ASTM E693-94
(Practice)Standard Practice for Characterizing Neutron Exposures in Iron and Low Alloy Steels in Terms of Displacements Per Atom (DPA), E706(ID)
Standard Practice for Characterizing Neutron Exposures in Iron and Low Alloy Steels in Terms of Displacements Per Atom (DPA), E706(ID)
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 general procedures of this practice apply to any material for which a displacement cross section d(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 and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: E 693 – 94
Standard Practice for
Characterizing Neutron Exposures in Iron and Low Alloy
Steels in Terms of Displacements Per Atom (DPA), E706(ID)
This standard is issued under the fixed designation E 693; 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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope 3. Terminology
1.1 This practice describes a standard procedure for charac- 3.1 Definitions for terms used in this practice can be found
terizing neutron irradiations of iron (and low alloy steels) in in Terminology E 170.
terms of the exposure index displacements per atom (dpa) for
4. Significance and Use
iron.
4.1 A pressure vessel surveillance program requires a meth-
1.2 Although the general procedures of this practice apply
odology for relating radiation-induced changes in materials
to any material for which a displacement cross section s (E)is
d
known (see Practice E 521), this practice is written specifically exposed in accelerated surveillance locations to the condition
of the pressure vessel (see Practices E 560 and E 853). An
for iron.
1.3 It is assumed that the displacement cross section for iron important consideration is that the irradiation exposures be
expressed in a unit that is physically related to the damage
is an adequate approximation for calculating displacements in
steels that are mostly iron (95 to 100 %) in radiation fields for mechanisms.
4.2 A major source of neutron radiation damage in metals is
which secondary damage processes are not important.
1.4 Procedures analogous to this one can be formulated for the displacement of atoms from their normal lattice sites.
Hence, an appropriate damage exposure index is the number of
calculating dpa in charged particle irradiations. (See Practice
E 521.) times, on the average, that an atom has been displaced during
an irradiation. This can be expressed as the total number of
1.5 The application of this practice requires knowledge of
the total fluence and the neutron-flux spectrum. Refer to displaced atoms per unit volume, per unit mass, or per atom of
the material. Displacements per atom is the most common. The
Practice E 521 for determining these quantities.
1.6 The correlation of radiation effects data is beyond the number of dpa associated with a particular irradiation depends
on the amount of energy deposited in the material by the
scope of this practice.
1.7 This standard does not purport to address all of the neutrons, hence, depends on the neutron spectrum. (For a more
extended discussion, see Practice E 521.)
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro- 4.3 No simple correspondence exists in general between dpa
and a particular change in a material property. A reasonable
priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use. starting point, however, for relative correlations of property
changes produced in different neutron spectra is the dpa value
2. Referenced Documents
associated with each environment. That is, the dpa values
2.1 ASTM Standards: themselves provide a spectrum-sensitive index that may be a
E 170 Terminology Relating to Radiation Measurements useful correlation parameter, or some function of the dpa
and Dosimetry values may affect correlation.
E 521 Practice for Neutron Radiation Damage Simulation 4.4 Since dpa is a construct that depends on a model of the
by Charged-Particle Irradiation neutron interaction processes in the material lattice, as well as
E 560 Practice for Extrapolating Reactor Vessel Surveil- the cross section (probability) for each of these processes, the
lance Dosimetry Results, E706 (IC) value of dpa would be different if improved models or cross
E 853 Practice for Analysis and Interpretation of Light- sections are used. The calculated dpa cross section for ferritic
Water Reactor Surveillance Results, E706 (IA) iron, as given in this practice, is determined by the procedure
given in 6.3. This dpa cross section has been used as a neutron
exposure parameter for reporting a considerable body of
This practice is under the jurisdiction of ASTM Committee E-10 on Nuclear
irradiated materials data. Therefore, the cross section has not
Technology and Applications and is the direct responsibility of Subcommittee
been updated to reflect model or cross section improvements.
E10.05 on Nuclear Radiation Metrology.
Current edition approved June 15, 1994. Published August 1994. Originally
e1
published as E 693 – 79. Last previous edition E 693 – 79 (1985) .
Annual Book of ASTM Standards, Vol 12.02.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
E 693
The continued used of the same cross section is justified 6.2.1.1 If the DE are constant (as above 1 MeV in Table 1),
ik
pending improved damage theories that can determine expo- this becomes a simple average of the M groups in DE as
i i
sure parameters that do correspond to materials property follows:
changes.
M
i
~s ! 5 ~s ! (6)
(
d i d ik
M
k 5 1
i
5. Procedure
6.2.2 For a coarse group representation of f(E), the group
5.1 The displacement rate at time t is calculated as follows:
averages of s (E) should be weighted averages, unless such
‘ d
dpa/s 5 s ~E!f~E,t! dE (1)
* d weighting has been shown to have negligible effects. The ideal
weighting function is, of course, the actual spectrum f(E). For
where:
light-water reactor applications, a generalized spectrum is
s (E) 5 the displacement cross section for a particular
d
often used consisting of a fission spectrum plus a low energy
material, and
1/E tail. Let the weighting spectrum be designated by W (E).
f(E,t) dE 5 the fluence rate of neutrons in the energy
Then the recommended form and energy regimes are as
interval E to E + dE.
follows:
5.2 The exposure index, dpa, is then the time integrated
W(E)5 C /E E < 0.82 MeV
1/2 − E/1.4
value of the displacement rate, calculated as follows:
5 C E e E $ 0.82 MeV
t ‘
r
The constants C and C are arbitrary.
dpa 5 f ~t! s ~E!c~E,t! dE dt (2)
1 2
* tot * d
0 0
The group averages are then computed from the following
equation:
where:
f (t) 5 the time dependent fluence rate intensity, and M
i
tot
~s ! W~E !DE
c(E,t) 5 the fluence rate spectrum normalized to give unit (
d ik ik ik
k 5 1
~s ! 5 (7)
integral fluence rate when integrated over energy.
d i
M
i
W~E !DE
( ik ik
k 5 1
5.2.1 If the fluence rate spectrum is constant over the
where Ê 5 the average energy of the kth group, or
ik
duration, t , of the irradiation, then:
r
E [ ~E 1 E !/2 (8)
‘
ik ik 1 1 ik
dpa5f t s E c E dE5f t s¯ (3)
~ ! ~ !
tot r* d tot r d
6.2.3 It may be that the group structure of f (E) is not a
d
where s¯ 5 the spectrum-average displacement cross sec- subset of the group structure of s (E); that is, none of the
d d
tion. values of E coincide with E or E , or both. This should pose
ik i i+1
5.3 It is assumed for purposes of this practice that the no problem because the s (E) group structure is sufficiently
d
fluence f t and the spectrum (E) are known. fine that accurate interpolation is easily accomplished.
tot r
6.3 The recommended displacement cross section for iron
6. Calculation
s (E), is given as a function of energy in Table 1. The energy
d
6.1 The integral can be evaluated by a simple numerical
values chosen for the table entries are those of the SAND-II
integration as follows:
energy group structure (2). The table is a listing of energies and
N
‘ corresponding displacement cross sections. A graphical display
s ~E!f~E! dE 5 ~s ! f DE (4)
* d ( d i i i
of the displacement cross sections as a function of energy
i 5 1
appears in Fig. 1. The values of the displacement cross section
where (s ) and f are grouped-averaged values over the
d i i
are based on ENDF/B IV cross sections (3), the Robinson
interval E < E < E , and DE is the width of the interval and
i i+1 i
analytical function (4) of the Lindhard model of energy
is given by E − E .
i+1 i
partition between atoms and electrons (5), and the IAEA
6.2 The only computational problem, then, is to obtain
recommended conversion of damage energy to displacements
s (E) and f(E) in the same group structure. s (E) is available
d d
(6), as calulated in Ref (7).
(1) in the SAND-II group structure (included here as Table 1),
6.4 A single calculation suffices, of course, to characterize a
which is as fine or finer than the group structure in which f(E)
given spectrum in terms of the spectrum-averaged displace-
is generally available. Hence the problem is to collapse s (E)
d
ment cross section s¯ .
d
to match the f(E) group structure.
6.4.1 The quantity s¯ is a good measure of spectrum
6.2.1 If the f(E) group structure is sufficiently fine, for d
hardness if the thermal-to-fast ratio is not large. However, a
example, one-quarter lethargy or less, a simple group averag-
modified s can be used with any thermal-to-fast ratio, if it is
ing is sufficient: d
assumed that displacements are caused predominantly by
M
i
neutrons of energies greater than E . Then one can define s¯ (E
~s ! 5 ~s ! DE (5) o d
(
d i d ik ik
DE
k 5 1
i
>E ) by the following equation:
o
where M is the number of groups in s E between E and
‘
i d i
s ~E!f~E!dE
* d
E , and the DE [ E − E are the group widths.
i+1 ik ik+1 ik E
o
s ~E . E ! 5 (9)
d 0 ‘
f~E! dE
*
E
o
The boldface numbers in parentheses refer to the list of references appended to
this practice. and
E 693
FIG. 1 Displacement Cross Section for Iron, Plotted as a Function of Neutron Energy
dpa/s > s¯ ~E . E !3f~E .E ! (10)
spectrum determinations. For a discussion of the effect of the
d o o
energy dependence of s (E) on the relative accuracy of the dpa
A reasonable value for E is 0.01 MeV. The quantity s¯ (E > d
o d
calculation see Ref 7 and Practice E 521. Losses in the relative
0.01 MeV) is then a good index of spectrum hardness irrespec-
accuracy of the dpa calculation due to this effect are estimated
tive of the thermal-to-fast ratio.
to be less than 10 % for most reactor spectra (7). The relative
accuracy of the fluence-spectrum determination depends on the
7. Precision and Accuracy
method of determination. (For recommended methods see
7.1 Precision—For a neutron fluence spectrum in a fine-
E 10.05 Matrix Standard, E 706.) Any uncertainty in the total
group structure, the precision of the dpa calculation is esti-
fluence is, of course, reflected directly in the dpa calculation
mated to be better than 1 %. For typical coarse group struc-
(see 5.2.1).
tures, the need for more group averaging of s (E) will lead to
d
some loss of precision.
8. Damage Correlation
7.2 Accuracy:
8.1 This practice is concerned with standardizing a radia-
7.2.1 Absolute Accuracy—The absolute accuracy of the dpa
tion exposure unit. It is concerned only secondarily with the
calculation is not important when dpa is used as an exposure
correlation of damage produced in different environments. As
unit or correlation parameter for neutron irradiations, so long
stated in 4.1, the dpa is a logical first step in attempting to
as a standard practice is used by all laboratories in calculating
correlate displacement damage. Active research programs on
dpa. The absolute uncertainty is estimated to be 40 % or more
improving correlation methodology are in progress. Because
when applied to a light water reactor spectrum (less in a softer
many past data correlations have been based on “fast fluence”
spectrum). The major sources of error are the fluence spectrum,
(E > 1 MeV), this quantity should also be given, along with the
the reaction cross sections used in calculating s (E), the
d
dpa value, when expressing irradiation exposures. (For a
Lindhard model for the partition of energy between atoms and
general discussion of the damage correlation problem, see Ref
electrons, and the conversion of deposited energy to displace-
8.)
ments.
9. Keywords
7.2.2 Relative Accuracy—The relative accuracy of dpa cal-
culations for different environments depends on the energy
9.1 atomic displacements; cross section; irradiation; mate-
dependence of s (E) and on the relative accuracy of fluence- rials damage; neutron; steel
d
E 693
TABLE 1 Displacement Cross Section for Iron
A A
Energy, Sigma, Energy, Sigma, Energy, Sigma, Energy, Sigma, Energy, Sigma, Energy, Sigma,
MeV barns MeV barns MeV barns MeV barns MeV barns MeV barns
1.000E − 10 1.710E + 02 1.050E − 10 1.669E + 02 1.100E − 10 1.632E + 02 1.150E − 10 1.597E + 02 1.200E − 10 1.556E + 02 1.275E − 10 1.511E + 02
1.350E − 10 1.470E + 02 1.425E − 10 1.431E + 02 1.500E − 10 1.391E + 02 1.600E − 10 1.348E + 02 1.700E − 10 1.309E + 02 1.800E − 10 1.273E + 02
1.900E − 10 1.240E + 02 2.000E − 10 1.209E + 02 2.100E − 10 1.180E + 02 2.200E − 10 1.154E + 02 2.300E − 10 1.129E + 02 2.400E − 10 1.100E + 02
2.550E − 10 1.068E + 02 2.700E − 10 1.044E + 02 2.800E − 10 1.017E + 02 3.000E − 10 9.833E + 01 3.200E − 10 9.530E + 01 3.400E − 10 9.253E + 01
3.600E − 10 8.999E + 01 3.800E − 10 8.765E + 01 4.000E − 10 8.524E + 01 4.250E − 10 8.276E + 01 4.500E − 10 8.049E + 01 4.750E − 10 7.840E + 01
5.000E − 10 7.646E + 01 5.250E − 10 7.466E + 01 5.500E − 10 7.298E + 01 5.750E − 10 7.141E + 01 6.000E − 10 6.980E + 01 6.300E − 10 6.816E + 01
6.600E − 10 6.662E + 01 6.900E − 10 6.519E + 01 7.200E − 10 6.364E + 01 7.600E − 10 6.198E + 01 8.000E − 10 6.045E + 01 8.400E − 10 5.903E + 01
8.800E − 10 5.770E + 01 9.200E − 10 5.646E + 01 9.600E − 10 5.529E + 01 1.000E − 09 5.407E + 01 1.050E − 09 5.279E + 01 1.100E − 09 5.161E + 01
1.150E − 09 5.050E + 01 1.200E − 09 4.921E + 01 1.275E − 09 4.778E + 01 1.350E − 09 4.647E + 01 1.425E − 09 4.526E + 01 1.500E − 09 4.397E + 01
1.600E − 09 4.262E + 01 1.700E − 09 4.138E + 01 1.800E − 09 4.025E + 01 1.900E − 09 3.920E + 01 2.000E − 09 3.823E + 01 2.100E − 09 3.733E + 01
2.200E − 09 3.649E + 01 2.300E − 09 3.571E + 01 2.400E − 09 3.480E + 01 2.550E − 09 3.379E + 01 2.700E − 09 3.301E + 01 2.800E − 09 3.215E + 01
3.000E − 09 3.109E + 01 3.200E − 09 3.014E + 01 3.400E − 09 2.926E + 01 3.600E − 09 2.846E + 01 3.800E − 09 2.772E + 01 4.000E − 09 2.695E + 01
4.250E − 09 2.617E + 01 4.500E − 09 2.545E + 01 4.750E − 09 2.479E + 01 5.000E − 09 2.418E + 01 5.250E − 09 2.361E + 01 5.500E − 09 2.308E + 01
5.750E − 09 2.258E + 01 6.000E − 09 2.207E + 01 6.300E − 09 2.155E + 01 6.600E − 09 2.107E + 01 6.900E − 09 2.061E + 01 7.200E − 09 2.012E + 01
7.600E − 09 1.960E + 01 8.000E − 09 1.912E + 01 8.400E − 09 1.866
...
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