ASTM E693-23
(Practice)Standard Practice for Characterizing Neutron Exposures in Iron and Low Alloy Steels in Terms of Displacements Per Atom (DPA)
Standard Practice for Characterizing Neutron Exposures in Iron and Low Alloy Steels in Terms of Displacements Per Atom (DPA)
SIGNIFICANCE AND USE
4.1 A pressure vessel surveillance program requires a methodology for relating radiation-induced changes in materials exposed in accelerated surveillance locations to the condition of the pressure vessel (see Practice E853). An important consideration is that the irradiation exposures be expressed in a unit that is physically related to the damage mechanisms.
4.2 A major source of neutron radiation damage in metals is the displacement of atoms from their normal lattice sites. Hence, an appropriate damage exposure index is the number of times, on the average, that an atom has been displaced during an irradiation. This can be expressed as the total number of displaced atoms per unit volume, per unit mass, or per atom of the material. Displacements per atom is the most common way of expressing this quantity. The number of dpa associated with a particular irradiation depends on the amount of energy deposited in the material by the neutrons, and hence, depends on the neutron spectrum. (For a more extended discussion, see Practice E521.)
4.3 No simple correspondence exists in general between dpa and a particular change in a material property. A reasonable starting point, however, for relative correlations of property changes produced in different neutron spectra is the dpa value associated with each environment. That is, the dpa values themselves provide a spectrum-sensitive index that may be a useful correlation parameter, or some function of the dpa values may affect correlation.
4.4 Since dpa is a construct that depends on a model of the neutron interaction processes in the material lattice, as well as the cross section (probability) for each of these processes, the value of dpa would be different if improved models or cross sections are used. The calculated displacement cross section for ferritic iron, as given in this practice, is determined by the procedure given in 6.3. The currently recommended iron displacement cross section in this practice (Table 1) wa...
SCOPE
1.1 This practice describes a standard procedure for characterizing neutron irradiations of iron (and low alloy steels) in terms of the exposure index displacements per atom (dpa) for iron.
1.2 Although the methods of this practice apply to any material for which a displacement cross section σd(E) is known (see Practice E521), this practice is written specifically for iron.
1.3 It is assumed that the displacement cross section for iron is an adequate approximation for calculating displacements in steels that are mostly iron (95 to 100 %) in radiation fields for which secondary damage processes are not important.
1.4 Procedures analogous to this one can be formulated for calculating dpa in charged particle irradiations. (See Practice E521.)
1.5 The application of this practice requires knowledge of the total neutron fluence and flux spectrum. Refer to Practice E521 for determining these quantities.
1.6 The correlation of radiation effects data is beyond the scope of this practice.
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.
1.8 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
General Information
- Status
- Published
- Publication Date
- 31-Dec-2022
- Technical Committee
- E10 - Nuclear Technology and Applications
- Drafting Committee
- E10.05 - Nuclear Radiation Metrology
Relations
- Effective Date
- 01-Jun-2017
- Effective Date
- 01-Oct-2016
- Effective Date
- 15-Feb-2016
- Effective Date
- 01-Sep-2015
- Effective Date
- 15-Mar-2015
- Effective Date
- 15-Oct-2014
- Effective Date
- 01-Sep-2014
- Effective Date
- 01-Jun-2013
- Effective Date
- 01-Jun-2010
- Effective Date
- 15-Aug-2009
- Effective Date
- 01-Aug-2009
- Effective Date
- 01-Aug-2009
- Effective Date
- 01-Aug-2009
- Effective Date
- 01-Aug-2009
- Effective Date
- 15-Jun-2009
Overview
ASTM E693-23, titled Standard Practice for Characterizing Neutron Exposures in Iron and Low Alloy Steels in Terms of Displacements Per Atom (DPA), establishes a standardized methodology for quantifying neutron irradiation in iron and iron-based alloys by using the “displacements per atom” (dpa) exposure index. Administered by ASTM International, this practice is essential for correlating neutron radiation effects, especially for pressure vessel surveillance in nuclear reactors.
This standard is a vital tool for engineers, material scientists, and professionals in nuclear technology and materials research. By characterizing neutron exposures with a unit directly linked to atomic-scale damage mechanisms, ASTM E693-23 supports reliable material evaluation and structural safety assessments in irradiated environments.
Key Topics
- Displacements Per Atom (DPA): The central exposure index recommended for expressing neutron irradiation damage in metals. DPA quantifies the average number of times an atom in a solid has been displaced from its lattice site due to neutron interactions.
- Model and Cross Section Dependence: The dpa value relies on neutron displacement cross sections that are specific to iron. Cross section data may evolve with improved models or underlying nuclear data.
- Neutron Spectrum Sensitivity: DPA calculation depends both on the neutron fluence (total number of neutrons per area) and the neutron energy spectrum. Values vary across different reactor environments and exposure locations.
- Applicability: While specifically written for iron and iron-rich low alloy steels (typically 95-100% Fe), the methodology can be extended to any material with known displacement cross sections.
- Comparison of Standards: The standard reflects changes in recommended cross sections over time (e.g., shifts from ENDF/B-IV to ENDF/B-VI and ENDF/B-VII), affecting dpa computations, particularly in benchmarking and surveillance applications.
Applications
ASTM E693-23 is widely used in the nuclear energy industry and materials science research, with key practical applications including:
- Nuclear Reactor Pressure Vessel Surveillance: Supports reactor operators and regulators in interpreting results from accelerated irradiation surveillance programs through physically relevant metrics for neutron-induced damage.
- Irradiated Material Qualification: Enables laboratories and engineers to characterize and compare the neutron exposure experienced by test specimens and structural components, facilitating material property correlation across different irradiation environments.
- Standardization in Materials Testing: Allows for consistent calculation and reporting of neutron exposure in research studies and safety evaluations, enhancing reproducibility and comparison of results.
- Radiation Effects Benchmarking: Provides a reliable method to estimate damage evolution in ferritic steels and iron alloys, forming the basis for modeling the longevity and resilience of reactor components.
- Transferability: While focused on iron, the procedure can be adapted for dpa calculations under other radiation sources, such as charged particle irradiation, supporting broader materials development and qualification.
Related Standards
Several ASTM standards complement ASTM E693-23 and are frequently referenced for an integrated approach to neutron irradiation testing:
- ASTM E521: Practice for Investigating the Effects of Neutron Radiation Damage Using Charged-Particle Irradiation
- ASTM E706: Master Matrix for Light-Water Reactor Pressure Vessel Surveillance Standards
- ASTM E821: Practice for Measurement of Mechanical Properties During Charged-Particle Irradiation
- ASTM E853: Practice for Analysis and Interpretation of Light-Water Reactor Surveillance Neutron Exposure Results
- ASTM E170: Terminology Relating to Radiation Measurements and Dosimetry
Summary
ASTM E693-23 provides a robust framework for characterizing neutron exposures in iron and low alloy steels via displacements per atom (dpa), a key metric in understanding radiation damage. The standard is indispensable for nuclear plant operators, material researchers, and laboratory personnel, supporting safe reactor operation, materials testing, and standardized reporting across the nuclear industry.
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Frequently Asked Questions
ASTM E693-23 is a standard published by ASTM International. Its full title is "Standard Practice for Characterizing Neutron Exposures in Iron and Low Alloy Steels in Terms of Displacements Per Atom (DPA)". This standard covers: SIGNIFICANCE AND USE 4.1 A pressure vessel surveillance program requires a methodology for relating radiation-induced changes in materials exposed in accelerated surveillance locations to the condition of the pressure vessel (see Practice E853). An important consideration is that the irradiation exposures be expressed in a unit that is physically related to the damage mechanisms. 4.2 A major source of neutron radiation damage in metals is the displacement of atoms from their normal lattice sites. Hence, an appropriate damage exposure index is the number of times, on the average, that an atom has been displaced during an irradiation. This can be expressed as the total number of displaced atoms per unit volume, per unit mass, or per atom of the material. Displacements per atom is the most common way of expressing this quantity. The number of dpa associated with a particular irradiation depends on the amount of energy deposited in the material by the neutrons, and hence, depends on the neutron spectrum. (For a more extended discussion, see Practice E521.) 4.3 No simple correspondence exists in general between dpa and a particular change in a material property. A reasonable starting point, however, for relative correlations of property changes produced in different neutron spectra is the dpa value associated with each environment. That is, the dpa values themselves provide a spectrum-sensitive index that may be a useful correlation parameter, or some function of the dpa values may affect correlation. 4.4 Since dpa is a construct that depends on a model of the neutron interaction processes in the material lattice, as well as the cross section (probability) for each of these processes, the value of dpa would be different if improved models or cross sections are used. The calculated displacement cross section for ferritic iron, as given in this practice, is determined by the procedure given in 6.3. The currently recommended iron displacement cross section in this practice (Table 1) wa... SCOPE 1.1 This practice describes a standard procedure for characterizing neutron irradiations of iron (and low alloy steels) in terms of the exposure index displacements per atom (dpa) for iron. 1.2 Although the methods of this practice apply to any material for which a displacement cross section σd(E) is known (see Practice E521), this practice is written specifically for iron. 1.3 It is assumed that the displacement cross section for iron is an adequate approximation for calculating displacements in steels that are mostly iron (95 to 100 %) in radiation fields for which secondary damage processes are not important. 1.4 Procedures analogous to this one can be formulated for calculating dpa in charged particle irradiations. (See Practice E521.) 1.5 The application of this practice requires knowledge of the total neutron fluence and flux spectrum. Refer to Practice E521 for determining these quantities. 1.6 The correlation of radiation effects data is beyond the scope of this practice. 1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use. 1.8 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
SIGNIFICANCE AND USE 4.1 A pressure vessel surveillance program requires a methodology for relating radiation-induced changes in materials exposed in accelerated surveillance locations to the condition of the pressure vessel (see Practice E853). An important consideration is that the irradiation exposures be expressed in a unit that is physically related to the damage mechanisms. 4.2 A major source of neutron radiation damage in metals is the displacement of atoms from their normal lattice sites. Hence, an appropriate damage exposure index is the number of times, on the average, that an atom has been displaced during an irradiation. This can be expressed as the total number of displaced atoms per unit volume, per unit mass, or per atom of the material. Displacements per atom is the most common way of expressing this quantity. The number of dpa associated with a particular irradiation depends on the amount of energy deposited in the material by the neutrons, and hence, depends on the neutron spectrum. (For a more extended discussion, see Practice E521.) 4.3 No simple correspondence exists in general between dpa and a particular change in a material property. A reasonable starting point, however, for relative correlations of property changes produced in different neutron spectra is the dpa value associated with each environment. That is, the dpa values themselves provide a spectrum-sensitive index that may be a useful correlation parameter, or some function of the dpa values may affect correlation. 4.4 Since dpa is a construct that depends on a model of the neutron interaction processes in the material lattice, as well as the cross section (probability) for each of these processes, the value of dpa would be different if improved models or cross sections are used. The calculated displacement cross section for ferritic iron, as given in this practice, is determined by the procedure given in 6.3. The currently recommended iron displacement cross section in this practice (Table 1) wa... SCOPE 1.1 This practice describes a standard procedure for characterizing neutron irradiations of iron (and low alloy steels) in terms of the exposure index displacements per atom (dpa) for iron. 1.2 Although the methods of this practice apply to any material for which a displacement cross section σd(E) is known (see Practice E521), this practice is written specifically for iron. 1.3 It is assumed that the displacement cross section for iron is an adequate approximation for calculating displacements in steels that are mostly iron (95 to 100 %) in radiation fields for which secondary damage processes are not important. 1.4 Procedures analogous to this one can be formulated for calculating dpa in charged particle irradiations. (See Practice E521.) 1.5 The application of this practice requires knowledge of the total neutron fluence and flux spectrum. Refer to Practice E521 for determining these quantities. 1.6 The correlation of radiation effects data is beyond the scope of this practice. 1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use. 1.8 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
ASTM E693-23 is classified under the following ICS (International Classification for Standards) categories: 77.080.20 - Steels. The ICS classification helps identify the subject area and facilitates finding related standards.
ASTM E693-23 has the following relationships with other standards: It is inter standard links to ASTM E170-17, ASTM E170-16a, ASTM E170-16, ASTM E170-15a, ASTM E170-15, ASTM E170-14a, ASTM E170-14, ASTM E853-13, ASTM E170-10, ASTM E170-09a, ASTM E521-96(2009), ASTM E821-96(2009), ASTM E521-96(2009)e2, ASTM E521-96(2009)e1, ASTM E170-09. Understanding these relationships helps ensure you are using the most current and applicable version of the standard.
ASTM E693-23 is available in PDF format for immediate download after purchase. The document can be added to your cart and obtained through the secure checkout process. Digital delivery ensures instant access to the complete standard document.
Standards Content (Sample)
This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E693 − 23
Standard Practice for
Characterizing Neutron Exposures in Iron and Low Alloy
Steels in Terms of Displacements Per Atom (DPA)
This standard is issued under the fixed designation E693; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 2. Referenced Documents
2.1 ASTM Standards:
1.1 This practice describes a standard procedure for charac-
E170 Terminology Relating to Radiation Measurements and
terizing neutron irradiations of iron (and low alloy steels) in
Dosimetry
terms of the exposure index displacements per atom (dpa) for
E521 Practice for Investigating the Effects of Neutron Ra-
iron.
diation Damage Using Charged-Particle Irradiation
1.2 Although the methods of this practice apply to any
E706 Master Matrix for Light-Water Reactor Pressure Vessel
material for which a displacement cross sectionσ (E) is known
Surveillance Standards
d
(see Practice E521), this practice is written specifically for iron.
E821 Practice for Measurement of Mechanical Properties
During Charged-Particle Irradiation
1.3 It is assumed that the displacement cross section for iron
E853 Practice for Analysis and Interpretation of Light-Water
is an adequate approximation for calculating displacements in
Reactor Surveillance Neutron Exposure Results
steels that are mostly iron (95 to 100 %) in radiation fields for
which secondary damage processes are not important.
3. Terminology
1.4 Procedures analogous to this one can be formulated for
3.1 Definitions for terms used in this practice can be found
calculating dpa in charged particle irradiations. (See Practice
in Terminology E170.
E521.)
4. Significance and Use
1.5 The application of this practice requires knowledge of
4.1 A pressure vessel surveillance program requires a meth-
the total neutron fluence and flux spectrum. Refer to Practice
odology for relating radiation-induced changes in materials
E521 for determining these quantities.
exposed in accelerated surveillance locations to the condition
1.6 The correlation of radiation effects data is beyond the
of the pressure vessel (see Practice E853). An important
scope of this practice.
consideration is that the irradiation exposures be expressed in
a unit that is physically related to the damage mechanisms.
1.7 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
4.2 A major source of neutron radiation damage in metals is
responsibility of the user of this standard to establish appro-
the displacement of atoms from their normal lattice sites.
priate safety, health, and environmental practices and deter-
Hence, an appropriate damage exposure index is the number of
mine the applicability of regulatory limitations prior to use. times, on the average, that an atom has been displaced during
an irradiation. This can be expressed as the total number of
1.8 This international standard was developed in accor-
displaced atoms per unit volume, per unit mass, or per atom of
dance with internationally recognized principles on standard-
the material. Displacements per atom is the most common way
ization established in the Decision on Principles for the
of expressing this quantity. The number of dpa associated with
Development of International Standards, Guides and Recom-
a particular irradiation depends on the amount of energy
mendations issued by the World Trade Organization Technical
deposited in the material by the neutrons, and hence, depends
Barriers to Trade (TBT) Committee.
on the neutron spectrum. (For a more extended discussion, see
Practice E521.)
This practice is under the jurisdiction of ASTM Committee E10 on Nuclear
Technology and Applications and is the direct responsibility of Subcommittee
E10.05 on Nuclear Radiation Metrology. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Jan. 1, 2023. Published January 2023. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1979. Last previous edition approved in 2017 as E693 – 17. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E0693-23. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E693 − 23
4.3 No simple correspondence exists in general between dpa 5.2.1 If the fluence rate spectrum is constant over the
and a particular change in a material property. A reasonable duration, t , of the irradiation, then:
r
starting point, however, for relative correlations of property
`
dpa 5φ t * σ ~E!ψ~E! dE 5φ t σ¯ (3)
tot r d tot r d
changes produced in different neutron spectra is the dpa value 0
associated with each environment. That is, the dpa values
where σ¯ = the spectrum-average displacement cross sec-
d
themselves provide a spectrum-sensitive index that may be a
tion.
useful correlation parameter, or some function of the dpa
5.3 It is assumed for purposes of this practice that the
values may affect correlation.
fluence φ t and the spectrum ψ(E) are known.
tot r
4.4 Since dpa is a construct that depends on a model of the
neutron interaction processes in the material lattice, as well as
6. Calculation
the cross section (probability) for each of these processes, the
6.1 The integral can be evaluated by a simple numerical
value of dpa would be different if improved models or cross
integration as follows:
sections are used. The calculated displacement cross section
N
for ferritic iron, as given in this practice, is determined by the
`
σ E φ E dE 5 σ φ ∆E (4)
* ~ ! ~ ! ~ !
procedure given in 6.3. The currently recommended iron d ( d i i i
i51
displacement cross section in this practice (Table 1) was
where (σ ) and φ are grouped-averaged values over the
d i i
generated using the ENDF/B-VI iron cross section (1). A
interval E < E < E , and ∆E is the width of the interval and
recent calculation using ENDF/B-VII.0 produced identical i i+1 i
is given by E − E .
i+1 i
results (2, 3). The iron cross section data in ENDF/B-VII.1
does not differ from ENDF/B-VII.0. Although the ENDF/B-VI
6.2 The only computational problem, then, is to obtain
based iron displacement cross section differs from the previ-
σ (E) and φ(E) in the same group structure. σ (E) is available
d d
ously recommended ENDF/B-IV iron displacement cross sec-
(15) in the SAND-II group structure (included here as Table 1),
tion (1) by about 60 % in the energy region around 10 keV, by
which is as fine or finer than the group structure in whichφ(E)
about 10 % for energies between 100 keV and 2 MeV, and by
is generally available. Hence the problem is to collapse σ (E)
d
a factor of 4 near 1 keV due to the opening of reaction channels
to match the φ(E) group structure.
in the cross section, the integral iron dpa values are much less
6.2.1 If theφ(E) group structure is sufficiently fine, a simple
sensitive to the change in cross sections. The update from
group averaging is sufficient:
ENDF/B-IV to ENDF/B-VI dpa rates, when applied to the
M
i
H. B. Robinson-2 pressurized water reactor, resulted in “up to σ 5 σ ∆E (5)
~ ! ~ !
d d ik
i ( ik
∆E
i k51
;4 % higher dpa rates in the region close to the pressure vessel
outer surface” and in “slightly lower dpa rates . close to the where M is the number of groups in σ E between E and
i d i
pressure vessel inner wall” (4, 5). Table 2 presents a compari- E , and the ∆E ≡ E − E are the group widths.
i+1 ik ik+1 ik
son of a previous edition (Practice E693–94) and currently 6.2.1.1 If the∆E are constant (as above 1 MeV in Table 1),
ik
recommended dpa estimates for several neutron spectra. this becomes a simple average of the M groups in ∆E as
i i
follows:
5. Procedure
M
i
σ 5 σ (6)
~ ! ~ !
5.1 The displacement rate at time t is calculated as follows: d d
i ( ik
M
i k51
`
dpa/s 5 σ E φ E,t dE (1)
* ~ ! ~ !
d 6.2.2 For a coarse group representation of φ(E), the group
averages of σ (E) should be weighted averages, unless such
d
where:
weighting has been shown to have negligible effects. The ideal
σ (E) = the displacement cross section for a particular
d weighting function is the actual spectrumφ(E). For light-water
material, and
reactor applications, a generalized spectrum is often used
φ(E,t) dE = the fluence rate of neutrons in the energy
consisting of a fission spectrum plus a low energy 1/E tail. Let
interval E to E + dE.
the weighting spectrum be designated by W(E). Then the
recommended form and energy regimes are as follows:
5.2 The exposure index, dpa, is then the time integrated
value of the displacement rate, calculated as follows:
W E 5 C /E E,0.82 MeV (7)
~ !
t `
r
dpa 5 * φ ~t! * σ ~E!ψ~E,t! dE dt (2) 1/2 2E/1.4
tot d
5 C E e E$ 0.82 MeV
0 0
where: The constants C and C are arbitrary.
1 2
The group averages are then computed from the following
φ (t) = the time dependent fluence rate intensity, and
tot
equation:
ψ(E,t) = the fluence rate spectrum normalized to give unit
M
integral fluence rate at any time when integrated
i
ˆ
~ !
~σ ! W E ∆E
over energy.
( d ik ik ik
k51
σ 5 (8)
~ !
M
d i
i
ˆ
W~E !∆E
( ik ik
k51
The boldface numbers in parentheses refer to a list of references at the end of
th
this standard. where Ê = the average energy of the k group, or
ik
E693 − 23
TABLE 1 ENDF/B-VI-based Iron Displacement Cross Section
A A A
Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns)
d d d
1 0.100E-09 158.3543 2 0.1050E-09 154.6209 3 0.110E-09 151.1395
4 0.1150E-09 147.8895 5 0.120E-09 144.1054 6 0.1275E-09 139.9202
7 0.1350E-09 136.0860 8 0.1425E-09 132.5445 9 0.150E-09 128.7502
10 0.160E-09 124.7860 11 0.170E-09 121.1728 12 0.180E-09 117.8527
13 0.190E-09 114.8137 14 0.200E-09 111.9561 15 0.210E-09 109.3199
16 0.220E-09 106.8646 17 0.230E-09 104.5694 18 0.240E-09 101.8930
19 0.2550E-09 98.93331 20 0.270E-09 96.65981 21 0.280E-09 94.12717
22 0.300E-09 91.05218 23 0.320E-09 88.24872 24 0.340E-09 85.68787
25 0.360E-09 83.33912 26 0.380E-09 81.17265 27 0.400E-09 78.92472
28 0.4250E-09 76.63646 29 0.450E-09 74.53734 30 0.4750E-09 72.59930
31 0.500E-09 70.81827 32 0.5250E-09 69.14790 33 0.550E-09 67.59222
34 0.5750E-09 66.13822 35 0.600E-09 64.64189 36 0.630E-09 63.12039
37 0.660E-09 61.70157 38 0.690E-09 60.37332 39 0.720E-09 58.92732
40 0.760E-09 57.39681 41 0.800E-09 55.97892 42 0.840E-09 54.65984
43 0.880E-09 53.43220 44 0.920E-09 52.28703 45 0.960E-09 51.21545
46 0.100E-08 50.07727 47 0.1050E-08 48.89598 48 0.110E-08 47.79609
49 0.1150E-08 46.76870 50 0.120E-08 45.57125 51 0.1275E-08 44.25006
52 0.1350E-08 43.03653 53 0.1425E-08 41.91761 54 0.150E-08 40.71708
55 0.160E-08 39.46333 56 0.170E-08 38.32018 57 0.180E-08 37.26968
58 0.190E-08 36.30967 59 0.200E-08 35.40710 60 0.210E-08 34.57391
61 0.220E-08 33.79705 62 0.230E-08 33.06956 63 0.240E-08 32.22424
64 0.2550E-08 31.28942 65 0.270E-08 30.57002 66 0.280E-08 29.76999
67 0.300E-08 28.79791 68 0.320E-08 27.91048 69 0.340E-08 27.10139
70 0.360E-08 26.35879 71 0.380E-08 25.67357 72 0.400E-08 24.96309
73 0.4250E-08 24.23960 74 0.450E-08 23.57548 75 0.4750E-08 22.96268
76 0.500E-08 22.39920 77 0.5250E-08 21.87094 78 0.550E-08 21.37982
79 0.5750E-08 20.91994 80 0.600E-08 20.44705 81 0.630E-08 19.96509
82 0.660E-08 19.51724 83 0.690E-08 19.09670 84 0.720E-08 18.63984
85 0.760E-08 18.15581 86 0.800E-08 17.70708 87 0.840E-08 17.29049
88 0.880E-08 16.90205 89 0.920E-08 16.54074 90 0.960E-08 16.20166
91 0.100E-07 15.84242 92 0.1050E-07 15.46908 93 0.110E-07 15.12094
94 0.1150E-07 14.79594 95 0.120E-07 14.41855 96 0.1275E-07 14.00095
97 0.13050E-07 13.61661 98 0.1425E-07 13.26338 99 0.150E-07 12.88403
100 0.160E-07 12.48759 101 0.170E-07 12.12633 102 0.180E-07 11.79428
103 0.190E-07 11.49039 104 0.200E-07 11.20760 105 0.210E-07 10.94298
106 0.220E-07 10.69745 107 0.230E-07 10.46804 108 0.240E-07 10.20132
109 0.2550E-07 9.906717 110 0.270E-07 9.679449 111 0.280E-07 9.427035
112 0.300E-07 9.118745 113 0.320E-07 8.838819 114 0.340E-07 8.582926
115 0.360E-07 8.347962 116 0.380E-07 8.131618 117 0.400E-07 7.907534
118 0.4250E-07 7.678809 119 0.450E-07 7.468805 120 0.4750E-07 7.276812
121 0.500E-07 7.097598 122 0.5250E-07 6.930767 123 0.550E-07 6.775607
124 0.5750E-07 6.630701 125 0.600E-07 6.482083 126 0.630E-07 6.330435
127 0.660E-07 6.188963 128 0.690E-07 6.056631 129 0.720E-07 5.913148
130 0.760E-07 5.760298 131 0.800E-07 5.618617 132 0.840E-07 5.486900
133 0.880E-07 5.364337 134 0.920E-07 5.250029 135 0.960E-07 5.143171
136 0.100E-06 5.029254 137 0.1050E-06 4.911427 138 0.110E-06 4.801945
139 0.1150E-06 4.699714 140 0.120E-06 4.581585 141 0.1275E-06 4.450361
142 0.1350E-06 4.329614 143 0.1425E-06 4.218222 144 0.150E-06 4.099185
145 0.160E-06 3.974304 146 0.170E-06 3.860402 147 0.180E-06 3.756055
148 0.190E-06 3.660761 149 0.200E-06 3.571313 150 0.210E-06 3.488699
151 0.220E-06 3.411616 152 0.230E-06 3.339466 153 0.240E-06 3.256051
154 0.2550E-06 3.163276 155 0.270E-06 3.091628 156 0.280E-06 3.013147
157 0.300E-06 2.916945 158 0.320E-06 2.829403 159 0.340E-06 2.749808
160 0.360E-06 2.676750 161 0.380E-06 2.608835 162 0.400E-06 2.527930
163 0.4250E-06 2.440897 164 0.450E-06 2.374384 165 0.4750E-06 2.313606
166 0.500E-06 2.257462 167 0.5250E-06 2.205331 168 0.550E-06 2.154114
169 0.5750E-06 2.108733 170 0.600E-06 2.060134 171 0.630E-06 2.011735
172 0.660E-06 1.966045 173 0.690E-06 1.923586 174 0.720E-06 1.877395
175 0.760E-06 1.828596 176 0.800E-06 1.783008 177 0.840E-06 1.741254
178 0.880E-06 1.703417 179 0.920E-06 1.667792 180 0.960E-06 1.632082
181 0.100E-05 1.595754 182 0.1050E-05 1.558720 183 0.110E-05 1.522295
184 0.1150E-05 1.490200 185 0.120E-05 1.451554 186 0.1275E-05 1.409592
187 0.1350E-05 1.370247 188 0.1425E-05 1.334635 189 0.150E-05 1.296298
190 0.160E-05 1.256143 191 0.170E-05 1.219824 192 0.180E-05 1.187621
193 0.190E-05 1.156028 194 0.200E-05 1.126746 195 0.210E-05 1.099981
196 0.220E-05 1.075226 197 0.230E-05 1.051885 198 0.240E-05 1.026221
199 0.2550E-05 0.9965719 200 0.270E-05 0.9722222 201 0.280E-05 0.9476671
202 0.300E-05 0.9157118 203 0.320E-05 0.8876799 204 0.340E-05 0.8611951
205 0.360E-05 0.8377314 206 0.380E-05 0.8153836 207 0.400E-05 0.7928756
208 0.4250E-05 0.7695923 209 0.450E-05 0.7481711 210 0.4750E-05 0.7286609
211 0.500E-05 0.7107515 212 0.5250E-05 0.6941600 213 0.550E-05 0.6778895
214 0.5750E-05 0.6635014 215 0.600E-05 0.6480775 216 0.630E-05 0.6327240
217 0.660E-05 0.6182052 218 0.690E-05 0.6047435 219 0.720E-05 0.5900444
220 0.760E-05 0.5745604 221 0.800E-05 0.5600318 222 0.840E-05 0.5467011
223 0.880E-05 0.5345984 224 0.920E-05 0.5232391 225 0.960E-05 0.5118709
E693 − 23
TABLE 1 Continued
A A A
Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns)
d d d
226 0.100E-04 0.5002917 227 0.1050E-04 0.4884902 228 0.110E-04 0.4769112
229 0.1150E-04 0.4666898 230 0.120E-04 0.4543560 231 0.1275E-04 0.4409762
232 0.1350E-04 0.4284223 233 0.1425E-04 0.4170648 234 0.150E-04 0.4048129
235 0.160E-04 0.3919477 236 0.170E-04 0.3802993 237 0.180E-04 0.3699498
238 0.190E-04 0.3598211 239 0.200E-04 0.3504475 240 0.210E-04 0.3418580
241 0.220E-04 0.3339029 242 0.230E-04 0.3263810 243 0.240E-04 0.3181047
244 0.2550E-04 0.3085413 245 0.270E-04 0.3006880 246 0.280E-04 0.2927655
247 0.300E-04 0.2824593 248 0.320E-04 0.2733916 249 0.340E-04 0.2648267
250 0.360E-04 0.2572175 251 0.380E-04 0.2499703 252 0.400E-04 0.2426542
253 0.4250E-04 0.2350771 254 0.450E-04 0.2280936 255 0.4750E-04 0.2217044
256 0.500E-04 0.2158471 257 0.5250E-04 0.2104036 258 0.550E-04 0.2050605
259 0.5750E-04 0.2003403 260 0.600E-04 0.1952700 261 0.630E-04 0.1902102
262 0.660E-04 0.1854221 263 0.690E-04 0.1809756 264 0.720E-04 0.1761094
265 0.760E-04 0.1709726 266 0.800E-04 0.1661474 267 0.840E-04 0.1616956
268 0.880E-04 0.1576549 269 0.920E-04 0.1538460 270 0.960E-04 0.1500470
271 0.100E-03 0.1461601 272 0.1050E-03 0.1421933 273 0.110E-03 0.1382971
274 0.1150E-03 0.1348528 275 0.120E-03 0.1306799 276 0.1275E-03 0.1261477
277 0.1350E-03 0.1218873 278 0.1425E-03 0.1180186 279 0.150E-03 0.1138330
280 0.160E-03 0.1094287 281 0.170E-03 0.1054279 282 0.180E-03 0.1018602
283 0.190E-03 0.9837523E-01 284 0.200E-03 0.9515446E-01 285 0.210E-03 0.9224781E-01
286 0.220E-03 0.1048459 287 0.230E-03 0.1028288 288 0.240E-03 0.8397242E-01
289 0.2550E-03 0.8057346E-01 290 0.270E-03 0.7782596E-01 291 0.280E-03 0.7506079E-01
292 0.300E-03 0.7147984E-01 293 0.320E-03 0.6842791E-01 294 0.340E-03 0.1581741
295 0.360E-03 0.7452445E-01 296 0.380E-03 0.6020231E-01 297 0.400E-03 0.5752645E-01
298 0.4250E-03 0.5484677E-01 299 0.450E-03 0.5239946E-01 300 0.4750E-03 0.5017326E-01
301 0.500E-03 0.4855164E-01 302 0.5250E-03 0.4750492E-01 303 0.550E-03 0.8634498E-01
304 0.5750E-03 0.3684567 305 0.600E-03 0.7230662 306 0.630E-03 1.085166
307 0.660E-03 1.433057 308 0.690E-03 1.753764 309 0.720E-03 2.100540
310 0.760E-03 2.428895 311 0.800E-03 2.722788 312 0.840E-03 2.998771
313 0.880E-03 3.258461 314 0.920E-03 3.465372 315 0.960E-03 3.618973
316 0.100E-02 3.787081 317 0.1050E-02 3.964271 318 0.110E-02 13.13789
319 0.1150E-02 10.69382 320 0.120E-02 4.262693 321 0.1275E-02 4.338387
322 0.1350E-02 4.435367 323 0.1425E-02 4.534225 324 0.150E-02 4.592575
325 0.160E-02 4.783180 326 0.170E-02 4.701623 327 0.180E-02 4.841220
328 0.190E-02 4.999009 329 0.200E-02 5.111335 330 0.201E-02 5.183993
331 0.220E-02 5.279069 332 0.230E-02 5.408910 333 0.240E-02 5.523736
334 0.2550E-02 5.695442 335 0.270E-02 5.826853 336 0.280E-02 5.975410
337 0.300E-02 6.173523 338 0.320E-02 6.395415 339 0.340E-02 6.658582
340 0.360E-02 7.183939 341 0.380E-02 10.01168 342 0.400E-02 9.194485
343 0.4250E-02 8.178266 344 0.450E-02 8.229657 345 0.4750E-02 8.508525
346 0.500E-02 8.910876 347 0.5250E-02 9.525395 348 0.550E-02 10.59739
349 0.5750E-02 13.20411 350 0.600E-02 21.17466 351 0.630E-02 19.67340
352 0.660E-02 18.59203 353 0.690E-02 24.36627 354 0.720E-02 39.42936
355 0.760E-02 56.38621 356 0.800E-02 48.66102 357 0.840E-02 35.11790
358 0.880E-02 27.24892 359 0.920E-02 23.52159 360 0.960E-02 20.66808
361 0.100E-01 19.98392 362 0.1050E-01 18.41869 363 0.110E-01 18.51923
364 0.1150E-01 16.80365 365 0.120E-01 16.40945 366 0.1275E-01 16.00651
367 0.1350E-01 16.06792 368 0.1425E-01 15.55876 369 0.150E-01 15.08970
370 0.160E-01 14.61809 371 0.170E-01 13.99511 372 0.180E-01 13.21823
373 0.190E-01 12.01959 374 0.200E-01 10.61530 375 0.210E-01 8.888706
376 0.220E-01 6.857686 377 0.230E-01 4.435299 378 0.240E-01 4.034283
379 0.2550E-01 51.58856 380 0.270E-01 462.4204 381 0.280E-01 374.2036
382 0.300E-01 138.8582 383 0.320E-01 91.99242 384 0.340E-01 75.21491
385 0.360E-01 66.92896 386 0.380E-01 62.40611 387 0.400E-01 65.56062
388 0.4250E-01 59.51893 389 0.450E-01 61.42897 390 0.4750E-01 55.61853
391 0.500E-01 80.54994 392 0.5250E-01 84.93746 393 0.550E-01 61.63473
394 0.5750E-01 61.83547 395 0.600E-01 61.39486 396 0.630E-01 51.44463
397 0.660E-01 41.05520 398 0.690E-01 35.18787 399 0.720E-01 195.2115
400 0.760E-01 72.97270 401 0.800E-01 139.3801 402 0.840E-01 276.0543
403 0.880E-01 138.4568 404 0.920E-01 104.0743 405 0.960E-01 113.7160
406 0.100 105.5489 407 0.1050 78.43095 408 0.110 78.06753
409 0.1150 60.44543 410 0.120 70.47430 411 0.1275 134.1587
412 0.1350 255.3630 413 0.1425 293.0161 414 0.150 133.0900
415 0.160 122.7596 416 0.170 156.0143 417 0.180 244.4100
418 0.190 370.7627 419 0.200 205.3339 420 0.210 101.0349
421 0.220 307.5111 422 0.230 146.9613 423 0.240 171.8077
424 0.2550 135.3387 425 0.270 282.5501 426 0.280 187.6945
427 0.300 142.0391 428 0.320 315.5791 429 0.340 166.5530
430 0.360 302.1184 431 0.380 545.7117 432 0.400 528.4010
433 0.4250 400.4412 434 0.450 309.7825 435 0.4750 351.4453
436 0.500 381.0001 437 0.5250 327.4008 438 0.550 316.9469
439 0.5750 264.2091 440 0.600 190.8042 441 0.630 255.529
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E693 − 17 E693 − 23
Standard Practice for
Characterizing Neutron Exposures in Iron and Low Alloy
Steels in Terms of Displacements Per Atom (DPA)
This standard is issued under the fixed designation E693; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This practice describes a standard procedure for characterizing neutron irradiations of iron (and low alloy steels) in terms of
the exposure index displacements per atom (dpa) for iron.
1.2 Although the methods of this practice apply to any material for which a displacement cross section σ (E) is known (see
d
Practice E521), this practice is written specifically for iron.
1.3 It is assumed that the displacement cross section for iron is an adequate approximation for calculating displacements in steels
that are mostly iron (95 to 100 %) in radiation fields for which secondary damage processes are not important.
1.4 Procedures analogous to this one can be formulated for calculating dpa in charged particle irradiations. (See Practice E521.)
1.5 The application of this practice requires knowledge of the total neutron fluence and flux spectrum. Refer to Practice E521 for
determining these quantities.
1.6 The correlation of radiation effects data is beyond the scope of this practice.
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
1.8 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
E170 Terminology Relating to Radiation Measurements and Dosimetry
E521 Practice for Investigating the Effects of Neutron Radiation Damage Using Charged-Particle Irradiation
E706 Master Matrix for Light-Water Reactor Pressure Vessel Surveillance Standards
This practice is under the jurisdiction of ASTM Committee E10 on Nuclear Technology and Applications and is the direct responsibility of Subcommittee E10.05 on
Nuclear Radiation Metrology.
Current edition approved Aug. 1, 2017Jan. 1, 2023. Published September 2017January 2023. Originally approved in 1979. Last previous edition approved in 20122017
ɛ1
as E693 – 12E693 – 17. . DOI: 10.1520/E0693-17.10.1520/E0693-23.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E693 − 23
E821 Practice for Measurement of Mechanical Properties During Charged-Particle Irradiation
E853 Practice for Analysis and Interpretation of Light-Water Reactor Surveillance Neutron Exposure Results
3. Terminology
3.1 Definitions for terms used in this practice can be found in Terminology E170.
4. Significance and Use
4.1 A pressure vessel surveillance program requires a methodology for relating radiation-induced changes in materials exposed
in accelerated surveillance locations to the condition of the pressure vessel (see Practice E853). An important consideration is that
the irradiation exposures be expressed in a unit that is physically related to the damage mechanisms.
4.2 A major source of neutron radiation damage in metals is the displacement of atoms from their normal lattice sites. Hence, an
appropriate damage exposure index is the number of times, on the average, that an atom has been displaced during an irradiation.
This can be expressed as the total number of displaced atoms per unit volume, per unit mass, or per atom of the material.
Displacements per atom is the most common way of expressing this quantity. The number of dpa associated with a particular
irradiation depends on the amount of energy deposited in the material by the neutrons, and hence, depends on the neutron spectrum.
(For a more extended discussion, see Practice E521.)
4.3 No simple correspondence exists in general between dpa and a particular change in a material property. A reasonable starting
point, however, for relative correlations of property changes produced in different neutron spectra is the dpa value associated with
each environment. That is, the dpa values themselves provide a spectrum-sensitive index that may be a useful correlation
parameter, or some function of the dpa values may affect correlation.
TABLE 1 ENDF/B-VI-based Iron Displacement Cross Section
A A A
Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns)
d d d
1 0.100E-09 158.3543 2 0.1050E-09 154.6209 3 0.110E-09 151.1395
4 0.1150E-09 147.8895 5 0.120E-09 144.1054 6 0.1275E-09 139.9202
7 0.1350E-09 136.0860 8 0.1425E-09 132.5445 9 0.150E-09 128.7502
10 0.160E-09 124.7860 11 0.170E-09 121.1728 12 0.180E-09 117.8527
13 0.190E-09 114.8137 14 0.200E-09 111.9561 15 0.210E-09 109.3199
16 0.220E-09 106.8646 17 0.230E-09 104.5694 18 0.240E-09 101.8930
19 0.2550E-09 98.93331 20 0.270E-09 96.65981 21 0.280E-09 94.12717
22 0.300E-09 91.05218 23 0.320E-09 88.24872 24 0.340E-09 85.68787
25 0.360E-09 83.33912 26 0.380E-09 81.17265 27 0.400E-09 78.92472
28 0.4250E-09 76.63646 29 0.450E-09 74.53734 30 0.4750E-09 72.59930
31 0.500E-09 70.81827 32 0.5250E-09 69.14790 33 0.550E-09 67.59222
34 0.5750E-09 66.13822 35 0.600E-09 64.64189 36 0.630E-09 63.12039
37 0.660E-09 61.70157 38 0.690E-09 60.37332 39 0.720E-09 58.92732
40 0.760E-09 57.39681 41 0.800E-09 55.97892 42 0.840E-09 54.65984
43 0.880E-09 53.43220 44 0.920E-09 52.28703 45 0.960E-09 51.21545
46 0.100E-08 50.07727 47 0.1050E-08 48.89598 48 0.110E-08 47.79609
49 0.1150E-08 46.76870 50 0.120E-08 45.57125 51 0.1275E-08 44.25006
52 0.1350E-08 43.03653 53 0.1425E-08 41.91761 54 0.150E-08 40.71708
55 0.160E-08 39.46333 56 0.170E-08 38.32018 57 0.180E-08 37.26968
58 0.190E-08 36.30967 59 0.200E-08 35.40710 60 0.210E-08 34.57391
61 0.220E-08 33.79705 62 0.230E-08 33.06956 63 0.240E-08 32.22424
64 0.2550E-08 31.28942 65 0.270E-08 30.57002 66 0.280E-08 29.76999
67 0.300E-08 28.79791 68 0.320E-08 27.91048 69 0.340E-08 27.10139
70 0.360E-08 26.35879 71 0.380E-08 25.67357 72 0.400E-08 24.96309
73 0.4250E-08 24.23960 74 0.450E-08 23.57548 75 0.4750E-08 22.96268
76 0.500E-08 22.39920 77 0.5250E-08 21.87094 78 0.550E-08 21.37982
79 0.5750E-08 20.91994 80 0.600E-08 20.44705 81 0.630E-08 19.96509
82 0.660E-08 19.51724 83 0.690E-08 19.09670 84 0.720E-08 18.63984
85 0.760E-08 18.15581 86 0.800E-08 17.70708 87 0.840E-08 17.29049
88 0.880E-08 16.90205 89 0.920E-08 16.54074 90 0.960E-08 16.20166
91 0.100E-07 15.84242 92 0.1050E-07 15.46908 93 0.110E-07 15.12094
94 0.1150E-07 14.79594 95 0.120E-07 14.41855 96 0.1275E-07 14.00095
97 0.13050E-07 13.61661 98 0.1425E-07 13.26338 99 0.150E-07 12.88403
100 0.160E-07 12.48759 101 0.170E-07 12.12633 102 0.180E-07 11.79428
103 0.190E-07 11.49039 104 0.200E-07 11.20760 105 0.210E-07 10.94298
106 0.220E-07 10.69745 107 0.230E-07 10.46804 108 0.240E-07 10.20132
109 0.2550E-07 9.906717 110 0.270E-07 9.679449 111 0.280E-07 9.427035
112 0.300E-07 9.118745 113 0.320E-07 8.838819 114 0.340E-07 8.582926
115 0.360E-07 8.347962 116 0.380E-07 8.131618 117 0.400E-07 7.907534
E693 − 23
TABLE 1 Continued
A A A
Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns)
d d d
118 0.4250E-07 7.678809 119 0.450E-07 7.468805 120 0.4750E-07 7.276812
121 0.500E-07 7.097598 122 0.5250E-07 6.930767 123 0.550E-07 6.775607
124 0.5750E-07 6.630701 125 0.600E-07 6.482083 126 0.630E-07 6.330435
127 0.660E-07 6.188963 128 0.690E-07 6.056631 129 0.720E-07 5.913148
130 0.760E-07 5.760298 131 0.800E-07 5.618617 132 0.840E-07 5.486900
133 0.880E-07 5.364337 134 0.920E-07 5.250029 135 0.960E-07 5.143171
136 0.100E-06 5.029254 137 0.1050E-06 4.911427 138 0.110E-06 4.801945
139 0.1150E-06 4.699714 140 0.120E-06 4.581585 141 0.1275E-06 4.450361
142 0.1350E-06 4.329614 143 0.1425E-06 4.218222 144 0.150E-06 4.099185
145 0.160E-06 3.974304 146 0.170E-06 3.860402 147 0.180E-06 3.756055
148 0.190E-06 3.660761 149 0.200E-06 3.571313 150 0.210E-06 3.488699
151 0.220E-06 3.411616 152 0.230E-06 3.339466 153 0.240E-06 3.256051
154 0.2550E-06 3.163276 155 0.270E-06 3.091628 156 0.280E-06 3.013147
157 0.300E-06 2.916945 158 0.320E-06 2.829403 159 0.340E-06 2.749808
160 0.360E-06 2.676750 161 0.380E-06 2.608835 162 0.400E-06 2.527930
163 0.4250E-06 2.440897 164 0.450E-06 2.374384 165 0.4750E-06 2.313606
166 0.500E-06 2.257462 167 0.5250E-06 2.205331 168 0.550E-06 2.154114
169 0.5750E-06 2.108733 170 0.600E-06 2.060134 171 0.630E-06 2.011735
172 0.660E-06 1.966045 173 0.690E-06 1.923586 174 0.720E-06 1.877395
175 0.760E-06 1.828596 176 0.800E-06 1.783008 177 0.840E-06 1.741254
178 0.880E-06 1.703417 179 0.920E-06 1.667792 180 0.960E-06 1.632082
181 0.100E-05 1.595754 182 0.1050E-05 1.558720 183 0.110E-05 1.522295
184 0.1150E-05 1.490200 185 0.120E-05 1.451554 186 0.1275E-05 1.409592
187 0.1350E-05 1.370247 188 0.1425E-05 1.334635 189 0.150E-05 1.296298
190 0.160E-05 1.256143 191 0.170E-05 1.219824 192 0.180E-05 1.187621
193 0.190E-05 1.156028 194 0.200E-05 1.126746 195 0.210E-05 1.099981
196 0.220E-05 1.075226 197 0.230E-05 1.051885 198 0.240E-05 1.026221
199 0.2550E-05 0.9965719 200 0.270E-05 0.9722222 201 0.280E-05 0.9476671
202 0.300E-05 0.9157118 203 0.320E-05 0.8876799 204 0.340E-05 0.8611951
205 0.360E-05 0.8377314 206 0.380E-05 0.8153836 207 0.400E-05 0.7928756
208 0.4250E-05 0.7695923 209 0.450E-05 0.7481711 210 0.4750E-05 0.7286609
211 0.500E-05 0.7107515 212 0.5250E-05 0.6941600 213 0.550E-05 0.6778895
214 0.5750E-05 0.6635014 215 0.600E-05 0.6480775 216 0.630E-05 0.6327240
217 0.660E-05 0.6182052 218 0.690E-05 0.6047435 219 0.720E-05 0.5900444
220 0.760E-05 0.5745604 221 0.800E-05 0.5600318 222 0.840E-05 0.5467011
223 0.880E-05 0.5345984 224 0.920E-05 0.5232391 225 0.960E-05 0.5118709
226 0.100E-04 0.5002917 227 0.1050E-04 0.4884902 228 0.110E-04 0.4769112
229 0.1150E-04 0.4666898 230 0.120E-04 0.4543560 231 0.1275E-04 0.4409762
232 0.1350E-04 0.4284223 233 0.1425E-04 0.4170648 234 0.150E-04 0.4048129
235 0.160E-04 0.3919477 236 0.170E-04 0.3802993 237 0.180E-04 0.3699498
238 0.190E-04 0.3598211 239 0.200E-04 0.3504475 240 0.210E-04 0.3418580
241 0.220E-04 0.3339029 242 0.230E-04 0.3263810 243 0.240E-04 0.3181047
244 0.2550E-04 0.3085413 245 0.270E-04 0.3006880 246 0.280E-04 0.2927655
247 0.300E-04 0.2824593 248 0.320E-04 0.2733916 249 0.340E-04 0.2648267
250 0.360E-04 0.2572175 251 0.380E-04 0.2499703 252 0.400E-04 0.2426542
253 0.4250E-04 0.2350771 254 0.450E-04 0.2280936 255 0.4750E-04 0.2217044
256 0.500E-04 0.2158471 257 0.5250E-04 0.2104036 258 0.550E-04 0.2050605
259 0.5750E-04 0.2003403 260 0.600E-04 0.1952700 261 0.630E-04 0.1902102
262 0.660E-04 0.1854221 263 0.690E-04 0.1809756 264 0.720E-04 0.1761094
265 0.760E-04 0.1709726 266 0.800E-04 0.1661474 267 0.840E-04 0.1616956
268 0.880E-04 0.1576549 269 0.920E-04 0.1538460 270 0.960E-04 0.1500470
271 0.100E-03 0.1461601 272 0.1050E-03 0.1421933 273 0.110E-03 0.1382971
274 0.1150E-03 0.1348528 275 0.120E-03 0.1306799 276 0.1275E-03 0.1261477
277 0.1350E-03 0.1218873 278 0.1425E-03 0.1180186 279 0.150E-03 0.1138330
280 0.160E-03 0.1094287 281 0.170E-03 0.1054279 282 0.180E-03 0.1018602
283 0.190E-03 0.9837523E-01 284 0.200E-03 0.9515446E-01 285 0.210E-03 0.9224781E-01
286 0.220E-03 0.1048459 287 0.230E-03 0.1028288 288 0.240E-03 0.8397242E-01
289 0.2550E-03 0.8057346E-01 290 0.270E-03 0.7782596E-01 291 0.280E-03 0.7506079E-01
292 0.300E-03 0.7147984E-01 293 0.320E-03 0.6842791E-01 294 0.340E-03 0.1581741
295 0.360E-03 0.7452445E-01 296 0.380E-03 0.6020231E-01 297 0.400E-03 0.5752645E-01
298 0.4250E-03 0.5484677E-01 299 0.450E-03 0.5239946E-01 300 0.4750E-03 0.5017326E-01
301 0.500E-03 0.4855164E-01 302 0.5250E-03 0.4750492E-01 303 0.550E-03 0.8634498E-01
304 0.5750E-03 0.3684567 305 0.600E-03 0.7230662 306 0.630E-03 1.085166
307 0.660E-03 1.433057 308 0.690E-03 1.753764 309 0.720E-03 2.100540
310 0.760E-03 2.428895 311 0.800E-03 2.722788 312 0.840E-03 2.998771
313 0.880E-03 3.258461 314 0.920E-03 3.465372 315 0.960E-03 3.618973
316 0.100E-02 3.787081 317 0.1050E-02 3.964271 318 0.110E-02 13.13789
319 0.1150E-02 10.69382 320 0.120E-02 4.262693 321 0.1275E-02 4.338387
322 0.1350E-02 4.435367 323 0.1425E-02 4.534225 324 0.150E-02 4.592575
325 0.160E-02 4.783180 326 0.170E-02 4.701623 327 0.180E-02 4.841220
328 0.190E-02 4.999009 329 0.200E-02 5.111335 330 0.201E-02 5.183993
331 0.220E-02 5.279069 332 0.230E-02 5.408910 333 0.240E-02 5.523736
334 0.2550E-02 5.695442 335 0.270E-02 5.826853 336 0.280E-02 5.975410
337 0.300E-02 6.173523 338 0.320E-02 6.395415 339 0.340E-02 6.658582
340 0.360E-02 7.183939 341 0.380E-02 10.01168 342 0.400E-02 9.194485
E693 − 23
TABLE 1 Continued
A A A
Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns)
d d d
343 0.4250E-02 8.178266 344 0.450E-02 8.229657 345 0.4750E-02 8.508525
346 0.500E-02 8.910876 347 0.5250E-02 9.525395 348 0.550E-02 10.59739
349 0.5750E-02 13.20411 350 0.600E-02 21.17466 351 0.630E-02 19.67340
352 0.660E-02 18.59203 353 0.690E-02 24.36627 354 0.720E-02 39.42936
355 0.760E-02 56.38621 356 0.800E-02 48.66102 357 0.840E-02 35.11790
358 0.880E-02 27.24892 359 0.920E-02 23.52159 360 0.960E-02 20.66808
361 0.100E-01 19.98392 362 0.1050E-01 18.41869 363 0.110E-01 18.51923
364 0.1150E-01 16.80365 365 0.120E-01 16.40945 366 0.1275E-01 16.00651
367 0.1350E-01 16.06792 368 0.1425E-01 15.55876 369 0.150E-01 15.08970
370 0.160E-01 14.61809 371 0.170E-01 13.99511 372 0.180E-01 13.21823
373 0.190E-01 12.01959 374 0.200E-01 10.61530 375 0.210E-01 8.888706
376 0.220E-01 6.857686 377 0.230E-01 4.435299 378 0.240E-01 4.034283
379 0.2550E-01 51.58856 380 0.270E-01 462.4204 381 0.280E-01 374.2036
382 0.300E-01 138.8582 383 0.320E-01 91.99242 384 0.340E-01 75.21491
385 0.360E-01 66.92896 386 0.380E-01 62.40611 387 0.400E-01 65.56062
388 0.4250E-01 59.51893 389 0.450E-01 61.42897 390 0.4750E-01 55.61853
391 0.500E-01 80.54994 392 0.5250E-01 84.93746 393 0.550E-01 61.63473
394 0.5750E-01 61.83547 395 0.600E-01 61.39486 396 0.630E-01 51.44463
397 0.660E-01 41.05520 398 0.690E-01 35.18787 399 0.720E-01 195.2115
400 0.760E-01 72.97270 401 0.800E-01 139.3801 402 0.840E-01 276.0543
403 0.880E-01 138.4568 404 0.920E-01 104.0743 405 0.960E-01 113.7160
406 0.100 105.5489 407 0.1050 78.43095 408 0.110 78.06753
409 0.1150 60.44543 410 0.120 70.47430 411 0.1275 134.1587
412 0.1350 255.3630 413 0.1425 293.0161 414 0.150 133.0900
415 0.160 122.7596 416 0.170 156.0143 417 0.180 244.4100
418 0.190 370.7627 419 0.200 205.3339 420 0.210 101.0349
421 0.220 307.5111 422 0.230 146.9613 423 0.240 171.8077
424 0.2550 135.3387 425 0.270 282.5501 426 0.280 187.6945
427 0.300 142.0391 428 0.320 315.5791 429 0.340 166.5530
430 0.360 302.1184 431 0.380 545.7117 432 0.400 528.4010
433 0.4250 400.4412 434 0.450 309.7825 435 0.4750 351.4453
436 0.500 381.0001 437 0.5250 327.4008 438 0.550 316.9469
439 0.5750 264.2091 440 0.600 190.8042 441 0.630 255.5292
442 0.660 529.8745 443 0.690 389.0167 444 0.720 680.4310
445 0.760 627.3019 446 0.800 427.2328 447 0.840 461.2467
448 0.880 327.1398 449 0.920 278.1719 450 0.960 479.7678
451 1.00 498.4922 452 1.10 477.6893 453 1.20 707.1735
454 1.30 616.4640 455 1.40 716.4101 456 1.50 734.1659
457 1.60 758.8353 458 1.70 784.5580 459 1.80 819.3325
460 1.90 989.3265 461 2.00 928.7681 462 2.10 923.3754
463 2.20 969.4800 464 2.30 1079.716 465 2.40 1143.224
466 2.50 1348.954 467 2.60 1192.105 468 2.70 1263.538
469 2.80 1277.801 470 2.90 1271.578 471 3.00 1364.006
472 3.10 1387.724 473 3.20 1358.466 474 3.30 1346.851
475 3.40 1398.034 476 3.50 1334.743 477 3.60 1424.447
478 3.70 1440.708 479 3.80 1483.880 480 3.90 1464.868
481 4.00 1526.371 482 4.10 1560.443 483 4.20 1530.309
484 4.30 1582.916 485 4.40 1523.340 486 4.50 1626.724
487 4.60 1600.863 488 4.70 1617.455 489 4.80 1653.609
490 4.90 1642.833 491 5.00 1600.075 492 5.10 1682.554
493 5.20 1687.286 494 5.30 1716.469 495 5.40 1731.089
496 5.50 1729.785 497 5.60 1760.852 498 5.70 1760.538
499 5.80 1768.656 500 5.90 1792.105 501 6.00 1811.511
502 6.10 1800.940 503 6.20 1811.547 504 6.30 1859.081
505 6.40 1859.125 506 6.50 1879.237 507 6.60 1890.037
508 6.70 1891.762 509 6.80 1909.485 510 6.90 1909.076
511 7.00 1914.442 512 7.10 1936.414 513 7.20 1941.750
514 7.30 1966.663 515 7.40 1963.306 516 7.50 1986.044
517 7.60 1976.213 518 7.70 1989.243 519 7.80 2003.646
520 7.90 2006.771 521 8.00 2009.093 522 8.10 2013.259
523 8.20 2032.588 524 8.30 2064.755 525 8.40 2063.837
526 8.50 2061.365 527 8.60 2059.507 528 8.70 2072.344
529 8.80 2089.976 530 8.90 2107.525 531 9.00 2122.580
532 9.10 2135.077 533 9.20 2147.577 534 9.30 2160.074
535 9.40 2172.482 536 9.50 2185.892 537 9.60 2199.950
538 9.70 2213.918 539 9.80 2226.698 540 9.90 2238.281
541 10.0 2250.482 542 10.10 2263.392 543 10.20 2276.220
544 10.30 2288.971 545 10.40 2301.725 546 10.50 2313.910
547 10.60 2325.628 548 10.70 2337.342 549 10.80 2348.869
550 10.90 2360.301 551 11.0 2371.744 552 11.10 2383.112
553 11.20 2395.212 554 11.30 2407.952 555 11.40 2421.344
556 11.50 2434.325 557 11.60 2446.243 558 11.70 2458.956
559 11.80 2471.205 560 11.90 2482.247 561 12.0 2493.659
562 12.10 2506.016 563 12.20 2519.598 564 12.30 2534.971
565 12.40 2549.086 566 12.50 2562.977 567 12.60 2576.115
E693 − 23
TABLE 1 Continued
A A A
Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns)
d d d
568 12.70 2586.936 569 12.80 2600.011 570 12.90 2615.468
571 13.0 2630.343 572 13.10 2644.455 573 13.20 2658.475
574 13.30 2672.218 575 13.40 2685.520 576 13.50 2698.683
577 13.60 2711.990 578 13.70 2725.313 579 13.80 2738.112
580 13.90 2750.418 581 14.0 2763.164 582 14.10 2775.980
583 14.20 2788.331 584 14.30 2800.214 585 14.40 2811.915
586 14.50 2824.208 587 14.60 2837.183 588 14.70 2849.781
589 14.80 2862.184 590 14.90 2874.421 591 15.0 2877.552
592 15.10 2871.084 593 15.20 2864.617 594 15.30 2858.147
595 15.40 2851.581 596 15.50 2844.839 597 15.60 2837.641
598 15.70 2830.538 599 15.80 2823.427 600 15.90 2816.329
601 16.0 2813.386 602 16.10 2814.819 603 16.20 2816.344
604 16.30 2817.782 605 16.40 2819.124 606 16.50 2819.920
607 16.60 2819.883 608 16.70 2819.846 609 16.80 2819.725
610 16.90 2819.631 611 17.0 2823.437 612 17.10 2831.455
613 17.20 2839.475 614 17.30 2847.220 615 17.40 2855.056
616 17.50 2862.956 617 17.60 2870.913 618 17.70 2878.960
619 17.80 2886.826 620 17.90 2894.594 621 18.0 2903.983
622 18.10 2914.913 623 18.20 2925.791 624 18.30 2936.340
625 18.40 2946.712 626 18.50 2956.448 627 18.60 2965.448
628 18.70 2974.450 629 18.80 2983.453 630 18.90 2992.455
631 19.0 2999.561 632 19.10 3004.583 633 19.20 3009.698
634 19.30 3014.721 635 19.40 3019.741 636 19.50 3025.406
637 19.60 3031.526 638 19.70 3037.737 639 19.80 3043.950
640 19.90 3050.161 641
A
Energies represent the lower bin boundary. The upper bin limit is 20.0 MeV
4.4 Since dpa is a construct that depends on a model of the neutron interaction processes in the material lattice, as well as the cross
section (probability) for each of these processes, the value of dpa would be different if improved models or cross sections are used.
The calculated displacement cross section for ferritic iron, as given in this practice, is determined by the procedure given in 6.3.
The currently recommended iron displacement cross section in this practice (Table 1) was generated using the ENDF/B-VI iron
cross section (1). A recent calculation using ENDF/B-VII.0 produced identical results.results (2, 3)). The iron cross section data
in ENDF/B-VII.1 does not differ from ENDF/B-VII.0. Although the ENDF/B-VI based iron displacement cross section differs
from the previously recommended ENDF/B-IV iron displacement cross section (1) by about 60 % in the energy region around 10
keV, by about 10 % for energies between 100 keV and 2 MeV, and by a factor of 4 near 1 keV due to the opening of reaction
channels in the cross section, the integral iron dpa values are much less sensitive to the change in cross sections. The update from
ENDF/B-IV to ENDF/B-VI dpa rates, when applied to the H. B. H. B. Robinson-2 pressurized water reactor, resulted in “up to
;4 % higher dpa rates in the region close to the pressure vessel outer surface” and in “slightly lower dpa rates . close to the
pressure vessel inner wall” (4, 5).Table 2 presents a comparison of a previous edition (Practice E693-94)–94) and currently
recommended dpa estimates for several neutron spectra.
5. Procedure
5.1 The displacement rate at time t is calculated as follows:
`
dpa/s5* σ ~E!φ~E,t! dE (1)
d
where:
σ (E) = the displacement cross section for a particular material, and
d
φ(E,t) dE = the fluence rate of neutrons in the energy interval E to E + dE.
5.2 The exposure index, dpa, is then the time integrated value of the displacement rate, calculated as follows:
t `
r
dpa 5* φ ~t! * σ ~E!ψ~E,t! dE dt (2)
tot d
0 0
where:
φ (t) = the time dependent fluence rate intensity, and
tot
ψ(E,t) = the fluence rate spectrum normalized to give unit integral fluence rate at any time when integrated over energy.
The boldface numbers in parentheses refer to a list of references at the end of this standard.
E693 − 23
TABLE 1 ENDF/B-VI-based Iron Displacement Cross Section
A A A
Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns)
d d d
1 0.100E-09 158.3543 2 0.1050E-09 154.6209 3 0.110E-09 151.1395
4 0.1150E-09 147.8895 5 0.120E-09 144.1054 6 0.1275E-09 139.9202
7 0.1350E-09 136.0860 8 0.1425E-09 132.5445 9 0.150E-09 128.7502
10 0.160E-09 124.7860 11 0.170E-09 121.1728 12 0.180E-09 117.8527
13 0.190E-09 114.8137 14 0.200E-09 111.9561 15 0.210E-09 109.3199
16 0.220E-09 106.8646 17 0.230E-09 104.5694 18 0.240E-09 101.8930
19 0.2550E-09 98.93331 20 0.270E-09 96.65981 21 0.280E-09 94.12717
22 0.300E-09 91.05218 23 0.320E-09 88.24872 24 0.340E-09 85.68787
25 0.360E-09 83.33912 26 0.380E-09 81.17265 27 0.400E-09 78.92472
28 0.4250E-09 76.63646 29 0.450E-09 74.53734 30 0.4750E-09 72.59930
31 0.500E-09 70.81827 32 0.5250E-09 69.14790 33 0.550E-09 67.59222
34 0.5750E-09 66.13822 35 0.600E-09 64.64189 36 0.630E-09 63.12039
37 0.660E-09 61.70157 38 0.690E-09 60.37332 39 0.720E-09 58.92732
40 0.760E-09 57.39681 41 0.800E-09 55.97892 42 0.840E-09 54.65984
43 0.880E-09 53.43220 44 0.920E-09 52.28703 45 0.960E-09 51.21545
46 0.100E-08 50.07727 47 0.1050E-08 48.89598 48 0.110E-08 47.79609
49 0.1150E-08 46.76870 50 0.120E-08 45.57125 51 0.1275E-08 44.25006
52 0.1350E-08 43.03653 53 0.1425E-08 41.91761 54 0.150E-08 40.71708
55 0.160E-08 39.46333 56 0.170E-08 38.32018 57 0.180E-08 37.26968
58 0.190E-08 36.30967 59 0.200E-08 35.40710 60 0.210E-08 34.57391
61 0.220E-08 33.79705 62 0.230E-08 33.06956 63 0.240E-08 32.22424
64 0.2550E-08 31.28942 65 0.270E-08 30.57002 66 0.280E-08 29.76999
67 0.300E-08 28.79791 68 0.320E-08 27.91048 69 0.340E-08 27.10139
70 0.360E-08 26.35879 71 0.380E-08 25.67357 72 0.400E-08 24.96309
73 0.4250E-08 24.23960 74 0.450E-08 23.57548 75 0.4750E-08 22.96268
76 0.500E-08 22.39920 77 0.5250E-08 21.87094 78 0.550E-08 21.37982
79 0.5750E-08 20.91994 80 0.600E-08 20.44705 81 0.630E-08 19.96509
82 0.660E-08 19.51724 83 0.690E-08 19.09670 84 0.720E-08 18.63984
85 0.760E-08 18.15581 86 0.800E-08 17.70708 87 0.840E-08 17.29049
88 0.880E-08 16.90205 89 0.920E-08 16.54074 90 0.960E-08 16.20166
91 0.100E-07 15.84242 92 0.1050E-07 15.46908 93 0.110E-07 15.12094
94 0.1150E-07 14.79594 95 0.120E-07 14.41855 96 0.1275E-07 14.00095
97 0.13050E-07 13.61661 98 0.1425E-07 13.26338 99 0.150E-07 12.88403
100 0.160E-07 12.48759 101 0.170E-07 12.12633 102 0.180E-07 11.79428
103 0.190E-07 11.49039 104 0.200E-07 11.20760 105 0.210E-07 10.94298
106 0.220E-07 10.69745 107 0.230E-07 10.46804 108 0.240E-07 10.20132
109 0.2550E-07 9.906717 110 0.270E-07 9.679449 111 0.280E-07 9.427035
112 0.300E-07 9.118745 113 0.320E-07 8.838819 114 0.340E-07 8.582926
115 0.360E-07 8.347962 116 0.380E-07 8.131618 117 0.400E-07 7.907534
118 0.4250E-07 7.678809 119 0.450E-07 7.468805 120 0.4750E-07 7.276812
121 0.500E-07 7.097598 122 0.5250E-07 6.930767 123 0.550E-07 6.775607
124 0.5750E-07 6.630701 125 0.600E-07 6.482083 126 0.630E-07 6.330435
127 0.660E-07 6.188963 128 0.690E-07 6.056631 129 0.720E-07 5.913148
130 0.760E-07 5.760298 131 0.800E-07 5.618617 132 0.840E-07 5.486900
133 0.880E-07 5.364337 134 0.920E-07 5.250029 135 0.960E-07 5.143171
136 0.100E-06 5.029254 137 0.1050E-06 4.911427 138 0.110E-06 4.801945
139 0.1150E-06 4.699714 140 0.120E-06 4.581585 141 0.1275E-06 4.450361
142 0.1350E-06 4.329614 143 0.1425E-06 4.218222 144 0.150E-06 4.099185
145 0.160E-06 3.974304 146 0.170E-06 3.860402 147 0.180E-06 3.756055
148 0.190E-06 3.660761 149 0.200E-06 3.571313 150 0.210E-06 3.488699
151 0.220E-06 3.411616 152 0.230E-06 3.339466 153 0.240E-06 3.256051
154 0.2550E-06 3.163276 155 0.270E-06 3.091628 156 0.280E-06 3.013147
157 0.300E-06 2.916945 158 0.320E-06 2.829403 159 0.340E-06 2.749808
160 0.360E-06 2.676750 161 0.380E-06 2.608835 162 0.400E-06 2.527930
163 0.4250E-06 2.440897 164 0.450E-06 2.374384 165 0.4750E-06 2.313606
166 0.500E-06 2.257462 167 0.5250E-06 2.205331 168 0.550E-06 2.154114
169 0.5750E-06 2.108733 170 0.600E-06 2.060134 171 0.630E-06 2.011735
172 0.660E-06 1.966045 173 0.690E-06 1.923586 174 0.720E-06 1.877395
175 0.760E-06 1.828596 176 0.800E-06 1.783008 177 0.840E-06 1.741254
178 0.880E-06 1.703417 179 0.920E-06 1.667792 180 0.960E-06 1.632082
181 0.100E-05 1.595754 182 0.1050E-05 1.558720 183 0.110E-05 1.522295
184 0.1150E-05 1.490200 185 0.120E-05 1.451554 186 0.1275E-05 1.409592
187 0.1350E-05 1.370247 188 0.1425E-05 1.334635 189 0.150E-05 1.296298
190 0.160E-05 1.256143 191 0.170E-05 1.219824 192 0.180E-05 1.187621
193 0.190E-05 1.156028 194 0.200E-05 1.126746 195 0.210E-05 1.099981
196 0.220E-05 1.075226 197 0.230E-05 1.051885 198 0.240E-05 1.026221
199 0.2550E-05 0.9965719 200 0.270E-05 0.9722222 201 0.280E-05 0.9476671
202 0.300E-05 0.9157118 203 0.320E-05 0.8876799 204 0.340E-05 0.8611951
205 0.360E-05 0.8377314 206 0.380E-05 0.8153836 207 0.400E-05 0.7928756
208 0.4250E-05 0.7695923 209 0.450E-05 0.7481711 210 0.4750E-05 0.7286609
211 0.500E-05 0.7107515 212 0.5250E-05 0.6941600 213 0.550E-05 0.6778895
214 0.5750E-05 0.6635014 215 0.600E-05 0.6480775 216 0.630E-05 0.6327240
217 0.660E-05 0.6182052 218 0.690E-05 0.6047435 219 0.720E-05 0.5900444
220 0.760E-05 0.5745604 221 0.800E-05 0.5600318 222 0.840E-05 0.5467011
223 0.880E-05 0.5345984 224 0.920E-05 0.5232391 225 0.960E-05 0.5118709
E693 − 23
TABLE 1 Continued
A A A
Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns) Bin Eng (MeV) σ (barns)
d d d
226 0.100E-04 0.5002917 227 0.1050E-04 0.4884902 228 0.110E-04 0.4769112
229 0.1150E-04 0.4666898 230 0.120E-04 0.4543560 231 0.1275E-04 0.4409762
232 0.1350E-04 0.4284223 233 0.1425E-04 0.4170648 234 0.150E-04 0.4048129
235 0.160E-04 0.3919477 236 0.170E-04 0.3802993 237 0.180E-04 0.3699498
238 0.190E-04 0.3598211 239 0.200E-04 0.3504475 240 0.210E-04 0.3418580
241 0.220E-04 0.3339029 242 0.230E-04 0.3263810 243 0.240E-04 0.3181047
244 0.2550E-04 0.3085413 245 0.270E-04 0.3006880 246 0.280E-04 0.2927655
247 0.300E-04 0.2824593 248 0.320E-04 0.2733916 249 0.340E-04 0.2648267
250 0.360E-04 0.2572175 251 0.380E-04 0.2499703 252 0.400E-04 0.2426542
253 0.4250E-04 0.23507
...
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