ASTM E721-22

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: E721 − 22
Standard Guide for
Determining Neutron Energy Spectra from Neutron Sensors
for Radiation-Hardness Testing of Electronics
This standard is issued under the fixed designation E721; 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.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
1.1 This guide covers procedures for determining the
energy-differential fluence spectra of neutrons used in
2. Referenced Documents
radiation-hardness testing of electronic semiconductor devices.
2.1 ASTM Standards:
The types of neutron sources specifically covered by this guide
E170 Terminology Relating to Radiation Measurements and
are fission or degraded energy fission sources used in either a
Dosimetry
steady-state or pulse mode.
E261 Practice for Determining Neutron Fluence, Fluence
1.2 This guide provides guidance and criteria that can be
Rate, and Spectra by Radioactivation Techniques
applied during the process of choosing the spectrum adjust-
E262 Test Method for Determining Thermal Neutron Reac-
ment methodology that is best suited to the available data and
tion Rates and Thermal Neutron Fluence Rates by Radio-
relevant for the environment being investigated.
activation Techniques
1.3 This guide is to be used in conjunction with Guide E720
E263 Test Method for Measuring Fast-Neutron Reaction
to characterize neutron spectra and is used in conjunction with
Rates by Radioactivation of Iron
Practice E722 to characterize damage-related parameters nor-
E264 Test Method for Measuring Fast-Neutron Reaction
mally associated with radiation-hardness testing of electronic
Rates by Radioactivation of Nickel
semiconductor devices.
E265 Test Method for Measuring Reaction Rates and Fast-
Neutron Fluences by Radioactivation of Sulfur-32
NOTE 1—Although Guide E720 only discusses activation foil sensors,
any energy-dependent neutron-responding sensor for which a response E266 Test Method for Measuring Fast-Neutron Reaction
function is known may be used (1).
Rates by Radioactivation of Aluminum
NOTE 2—For terminology used in this guide, see Terminology E170.
E393 Test Method for Measuring Reaction Rates by Analy-
1.4 The values stated in SI units are to be regarded as
sis of Barium-140 From Fission Dosimeters
standard. No other units of measurement are included in this E523 Test Method for Measuring Fast-Neutron Reaction
standard.
Rates by Radioactivation of Copper
E526 Test Method for Measuring Fast-Neutron Reaction
1.5 This standard does not purport to address all of the
Rates by Radioactivation of Titanium
safety concerns, if any, associated with its use. It is the
E704 Test Method for Measuring Reaction Rates by Radio-
responsibility of the user of this standard to establish appro-
activation of Uranium-238
priate safety, health, and environmental practices and deter-
E705 Test Method for Measuring Reaction Rates by Radio-
mine the applicability of regulatory limitations prior to use.
activation of Neptunium-237
1.6 This international standard was developed in accor-
E720 Guide for Selection and Use of Neutron Sensors for
dance with internationally recognized principles on standard-
Determining Neutron Spectra Employed in Radiation-
ization established in the Decision on Principles for the
Hardness Testing of Electronics
Development of International Standards, Guides and Recom-
E722 PracticeforCharacterizingNeutronFluenceSpectrain
Terms of an Equivalent Monoenergetic Neutron Fluence
This guide is under the jurisdiction of ASTM Committee E10 on Nuclear
for Radiation-Hardness Testing of Electronics
Technology and Applications and is the direct responsibility of Subcommittee
E10.07 on Radiation Dosimetry for Radiation Effects on Materials and Devices.
Current edition approved July 1, 2022. Published July 2022. Originally approved
in 1980. Last previous edition approved in 2016 as E721 – 16. DOI: 10.1520/ For referenced ASTM standards, visit the ASTM website, www.astm.org, or
E0721-22. contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
The boldface numbers in parentheses refer to the list of references at the end of Standards volume information, refer to the standard’s Document Summary page on
this guide. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E721 − 22
E844 Guide for Sensor Set Design and Irradiation for ingofelectronicdevicesinordertorelateradiationeffectswith
Reactor Surveillance device performance degradation.
E944 Guide for Application of Neutron Spectrum Adjust-
4.2 This guide describes the factors which must be consid-
ment Methods in Reactor Surveillance
eredwhenthespectrumadjustmentmethodologyischosenand
E1018 Guide for Application of ASTM Evaluated Cross
implemented.Although the selection of sensors (foils) and the
Section Data File
determination of responses (activities) is discussed in Guide
E1297 Test Method for Measuring Fast-Neutron Reaction
E720,theexperimentshouldnotbedivorcedfromtheanalysis.
Rates by Radioactivation of Niobium
In fact, it is advantageous for the analyst conducting the
E1855 Test Method for Use of 2N2222A Silicon Bipolar
spectrum determination to be closely involved with the design
Transistors as Neutron Spectrum Sensors and Displace-
of the experiment to ensure that the data obtained will provide
ment Damage Monitors
the most accurate spectrum possible. These data include the
following:(1)measuredresponsessuchastheactivitiesoffoils
3. Terminology
exposed in the environment and their uncertainties, (2) re-
3.1 Definitions: The following list defines some of the sponse functions such as reaction cross sections along with
special terms used in this guide: appropriate correlations and uncertainties, (3) the geometry
andmaterialsinthetestenvironment,and(4)atrialfunctionor
3.1.1 effect—the characteristic which changes in the sensor
prior spectrum and its uncertainties obtained from a transport
when it is subjected to the neutron irradiation. The effect may
calculation or from previous experience.
be the reactions in an activation foil.
3.1.2 prior spectrum—an estimate of the neutron spectrum
5. Spectrum Determination with Neutron Sensors
obtained by transport calculation or otherwise and used as
input to a least-squares adjustment. 5.1 Experiment Design:
5.1.1 The primary objective of the spectrum characteriza-
3.1.3 response—the magnitude of the effect. It can be the
tion experiment should be the acquisition of a set of response
measured value or that calculated by integrating the response
values (activities) from effects (reactions) with well-
function over the neutron fluence spectrum. The response is an
characterized response functions (cross sections) with re-
integral parameter mathematically approximated by a discrete
sponses which adequately define (as a set) the fluence values at
summation, R5 R, where R is the response in each differ-
( i i
i
energies to which the device to be tested is sensitive. For
ential energy region at E of width ∆E.
i i
silicon devices in fission-driven environments the significant
3.1.4 response function—the set of values of R in each
i neutron energy range is usually from 10 keV to 15 MeV. Lists
differentialenergyregiondividedbytheneutronfluenceinthat
of suitable reactions along with approximate sensitivity ranges
differential energy region, that is, the set f = R/(Φ(E)∆E).
i i i i are included in Guide E720. Reactor sensor set design is also
discussed in Guide E844. The foil set may include the use of
3.1.5 sensor—an object or material (sensitive to neutrons)
responses with sensitivities outside the energy ranges needed
the response of which is used to help define the neutron
for the DUT to aid in interpolation to other regions of the
environment. A sensor may be an activation foil.
spectrum. For example, knowledge of the spectrum below
3.1.6 spectrum adjustment—the process of changing the
10 keV aids in the determination of the spectrum fraction
shape and magnitude of the neutron energy spectrum so that
above that energy.
quantitiesintegratedoverthespectrumagreemorecloselywith
5.1.2 An example of the difficulty encountered in ensuring
their measured values. Other physical constraints on the
response coverage (over the energy range of interest) is the
spectrum may be applied.
following: If fission foils cannot be used in an experiment
3.1.7 trial function—a neutron spectrum which, when inte-
because of licensing problems, cost, or radiological handling
235 237 239
grated over sensor response functions, yields calculated re-
difficulties (especially with U, Np, or Pu), a large gap
sponses that can be compared to the corresponding measured
may be left in the foil set response between 100 keV and
responses.
2 MeV—a region important for silicon and gallium arsenide
damage(seeFigs.A1.1andA2.3ofPracticeE722).Inthiscase
3.2 Abbreviations:
two options are available. First, seek other sensors to fill the
3.2.1 DUT—device under test.
gap (such as silicon devices sensitive to displacement effects
3.2.2 ENDF—evaluated nuclear data file.
93 93m
(see Test Method E1855)), Nb(n,n') Nb (see Test Method
103 103m
3.2.3 NNDC—National Nuclear Data Center (at
E1297)or Rh(n,n') Rh. Second, devote the necessary
Brookhaven National Laboratory).
resources to determine a trial function that is close to the real
spectrum. In the latter case it may be necessary to carry out
3.2.4 RSICC—Radiation Safety Information Computation
transport calculations to generate a prior spectrum which
Center (at Oak Ridge National Laboratory).
incorporatestheuseofuncertaintyandcovarianceinformation.
3.2.5 TREE—transient radiation effects on electronics.
5.1.3 Other considerations that affect the process of plan-
ning an experiment are the following:
4. Significance and Use
5.1.3.1 Are the fluence levels low and of long duration so
4.1 It is important to know the energy spectrum of the that only long half-life reactions are useful? This circumstance
particular neutron source employed in radiation-hardness test- can severely reduce the response coverage of the foil set.
E721 − 22
(aluminum), E393 (barium-140 from fission foils), E523 (copper), E526
5.1.3.2 Arehighgamma-raybackgroundspresentwhichcan
(titanium), E704 (uranium-238), E705 (neptunium-237), and E1297 (nio-
also affect the sensors (or affect the devices to be tested)?
bium).
5.1.3.3 Can the sensors be placed so as to ensure equal
exposure?This may require mounting the sensors on a rotating
5.2.2 One important characteristic of the set of equations
fixture in steady-state irradiations or performing multiple
(Eq 1) is that with a finite number of sensors, n, which yield n
irradiations with monitor foils to normalize the fluence be-
equations, there is no unique solution. Exact solutions to
tween runs.
equations (Eq 1) may be readily found, but are not generally
5.1.3.4 Do the DUT or the spectrum sensors perturb the
considered useful. When the least-squares adjustment method
neutron spectrum?
is used, equations (Eq 1) are supplemented by the constraint
5.1.3.5 Are response functions available that account for
that the solution spectrum must be approximately equal to the
self-shielding for all sensors using (n,γ) or non-threshold (n,f)
prior spectrum. This additional constraint guarantees that the
reactions, unless the material is available in a dilute form of
set of equation is overdetermined and that a unique least-
certified composition?
squares solution does exist. The tolerances of the approxima-
5.1.3.6 Can the fluence and spectrum seen in the DUT test
tions are dependent on the specified variances and covariances
later be directly scaled to that determined in the spectrum
ofthepriorspectrum,theresponsefunctions,andthemeasured
characterization experiment (by monitors placed with the
responses. When other adjustment methods are used it must be
tested device)?
assumed that the range of physically reasonable solutions can
5.1.3.7 Can the spectrum shape and intensity be character-
be limited to an acceptable degree.
ized by integral parameters that permit simple intercomparison
5.2.3 Neutron spectra generated from sensor response data
of device responses in different environments? Silicon is a
may be obtained with several types of spectrum adjustment
semiconductor material whose displacement damage function
codes. One type is linear least-squares minimization used by
is well established. This makes spectrum parameterization for
codes such as STAY’SL (2) or the logarithmic least-squares
damage predictions feasible for silicon.
minimization as used by LSL-M2 (3). When the spectrum
5.1.3.8 What region of the spectrum contributes to the
adjustments are small, these methods yield almost identical
responseoftheDUTandisthespectrumwelldeterminedinall
energy regions that affect device performance? results. Another type is the iterative method, an example of
5.1.3.9 How is the counting system set up for the determi- which is SAND II (4). If used properly and with sufficient,
nationoftheactivities?Forexample,arethereenoughcounters
high-quality data, this method will usually yield nearly the
available to handle up to 25 reactions from a single exposure? same values as the least-squares methods for the primary
(This may require as many as six counters.) Or can the
integral parameters discussed in Practice E722.
available system only handle a few reactions before the
NOTE 4—Another class of codes often referred to as Maximum Entropy
activities have decayed below detectable limits?
(5) has also been used for this type of analysis.
5.1.4 Once the experimental opportunities and constraints
have been addressed and the experiment designed to gather the 5.2.4 Appendix X1 and Appendix X2 discuss in some detail
most useful data, a spectrum adjustment methodology must be the implementation and the advantages and disadvantages of
chosen.
the two approaches as represented by LSL-M2 and SAND-II.
5.2 Spectrum Adjustment Methodology:
5.3 Least-Squares Code Characteristics:
5.2.1 After the basic measured responses, response
5.3.1 The least-squares codes, represented by STAY’SL (2)
functions, and trial or prior spectrum information have been
and LSL-M2 (3), use variance and covariance data for the
assembled, apply a suitable spectrum adjustment procedure to
measured responses, response functions, and prior spectrum.
reach a solution that satisfies the criteria of the chosen
The STAY’SL code finds the unique maximum likelihood
procedure. It must also meet other constraints, such as, the
solution spectrum when the uncertainties are assumed to be
fluence spectrum must be positive and defined for all energies.
distributed according to a normal distribution. The LSL-M2
The solution is the energy-dependent spectrum function, Φ(E),
code finds the unique maximum likelihood solution spectrum
which approximately satisfies the series of Fredholm equations
when the uncertainties are assumed to be distributed according
of the first kind represented by Eq 1 as follows:
to a multivariate lognormal distribution. The codes allow not
`
only the prior spectrum but also the responses and the response
R 5 σ ~E!Φ~E! dE 1# j# n (1)
*
j j
functions to be adjusted in a manner constrained by their
where:
individual uncertainties and correlations in order to find the
R = measured response of sensor j, most likely solution. In principle this approach provides the
j
σ(E) = neutron response function at energy E for sensor j,
best estimate of a spectrum and its uncertainties. The least-
j
Φ(E) = incident neutron fluence versus energy, and
squares method is described more fully in Guide E944 and in
n = number of sensors which yield n equations.
Appendix X2.
NOTE3—GuidesE720andE844providegeneralguidanceonobtaining
5.3.2 The solution to the linear least-squares spectrum
a suitable set of responses (activities) when foil monitors are used.
adjustment problem is given in matrix form by:
Practice E261 and Test Method E262 provide more information on the
data analysis that generally is part of an experiment with activation
' T T T 21
Φ 2 Φ 5 C S S C S 1 S C S 1 C R 2 R
~ ! ~ !
0 Φ Φ Φ Φ Φ Σ Σ Σ R m 0
0 0 0 0 0 0 0 0 m
monitors. Specific instructions for some individual monitors can be found
in Test Methods E263 (iron), E264 (nickel), E265 (sulfur-32), E266 (2)
E721 − 22
where: scoringerrorsfromaMonteCarlotransportcalculationanduse
these as a measure of the uncertainty in the trial spectrum.All
Φ' = a column vector of the adjusted groupwise fluences,
uncertainties, and in particular, uncertainties in the reactor
Φ = a column vector of the prior spectrum fluences,
C = the covariance matix of the prior spectrum, modeling, material densities, and response functions should be
Φ
S = the matrix of sensitivities of the calculated responses
represented in the input uncertainty. The value of the chi-
Φ
to the prior fluences,
squared (χ ) parameter may be used as a good indication of the
S = the matrix of sensitivities of the calculated responses
Σ consistency of the input data (including the uncertainty data).
to the response functions,
5.4 Suitability of the Least-Squares Adjustment Codes—The
C = the covariance matrix of the response functions,
Σ
least-squares codes are particularly well suited to situations in
C = the covariance matrix of the measured responses,
R
m
which the environment is fairly well characterized physically
R = a column vector of the measured responses,
m
so that a prior spectrum can be calculated. They work best
R = a column vector of the responses calculated using the
prior spectrum and response functions, when detailed transport calculated spectra are available for use
as the prior spectra for the analysis. However, it is often
superscript T indicates the transpose of a matrix, and
difficult to obtain a statistically defensible covariance matrix
superscript –1 indicates the inverse of a matrix.
for these spectra. In such cases, the specified uncertainties in
5.3.3 Further details, including the sensitivity matrix
the prior spectrum should be large enough to ensure that the
entries, may be found in Ref (2). In the case of logarithmic
measured response uncertainties are smaller than their calcu-
least-squares, the fluences and the responses are replaced by
lated prior uncertainties. In principle, a sensitivity analysis
their natural logarithms, and the covariance matrices are
based on the radiation transport code methodology could be
replaced by the fractional covariance matrices; see Ref (3).
used to provide the prior spectrum uncertainty and energy-
5.3.4 The input variance and covariance matrix quantities
dependent correlation, but this is not an easy analysis and is
are not always well known, and some may have to be
seldom attempted.
estimated. The analyst must understand that his estimates of
5.5 Iterative Code Characteristics:
these quantities can affect the results.
5.5.1 The “iterative” codes use a trial function supplied by
5.3.5 No least-squares code in the form distributed by code
libraries conveniently handles the effects of covers over the the analyst and integrate it over the response functions of the
foils even though the use of covers is strongly recommended. sensorsexposedintheunknownenvironmenttopredictasetof
See Subsection 7.2 of Guide E720 and X1.5.1 of this standard calculated responses for comparison with the measured values.
for more information. The calculated responses are obtained from Eq 1. The code
obtainstheresponsefunctionsfromalibrary.SeeGuideE1018
5.3.6 The code automatically weights the data according to
for the recommendations in the selection of dosimetry-quality
uncertainties. Therefore, data with large uncertainties can be
cross sections.
used in the analysis, and will have the appropriately small
influence on the results.
5.5.2 The code compares the measured and calculated
5.3.7 The solution spectrum shape must correspond fairly
responses for each effect and invokes an algorithm designed to
well to the prior spectrum (within one or two standard alter the trial function so as to reduce the deviations between
deviations) if the results are to be reliable (6). The prior
themeasuredandcalculatedresponses.Theprocessisrepeated
spectrum determines the solution spectrum when its uncertain- with code-altered spectra until the standard deviation drops
ties are so small that the uncertainties of the prior calculated
below a specified value, at which time the coder declares that
responses are small compared to those of the measured a solution has been obtained and prepares a table of the last
responses. Conversely, the prior spectrum does not strongly
spectrum. This should not be the end of the process unless the
constrain the solution spectrum when the prior calculated initial trial was very close to the final result. In each iteration,
response uncertainties are large compared to the measured
the SAND II-type code will alter the trial most rapidly where
response uncertainties. See Ref (3). the foil set has the highest response. If the trial is incompatible
with the measurements, the spectrum can become distorted in
5.3.8 If a transport code calculation of the spectrum is used
a very unphysical manner.
asthestartingpointfortheanalysis,thenthismethodologycan
be useful for adjusting spectra at a different location from that
5.5.3 For example, if a trial function predicts an incorrect
in which the foils were exposed. If the transport calculation
gold activity, it may alter the spectrum by orders of magnitude
includes a location where an experiment can be conducted and
at the gold high-response resonance at 5 eV while leaving the
a similar one where such an experiment would be difficult or
trialspectrumaloneintheimmediatevicinity.Theanalystmust
impossible(suchasinsideatestfixtureorotherstructure),then
recognize that the trial must be changed in a manner suggested
this type of code can be used to adjust both spectra simulta-
by the previous result. For example, if a peak develops at the
neously. In accepting the results for the unmonitored location,
gold resonance, this suggests that the trial spectrum values are
it is important that the transport calculation be adjusted
too low in that whole energy region. A new trial drawn
minimally. A prior covariance matrix between the fluence
smoothly near the spectrum values where the sensor set has
spectra at the two locations is needed.
high response may improve the solution. This direct modifica-
5.3.9 The analyst must be careful the input variances and tion becomes an outer iteration on the spectrum adjustment
covariances, including those associated with the prior process, as described in Refs (7, 8). The outer iteration
spectrum, are realistic. It is not sufficient to take statistical methodology coupled with good activity data is sometimes so
E721 − 22
successful that the form of the initial trial does not overly rial. There is considerable evidence that for some spectra the
influence the integral results. calculated exponential attenuation is not accurate because of
5.5.4 For any of the iterative type codes to succeed at scattering.
producing a spectrum that is both representative of the mea-
6. Discussion and Comparison of Methodology
sured data and likely to be close to the true spectrum of
Characteristics
neutrons that caused the activation data, experience has shown
that the following are important: (1) the use of sensors with
6.1 The least-squares codes are superior because it should
well-established response functions (≤ 68 % for spectrum-
be possible to directly incorporate all that is known about the
averaged cross sections), (2) a sensor set that has good
test environment and about the response functions to arrive at
responseoveralltheimportantregionsofthespectrum,and(3)
the most likely solution in a least-squares sense. The codes
sufficiently accurate measured responses (on the order of
provide statistically defensible output with uncertainties when
65 %).Nodirectuseismadeofuncertaintydata(varianceand
covariance data is available for all the input quantities. The
covariance information) that exists for each cross section, of
iterative codes do not propagate uncertainties nor make use of
uncertainty in the trial spectrum, or in the uncertainties in the
any variance or covariance information which may exist.
measured responses. These uncertainties can vary greatly
6.2 Considerable experience with both approaches has dem-
among sensors or environments. It follows that data with large
onstrated that they yield approximately the same integral
uncertainties should not be used in the final stages of this
parameter values when applied to the methodology in Practice
methodology because it can cripple the final results.
E722, provided that adequate and accurate primary experimen-
NOTE 5—Response data that exhibits a strong disagreement with other
tal information is available. This means the analyst must have
data in the data ensemble can be very useful in the early stages of an
access to a set of carefully measured responses, usually
analysis. For example, if the activity of a particular reaction is incompat-
ible with the other foils in the spectrum adjustment process, it can indicate activation data. The associated set of responses functions,
one of two important possibilities. First, if it is a reaction whose
usually activation cross sections, must cover a broad range of
energy-dependent cross section is well known and has repeatedly demon-
energies. And, the response functions for the measured data
strated compatibility in the past, an experimental or transcription error is
must be well established over these energy ranges.
suggested.Second,iftheactivitymeasurementwasaccuratelycarriedout,
and this reaction has repeatedly demonstrated incompatibility in the same
6.3 Transient radiation effects testing of electronics (TREE
direction in other spectra determinations in different environments, an
testing) is carried out in a wide variety of different environ-
incorrect cross section or energy-specific counting calibration error is
ments that are often customized with complicated filters and
indicated (8). A number of specific cross section problems have been
shields. For these cases, detailed transport calculations can be
uncovered by analysis of incompatibility data. But in the construction of
the neutron spectrum, these “bad” reactions should not be used with a
time-consuming and expensive. The user may not be aware of
method that does not incorporate uncertainty data.
the total assemblage of material structure that affects the
5.6 Suitability of the Iterative Adjustment Codes: radiation environment.
5.6.1 Iterative codes usually do not have a capability to
6.4 Theiterativetypecodeperformsatitsbestwithaccurate
weight the responses according to uncertainties, do not provide
response data and well-known response functions because the
error or uncertainty analysis, do not use variance or covariance
range of acceptable solutions is then severely restricted, and
information, and provide no direct quantification of the output
the acceptance criterion of measured-to-calculated activity
uncertainties for any calculated quantities. However, it is
values can be set to a low value.Also, incompatible responses,
possible to assign errors in the spectrum in appropriate energy
perhaps caused by experimental errors, stand out clearly in the
regions using perturbation analysis. (Also, computerized per-
results. The least-squares type code seems much more forgiv-
turbation and random draw from response error may be
ing because wide variances are assigned to less well-known
utilized.) The analyst perturbs the trial spectrum upwards and
cross sections and activities, so marginal data can be more
downwards in each energy region and observes to what degree
easilytolerated.Forbothmethods,averygoodtrialfunctionor
the code brings the two trials into agreement.This is, however,
prior spectrum is required when limited or imprecise measured
a laborious process and has to be interpreted carefully. In the
responses are available. In these cases, the solution cannot be
resonance region where foil responses are spiked, the code will
allowed to deviate very much from the trial because less use
only yield agreement at resonances where there exists high
should be made of the measured data.
response. The analyst must not only interpolate the spectrum
6.5 SAND II should not be used to generate trial functions
values between high response regions but also the spectrum
for LSL-M2, because the SAND II solution spectrum is
uncertainties. This step can be rationalized with physical
correlated to the activities, but the LSL method assumes there
arguments based on the energy-dependence of cross sections
is no such correlation.
butitisdifficulttojustifymathematically.Thissituationfurther
supports the arguments for maximizing response coverage. In
6.6 Neither methodology can be used indiscriminately and
addition, it is usually the uncertainties of integral parameters without careful monitoring by a knowledgeable analyst. The
that are of primary importance, not the uncertainty of Φ(E)at
analyst must not only apply physical reasoning but must
individual energy values examinethedatatodetermineifitisofadequatequality.Atthe
5.6.2 Covers are used over many of the foils to restrict the veryleasttheanalystmustevaluatewhatisseeninaplotofthe
response ranges, as is explained in Guide E720. The SAND II solution spectrum. Available versions of the SAND II code
code handles the attenuations in the covers in a simple manner provide less subsidiary information than least-squares codes
by assuming exponential attenuation through the cover mate- can supply, particularly with regards to uncertainties. More
E721 − 22
detailed discussions of the LSL-M2 and SAND II methodolo- 8. Keywords
gies are provided in the appendixes.
8.1 neutron sensors; neutron spectra; radiation-hardness
testing; spectrum adjustment
7. Precision and Bias
7.1 Precision and bias statements are included in each of the
appendixes.
APPENDIXES
(Nonmandatory Information)
X1. APPLICATION OF THE LSL-M2 CODE
X1.1 The Least-Squares Method, LSL-M2 X1.2.5 An error estimate of the groupwise fluences, with
correlations, is essential to LSL-M2, but is not always readily
X1.1.1 This appendix provides guidance for the application
available to the analyst. The error analysis distributed with the
of the LSL-M2 adjustment code to hardness testing of elec-
code may be applied, with caution, to pool-type reactors if
tronic devices.The code is described in Refs (9, 10). However,
nothing else is available, but it is not applicable to fast-burst
it is designed for commercial power reactor pressure vessel
reactors or Cf sources and should not be used. However, the
surveillance applications and the documentation was devel-
LSL-M2 code can be applied to most reactors used for testing
oped accordingly. This appendix provides guidance for those
of electronic devices whether an error estimate of the spectrum
circumstances where the documentation is inadequate or inap-
is available or not. The practical aspects of this will be
propriate for hardness-testing applications.
described in X1.4.
X1.2 Introduction
X1.3 Constraints on the Use of the Code
X1.2.1 As Eq 1 implies, three basic data sets are required in
X1.3.1 The LSL-M2 code is distinguished by its use of
the determination of the neutron energy-fluence spectrum: (1)
lognormal distributions for all the parameters of interest. This
a set of measured responses (see Guide E720 for guidance on
imposesthephysicallyrealisticconstraintthatallquantitiesare
foil selection), (2) energy-response functions, and (3)an
positiveandreal.Theformulationoftheequationsdescribedin
approximation to the solution.
Section 3 of Guide E944 were all converted to logarithmic
X1.2.2 Several codes have been developed which imple-
counterparts by the writers of LSL-M2. As stated in the
ment a least-squares approach to the determination of the
manual, care should be taken to input covariances as fractional
neutron spectrum from sensor data. The least-squares codes
δx δx
i j
covariances:theexpectedvaluesof .Inthesamefashion,
require a minimum of three additional data sets in the form of
x x
i j
uncertainty estimates for all the above data, complete with the the output uncertainties are actually logarithmic ratios of the
correlations between all the data. These additional data are
standarddeviationtotheexpectedvalue.Theprimaryoutputof
used to establish uncertainty estimates on the output data. See LSL-M2 is not the adjusted spectrum, but rather the damage-
Subsection 3.2 of Guide E944 for more information.
related integral parameters with their errors. This feature is
ideally suited to the calculation of silicon damage as defined in
X1.2.3 The LSL-M2 code (10) is one example of a least-
Practice E722.
square code package which is distributed with a suitable set of
NOTE X1.1—There is little difference between these logarithmic ratios
auxiliary data (cross sections and covariance files) to permit its
and the more normal values if the percentages quoted are less than 10 %.
application for the adjustment of reactor pressure vessel
But, as the ratio of (observed/actual) increases, the LSL ratio diverges
neutron spectra. As part of the REAL exercises (11-13) the
from the non-logarithmic ratio.
International Atomic Energy Agency (IAEA) compiled and
X1.3.1.1 Dosimetry cross-section sets and associated cova-
distributed a Neutron Metrology File NMF-90 (14) which
riance matrices are available with the LSL-M2 code package.
includes versions of the MIEKE (15) and STAY’SL (2)
The cross sections distributed by RSICC with this code have
least-square adjustment codes along with compatible cross
been derived from ENDF/B-V evaluations (10). The newer
sections and sample input decks. These three codes are
IRDFF-II distribution (16) is recommended as a replacement
examples of least-square adjustment codes which are available
for the code’s built-in data sets. In most cases, it contains
to the general community and include interfaces with suitable
newer evaluations for the actual cross sections and much more
cross section libraries.
refined evaluations of the associated covariance data for each
X1.2.4 An adequate prior or theoretical prediction of the reaction.
fluence spectrum (with its covariance matrix) is often the most X1.3.1.2 The response data is obtained through the applica-
difficult information set to obtain. If a transport calculation is tion of Guides E720 and E844, Practice E261, and Test
available, it may be a generic type of run such as a leakage Methods E262, E263, E264, E265, E393, E704, and E705.The
spectrum from the reactor or a criticality calculation that uncertainty estimate for each response should not be simply an
provides a typical spectrum for some location. estimate of the counting statistics, but rather should include all
E721 − 22
contributors of uncertainty to the measured value, such as X1.4.4.1 TheparameterAcanbeviewedasameasureofthe
uncertainties in counting efficiency, branching ratio, foil group-to-groupstiffnessofthecalculation.Inawell-moderated
composition, mass, experimental positioning, etc. Correlations spectrum, the lower energy groups are all populated by
between reactions may be important, particularly when the down-scattering events, the group-to-group correlations are
therefore strong and a large value for A “near 1.0” is justified.
same radioactive product is measured on the same detector.
Such would be appropriate for a TRIGA-type reactor, or the
X1.3.1.3 The code requires a prior fluence or fluence-rate
epithermal groups of a GODIVA-like reactor. But, the high-
spectrum and an estimate of its uncertainties with correlations.
energy part of all reactor spectra is dominated by the fission-
Experience has shown that the better the quality of the input
neutron production process, and therefore the uncertainties are
spectrum, the better the quality of the results from LSL-M2.
dominated by those in the fission-spectrum representation
There is no ideal substitute for a transport calculation com-
used. In these spectra a small value of A “near 0.0” is
bined with a sensitivity analysis for error propagation.
appropriate. See Ref (6).
However, a parametric model derived from reactor physics
may be utilized, with typical expected uncertainties, for fast
X1.4.5 The uncertainties assigned to each group (the diago-
and light water reactor leakage spectra to estimate covariance nal of the matrix) may have a marked effect on the results. If
matrices (17). This method can give acceptable results if the
there is no knowledge as to what these uncertainties may be,
uncertainties assigned to the calculation are appropriately then the only alternative is to carry out a series of runs to
chosen. (The guidance in X1.4.3 may be followed.) determine the sensitivity of the results to the selection of
uncertainties. The value of χ per degree of freedom should be
monitored for unrealistically high and low values. Those runs
X1.4 Operation of the Code
with such unrealistic values of χ per degree of freedom should
X1.4.1 The application of the code is adequately described
be discarded or serve as boundaries.
in the documentation. The six data sets required by LSL-M2,
X1.4.6 Very large assigned uncertainties for all groups (100
along with the damage functions, are stored in individual files
to 1000 %) in the input spectrum will produce output only
and the code’s output is designed to go into individual files.An
dependent upon the responses and response functions so long
adequate method of assigning file names and keeping track of
as the entire energy range is covered by the reaction cross
input and output files is required.
sections. The temptation to use these results will be great for
X1.4.2 If a covariance analysis, such as described by
this reason. However, this should be considered as a limiting
Maerker (9),ofatransportcalculationforasimilarreactortype
case. This solution spectrum should produce a very low value
and location is available, it can be used. The Maerker analysis
for the χ per degree of freedom. If it does not, then there is a
will be generally applicable to water-moderated reactors such
verylargeerrorinoneormoreoftheresponses.Largeassigned
as some positions of pool-type reactors. It is not applicable to
uncertainties may be appropriately used for limited neutron
GODIVA or similar fast-fission types of reactor spectra.
energy ranges, for example, the thermal or epithermal part of a
Similarly, the covariance data with the reference spectra
fast-reactor spectrum.
provided as part of IRDFF-II (16) may or may not be
X1.4.7 Very small assigned uncertainties in the input spec-
appropriate depending upon the type of test configuration and
trum will produce adjusted spectra which are essentially the
neutron source used.
same as the calculated spectrum (regardless of what is in the
covariance matrix). While this will normally produce abnor-
X1.4.3 Subsection 5.3 of Guide E944 describes the general
mally high chi-squared per degree of freedom values, it may
principles for constructing usable covariance matrices for
not if there are only a few sensor responses available.
fluence spectra when a full sensitivity analysis is not available.
However, the uncertainty assignments to the results may be
Equation 14 of Guide E944 is a general representation of a
unrealistically low. This is the other limiting case.
distance formula. Several functions that satisfy the require-
ments of Eq. 14 follow in the standard. Experience has shown
X1.4.8 When a good estimate of the input uncertainties on
that this type of procedure produces acceptable results. For the
the group fluences is not available, the uncertainties on the
purposes of hardness testing, the following distance formula is
resulting damage parameters are not well defined regardless of
suggested:
the value of χ per degree of freedom. This is true unless it can
be shown in a particular case that these uncertainties are
abs ln E 2 ln E
@ ~ ! ~ !#
i k
c 5 exp 2 (X1.1)
S D
ik
insensitive to the uncertainties of the prior fluences.
A
X1.4.9 The LSL-M2 code documentation recommends that
X1.4.4 If Eq X1.1 is used, it then only remains to provide
the prior fluence values be normalized in an absolute fashion.
guidanceontheproperselectionofavaluefortheparameter A.
However, if a generic calculation is used, absolute normaliza-
As seen from the structure of Eq X1.1, A is a measure of how
tion of the fluences is not justified. Therefore, for most
closely correlated are spectrum values at energies E and E.It
i k
hardness-testing applications, the use of a scaling reaction is
is neither possible nor desirable to specify a value for A in this
recommended. Only in those cases where core modeling was
guide since the best value is somewhat dependent upon the
performed for the specific irradiation conditions is absolute
nature of the exposure environment. Instead, a discussion of
normalization of the fluence spectrum justified.
the effects of varying the value of A will allow the tester to
make an appropriate selection of A for the exposure environ- X1.4.10 As in all adjustment codes, bad response data will
ment. invalidate the results. Since bad response data are sometimes
E721 − 22
hard to spot from the output of LSL-M2, it is imperative that σ' E 5 σ E 3exp 2Nσ E X (X1.2)
~ ! ~ ! @ ~ ! #
j i j i c i
the response data be checked prior to accepting the results.
where:
Further, if there is a known systematic uncertainty in the
σ(E) = jth response function at energy E,
j i i
response data, suspect responses should not be included in the
σ (E) = cover absorption cross section at energy E, and
c i i
analysis. If there is a known but unquantified systematic error
NX = number density per unit area of the cover.
in a response, that response should not be used until a suitable
NOTE X1.2—As described in Guide E720, this treatment may not be
correction factor can be obtained. Its inclusion will adversely
adequate in that it ignores the scattering effects of the cover. It almost
affect the resulting spectrum and damage parameters. (There is
certainlyleadstoappreciableerrorintheattenuation(ontheorderof10 %
or more) for threshold foils when boron-10 encapsulation is used.
a temptation to include bad data by ascribing large uncertain-
ties because the algorithm can tolerate it. However, it will hurt
X1.5.2 Each reaction may require several response
the output and usually will invalidate the results.)
functions, each differing from the others by the cover assumed
in the calculation, and by the cover thickness assumed. This
X1.4.11 The consistency of the data ensemble input to
2 method ignores the effect of the cover adjustment on the
LSL-M2 is tested by the code using a χ test. The output value
2 covariance for the response function.
of the χ should approximate the number of degrees of
X1.5.2.1 When a sensor is used with and without a cover
freedom. Deviations from this value, if significant, should
which absorbs strongly in some energy region, it is preferable
always result in rejection of the results and a re-examination of
2 to use the measured response with the cover and the difference
the input. The value obtained for χ should be reported in all
between the two measured responses. The response function
cases.
for the difference is simply the difference of the two response
functions. The reason for this is that the response with the
X1.5 Deficiencies of the Code
cover and the difference response are nearly uncorrelated with
X1.5.1 Sensor Foil Covers—Unlike the SAND II code,
each other.
which has a built-in method of handling covers, LSL-M2 does
X1.6 Precision and Bias
not directly handle this aspect of the measurement. LSL-M2
X1.6.1 In the rare case where all the input uncertainties data
allows the use of sensor covers by allowing the testing of th
...