oher diffusion processes are relaed wih emperaure The number of iniially knocked ou aoms a he momen of ineracion of radiaion wih he maerial a low and high emperaures is pracically he same, however, mobiliy of hese aoms a high emperaure is higher, ie hey annihilae faser This leads o decrease of defecs concenraion and herefore o lesser change of properies during irradiaion Decrease of irradiaion emperaure and aendan gamma-radiaion flux densiy in he range С due o decrease of hermal and radiaion gamma-annealing leads o increase in concenraion of defecs and consequenly o decrease of criical neuron fluence (Avdohin e al, 2013; Karpuhin e al, 1997) Criical fluence is he fas neuron fluence ha enables polycrysalline graphie o compensae shrinkage The value of his fluence defines he lifeime of reacor graphie and limi concenraion of defecs because during furher growh of fas neuron *Corresponding auhor's agn@puru

2 438 fluence hermal-physical and srengh properies of graphie deeriorae abruply In higher emperaure range (higher 300 С) prevail much more complex defecs han poin defecs These complex defecs have lile effec on laice parameers bu ake par in formaion of addiional basal planes in he graphie irreversibly changing form of graphie crysallies (Karpuhin e al, 1997; Golovasky e al, 2011; Baybakov e al, 2015; Golovasky e al, 2011; Neserov, 2013) Nowadays research in he field of radiaion damage of reacor graphie is mainly experimenal MATERIALS AND METHODS This paper ses he goal of analyical descripion of damaging and recovery process of he crysal srucure of reacor graphie o deermine he dependence of Wigner energy on he fluence of damaging neurons Formulaion of he problem requires selecing 3 ypes of aoms in graphie srucure: Aoms presen in he laice Is concenraion is denoed N Aoms relaing o poin defecs N Aoms creaing complex defecs N c The sum of hese aoms represens he concenraion of all aom ypes and is defined by he relaion: Na ρ NÓ = = N + N + N (1) c M where М molar mass of carbon; ρ densiy of reacor graphie MOCHALOV ET AL The problem is formulaed using he following approximaions: Process of damaging of he graphie does no lead o significan change of specific volume Number of poin defecs formed during he ineracion of neuron wih nuclei of carbon is equal for aoms presen in he laice and for aoms forming complex defecs The number of defecs formed per neuron wih energy of 1 MeV is value of 10 3 order Recombinaion consan of poin defecs λ is a sum of consan fracion of poin defecs reurning o he iniial sae (recombining) λ а and consan fracion of defecs ha are ransformed ino complex defecs λ с The recombinaion consan of poin defecs is defined by he relaion: ( T,Ö γ ) a( T,Ö γ ) c( T,Ö γ ) λ = λ (2) where all he values depend on equivalen irradiaion emperaure (Т) and on aendan gamma-radiaion flux densiy The scheme of defec formaion process for graphie is shown in Fig 1 and is described as follows: Change of he number of aoms in he laice ( d N / dt ) is affeced by wo compeing processes: he firs one increase due o recombinaion process of poin defecs (ransiion of aoms of poin defecs o he laice nodes λ a N ); he second one decrease due o ineracion of neuron flux wih he laice (knocking ou of aoms from he laice and formaion of poin defecs Ôσ s nn ) Fig 1 Scheme of defec formaion

3 EFFECT OF OPERATING PARAMETERS ON FORMATION PROCESS OF Change of he number of aoms forming complex defecs ( d N c / dt ) is affeced by wo compeing processes: he firs one increase due o ransiion of aoms of poin defecs ino complex defec ( λ c N ); he second one decrease due o effec of neuron flux on complex defecs (ransiion of aoms of complex defecs ino poin defecs Ôσ s nn c ) Change of he number of aoms of poin defecs ( d N / dt ) is affeced by wo compeing processes: he firs one decrease due o recombinaion process of poin defecs and is ransiion ino complex defecs ( λ N ); he second one increase due o effec of neuron flux on he laice and complex defecs (ransiion of aoms in he laice and complex defecs ino poin defecs Ôσ sn(n + Nc) Thus, he sysem of differenial equaions describing he change of he number of aoms in he laice as well as change of complex and poin defecs is as follows: dn dn dnc = =Φ σsn( N + Nc) λ; d d d (3) dn = λan ΦσsnN; d dnc = λcn ΦσsnNc d where n he number of formed poin defec per one ac of neuron scaering from nucleus of carbon; ime; Ф damaging neurons flux densiy; scaering microscopic cross-secion for he damaging neurons The soluion of his sysem are he following expressions: 439 To displace one aom in he laice i is required around 25 ev of energy I can be assumed ha he same amoun of energy is released when aom reurns o vacan place in he laice Soluion of he sysem of differenial equaions (3) defines he raio for he amoun of poin defecs: ( + ( + N = ( 1 e ) + N0e (5) In his raio he firs erm describes increase of he number of poin defecs during irradiaion process; he second erm describes decrease of he number of poin defecs presen in graphie a he beginning of irradiaion Thus, for sufficienly long ime (abou one year) his raio ends asympoically The dependence of Wigner energy per weigh uni of graphie on irradiaion emperaure for Ö 10 cm = s, σ s = cm, n= 500 NÓ = 5 10 g is defined by he relaion: E = Ed N = ( 25 ev ) =, cal / g (6) 9 ( T) ( T) Then he problem is reduced o deermining he funcion, which approximaes he dependence of recombinaion consan on emperaure λ ( T ) Where in values E and T are known (experimenal daa), he end resul is shown in Fig 2 can be excluded from consideraion The dynamics of concenraion of poin defecs vs irradiaion ime for differen irradiaion emperaures and, accordingly, Wigner energy vs fluence a consan flux densiy of damaging neurons can be described by using polynomial and power dependencies of recombinaion consan on Exponenial dependence λ ( T ) ( + N = k me ; (4) λ k λ m N = N e + 1 e + e e ; c ( + n c n n c 0c s λ λ k λ m N= Ne + e + e e where ( 1 ) a ( + n a n n 0 λ k = sn ; ( NÓ N0) λn0 m= = k N 0 ; N 0, N, 0c N concenraions of aoms of poin defecs, 0 complex defecs and aoms in he laice a iniial ime, respecively RESULTS The amoun of energy sored in graphie is in direc proporion o he amoun of poin defecs This allows deermining he dependence of recombinaion consan of poin defecs on irradiaion emperaure Experimenal daa on Wigner energy for he reacors of Siberian Chemical Combine allowed deermining his dependence Fig 2 Dependence of sored energy on irradiaion emperaure for differen approximaion funcions λ(t)

4 440 irradiaion emperaure Fig 3 shows calculaed dependence of Wigner energy on he fluence The dependence is obained assuming ha all neurons are damaging and irradiaion condiions are consan Experimenal dependence of sore energy on neuron fluence is shown in Fig 4 As seen from resuls, maximum deviaion of he calculaed value from he experimenal one corresponds o emperaure of 260 С which is quie close o he ransiion region (around 300 С) In his region, one would expec a significan deviaion due o uncerainy of he experimenal daa on criical fluence vs irradiaion emperaure dependence Fig 3 Calculaed dependency of sored energy on he neuron fluence (Φ=10 13 cm -2 s -1 ) Fig 4 Experimenal dependence of sored energy on he neuron fluence (Tsiganov e al, 2008) The dependence MOCHALOV ET AL CONCLUSION Thus, he dependence of recombinaion consan on graphie irradiaion emperaure a he condiions presen in indusrial graphie reacors is deermined in his paper To specify he ype of funcional dependence of criical fluence on irradiaion emperaure and aendan gamma-radiaion flux densiy i is required o carry ou furher analysis o selec specific funcion ype describing recombinaion of poin defecs ( λ ( T a, Φ γ )) and ransiion of poin defecs ino complex defecs ( λ ( T c, Φ γ )) of laice nodes concenraion on irradiaion emperaure is in saisfacory agreemen wih he experimenal daa obained by defining he value of sored energy in graphie blocks and reacor core bushings of graphie reacors as a funcion of irradiaion emperaure ACKNOWLEDGMENT This work was performed on he unique scienific IRT-T equipmen and financially suppored by Governmen represened by he Minisry of Educaion and Science of he Russian Federaion (RFMEFI59114X0001) REFERENCES Avdohin MS, Neserov VN 2013 Proc of Tomsk Polyechnic Universiy 56 Baybakov DF, Golovasky AV, Naymushin AG, Neserov VN, Savanyuk SN, Shamanin IV 2015 Influence of he Graphie s Lifespan on he Design Value of Fuel Burnup in High Temperaure Gas-Cooled Reacors Adv Maer Res 1084: Baybakov DF, Naymushin AG, Neserov VN, Savanyul SN, Shamanin IV 2015 Deermining Reacor Graphie Lifespan from Thermal Properies Degradaion Adv Ma Res 1084: Glushkov ES, Demin VE, Ponomarev-Sepnoy NN, Chrulev AA 1985 Energy release in nuclear reacor Energoaomizda Moscow Golovasky AV, Neserov VN 2011 VNKSF-17 Golovasky AV, Neserov VN, Shamanin IV 2011 Proc of Tomsk Polyechnics Universiy 2 Karpuhin VI, Nikolaenko VA 1997 Criical neuron fluence as a facor deermining he service life of RBMK graphie masonry A Energy 83: Neserov VN 2013 Proc of Tomsk Polyechnic Universiy 2 Neserov VN, Chikov MS 2013 Proc of Tomsk Polyechnic Universiy 56

5 EFFECT OF OPERATING PARAMETERS ON FORMATION PROCESS OF Tsiganov AA, Savinikh PG, Komarov EA, Kolyarovsky SG, Pavlyuk AO, Neserov VN, Shamanin IV 2008 Proc of Toms Polyechnic Universiy Virgilev US 2001 Characerisics and operabiliy of reacor graphie in waer-graphie reacors Maer Sci 2: 44-52