Ra-226 SOURCES IN METAL MATRICES: GAS PRESSURE

The process of gas generation for radium sources embedded in metal matrices (or metal capsules) is described in order to obtain the conditions of safe immobilisation of radium sources in metal matrices. For this purpose a simple model describing immobilisation of sources in a metal housing is proposed. Both helium and radon generation is considered near a radium source. Partial pressures of helium and radon were found depending on time. The diffusion of helium in the metal and decay of Rn-222 were taken into account. It is shown that the pressures of both radon and helium increase until some maximum values, after that the pressures slowly fall. The maximum radon pressure is achieved during months whereas helium increases its pressure during one-a few years. The formulae for maximum pressures and times necessary to achieve these pressures were obtained. The helium overpressure depends on the diffusion coefficient in the metal. Therefore for a lead or lead based alloys the overpressure it is much lower than for copper or steel matrices. Safe conditions of immobilisation of radium sources are determined on the base of obtained values. INTRODUCTION Sealed radiation sources containing Ra-226 were widely used in the past mainly for medical applications. After 1950s radium sources were replaced by more cheaper, safer and efficient sources containing artificial radionuclides. Ra-226 is a long lived radionuclide therefore radium sources containing sources must be disposed of in a deep underground repository. Spent radium sources shall be safely stored until their disposal into a deep geological formation. Immobilisation of radium sources by metal matrices or using metal hermetic capsules provide safe conditions for storage for a long time period. Dues to the decay of Ra-226 gaseous products are generated, which cause overpressure in a sealed source and facilitate the leakage of radionuclides. Helium gas as final stable product and radon-222 gas as intermediate unstable product is produced due to the natural decay of Ra-226. One gram of radium produces about 0.2 atmospheres in a free volume of one cubic cm per year [2]. Accumulation of gases can cause even explosive ruptures of sources. In the early days there were explosions of large standard Ra-226 sources encapsulated in glass, and explosive ruptures of metal sealed sources have also been reported [2]. IMMOBILISATION IN METAL MATRICES There are many options for radium sources immobilisation [2, 3]. One of most reliable is the embedding of sources into a metal matrix material. The immobilisation of Ra-226 sources using metal matrices aims to ensure safe conditions of long term storage in repositories as well as to facilitate transportation and final disposal of sources in deep underground repositories. The WM’01 Conference, February 25-March 1, 2001, Tucson, AZ immobilisation process usually implies the embedding of a radium source into a metal matrix. As a result metal blocks are produced, which contain radium sources surrounded by a metal material. Due to very low corrosion rate and suitable technological parameters lead and lead based alloys are considered as most appropriate matrix materials [4]. The conditions of safe immobilisation of radium sources in a metal matrix are thereafter of primary importance. RADIUM DECAY AND GAS GENERATION The Ra-226 decay scheme belongs to so called uranium-actinium series. In the following figure one can see the most important chains of this scheme. Fig.1. The main decay pathway of Ra-226. What is the most important for our task is that the decay of one Ra-226 atom give rise to appearance of one radon-222 atom as intermediate product and finally causes production of five helium atoms. Therefore the number of helium atoms NHe produced finally as a result of Ra-226 decay can be written as Ra Ra He N dt dN λ 5 = , (Eq. 1) where λRa is the decay constant of Ra-226 and NRa is the number of Ra-226 atoms in the source. The number of Ra-226 atoms changes accordingly with the law of natural decay as NRa= NRa(0)exp(-λRat). So if we consider the accumulation of helium atoms produced by the decay of Ra-226 atoms we obtain the following formula for the number of helium atoms: WM’01 Conference, February 25-March 1, 2001, Tucson, AZ )] exp( 1 )[ 0 ( 5 t N N Ra Ra He λ − − = (Eq. 2) HELIUM OVERPRESSURE If the helium atoms are accumulated in a given volume V the gas overpressure can be calculated from the state equation of gas as: V kT N p He He = (Eq. 3) Let consider a Ra-226 source embedded into a metal matrix. We can suppose the source in a form of a sphere with radius R being surrounded by a metal material. Fig.2. The Ra-226 source in a metal matrix material. There is a small gap between the source case (with radius R) and metal housing which can be due to normal roughness of materials or technological method applied for immobilisation of source. The dimension of this gap is l<>R/DHe, where DHe is the diffusion coefficient of helium in the housing material. Therefore the distribution of helium atoms around source (at distances r>R) in the housing material can be supposed as stationary accordingly with the equation: ∆nHe(r)=0, (Eq. 6) where nHe is the concentration of helium in the metal matrix surrounding the source. This equation has the general solution nHe=a/r+b, where a and b are some constants to be determined from boundary conditions. Since the concentration of helium at very large distances from the source is nil the constant b=0. The concentration of helium in the free volume of the gap between the source casing and housing V=4πRl is nHe=NHe/V, from where we find that a= NHe/4πRl. From equations (5) and (6) we obtain thereby l R N D j He He R π = (Eq. 7) By substituting this relationship into equation (4) we obtain the following formula for the number of helium atoms accumulated in the source housing: )] / exp( ) [exp( ) / ( ) 0 ( 5 Rl t D t Rl D N N He Ra Ra He Ra Ra He − − − − = λ λ λ (Eq. 8) The overpressure in the housing can be found accordingly from the equation (3). One can see that the number of helium atoms as well as gas overpressure in the housing at the time equal to t0 ) / ln( / 1 Ra He Ra He Rl D Rl D λ λ − = (Eq. 9) reach the maximum values. Since the inequality is valid: (DHe/Rl)>>λRa the working formulae can be simplified to following: t0=(Rl/DHe)ln(DHe/RlλRa), (Eq. 10) WM’01 Conference, February 25-March 1, 2001, Tucson, AZ NHe, max=5NRa(0) λRaRl/DHe (Eq. 11) pHe, max=5NRa(0) λRakT/4πRDHe (Eq. 12) The maximal helium overpressure can be expressed using the initial radioactivity of Ra-226 source ARa(0) as: pHe, max=5ARa(0) kT/4πRDHe (Eq. 13) The time when the helium pressure reaches maximal value depends on the size of the gap between the source and housing, whereas the value of this maximum pressure does not depend on the gap size, being determined only by source dimension R, initial radioactivity and helium diffusion coefficient. If the maximum overpressure of helium not cause any destroying of matrix material the immobilisation can be regarded as reliable. We now can estimate the gas overpressure for typical sources. RADON-222 OVERPRESSURE We mentioned above that the decay of one Ra-226 atom produces one Rn-222 atom, which consequently decays. The process of radon gas accumulation is described by equation: Rn Rn Ra Ra Rn N N dt dN λ λ − = (Eq. 14) The diffusion process for radon gas in a metal matrix can be ignored due to small diffusion coefficients. From equation (14) we obtain for the number of radon atoms in the housing the formula: )] exp( ) [exp( ) 0 ( t t N N Rn Ra Ra Rn Ra Ra Rn λ λ λ λ λ − − − − = (Eq. 15) One can see that the maximum radon overpressure is reached at the time: