BASIC RADIATION PHYSICS AND SOURCES OF RADIATION

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Chapter 1BASIC RADIATION PHYSICS AND SOURCESOF RADIATIONDiana AdlienėKaunas University of Technology, Physics Department, Studentų g. 50,LT-51368 Kaunas, Lithuania1. INTRODUCTIONTreatment of materials and products with radiation in order to modify theirphysical, chemical and biological properties is defined as radiation processingof materials. Radiation processing can be controlled and used for the development of the novel materials and products with desirable properties.The knowledge of the basic radiation physics, including the structure ofmatter, elements of nuclear physics, the nature of electromagnetic radiation,and radiation interaction with matter is required to understand irradiation processing and its potential in material sciences.1.1. CLASSIFICATION OF RADIATIONRadiation-induced changes in materials depend on the origin and type ofradiation and the deposited energy (Fig.1).Energy deposition processes in turn depend on the origin of the radiation: particulate radiation, including electrons, positrons, protons, neutrons, ions; electromagnetic radiation, which covers a broad wavelength range, including infrared, visible and ultraviolet radiation and X-rays and gamma rays.The following Table 1 gives approximate wavelengths, frequencies, and energiesfor selected regions of the electromagnetic spectrum.Deposition of kinetic energy of accelerated particles in a target is consideredwhen discussing the interaction of particulates with matter. In the case ofelectromagnetic radiation, interaction with matter, in general, energy transferredby the individual quanta, known as photons, is taken into account. The energyof photon (quantum energy), E, is given by:

8Applications of ionizing radiation in materials processingFig.1. Comparison of energies.Table 1. Spectrum of the electromagnetic radiation.Wave ysGamma raysWavelength [m] 0.10.1-10–410–4-7 10–77 10–7-4 10–74 10–7-10–910–9-10–13 10–11Fig.2. Classification of radiation.Frequency [Hz] 3 1093 109-3 10123 1012-4.3 10144.3 1014-7.5 10147.5 1014-3 10173 1017-3 1021 3 1019Energy [eV] 10–510–5-0.010.01-22-33-103103-107 105

9Chapter 1c(1) where: the constant h is known as Planck’s constant, – a frequency, c – aspeed of light in vacuum, λ – wavelength.Radiation is classified in two main categories, non-ionizing and ionizingradiation depending on its ability to ionize matter (Fig.2): Direct ionizing radiation corresponds to the energy deposition in the material by energetic charged particle which have Coulomb interaction with anorbital electron of a target atom. Indirect ionizing radiation is realized in two steps. First, fast charged particles (electrons and positrons) are released in the material due to the photonenergy deposition or due to kinetic energy deposition by neutrons, protonsor heavier ions. Second, the released charged particles deposit their energydirectly in the material through Coulomb interactions between these particlesand orbital electrons of an atom.E h h2. ATOMIC AND NUCLEAR STRUCTURE2.1. BASIC DEFINITIONS FOR ATOMIC STRUCTUREThe atom is composed of a central nucleus surrounded by a cloud of negatively charged electrons. An atomic nucleus consists of Z protons, and N neutrons.The main characteristics of the constituents of an atom are shown in Table 2.Table 2. Main characteristics of the atom constituents.ParticleSymbolMass [kg]Energy [MeV]ChargeProtonp1.672 10–27938.2 Neutronn1.675 10–27939.20Electrone0.911 10–300.511–The radius of an atom is 10–10 m, the radius of the nucleus is about 10–14 m.Protons and neutrons are commonly referred to as nucleons.The number of protons in atom is known as the atomic number, Z. It equalsthe number of electrons in a non-ionized atom, thus making an atom neutral.Atomic mass number, A, equals to the number of protons plus neutrons inthe nucleus.Atomic mass, M, might be expressed in mass units – g or in atomic massunits – u, where u is equal to 1/12 of the mass of the 12C atom or 931.5 MeV/c2.

10Applications of ionizing radiation in materials processingSome binding energy is required to keep the nucleons within the nucleus. Thusthe atomic mass of particular nuclide is smaller than the sum of the individualmasses of constituent particles.Number of atoms, Na, per mass of an element is:Na NA mA(2)where NA is Avogadro’s number (NA 6.022 1023 atoms/g-atom).Number of electrons, Ne, per mass of element is:NeNZ Z a NAmm ANumber of electrons, Ne, per volume, V, of an element is:(3)NeNN(4) Z a Z AVmAIn nuclear physics, a nucleus X with atomic mass number A and atomic60Co and 137number Z is denoted as AZ X , for example 2755 Cs.An atomic nucleus identified by its atomic element and its mass number isdefined as nuclide.Atoms having an identical atomic number, Z, but different atomic massnumbers, A, related to different numbers of neutrons in the nucleus are calledisotopes of a given element, for example: 116 C, 126 C, 136 C, 146 C.In ion physics it is usual to provide ions with superscripts /–. For example,42 2 He stands for a doubly ionized He atom which is the alpha particle [1].2.2. ATOMIC STRUCTUREThe currently accepted simplified atom model relies on the 1913 Bohrtheory [2, 3] and his famous postulates that combine classical non-relativisticmechanics with quantum mechanics adding the concept of angular momentumquantization. A variety of postulated formulations (physical content being thesame) are provided in the literature [4-6]. Here is a summary of Bohr’s postulates, as noted in Ref. [7]: Postulate 1: Electrons revolve about the Rutherford nucleus in well-defined,allowed orbits (planetary-like motion):m e e21 Ze 2Fcoul Fcent (5)4 0 rere Postulate 2: While in orbit, the electron does not lose any energy despitebeing constantly accelerated (no energy loss while electron is in an allowedorbit).

11Chapter 1 Postulate 3: The angular momentum L meνr of the electron in an allowedorbit is quantized and given as L nħ, where n is an integer referred to as aprincipal quantum number, ħ h/2π and h is Planck’s constant. Postulate 4: An atom emits radiation only when an electron makes a transitionfrom the initial orbit with a quantum number ni to final orbit with a quantumnumber nf (energy emission during orbital transitions).h E i E f(6)Electron transitions result in the emission of photons. The wavenumber kof the emitted photon is given by: 1 111 1 R 2 2 109737 cm 1Z2 2 2 nf ni nf ni where R is the Rydberg constant.The radius rn of one-electron Bohr atom is given by:k (7) n2 n2 (8)rn a 0 0.529 Å ZZ where a0 0.529 Å is the Bohr’s radius.The energy levels for orbital electron shells in one-electron atomic structureare given by:22 Z Z E n E R 13.6 eV (9) n n where: ER – the Rydberg energy, n – the principal quantum number (n 1,ground state, n 1, excited state), Z – atomic number of one-electron atomicstructure.An energy level diagram for the hydrogen (H) atom is shown in Fig.3A.Bohr’s theory works well for one-electron structures (hydrogen atom,singly ionized helium atom and doubly ionized lithium atom, etc.), but it doesnot apply directly to multi-electron atoms because of the repulsive Coulombinteractions among the atomic electrons. Development of the theory of quantummechanics by Heisenberg, Schrödinger, Dirac, Pauli and others, contributedsignificantly to the explanation of possible energy levels (states) that might beoccupied by electrons in a multi-electron atom. In this theory, individual energystates are defined by four quantum numbers as follows [8]: the principal quantum number, n, which specifies the ground (main) energyshell and can take integer values; the azimuthal quantum number, l, which specifies the total rotational angularmomentum for the electron and can take integer values between 0 and n – 1; the magnetic quantum number, m, which specifies a component of the angularmomentum and can take integer values between –l and l; the spin quantum number, s, which specifies a component of the spin angularmomentum of the electron and takes values –½ or ½.

12AApplications of ionizing radiation in materials processingBFig.3. Energy level diagrams: A – for a hydrogen atom, B – for a lead atom. (Adaptedfrom Ref. [7]).Electrons occupy allowed shells; however, the number of electrons per shellaccording to the Pauli exclusion principle is limited to 2n2.The distribution of energy levels in a multi-electron atom (Pb) is shown inFig.3B.The energy levels associated with the various electron orbits (not drawn toscale) increase with Z and decrease with quantum number n and the averagedistance from the nucleus. The outer electronic shell (the valence shell) determines the chemical properties of the element. The energy bands associated withn 1, 2, 3, etc., are known as the K, L, M, etc., bands. The structure of eachband arises from small differences in energy associated with both the l and squantum numbers.In a multi-electron atom, inner shell electrons are bound with much larger2energies En than ER in single-electron model: En –ER(Zeff/n2), and the corre2sponding atomic radius is: rn a0(n /Zeff), where Zeff is the effective atomicnumber, given by Zeff Z – sc, with sc as the screening constant, which equalsto 2 for K-shell electrons.There are two main processes when an electron is removed from a givenshell in the atom: excitation and ionization. Both of them occur within the atomthrough various possible interactions (energy transition) which will be discussedin Chapter 2.Excitation of an atom is present when an electron is moved from a givenshell to a higher n shell which is empty or is not filled by corresponding numberof electrons. Excitation energy (excitation potential) is a minimum energy required to excite an atom from its ground state to a higher state (Fig.4A).Ionization of an atom occurs when an electron is removed from the atom(a certain amount of energy is transferred to the electron which is sufficient to

13Chapter 1AB1st excitation energy of hydrogen 10.2 eV(level n 1 to level n 2)2nd excitation energy of hydrogen 12.1 eV(level n 1 to level n 3)1st ionization energy of hydrogen is 13.6 eV(level n 1 to ionization level n )2nd ionization energy of hydrogen is 3.39 eV(level n 2 to ionization level n Fig.4. Excitation scheme (A) and ionization scheme (B) of hydrogen atom.overcome its binding energy in the shell). Ionization energy (ionization potential) is a minimum energy required to release electron from atom or ion (Fig.4B).An orbital electron from a higher n shell will fill the electron vacancy in alower n atomic shell. The energy difference between two shells will be eitheremitted as a (fluorescent) photon or it will be transferred to the higher n-shellelectron, which will be ejected from the atom as an Auger electron.The minimum energy required to ionize the atom (ionization potential)ranges from a few (alkali elements) to 24.5 eV (helium) [9].2.3. NUCLEAR STRUCTUREMost of the mass of an atom is concentrated in the atomic nucleus, consisting of Z protons and N (A – Z) neutrons and having radius:r r0 3 A(10)where r0 is a constant ( 1.4 fm) assumed equal to ½ of re, the classical electronradius.The constituents of the nucleus, protons and neutrons (nucleons), are boundin the nucleus with a strong force. This short-range (10–15 m) force exceeds notonly the long-range electromagnetic force between charged nucleons (protons),which is repulsive and tends to disrupt the nucleus, but also other knownnatural forces (gravitational, weak interaction) by several orders of magnitudeand holds different nucleons (protons-neutrons) together in the nucleus. Theenergy associated with the strong force is called binding energy.

14Applications of ionizing radiation in materials processingFig.5. Binding energy per nucleon for different elements. (Adapted from Ref. [10]).Z, number of protonsThe binding energy per nucleon, EB/A, in a nucleus varies gradually withthe number of nucleons, A (Fig.5). It may be calculated from the energy equivalent of the mass deficit (defect), Δm, of a given nucleus as:Proton rich nucleiN, number of neutronsFig.6. Nuclear stability chart. The stability line is indicated in black. (Adapted fromRef. [11]).

15Chapter 1222E B mc 2 Zm p c (A Z)m n c Mc AAA(11)where: M – the nuclear mass, expressed in atomic mass units – u (Mc2 931.5MeV); mpc2 – the proton rest energy; mnc2 – the neutron rest energy.A stable nucleus has enough binding energy to hold the nucleons togetherpermanently. There is no basic relation between the atomic mass number A andatomic number Z of a nucleus, but an empirical relationship:A(12)1.98 0.0155A 2/3gives a good approximation for a stable nucleus.Strong nuclear forces and the associated binding energy in the nucleusdetermine the stability of the nucleus (balance of protons and neutrons). Toomany neutrons or too many protons upset this balance disrupting the bindingenergy of the strong nuclear forces making the nucleus unstable (Fig.6).Z 3. NUCLEAR TRANSFORMATIONSThe nuclear transformations (transmutations) play a significant role in the development of new materials. Materials in which nuclear transformation processestake place are known as natural radiation sources. They represent a powerfultool for radiation-induced modification of materials (especially in nuclearenergy and in the biomedical field), since the result of every transmutationprocess is an energy release [12]. Nuclear transmutation energy is released as: Kinetic energy of the product particles. Almost immediate emission of very high energy photons, i.e. prompt gammarays, or it is a postponed energy release through gamma decay to the groundstate of the nucleus, which is present, when nucleus is firstly transformedto a metastable state. A small amount of energy may also emerge in the form of X-rays. (Generally,the product nucleus has a modified atomic number, so the configuration of itselectron shells is destroyed. As the electrons rearrange themselves and dropto lower energy levels, X-rays, due to internal transitions, may be emitted).There are four major types of nuclear transmutation [4]: Radioactive decay, in which nuclei spontaneously eject one or more particlesand lose energy to become the nuclei of lighter atoms. Examples are alpha,beta and gamma decays. Fission, which is the splitting of a nucleus into two “daughter” nuclei, e.g.23614192n 23592 U 92 U 56 Ba 36 Kr 3n.

16Applications of ionizing radiation in materials processing Fusion of two parent nuclei into one daughter nucleus, e.g. 11 N 11 N 21 N e νe, where νe stands for (electron) neutrino – which is an elementaryparticle holding no electrical charge, travelling at nearly the speed of light,and passing through ordinary matter with virtually no interaction. Neutron capture, in which the nuclear charge (Z, the atomic number) is unchanged, the nuclear mass (A number of protons neutrons, the atomicmass) increases by one, and the number of neutrons (N) increases by one.The simplified overview of nuclear transmutations is provided in Fig.7.Fig.7. Nucler transmutation processes. Processes indicated in gray boxes are not considered for discussion in this book.3.1. RADIOACTIVITYRadioactivity is a process characterized by a transformation of an unstablenucleus into more stable state that may also be unstable and will decay furtherthrough a chain of decays until a stable nuclear configuration is reached. Theenergy difference between the two quantum states is called the decay energy,Q, and is emitted from the nucleus in the form of electromagnetic radiation(gamma rays) or in the form of kinetic energy of the reaction products.All radioactive processes are governed by the same formalism based on: substance related characteristic parameter called the decay constant λ; activity, A(t), which represents the total number of disintegrations (decays)of nuclei per unit time and is defined as:A(t) λN(t)(13)where N(t) is the number of radioactive nuclei at time t.The SI unit of activity is the becquerel, Bq (1 Bq 1 s–1), but the older unitof activity, the curie, Ci (1 Ci 3.7 1010 Bq), originally defined as theactivity of 1 g of 226Ra, is also used.The simplest radioactive decay involves a transition with a decay constantλP from a quantum state of the unstable parent nucleus, P, to the quantum state Pof the stable daughter nucleus, D: P D.

17Chapter 1The rate of depletion of the number of radioactive parent nuclei, NP, is equalto the activity of radioactive parent, AP(t), at time t:dN P (t) A P (t) P N P (t),dtN P (t )tdN P P dt NPN P (0)0(14)where NP(0) is the initial number of parent nuclei at time t 0.The number of radioactive parent nuclei NP(t) in radioactive substance andthe activity of radioactive parent AP(t) as a function of time (Fig.8) may bedefined as:N P (t) N P (0)e P t(15)A P (t) P N P (t) P N P (0)e P t A P (0)e P twhere AP(0) is the initial activity at time t 0.AActivityA(t)A(0)Area BArea с ;ϬͿʏA(t) -ʄ ;ϬͿƚн ;ϬͿ ( ) A(t) A(0)e-ʄƚ ( ) ஶArea C A(0) ି Ěƚ с ;ϬͿʏ Area Cɒt1/2//2Time, tTFig.8. Plot of activity as a function of time.The half-life, (t1/2)P, of radioactive parent, P, is the time during which thenumber of radioactive parent nuclei decay from the initial value NP(0) at timet 0 to half of the initial value:N P (0) N P (0)e P (t1/2 )P(16)2The same relationship is valid for the activity.The average (mean) lifetime, τP, of a radioactive substance is the averagelife expectancy of all parent radioactive nuclei in the substance at time t 0:N P (t t1/2 ) A P (0)(17) P0The decay constant λP, the half-life (t1/2)P and average lifetime τP of a radioactive substance are related to each other as follows:A P (0) A P (0)e P t dt

18Applications of ionizing radiation in materials processing P ln 21 ,(t1/2 ) P P(t1/2 ) P P ln 2(18)Specific activity a is the activity per unit mass:a A(t) N(t) N A N A ln 2 MMAA( 1/2 ) P(19)where NA stands for Avogadro’s number and A is the atomic mass number.A more complicated radioactive decay occurs when a radioactive parentnucleus, P, decays with its decay constant λP into unstable daughter nucleus,D, which in turn decays with a decay constant λD into a stable granddaughter, P DG: P D G.Time-dependent parent and daughter activities are shown in Fig.9.Relative activity4 AP;ϬͿ сʄPNP(t)AP;ƚͿ сʄPNP;ƚͿс ʄPNP(0)e-ʄ t3P2AD;ƚͿ сʄDND(t)1tmax0213456Time t (arbitratry units)Fig.9. Parent and daughter activities plotted as a functions of time.The activity of the daughter nuclei is expressed as: DA(0)(e P t e D t ) D PThe maximum activity of daughter nuclei occurs at time tmax:AD (20)ln( D / P )(21) D Punder condition, that ND 0 at time t 0.There are some special considerations in the parent-daughter-granddaughterrelationship: for non-equilibrium:t max

19Chapter 1 D P or (t1/2 ) D (t1/2 ) P ,AD D 1 e ( D P ) t AP D P(22) DAD , for t tmaxAP D P(23) for transient equilibrium: D P or (t1/2 ) D (t1/2 ) P , for secular equilibrium:λD λP or (t1/2)D (t1/2)P, AD/AP 1(24)3.2. ACTIVATION OF NUCLIDESActivation of nuclides is possible when a parent nuclide, P, interacts withthermal neutrons in a nuclear reactor. This interaction is followed by occuranceof a radioactive daughter nuclide, D, that decays into a granddaughter nuclide, D G: P D G , where (in cm–2·s–1) indicates neutron fluence rate.The probability for the parent nuclei activation is determined by nuclearreaction cross section, σ, expressed in barn/atom (1 barn 10–24 cm2). In thecase of parent nuclei activation, the expression for daughter activity is givenin Eq. (21) where λP is replaced by the :

BASIC RADIATION PHYSICS AND SOURCES OF RADIATION Diana Adlien ė Kaunas University of Technology, Physics Department, Studentų g. 50, LT-51368 Kaunas, Lithuania 1. INTRODUCTION Treatment of materials and products with radiation in order to modify their physical, chemical and biological pro

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