# ASTM E666-14

Designation: E666 − 14Standard Practice forCalculating Absorbed Dose From Gamma or X Radiation1This standard is issued under the fixed designation E666; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.This standard has been approved for use by agencies of the U.S. Department of Defense.1. Scope1.1 This practice presents a technique for calculating theabsorbed dose in a material from knowledge of the radiationfield, the composition of the material, (1-5)2,3and a relatedmeasurement. The procedure is applicable for X and gammaradiation provided the energy of the photons fall within therange from 0.01 to 20 MeV.1.2 A method is given for calculating the absorbed dose ina material from the knowledge of the absorbed dose in anothermaterial exposed to the same radiation field. The procedure isrestricted to homogeneous materials composed of the elementsfor which absorption coefficients have been tabulated. All 92natural elements are tabulated in (2). It also requires someknowledge of the energy spectrum of the radiation fieldproduced by the source under consideration. Generally, theaccuracy of this method is limited by the accuracy to which theenergy spectrum of the radiation field is known.1.3 The results of this practice are only valid if chargedparticle equilibrium exists in the material and at the depth ofinterest. Thus, this practice is not applicable for determiningabsorbed dose in the immediate vicinity of boundaries betweenmaterials of widely differing atomic numbers. For more infor-mation on this topic, see Practice E1249.1.4 Energy transport computer codes4exist that are formu-lated to calculate absorbed dose in materials more preciselythan this method. To use these codes, more effort, time, andexpense are required. If the situation warrants, such calcula-tions should be used rather than the method described here.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:5E170 Terminology Relating to Radiation Measurements andDosimetryE668 Practice for Application of Thermoluminescence-Dosimetry (TLD) Systems for Determining AbsorbedDose in Radiation-Hardness Testing of Electronic DevicesE1249 Practice for Minimizing Dosimetry Errors in Radia-tion Hardness Testing of Silicon Electronic Devices UsingCo-60 Sources2.2 International Commission on Radiation Units and Mea-surements (ICRU) Reports:6ICRU Report 18 Specification of HighActivity Gamma-RaySourcesICRU Report 21 Radiation Dosimetry: Electrons with InitialEnergies Between 1 and 50 MeVICRU Report 51 Radiation Quantities and Units in RadiationProtection DosimetryICRU Report 60 Radiation Fundamental Quantities andUnits for Ionizing RadiationICRU Report 34 The Dosimetry of Pulsed RadiationICRU Report 80 Dosimetry Systems for Use in RadiationProcessing3. Terminology3.1 energy fluence spectrum, ψ(E)—the product of theparticle fluence spectrum (see Terminology E170) and the1This practice is under the jurisdiction of ASTM Committee E10 on NuclearTechnology and Applicationsand is the direct responsibility of SubcommitteeE10.07 on Radiation Dosimetry for Radiation Effects on Materials and Devices.Current edition approved Jan. 1, 2014. Published February 2014. Originallyapproved in 1997. Last previous edition approved in 2009 as E666-09. DOI:10.1520/E0666-14.2The boldface numbers in parentheses refer to the list of references appended tothis practice.3See also ICRU Report 80. For calculation of absorbed dose in dosimetrysystems and materials used in radiation processing, mass attenuation coefficients andmass-energy absorption coefficients for key elements, compounds and materialsused in radiation processing dosimetry over the photon range from 100 keV to 20MeV are given in Appendix 1 of that report.4Information on and packages of computer codes can be obtained from TheRadiation Safety Information Computational Center, Oak Ridge NationalLaboratory, P.O. Box 2008, Oak Ridge, TN 37831-6362. This information centercollects, organizes, evaluates, and disseminates shielding information related toradiation from reactors, weapons, and accelerators and to radiation occurring inspace.5For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.6Available from International Commission on Radiation Units and Measure-ments (ICRU), 7910 Woodmont Ave., Suite 400, Bethesda, MD 20841.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1particle energy. In this standard, the particles referred to arephotons. The energy fluences spectrum is the same as theenergy fluence per unit energy.3.2 energy fluence, ψ—the integral of the energy fluencespectrum over the complete range of particle energies that arepresent.3.3 mass-depth and mass-thickness, t—the product of alength traversed in a material and the mass density of thematerial. The mass-depth and the mass-thickness have dimen-sions of mass per unit area.4. Significance and Use4.1 The absorbed dose is a more meaningful parameter thanexposure for use in relating the effects of radiation on materi-als. It expresses the energy absorbed by the irradiated materialper unit mass, whereas exposure is related to the amount ofcharge produced in air per unit mass. Absorbed dose, asreferred to here, implies that the measurement is made underconditions of charged particle (electron) equilibrium (seeAppendix X1). In practice, such conditions are not rigorouslyachievable but, under some circumstances, can be approxi-mated closely.4.2 Different materials, when exposed to the same radiationfield, absorb different amounts of energy. Using the techniquesof this standard, charged particle equilibrium must exist inorder to relate the absorbed dose in one material to theabsorbed dose in another.Also, if the radiation is attenuated bya significant thickness of an absorber, the energy spectrum ofthe radiation will be changed, and it will be necessary tocorrect for this.NOTE 1—For comprehensive discussions of various dosimetry methodsapplicable to the radiation types and energies and absorbed dose rateranges discussed in this method, see ICRU Reports 34 and 80.5. Calculation of Absorbed Dose5.1 The absorbed dose, D, at a point may be expressed as:D 5 I *0`ψ~E!@µen~E!/ρ#dE (1)where ψ(E) is the energy fluence per unit energy at the pointof interest; µen(E)/ρ is the mass energy absorption coefficient(2); and I is a normalizing factor. If all of the variables in Eq1 are expressed in SI units,I=1.Inthis case the units for Dare Gy (J kg·–1), of ψ(E), are m–2,ofµen/ρ are m2·kg–1, and ofE are J. For an alternative use of the normalizing factor I, seeAppendix X2. For further information on the use of energyabsorption coefficients to calculate absorbed dose see thediscussion in Attix (1). The energy fluence spectrum, ψ(E), isthat which is incident at the point where the dose is to bedetermined. In practice, the limits of integration are the limitsof energy over which ψ(E) is of a significant magnitude. Ifmaterial intervenes between the source and the point of dosedetermination, then the spectrum used in the calculation mustbe the output spectrum of the source modified by the absorbingeffects of the intervening material. The values of µen(E)/ρ arefound in the tables of Ref 2.NOTE 2—For units and terminology in reports of data, E170 and ICRUReports 51 and 60 may be used as guides.5.2 If the material in which the absorbed dose is to becalculated is a homogeneous combination of materials notlisted in the tables of Ref 2,µen(E)/ρ is determined as follows:5.2.1 From Ref 2, obtain values of µeni~E!/ρ for eachcomponent, i.5.2.2 Determine the mass fraction, wi, for each component.5.2.3 Calculate µen(E)/ρ from the following equation:µen~E!/ρ 5(iwi@µeni~E!/ρ# (2)5.2.4 Values of µen(E)/ρ must be determined for each valueof E for which ψ(E) is significant, where E is the photonenergy.5.3 The integral contained in Eq 1 is evaluated numerically.The values of µen(E)/ρ in Ref 2 are tabulated for specificenergies. In evaluation of the integral referred to in actualpractice, it is often desirable to choose energy intervals thatwould not correspond to the tabulated values in Ref 2. In suchcases, the appropriate value of µen(E)/ρ for the chosen energiesshould be determined by an acceptable interpolation procedure.The range of energy over the total photon spectrum is dividedinto energy intervals or bins. The width of these bins issomewhat flexible but should be chosen small enough so as notto distort the shape of the spectrum. For the purpose ofselecting appropriate values of µen(E)/ρ, the energy valueselected for each energy interval can be taken either as thatenergy at the beginning or midpoint of each energy intervalover the entire spectrum.5.4 The energy fluence spectrum, ψ(E), is commonly givenin arbitrary units and may be normalized to some sourceparameter. If a standard or calibrated dosimeter is used, thenthe integral in Eq 1 must be calculated for the material fromwhich this dosimeter is constructed. The value of I is thengiven by the observed dose, D, measured by the dosimeter,divided by the value of the integral.6. Estimating the Absorbed Dose in One Material fromThat Measured in Another Material6.1 If the absorbed dose is known in one material, A, thenthe absorbed dose can be estimated in another material, B,using the method described in this section.6.1.1 The absorbed dose observed inAoccurs at some depthin the region of material A; similarly, it is desired to know theabsorbed dose in material B at some depth in the region ofmaterial B. If it is presumed that we know the surface energyfluence spectrum ψo(E) (the energy fluence spectrum incidenton the surface of materials A and B) then the energy fluencespectrum ψ(E) to be used in Eq 1 must be related to the knownsurface energy fluence spectrum ψo(E). A good approximationto the attenuated energy fluence spectrum at mass-depth t isgiven byψt~E! 5 ψo~E!exp~2@µen~E!/ρ#t! (3)where t is the mass-depth (in kg·m−2) of material betweenthe surface and the depth of interest, E is a particular energyrepresented in the spectrum, and ψt(E) is the energy fluence perunit energy at mass-depth t. For a derivation of Eq 3 seeE666 − 142Appendix X4. See also the qualifications of 6.1.3 and 6.1.4. Fora demonstration of the experimental plausibility of Eq 3, seeAppendix X5.6.1.2 Using Eq 1 and 3, the relationship between the knowndose DAand the desired dose DBcan be expressed asDADB5*0`@ψo~E!exp~2@µenA~E!/ρA#tA!#@µenA~E!/ρA#dE*0`@ψo~E!exp~2@µenB~E!/ρB#tB!#@µenB~E!/ρB#dE(4)where µenA, ρA, and tAare the energy absorption coefficient, thedensity and the relevant mass-depth for material A, and wheresimilar notation is used for material B. For further details onthe derivation of Eq 4, see Appendix X6. All the variables inEq 4 are presumed to be known except the desired value forDB. The integrals in Eq 4 must be performed numerically.6.1.3 The use of Eq 3 is based on the existence of chargedparticle equilibrium (for further discussion see 1.3). Thiscondition may be reasonably well met when the region ofinterest is at a sufficient distance from boundaries representingchanges in atomic number or material density (see AppendixX1).6.1.4 Wide Beam vs. Narrow Beam Approximation.6.1.4.1 The use of the energy coefficient, µen,inEq 3 isbased on the assumption that the irradiation approaches the“wide beam” as opposed to “narrow beam” condition. Thewide beam and narrow beam conditions represent limitingcases which are only approximately realized for real experi-ments. In the narrow beam case, photons which are scatteredout of the narrow beam are assumed to be lost from the beam,and are assumed to have no further importance to the experi-ment. In the broad beam case, photons which are scattered outof a given small region of the broad beam are presumed to bereplaced by photons scattering in from adjacent regions of thebeam. For the narrow beam limiting case, Eq 3 should bereplaced byψt~E! 5 ψo~E!exp~2@µ~E!/ρ#t! (5)where µ is the photon attenuation coefficient. Values ofµ(E)/ρ are found in the tables of Ref 2. For most practicalproblems the results of photon attenuation lie between theresults of Eq 3 and Eq 5.6.1.4.2 It is possible to determine the magnitude of thechange which would have resulted had Eq 1 and Eq 5 beenused rather than using Eq 1 and Eq 3 in order to develop Eq 4.The resulting change in the ratio DA/DBcalculated by Eq 4 isrelated to the factorF~E! 5exp~2@µenB~E!/ρB#t!exp~2@µB~E!/ρB#t!exp~2@µA~E!/ρA#t!exp~2@µenA~E!/ρA#t!(6)If, over the energy range of interest, F(E) differs from unityby a percentage which is greater than the acceptable dosimetryerror, then the application of this practice may be inappropri-ate. In that case an appropriate transport calculation is recom-mended (see 1.5).6.1.4.3 Depending on the scattering geometry, it is possiblefor the absorbed dose to be different from that calculated usingeither µ or µen. The use of µenin Eq 3 is an expedient devicethat is used as a means for yielding what is usually aconservative value, so that exact calculation of the scatteringcomponent can be circumvented. For an extensive discussionof this and similar effects, see Ref 1.7. Accuracy7.1 The accuracy of this practice depends primarily on theaccuracy to which the incident energy spectrum is known. Ingeneral, even a poor estimate of a spectrum will give a betterestimate of the absorbed dose at a given location than onewould get by assuming some sort of single“ effective photonenergy.” Although60Co and137Cs have well-defined primarygamma-ray energies, the radiation energy spectrum from mostpractical sources contains a significant Compton scatteredcomponent that could lead to significant errors if neglected (seeICRU Report 18).7.2 As stated in 1.3, the results of this practice are not validunless charged particle equilibrium conditions exist in thematerial at the depth of application. For depths less than thatrequired for equilibrium, the absorbed dose could be higher orlower than this method would predict. At depths greater thanrequired for equilibrium, the accuracy of the results dependsprimarily upon the accuracy of the attenuation correctionapplied in Eq 3 and the knowledge of the incident energyspectrum.7.3 The procedures used in this method neglect the possiblenonlocality of energy deposition by secondar