ASTM E521-23

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: E521 − 23
Standard Practice for
Investigating the Effects of Neutron Radiation Damage
Using Charged-Particle Irradiation
This standard is issued under the fixed designation E521; 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.
INTRODUCTION
This practice is intended to provide the nuclear research community with recommended procedures
for using charged-particle irradiation to investigate neutron radiation damage mechanisms as a
surrogate for neutron irradiation. It recognizes the diversity of energetic-ion producing devices, the
complexities in experimental procedures, and the difficulties in correlating the experimental results
with those produced by reactor neutron irradiation. Such results may be used to estimate density
changes and the changes in microstructure that would be caused by neutron irradiation. The
information can also be useful in elucidating fundamental mechanisms of radiation damage in reactor
materials.
1. Scope
Section
Apparatus 4
1.1 This practice provides guidance on performing charged-
Specimen Preparation 5 – 10
Irradiation Techniques (including Helium Injection) 11 – 12
particle irradiations of metals and alloys, although many of the
Damage Calculations 13
methods may also be applied to ceramic materials. It is
Postirradiation Examination 14 – 16
generally confined to studies of microstructural and micro- Reporting of Results 17
Correlation and Interpretation 18 – 22
chemical changes induced by ions of low-penetrating power
1.4 The values stated in SI units are to be regarded as
that come to rest in the specimen. Density changes can be
measured directly and changes in other properties can be standard. No other units of measurement are included in this
standard.
inferred. This information can be used to estimate similar
changes that would result from neutron irradiation. More
1.5 This standard does not purport to address all of the
generally, this information is of value in deducing the funda-
safety concerns, if any, associated with its use. It is the
mental mechanisms of radiation damage for a wide range of
responsibility of the user of this standard to establish appro-
materials and irradiation conditions.
priate safety, health, and environmental practices and deter-
mine the applicability of regulatory limitations prior to use.
1.2 Where it appears, the word “simulation” should be
1.6 This international standard was developed in accor-
understood to imply an approximation of the relevant neutron
dance with internationally recognized principles on standard-
irradiation environment for the purpose of elucidating damage
ization established in the Decision on Principles for the
mechanisms. The degree of conformity can range from poor to
Development of International Standards, Guides and Recom-
nearly exact. The intent is to produce a correspondence
mendations issued by the World Trade Organization Technical
between one or more aspects of the neutron and charged-
Barriers to Trade (TBT) Committee.
particle irradiations such that fundamental relationships are
established between irradiation or material parameters and the
2. Referenced Documents
material response.
2.1 ASTM Standards:
1.3 The practice appears as follows:
C859 Terminology Relating to Nuclear Materials
E170 Terminology Relating to Radiation Measurements and
Dosimetry
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 June 1, 2023. Published July 2023. Originally approved contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
in 1976. Last previous edition approved in 2016 as E521 – 16. DOI: 10.1520/ Standards volume information, refer to the standard’s Document Summary page on
E0521-23. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E521 − 23
E821 Practice for Measurement of Mechanical Properties fluence.
During Charged-Particle Irradiation heavy ion—used here to denote an ion of mass >4.
E910 Test Method for Application and Analysis of Helium light ion—an arbitrary designation used here for conve-
Accumulation Fluence Monitors for Reactor Vessel Sur- nience to denote an ion of mass ≤4.
veillance
T —an effective value of the deposited energy required to
d
E942 Guide for Investigating the Effects of Helium in displace an atom from its lattice site. Usual unit is eV.
Irradiated Metals
σ (E)—an energy-dependent displacement cross section; σ¯
d d
denotes a spectrum-averaged value. Usual unit is barns.
2.2 ICRU Documents:
σ (E)—an energy-dependent damage energy cross section;
ICRU 60 Fundamental Quantities and Units for Ionizing
de
σ¯ denotes a spectrum-averaged value. Usual unit is barns-eV
Radiation
de
or barns-keV.
ICRU 85a Fundamental Quantities and Units for Ionizing
Radiation
4. Significance and Use
3. Terminology
4.1 A characteristic advantage of charged-particle irradia-
3.1 Definitions of Terms Specific to This Standard:
tion experiments is the precise, individual control over most of
3.1.1 Descriptions of relevant terms are found in Terminol-
the important irradiation conditions such as dose, dose rate,
ogy C859 and Terminology E170.
temperature, and quantity of gases present. Additional attri-
3.2 Definitions:
butes are the lack of induced radioactivation of specimens and,
3.2.1 damage energy, T —that portion of the energy lost
dam
in general, a substantial compression of irradiation time, from
by an ion moving through a solid that is transferred as kinetic
years to hours, to achieve comparable damage as measured in
energy to atoms of the medium; strictly speaking, the energy
displacements per atom (dpa). An important application of
transfer in a single encounter must exceed T .
d
such experiments is the investigation of radiation effects that
3.2.2 displacement—the process of dislodging an atom from
may occur in materials exposed to environments which do not
its normal site in the lattice. currently exist, such as in first wall materials used in fusion
reactors.
3.2.3 path length—the total length of path measured along
the actual path of the particle.
4.2 The primary shortcoming of ion bombardments stems
3.2.4 penetration depth—a projection of the range along the
from the damage rate, or temperature dependences of the
normal to the entry face of the target. microstructural evolutionary processes in complex alloys, or
both. It cannot be assumed that the time scale for damage
3.2.5 projected range—the projection of the range along the
evolution can be comparably compressed for all processes by
direction of the incidence ion prior to entering the target.
increasing the displacement rate, even with a corresponding
3.2.6 range—the distance from the point of entry at the
shift in irradiation temperature. In addition, the confinement of
surface of the target to the point at which the particle comes to
damage production to a thin layer just (often ;1 μm) below the
rest.
irradiated surface can present substantial complications. It
3.2.7 stopping power (or stopping cross section)—the en-
must be emphasized, therefore, that these experiments and this
ergy lost per unit path length due to a particular process;
practice are intended for research purposes and not for the
usually expressed in differential form as − dE/dx.
certification or the qualification of materials.
3.2.7.1 Discussion—The stopping power is commonly di-
4.3 This practice relates to the generation of irradiation-
vided into an electronic and a nuclear component (ICRU).
induced changes in the microstructure of metals and alloys
3.2.8 straggling—the statistical fluctuation due to atomic or
using charged particles. The investigation of mechanical be-
electronic scattering of some quantity such as particle range or
havior using charged particles is covered in Practice E821.
particle energy at a given depth.
3.3 Symbols:
5. Apparatus
3.3.1 A , Z —the atomic weight and the number of the
1 1
5.1 Accelerator—The major item is the accelerator, which
bombarding ion.
in size and complexity dwarfs any associated equipment.
A , Z —the atomic weight and number of the atoms of the
2 2
Therefore, it is most likely that irradiations will be performed
medium undergoing irradiation.
at a limited number of sites where accelerators are available (a
depa—damage energy per atom; a unit of radiation expo-
1-MeV electron microscope may also be considered an accel-
sure. It can be expressed as the product of σ¯ and the fluence.
de
erator).
dpa—displacements per atom; a unit of radiation exposure
giving the mean number of times an atom is displaced from its
5.2 Fixtures, for holding specimens during irradiation are
lattice site. It can be expressed as the product of σ¯ and the
d
generally custom-made as are devices to measure and control
particle energy, particle fluence rate (recommended terminol-
ogy for the deprecated term “flux”), and specimen temperature.
ICRU Report 60 has been superseded by ICRU Report 85a on Fundamental
Decisions regarding apparatus are therefore left to individual
Quantities and Units for Ionizing Radiation, October 2011. Both of these documents
workers with the request that accurate data on the performance
are available from International Commission on Radiation Units and Measurements
(ICRU), 7910 Woodmont Ave., Suite 800, Bethesda, MD 20814. of their equipment be reported with their results.
E521 − 23
6. Composition of Specimen expressed in terms of the principal orthogonal natural strain
components (ε , ε , ε ) or the geometric shape changes that will
1 2 3
6.1 An elemental analysis of stock from which specimens
allow the reader to compute the strains; (3) procedure used to
are fabricated should be known. The manufacturer’s heat
reach the total strain level (for example, number of rolling
number and analysis are usually sufficient in the case of
passes and reductions in each); (4) strain rate; and (5) defor-
commercially produced metals. Additional analysis should be
mation temperature, including an estimate of temperature
performed after other steps in the experimental procedure if
changes caused by adiabatic work.
there is cause to believe that the composition of the specimen
8.2.1 Many commonly used deformation processes (for
may have been altered. It is desirable that uncertainties in the
example, rolling and swaging) tend to be nonhomogeneous. In
analyses be stated and that an atomic basis be reported in
such cases the strain for each pass can be best stated by the
addition to a weight basis.
dimensions in the principal working directions before and after
7. Pre-irradiation Heat Treatment of Specimen each pass. The strain rate can then be specified sufficiently by
stating the deformation time of each pass.
7.1 Temperature and time of heat treatments should be well
controlled and reported. This applies to intermediate anneals
9. Pre-irradiation Metallography of Specimen
during fabrication, especially if a metal specimen is to be
9.1 A general examination by light microscopy and
irradiated in the cold-worked condition, and it also applies to
transmission-electron microscopy should be performed on the
operations where specimens are bonded to metal holders by
specimen in the condition in which it will be irradiated. In
diffusion or by brazing. The cooling rate between annealing
some cases, this means that the examination should be done on
steps and between the final annealing temperature and room
specimens that were mounted for irradiation and then un-
temperature should also be controlled and reported.
mounted without being irradiated. The microstructure should
7.2 The environment of the specimen during heat treatment
be described in terms of grain size, phases, precipitates,
should be reported. This includes description of container,
dislocations, and inclusions.
measure of vacuum, presence of gases (flowing or steady), and
9.2 A section of a representative specimen cut parallel to the
the presence of impurity absorbers such as metal sponge. Any
particle beam should be examined by light microscopy. Atten-
discoloration of specimens following an anneal should be
tion should be devoted to the microstructure within a distance
reported.
from the incident surface equal to the range of the particle, as
7.3 High-temperature annealing of metals and alloys from
well as to the flatness of the surface.
Groups IV, V, and VI frequently results in changes, both
10. Surface Condition of Specimen
positive and negative, in their interstitial impurity content.
Since the impurity content may have a significant influence on
10.1 The surface of the specimen should be clean and flat.
void formation, an analysis of the specimen or of a companion
Details of its preparation should be reported. Electropolishing
piece prior to irradiation should be performed. Other situations,
of metallic specimens is a convenient way of achieving these
such as selective vaporization of alloy constituents during
objectives in a single operation. The possibility that hydrogen
annealing, would also require a final analysis.
is absorbed by the specimen during electropolishing should be
investigated by analyses of polished and nonpolished speci-
7.4 The need for care with regard to alterations in compo-
mens. Deviations in the surface from the perfect-planar condi-
sition is magnified by the nature of the specimens. They are
tion should not exceed, in dimension perpendicular to the
usually very thin with a high exposed surface-to-volume ratio.
plane, 10 % of the expected particle range in the specimen.
Information is obtained from regions whose distance from the
surface may be small relative to atomic diffusion distances.
10.2 The specimen may be irradiated in a mechanically
polished condition provided damage produced by polishing
8. Plastic Deformation of Specimen
does not extend into the region of postirradiation examination.
8.1 When plastic deformation is a variable in radiation
11. Dimension of Specimen Parallel to Particle Beam
damage, care must be taken in the geometrical measurements
used to compute the degree of deformation. The variations in
11.1 Specimens without support should be thick enough to
dimensions of the larger piece from which specimens are cut
resist deformation during handling. If a disk having a diameter
should be measured and reported to such a precision that a
of 3 mm is used, its thickness should be greater than 0.1 mm.
standard deviation in the degree of plastic deformation can be
11.2 Supported specimens may be considerably thinner than
assigned to the specimens. A measuring device more accurate
unsupported specimens. The minimum thickness should be at
and precise than the common hand micrometer will probably
least fourfold greater than the distance below any surface from
be necessary due to the thinness of specimens commonly
which significant amounts of radiation-produced defects could
irradiated.
escape. This distance can sometimes be observed as a void-free
8.2 The term cold-worked should not stand alone as a zone near the free surface of an irradiated specimen.
description of state of deformation. Every effort should be
12. Helium
made to completely characterize the deformation. The param-
eters which should be stated are: (1) deformation process (for 12.1 Injection:
example, simple tension or compression, swaging, rolling, 12.1.1 Alpha-particle irradiation is frequently used to inject
rolling with applied tension); (2) total extent of deformation, helium into specimens to simulate the production of helium
E521 − 23
−8
during neutron irradiations where helium is produced by should be done in a vacuum of 1.33 μPa (10 torr) or smaller.
transmutation reactions. Helium injection may be completed Oil-diffusion pumps should be cold-trapped to restrict the
before particle irradiation begins. It may also proceed incre- passage of hydrocarbons into the target chamber and beam
mentally during interruptions in the particle irradiation or it tube. The target chamber should be baked periodically or as
may proceed simultaneously with particle irradiation. The last needed to limit the buildup of contaminants on the walls of the
case is the most desirable as it gives the closest simulation to chamber and that a cold-trapped, liquid nitrogen or similarly
neutron irradiation. Some techniques for introducing helium cold anti-contamination device be installed near the target to
are set forth in Guide E942. trap as many contaminants as possible. The visual appearance
12.1.2 The influence of implantation temperature on how of the specimen after irradiation and the vacuum maintained
helium is distributed in the material (that is, whether helium is during irradiation should be reported.
dispersed in the lattice, in small clusters, in bubbles, etc.) is
13.2 Specimen Temperature:
known to be important. The consequences of the choice of
13.2.1 The temperature of the specimen should not be
injection temperature on the simulation should be evaluated
allowed to vary by more than 610 °C. It should be controlled,
and reported.
measured, and recorded continuously during irradiation. Infra-
12.2 Analysis and Distribution:
red sensors offer a direct method of measuring actual tempera-
12.2.1 Analysis of the concentration of helium injected into
ture of the specimen surface. If thermocouples are used, they
the specimens should be performed by mass spectrometry.
should be placed directly on the specimen to avoid temperature
Using this technique, the helium content is determined by
gradients and interfaces between the thermocouple and the
vaporizing a helium-containing specimen under vacuum, add-
specimen, which will produce a difference between the ther-
3 4 3
ing a known quantity of He, and measuring the He/ He ratio.
mocouple reading and the actual temperature of the specimen
This information, along with the specimen weight, will give the
volume being irradiated. A thermocouple should not be ex-
average helium content in the specimen. The low-level He
posed to the particle beam because spurious signals may be
addition is obtained by successive expansion through cali-
generated.
brated volumes. The mass spectrometer is repeatedly calibrated
13.2.2 Beam heating should be minimized relative to non-
for mass fractionation during each series of runs by analyzing
beam heating to minimize temperature fluctuations of the
3 4
known mixtures of He and He. Other methods of
specimen due to fluctuations in beam fluence rate and energy.
measurement, such as the nondestructive α-α scattering
If a direct measurement of specimen temperature during
technique, may be employed. Refer to Test Method E910 and
irradiation cannot be made, then the specimen temperature
Guide E942 for additional details.
should be calculated. Details of the calculation should be fully
12.2.2 In many experiments, attempts are made to achieve
reported.
uniformity of helium content within the damage region by
13.3 Choice of Particle—Since the accelerated particles
varying the incident energy of the alpha-particle beam and by
usually come to rest within the specimen, the possibility of
avoiding fluence variations on the specimen surface. The
significant alterations in specimen composition exists with
success of these attempts should be measured by analyzing
concomitant effects on radiation damage. If metallic ions are
separate sections of the specimen for helium. It may be
used, they should be of the major constituents of the specimen.
necessary to use several companion specimens for this pur-
Electron irradiation poses no problems in this regard.
pose. Variation of helium concentration through the thickness
of the specimen as well as variations across the specimen can
13.4 Choice of Particle Energy:
also be nondestructively measured with the α-α scattering
13.4.1 Three criteria should be considered in the choice of
technique.
particle energy:
12.3 Alpha-Particle Damage—Alpha-particle irradiation
(1) The range of the particle should be large enough to
produces some displacement damage in the specimen. This
ensure that the region to be examined possesses a pre-
damage, which changes as the specimen is heated for irradia-
irradiation microstructure that is unperturbed by its proximity
tion by other particles, may influence the radiation effects
to the surface.
subsequently produced. Therefore, in those cases where helium
(2) The point defect concentration during irradiation in the
injection precedes the particle irradiation, a specimen should
observed volume should not differ substantially from that
be brought to the irradiation temperature in the same manner as
expected of irradiated volumes located far from free surfaces.
if it were going to be irradiated and then examined by
(3) The energy deposition gradient parallel to the beam
transmission-electron microscopy at ambient temperature to
across the volume chosen for observation should be small over
characterize the microstructure.
a distance that is large compared to typical diffusion distances
of defects at the temperature of interest. The best measure of
13. Irradiation Procedure
surface influence is the observation of denuded zones for the
13.1 Quality of Vacuum—Contamination of the specimen microstructural feature of interest. The width of denuded zones
surface by oxidation or deposition of foreign matter and for voids can be significantly larger or smaller than those
diffusion of impurities into the specimen must be avoided. A observed for dislocations. The volume of the specimen to be
–6
vacuum of 133 μPa (10 torr) or smaller should be maintained examined should lie well beyond the denuded zone because
during irradiation for most nonreactive metals. High- steep concentration gradients of point defects may exist on the
temperature irradiation of metals from Groups IV, V, or VI boundary of such zones. Gradients in the deposited energy can
E521 − 23
be reduced by rocking the specimen (varying the angle is used (1, 2). It should be noted that pulsed operation is an
between the beam and the specimen surface), but local time- inherent characteristic of many accelerators.
dependent fluence rate variations will exist.
14. Damage Calculations
13.4.2 The nominal energy of the accelerated particle
should be verified periodically by calibration experiments. 14.1 Scope—This section covers methods and problems of
determining displacement rates for ions and electrons in the
These experiments should be reported and an uncertainty
energy ranges most likely to be employed in simulations of
assigned to the energy.
fission and fusion reactor radiation effects. These are 0.1 to 70
13.5 Purity of Beam:
MeV for ions and 0.2 to 10 MeV for electrons, although not all
13.5.1 The use of a bending magnet is an effective way of
energies within these ranges are treated with equal precision.
selecting a particular ion for transit through the beam tube to
To provide the basis for subsequent descriptions of neutron-
the specimen. However, it is possible that the selected ions will
charged particle correlations, the calculation of displacement
interact with foreign atoms in the beam tube, causing foreign rates in neutron irradiations is also treated.
atoms to strike the specimen also and altering the charge and
14.2 Energy Dissipation by Neutrons and Charged
energy on the selected ion.
Particles—See Appendix X1.
13.5.2 A good vacuum in the beam tube will eliminate the
14.3 Particle Ranges—Ions suffer negligible deflections in
significance of these effects, and therefore this vacuum should
encounters with electrons; hence, if electron losses dominate,
be monitored during irradiation. A discoloration of the speci-
differences between range, projected range, and path length
men surface could indicate a problem in this regard even
will be small. Furthermore, energy dissipation in this case is by
though a satisfactory vacuum exists in the vicinity of the
a large number of low-energy-exchange events, so range
specimen.
straggling will be small and, at a given depth (except near end
of range), energy straggling will be small. These conditions
13.6 Fluence Rate:
apply to light ions for energies down to the tens of keV range,
13.6.1 The particle fluence rate on the specimen should be
but only at much higher energies for heavy ions such as nickel.
recorded continuously during irradiation and integrated with
14.3.1 Light Ions:
time to give the fluence. This is particularly important since
14.3.1.1 Stopping powers of light ions are easiest to calcu-
most accelerators do not produce a constant fluence rate.
late in the range of several MeV to several tens of MeV, but
Fluence rate and fluence should be reported as particles/m ·s
these calculations cannot be done accurately from first prin-
and particles/m . For the case where the particle comes to rest
ciples (3-5). At lower energies, heavy reliance must be placed
within the specimen, the specimen holder assembly should be
on the few experimental measurements of stopping powers.
designed as a Faraday cup. The fluence rate measured this way
Several tabulations of stopping powers and the path lengths
should be checked with a true Faraday cup that can be moved
deduced from them exist (6-10). A modern Monte Carlo code,
in and out of the beam. If the particles are transmitted through
SRIM, can also be easily used to compute the required ranges
the specimen, a Faraday cup can be positioned on the exit side
and stopping powers (11).
for fluence rate measurement. Variations in fluence rate during
14.3.1.2 Although the work by Janni (9) appears to be the
the irradiation should be reported.
most comprehensive one for protons, experimental range data
(12) have been produced that are in disagreement with his
13.6.2 It is desirable that the fluence rate be the same
tables for 1-MeV protons incident on steel. In view of the better
everywhere on the specimen surface. The actual fluence rate
agreement of the tables of Williamson et al. (7) with these data,
variation in a plane parallel to the specimen surface should be
it was recommended (13) that the latter tables be used for the
measured and considered when interpreting results of postir-
path length of protons in iron and nickel and their alloys.
radiation examination. A beam profile monitor is recommended
Ranges can be obtained from these path length values by
for this purpose. It is possible to mitigate the effects of a
subtracting a correction for multiple scattering as given by
spatially nonhomogeneous beam by moving the beam over the
Janni, but this correction is only −2.2 % at 0.1 MeV, decreasing
surface of the specimen during irradiation. A defocused beam
to −0.8 % at 5 MeV for protons incident on iron. Ranges for
should be used; the maximum translation should be less than
iron should be valid also for steels and nickel-base alloys to
the beam half-width. The uniformity or nonuniformity of the
within the accuracy of the tables (several percent). The
beam should be reported with the method used for this purpose.
referenced tables should be consulted for data on proton ranges
13.6.3 Rastering (periodic scanning) of a focused beam over
in other metals (the distinction between path length and range
the specimen will subject the specimen to periodic local
is generally ignored) and for deuteron and alpha ranges (10).
fluence rate variations. It is recommended that a rastered beam
Range estimates can conveniently be made for deuterons and
be avoided for the simulation of a constant neutron fluence
alphas in terms of those for protons for energies at which the
rate, although it may be appropriate for the simulation of a
stopping power is primarily electronic by employing the
pulsed neutron fluence rate. Radiation-induced defect struc-
following equations:
tures that evolve under such pulsed conditions can differ
substantially from those that evolve in a constant fluence rate.
Recent work has identified conditions in which significant 4
The boldface numbers in parentheses refer to the list of references appended to
microstructural differences are observed when a rastered beam this practice.
E521 − 23
α p
R E >R E/4 (1) Using this relation to evaluate the proportionality factors for
~ ! ~ !
d p a second material with atomic number Z and atomic mass A
2 2
R E >2 R E/2 (2)
~ ! ~ !
yields:
These approximations agree with tabulated values to within
dE/dx >0.357 p Z /A keV/µm (6)
? ion 0 2 2
better than 5 % for alpha energies >8 MeV and deuteron
or:
energies >2 MeV, the accuracy increasing with increasing
energy.
3.57 p Z /A MeV/cm
0 2 2
14.3.2 Heavy Ions: 2
dE/dx >0.000435 E MeV p Z /A keV/µm
~ !
? rad 0 2 2
14.3.2.1 Heavy ions suffer increasing range straggling as the
or:
energy is decreased—the spread in range is a large fraction of
the mean range at 1 MeV. This corresponds to an increasing 0.00435 E MeV p Z /A MeV/cm (7)
~ !
0 2 2
fraction of energy lost as kinetic energy imparted to atoms
where p is the mass density. For example, these relations
(nuclear stopping) as opposed to excitation and ionization of
give:
electrons (electronic stopping).
dE/dx >13 MeV/cm
? ion
14.3.2.2 Ranges of heavy ions in the low MeV range cannot
be calculated with high accuracy. A semi-empirical tabulation
and:
of ranges by Northcliffe and Schilling is available (6), and a
dE/dx >4 MeV/cm
? rad
more recent tabulation of range distributions and stopping
powers is contained in a series of books edited by Ziegler and
for 10-MeV electrons in iron. For 1-MeV electrons in iron,
coworkers (10). Note that the ranges in Ref (6) (actually path
this procedure overestimates the radiation loss by a factor of 3
lengths) have been corrected for nuclear stopping, whereas
but at this energy the ionization loss accounts for over 90 % of
their tabulated stopping powers are for electronic stopping
the energy loss.
only.
14.4 Damage Energy Calculations:
14.3.2.3 Ranges are generally tabulated as areal densities,
14.4.1 Damage Energy—A necessary (but not sufficient)
for example, mg/cm ; as such they are invariant to changes in
condition for consistency between displacement damage esti-
mass density. In particular, they apply to material containing
mates for neutrons and charged particles is that the same
voids. The linear range is obtained by dividing the areal density
energy partition model be used in calculating the damage
by the mass density—the latter must of course be the actual
energy. The currently recommended model (13, 16, 17) is due
density, including a correction for void volume if present. An
to Lindhard et al. (18); the expression for the damage energy
increase in range straggling and energy straggling is caused by
T (T) lost by a knock-on of initial kinetic energy T is:
dam
the production of voids during an irradiation (14).
T T 5 T 11kg ε (8)
~ ! @ ~ !#
dam
14.3.2.4 Ranges can be computed with a code developed by
Johnson and Gibbons (15). It is included as a subroutine in the
When the incident ion and the lattice ion are the same:
E-DEP-1 Code (see 14.4.3.1). It permits evaluations of pro-
2⁄3 1⁄2
k 5 0.1337Z ⁄A
1 1
jected ranges and range straggling as well. More recently, the 7⁄3
ε 5 T⁄ 0.08693 Z keV
~ !~ !
SRIM code (11) has been used for such calculations.
Following Robinson and coworkers (19, 20):
14.3.3 Electrons:
¾ 1⁄6
g ε 5 ε10.40244ε 13.4008ε (9)
~ !
14.3.3.1 Electrons are subject to many large-angle scatter-
ing events, hence range straggling is severe. In radiation
The general expression for ε, when the incident and lattice
damage studies, however, the primary concern is with the
atoms are different, is given by:
passage of electrons through relatively thin targets in which the
A T a
fractional energy loss is small. This loss can be estimated for
ε 5 (10)
A 1A Z Z e
~ !
1 2 1 2
many purposes using the following general prescription. The
2 ⅓
9π
principal loss mechanisms are ionization and radiation. If x is
⅔ ⅔ 2½
a 5 a ~Z 1Z ! (11)
S D
o 1 2
the projected range and N and Z are the atomic density and
atomic number of the target, respectively: −9
where a is the Bohr radius (5.292 × 10 cm), e is the
o
−10
dE/dx α NZ (3) electronic charge (4.803 × 10 statcoulomb), and the sub-
? ion
scripts 1 and 2 on the atomic numbers (Z) and atomic masses
dE/dx α NZ E (4)
? rad
(A) denote the incident ion and the target atoms, respectively.
for E > 1 MeV. Hence, given values for some reference These units require that the kinetic energy, T, in Eq 10 be
material, energy dissipation for any other material can be expressed in ergs.
estimated. A convenient reference material is lead, in which
14.4.1.1 Strictly speaking, this expression for the energy
both mechanisms contribute approximately equally at 10 MeV:
partitioning model, as derived by Robinson, can only be
applied to monatomic systems, and was developed for the
dE/dx >dE/dx >16 MeV/cm (5)
? ion ? rad
cases where Z = Z . However, it can reasonably be applied as
1 2
· or 1.6 keV/µm 10 MeV in Pb long as these two values are sufficiently close (19). In the case
~ !
E521 − 23
of alloy (polyatomic) targets, an effective Z should be calcu- This can be converted to damage energy per cubic centime-
lated by weighting the alloy constituents by their respective ter per second by multiplying by N, the atom density. The
atomic fractions. For polyatomic lattice materials where the cumulative damage energy density is obtained by integrating
atoms have significant differences in the Z, this use of an over the irradiation time.
effective Z has limitations (21). In addition, the Lindhard 14.4.2.4 Since, for most reactor spectra, the damage energy
4⁄3
model is limited to energies T less than about 25·Z · A (in contributed by neutrons of energy less than a few keV is
1 1
negligible, the depa for neutron irradiations is generally inde-
keV) (19).
pendent of the value used for T (see further discussion under
d
14.4.2 Neutrons:
14.4.4.1).
14.4.2.1 The calculation of damage energy for neutron
14.4.3 Heavy Ions:
irradiations is most conveniently expressed in terms of an
14.4.3.1 In general, the damage energy depends on the ion
energy-dependent damage energy cross section, σ (E). This
de
energy so it will vary with penetration. A simple computer
expresses the damage energy per atom per unit neutron fluence;
code, E-DEP-1 (26), was developed and extensively applied
a convenient unit is eV-barns. In calculating this cross section,
for calculating damage energy versus depth distributions for
all possible reactions that can transfer sufficient energy to an
heavy ions. It made the simplifying assumption of approximat-
atom of the medium to displace it must be considered. These
ing energy straggling by using the range straggling theory of
include elastic scattering, inelastic scattering, neutron multipli-
Lindhard et al. (27). Also implicit is the additional assumption
cation reactions (for example, (n,2n)), charged-particle produc-
that the ranges of knock-on atoms are negligible; that is, all
tion reactions (for example, (n,p)), and absorption reactions
damage energy is deposited in the immediate vicinity of the
(n,γ). Most of the necessary data are included in the ENDF/B-
point at which the incident ion produces the knock-on atom
VIII.0 files (22), and it is recommended that these be used in
(energy transport is neglected). Beeler (28) has performed
damage calculations.
computer experiments and Winterbon (29) has made analytical
14.4.2.2 The treatment of the kinematics for these reactions
calculations to estimate the effect of this assumption on the
has been documented (23-25); the result is a cross section shape of the damage energy-depth profile. The effect is not
dσ(T,E) for the production, by all possible reactions, of a
large for experiments that effectively integrate over macro-
primary knock-on atom (PKA) of energy T by a neutron of scopic intervals (for example, 50 nm) of the profile. The more
energy E. The damage energy cross section is then simply the modern Monte Carlo code SRIM (11, 30, 31) is now most
integral of the product of this primary cross section and the commonly used to perform these calculations. The use of
damage energy, T , associated with a PKA of energy T: SRIM permits more sophisticated analyses to be performed
dam
than does EDEP-1. SRIM is relatively fast and can be used for
T
m
σ E 5 T dσ T,E /dT dT) eV 2 barns (12)
~ ! * @ ~ ! # ~ !
de dam
both light- and heavy-ion irradiations as long as nuclear
reactions are not involved.
The upper limit of the integral, T , is the maximum possible
m
14.4.3.2 The damage-energy density increases with depth,
PKA energy, in the absence of charged particle emission. For
reaches a peak, and then drops rapidly to zero. In the vicinity
elastic scattering reactions, the conservation of energy and
of the peak, the uncertainty in the E-DEP-1 calculation must be
momentum imply that the maximum transferred energy results
assumed large—perhaps 25 to 50 % (13). Nearer the specimen
from a head-on collision and is given by:
surface where the gradient and damage energy is less, the
T 5 4A /~A 11! E (13)
uncertainty is perhaps 20 %. The uncertainty in SRIM calcu-
m 2 2
lations may be lower. Measurements of observed damage
where the atomic weight is expressed in terms of neutron
versus depth are highly recommended if the intent is to make
masses, as in ENDF/B-6 notation. Higher values of T are
m
damage observations in the peak damage region.
possible in some charged-particle-out reactions that are exoer-
14.4.3.3 In applying E-DEP-1, the user has the option of
gic. The lower limit in Eq 12 is zero since, even when the PKA
describing electronic stopping of the incident ion using the
energy is less than T , an effective displacement energy, the
d
expression for k given by Lindhard et al. (27), or reading in
non-ionizing portion of the PKA energy is deposited in the
some other value. k is the proportionality factor between the
material lattice as phonon energy, while not resulting in a
electronic stopping power and the ion velocity. SRIM includes
lattice atom displacement and the production of a Frenkel pair.
a more modern description of electronic stopping. Lindhard et
Note that the integral in Eq 12 is over the PKA energy while T ,
d
al. gives the approximate expression:
based on the Kinchin-Pease and NRT formulations, refers to
1⁄6 ½ 3⁄2
k 5 0.0793 Z Z Z /Z A /A (15)
~ !
the non-ionizing damage energy that corresponds to the energy 1 1 2 2 0
of this recoil atom. When the incident neutron energy, E,
in which:
exceeds several keV, the difference between using T and 0 in
d
⅔ ⅔ ⅔
Z 5 Z 1Z , A 5 A A /~A 1A ! (16)
1 2 0 1 2 1 2
this equation is small.
14.4.2.3 To determine the damage energy density in a It is suggested that better k values may be determined
neutron-irradiated material, the neutron fluence rate spectrum directly from the tabulated stopping powers of Northcliffe and
φ(E) must be known. The damage energy deposition per atom Schilling (6).
(depa) per second is then: 14.4.4 Light Ions:
` 14.4.4.1 Damage energy estimates for light ions at low
depa/s 5 * φ ~E!σ ~E!dE (14)
de
0 energies can be made in a more straightforward manner. The
E521 − 23
mean energy, E , at depth x is first determined from tables as more than offset the decrease in the elastic contribution relative
x
follows. Let E be the incident ion energy and R(E) the mean to coulomb scattering. That is, Eq 2 may significantly under-
range of an ion of energy E. Assume range and energy estimate the damage energy cross section for light ions above
straggling are negligible. Then the residual range of an ion at ;10 MeV.
x is R(E ) = R(E ) − x. Given E and x, one can find R(E ) in 14.4.5 Electrons—The concept of damage-energy density is
x 0 0 0
the range-energy tables, calculate R(E ), and thus determine E not particularly helpful in electron irradiations except for very
x x
from the tables. A knowledge of E permits application of the high electron energies because mean knock-on energies gen-
x
Rutherford scattering cross section, dσ (T,E ), which gives the erally do not greatly exceed displacement thresholds. However,
R x
approximate number of knock-ons in the interval dT at the damage energy can be estimated from Oen’s tables (35) as
knock-on energy T that is produced by an ion of energy T > 2T σ , where σ is Oen’s displacement cross section.
dam d d d
E (32): Note that Oen used the sharp threshold displacement model of
x
2 2 original Kinchin and Pease (36) rather than Lindhard or NRT
dσ T,E 5 Bγ /E dT/T (17)
~ ! ~ !~ !
R x x
threshold treatment (18).
where:
14.5 Conversion of Damage Energy to DPA:
2 2 2 2
B = 4πa E (A /A )Z Z ,
0 R 1 2 1 2
14.5.1 Model:
γ Z = effective charge of the moving ion,
1 1
14.5.1.1 A secondary displacement model describes the
a = 0.053 nm, and
number of displacements N produced in a cascade initiated by
d
E = 13.6 eV.
R
a PKA of kinetic energy T. The simplified model recommended
A convenient expression for γ given by Bichsel (33) is
here is based on Ref (19) and has been adopted by both the
2 3
γ = 1 − exp (−1.316 y + 0.1112 y − 0.0650 y ); y = 100β ⁄Z ⁄3
1 IAEA (16) and researchers in the U.S. (13, 17) (for iron, nickel,
where β(<< 1) is the ratio of the particle velocity to that of
and their alloys):
light. Expressed as a function of particle energy, y = (4.63 ⁄Z ⁄3
T,T
N 5 0 d
) [E (MeV)/A ] ⁄2 . The damage energy cross section is given by
d
x 1
integrating over the product of the number of events producing
T #T,2T ⁄β
d d
N 5 1
a knock-on of energy T [dσ (T,E )] and the damage energy d
R x
associated with the knock-on, T :
dam
N 5 βT ⁄2T T $ 2T ⁄β (20)
d dam d d
T T T
~ !
m dam
σ ~E ! 5 ~Bγ /E ! dt (18)
*
de x x 21 2
T T
~ ! T
dam d
The previously recommended values for iron, steel, and
nickel-base alloys are β = 0.8 and T = 40 eV, or N = 10 T ,
Unlike Eq 12, the lower limit of this integral which includes
d d dam
if T is expressed in keV. While the value assigned to the
an explicit form for the cross section is the mean energy
dam
effective displacement energy, T , is somewhat arbitrary, it is
required to displace an atom, that is, to deliver a damage
d
most important that a specific secondary displacement model
energy of T . From Eq 8, this corresponds to a recoil energy, T,
d
be used for the purpose of standardization; hence the model
such that T (T) = T , and thus, the lower integration bound is
dam d
–1
presented in Eq 20 is recommended. There is some error
given by the inverse function, T (T ). T is the upper limit
dam d m
incurred in using Eq 20 due to the neglect of inelastic energy
and represents the maximum possible energy transferred to an
losses at very low energies. Robinson and Oen have discussed
atom through an elastic scattering and is given by:
this in detail and provide an expression for a simple correction
T 5 4A A /~A 1A ! E (19)
m 1 2 1 2 x
factor (37).
Then depa/s is the product of the particle fluence rate φ and
14.5.1.2 The actual displacement energy depends on the
σ . If the atom density is N and the irradiation time is t, the
direction of ejection of the atom (38) (see Appendix X1). The
de
damage energy density (eV/cm ) is given by φtNσ .
value of T used in Eq 20 should represent an average taken
de d
14.4.4.2 The Rutherford scattering cross section describes
over all of the ejection directions. Sufficient data to permit
only coulomb scattering. Another source of elastic scattering calculation of T exist for only a few metals. In any event, the
d
for light ions above several MeV is nuclear potential scattering. value of 40 eV recommended for steels is based largely on
Large-angle coulomb scattering is rare and hence large-angle computer simulation of low-energy cascades, rather than di-
elastic scattering will be dominated by potential scattering rectly on displacement threshold measurements. The point here
above several MeV, as discussed by Logan et al. (34) for is that there is no basis for assigni
...