Critical Mass and Subcritical Experiments Interlaced with Nb-1Zr, Re, Mo, Ta-2.5W Fueled with Highly Enriched Uranium in Support of the Prometheus Project

Abstract

The National Aeronautics and Space Administration is considering nuclear power sources for space exploration. A series of critical mass experiments was designed to address the development, performance, and design of a space nuclear reactor being considered to support the Prometheus project. These experiments consisted of interlacing the refractory metals rhenium (Re), molybdenum (Mo), tantalum2.5 wt% tungsten (Ta-2.5W), and niobium-1 wt% zirconium (Nb-1Zr) with moderating materials (graphite or polyethylene) and were fueled by highly enriched uranium plates. These experiments are designed to assess the adequacy of and uncertainty in refractory metal neutron cross-section evaluations for use in Prometheus nuclear reactor design work. The critical experiments were designed in the energy spectrum closely resembling or bracketing that in the proposed space reactor. For each material (Re, Mo, Ta-2.5W and Nb-1Zr), four critical configurations were designed and performed to measure the sensitivity of keff to the material under four different and progressively softer neutron spectra (core center spectrum, harder than core average spectrum, softer than core average spectrum, and accident flooded spectrum). The thicknesses of the graphite or polyethylene moderator and reflector plates were adjusted to achieve the desired neutron spectrum. One critical and 18 subcritical experiments provided for measurements of material neutronic behavior in a simple cylindrical geometry configuration that was modeled in MCNP with ENDF/B-VI.6 cross-section data and compared to the extrapolated or predicted critical mass for all the experiments. These experiments were performed at the Los Alamos National Laboratory using the Planet vertical lift critical assembly at the Los Alamos Critical Experiment Facility.

Full text

Critical Mass and Subcritical Experiments Interlaced
with Nb-1Zr, Re, Mo, Ta-2.5W Fueled with Highly Enriched
Uranium in Support of the Prometheus Project
David J. Loaiza,* Daniel Gehman, Rene Sanchez, and David Hayes
Los Alamos National Laboratory
P.O. Box 1663, MS B220
Los Alamos, New Mexico 87545
and
Michael Zerkle
Bettis Atomic Power Laboratory, West Mifflin, Pennsylvania
Received August 17, 2007
Accepted February 24, 2008
Abstract
–
The National Aeronautics and Space Administration is considering nuclear power sources for
space exploration. A series of critical mass experiments was designed to address the development, per-
formance, and design of a space nuclear reactor being considered to support the Prometheus project.
These experiments consisted of interlacing the refractory metals rhenium (Re), molybdenum (Mo), tantalum–
2.5 wt% tungsten (Ta-2.5W), and niobium–1 wt% zirconium (Nb-1Zr) with moderating materials (graphite
or polyethylene) and were fueled by highly enriched uranium plates. These experiments are designed to
assess the adequacy of and uncertainty in refractory metal neutron cross-section evaluations for use in
Prometheus nuclear reactor design work. The critical experiments were designed in the energy spectrum
closely resembling or bracketing that in the proposed space reactor. For each material (Re, Mo, Ta-2.5W
and Nb-1Zr), four critical configurations were designed and performed to measure the sensitivity of k
eff
to
the material under four different and progressively softer neutron spectra (core center spectrum, harder
than core average spectrum, softer than core average spectrum, and accident flooded spectrum). The
thicknesses of the graphite or polyethylene moderator and reflector plates were adjusted to achieve the
desired neutron spectrum. One critical and 18 subcritical experiments provided for measurements of
material neutronic behavior in a simple cylindrical geometry configuration that was modeled in MCNP
with ENDF/B-VI.6 cross-section data and compared to the extrapolated or predicted critical mass for all
the experiments. These experiments were performed at the Los Alamos National Laboratory using the
Planet vertical lift critical assembly at the Los Alamos Critical Experiment Facility.
I. INTRODUCTION
As part of a new exploration mission of the National
Aeronautics and Space Administration, various space nu-
clear reactor modules were under consideration for pro-
viding a source of electrical power to the planned ion
propulsion system for spacecrafts. Space fission power
systems have been identified for many years as a tech-
nology that can enable exploration and subsequently ex-
pansion into the solar system. Since the 1950s, the United
States has performed research into space fission systems
at various levels, but to date the United States has flown
only one fission system: the SNAP-10A ~Ref. 1!. Some
of the reasons for not fielding a space nuclear reactor
have been high costs and long development times, which
are not inherent to the use of space power systems, as
*E-mail: dloaiza@lanl.gov
NUCLEAR SCIENCE AND ENGINEERING: 160, 217–231 ~2008!
217

these factors are intrinsic to any programs that try to
push the advancement of any technology.
Many space fission system technologies can ulti-
mately be developed to produce the necessary power for
ion propulsion. Each technology used by the reactor con-
cept will impact the cost, schedule, and resources re-
quired to develop a successful space fission system. Over
the past decades the design of a space reactor power
system has triggered a flood of activities in academia,
industry, and the government. A wide variety of space
fission systems has been examined including liquid-
metal reactors, gas-cooled reactors, and heat pipe reac-
tors. The power conversion systems examined include
Stirling engines, closed Brayton cycle, thermal electric,
thermionic, and alkali metal thermal electric conver-
sion.
2
In order to select an optimal design, mission re-
quirements ~power, lifetime, and mass!and programmatic
risks ~cost, schedule, and resources!need to be satisfied.
Work performed to date has indicated that compact fast
space reactor concepts tend to minimize the overall sys-
tem mass.
3
Regardless of the space fission system selected, it is
almost certain that high-temperature refractory metals
will be required. Because of the high-temperature re-
quirements in space fission systems, refractory metal al-
loys offer the best solution to the mission requirements.
The mission requirements for space reactors in general
are reliability, safety ~launch and return!, compact sys-
tem, longevity, vacuum operation, radiation tolerance,
and low mass. Material selection is then fundamentally
affected by these requirements. Super alloys do not pos-
sess the strength, and the more exotic materials, ceram-
ics, carbon composites, and the intermetallics are not
practical in terms of fabrication for complex systems.
Conventional iron-, nickel-, and cobalt-base alloys are
eliminated for structural and fuel-cladding applications
by strength and compatibility limitations. Refractory metal
alloys become the only option for core components at
the anticipated service temperatures ~1200 to 1400 K!.
The refractory alloys usually considered are the al-
loys of niobium, rhenium, molybdenum, and tantalum.
Of the refractory materials, Nb-1Zr is a strong candidate
for a space reactor because of its ease of fabrication as
compared to molybdenum alloys and because of its high
strength-to-density ratio as compared to tantalum al-
loys.
4
Tantalum alloys have higher strength, but higher
absorption neutron cross sections, higher density, and
decreased weldability when compared to niobium al-
loys. Molybdenum has fabrication issues and less than
desirable weld ability properties. Tantalum is signifi-
cantly stronger than niobium alloys, but it has twice the
density of niobium, which reduces the advantages since
many niobium components could be utilized for the same
weight penalty. Niobium alloys are easier to fabricate
and have high ductility, higher melting point, and rela-
tively low density. However, niobium alloys have low
strength and low oxidation resistance at elevated temper-
atures. In short, there is no perfect alloy for space appli-
cation, and a balance between competing properties must
be considered. In regard to rhenium, despite its very high
density and fabrication cost, using a Re liner is neces-
sary for three main reasons: ~a!the high reactor temper-
ature ~.1500 K!;~b!excellent compatibility with the
proposed fuel ~UN!; and ~c!its ability to absorb neu-
trons during the spectrum shift, which ensures a suffi-
cient negative reactivity margin during water submersion
accidents. Rhenium is primarily considered as liner ma-
terial for UN fuel systems because of its ability to serve
as a chemical barrier to protect Nb-1Zr embrittlement.
Rhenium also has the added ability to serve as a spectral
shift poison. Rhenium has a low fast spectrum absorp-
tion cross section and a high thermal spectrum absorp-
tion cross section, making it more difficult for the core to
become supercritical in a hypothetical flooding or disas-
sembly accident.
This paper describes the results and characterization
information for a series of rhenium ~Re!, molybdenum
~Mo!, tantalum–2.5 wt% tungsten ~Ta-2.5W !, niobium–1
wt% zirconium ~Nb-1Zr!, and baseline critical experi-
ments that were developed by the Naval Reactors Prime
Contractor Team ~NRPCT!for the Prometheus space re-
actor development project.
3
There exist little or no ex-
perimental critical data for an experiment with refractory
metals. There are no clean benchmark quality critical
experiments containing substantial amounts of Mo, Nb,
Re, or Ta in prototypical neutron energy spectra in the
international critical experiment handbook.
5
In order to
address this need, a series of critical experiments using
each of the refractory metals under consideration and a
series of baseline experiments without refractory metals
were developed. The objectives of these experiments
were
3
1. to assess the adequacy of existing Mo, Nb, Re, and
Ta neutron cross-section evaluations in neutron en-
ergy spectra characteristic of Prometheus reactor
designs under normal and accident conditions
2. to reduce the uncertainty in k
eff
for Prometheus
reactor designs containing substantial amounts of
Mo, Nb, Re, and Ta by performing benchmark
quality critical experiments that bracket the neu-
tron energy spectra expected under normal
conditions
3. to perform benchmark critical experiments to iden-
tify what improvements are needed in Mo, Nb,
Re, and Ta neutron cross sections and to provide
a qualification basis for revised evaluations.
For each of the refractory metals ~with the exception
of Nb!, three critical mass experiments were designed to
bracket the neutron energy spectra expected in the
Prometheus reactor under normal operating conditions,
and one experiment was designed to simulate an acci-
dent condition in which the core is flooded with water.
218 ENRICHED URANIUM WITH Nb-1Zr, Re, Mo, Ta EXPERIMENTS
NUCLEAR SCIENCE AND ENGINEERING VOL. 160 OCT. 2008

The experiments were labeled -1, -2, -3, and -4 depend-
ing upon the energy spectra being considered. The -1
series of experiments was designed to approximate the
neutron energy spectrum expected in the center of the
Prometheus reactor. This series has the hardest spectrum
of the four. The -2 and -3 experiments were designed to
bracket the average neutron energy spectrum expected in
the Prometheus reactor. The -4 experiments were de-
signed to approximate the neutron energy spectrum for
an accident condition in which the Prometheus reactor is
immersed in, and flooded with, water. The -1, -2, and -3
experiments were moderated and reflected by graphite
plates of increasing thickness to adjust the neutron en-
ergy spectrum in the experiments. The -4 experiments
were moderated and reflected by polyethylene. One crit-
ical and 18 subcritical hand-stacking experiments were
completed prior to the termination of NRPCT work on
Project Prometheus.
II. DESCRIPTION OF EXPERIMENTS
AND MATERIALS
These critical mass experiments were designed to be
performed on the Planet general-purpose vertical lift ma-
chine at the Los Alamos Critical Experiments Facility
~LACEF!. The configurations consist of a cylindrical
core region containing interlaced plates of highly en-
riched uranium ~HEU!, refractory metal plates, and graph-
ite or polyethylene plates of various thicknesses. The
core region is partially reflected by graphite or polyeth-
ylene top and bottom reflectors.
The critical configuration is typically divided into
two approximately equal portions. The upper core sec-
tion and the top reflector rest on the stationary platform
of the Planet machine. The upper plates of the core rest
on a thin, cylindrical stainless steel plate, called the di-
aphragm. The lower core region and the bottom reflector
are placed on a cylindrical aluminum spindle plate that
rests on the aluminum lower platen, which is connected
to the vertical drive of the assembly machine. The ver-
tical drive of the assembly machine uses a hydraulic ram
for coarse positioning and a stepping motor for fine po-
sitioning. The lower core plates and bottom reflector are
held in position by a central, hollow, aluminum align-
ment tube. A neutron source is placed inside the align-
ment tube to ensure indication of neutron multiplication.
The experiment is conducted by raising the lower por-
tion until it fully closes to the steel diaphragm that sup-
ports the upper segment of the core. There are no control
or safety rods inside the assembly.
Four BF
3
detectors are placed close to the configu-
rations to monitor the neutron leakage of the system. In
addition, three radiation monitors are placed at varying
distances from the assembly to monitor the neutron flux
of the configuration in the final approach to critical. If
the radiation level exceeds a predetermined limit, any
one of these monitors could initiate separation of the
assembly, a SCRAM, by deenergizing the assembly ma-
chine’s hydraulic system, which drops the lower assem-
bly. Figure 1 shows one of the Nb-1Zr configurations
mounted on the Planet assembly.
The subcritical configurations were mounted on a
table. The configuration rested on a cylindrical alumi-
num spindle plate that has a hollow center. The main
function of the hollow spindle plate is to secure the align-
ment tube and to decouple ~minimize reflection!the con-
figuration from the table. Four BF
3
detectors were also
used during the subcritical experiments to monitor the
neutron leakage from the system. Figure 2 is a represen-
tative photograph for the subcritical experiments.
The fuel consisted of HEU plates known as Jemima
plates. The fuel plates are composed of a pair of nested
plates. The smaller HEU plate fits inside a larger HEU
ring as shown in Fig. 3. The smaller plates have a 15-in.
outside diameter ~o.d.!while the larger HEU rings have
a 15-in. inside diameter and 21-in. o.d. All the HEU
plates have a nominal thickness of 0.118 in. The HEU
plates have an average density of 18.743 g0cm
3
and an
average
235
U enrichment of 93.219 wt%. Table I shows
the nominal dimensions and average mass for the HEU
plates used in the experiments.
Graphite plates of various thicknesses were used as
moderator to achieve the desired fission spectrum for
the -1, -2, and -3 experiments. The graphite plates were
interlaced between the refractory metal test plates in
the core region and were also used as axial reflectors.
The dimensions of the various graphite plates used in the
core region of the subcritical experiments are provided
in Table I.
a
The graphite had an average density of 1.732
g0cm
3
and a maximum ash content of 0.07 wt% ~Ref. 6!.
Polyethylene plates were used to achieve the softer spec-
trum in the -4 critical experiments, which approximate a
hypothetical flooding accident. The high-density poly-
ethylene plates have an average density of 0.957 g0cm
3
and are reported to have negligible impurities.
6b
The nom-
inal dimensions for the polyethylene plates are provided
in Table I.
The NRPCT furnished Los Alamos National Labo-
ratory ~LANL!with solid and annular molybdenum,
rhenium, and tantalum plates for the critical mass ex-
periments.
c
The dimensional specifications for the Mo
plates are provided in Table I. Figure 4 shows photo-
graphs for the refractory plates including the Mo plate.
The differences between the nominal and measured
diameters are judged to be negligible.
3
The Mo plates were
either 0.060 in. or 0.030 in. thick. Bettis Atomic Power
a
The graphite plates were fabricated by UCAR Carbon
Company with PGX-grade graphite.
b
These high-density polyethylene plates were manufac-
tured by Standard Machine Company.
c
The Mo critical experiment plates were fabricated by
Schwarzkopf Technologies.
LOAIZA et al. 219
NUCLEAR SCIENCE AND ENGINEERING VOL. 160 OCT. 2008

Laboratory ~BAPL!performed high-accuracy density mea-
surements on remnant samples from the Mo plates and
found the average Mo density to be 10.218 g0cm
3
. The
chemical impurities in the Mo plates are considered to be
insignificant; therefore, the Mo plate material was approx-
imated to be pure Mo ~Refs. 3 and 7!.
The Re critical experiment plates were fabricated by
stitch welding together three ;8- ⫻22- ⫻0.015-in. Re
Fig. 1. Nb-1Zr fueled with HEU experiment mounted on the planet assembly.
Fig. 2. Subcritical configuration with BF
3
detectors.
220 ENRICHED URANIUM WITH Nb-1Zr, Re, Mo, Ta EXPERIMENTS
NUCLEAR SCIENCE AND ENGINEERING VOL. 160 OCT. 2008

plates using a laser welder.
d
These stitch-welded plates
were then electric discharged machined to their final di-
mensions.
3
The dimensional specifications for the Re
plates are provided in Table I. A photograph of a Re plate
is also provided in Fig. 4. The Re plates have been fab-
ricated from two lots of high-purity Re powder material:
R-1478 and R-1481. The nominal thickness for the Re
plates is 0.0150-in. ~Refs. 8 and 9!. BAPL performed
high-accuracy density measurements using remnant sam-
ples from the Re plates and found the average Re density
to be 21.001 g0cm
3
. The chemical impurities in the Re
plates are considered to be insignificant, thus, the Re
plate material was approximated as pure Re.
The Ta-2.5W was selected as the tantalum alloy to
be used in this series of experiments mainly for sched-
uling reasons. A vendor was identified that had a suffi-
cient quantity of Ta-2.5W sheet in inventory and could
complete the fabrication of the plates before the end of
December 2004. The 2.5 wt% tungsten content in Ta-
2.5W was judged to be acceptable for the experiments.
Pure Ta was also considered for the experiment, but it
was found to be more expensive than Ta-2.5W, and a
sufficient quantity could not be fabricated in time to sup-
port the experiments.
3
The chemical analysis performed
on the Ta-2.5W demonstrated that the impurities were
negligible. The dimensional specifications for the Ta-
2.5W plates are provided in Table I ~Ref. 10!.
e
Figure 4
shows photographs of a Ta-2.5W plate. The Ta-2.5W
plates have been fabricated from two heats of Ta-2.5W
material: 11-19-2 and 10-20-2. BAPL performed high-
accuracy density measurements using remnant samples
from the Ta-2.5W plates and found the average Ta-2.5W
density to be 16.726 g0cm
3
.
Oak Ridge National Laboratory ~ORNL!furnished
LANL with solid and annular Nb-1Zr plates. The Nb-
1Zr plates were fabricated from a single heat ~heat num-
ber 531048!of commercial-grade Nb-1Zr.
f
Table I
provides the nominal dimensions of the Nb-1Zr plates
and the mass measurements performed by LANL. The
average density for the Nb-1Zr plates was calculated to
be 8.686 g0cm
3
. The impurities in the Nb-1Zr plates are
considered to be negligible.
III. DESIGN OF EXPERIMENTS
Three critical mass experiments were designed to
bracket the neutron energy spectrum likely to be found in
the Prometheus reactor designs under normal operating
conditions. In addition, one other experiment was de-
signed to approximate a hypothetical accident in which
the reactor is flooded with water. Experiment -1 is de-
signed to approximate the neutron energy spectrum in the
center of the core. This experiment has the fastest spec-
trum of the four experiments designed. Experiments -2 and
-3 are designed to bracket the core average neutron en-
ergy spectrum. Experiment -4 is designed to simulate the
average neutron energy spectrum when the core is flooded
with water.The first three experiments ~-1, -2, and -3!were
moderated and reflected by graphite plates of increasing
thickness to achieve the desired energy spectrum. The
fourth experiment has the softest spectrum. It is moder-
ated and reflected by polyethylene plates. Figure 5 presents
d
The Re critical experiment plates were fabricated by Rhe-
nium Alloys.
e
The Ta-2.5W plates were fabricated by Allegheny Tele-
dyne, Inc., Wah Chang.
f
The commercial-grade Nb-1Zr was produced by Wah
Chang in 1988 ~Ref. 11!.
Fig. 3. Nested HEU fuel plates.
TABLE I
Nominal Specification for Materials Used
in the Experiments
Material
Thickness
~in.!
Inside
Diameter
~in.!
Outside
Diameter
~in.!
Average
Mass
~g!
HEU 0.118 0.002.51 15.0 6 374.16
0.118 15.0 21.0 6 116.34
Graphite 0.10 0.002.51 21.0 964.92
0.20 0.002.51 21.0 1 850.94
0.40 0.002.51 21.0 3 707.35
1.0 0.002.51 21.0 10 025.21
Polyethylene 0.040 0.002.51 21.0 215.82
1.125 0.002.51 21.0 6 077.15
Molybdenum 0.030 0.002.51 21.0 1 722.12
0.060 0.002.51 21.0 3 420.54
Rhenium 0.015 0.002.51 21.0 1 911.62
Ta-2.5W 0.025 0.0 02.51 21.0 2 328.73
Nb-1Zr 0.010 0.002.51 21.0 487.45
0.030 0.002.51 21.0 1 471.63
0.060 0.002.51 21.0 2 944.68
LOAIZA et al. 221
NUCLEAR SCIENCE AND ENGINEERING VOL. 160 OCT. 2008

Fig. 4. Refractory metal plates.
Fig. 5. Representative fission distribution for the Ta-2.5W experiments in the center of the core.
222 ENRICHED URANIUM WITH Nb-1Zr, Re, Mo, Ta EXPERIMENTS
NUCLEAR SCIENCE AND ENGINEERING VOL. 160 OCT. 2008

the predicted fission reaction rate distribution for the
Ta-2.5W experiments at the center of the configuration.
This spectrum is representative for the refractory metals
and baseline experiments. It is worth noting that the fourth
experiment with Nb-1Zr designated as Nb-1Zr-4 was
designed by ORNL ~Ref. 12!prior to transferring the
responsibilities for the Prometheus project to Naval Re-
actor Programs. Because of time constraints a Nb-1Zr-1
experiment was not designed under the Naval Reactor
Programs. Table II summarizes the designed critical
experiments.
All the proposed experiments were devised to be
critical or slightly supercritical ~excess reactivity less
than 50 ¢!. The goal of the experiments is to match the
energy-dependent experimental k
eff
due to the intersti-
tial material to that of the predicted or computed k
eff
in
MCNP using ENDF0B-VI cross-section datum libraries
in the energy spectrum that matches or brackets that of
the proposed space reactor. If significant deficiencies in
the interstitial material ~Mo, Nb, Re, or Ta!neutron
cross-section evaluations are identified by the critical
experiments, then differential neutron cross-section mea-
surements will need to be performed to resolve the ex-
perimental discrepancies. The ultimate objective of these
experiments is to reduce the uncertainty in k
eff
due to
the nuclear data of the proposed refractory materials
under consideration.
The critical configuration for Experiment -1 con-
sisted of a 0.1-in.-thick graphite plate between the inter-
stitial material under investigation. The configuration also
included 1-in. top and bottom graphite reflectors. This
configuration provided the hardest neutron spectrum and
approximates the spectrum in the center of the reactor
core under normal operation conditions. Figure 6 shows
a schematic for the Re-1 experiment illustrating the stack-
ing of the reflector, interstitial ~Re!, fuel, and graphite
moderating plates. The configuration for Experiment -2
consisted of a 0.2-in.-thick graphite plate between the
interstitial materials. It also had a 2-in.-thick graphite
plate as bottom and top reflectors. This configuration
provided a spectrum that is harder than the average neu-
tron energy spectrum expected in the reactor core. For
the -3 experiments, the thickness of the graphite plate
was increased to 0.4-in. between the interstitial material.
The top and bottom reflectors were 5-in.-thick graphite
plates. This configuration provided a spectrum that is
softer than the average neutron energy spectrum expected
in the reactor core. The final configuration in the series
of four experiments consisted of a 0.080-in.-thick poly-
ethylene plate between the interstitial material. This con-
figuration simulated the average neutron spectrum of the
reactor core when flooded with water. The top and bot-
tom reflectors were 1-in.-thick polyethylene plates.
Some refractory materials ~Nb-1Zr and Mo!were
machined at various thicknesses for two main reasons:
~a!to achieve criticality at the desired neutron spectrum
and ~b!to perform perturbation experiments after the
initial assessment has been completed.
IV. RESULTS AND ANALYSIS
In all, 19 experiments were performed to support
the Prometheus project. One experiment was critical, and
18 experiments were subcritical. The subcritical experi-
ments were not taken to critical because of the July 2004
security and safety shutdown of LANL and the Septem-
ber 2005 National Nuclear Security Administration com-
mitment to de-inventory category I0II special nuclear
material from TA-18, which is the home of LACEF.
The first experiment performed and taken critical
was the Nb-1Zr experiment, which simulates the aver-
age neutron spectrum of the reactor core when flooded
with water. This experiment was performed on the Planet
general-purpose vertical lift machine shown in Fig. 1.
This machine consists of a hydraulic lift directly beneath
a stationary aluminum platform, which lifts the bottom
part of the experiment that rests on a movable platen
with 20- to 30-cm travel distance. Four jackscrews driven
very precisely by a stepping motor move the platen the
final 4 cm of separation. The starting configuration for
TABLE II
Description of Designed Critical Experiments
Designation Interstitial Material Desired Spectrum
Re-1 Re Core center spectrum
Re-2 Re Harder than core average
spectrum
Re-3 Re Softer than core average
spectrum
Re-4 Re Flooded spectrum
Mo-1 Mo Core center spectrum
Mo-2 Mo Harder than core average
spectrum
Mo-3 Mo Softer than core average
spectrum
Mo-4 Mo Flooded spectrum
Ta-2.5W-1 Ta-2.5W Core center spectrum
Ta-2.5W-2 Ta-2.5W Harder than core average
spectrum
Ta-2.5W-3 Ta-2.5W Softer than core average
spectrum
Ta-2.5W-4 Ta-2.5W Flooded spectrum
Nb-1Zr-2 Nb-1Zr Harder than core average
spectrum
Nb-1Zr-3 Nb-1Zr Softer than core average
spectrum
Nb-1Zr-4 Nb-1Zr Flooded spectrum
Baseline-1 Graphite only Core center spectrum
Baseline-2 Graphite only Harder than core average
spectrum
Baseline-2 Graphite only Softer than core average
spectrum
Baseline-4 Polyethylene only Flooded spectrum
LOAIZA et al. 223
NUCLEAR SCIENCE AND ENGINEERING VOL. 160 OCT. 2008

all experiments contained ;25 kg of HEU, which corre-
sponds to 20% of the predicted critical mass by MCNP
with ENDF0B-VI cross-section library data. A 10M~in-
verse of the multiplication!approach to critical was per-
formed following the guidelines of the existing operating
procedure. The starting configuration also contained a
Pu-Be neutron source to enhance the neutron multiplica-
tion and neutron leakage of the system. The neutron leak-
age from the assembly was measured with four BF
3
detectors to obtain the multiplication of the system. The
multiplication values are defined as the count rate ob-
tained by the four BF
3
detectors in a subcritical step
divided by the initial or base count rate. The inverse of
the multiplication ~10M!is plotted as a function of units
or separation between the top and bottom sections.
This critical experiment consisted of a cylindrical
core region containing HEU plates, Nb-1Zr plates, and
polyethylene plates. The configuration had bottom and
top reflectors but no radial reflector. The configuration
was critical with 149.56 kg of HEU and utilized a total
of 57.668 kg of Nb-1Zr. Figure 7 shows a picture of the
Nb-1Zr experiment mounted on the Planet vertical lift
machine. The construction of the experimental configu-
ration began with a hand-stacking approach to critical.
Once the hand-stacking limit was reached, the core was
split into two sections. The bottom part of the core, which
contained approximately half of the critical mass, was
placed on the movable platen of the Planet vertical lift
machine. The top part of the core was placed on the
stationary platform. The lower portion of the assembly,
which contained a Pu-Be source, was then raised re-
motely until it contacted the top portion of the assembly.
The nominal dimensions of a unit were defined as a 40-
mil polyethylene plate, 40-mil of Nb-1Zr, an HEU plate,
and 40-mil of Nb-1Zr. Table III defines a unit in the
Nb-1Zr experiment. The Nb-1Zr experiment was critical
with 12 units. Seven units were placed on the bottom
part of the assembly, and five units were placed on the
top part of the assembly. Criticality was achieved when
the assembly was fully closed. The final configuration
was modeled in MCNP using the continuous-energy cross
sections from ENDF0B-VI.8. The calculation employed
1250 generations of 5000 neutron histories. The MCNP
calculated k
eff
was 0.9972 60.0003. The experiment had
a positive reactor period of 47.42 s, which is ;15 ¢ of
excess reactivity ~k
eff
⫽1.001!~Ref. 13!. Simplified and
detailed benchmark evaluations for this critical experi-
ment ~HEU-MET-FAST-047!were prepared and in-
cluded in the 2006 edition of the International Criticality
Safety Benchmark Evaluation Project handbook.
11
The remaining 18 subcritical experiments were per-
formed in a similar manner as the previously described
critical experiment. Construction of the subcritical con-
figurations began by placing the graphite or polyethyl-
ene reflector plate on top of a 3-in.-thick hollow aluminum
spindle plate, which is used to decouple the configura-
tion from neutron reflection from the table. Next, a bot-
tom metal reflector plate ~with the exception of the
Fig. 6. Expanded view for the hand-stacking of Re-1 configuration.
224 ENRICHED URANIUM WITH Nb-1Zr, Re, Mo, Ta EXPERIMENTS
NUCLEAR SCIENCE AND ENGINEERING VOL. 160 OCT. 2008

baseline and Re experiments, which do not include a
bottom metal reflector plate!and one graphite or poly-
ethylene plate are placed on top of the graphite or poly-
ethylene reflector plate to approximate the reactor vessel.
Then, stacking units required to reach the hand-stacking
limit are placed on top of the bottom reflector plate. For
the baseline experiments a stacking unit is defined as a
set of two plates consisting of an HEU plate and a graph-
ite or polyethylene plate. For the Mo, Nb-1Zr, Re, and
Ta-2.5W critical experiments, a stacking unit is defined
as a set of four plates consisting of a lower metal plate,
an HEU plate, an upper metal plate, and a graphite or
polyethylene plate. Finally, the upper metal reflector plate
~with the exception of the baseline and Re experiments,
which do not include a top metal reflector plate!and the
graphite or polyethylene reflector plate are placed on top
of the stack. Table III summarizes the definition of a unit
for all the configurations performed.
These subcritical experiments were set up on top of
a table, and units were added until the hand-stacking
limit was reached ~75% of the predicted critical mass!.
The neutron leakage from the assembly was measured
with four BF
3
detectors to obtain the multiplication of
the system. Figure 8 shows the normalized inverse multi-
plication ~10M!as a function of units for the Re-1 ex-
periment. The total number of counts in a 100-s interval
was normalized to 1 and plotted as counting rate ratios
versus number of units. The next unit was added, and
once again the neutron leakage was measured. The new
total number of counts in a 100-s time interval was di-
vided by the total number of counts obtained in the pre-
vious step. The reciprocal of this number was plotted
again as counting rate ratios ~10M!versus number of
units. A line that passes through the last two data points
was drawn to intercept the abscissa to find the number of
units ~critical mass!necessary to reach critical. The red
line in Fig. 8
g
shows the extrapolation of the first two
data points to zero ~x-axis!.
Once the extrapolated critical number of units or
mass was obtained, then two guidelines or rules were
observed before adding more fuel into the hand-stacking
configuration. The first rule was the 75% critical mass
rule, which states that hand-stacking multiplying sys-
tems shall never exceed 75% of the extrapolated ~or
predicted!critical mass. The second rule was the half-
way rule, which states that the size of each step shall
not exceed one-half the increment to the predicted criti-
cal mass or double the multiplication of the system or
the count rate. This rule is based on the assumption that
there is a linear relationship between the multiplication
of the system and the changing parameter. In all the
experiments, the more conservative rule was taken when
adding an additional unit. Once the hand-stacking limit
was reached, the experiment was terminated. One inter-
esting characteristic in Fig. 8 is the conservative and
nonconservative behavior exhibited in the plot. A con-
servative 10M curve provides a safe extrapolation to
critical mass, which means that the curve underpredicts
g
Figures in this paper are in color only in the electronic
version.
Fig. 7. Nb-1Zr critical mass experiment.
LOAIZA et al. 225
NUCLEAR SCIENCE AND ENGINEERING VOL. 160 OCT. 2008

the critical mass of the system. A nonconservative 10M
curve provides a “risky” extrapolation to critical mass,
which means that the critical mass of the system is over-
predicted. The first two data points in Fig. 8 used to
extrapolate the predicted critical mass ~red line!exhibit
conservative behavior. The second curve ~orange line!
exhibits nonconservative behavior. The third curve ~blue
line!dips in for nonconservative behavior. The yellow
line switches to conservative behavior and the green line
to nonconservative behavior. The last data point ~black!
line begins to converge to 18 units predicted critical mass.
In general, most 10M curves exhibit either pure conser-
vative behavior or pure nonconservative behavior. These
series of experiments have very unique 10M curves where
the nonconservative and conservative behavior is exhib-
ited in the same system. As the cylindrical system in
TABLE III
Definition of a “Unit” for all Configurations with Nominal Dimensions.
Material
Thickness
~in.!Material
Thickness
~in.!Material
Thickness
~in.!Material
Thickness
~in.!
Re-1 Re-2 Re-3 Re-4
Reflector Graphite 1.0 Graphite 2.0 Graphite 5.0 Polyethylene 1.0
Unit Re 0.015 Re 0.015 Re 0.015 Re 0.015
HEU 0.118 HEU 0.118 HEU 0.118 HEU 0.118
Re 0.015 Re 0.015 Re 0.015 Re 0.015
Graphite 0.100 Graphite 0.200 Graphite 0.400 Polyethylene 0.080
Mo-1 Mo-2 Mo-3 Mo-4
Reflector Graphite 1.0 Graphite 2.0 Graphite 5.0 Polyethylene 1.0
Mo 0.060 Mo 0.060 Mo 0.060 Mo 0.060
Unit Mo 0.030 Mo 0.030 Mo 0.030 Mo 0.030
HEU 0.118 HEU 0.118 HEU 0.118 HEU 0.118
Mo 0.030 Mo 0.030 Mo 0.030 Mo 0.030
Graphite 0.100 Graphite 0.200 Graphite 0.400 Polyethylene 0.080
Ta-2.5W-1 Ta-2.5W-2 Ta-2.5W-3 Ta-2.5W-4
Reflector Graphite 1.0 Graphite 2.0 Graphite 5.0 Polyethylene 1.0
Ta-2.5W 0.150 Ta-2.5W 0.150 Ta-2.5W 0.150 Ta-2.5W 0.150
Unit Ta-2.5W 0.025 Ta-2.5W 0.025 Ta-2.5W 0.025 Ta-2.5W 0.025
HEU 0.118 HEU 0.118 HEU 0.118 HEU 0.118
Ta-2.5 0.025 Ta-2.5 0.025 Ta-2.5 0.025 Ta-2.5 0.025
Graphite 0.100 Graphite 0.200 Graphite 0.400 Polyethylene 0.080
Not Performed Nb-1Zr-2 Nb-1Zr-3 Nb-1Zr-4
Reflector Graphite 2.0 Graphite 1.0 Polyethylene 1.0
Nb-1Zr 0.180 Nb-1Zr 0.180 Nb-1Zr 0.110
Unit Nb-1Zr 0.040 Nb-1Zr 0.040 Nb-1Zr 0.040
HEU 0.118 HEU 0.118 HEU 0.118
Nb-1Zr 0.040 Nb-1Zr 0.040 Nb-1Zr 0.040
Graphite 0.200 Graphite 0.400 Polyethylene 0.040
Baseline-1 Baseline-2 Baseline-3 Baseline-4
Reflector Graphite 1.0 Graphite 2.0 Graphite 1.0 Polyethylene 1.125
Unit HEU 0.118 HEU 0.118 HEU 0.118 HEU 0.118
Graphite 0.100 Graphite 0.200 Graphite 0.400 Polyethylene 0.080
226 ENRICHED URANIUM WITH Nb-1Zr, Re, Mo, Ta EXPERIMENTS
NUCLEAR SCIENCE AND ENGINEERING VOL. 160 OCT. 2008

these series of experiments increases in the number of
units, the volume-to-surface ratio increases. They tran-
sition from flat pancake-type systems to tall, skinny cyl-
inders. This causes the neutron leakage of the system to
change and thus exhibit nonconservative behavior. Then,
as more material is added to the system, the parasitic
absorption changes the leakage of the system, and con-
servative behavior is observed.
Figure 9 shows the hand-stacking configurations for
the four different critical assembly configurations under
investigation. Figure 9a shows the fastest spectrum of
the experiments designed. This spectrum is achieved by
placing a 0.10-in.-thick graphite plate and 1-in.-thick ax-
ial reflectors between the refractory materials and the
fuel. Figure 9b shows the hand-stacking configuration
for the harder-than-average core spectrum achieved with
a 0.20-in.-thick moderating graphite plate and 2-in.-
thick bottom and top reflector plates. Figure 9c shows
the softer-than-average core spectrum configuration
achieved by placing a 0.40-in.-thick moderating graphite
plate between the refractory material and HEU fuel. Fig-
ure 9 also shows the thick 5-in.-thick graphite bottom
and top reflector plates. Finally, the flooded spectrum
configuration is shown in Fig. 9d. This spectrum is
achieved by placing 0.080-in.-thick polyethylene plates
and 1-in.-thick axial polyethylene reflectors.
The results for the hand-stacking experiment are pre-
sented in Table IV. The hand-stacking limit was typically
reached at ;75% of the predicted critical mass. All con-
figurations were taken as closely to 75% of the predicted
critical mass as possible. Notice that the Re-2 and Re-3
experiments were terminated at 11 units; however, Re-2
was stopped at 72% of predicted critical while Re-3 was
stopped at 71% of predicted critical.Table IValso presents
the amount of refractory material in each configuration.
These hand-stacking data will be used when and if these
experiments are taken critical since the location and iden-
tification number of all the components were carefully
annotated.
6–10
Useful information can be inferred from these sub-
critical experiments regarding the adequacy of the re-
fractory material cross-section data. Table V describes
the subcritical experiments and provides the predicted
critical mass derived from subcritical neutron multipli-
cation measurements. These predicted or extrapolated
critical mass values are compared to calculated critical
mass values to provide a basis for determining the rel-
ative need for critical experiments of a particular refrac-
tory metal for each specific neutron energy spectrum.
The configurations were modeled in MCNP with ENDF0
B-VI.6 cross-section data to compare the experimental
critical mass values to the calculated critical mass val-
ues. The critical mass values calculated by MCNP have
been obtained for k
eff
⫽1.00 to facilitate comparison to
the extrapolated critical mass from the subcritical mea-
surements. In order to obtain a critical mass value for
k
eff
⫽1.00, the following empirical relationship was
used
14
:
k
eff
⫽
冉
M
U
M
cm
冊
103
,~1!
where M
U
is the MCNP-calculated mass of uranium nec-
essary for the system to have a k
eff
greater than 1 and
M
cm
is the critical mass for a k
eff
exactly to 1.00. Solving
for M
cm
in the above relationship provides the critical
mass for a system with a k
eff
exactly 1.00. These values
are reported in the fourth column of Table V. This em-
pirical equation is very accurate for systems very close
to critical ~k
eff
⫽1!since the calculated critical mass k
eff
is exactly 1.00. The uncertainty for Eq. ~1!is ,1%. The
relative difference between the predicted critical mass
and the calculated critical mass can be used to provide
an estimate of the relative need for critical mass data for
Fig. 8. Hand-stacking approach-to-critical for Re-1 configuration.
LOAIZA et al. 227
NUCLEAR SCIENCE AND ENGINEERING VOL. 160 OCT. 2008

each refractory metal and neutron energy spectrum un-
der consideration.
The information in Table V is useful for prioritizing
future experimental needs for space reactor materials.
TableV stresses that the highest need for experimental data
is not for the refractory materials but rather for the graphite-
only or baseline experiments. The baseline experiments
have the highest relative difference between the predicted
and the calculated values. The relative differences for the
graphite experiments range from 7.5 to 9.5%. This is not a
surprise as other researchers have requested experimental
data for graphite-moderated systems in the intermediate
and fast energy spectrums. In May 1998, the chair of
the Experiment Needs Identification Workgroup ranked
the need for experiments with graphite, Be, BeO, and D
2
O
in the top ten in the revised recommendations for priority
of critical experiments.
15
These experiments were identi-
fied as “Special Moderator Experiments,” and they were
next in the queue for experiments to be formed at the
LACEF prior to the shutdown and subsequent move of
critical assemblies to the Device Assembly Facility in Las
Vegas, Nevada. Graphite has a large number of reso-
nances for the scattering cross sections in the intermedi-
ate energy region, and little or no experimental data exist
in this energy region.
For the Re experiments, the highest relative differ-
ence is observed in Re-2 ~harder than core average spec-
trum!. The Re-3 and Re-4 configurations also deserve
special attention because of their spectrum and impor-
tance in poisoning the reactor. The core center spectrum
Fig. 9. Hand-stacking configurations bracketing the neutron spectrum in the reactor core.
228 ENRICHED URANIUM WITH Nb-1Zr, Re, Mo, Ta EXPERIMENTS
NUCLEAR SCIENCE AND ENGINEERING VOL. 160 OCT. 2008

~Re-1!produces the lowest difference between the cal-
culated and the predicted values. In general, the Re ex-
periments calculate better results than the other refractory
materials.
In the Mo experiments, Mo-4 deserves attention as
its difference between calculated and predicted values is
the highest at 7.2%. The three other configurations have
a relatively low difference between the calculated and
the predicted values. The comparative need for the Mo
experiments is second from the bottom, as they tend to
calculate well.
Since the relative difference for the Ta-2.5W-2 ex-
periment has the greatest difference between the calcu-
lated and the predicted values at 9.25%, high importance
should be placed in performing this experiment as
compared to other Ta-2.5W experiments. Ta-2.5W-3 and
Ta-2.5W-4 also exhibit large differences at ;7%. The
lowest-priority configuration is Ta-2.5W-1 with only a
0.17% relative difference. Last, the only experiment taken
to critical ~Nb-1Zr-4!is also shown in Table V. The ex-
trapolated critical mass to calculated critical mass shows
a difference of 8.33%. However, the actual HEU mass
used to achieve criticality was 149.56 kg, which is prac-
tically the same as the calculated critical mass ~150.01 kg!
with a calculated k
eff
equal to 0.9972 60.0003. The
Nb-1Zr configurations calculate between 3 to 6% differ-
ence. The harder and softer than core average spectrums
TABLE IV
Results of Hand-Stacking Subcritical Experiments
Configuration
Number
Number
of Units
Total
HEU Mass
~kg!
Total Refractory
Material Mass
~kg!
Re-1 13 162.564 49.258
Re-2 11 137.455 41.711
Re-3 11 137.455 41.711
Re-4 10 124.907 37.929
Mo-1 12 150.011 61.705
Mo-2 10 124.907 54.890
Mo-3 9 112.229 51.454
Mo-4 8 99.572 47.974
Ta-2.5W-1 12 150.011 82.938
Ta-2.5W-2 10 124.907 74.034
Ta-2.5W-3 11 137.455 78.456
Ta-2.5W-4 10 124.907 74.034
Nb-1Zr-2 10 124.907 56.536
Nb-1Zr-3 10 124.907 56.404
Nb-1-Zr-4 8 99.572 45.289
Baseline-1 10 124.907 —
Baseline-2 10 124.907 —
Baseline-3 9 112.229 —
Baseline-4 7 86.936 —
TABLE V
Relative Comparison Between Predicted and Calculated Critical Mass
Configuration
Number
Number
of Units
Predicted Mass
~kg!
Calculated Mass
~kg!
Percent
Difference Neutron Spectrum
Re-1 13 220.74 68.8 219.52 0.55 Core average
Re-2 11 191.01 67.6 205.46 7.56 Harder
Re-3 11 190.52 67.6 192.10 0.83 Softer
Re-4 10 184.50 67.4 182.54 ⫺1.06 Flooded
Mo-1 12 200.44 68.0 196.97 1.73 Core average
Mo-2 10 176.40 67.1 186.42 5.68 Harder
Mo-3 9 169.45 66.8 172.69 1.91 Softer
Mo-4 8 129.76 65.2 139.04 7.15 Flooded
Ta-2.5W-1 12 212.49 68.5 212.85 0.17 Core average
Ta-2.5W-2 10 186.04 67.4 203.24 9.25 Harder
Ta-2.5W-3 11 193.42 67.7 208.25 7.67 Softer
Ta-2.5W-4 10 184.39 67.3 198.19 7.48 Flooded
Nb-1Zr-2 10 186.92 67.5 194.17 3.88 Harder
Nb-1Zr-3 10 173.48 66.9 184.07 6.10 Softer
Nb-1Zr-4 8 137.50 67.1 150.01 8.33 Flooded
Baseline-1 10 184.18 67.4 199.83 8.50 Core average
Baseline-2 10 176.94 67.1 191.03 7.96 Harder
Baseline-3 9 152.61 66.1 167.03 9.45 Softer
Baseline-4 7 127.06 65.1 136.63 7.53 Flooded
LOAIZA et al. 229
NUCLEAR SCIENCE AND ENGINEERING VOL. 160 OCT. 2008

calculate about the same difference, and after perform-
ing the graphite experiments, the Nb-1Zr experiments
should be performed.
In general, based on the subcritical experiments
the baseline experiments have the highest need for data
since the baseline experiments yield such a large dis-
crepancy. Then, the refractory metal experiments with
harder than core average spectrum configurations need
to be performed. The harder spectrum experiments have
the highest difference for the Re, Nb-1Zr, and baseline
experiments. The configurations in the flooded spec-
trum tend to calculate well as compared to the other
spectrums. These experiments should be assigned the
lowest priority for experimental data. However, the im-
portance for data on the flooded spectrum is essential to
decrease the mass of the Re in any proposed space
reactor. No changes in the nuclear data for the refrac-
tory metals should be made until the baseline experi-
ments have been performed and analyzed.
V. CONCLUSION
Critical and subcritical data for experiments fueled
with HEU, moderated with graphite and polyethylene,
and mixed with refractory metals were obtained. These
data provide information for material neutronic behavior
in simple cylindrical configurations at four neutron en-
ergy spectrums. Experiment -1 was designed to approx-
imate the neutron energy spectrum in the center of the
core. Experiments -2 and -3 are designed to bracket the
core average neutron energy spectrum. Experiment -4 is
designed to simulate the average neutron energy spec-
trum when the core is flooded with water. The results of
these experiments were aimed at providing information
about the critical mass k
eff
and sensitivity to refractory
metal energy-dependent neutron reactions that will sup-
port assessment of uncertainties in the design of space
nuclear reactors.
The principal components used in these experiments
included HEU, rhenium, molybdenum, tantalum alloy,
niobium alloy, graphite, and polyethylene plates. These
materials were considered for use in the Prometheus re-
actor. The Prometheus reactor concepts utilize substan-
tial amounts of these materials; however, there are few
or no prototypical critical experimental data for these
materials. The advantage of performing these experi-
ments with the refractory metals is that the importance
of the refractory metal at a prototypical neutron energy
spectrum will have exaggerated sensitivity in a simple,
clean configuration. Thus, the importance and effect
of the refractory material can be isolated through the
performance of these experiments. Then, the objective
of these experiments becomes to assess the adequacy
of existing Re, Mo, Ta, and Nb neutron cross-section
data in the neutron energy spectra characteristic of the
Prometheus reactor. The critical data will also help re-
duce the uncertainty in k
eff
reactor designs containing
large amounts of these refractory materials.
The rationale for presenting the subcritical experi-
ments is to provide useful information to determine the
need and priority of critical experiments in a time that
the United States is without the capability to perform
critical mass experiments. From the data presented, ex-
periments with a hard spectrum have the greatest need of
critical data. The large discrepancy in the baseline exper-
iments also supports previous requests for critical exper-
iments with large quantities of graphite as moderator or
reflector. The Re experiments have the lowest relative
difference between calculated and predicted critical
masses. But, they are important to assess the amount of
Re needed in the reactor concept to prevent inadvertent
criticality in case the reactor was flooded by water dur-
ing a reentry accident.
ACKNOWLEDGMENTS
The authors would like to express their gratitude to the
many people who contributed ideas and discussions to this
study. The work described represents the cooperative com-
bined efforts of many individuals working for different orga-
nizations in numerous locations. Some provided sustained effort
over a period of time while others provided important input
or constructive suggestions when needed. Special thanks goes
to C. Hopper and M. Westfall of ORNL for initiating the
design of the critical experiments: “Sensitivity and Uncer-
tainty Evaluations of the JIMO LMR and Generic Physics
Criticality Experiments Design Suggestions for Simulating
LMR Sensitivities,” Oak Ridge National Laboratory Report,
ORNL0TM-2004056.
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