neutronic evaluation of gcfr core diluents and reflectors
TRANSCRIPT
Neutronic Evaluation of GCFR Core Diluents and Reflectors
by
Kun Yu
B.E., Engineering Physics, Tsinghua University, P.R.China (1998)
Submitted to the Department of Nuclear Engineering in partial fulfillment of the requirements for the degree of
Master of Science in Nuclear Engineering
At The MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2003
© 2003 Massachusetts Institute of Technology. All rights reserved
Signature of Author Kun Yu Department of Nuclear Engineering June 10, 2003 Certified by Michael J. Driscoll Professor Emeritus of Nuclear Engineering Thesis Supervisor Certified by Pavel Hejzlar Program Director, Center for Advanced Nuclear Energy Systems Thesis Reader Accepted by Jeffrey Coderre Associate Professor of Nuclear Engineering Chairman, Department Committee on Graduate Students
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Neutronic Evaluation of GCFR Core Diluents and Reflectors
By
Kun Yu
Submitted to the Department of Nulcear Engineering
on June 11, 2003 in Partial Fullfillment of the Requirements for the Degree of Master of Science in
Nuclear Engineering
ABSTRACT
Materials are evaluated for use as in-core diluents and as peripheral reflectors for Gas-Cooled Fast Reactor (GFR) service, using coupled Monte Carlo (MCNP) and isotopics (ORIGEN) codes. The principal performance indices compared were effects on beginning of irradiation multiplication factor, reactivity-lineated burnup, and coolant (here CO2) void reactivity.
While low values of the macroscopic absorption cross section, Σa, and slowing down power, ξΣs, are qualitatively useful predictors of good performance, it was found that only full scope calculations were valid for quantitative assessment. For example, several materials (Ni, Nb) having poor performance as in-core diluents proved to be good reflectors. Many materials which reduced coolant void reactivity also proved detrimental to reactivity lifetime. Others, mostly the strong moderators, increased initial reactivity, but decreased reactivity lifetime. Cores fueled with plutonium exhibited a much larger void reactivity than those started up using U-235 as the fissile material.
While there are no ideal candidates that are superior in all respects, considering only neutronic performance, the following appear worthy of further investgation: Metallic fuel diluents or matrices (eg. CERMET or METMET): Zr, Ti, V, Ba2Pb; High temperature fuel diluents or matrices (eg, CERMET, CERCER): SiC, BaS Cladding: Fe alloys with Cr, Al (eg ODS) Reflector: Zr3Si2, Pb, Ba2Pb, ZrS2, MoSi2 plus a variety of sulfides and silicides
Thesis Supervisor: Michael J. Driscoll
Title: Professor Emeritus of Nuclear Engineering
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ACKNOWLEDGMENTS
The help, patient guidance and generous support of Professor Michael J. Driscoll
and Dr Pavel Hejzlar, my thesis supervisors, are greatly appreciated.
I am also grateful to two members of the Physics and Materials group of the Gas
Cooled Fast Reactor Project at MIT: Pete Yarsky for his discovery of the possible cross
section library deficiency of Potassium, and Mike Pope for beneficial discussions on the
coolant void coefficient.
This work has been funded by the Idaho National Engineering & Environmental
Laboratory (INEEL) under their LDRD program.
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TABLE OF CONTENTS
ABSTRACT......................................................................................................................... i ACKNOWLEDGMENTS .................................................................................................. ii TABLE OF CONTENTS ................................................................................................ iii LIST OF TABLES ............................................................................................................ v LIST OF FIGURES ......................................................................................................... vi Chapter 1 Introduction ........................................................................................................ 1
1.1 Foreword ................................................................................................................... 1 1.2 Background............................................................................................................... 1 1.3 Organization of this report ........................................................................................ 8
Chapter 2 Computer Codes and Models ........................................................................... 10 2.1 Introduction............................................................................................................. 10 2.2 MCODE Description .............................................................................................. 10
2.2.1 Introduction...................................................................................................... 10 2.2.2 Normalization .................................................................................................. 11 2.2.3 Predictor-Corrector Algorithm......................................................................... 13 2.2.4 Running MCODE ............................................................................................ 14
2.4 Whole Core Model for matrix and reflector configuration..................................... 16 2.5 Summary ................................................................................................................. 26
Chapter 3 Review of core diluent material candidates ..................................................... 27 3.1 Introduction............................................................................................................. 27 3.2 Review of element properties ................................................................................. 27 3.3 Review of material candidates for matrix core ....................................................... 28
3.3.1 Neutronic Evaluation parameters..................................................................... 28 3.3.2 Results for matrix study ................................................................................... 30 3.3.3 Fissile and fertile properties in the energy range of interest ............................ 32 3.3.4 Promising materials ......................................................................................... 34
3.4 Applicability of superposition................................................................................. 42 3.4.1 Non-linearity of neutronic effects as a function of matrix concentration........ 42 3.4.2 Neutronic effects for a compound and its constituents.................................... 43 3.4.3 Relation of reactivity to enrichment ................................................................ 45
3.5 Conclusions............................................................................................................. 47 Chapter 4 Review of reflector material candidates........................................................... 48
4.1 Introduction............................................................................................................. 48 4.2 Review of material candidates for reflector............................................................ 48
4.2.1 Albedo calculation ........................................................................................... 48 4.2.2 General Results ................................................................................................ 50 4.2.3 Detailed evaluation and explanation................................................................ 51 4.2.4 Brief summary ................................................................................................. 56
4.3 Parameter Studies.................................................................................................... 56 4.3.1 Reflector thickness requirement ...................................................................... 56 4.3.2 UPuC fuel – UC fuel........................................................................................ 57 4.3.3 keff – albedo...................................................................................................... 59 4.3.4 Full burnup study of several interesting reflector materials ............................ 60
4.4 Conclusions............................................................................................................. 61 Chapter 5 Summary, Conclusions and Recommendations ............................................... 62
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5.1 Summary and Conclusions ..................................................................................... 62 5.2 General Evaluation Results..................................................................................... 62 5.3 Recommendations for future work ......................................................................... 65
References......................................................................................................................... 67 Appendix A Estimate of Gas Produced By Sulfur........................................................... 69 Appendix B Relation of reactivity ρ to enrichment x...................................................... 70 Appendix C Sample input files for matrix material study............................................... 72
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LIST OF TABLES
Table 1-1 Periodic table of the chemical elements showing excluded candidates....... 2
Table 1-2 Footnotes to Table 1–1..................................................................................... 3
Table 1-3 Representative Hard-Spectrum σ Values...................................................... 3
Table 1-4 Roster of Potential Diluent Candidates ......................................................... 8
Table 2-1 Matrix test core model parameters .............................................................. 17
Table 2-2 Initial region–homogenized compositions in matrix test core model........ 18
Table 2-3 Reflector test core model parameters .......................................................... 18
Table 2-4 Initial region homogenized compositions in reflector test core model...... 19
Table 2-5 Matrix material cell 1 homogenized composition for whole core model .. 19
Table 2-6 Description of chosen actinides..................................................................... 22
Table 2-7 Description of chosen fission products......................................................... 23
Table 2-8 Description of chosen matrix materials ....................................................... 25
Table 3-1 Results of matrix comparisons...................................................................... 30
Table 4-1 Neutronic Comparisons of GFR Reflectors................................................. 50
Table 5-1 General Evaluation Results........................................................................... 63
vi
LIST OF FIGURES
Figure 2-1 Flow diagram for MCODE.......................................................................... 15
Figure 2-2 Original fuel assembly and core layout of the MFGR-GT [6] ................. 16
Figure 2-3 Final homogenized cylindrical core layout ................................................ 17
Figure 3-1 Definition of B1 ............................................................................................. 29
Figure 3-2 Examples of error of linear extrapolation method.................................... 29
Figure 3-3 Relation of initial multiplication factor and burnup potential ................ 31
Figure 3-4 Relation of multiplication factor and macroscopic absorption................ 32
Figure 3-5 U235 capture, fission and elastic scattering cross sections * ...................... 33
Figure 3-6 U238 fission, elastic scatter, absorption cross sections ............................... 34
Figure 3-7 Map of diluent material performance ........................................................ 35
Figure 3-8 Capture and elastic scattering cross sections for minor Ba isotopes....... 36
Figure 3-9 Comparison of BaS and BaO diluent core spectra.................................... 41
Figure 3-10 Non-linearity of neutronic effects vs. Pb matrix concentration ............. 42
Figure 3-11 ρ vs. compound components...................................................................... 44
Figure 3-12 Relationship between enrichment and keff for a representative core .... 46
Figure 4-1 Variation of albedo with absorption........................................................... 49
Figure 4-2 Map of reflector material performance ..................................................... 52
Figure 4-3 keff versus nickel reflector thickness ........................................................... 57
Figure 4-4 keff (UC fuel) – keff (UPuC) fuel ................................................................... 58
Figure 4-5 Comparison of ∆keff(void) for UPuC fuel and UC fuel ............................. 58
Figure 4-6 The ∆k(void) increase with burnup ............................................................ 59
Figure 4-7 Relationship of multiplication factor and albedo...................................... 60
Figure 4-8 Full burnup runs for different reflectors ................................................... 61
1
Chapter 1 Introduction
1.1 Foreword
Gas cooled fast reactors have attracted new interest in the past several years both
within the US and internationally. It is widely recognized, however, that passive post-
LOCA decay heat removal is a challenge for reactors of this type. One approach to
amelioration is to increase the heat capacity of the fuel assemblies, and thereby store
energy until decay heat power levels decrease sufficiently (approximately as
1/(time)0.3 ) to facilitate energy removal via some combination of convection,
conduction and radiation. This leads to consideration of fuel diluents in the form of
alloys or ceramics in either homogeneous or dispersion form. The latter can be all-
metallic (METMET) ceramic (CERCER) or a combination (CERMET). It was the
objective of the work reported here to evaluate various candidate materials primarily
in terms of their effect on core neutronics, as a guide to future studies of specific core
designs. Most of these same considerations apply to the selection of reflector
materials, which are also essential to good neutronic performance. There are,
however, some differences in performance for this application which motivated a
separate set of comparisons.
1.2 Background
If one starts with the full periodic table of the elements (see Table 1.1) and all
possible combinations as chemical compounds, the task faced in any comprehensive
evaluation would be truly daunting. Fortunately preliminary screening according to a
few simple criteria greatly reduces the list of potential candidates; specifically we
exclude at the outset:
• All inert gases (e.g. He, Ar etc…)
• Candidates costing more than 200$/kg
• Heavy nuclei above 220 AMU (which are either unstable or fissionable)
2
• Species having spectrum-average microscopic absorption cross sections
greater than about 200 mbarn
• Excessively strong moderators such as H
• Radioactive materials such as Ra, Po, etc.
Other important criteria such as thermal conductivity, heat capacity, melting point
and corrosion resistance were not explicitly applied at this point, but must be in any
final downselection. In addition, some elements rejected because of their high σa will
find use as control absorbers, for example B and Ta.
Table 1-1 Periodic table of the chemical elements showing excluded candidates
H He
Li Be B C N O F Ne
Na Mg Al Si P S Cl Ar
K Ca Sr Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
Rb Sr Y Zr Nb Mo Tc* Ru Rh Pd Ag Cd In Sn Sb Te* I Xe
Cs Ba Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po* At* Rn
Fr* Ra* Ac* Rf Db Sg Bh Hs Mt
La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb
Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No
Key to rating:
1 2 3 4 5 6* 7
1. Strong moderator. (Atomic weight < 5) (1) 2. Actinides/fissionable. (Atomic number > = 90) (20) 3. Expensive or rare. (Price > 200$/kg) (30) 4. Inert gas. (6) 5. Strong absorber. (σc > 200 millibarns) (13) 6. Radioactive. (7) 7. Potentially usable matrix material. (32)
────────────────────────────────────────────────── Total 109
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Table 1-2 Footnotes to Table 1–1
(a) Some elements have more than one reason for exclusion. We assign only one, based on its most serious shortcoming. (b) Some elements could only be used in compounds, such as N, O, F, Cl, Br, I. (c) Metal prices were obtained from ref. [1].
(d) Li-7 and Be are light moderators. But FLiBe molten salt is used as coolant in some
recent concepts (see ref [2]). Beryllium also has a relatively large (n, 2n) cross section,
which improves the neutron economy, so we re-instate these two materials as candidates.
(e) The one group spectrum averaged neutron absorption cross sections of 90 elements
were obtained using the Pb matrix core model discussed in Chapter 2. The results are
shown in Table 1.3. The results are generally consistent with the central worth
measurements in fast critical assemblies compiled in ref [3].
(f) Some strong absorbers could not be used as matrix material but could be used as a reflector. Thus there are 45 potentially usable reflector elements, 13 more than as matrix candidates (Li, B, As, Se, Br, Ag, Cd, In, Sb, I, Cs, Ta, W).
Table 1-3 Representative Hard-Spectrum σ Values
ZAID Nuclei Abundance σ(n,γ)∗∗ σ(n,α)∗∗ σ(n,p)∗∗ σa(total)**
Atom fraction millibarns millibarns millibarns millibarns
1001.60c H1 0.999885 0.153 0.0 0.0 0.153 1002.60c H2 0.000115 0.003 0.0 0.0 0.003
- H(nat)* 0.153 0.0 0.0 0.153 2003.60c He3 1.37E-06 0.0 0.0 2513.2 2513.4 2004.60c He4 0.999999 0.0 0.0 0.0 0.0
- He(nat) 0.0 0.0 0.0 0.003 3006.60c Li6 0.0759 0.024 0.0 0.3 972.7 3007.60c Li7 0.9241 0.032 0.0 0.0 0.033
- Li(nat) 0.032 0.0 0.0 73.9 4009.60c Be9 0.100 3.9 0.0 4.03 5010.60c B10 0.199 0.278 2167.5 1.1 2173.0 5011.60c B11 0.801 0.033 0.0 0.0 0.036
- B(nat) 0.082 431.3 0.2 432.4 6000.60c C 0.002 0.1 0.0 0.064 6012.50c C12 0.9893 0.002 0.1 0.0 0.071
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ZAID Nuclei Abundance σ(n,γ)∗∗ σ(n,α)∗∗ σ(n,p)∗∗ σa(total)**
Atom fraction millibarns millibarns millibarns millibarns
6013.42c C13 0.0107 0.278 0.0 0.0 0.280 7014.60c N14 0.99632 0.049 8.4 14.2 22.7 7015.60c N15 0.00368 0.012 0.004 0.001 0.020
- N(nat) 0.048 8.4 14.1 22.6 8016.60c O16 0.99757 0.000 0.724 0.001 0.725 8017.60c O17 0.00038 0.061 30.2 0.0 30.3 9019.60c F19 2.71 0.91 0.06 3.68
11022.96c Na22 8.2 70.7 1318.1 1397.2 11023.60c Na/Na23 1.9 0.0 0.1 2.0 12000.60c Mg 0.7 0.2 0.1 1.0 12024.96c Mg24 0.7899 1.6 0.3 0.1 2.0 12025.96c Mg25 0.1 2.1 1.1 0.1 3.3 12026.96c Mg26 0.1101 0.3 0.0 0.0 0.4 13027.60c Al27 2.5 0.0 0.3 2.8 14000.60c Si 2.5 0.2 0.4 3.1 14028.96c Si28 0.922297 0.8 0.1 0.3 1.3 14029.96c Si29 0.046832 2.6 0.4 0.2 3.1 14030.96c Si30 0.030872 10.9 0.0 0.0 10.9 15031.60c P31 4.2 0.1 2.8 7.2 16000.60c S 2.3 12.4 5.2 19.8 16032.60c S32 0.9493 2.8 8.2 5.0 16.0 16033.96c S33 0.0076 1.1 172.6 10.7 184.3 16034.96c S34 0.0429 0.3 0.2 0.0 0.6 16036.96c S36 0.0002 0.4 0.0 0.0 0.4 17000.60c Cl 3.9 0.9 3.5 8.3 17035.96c Cl35 0.7578 5.9 3.7 13.9 23.6 17037.96c Cl37 0.2422 1.6 0.1 0.0 1.7 19000.60c K 11.3 1.5 7.3 20.1 19039.96c K39 0.932581 11.1 2.8 11.0 24.9 19040.96c K40 0.000117 12.1 41.0 13.7 66.8 19041.96c K41 0.067302 25.2 0.1 0.1 25.4 20000.60c Ca 3.8 5.7 8.2 17.8 20040.21c Ca40 3.8 0.0 0.0 3.8 21045.60c Sc45 40.4 0.0 4.3 44.8 22000.60c Ti 12.6 0.1 0.2 12.9 22046.96c Ti46 0.0823 12.5 0.1 0.7 13.2 22047.96c Ti47 0.0744 31.9 0.2 2.0 34.2 22048.96c Ti48 0.7372 17.4 0.0 0.0 17.4 22049.96c Ti49 0.0541 8.6 0.0 0.1 8.7 22050.96c Ti50 0.0518 1.1 0.0 0.0 1.1 23000.60c V 17.3 0.0 0.0 17.4 23051.96c V51 20.3 0.0 0.0 20.3 24000.50c Cr 16.3 0.0 0.3 16.5 24052.60c Cr52 0.83789 5.7 0.0 0.1 5.8 24053.60c Cr53 0.09501 24.6 0.1 0.0 24.7 24054.60c Cr54 0.02365 5.3 0.0 0.0 5.3
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ZAID Nuclei Abundance σ(n,γ)∗∗ σ(n,α)∗∗ σ(n,p)∗∗ σa(total)**
Atom fraction millibarns millibarns millibarns millibarns
25055.60c Mn55 24.0 0.0 0.0 24.0 26000.55c Fe 11.0 0.0 0.4 11.4 26054.60c Fe54 0.05845 16.9 0.1 6.0 22.9 26056.60c Fe56 0.91754 7.7 0.0 0.1 7.8 26057.60c Fe57 0.02119 20.1 0.1 0.0 20.2 26058.60c Fe58 0.00282 11.3 0.0 0.0 11.3 27058.96c Co58 37.4 0.5 709.7 747.7 27059.60c Co/Co59 32.0 0.0 0.1 32.1 28000.50c Ni 20.3 0.3 5.8 26.4 28058.60c Ni58 0.680769 23.2 0.6 8.6 32.4 28059.96c Ni59 58.3 8.9 43.3 110.4 28060.60c Ni60 0.262231 17.5 0.1 0.1 17.7 28061.60c Ni61 0.011399 40.1 0.2 0.2 40.5 28062.60c Ni62 0.036345 28.0 0.0 0.0 28.0 28064.60c Ni64 0.009256 12.1 0.0 0.0 12.1 29000.50c Cu 44.4 0.0 1.1 45.5 29063.60c Cu63 0.6917 51.2 0.0 1.9 53.1 29065.60c Cu65 0.3083 26.3 0.0 0.0 26.4 30000.62c Zn 34.8 3.7 2.4 40.8 30064.96c Zn64 50.5 0.0 3.3 53.8 31000.60c Ga 71.4 0.1 0.0 71.5 32072.96c Ge72 0.3479 53.0 0.0 0.0 53.0 32073.96c Ge73 0.09765 197.6 0.0 0.0 197.6 32074.96c Ge74 0.45831 32.9 0.0 0.0 32.9 32076.96c Ge76 0.09614 11.6 0.0 0.0 11.6 32072.96c Ge(but no Ge70) 53.9 0.0 0.0 53.9 37085.96c Rb85 0.7217 131.4 0.0 0.0 131.4 37086.96c Rb86 98.8 0.0 0.0 98.8 37087.96c Rb87 0.2783 10.7 0.0 0.0 10.7
- Rb(nat) 97.8 0.0 0.0 97.8 38084.96c Sr84 0.0056 165.0 0.0 0.0 165.0 38086.96c Sr86 0.0986 45.9 0.0 0.0 45.9 38087.96c Sr87 0.07 79.9 0.0 0.0 79.9 38088.96c Sr88 0.8258 1.1 0.0 0.0 1.1 38089.96c Sr89 19.0 0.0 0.0 19.0 38090.96c Sr90 13.1 0.0 0.0 13.1
- Sr 11.9 0.0 0.0 11.9 39088.35c Y88 49.7 0.0 412.8 462.5 39089.60c Y/Y89 16.5 0.0 0.0 16.6 39090.96c Y90 107.8 0.0 0.0 107.8 39091.96c Y91 32.5 0.0 0.0 32.5 40000.60c Zr 22.8 0.0 0.0 22.8 40090.86c Zr90 0.5145 16.6 0.0 0.0 16.6 40091.96c Zr91 0.1122 44.0 0.0 0.0 44.0 40092.86c Zr92 0.1715 30.5 0.0 0.0 30.5 40093.86c Zr93 56.0 0.0 0.0 56.0
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ZAID Nuclei Abundance σ(n,γ)∗∗ σ(n,α)∗∗ σ(n,p)∗∗ σa(total)**
Atom fraction millibarns millibarns millibarns millibarns
40094.86c Zr94 0.1738 20.4 0.0 0.0 20.4 40095.60c Zr95 117.6 0.0 0.0 117.6 41093.60c Nb/Nb93 170.0 0.0 0.0 170.0 41094.96c Nb94 172.6 0.0 0.0 172.6 41095.96c Nb95 263.6 0.0 0.0 263.6 42000.60c Mo 110.8 0.0 0.0 110.8 42092.96c Mo92 0.1484 49.6 0.0 0.7 50.2 42094.96c Mo94 0.0925 65.8 0.0 0.0 65.8 42095.50c Mo95 0.1592 236.2 0.0 0.0 236.2 42096.96c Mo96 0.1668 74.7 0.0 0.0 74.7 42097.60c Mo97 0.0955 227.4 0.0 0.0 227.4 42098.50c Mo98 0.2413 76.6 0.0 0.0 76.6 42099.60c Mo99 398.8 0.0 0.0 398.8 42100.96c Mo100 0.0963 65.7 0.0 0.0 65.7 46102.96c Pd102 0.0102 132.5 0.0 0.0 132.5 46104.96c Pd104 0.1114 250.3 0.0 0.0 250.3 46105.50c Pd105 0.2233 708.1 0.0 0.0 708.1 46106.96c Pd106 0.2733 210.0 0.0 0.0 210.0 46107.96c Pd107 763.0 0.0 0.0 763.0 46108.50c Pd108 0.2646 194.3 0.0 0.0 194.3 46110.96c Pd110 0.1172 121.2 0.0 0.0 121.2
- Pd(nat) 310.4 0.0 0.0 310.4 50000.42c Sn(nat) 54.0 0.0 0.0 54.0 50112.96c Sn112 0.0097 238.9 0.0 0.0 238.9 50114.96c Sn114 0.0066 224.2 0.0 0.0 224.2 50115.96c Sn115 0.0034 33.0 0.0 0.0 33.0 50116.96c Sn116 0.1454 45.5 0.0 0.0 45.5 50117.96c Sn117 0.0768 163.0 0.0 0.0 163.0 50118.96c Sn118 0.2422 89.5 0.0 0.0 89.5 50119.96c Sn119 0.0859 40.0 0.0 0.0 40.0 50120.96c Sn120 0.3258 33.5 0.0 0.0 33.5 50122.96c Sn122 0.0463 21.8 0.0 0.0 21.8 50123.96c Sn123 87.3 0.0 0.0 87.3 50124.96c Sn124 0.0579 13.2 0.0 0.0 13.2 50125.96c Sn125 127.0 0.0 0.0 127.0 50126.96c Sn126 7.2 0.0 0.0 7.2 52120.96c Te120 0.0009 311.8 0.0 0.0 311.8 52122.96c Te122 0.0255 256.8 0.0 0.0 256.8 52123.96c Te123 0.0089 495.6 0.0 0.0 495.6 52124.96c Te124 0.0474 196.7 0.0 0.0 196.7 52125.96c Te125 0.0707 256.5 0.0 0.0 256.5 52126.96c Te126 0.1884 84.5 0.0 0.0 84.5 52127.96c Te127 0.3174 271.2 0.0 0.0 271.2 52128.96c Te128 0.3408 82.9 0.0 0.0 82.9 52129.96c Te129 84.0 0.0 0.0 84.0 52130.96c Te130 11.6 0.0 0.0 11.6
7
ZAID Nuclei Abundance σ(n,γ)∗∗ σ(n,α)∗∗ σ(n,p)∗∗ σa(total)**
Atom fraction millibarns millibarns millibarns millibarns
52132.96c Te132 0.4 0.0 0.0 0.4 - Te(nat) 84.9 0.0 0.0 84.9
56130.96c Ba130 0.00106 598.6 0.0 0.0 598.6 56132.96c Ba132 0.00101 361.2 0.0 0.0 361.2 56134.96c Ba134 0.02417 87.9 0.0 0.0 87.9 56135.96c Ba135 0.06592 231.1 0.0 0.0 231.1 56136.96c Ba136 0.07854 33.9 0.0 0.0 33.9 56137.96c Ba137 0.11232 38.1 0.0 0.0 38.1 56138.60c Ba138 0.71698 4.7 0.1 0.0 4.9 56140.60c Ba140 9.5 0.0 0.0 9.5
- Ba(nat) 28.7 0.1 0.0 28.8 57138.96c La138 0.0009 204.0 0.0 0.0 204.0 57139.60c La139 0.9991 28.1 0.0 0.0 28.1 57140.60c La140 156.7 0.0 0.0 156.7
- La(nat) 28.2 0.0 0.0 28.2 58140.96c Ce140 0.88837 17.3 0.0 0.0 17.3 58141.60c Ce141 108.2 0.0 0.0 108.2 58142.96c Ce142 0.11163 31.9 0.0 0.0 31.9 58143.60c Ce143 120.0 0.0 0.0 120.0 58144.96c Ce144 28.9 0.0 0.0 28.9
- Ce(nat) 19.0 0.0 0.0 19.0 82000.50c Pb(nat) 3.6 0.0 0.0 3.6 82206.86c Pb206 0.241 9.6 0.0 0.0 9.6 82207.60c Pb207 0.221 7.2 0.0 0.0 7.2 82208.60c Pb208 0.524 0.7 0.0 0.0 0.7 83209.60c Bi209 4.1 0.0 0.0 4.1 *some cross sections of natural materials are obtained by abundance weighted summation
We now have in all 33 matrix candidate elements and 45 reflector candidate elements
remaining.(including Li-7) Based on their distinctive properties, we can classify them
under 4 main categories; see Table 1.4.
8
Table 1-4 Roster of Potential Diluent Candidates
Possible Form of Use Elements
In Ceramics (6)
(including CERCER, CERMET) C, N, O, P, S, Si
As metals and alloys (19)
(including CERMET, METMET)
Mg, Ca, Sr, Ba, Ti, V, Cr, Mn, Fe, Co, Ni,
Cu, Zn, Al, Sn, Zr, Nb, Mo
As liquid metal (5)
(coolants, pools) Na, K, Pb, Bi, Hg
In molten salts (3 + 1)**
(coolants, pools)
F, Cl, Be*
(also the separated isotope Li-7) [2]
*Be could also be used in metallic form and as BeO ceramic.
** see ref [2]
1.3 Organization of this report
Chapter 2 describes the computer codes employed and the whole-core model used to
evaluate important neutronic parameters such as multiplication factor, its rate of change
with burnup, initial conversion ratio and spectrum-averaged cross sections. This degree
of sophistication is necessary because a priori judgments are unreliable for hard spectrum
fast reactors in view of the influence of less familiar phenomena such as (n,p) (n,α) and
(n,2n) reactions, the effect of scattering resonances on leakage and inelastic scattering on
moderation.
In chapter 3 results for matrix studies are shown and analyzed. Issues such as the non-
linearity of neutronic effects vs. diluent concentration and the failure of the superposition
principle in predicting the effect of compounds based on their individual components are
discussed.
Chapter 4 reports a detailed study for reflector material candidates. The candidate
material range is broadened and more compounds are included. Materials good as in-core
9
matrix diluents are not necessarily good as reflectors. The different demands for different
functions are discussed.
Chapter 5 presents a summary, principal overall conclusions, and recommendations
for follow-on work.
An appendix is included discussing the potential problem due to helium production
via (n, α) reactions in sulfur.
10
Chapter 2 Computer Codes and Models
2.1 Introduction
In this chapter descriptions are presented of the computer codes employed in the
evaluation of core diluents in whole core models. Sufficient descriptive information and
data are provided that others could reproduce or extend the results to be presented later in
chapters 3 and 4. Appendices to this report provide sample copies of code input and
output in further fulfillment of this goal.
2.2 MCODE Description
2.2.1 Introduction MCODE (MCNP-ORIGEN Depletion program)[4] is a linkage program (~3000
lines of ANSI C), which uses MCNP and ORIGEN to do burnup calculations for
arbitrarily-defined MCNP regions[5]. MCNP is used to calculate neutron flux and from it
determine the effective one-group cross sections for materials in different MCNP-defined
regions. ORIGEN, in turn, can carry out depletion calculations for each region and output
time-dependent isotopic composition. MCODE serves as a console program to control the
data flow between MCNP and ORIGEN as well as the alternate running of these two
codes.
MCNP-4c, the latest MCNP version, was used, which is a general purpose,
generalized geometry, continuous energy, time-dependent, Monte Carlo transport code
for neutrons/photons/electrons developed at the Los Alamos National Laboratory
(LANL)[5]. The Monte Carlo method is employed in MCNP, which sets up a virtual
world analog to reality to solve neutron transport problems. It follows each of many
particles from a source to their death in some terminal category (absorption, escape, etc.).
Probability distributions are randomly sampled to determine the outcome at each step. In
MCODE burnup calculations, three kinds of data are needed from MCNP:
1. criticality or eigenvalue, keff,
2. effective one-group cross sections,
11
3. one-group neutron flux data.
Specifically, the effective one-group cross sections of fission products and actinides are
needed. For fission products, only neutron capture cross sections are calculated. For
actinides, four types of cross sections are considered including capture, fission, (n, 2n),
and (n, 3n) reactions. Although not all nuclides and all reactions are calculated, the
representation of fission products and actinides is quite complete for burnup calculations
(i.e. altogether the chosen isotopes account for more than 99% of neutron absorption). In
addition to the effective one-group cross sections, the one-group flux value in each
MCNP depletion cell is needed.
ORIGEN (version 2.1) is a one-group depletion and radioactive decay computer
code developed at the Oak Ridge National Laboratory (ORNL)[6]. Given appropriate
one-group cross sections and decay constants, ORIGEN 2.1 uses a matrix exponential
method to solve a large system of coupled, linear, first-order ordinary differential
equations with constant coefficients. Both nuclear reactions and isotope decay are
considered. Several generic reaction specific cross section and fission product yield data
libraries are available with ORIGEN 2.1. For cross sections not provided from MCNP,
ORIGEN uses library values, which are fairly representative of a given type of reactor.
The cross section data used in our work is from the fast flux test facility core library
(FFTFC.LIB).
2.2.2 Normalization
Since there are two modes of depletion in ORIGEN, constant power or constant
flux, there are two corresponding ways to do depletions. In burnup calculations, the total
power of the reactor is usually assumed to be known and maintained constant. However,
the power fractions among different zones vary. Therefore, the two options should not
affect final results if small time steps are used. MCODE provides the user with both of
the above options to run depletion calculations. The flux values from MCNP are in units
of number of neutrons per fission source neutron per cm2, which must be multiplied by an
appropriate factor to convert into n/cm2 per second if an actual flux value is wanted.
12
For power normalization, the power of each cell is determined and fixed in each
time step. It is not necessary to normalize relative flux values from MCNP because the
power fractions for each cell can be obtained using only these relative values:
( ) ( ){ }( ) ( ){ }∑∑ ∫
∑ ∫
= =
=
⋅⋅
⋅⋅= n
k
m
j
jkkk
jfk
jk
m
j
jiii
jfi
ji
i i
i
RVdEEEN
RVdEEENf
1 1,
1,
φσ
φσ, (2-1)
where fi is the power fraction of cell i,
jiN is the number density of isotope j in cell i,
Vi is the volume of cell i,
jiR is the recoverable energy of isotope j in cell i,
( )Ejfi,σ is the fission cross section at energy E for isotope j in cell i,
( )Eiφ is the neutron flux at energy E,
The j summation is over all actinides,
and the k summation is over all depletion cells.
Then, the power of each cell can be determined by multiplying the fraction factor fi by the
given total power.
For flux normalization, the absolute flux value for each depletion cell is needed.
Therefore, the relative flux values from MCNP are multiplied by a constant factor. This
flux multiplication factor (FMF) in units of fission neutrons per second can be calculated
by either of the following two ways:
eff
FMFkQ
P⋅⋅
=ν , (2-2)
where P is the total power of the modeled system (watts),
ν is the average number of neutrons per fission,
Q is the average recoverable energy per fission (Joules/fission),
keff is the eigenvalue of the system;
( ) ( ){ }∑∑ ∫= =
⋅⋅= n
i
m
j
jiii
jfi
ji
i
RVdEEEN
P
1 1,
FMFφσ
. (2-3)
13
Equation (2-2) has a simpler form but with some ambiguities in its quantities. For
instance, the average recoverable energy per fission needs to be computed carefully. One
can imagine that for different kinds of fuel Q can be very different. For a relevant
discussion see Ref. [16]. Equation (2-3) appears complicated, but has a very clear
meaning and no ambiguities with regard to its quantities. However, both Eq. (2-2) and
Eq. (2-3) give an instantaneous flux multiplying factor only. For the real situation in each
depletion cell, the flux level changes continuously with burnup. The time step average
flux should be used instead of beginning-of-time-step instantaneous flux. This might be
done by the internal “predictor-corrector”, namely after the first trial ORIGEN depletion
gives an average flux to satisfy given energy production, the second ORIGEN depletion
uses the average flux (corrector).
In the ideal case, the two ways of normalization produce identical results. But
when the time step is long, power normalization assumes constant power in each cell,
which is incorrect; flux normalization assumes constant flux in each cell, which is also
incorrect. Hence the specified time step length must be sufficiently short such that the
two approaches give comparable results.
2.2.3 Predictor-Corrector Algorithm The coupling of MCNP and ORIGEN requires careful attention to detail. Because
the cross sections, flux and power fraction in each depletion cell are varying during
reactor operation, it is not valid to use beginning-of-time-step values to represent the
entire time step. A better estimate of time step average value is required.
The predictor-corrector algorithm is the standard algorithm to solve depletion
problems. For each burnup step the depletion is calculated twice, first using the spectra at
the start of the step and then, after a new spectrum calculation, using the spectra at the
end of the step. Average number densities from these two calculations are used as start
values for the next burnup step. This algorithm has proven to be efficient and useful to
solve depletion problems, especially in poisoned assemblies [4]. It has been implemented
in MCODE, which distinguishes MCODE from other MCNP-ORIGEN linkage codes,
such as MOCUP, MONTEBURNs, etc.
14
2.2.4 Running MCODE
One of the best features of MCODE is its user-friendly interface. Users need a
minimal amount of time to learn and initiate MCODE runs. Only three input files are
needed:
• initial MCNP input,
• MCODE input file,
• MCNP source file (optional).
Users have many options to run the code, such as the predictor-corrector option,
normalization option, etc. The flow chart is shown in Figure: 1.
The default and recommended settings are to employ the predictor-corrector, plus
flux normalization. Power normalization is usually used to check the result. When time is
limiting, the predictor-corrector can be turned off: this reduces overall time per step by
approximately a factor of two.
15
Parse MCODE input and initialize variables
Initial run?
Preprocess initial mcnp input and run MCNP
Extract beginning-of-timestep cross-sections and flux values
Loop through all timesteps
Run ORIGEN depletions for all active cells
Update MCNP input based on ORIGEN outputmaterial composition (predictor), and run MCNP
Predictor-Corrector?
Finish all timesteps?
Extract end-of-timestep cross-sections and flux values
Re-run ORIGEN depletions for all active cells
Average the predictor and corrector material,update MCNP input, and re-run MCNP
NO (restart)
YES
YES
YES
NO
NO
END Figure 2-1 Flow diagram for MCODE
16
2.4 Whole Core Model for matrix and reflector configuration
A simplified matrix core model was developed from the homogenization of the
hexagonal cell core developed in ref[9]. See Figure: 2.3. Axial leakage is assumed to be
zero. The extruded coolant tubes and the cladding of the assembly are made of the same
material as the matrix. These two parts are included in the calculated matrix volume
fraction. The core parameters for matrix tests are given in tables 2.5 and 2.6. Similarly,
the parameters for reflector tests are given in tables 2.7 and 2.8.
Figure 2-2 Original fuel assembly and core layout of the MFGR-GT [6]
2)
matrix metal serves as clad
extruded sheath matrix metal
CERMET or METMET fuel in matrix
active core
reflector
36 cm
Gas coolant (CO2) D = 1.2cm, 106holes/cell
17
Figure 2-3 Final homogenized cylindrical core layout
For matrix tests, the reflector is always Nickel and the core diameter 300cm; for reflector
tests, the matrix is always Lead and the core diameter 180cm. The reflector thickness is
always 90cm.
Table 2-1 Matrix test core model parameters
Parameters Values Parameters Values
Fuel* UC, UPuC Coolant CO2 Fuel temperature (ºK) 773.15 reflector thickness (cm) 90.00 Fuel percent of theoretical density 100.00 volume percent of fuel (%) 26.92 Fuel enrichment (%) 13.00 volume percent of coolant (%) 10.28 core diameter (cm) 300.00 volume percent of matrix (%)** 62.80 core height (m) 1.00 Power density (kW/l) 10.61 * We are mainly using UC fuel. The UPuC fuel with matrix study is limited.
** volume fraction of matrix material is kept the same for performance comparisons.
18
Table 2-2 Initial region–homogenized compositions in matrix test core model
Nuclide Weight percent
Number density
(w/o) (#/barn.cm) Fuel U238 - 7.685943E-03
(UC+matrix+CO2) U235 - 1.163166E-03 Cell1* C - 9.041788E-03
O - 3.853585E-04 Fuel U238 - 7.685943E-03
(US+matrix+CO2) U235 - 1.163166E-03 Cell1* C - 1.926790E-04
O - 3.853585E-04 S - 8.849109E-03
Fuel U238 - 7.685943E-03 (UPuC+matrix+CO2) Pu238 - 1.170402E-05
Cell1* Pu239 - 7.342604E-04 Pu240 - 3.365826E-04 Pu241 - 1.155801E-05 Pu242 - 6.906098E-05 C - 9.041788E-03 O - 3.853585E-04
Reflector Ni 9.995943E+01 8.898912E-02 (Ni+CO2) C 1.107238E-02 4.816981E-05
Cell2 O 2.949893E-02 9.633962E-05
* Since UC/US/UPuC and CO2 keep their same volume percentages when matrix
material changes, the homogenized atom number densities of uranium carbide and
carbon dioxide in the core cell are always the same. The parameters for the reflector
cell are fixed. The weight percent of UC/US/UPuC and CO2 depend on the density
and formula weight of the specified matrix.
Table 2-3 Reflector test core model parameters
Parameters Values Parameters Values
Fuel UC Coolant CO2 Fuel temperature (ºK) 773.15 reflector thickness (cm) 90.00 Fuel percent of theoretical density 100.00 volume percent of fuel (%) 26.92 Fuel enrichment (%) 13.00 volume percent of coolant (%) 10.28 core diameter (cm) 180.00 volume percent of matrix (%)* 62.80 core height (m) 1.00 Power density (kW/l) 10.61 * Volume fraction of reflector material is kept the same for performance
comparisons.
19
In the matrix model, the core diameter is set to 300.0cm, which makes the core’s leakage
negligible. When assessing radial reflector performance, we need larger leakage to get
accurate performance comparisons. The 180cm(d) × 100cm(h) cylinder bare(unreflected)
core has keff = 1.02368. Thus keff – 1.02368 can be considered as mainly gains
attributable to the reflector.
Table 2-4 Initial region homogenized compositions in reflector test core model
Nuclide Weight percent Number density
(w/o) (#/barn.cm) Fuel U238 28.10 7.685943E-03 (UC+Pb+CO2) U235 4.20 1.163166E-03 Cell1 C 1.67 9.041788E-03 O 0.09 3.853585E-04 Pb 65.94 2.071776E-02
reflector C - 4.816981E-05 (reflector+CO2) O - 9.633962E-05 Cell2
Since CO2 keeps the same volume percentage when reflector material changes, the
homogenized atom number densities of carbon dioxide in the reflector cell are always the
same. The parameters for the matrix/fuel cell are fixed.
Table 2-5 Matrix material cell 1 homogenized composition for whole core model
matrix component weight percent numberdensity ( % ) (#/barn.cm) Al Al 100.00 3.783206E-02 Al4C3 Al 74.97 2.480135E-02 C 25.03 1.860101E-02 Ba Ba130 0.10 1.024670E-05 Ba132 0.10 9.763390E-06 Ba134 2.36 2.336450E-04 Ba135 6.48 6.372300E-04 Ba136 7.77 7.592240E-04 Ba137 11.20 1.085766E-03 Ba138 72.00 6.930846E-03 BaO Ba130 0.09 1.495680E-05 Ba132 0.09 1.425130E-05 Ba134 2.18 3.410430E-04 Ba135 6.00 9.301440E-04
20
matrix component weight percent numberdensity ( % ) (#/barn.cm) Ba136 7.20 1.108214E-03 Ba137 7.26 1.108214E-03 Ba138 66.73 1.011672E-02 O 10.43 1.363355E-02 BaS Ba130 0.08 1.055130E-05 Ba132 0.08 1.005360E-05 Ba134 1.91 2.405890E-04 Ba135 5.25 6.561700E-04 Ba136 6.30 7.817900E-04 Ba137 9.08 1.118037E-03 Ba138 58.37 7.136843E-03 S 18.93 9.954034E-03 BeO Be 36.03 4.536367E-02 O 63.97 4.536367E-02 Bi Bi 100.00 1.769952E-02 C C 100.00 8.344854E-02 Ca Ca 100.00 1.462735E-02 CaC2 Ca 62.52 1.311143E-02 C 37.48 2.622286E-02 CeO2 Ce 81.41 1.566749E-02 O 18.59 3.133498E-02 Co Co 100.00 7.539229E-02 Cr Cr 100.00 5.193445E-02 Cu Cu 100.00 5.325470E-02 Fe Fe 100.00 5.282486E-02 Fe3C Fe 93.31 4.862416E-02 C 6.69 1.620805E-02 HT9 Fe 84.7 4.474266E-02 Ni 0.5 2.513063E-04 Cr 12 6.808213E-03 Mo 1 3.074843E-04 Si 0.2 2.100731E-04 V 0.3 1.737289E-04 W 0.5 8.023293E-05 C 0.2 4.912298E-04 Mn 0.6 3.221816E-04 K K 100 8.280259E-03 Mg Mg 100.00 2.704544E-02 Mn Mn 100.00 5.142513E-02 Mo Mo 100.00 4.052822E-02 Na Na 100.00 1.592461E-02 Nb Nb 100.00 3.488987E-02 Ni Ni 100.00 5.740094E-02 P P 100.00 2.225978E-02 Pb Pb 100.00 2.071776E-02 PbO Pb 92.83 1.633518E-02
21
matrix component weight percent numberdensity ( % ) (#/barn.cm) O 7.17 1.633518E-02 PbS Pb 86.60 1.201358E-02 S 13.40 1.201358E-02 Ba2Pb Ba130 0.06 8.172440E-06 Ba132 0.06 7.786950E-06 Ba134 1.34 1.863470E-04 Ba135 3.69 5.082330E-04 Ba136 4.43 6.055320E-04 Ba137 6.38 8.659700E-04 Ba138 41.04 5.527809E-03 Pb 43.00 3.854926E-03 S S 100.00 2.311814E-02 Si Si 100.00 3.137716E-02 SiC Si 70.05 3.034421E-02 C 29.95 3.034421E-02 Sn Sn 100.00 2.328939E-02 Sr Sr84 0.54 6.35777E-05 Sr86 9.67 0.001119422 Sr87 6.94 0.000794721 Sr88 82.85 0.00937544 SrO Sr84 0.45 9.61E-05 Sr86 8.18 0.001691917 Sr87 5.87 0.001201158 Sr88 70.06 0.014170237 O 15.44 1.72E-02 SrS Sr84 0.39 6.55E-05 Sr86 7.08 0.001152786 Sr87 5.08 0.000818408 Sr88 60.65 0.009654873 S 26.79 0.011691539 Sr2Pb Sr84 0.11 4.90E-05 Sr86 1.95 0.000862324 Sr87 1.40 0.000612197 Sr88 16.68 0.007222178 Pb 79.86 1.47E-02 Ti Ti 100.00 3.56E-02 TiC Ti 79.94 3.118990E-02 C 20.06 3.118990E-02 TiN Ti 77.36 3.184884E-02 N 22.64 3.184884E-02 TiN15 Ti 77.36 3.184884E-02 N15 22.64 3.184884E-02 U238 U238 100.00 3.027119E-02 V V 100.00 4.536256E-02 VC V 80.92 3.466758E-02 C 19.08 3.466758E-02
22
matrix component weight percent numberdensity ( % ) (#/barn.cm) W W 100.00 3.960215E-02 Zn Zn 100.00 4.129666E-02 ZnC Zn 84.48 3.288503E-02 C 15.52 3.288503E-02 Zr Zr 100.00 2.696982E-02 ZrO2 Zr 74.03 1.743353E-02 O 25.97 3.486706E-02 ZrC Zr 88.37 2.465768E-02 C 11.63 2.465768E-02 Void - - -
A total of 39 actinides and 100 fission products (including some excited states as
different nuclides) have been tracked in MCODE burnup runs. 34 elements are used
singly or in combination as matrix material. See tables 2.10, 2.11 and 2.12.
Table 2-6 Description of chosen actinides
Number Actinides ZAID Library Name Source Temperature (°C) 1 Th-232 90232.60c endf60 B-V.0 294 2 Pa-231 91231.60c endf60 B-VI.0 294 3 Pa-233 91233.50c endf5u B-V.0 294 4 U-232 92232.60c endf60 B-VI.0 294 5 U-233 92233.60c endf60[14] B-VI.0 294 6 U-234 92234.60c endf60 B-VI.0 294 7 U-235 92235.60c endf60 B-VI.2 294 8 U-236 92236.60c endf60 B-VI.0 294 9 U-237 92237.50c endf5p B-VI.0 294
10 U-238 92238.60c endf60 B-VI.2 294 11 Np-236 93236.35c endl85 LLNL 0 12 Np-237 93237.60c endf60 B-VI.1 294 13 Np-238 93238.35c endl85 LLNL 0 14 Np-239 93239.60c endf60 B-VI.0 294 15 Pu-238 94238.60c endf60 B-VI.0 294 16 Pu-239 94239.60c endf60 B-VI.2 294 17 Pu-240 94240.60c endf60 B-VI.2 294 18 Pu-241 94241.60c endf60 B-VI.1 294 19 Pu-242 94242.60c endf60 B-VI.0 294 20 Pu-243 94243.60c endf60 B-VI.2 294 21 Am-241 95241.60c endf60 T-2 300 22 Am-242 95242.50c endf5u B-V.0 294 23 Am-242 95242.51c rmccs B-V.0 294 24 Am-243 95243.60c endf60 B-VI.0 294 25 Am-244 95244.96c hfirxs1 INEEL 300
23
Number Actinides ZAID Library Name Source Temperature (°C) 26 Cm-242 96242.60c endf60 B-VI.0 294 27 Cm-243 96243.60c endf60 B-VI.0 294 28 Cm-244 96244.60c endf60 B-VI.0 294 29 Cm-245 96245.60c endf60 B-VI.2 294 30 Cm-246 96246.60c endf60 B-VI.2 594 31 Cm-247 96247.60c endf60 B-VI.2 294 32 Cm-248 96248.60c endf60 B-VI.0 294 33 Cm-249 96249.96c hfirxs1 INEEL 300 34 Bk-249 97249.60c endf60 B-VI:XTM 294 35 Bk-250 97250.96c hfirxs1 INEEL 300 36 Cf-249 98249.60c endf60 B-VI:XTM 294 37 Cf-250 98250.60c endf60 B-VI.2 294 38 Cf-251 98251.60c endf60 B-VI.2 294 39 Cf-252 98252.60c endf60 B-VI.2 294
Table 2-7 Description of chosen fission products
Number Actinides ZAID Library Name Source Temperature (°C) 1 Br-81 35081.55c miscSxs[6,8] T-2 294.0 2 Kr-82 36082.50c rmwsa ENDF/B-V.0 294.0 3 Kr-83 36083.50c rmccsa ENDF/B-V.0 294.0 4 Kr-84 36084.50c rmccsa ENDF/B-V.0 294.0 5 Rb-85 37085.55c miscSxs[6,8] T-2 294.0 6 Rb-87 37087.55c Misc5xs[6,8] T-2 294.0 7 Sr-90 38090.96c hfirxs1 INEEL 300.0 8 Y-89 39089.60c endf60 ENDF/B-VI.0 294.0 9 Zr-91 40091.96c hfirxs1 INEEL 300.0
10 Zr-92 40092.62c Zr92.300 UTXS 300.0 11 Zr-93 40093.50c kidman ENDF/B-v.0 294.0 12 Zr-94 40094.62c Zr92.300 UTXS 300.0 13 Zr-96 40096.62c Zr92.300 UTXS 300.0 14 Nb-95 41095.96c hfirxs1 INEEL 300.0 15 Mo-95 42095.50c kidman ENDF/B-V:0 294.0 16 Mo-96 42096.96c hfirxs1 INEEL 300.0 17 Mo-97 42097.60c mason1 INEEL 294.0 18 Mo-98 42098.50c mason1 INEEL 294.0 19 Mo-100 42100.50c mason1 INEEL 294.0 20 Tc-99 43099.50c kidman ENDF/B-V.0 293.6 21 Ru-100 44100.96c hfirxs1 INEEL 300.0 22 Ru-101 44101.50c kidman ENDF/B-V.0 293.6 23 Ru-102 44102.60c mason1 INEEL 293.6 24 Ru-103 44103.50c kidman ENDF/B-V.0 293.6 25 Ru-104 44104.96c ornlxsb1 INEEL 300.0 26 Rh-103 45103.50c rmccsa ENDF/B-V.0 293.6 27 Rh-105 45105.50c kidman ENDFIB-V.0 293.6 28 Pd-104 46104.96c ornlxs1 INEEL 300.0
24
Number Actinides ZAID Library Name Source Temperature (°C) 29 Pd-105 46105.50c kidman ENDF/B-V.0 293.6 30 Pd-106 46106.96c ornlxs1 INEEL 300.0 31 Pd-107 46107.96c ornlxs1 INEEL 300.0 32 Pd-108 46108.50c kidman ENDF/B-V.0 293.6 33 Pd-110 46110.96c ornlxs1 INEEL 300.0 34 Ag-109 47109.60c endf60 ENDF/B-VI.0 293.6 35 Cd-110 48110.62c Cd110.300 INEEL 300.0 36 Cd-111 48111.62c Cd111.300 INEEL 300.0 37 Cd-112 48112.62c Cd112.300 INEEL 300.0 38 Cd-113 48113.60c mason1 INEEL 293.6 39 Cd-114 48114.62c Cd114.300 INEEL 300.0 40 In-115 49115.60c mason1 INEEL 293.6 41 Sb-121 51121.96c ornlxsb1 INEEL 300.0 42 Sb-123 51123.96c ornlxsb1 INEEL 300.0 43 Te-128 52128.96c ornlxsa1 INEEL 300.0 44 I-127 53127.60c endf60[121 LANL/T-2 293.6 45 I-129 53129.60c endf60 ENDF/B-VI.0 293.6 46 Xe-131 54131.50c kidman ENDF/B-V.0 293.6 47 Xe-132 54132.62c Xe132.300 INEEL 300.0 48 Xe-133 54133.60c mason1 INEEL 293.6 49 Xe-134 54134.62c Xe134.300 INEEL 300.0 50 Xe-135 54135.50c endf5mttll ENDFIB-V 293.6 51 Xe-136 54136.62c Xe136.300 INEEL 300.0 52 Cs-133 55133.60c endf60 ENDF/B-VI.0 293.6 53 Cs-134 55134.60c endf60 ENDF/B-VI.0 293.6 54 Cs-135 55135.60c endf60 ENDF/B-VI.0 293.6 55 Cs-137 55137.60c endf60 ENDF/B-VI.0 293.6 56 Ba-134 56134.62c Ba134.300 INEEL 300.0 57 Ba-137 56137.62c Ba136.300 INEEL 300.0 58 Ba-138 56138.60c endf60 ENDF/B-VI.0 293.6 59 La-139 57139.60c mason1 INEEL 293.6 60 Ce-140 58140.96c ornlxsb1 INEEL 300.0 61 Ce-141 58141.60c mason1 INEEL 293.6 62 Ce-142 58142.96c ornlxsb1 INEEL 300.0 63 Ce-144 58144.96c ornlxsb1 INEEL 300.0 64 Pr-141 59141.50c kidman ENDF/B-V.0 293.6 65 Pr-143 59143.60c mason1 INEEL 293.6 66 Nd-142 60142.96c ornlxsb1 INEEL 300.0 67 Nd-143 60143.50c kidman ENDF/B-V.0 293.6 68 Nd-144 60144.96c ornlxsb1 INEEL 300.0 69 Nd-145 60145.50c kidman ENDF/B-V.0 293.6 70 Nd-146 60146.96c ornlxsb1 INEEL 300.0 71 Nd-147 60147.50c kidman ENDFIB-V.0 293.6 72 Nd-148 60148.50c kidman ENDF/B-V.0 293.6 73 Nd-150 60150.96c ornlxsb1 INEEL 300.0 74 Pm-147 61147.50c kidman ENDF/B-V.0 293.6
25
Number Actinides ZAID Library Name Source Temperature (°C) 75 Pm-148 61148.50c kidman ENDF/B-V.0 293.6 76 Pm-148 61148.60c mason1 INEEL 293.6 77 Pm-149 61149.50c kidman ENDF/B-V.0 293.6 78 Sm-147 62147.50c kidman ENDFfB-V.0 293.6 79 Sm-148 62148.96c ornlxsa1 INEEL 300.0 80 Sm-149 62149.50c endf5u ENDF/B-V.0 293.6 81 Sm-150 62150.50c kidman ENDF/B-V.0 293.6 82 Sm-151 62151.50c kidman ENDP/B-V.0 293.6 83 Sm-152 62152.50c kidman ENDF/B-V.0 293.6 84 Sm-153 62153.60c mason1 INEEL 293.6 85 Sm-154 62154.96c ornlxsa1 INEEL 300.0 86 Eu-151 63151.60c endf60 ENDF/B-VI.0 293.6 87 Eu-153 63153.60c endf60 ENDF/B-VI.0 293.6 88 Eu-154 63154.50c endf5u ENDF/B-V.0 293.6 89 Eu-155 63155.50c kidman ENDF/B-V.0 293.6 90 Eu-156 63156.60c mason1 INEEL 293.6 91 Gd-154 64154.60c endf60 ENDF/B-VI.0 293.6 92 Gd-155 64155.60c endf60 ENDF/B-VI.0 293.6 93 Gd-156 64156.60c endf60 ENDF/B-VI.0 293.6 94 Gd-157 64157.60c endf60 ENDF/B-VI.0 293.6 95 Gd-158 64158.60c endf60 ENDF/B-VI.0 293.6 96 Tb-159 65159.96c ornlxsb1 INEEL 300.0 97 Dy-160 66160.96c ornlxsa1 INEEL 300.0 98 Dy-161 66161.96c ornlxsa1 INEEL 300.0 99 Dy-162 66162.96c ornlxsa1 INEEL 300.0 100 Dy-163 66163.96c ornlxsa1 INEEL 300.0
Table 2-8 Description of chosen matrix materials
Number Actinides ZAID Library Name Source Temperature (°C) 1 Li7 3007.60c endf60 ENDF/B-VI.0 293.6 2 Be 4009.60C endf60 ENDF/B-VI.0 293.6 3 C 6000.60c endf60 ENDF/B-VI.1 293.6 4 N 7014.60c endf60 LANL/T-2 293.6 5 O 8016.6OC endf60 ENDFIB-VI.0 293.6 6 F 9019.6Oc endf60 ENDFIB-VI.0 300 7 Na 11023.60c endf60 ENDF/B-VI.1 293.6 8 Mg 12000.60c endf60 ENDFIB-VI.0 293.6 9 Al 13027.60c endf60 ENDFIB-VI.0 293.6
10 Si 14000.60c endf60 ENDF/B-VI.0 293.6 11 P 15031.60c endf60 ENDF/B-VI.0 293.6 12 S 16000.60c endf60 ENDFIB-VI.0 293.6 13 Cl 17000.60C endf60 ENDFIB-VI.0 293.6 14 K 19000.60c endf60 ENDFIB-VI.0 293.6 15 Ca 20000.60c endf60 ENDFIB-VI.0 293.6 16 Ti 22000.60c endf60 ENDF/B-VI.0 293.6
26
Number Actinides ZAID Library Name Source Temperature (°C) 17 V 23000.60c endf60 ENDF/B-VI.0 293.6 18 Cr 24000.50c mlccs ENDF/B-V.0 293.6 19 Mn 25055.60c endf60 ENDFfB-VI.0 293.6 20 Fe 26000.55c rmccs LANL/T-2 293.6 21 Co 27059.6Oc endf60 ENDF/B-VI.2 293.6 22 Ni 28000.50c rmccs ENDF/B-V.0 293.6 23 Cu 29000.50c mccs ENDF/B-V.0 293.6 24 Zn 30000.42c end192 LLNL:XCI 300 25 Sr 38088.96c ornlxs1 INEEL 300 26 Zr 40000.60c endf60 ENDFfB-VI.1 293.6 27 Nb 41093.60c endf60 ENDF/B-VI.1 293.6 28 Mo 42000.60c endf60 ENDF/B-VI.0 293.6 29 Sn 50000.42c end192 LLNL:XCI 300 30 Te 52129.96c ornlxsa1 INEEL 300 31 Ba 56138.60c endf60 ENDF/B-VI.0 293.6 32 Hg 80000.42c end192 LLNL:xCI 300 33 Pb 82000.50c mccs ENDF/B-V.0 293.6 34 Bi 83209.60c endf60 ENDFIB-VI.0 293.6
2.5 Summary
In this chapter, we have described the computer code MCODE and set up whole
core models for matrix and reflector tests. The region-wise (MCNP cell) configurations
are documented. The roster and cross section libraries of all constituents are also
specifically identified.
27
Chapter 3 Review of core diluent material candidates
3.1 Introduction
In the present work candidate materials for gas-cooled fast reactor core design
were evaluated using static beginning-of-life reactivity calculations and fuel burnup
analyses. MCODE and MCNP were executed using the core model and regional
compositions given in Chapter 2. We first review the material candidate properties in
section 3.2. The importance of σa as an evaluation parameter is also discussed in
section 3.2. In section 3.3 burnup and k calculations for the matrix core model are
shown and compared with other material properties. In section 3.4 we discuss the
non-linearity of neutronic effects vs. diluent concentration and the failure of the
superposition principle in predicting the effect of compounds based on their
individual components. Then we discuss conclusions for the final selection of matrix
material in section 3.5.
3.2 Review of element properties
The most important neutronic property relative to use as a core diluent is a
material’s macroscopic absorption cross section Σa, the product of the microscopic value
and the nuclei’s number density, since this defines its tendency to consume neutrons
unproductively. A second, less easily quantified effect is the change in Σa of other
materials and core leakage due to changes induced in Φ(E). Considering that good heat
storage capacity (ρCp) is expected for matrix material, the ratio of Σa to ρCp is a useful
index of diluent suitability.
To be certain that no innovative option escaped it was decided to carry out a set of
very fundamental studies. These involved calculation, using MCNP, of the spectrum
average microscopic absorption cross section of all of the elements in the periodic table
in a representative GFR spectrum. In addition to the obvious goal of avoiding materials
having a σa even 10% of that of U-235 ( for which σa is roughly 2 barns), σa is also a good
index of the ability of a core diluent to store energy in a transient without excessive
neutron loss. Recall the law of Dulong and Petit, namely that solid elements have a heat
28
capacity close to 25 J/mol⋅K[1,2], thus the ratio of macroscopic absorption cross section
to volumetric heat capacity is just
25a A a A A
a a ap p p
N N NC A C AC
ρ σ σ σ σρ ρΣ
= = = ∼ (3-1)
Here NA is Avogadro’s Number, A is the atomic weight, and Cp is the heat capacity in the
units of J/g.K. Since all solid materials have very similar values of ACp, the molecular
heat capacity, the performance index reduces to only one variable, σa. Hence the σa
values displayed in Table 1.3 are a good preliminary indicator of potential suitability. The
heat capacity table for solid and liquid elements in ref(18) shows the systematic behavior
of molecular heat capacity which allows this simplification.
3.3 Review of material candidates for matrix core
3.3.1 Neutronic Evaluation parameters
Together with the inherent properties such as cross sections, we use keff(BOL),
∆keff(void), and B1 as the final evaluation parameters. High keff(BOL) increases the need
for compensatory control, but it will give a higher burnup potential. Negative or small
positive ∆keff(void) is desired for dynamic stability. The linearly extrapolated burnup
potential B1 is defined as B1 = (k – 1) / (∆k/∆B). It is mainly determined by the beginning
of life keff and conversion ratio. In our investigation, since a full burnup whole core
simulation is very time consuming, we use the first 3 keff – burnup points to linearly
extrapolate to the just-critical point. See fig3.1.
Linear extrapolation does not give a highly accurate estimate of the true B1, but
only an indicative trend, as shown in fig3.2 for two extreme cases, the moderator Al4C3
and Ba which has a low slowing down power as diluent.
29
Figure 3-1 Definition of B1
0.9
0.95
1
1.05
1.1
1.15
0 50 100 150 200 250 300 350 400 450
burnup (MWd/kg IHM)
k eff
Al4C3(actual) B1=95Ba(actual) B1=200Al4C3(linear) B1=89Ba(linear) B1=424
Figure 3-2 Examples of error of linear extrapolation method
Definition of B1
1
1.1
1.2
1.3
1.4
1.5
0 10 20 30 40 50 60 70 80 90
Burnup (MWd/kg)
keff
k0
k1
k2
B1
30
3.3.2 Results for matrix study All the materials in the candidate list were tested in single element form except
for some less common elements for which there is a lack of cross section libraries.
Several compounds of interest are also studied. Their density, heat capacity, and melting
point are also listed in table3.1. The descending slope of the keff vs B1 curve as well as the
internal conversion ratio is listed as well.
Table 3-1 Results of matrix comparisons
Matrix ρ(g/cc) ρCp(J/ccK) Tmelt( C) keff ∆keff(void) (pcm) ∆k/∆B (pcm) Β1 (MWd/kg) ICR Al 2.70 2.44 660 1.10184 -47 54 166 0.76
Al4C3 2.36 2.78 2100 1.13060 81 156 84 0.71 AlN 3.255 2.39 3000 1.02780 23 174 16 0.68 Ba 3.51 0.72 727 1.1085 275 24 424 0.72
Ba2Pb 4.91 - 928 1.11638 129 28 419 0.72 BaO 5.72 1.78 1973 1.04289 53 54 78 0.75 BaS 4.30 1.30 2229 1.04882 -43 27 183 0.73 BeO 3.01 3.08 2508 1.14914 -105 320 49 0.65
Bi 9.78 1.19 271 1.15112 288 43 351 0.73 C 2.60 1.52 3527 1.13513 46 249 54 0.69 Ca 1.55 0.98 842 1.10582 127 46 232 0.70
CaC2 2.22 2.17 2300 1.10741 103 146 74 0.83 CeO2 7.13 2.55 2400 1.07003 46 127 55 0.74
Co 8.90 3.75 1495 0.87239 90 30 - 0.75 Cr 7.14 3.20 1907 1.03173 190 43 74 0.76 Cu 8.92 3.41 1358 0.81876 103 50 -366 0.75 Fe 7.80 3.50 1538 1.01428 98 43 34 0.77
Fe3C 7.69 4.54 1227 1.00979 -16 119 8 0.77 HT9 7.69 4.54 - 1.00773 72 51 15 0.76
K 0.86 0.65 63 1.16061 150 22 441 0.70 Mg 1.74 1.78 650 1.13686 -1 73 188 0.74 Mn 7.47 3.58 1246 0.94022 214 38 - 0.79 Mo 10.28 2.58 2623 0.6403 -180 - - 0.73 Na 0.97 1.19 98 1.16882 148 73 230 0.71 Nb 8.57 2.27 2477 0.60907 224 - - - Ni 8.91 3.96 1455 0.9236 9 64 -120 0.74 P 1.82 1.40 44 1.1235 76 29 258 0.72 Pb 10.43 1.33 328 1.14233 268 28 424 0.74
PbO 9.64 1.98 888 1.12172 60 90 136 0.75 PbS 7.60 1.57 1118 1.09198 53 35 261 0.74
S 1.96 1.38 115 1.05176 120 12 414 0.73 Si 2.33 1.66 1414 1.12424 123 46 234 0.73
SiC 3.22 2.67 2700 1.12578 32 180 70 0.69
31
Matrix ρ(g/cc) ρCp(J/ccK) Tmelt( C) keff ∆keff(void) (pcm) ∆k/∆B (pcm) Β1 (MWd/kg) ICR Sn 7.31 1.59 232 0.97004 94 34 -89 0.72 Sr 2.63 0.78 777 1.15638 257 37 425 0.71
Sr2Pb 1.12379 255 28 445 0.74 SrO 4.7 1.20 2430 1.09621 41 82 117 0.74 SrS 3.7 1.51 2227 1.07972 183 37 217 0.73 Ti 4.51 2.35 1668 1.09353 124 116 80 0.68
TiC 4.93 2.78 3067 1.09154 18 239 38 0.67 TiN 5.21 - 2950 0.99394 12 184 -3 0.67
TiN15 5.21 - 2950 1.08545 25 191 45 0.68 U238 19.05 2.22 1132 0.71207 123 - - 3.41
V 6.11 2.99 1910 1.04644 36 142 33 0.69 VC 5.77 2.96 2810 1.05622 86 235 24 0.82
Void - - - 1.20575 222 28 736 0.69 Zn 7.14 2.77 420 0.83196 -36 71 -237 0.74 Zr 6.51 1.81 1852 1.04468 107 26 173 0.75
Zr90* 6.51 1.81 1852 1.09325 134 42 219 0.75 ZrC 6.73 2.47 3532 1.03446 232 145 24 0.79
ZrO2 5.68 2.59 2677 1.0457 -58 128 36 0.74 Zrot* 6.51 1.81 1852 1.01598 388 41 39 0.76
* Zrot: is natural Zr with Zr-90 removed. SDM of keff = ±0.0002 ≡ 20pcm, hence CO2 voiding comparisons are only qualitative.
1.20575
SrPbKSr2Pb
BaBa2PbS
Bi
PPbSNaSi
Zr90CaSrSMgZrBaS
AlPbO
SrO
SiCAl4C3CaC2Ti
BeOCTiN15TiC
CeO2
Cr
ZrCZrO2VCFe VHT9
ZrotAlNFe3CTiN
SnNi
ZnC
Zn
Cu-400
-300
-200
-100
0
100
200
300
400
500
600
0.7 0.8 0.9 1 1.1 1.2 1.3
keff
B1
Figure 3-3 Relation of initial multiplication factor and burnup potential
32
As shown in Fig3.3, there is no useful correlation of initial multiplication factor and burnup potential except for a rough positive trend.
P
No diluent
SrK
Ba
PbSi
CaAl Ti
CrVZr
Fe
Sn
Mn
Ni
Zn
Co
Cu
0.82
0.87
0.92
0.97
1.02
1.07
1.12
1.17
1.22
0.00E+00 5.00E-01 1.00E+00 1.50E+00 2.00E+00 2.50E+00
Σa, cm-1
1/k e
ff =
1 - ρ
Figure 3-4 Relation of multiplication factor and macroscopic absorption
Figure 3.4 shows that for metal matrix materials, 1/keff is linearly proportional to
the matrix material’s macroscopic absorption cross section.
We have
1 11 1f a a i
if f
kk k
νρ
ν νΣ − Σ Σ−
= = − = = −Σ Σ∑ (3-2)
For different metal matrix cores, the spectrum average fission cross section is
close in magnitude. The main difference of reactivity comes from the different neutron
absorption ability of matrix materials. As expected, the inverse of multiplication factor
and matrix absorption is linearly correlated.
3.3.3 Fissile and fertile properties in the energy range of interest
For the 13% enriched Uranium carbide fueled diluent core defined in Chapter 2,
the energy spectrum is usually concentrated to the range between 1kev and 1Mev. The
33
presence of moderators can extend this energy range to lower energies. Neutron
absorption reactions and capture peaks will change the shape of the spectrum, but the
spectrum energy range is around the same. Figure3.5 and figure3.6 show the fissile and
fertile capture and fission cross sections from 1kev to 10Mev.
Figure 3-5 U235 capture, fission and elastic scattering cross sections *
* The uppermost curve is the elastic scattering cross section; the middle curve is the
fission cross section. And the lowest curve is the capture cross section.
The figures show that the capture and fission cross section of U235 both decrease
with energy but the fission to capture ratio increases with energy. The U238 fission cross
section is threshold type, rising abruptly at ∼ 1Mev. Spectrum hardening will therefore
lead to an increase of reactivity in U235 and U238 mixtures.
34
Figure 3-6 U238 fission, elastic scatter, absorption cross sections
* The uppermost curve is the elastic scattering cross section.The curve having
resonances at lower energies but decreasing smoothly at higher energies is the capture
cross section. The threshold type curve is the fission cross section.
3.3.4 Promising materials
Since the test core volume is relatively large, ∆keff(void) is not very sensitive to
leakage changes. Since the volume fraction of coolant is relatively small (~10%), the
∆keff(void) is also not very sensitive to coolant capture changes. However, ∆keff(void)
would be much larger for more realistic values (eg 25-50%), thus ∆keff(void) is
nevertheless a key criteria. Note that the amplitude of ∆keff(void) for the diluent cores is
somewhat smaller than that for the reflector comparisons of chapter 4. Thus the selection
of neutronically attractive materials is mainly based on their burnup potential (see fig3.7)
and melting point.
35
Fe
ZrO2
TiC
BeO
CeO2CSiC
CaC2
Cr
BaO
Ti
Al4C3PbO
Zr
BaS
Mg
Al
NaCaSi
PPbS
Bi
S
BaPb
TiN15
Fe3C
HT9
ZrC
VC
Ba2PbK
Sr2PbSr
SrS
Zr90
SrO
Zrot
-200
-100
0
100
200
300
400
500
0 50 100 150 200 250 300 350 400 450 500
B1 MWd/kg IHM
∆k(
void
)
ATTRACTIVE PERFORMANCE
UNACCEPTABLEPERFORMANCE
Figure 3-7 Map of diluent material performance
Figure3.7 shows that, several materials are of potential interest, such as Sr2Pb,
Ba2Pb, K, S, Ba, Bi, P, PbS, Si, Ca, Na, Mg, BaS, Zr, Al. Sr, Ba and Pb have very close
∆keff(void) and B1; as expected, their compounds Ba2Pb and Sr2Pb, give even better
performance: higher B1, lower ∆keff(void). These materials will be discussed in detail in
the following sections. 3.3.4.1 Barium-2 Lead(Ba2Pb)
From table3.2, solid barium-2 lead has the longest burnup potential. The Ba2Pb
melting point is 928ºC, higher than both barium and lead. This gives Ba2Pb another
advantage over the individual constituents.
The diluent atom density of Ba2Pb is much less than that of BaS but a bit more
than Barium metal. Elimination of light moderators keeps the spectrum hard. The reduced
amount of barium and the small lead capture cross section lead to small diluent
absorption. The higher total diluent atom density and higher average lead scattering cross
section increase the interaction with neutrons hence reduce leakage. Thus, the overall
keff(BOL) is much higher than for the Ba diluent core.
36
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
1.00E+01
1.00E+02
1.00E+03
0.001 0.01 0.1 1 10
energy (Mev)
cros
s se
ctio
n (b
arn)
Ba137_elscatterBa137_captureBa136_elscatterBa136_captureBa135_elscatterBa135_captureBa134_elscatterBa134_capture
Figure 3-8 Capture and elastic scattering cross sections for minor Ba isotopes
One thing to note is that among the 7 siblings, Ba-138 is the most abundant
naturally occurring isotope. Its cross section data is well studied and recorded in detail.
But for the other 6 isotopes, it appears that 1/v behavior is assumed to estimate the cross
sections: See fig3.7. Since over 70% of natural Barium is Ba-138, the 1/v estimation of
other isotopes is probably not too detrimental.
Ba is the heaviest non-radioactive alkaline earth metal element. Hence its slowing
down power is quite small. Even though the microscopic average scattering cross section
is around the same as aluminum, the spectrum softening effect of barium is much less
than for aluminum. Lead is much heavier than barium, hence the overall impact of Ba2Pb
on the core spectrum is very small. However the total absorption by barium is not
negligible, due to which the keff(BOL) of the Ba2Pb diluent core is lower than for the Pb-
only core.
Due to their 1/v approximation, the Ba scattering and capture cross sections
change smoothly with increasing energy. Spectrum hardening reduces Ba’s capture, and
increases the fission to capture ratio. Since the fissile and fertile capture and fission are
37
very sensitive to spectrum hardening, ∆keff(void)leakage is less than ∆keff(void)spectrum. Since
∆keff(void)leakage is the only term which gives rise to negative total ∆keff(void), this will
lead to a positive ∆keff(void). Lead has smaller capture microscopic cross section and
smaller slowing down power than most other materials. It also has a lower atom density
in the core. The impact of lead on ∆keff(void) is much smaller than barium. Hence,
∆keff(void) is positive. The amplitude is a little smaller than pure barium metal but the
difference is whithin the standard error range.
The burnup potential of Ba2Pb is much larger than for the BaS core and is close to
that of the Ba core. This is mainly because of their similar hard spectra and almost the
same internal conversion ratio.
From the discussion above, if the library cross sections for Ba are valid, Ba2Pb
appears to be a good diluent candidate from a neutronic point of view. Its void coefficient
is a little bit high, but it is endurable.
3.3.4.2 Strontium-2 Lead (Sr2Pb)
Analogous to Ba2Pb, use of Sr2Pb can apply the small absorption of Sr and lead
while avoiding a low melting point. The absorption cross section of Sr is much lower
than barium, except for a few capture resonances below 0.2Mev.
Because of the smaller capture, Sr2Pb has a little higher keff at beginning of life
compared to the barium-2 lead core, consequently its burnup potential is close to that of
Ba2Pb. The difference of ∆keff(void) is inside the standard error range. The melting point
of Sr2Pb is a little higher than Ba2Pb, which gives it another advantage. It is a qualified
candidate, as good as Ba2Pb.
3.3.4.3 Potassium (K)
Na and K are an interesting pair in table3.2. The microscopic capture cross
section of K in a Pb matrix spectrum is around 20.1 mbarns, around 10 times that of Na
(2.0 mbarns), yet the B1 for K is almost twice that of Na. In the ENDF cross section set
used in MCNP, there is a resonance region in the epithermal range for Na, while for K,
38
the capture cross section curve is almost logarithmically linear, which probably indicates
1/v estimation. Although the integrated average total absorption cross section of Na is
much lower than that of K, Na’s resonance absorption is far stronger than K’s continuous
and flat curve. As will be seen in the later reflector study (chap 4), the difference between
Na and K is almost negligible when they are positioned peripherally as reflectors.
However, they both have very low melting points, not far above room temperature. Thus
it is not feasible to use them as a fuel matrix. However, both can be used as a fuel-to-clad
thermal bonding agent; and both are suitable LMR coolants.
3.3.4.3 Lead Sulfide (PbS)
Lead and Bismuth are good materials from the neutronic point of view. They are
heavy which makes the spectrum hard. Their absorption cross sections are small which
helps the neutron economy. No (n,α), or (n,p) reactions create annoying gas generation
problems. The lead matrix core has a positive void coefficient because of its greater
sensitivity to spectrum hardening and less sensitivity to increased leakage, but the
magnitude is acceptable. Pb and Bi would be the best choice if they had a high enough
melting point; thus different compounds of lead and bismuth are evaluated to exploit their
advantages.
S is a very interesting material based on our results. Except for the resonance
peaks, the absorption cross section of S is rather smooth. It also has a steep rise very
close to 1Mev caused by (n, α) reaction. That offsets the decrease of neutron capture as
the spectrum hardens and explains S matrix’s negative void response. The disadvantage
of using S as a matrix is obvious: it has a very low melting point (115.21ºC), a very low
density, and essentially no structural strength. Furthermore, it undergoes (n,α) reactions
to produce He, and (n,p) reactions to produce H. He, H2S, or H2 gas will be generated as
a result, thus additional internal pressure will be produced. On the other hand, S seems to
help improve internal conversion ratio: Almost all sulphur compounds have a low ∆k/∆B,
hence a bigger B1. The (n, α) cross section for natural S is 12.4 millibarns and its (n,p)
cross section is 5.2 millibarns based on the Pb matrix core spectrum. Considering the fact
that there is over 60% volume percentage of S in the core, using S will create a
significant amount of internal gas pressure. See Appendix A.
39
Accordingly we tried the compound PbS to avoid some of the above
disadvantages. PbS has a melting point of 1118ºC. The burnup potential is 258MWd/kg.
But its void response is bigger than both the Pb and S cases. The reactivity of a
compound diluent is not the simple summation of reactivities for that compound’s
components. This is explained in section 3.4.
3.3.4.4 Calcium (Ca)
Calcium is one of the alkaline earth elements. It is the fifth in abundance in the
earth's crust, of which it forms more than 3%. It undergoes (n, γ), (n, p), and (n, α)
reactions but the average total cross section is not very large. The elastic scattering cross
section has resonances in the range of interest. The atomic number of calcium is
intermediate. Its atomic density is lower than BaO, BeO and AlN, but higher than all the
other materials listed in the table. Less moderation makes its keff(BOL) higher than for
aluminum. More moderation and absorption make its keff(BOL) lower than for the barium
diluent core. For the ∆keff(void), since there is no significant Ca – U235 or Ca – U238
cross section coupling, the ∆keff(void) value is positive. The analysis is analogous to the
discussion in section 3.3.2.4. Considering that calcium’s total absorption increases at high
energy, the diluent absorption increases upon voiding. This compensates for the positive
∆keff(void) and the amplitude of ∆keff(void) is less than for a barium containing core.
The spectrum softening and larger absorption make the calcium core conversion
ratio lower than for barium. Thus the burnup curve is steeper and the burnup potential is
less. Overall considering the ∆keff(void) benefit, calcium is a usable material.
3.3.4.5 Silicon (Si)
Crystaline Si is expensive and its strength as a matrix is questionable. The
neutronic performance of Si is also mediocre. Thus we are more interested in its
frequently used compound, SiC. From our study, SiC is detrimental because of its carbon
content. Carbon down-scatters the neutrons and softens the spectrum significantly.
Together with several absorption peaks of Si, neutron economy is worsened. Even though
a softened spectrum can achieve a very high multiplication factor at the beginning of life,
the internal conversion ratio is very low. In addition, the generated fissile plutonium has a
40
poorer fission to capture ratio, thus keff drops down very quickly with the increase of
burnup. The extrapolated burnup B1 is only 70 MWd/kg. This performance of SiC is
much worse than pure Si. 3.3.4.6 Barium Sulfide (BaS)
Barium sulfide is a white crystal with the high melting point of 2229ºC. Its heat
capacity is around the same as BaO. Since sulfur has twice the atomic number of oxygen,
it is anticipated that a BaS diluent core will have a harder spectrum and inherit the high
burnup potential of Ba metal. BaS has some disadvantages. First sulfur has a relatively
large (n,α) cross section, so that the presence of sulfur will enhance gas generation and
increase the pressure inside the cladding (see appendix A). Second, some structural
materials may corrode in contact with barium sulfide (see ref[10]). Thus, a BaS diluent
core has more restrictions on material selection.
The atom density of BaS is less than BaO but they are of the same scale. Sulfur
has more and sharper elastic scattering resonances which begin at low energies. But
sulfur’s slowing down power is much smaller than oxygen; So their overall impact on the
neutron spectrum is around the same, except that the BaS core spectrum has fewer
moderated neutrons below ~50kev and has a deeper valley in the middle of the spectrum
peak compared with the BaO core(see Figure: 3.9). Thus the BaS core has more high
energy neutrons. The spectrum contribution to keff is higher. For the same reason, the
leakage of the BaS core is larger than for the BaO core, which is a not very important
drawback. Sulfur has 27 times the average total absorption cross section of oxygen in a
hard GFR spectrum. Hence the diluent absorption in BaS matrix cores is much more than
for BaO cores. This tends to depress its keff. Among the 3 factors, the spectrum impact is
the dominant one. Thus the BaS core has a slightly higher keff(BOL) than BaO.
41
0.00E+00
5.00E-03
1.00E-02
1.50E-02
2.00E-02
2.50E-02
3.00E-02
3.50E-02
1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01
energy (Mev)
frac
tion
BaS_spectrumBaO_spectrum
Figure 3-9 Comparison of BaS and BaO diluent core spectra
When void is introduced, the spectrum turns harder, and leakage increases. Since
sulfur has an increasing (n, p) cross section and (n, γ) capture resonances at relatively
high energy, the total absorption by sulfur increases a little. This leads to a small
∆keff(void).
Even though the BaS core has a lower conversion ratio than BaO, its burnup
potential is higher. The reason is a much harder spectrum (analogous to section 3.3.2.2).
For the same reason, BaS has lower burnup potential than for a Ba metal matrix core.
3.3.4.7 Zirconium (Zr)
Zirconium alloys are very popular in LWRs because of the small absorption cross
section of Zr in the thermal energy range. But at high energies, the significant resonance
absorption reduces its advantage. This also helps to increase the ∆keff(void). The poorer
neutron economy reduces the core’s burnup potential. Nevertheles, compared with strong
42
moderators such as carbide compounds and strong absorbers such as copper, zirconium is
a material worthy of consideration.
3.4 Applicability of superposition
There are many many more compounds than pure elements. If we could predict
the performance of compounds by combining results for their constituent elements,
considerable work would be avoided. However, our results show that the reactivity effect
of compounds can not be simply expressed as a weighted function of individual
constituents because of changes in spectrum. The results for different amounts of the
same matrix also show non-linearity (see fig3.10), and thus accurate extrapolation or
interpolation for a given volume of matrix material is possible only over a narrow range.
However, results for different fuel enrichments for fixed matrix material show that the
reactivity-enrichment curve can be fit to a simple derivable function.
3.4.1 Non-linearity of neutronic effects as a function of matrix concentration
1.14
1.16
1.18
1.2
1.22
1.24
1.26
1.28
1.3
1.32
0 50 100 150 200 250
volume ratio (matrix to fuel)
k eff
Pb(perfectly reflected)Pb(with leakage)
Figure 3-10 Non-linearity of neutronic effects vs. Pb matrix concentration
43
The non-linearity of core characteristics with diluent concentration was not
unexpected, in view of their tendency to soften the reactor spectrum. To show why this is
the case, and also to call attention to a way to take this effect into account, the approach
introduced by Sheafer [13] is noted. He showed that fast reactor-spectrum-averaged cross
sections can be correlated in the form: gS1σσ = (3-3)
where σ1 and g are constants for a given nuclide.
The spectral index S, the ratio of average neutron energy to fission neutron
energy, is given by:
el TR
f
f f
E SE
νν ξ
∑= =
∑ + ∑ (3-4)
in which
ΣTR and Σf = transport and fission macroscopic cross sections, respectively
ξel = logarithmic mean energy decrement for neutron scattering, (approximated
as that due to elastic scattering alone)
ν = mean neutron yield per fission
Since S is less than 1.0 and g typically a negative quantity, σ values increase as
the spectrum softens (S decreases), and by a different amount since different species have
different g values.
Sheafer studied a wide variation of oxide, carbide and metal fueled cores and
critical assemblies. He found that k could be calculated within ±0.59%
Even better results should result if one confines interest to a restricted range of
compositions, or focuses on relative comparisons.
3.4.2 Neutronic effects for a compound and its constituents
From Sheafer’s method, we would expect that since the spectrum of Al4C3 is softer
than that for Al, the average capture cross section of Al in an Al4C3 matrix is greater then
44
that in an Al only metal matrix. Thus a metal carbide matrix should always have a lower
keff than pure metal matrix.
In reality the opposite is true: the keff of cores with pure metal matrices are mostly
lower than their carbides. The reason is mainly because there are more reduced energy
neutrons contributing to total fission rate at the beginning of life in a softened spectrum.
Also, carbon has almost no neutron absorption cross section. That makes the neutron
utilization factor much larger than a metal core with the same diluent atom density.
We can approximate kinf by requiring linear addition of reactivity losses relative to
a no diluent (i.e. void in place of diluent) reference core
( )( ) (compound) ( ) (component i only)i
void voidρ ρ ρ ρ− = −∑ (3-5)
where component i is present at the some number density as in the compound.
0.2423
0.1176
0.1475
0.1962
0.1636
0
0.05
0.1
0.15
0.2
0.25
material
ρ
ρ(void) - ρ(Al)=0.078679
ρ(void) -ρ(C)=0.046076
ρ(void) - ρ(Al4C3)=0.094821
2ρ(void) − ρ(C) + ρ(Al)=0.124755
Void Al only C only Al4C3 actual Predicted by Superposition = ρ(Al) + ρ(C) -ρ(void)
Figure 3-11 ρ vs. compound components
In the comparison shown in Fig 3.11 note that
• The maximum standard error of keff is 0.00086
45
• “Al only” is a matrix with the same Al number density as in Al4C3 but without the
C component; similarly for “C only”.
• All the core models are perfectly reflected, hence leakage is not relevant.
Thus, the reactivity of Al4C3 could be expressed as
4 3(Al C ) (Al only) (C only) ( )voidρ ρ ρ ρ= + − (3-6)
The standard error of kinf is 80pcm, thus the estimation of the Al4C3 core’s reactivity
should be within ±240pcm. Figure3.11 shows that the deviation of ρ from the linear
approximation to the real MCNP simulation is 2990pcm, far beyond the standard error
change. This demonstrates the non-linearity relationship between multiplication factor in
the compound containing core and that inferred from its single component cores.
3.4.3 Relation of reactivity to enrichment
Reactivity is defined as
1f a
f
kk
νρ
ν∑ − ∑ −
= =∑
(3-7)
For a mixture containing U-235, U-238 and diluent materials, it is not difficult
(see Appendix B) to show that
25 28 28
25 28 28
[ 1 ( 1)] [ ( 1) ]( )
xx
η λ η λ η γρη λη λη
− − − + − −=
− + (3-8)
where
η = neutrons produced per absorption
λ = 28
25
a
a
σσ
γ = , &
, 235
a diluent other absorbers
a U −
∑ ∑
Hence if spectrum averaged cross sections remain unchanged, one expects a relation of
the form:
46
cxbaxkeff +
+= (3-9)
From curve fitting for a mirror-reflected infinite cylinder core with pure UO2 fuel, we
get:
a = 2.5098
b = 0.042
c = 0.1235
where fractional enrichment x ∈ [0, 1]
This relation is plotted in Fig3.12, and tracks the calculated points quite well. It is
anticipated that for the same diluent material, the relationship between enrichment and
keff is the same but with different values of a, b, and c.
Figure 3-12 Relationship between enrichment and keff for a representative core
47
3.5 Conclusions
We have compared approximately 50 materials as core diluents in this chapter. As
would be expected, strong moderators such as C and BeO are detrimental because they
soften the spectrum, reducing fissile η and increasing parasitic absorption. The metal Zr,
so useful in thermal reactors, is here a mediocre performer; nevertheless it has a high
volumetric heat capacity and better structural properties than most other metals with
higher B1. The alkaline earth metals (Mg, Ca, Sr, Ba) are relatively benign diluents, as
predictable from their relatively small absorption cross sections. Al and Ni confer a
negative coolant void coefficient by virtue of their relatively large (n,α) and/or (n,p )
threshold reactions. As expected, Pb excels. However, because of its low melting point, it
could only be employed in exotic concepts such as molten matrix cermet fuel (see
ref[15]) or perhaps as its oxide or sulfide compounds. SiC, which has favorable material
properties, is at best average with respect to neutronics, but should not be ruled out at this
point if ceramic cercer or cermet fuel is preferred. To summarize, we found some good
materials such as Pb, Bi, Ba, but they all have low melting points. Use of a molten salt
matrix or a liquid metal coolant design could be a feasible solution. There are also good
candidates such as Sr2Pb, Ba2Pb, PbS, if the requirement of void coefficient or burnup
potential is not too restrictive. What material is the best one depends on specific design
considerations. If a metal matrix (e.g. cermet fuel) is preferred, then Zr, V and Ti should
be evaluated.
48
Chapter 4 Review of reflector material candidates
4.1 Introduction
As for the evaluation of matrix materials in the core, the evaluation of reflector
candidate materials for gas-cooled fast reactor core design was based on static beginning-
of-life reactivity calculations and fuel burnup analyses. MCODE and MCNP were
executed using the core models and regional compositions given in Chapter 2. Since the
reflector acts more to set boundary conditions and has less impact on the core neutron
energy spectrum compared to matrix materials and since reflectors can tolerate more
neutron absorption, there are more reflector choices than for matrix use. In section 4.2 we
will present data for all the reflector candidates and then discuss them in groups.
Parameter studies are included in section 4.3. Conclusions drawn are presented in section
4.4.
4.2 Review of material candidates for reflector
4.2.1 Albedo calculation
Reflector performance is often characterized by the albedo values at core-reflector
boundary surfaces. The tabulated values of outgoing and return current at the radial
periphery in MCNP permit inference of albedo for the materials under study from the
relation:
JJ
α −
+
= (4-1)
For example, for Pb, one has α ≈ 89%. This shows the inferior nature of fast spectrum
reflector performance if one recalls that good thermal spectrum reflectors such as D2O,
Be and C have albedos of 95% and higher. Since thermal hydraulic and fuel economic
considerations favor radial and axial power flattening, it is also difficult to offset this
inherent shortcoming even by significantly increasing core size (hence plant power
rating).
49
Theory provides only rough and potentially misleading guidance in reflector
selection. In particular, simple one group theory provides an expression for the albedo of
a thick weakly absorbing slab:
413
a
s
σασ
= − (4-2)
Since at high neutron energies the scattering cross-section, σs, varies only slowly and
systematically with nuclide mass (roughly as A to the 2/3 power), a low value of the fast
spectrum average absorption cross section, σa, is a first order indicator of suitability. This
criterion is useful for initial screening purposes, but in reality the situation is more
complex since moderation also plays a role. Degradation in neutron energy causes a loss
of neutron worth (which varies roughly as k(E)), hence the effects of both elastic and
inelastic downscatter must also be taken into account. Figure4.1 plots α vs σa:
H2O
Si
Na
Al
SiC
Bi
B11BeO
NaClFe
FeSi2
Zr90
TiSi2
PbS
Mn
K
CaS
ZrH
Ba
ZrSi2
BaOFeS
Co
TiN Zn
CuBaSFeS2
CoS
Sn
ZnS
Rb
Mo
Nb
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0
σa (mbarn)
albe
do
Figure 4-1 Variation of albedo with absorption
The lack of coherent trend is obvious.
50
4.2.2 General Results Similar to the evaluation of matrix materials, aspects compared were beginning-
of-life multiplication factor, k, coolant void coefficient and the linearly extrapolated
burnup potential, B1=(k-1)/(∆k/∆B). Note that the core diameter was reduced to 180cm to
increase sensitivity to leakage. Table 4.1 summarizes the results.
Table 4-1 Neutronic Comparisons of GFR Reflectors
Species keff ∆kvoid, pcm B1,MWd/kg Albedo bare 1.02370 21 115 0
Al 1.07453 345 231 80.65% AlN 1.07197 183 157 77.20% B11 1.22993 294 83 91.76% Ba 1.06329 50 247 74.09%
Ba2Pb 1.09198 141 395 85.89% BaO 1.07023 86 217 78.67% BaS 1.06625 18 326 76.36% BeO 1.25383 262 83 93.50%
Bi 1.10477 392 326 88.70% C 1.24346 451 87 93.03%
Ca 1.04402 352 193 54.11% Co 1.07561 304 346 80.97%
CoS 1.07021 196 423 78.90% Cr 1.07297 335 247 78.75%
Cr3Si 1.07528 176 80.13% Cu 1.06921 399 299 77.70% Eu 1.03602 -14 154 42.42% Fe 1.06906 386 255 77.79%
FeS 1.06730 -1 249 77.26% FeS2 1.06738 102 267 77.06% FeSi2 1.07603 190 254 80.72% H2O 1.09463 -17 45 62.90% Hg 1.05132 365 231 66.98% K 1.03877 206 147 46.56%
Mg 1.09846 384 136 85.48% Mn 1.06678 315 298 77.45%
MnS 1.06372 138 262 75.40% Mo 1.06154 172 258 73.55%
MoSi2 1.06338 21 283 75.29% Na 1.07148 288 158 77.40%
NaCl 1.06556 407 216 75.70% natUC 1.05606 -198 290 70.24%
Nb 1.05723 139 239 70.11% Ni 1.07301 98 234 78.66%
51
Species keff ∆kvoid, pcm B1,MWd/kg Albedo NiS 1.07012 442 212 78.13% P 1.07274 247 183 77.77%
Pb 1.10855 198 317 89.51% PbO 1.11636 342 170 89.10% PbS 1.09047 390 359 85.63% Rb 1.04239 -31 168 S 1.04421 82 282 56.68% Sc 1.06058 31 239 73.68% Si 1.06382 415 232 74.06%
SiC 1.10772 376 105 85.17% Sn 1.06149 391 317 72.43% Sr 1.07046 376 303 77.84% Ti 1.07224 265 226 77.92%
TiN 1.06582 63 175 74.75% TiSi2 1.08096 6 193 81.62% Ti5Si3 1.08253 83 82.08%
V 1.07563 365 237 79.96% V3Si 1.07781 182 80.99% Zn 1.06459 375 297 75.19%
ZnS 1.06363 -12 267 75.02% Zr 1.08799 118 287 85.09%
Zr90 1.09148 19 265 85.54% ZrC 1.09773 134 144 85.03% ZrH 1.09921 97 53 69.27% ZrNi 1.07863 106 264 81.14% ZrS2 1.07190 55 403 ZrSi2 1.08877 1 233 84.98% Zr3Si2 1.08925 90 252 85.25% mirror 1.19830 310 778 100%
* The standard deviation of keff is ±30pcm, hence CO2 coolant voiding comparisons
are only qualitative.
** The uranium carbide reflector has a natural U235 enrichment.
4.2.3 Detailed evaluation and explanation
Similar to the selection of diluent material, materials with small ∆keff(void) and
large B1 are preferable. Since the reflector could be liquid in cans, there is no melting
temperature restriction on reflectors. Hence, the feasible choices are much more
numerous than for diluent candidates. The best reflectors are Zr3Si2, Ba2Pb, ZrS2, and
52
BaS. Many other sulfide and silicide compounds are also good candidates. The next
section will introduce these candidates in groups.
Si
H2O
ZrH
BeO
B11
C
SiC
bare
Mg
ZrC
K
PbO Ca
NiS
NaCl
HgV
PTi
CrAl
Na
AlN
EuRb
TiN
TiSi2
BaO
Ni
ZrSi2
Nb
ScBa
FeS
FeSi2
Fe
Mo
MnS
ZrNiFeS2
Zr90
ZnS
S
MoSi2
Zr
natUC
ZnSr
Mn
Cu
Pb
Sn
BaS
Bi
Co
CoS
ZrS2
Ba2Pb
PbS
-200
-100
0
100
200
300
400
500
0 50 100 150 200 250 300 350 400 450
B1 MWd/kg IHM
∆k(
void
)
AREA OF INTEREST
UNSUITABLE
Figure 4-2 Map of reflector material performance
4.2.3.1 Zirconium sulfide (ZrS2) and other sulfide compound reflectors
Except for CoS, the zirconium sulfide reflector system has the longest burnup
potential among all the materials tested. Since Co-59 produces Co-60 by (n, γ) reaction,
ZrS2 is preferable because of its lower induced radioactivity. Note that many other sulfide
compound reflectors (eg, BaS, ZnS, FeS2, MnS, FeS, and NiS), lead to reasonably high
burnup potential. This is mainly caused by the high reflectivity value at the core –
reflector surface for these sulfide compound systems.
Sulfur has a high resonance scattering microscopic cross section in the energy
range 0.1Mev ~ 1Mev. This reduces the core neutron leakage. But the slowing down
power of sulfur is not that large. This effectively changes the neutron’s direction without
softening the core neutron spectrum significantly. The hard spectrum leads to a high
burnup potential.
53
Comparing the scattering cross section of zirconium and sulfur, one finds that
Zr’s scattering resonances end at around 0.1Mev, which is at the beginning of sulfur’s
scattering resonances. Thus, almost all the important region of a GCFR neutron spectrum
is covered by the strong reflecting scattering in Zr or S. One thing to note is that even
though ZrS2 is a good reflector, it is not a good candidate as a diluent. This is because of
the absorption cross section resonances of Zr and S which increase in magnitude at lower
energies.
The other advantage of a sulfide reflector is that sulfur helps to depress the
coolant void coefficient because its microscopic absorption cross section increases at
high energy. For almost all sulfide compounds and sulfur itself, whether they are used as
diluent or reflector, the system’s void coefficients are always small and endurable
compared to most other materials.
4.2.3.2 2-Barium Lead (Ba2Pb)
As shown in chapter 3, Ba2Pb is a good candidate material as a diluent. It is also a
good candidate for reflector service. The relatively large average scattering cross section
of Pb helps reflect outgoing neutrons. Its large atomic number leads to a hard core
neutron spectrum and helps burnup potential. The void reactivity coefficient for Ba2Pb is
a little larger than for BaS and lead. It is caused by the descending slope of barium’s
absorption cross section as energy increases. Given an appropriate arrangement of
additional reflector layers, for example, if we add a reflector layer which enhances the
negative void coefficient outside of the Ba2Pb layer, the overall performance could
potentially be improved.
4.2.3.3 Molybdenum disilicide (MoSi2) and other silicide reflectors
Silicides attract attention because of their potential to withstand high operating
temperatures. Among them, MoSi2 is one of the best performers according to our study.
The MoSi2 reflector system’s burnup potential is around 300MWd/kg with a ∆keff(void)
which is negligible considering the estimated standard deviation of the MCNP runs.
The high average microscopic scattering cross section of Mo helps to reflect the
outgoing neutrons back into the core. Silicon does not have as high an average
54
microscopic scattering cross section as molybdenum. However, its scattering resonances
begin at around 0.3Mev, extending to over 3Mev, hence covering the fast neutron
spectrum. Even though the average absorption cross section of Mo is quite large at
energies of interest, it does not affect the core’s neutron economy significantly. This
shows that good peripheral reflector materials are not necessarily good in-core fuel
diluents. Co, Ni, Cu, Zn, Mn, Nb, Mo, Sn are inferior diluents due to their large
absorption cross sections, but fairly good reflectors, considering only burnup potential.
Most silicide reflectors exhibit a small ∆keff(void). This is partly caused by the
increase of absorption in silicon at higher energies via (n,p) and (n,α) threshold reactions.
4.2.3.4 Zirconium (Zr)
Zirconium is used in LWRs in alloy form as cladding material. Our result shows
that it is also useful as a GFR reflector. The relative high atomic number, and lower
energy absorption resonances help maintain a hard spectrum. The relatively large
scattering cross section reduces leakage. Loss of coolant sends more neutrons into the
reflector region and increases capture in zirconium. As for silicon, Zr also has an increase
of neutron capture at high energy. Although the ascending slope appears at an energy
higher than that of silicon and with smaller amplitude, this still helps reduce the positive
∆keff(void). We also tested use of separated Zr-90, but the advantage of less absorption is
not very large.
4.2.3.5 Nickel (Ni)
Nickel is one of the best reflectors from the coolant void coefficient point of view.
It is the reflector material with a very low void coefficient in uranium cores. Nickel’s
atom density is among the highest among our test materials; nickel also has a higher
average scattering cross section. This assures that a nickel reflector will have a high
albedo. Nickel’s absorption is stronger than zirconium and the high energy end total
absorption cross section increase caused by its (n,α) threshold reaction is much larger
than for zirconium in amplitude, (its threshold energy is also smaller). All of the above
leads to a reduced void coefficient.
55
However, nickel’s relatively low atomic number makes the reflected spectrum a
little softer than that for heavy metal compound reflectors such as Ba2Pb. It also is
sensitive to fissile component changes. Thus the burnup potential of a nickel reflected
system is not as high as that for ZrS2. If we give high priority of consideration to void
coefficient, nickel is a suitable choice. Again mixtures or layers combining nickel with
other good reflectors may be an alternative.
4.2.3.6 Nb, Ti, Rb, Eu, Sc, etc
Because of the less restrictive penalties of absorption, the choices of reflector are
broadened to a large extent. Nb, Ti, Rb, Eu, Sc, and their high melting point compounds
could all be considered as reasonable candidates. However, with the exception of Ti,
higher cost would undoubtedly rule them out.
4.2.3.7 Blanket (natural Uranium carbide)
A conventional blanket was also investigated as a reflector. Results show that the
reflecting capability of natural uranium carbide is much worse than lead(the albedo is
much smaller). A uranium blanket leads to a negative core coolant void coefficient.
Although blankets are not preferred because of non-proliferation concerns, at this stage
uranium carbide should be carried forward as a potential candidate – especially for axial
blankets, where they are an integral part of the fuel pin.
4.2.3.8 Trizirconium disilicide (Zr3Si2)
Zr3Si2 is recommended by the French GFR research group at CEA. It has a high
melting point of over 2000ºC, which is an additional advantage. Silicide is one of the best
low average absorption materials except for Na, Mg and some strong moderaters. It also
doesn’t have dense absorption resonances in the fast spectrum. The small scattering cross
section helps to reduce the overall contribution by silicon to core spectrum softening. The
relatively low zirconium scattering cross section and its high atomic number gives even
less contribution of slowing down. Small absorption and moderation lead to a long B1.
56
Figure4.8 shows that the B1 of Zr3Si2 determined by a full core lifetime burnup
calculation is longer than strontium and barium sulfide.
Silicon undergoes (n,α) and (n,p) reactions, which helps reduce the coolant void
coefficient.
4.2.4 Brief summary
From table(4.1) and the discussion above, several conclusions can be drawn. Strong
moderators such as BeO and C increase beginning-of-life reactivity, but significantly
decrease reactivity-limited burnup capability. Ni confers a reduced coolant void reactivity
in part because of its (n,α) threshold reaction, but some otherwise good reflectors such as
Cu cause significant increases. U-238 does not, in this example, breed sufficient
plutonium to confer a larger reactivity-limited burnup than many non-multiplying
reflectors. It does however contribute a significant negative ∆k void. Good peripheral
reflector materials are not necessarily good in-core fuel diluents. For example, Ni, Nb,
Eu, Rb, Sc are inferior diluents due to their large σa, but fairly good reflectors.
4.3 Parameter Studies
4.3.1 Reflector thickness requirement
As Figure 4.3 shows, for a nickel reflector, the multiplication factor reaches its
saturation value at around 25cm. Hence, 20 ~ 30cm of nickel (or other candidates)
suffices for the purpose of reflection. Our test cores use 90cm thick reflectors, which are
far more than necessary. The material beyond 25cm is necessary, however, to reduce fast
reactor fluence on the reactor vessel, and in fact should be optimized to best satisfy
shielding requirements.
57
1.126
1.128
1.13
1.132
1.134
1.136
1.138
1.14
1.142
1.144
1.146
0 10 20 30 40 50 60
reflector thickness (cm)
k eff
Pb matrixNi reflectorstd err = 20pcm
Figure 4-3 keff versus nickel reflector thickness
4.3.2 UPuC fuel – UC fuel Figure 4.4 shows that the beginning of life multiplication factors of UC fuel and
UPuC fuel for the various reflector materials are roughly proportional to each other, since
average capture and fission cross sections in a fast spectrum for U-235 and fissile Pu are
of the same magnitude. For both core types the fissile enrichment is 13% of heavy metal;
but the Pu has the isotopic composition of typical PWR spent fuel.
Unlike the case for uranium, for plutonium fueling the void coefficient does not
differ significantly among the different diluents. This is determined by the detailed cross
section energy variation of U-235 and Pu-239. For the latter, the capture and fission cross
sections are more sensitive to spectrum changes, and thus the void coefficient for UPuC
fuel is larger than for UC fuel. This is significant because even if one starts with U-235
enriched uranium, it is eventually replaced by plutonium, at which point any beginning of
life advantage is lost. Thus one must plan to accommodate the positive coolant void
reactivity under the worst case, namely end of a core burnup cycle. One thing to note is
that sulfur has a relatively small void coefficient for a plutonium core because of its large
(n,α) cross section. But its advantage is not inherited by its compounds.
58
UPuC_UC
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
1.0000 1.0500 1.1000 1.1500 1.2000 1.2500 1.3000
keff (UC)
k eff
(UPu
C)
Figure 4-4 keff (UC fuel) – keff (UPuC) fuel
NiSCSiNaClCuBiSnPbSFeMgSiCHgCaAlCr
MnCoB11NaBeOP
KCoSFeSi2AlNMoBa2PbNbMnS
FeS2NiBaOSZrS2Ba
ScBaSFeSEuH2ORb
-200
-100
0
100
200
300
400
500
600
700
800
1 6 11 16 21 26 31 36 41
reflector
∆kv
oid,
pcm
UPuCUC
Figure 4-5 Comparison of ∆keff(void) for UPuC fuel and UC fuel
Figure 4.6 shows an example of ∆k(void) increase with burnup for an initially
uranium carbide fuel and nickel reflector.
59
∆k(void)(Ni)
0
100
200
300
400
500
600
0 20 40 60 80 100 120 140 160 180 200
burnup (MWd/kg IHM)
∆kv
oid
(pcm
)
Figure 4-6 The ∆k(void) increase with burnup
4.3.3 keff – albedo As stated in 4.2.1, albedo is closely related to the multiplication factor since this
parameter characterizes the leakage at the periphery. Figure 4.7 shows that this
relationship is monotonically increasing, except for some strongly moderating
reflectors.The difference between 13w/o U-235 and Pu fueling appears to be constant and
due to the lower fissile Pu content.
60
CBeOB11
PbBi
SiC
AlBaO
BaSAlN
MnSMoBa
UCNb
RbHg
SCa
K
Eu
H2O
ZrH
Ni
BaSBaO
TiSi2
SiCBa2Pb
Bi
B11C BeO
UC ZrHHg
H2O
S
Ca
Eu
K
SnBa
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
1 1.05 1.1 1.15 1.2 1.25 1.3
keff
albe
do
albedo_keff_UPuCalbedo_keff_UC
Figure 4-7 Relationship of multiplication factor and albedo
4.3.4 Full burnup study of several interesting reflector materials Even though the linear extrapolation method gives a rough idea of multiplication
factor changes during burnup, the estimation has significant uncertainty. In light water
reactors, the reactivity (or multiplication factor) is a nearly linear function of burnup.
(ref[19]) But for fast reactors, the conversion ratio is high. As the U-235 burns out, more
and more plutonium is produced, and more and more additional reactivity is contributed
to the total. Hence the reactivity – burnup curve is a convex function instead of a linear
function. Thus for accurate comparisons a full burnup study is necessary. Because
MCNP/ORIGEN burns are very time consuming, only several materials of interest were
studied.
61
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
0 20 40 60 80 100 120 140 160 180 200
burnup (MWd/kg)
k eff
Zr3Si2PbNiSrBaSBa2Pb
Figure 4-8 Full burnup runs for different reflectors
Figure 4.8 gives the multiplication factor – burnup curves for several reflector
materials for uranium carbide fuel. It shows that Pb is the best reflector from neutronic
point of view, and Ba2Pb, Zr3Si2 maybe the best realistic choices since their melting point
is over 900ºC: much better than nickel and strontium, even though Zr3Si2’s linearly
extrapolated B1 in Table4.1 is lower than strontium. Hence all the materials in the
acceptable region in Figure 4.2 should be studied in detail. The results in figure 4.8 are
also interesting that BOL keff is a farely good performance index if one confines attention
to the best performers.
4.4 Conclusions
According to the discussion above, there are many choices of reflector material.
They all have their competing advantages. Among them, trizirconium disilicide,
zirconium sulfide, barium-2 lead and nickel appear to be the best four materials
considering both burnup potential and void coefficient. A natural uranium blanket does
not increase the core’s leakage significantly; thus it is also a feasible choice if non-
proliferation concerns are not a disqualifying issue. It has the (beginning of life)
advangage of a large negative coolant void contribution.
62
Chapter 5 Summary, Conclusions and Recommendations
5.1 Summary and Conclusions
The work documented in this report had as its objective a broad ranging
evaluation of potential materials for use in GFR service. The principal criteria were
neutronic, but qualitative consideration was given to thermal and mechanical properties.
In addition, the evaluation was conducted with specific reference to the proposed use of
CO2 as the coolant/working fluid, in a direct or indirect Brayton cycle. Finally our
concern was mainly with non-fuel constituents, hence UC was specified as the fuel phase
throughout.
The methodology employed involved use of Monte Carlo and burnup isotopics
codes: MCNP and ORIGEN, coupled by the in-house program MCODE. A simplified
standard whole core model was defined, consisting of two regions, a homogenized core
and a reflector, and individual constituents were tested one-by-one to generate
performance data: initial multiplication factor, coolant void reactivity, linearly-
extrapolated reactivity-limited burnup potential, and for reflector candidates, their albedo.
5.2 General Evaluation Results
Materials cause spectrum changes and absorb neutrons to an extent which differs
when they are used for different functions, e.g. diluent, cladding, coolant, and reflector.
Based on our results, the best of the candidate materials can be grouped into several
categories:
63
Table 5-1 General Evaluation Results
Element Possible
Use Usable Forms
Al REF SNG, ALY Ba DIL REF SNG, COM Bi COO REF ALY C DIL REF SNG, COM Ca DIL REF SNG Co REF SNG, ALY Cr REF CLA SNG ALY Si REF DIL SNG COM Cu REF SNG ALY Fe REF CLA ALY K COO DIL ALY SNG
Mn REF CLA ALY SNG
Mo REF CLA ALY SNG COM
Na COO DIL SNG ALY
Element Possible
Use Usable Forms
Ni REF CLA SNG ALY P DIL COM
Pb COO REF
DIL SNG ALY
COM S REF DIL SNG COM Sn REF SNG ALY
Ti REF CLA
DIL SNG ALY
COM U REF COM ALY
V REF CLA
DIL SNG ALY
Zn REF SNG ALY
COM
Zr REF CLA
DIL ALY COM
SNG
KEY: CLA = cladding,
REF = reflector,
COO = coolant,
DIL = diluent, cermet or metmet matrix,
ALY = alloy,
SNG = single element, principal constituent of alloy
COM = chemical compound, eg. sulfide, silicide, etc.
Criteria leading to the classification in table 5.1 are as follows:
CLA: Cladding. Requires low neutron absorption cross section, low neutron
scattering cross section, small slowing down power, adequate strength, adequate
resistance to radiation damage, high thermal conductivity, high melting point and high
corrosion resistance.
COO: Coolant. Requires low neutron absorption, low neutron scattering, small
slowing down power, high thermal conductivity, low melting point, and high boiling
point.
DIL: Diluent. Requires small neutron absorption, low neutron scattering, small
slowing down power, high thermal conductivity, large heat capacity, high melting point
and adequate strength.
64
REF: Reflector. Requires no more than moderate neutron absorption, high
neutron scattering cross section but small slowing down power, melting point above
normal operating temperature and adequate strength.
Also, because of their different chemical properties and manufacturing procedures,
including the objective of combining the neutronic properties of different materials, these
materials may appear in 3 forms:
SNG: Single element or major alloy constituent
ALY: minor alloy constituent (if minor, can have larger σa)
COM: use in chemical compound
To evaluate the overall performance of a certain material, we need to consider its
unalloyed properties, potential of alloying, fabrication strength and resistance to
corrosion, in addition to its neutronic properties. A Tmelt ≥ 1000ºC is probably needed. As
noted earlier, we mainly focus on a discussion of a material’s physical properties as a
matrix, cladding or reflector. Materials given serious further consideration have test cores
with a beginning-of-life multiplication factor, k bigger than 1. For matrix studies, the
coolant void coefficient of all materials should be less than β of Pu (~350pcm). A
negative ∆kvoid is a significant benefit, although hard to obtain. As an important
consideration in assessing fuel cycle performance, the linearly extrapolated burnup
potential, B1 varies significantly among materials. This is caused in part by the sensitivity
of the conversion ratio to spectrum hardness. For the diluent cases, B1≥150MWd/kg is a
reasonable requirement. For reflectors, since many reflector candidates give a
B1≥150MWd/kg, we give materials with B1≥200MWd/kg higher priority of
consideration. Rarely are materials advantageous for all three evaluation parameters.
Hence one must settle for a reasonable compromise. An important observation is that to
explain minor differences between material performance of interest, spectrum weighted
cross sections based on a standard reference spectrum can not necessarily indicate
neutron behavior accurately. It is necessary to use case-specific neutronic spectra.
65
5.3 Recommendations for future work
All things considered, the following materials appear best suited for further
consideration in specific GFR core designs:
Metallic fuel diluents or matrices (eg. CERMET or METMET): Zr, Ti, V, Ba2Pb;
High temperature fuel diluents or matrices (eg, CERMET, CERCER): SiC, BaS
Cladding: Fe alloys with Cr, Al (eg ODS)
Reflector: Zr3Si2, Pb, Ba2Pb, ZrS2, MoSi2 plus a variety of sulfides and silicides
Future work also needs more attention to the interaction of other core materials
with fuel type and composition. The present work was almost exclusively focused on UC
and U-235 enrichment. However enough was done to show that Pu-239 induces a
significantly different behavior – for example, a much higher coolant void reactivity,
which is less suspectible to mitigation by selection of other core or reflector constituents.
Future work should involve repeating tests for fuels other than UC, for example, UO2,
U10Zr, and fissile other than U-235, for example, plutonium fuel with representative
isotopic compositions.
The present work also used a block type fuel with a very low CO2 coolant volume
fraction. Since coolant void ∆k is of paramount importance in LOCA accidents, future
work should investigate its behavior at higher volume percent, means for positive void
∆k reduction, and the relative behavior of CO2 and He in this regard. In particular we
need to increase the volume fraction of coolant to 25%~50% to cover the parameter space
representative of pin-type cores. This will increase ∆kvoid by 2-4 times. A study of this
type is currently underway at MIT.
Another task left for future study is the optimization of radial reflector/shield
composition as a function of pressure vessel fluence. Only about 25cm are needed to
66
realize the maximum albedo. Thus one can modify outboard configuration to reduce
fluence on the reactor vessel.
In view of apparent cross section library differences, results should be compared
using different available libraries(JEF, JENDL). For some nuclei, (for example, K and
Ba,) their absorption cross section data from ENDF is suspicious since their cross section
vs. energy curves appear to be artificially smoothed at high energy.
67
References
[1] http://minerals.usgs.gov/minerals/pubs/metal_prices/
[2] G.J. Janz, “Molten Salts Handbook”, Academic press, (1967).
[3] ANL-5800, Reactor Physics Constants, U.S. Atomic Energy Commission, Division
of Technical Information , Washington, (1963).
[4] Zhiwen Xu, Pavel Hejzlar, Michael J. Driscoll, and Mujid S. Kazimi, An Improved MCNP-ORIGEN Depletion Program (MCODE) and Its Verification For High-Burnup Applications, PHYSOR, Seoul, Korea, (2002).
[5] Judith F. Briesmeister, MCNP TM — A General Monte Carlo N-Particle Transport Code, Version 4C, LA-13709-M, Los Alamos National Laboratory, (2000). [6] Allen G. Croff, A User’s Manual for the ORIGEN2 Computer Code, ORNL/TM-7175, Oak Ridge National Laboratory, (1980). [7] Xianfeng Zhao, Pavel Hejzlar, M.J. Driscoll, Comparison of Code Results for PWR Thorium/Uranium Pin Cell Burnup, MIT-NFC-TR-027, Center for Advanced Nuclear Energy Systems, MIT (2000). [8] C.M. Kang, R.O. Mosteller, Incorporation of a Predictor-Corrector Depletion Capability into the CELL-2 Code, Trans. Am. Nucl. Soc., (1983), vol. 45, pp. 729-731. [9] Hejzlar P., Driscoll M.J., and Todreas N.E., A Modular, Gas Turbine Fast Reactor Concept (MFGR-GT), Trans. Am. Nucl. Soc.Vol. 84, Milwaukee, June 17-21, p. 242, (2001). [10] John A. Dean, Lange’s Handbook of Chemistry, McGRAW-HILL, New York, (1999) [11] Corrosion Survey Database (COR·SUR), NACE and NIST, Gaithersburg, MD, (2002) [12] Eugene A. Avallone, Theodore Baumeister III, Marks' Standard Handbook for Mechanical Engineers, 10th ed., McGRAW-HILL, New York, (1996), pp. 6-82 [13] Charles A. Harper, Handbook of Materials for Product Design, McGRAW-HILL, New York, (2001), ch7, pp 7.41-7.42
68
[14] Richard P. Pohanish, Sittig's Handbook of Toxic and Hazardous Chemicals and Carcinogens, 4th ed. Noyes Publications, Norwich, NY, (2002) [15] L. Biondi, Research and Development Proposal for a Fuel Element Made up with Uranium Oxide Grains and a Lead Mixture Contained in a SAP Tube in Fuel Element Fabrication with Specific Emphasis on Cladding Materials(Proceedings of IAEA Symposium, Vienna May 10-13, 1960), Academic Press, (1961), vol. 2 [16] M. K. Sheaffer, M. J. Driscoll, I. Kaplan, A one-group method for fast reactor calculations Nucl. Sci. Eng. 48, P459(1972) [17] National Research Council of USA, International Critical Tables of Numerical Data, Physics, Chemistry and Technology, 1st ed., Knovel, Norwich, NY, (2003), vol. 5, pp. 92 [18] Michael de Podesta, Understanding the properties of matter, Taylor & Francis, Washington, DC (1996), pp.178 [19] M. J. Driscoll, T.J. Downar, E.E.Pilat, The linear reactivity model for nuclear fuel management, American Nuclear Society, La Grange Park, IL (1990)
69
Appendix A Estimate of Gas Produced By Sulfur
I Sulfur in the fuel For a 13wt% enriched US fuel, the gas produced by sulfur is estimated as following:
S-32 (n, α) gas production in US relative to fission
25 28 25
( , )( )(1 )
s
U f
N nR yN g
σ αχ δ σ
=⋅ ⋅ +
(B-1)
where y = abundance of S-32 in S = 0.95 g = gas atom yield per fission (Kr + Xe) = 0.30 δ28 = ratio of U-238 to U-235 fissions = 0.41 σf25 = U-235 fission cross section = 1525mb σ(n,α) = S-32 (n, α) cross section = 12.5mb χ25 = enrichment = 0.13 (Ns/Nu) = atom ratio of sulfur to uranium = 1.0 for US Thus R(n,α) = 0.14 which is significant. We also have production by (n,p) of H2: 0.5 molecules per reaction, thus:
1 ( , )( , ) ( , )2 ( , )
n pR n p R nn
σ ασ α
= •
(B-2)
where σ(n,p) of S-32 = 5.2mb Thus R(n,p) = 0.030, and Rgas(total) = 0.17. This is probably tolerable, but if we also use a sulfur compound for the matrix, the added gas would be quite significant. II Sulfur in the matrix For a pure natural sulfur matrix and 13wt% enriched UC fuel, the gas produced by sulfur can still be calculated by equation (B-1), but the parameters change to: y = abundance of S-32 in S = 0.95 g = gas atom yield per fission (Kr + Xe) = 0.30 δ28 = ratio of U-238 to U-235 fissions = 0.174 σf25 = U-235 fission cross section = 1685mb σ(n,α) = S-32 (n, α) cross section = 13.6mb χ25 = enrichment = 0.13 (Ns/Nu) = atom ratio of sulfur to uranium = 2.61 for S matrix, UC fuel Thus R(n,α) = 0.36 which is more than twice that of the US fuel case. Taking the H2 generation into consideration, R(n,p) = 0.089, one obtains Rgas(total) = 0.45. This is a quite large number, and would be even larger (~0.55) if US fuel is employed.
70
Appendix B Relation of reactivity ρ to enrichment x
25 28
25 28
025 028
025 028
028
025 025
02825
025
1
1
(1 )1(1 )
(1 )1
(1 )
f a
f
a
f
a a ad
f f
a a ad
f f
a ad
a a
f
a
x xx x
x x
x x
νρ
ν
ρν
ρν ν
ρν ν
ρ νη
Σ − Σ=
Σ
Σ= −
Σ
Σ + Σ + Σ= −
Σ + Σ
Σ + − Σ + Σ= −
Σ + − Σ
Σ Σ+ − +
Σ Σ= −
Σ+ −
Σ
Let
28
25
025
a
a
ad
a
σλσ
γ
=
Σ=
Σ
Then
25 28
25 28
25 28
25 28
25 28
(1 )1(1 )
(1 ) (1 )(1 )
( 1) (1 )( 1)(1 )
x xx x
x x x xx x
x xx x
λ γρη η λ
η η λ λ γρη η λ
η η λ γρη η λ
+ − += −
+ −+ − − − − −
=+ −
− + − − −=
+ −
η28 ≈ 0.46, for x → 0, 28
28
1 1.17ηρη
−= ≈ −
In a fission spectrum, η25 = 2.46. Omit the γ term, then
[ ][ ]
1.46 (1 ) ( 0.54)2.46 (1 ) (0.46)
1.46 0.37(1 )2.46 0.19(1 )
x xx xx xx x
λρλ
λρ
λ
+ − −≅
+ −
− −≅
+ −
Furthermore, 28
25
0.21 0.131.57
a
a
σλσ
= ≈ = for a very hard spectrum
71
If so, 0.64 0.0290.025
xx
ρ −=
+
The least square curve fit to MCNP calculation gives 0.60 0.0320.017
xx
ρ −=
+. Comparing
each term in the two equations, we can see that the theoretical deduction gives a fairly good explanation and estimation.
72
Appendix C Sample input files for matrix material study
Uranium carbide fuel, Ba2Pb matrix, nickel reflector
1. Beginning of life keff calculation, mcnp input:
MCNP INPUT DECK FOR MFGR YK_01
c cell cards
1 1 2.984103E-02 -1 2 -3 imp:n=1 tmp= 6.662234E-08
2 2 8.913363E-02 -1 2 3 -4 imp:n=1 tmp= 6.662234E-08
99 0 1:-2:4 imp:n=0
c end of cell cards
c surface cards
*1 pz 50
*2 pz -50
3 cz 150
4 cz 240
c end of surface cards
awtab 34079 78.240500 38089 88.143700 38090 89.135400
44105 104.007000 46107 105.987000
47111 109.953000 48115 113.919000 50123 121.850000
50125 123.835000 50126 124.826000 51124 122.842000
51125 123.832000 51126 124.826000 52127 125.815000
52129 127.800000 53130 128.791000 53131 129.781998
54133 131.764008 58141 139.697998
58144 142.677000 59142 140.691000
59143 141.682999 61151 149.625000
62153 151.608002 63156 154.585007 63157 155.577000
96249 246.936000 97250 247.930000
73
c Material cards
c Material 1: inner core,Material 2: reflector
c Material 3: reflecter, Material 4: cladding
m1 6000.60c 9.041788E-03 $C
8016.60c 3.853585E-04 $O
c 56138.60c 7.709851E-03 $Ba
82000.50c 3.854926E-03 $Pb
c 92235.60c 1.163166E-03 $U235
c 92238.60c 7.685943E-03 $U238
35081.55c 1.0000e-24 $ begin_mcode_FP
c 36082.50c 1.0000e-24
36083.50c 1.0000e-24 36084.50c 1.0000e-24 37085.55c 1.0000e-24
37087.55c 1.0000e-24 38090.96c 1.0000e-24 39089.60c 1.0000e-24
40090.62c 1.0e-24
40091.96c 1.0000e-24 40092.62c 1.0000e-24 40093.50c 1.0000e-24
40094.62c 1.0000e-24 40096.62c 1.0000e-24 41095.96c 1.0000e-24
42095.50c 1.0000e-24 42096.96c 1.0000e-24 42097.60c 1.0000e-24
42098.50c 1.0000e-24 42100.50c 1.0000e-24 43099.50c 1.0000e-24
44100.96c 1.0000e-24 44101.50c 1.0000e-24 44102.60c 1.0000e-24
44103.50c 1.0000e-24 44104.96c 1.0000e-24 45103.50c 1.0000e-24
c 45105.50c 1.0000e-24
46104.96c 1.0000e-24 46105.50c 1.0000e-24 46106.96c 1.0000e-24
46107.96c 1.0000e-24 46108.50c 1.0000e-24 46110.96c 1.0000e-24
47109.60c 1.0000e-24 48110.62c 1.0000e-24 48111.62c 1.0000e-24
48112.62c 1.0000e-24 48113.60c 1.0000e-24 48114.62c 1.0000e-24
49115.60c 1.0000e-24 50117.96c 1.0e-24
51121.96c 1.0000e-24 51123.96c 1.0000e-24 52125.96c 1.0e-24
52128.96c 1.0000e-24 52130.96c 1.0e-24
53127.60c 1.0000e-24 53129.60c 1.0000e-24
54128.62c 1.0e-24 54130.62c 1.0e-24 54131.50c 1.0000e-24
54132.62c 1.0000e-24
74
c 54133.60c 1.0000e-24
54134.62c 1.0000e-24
c 54135.50c 1.0000e-24
54136.62c 1.0000e-24 55133.60c 1.0000e-24
55134.60c 1.0000e-24 55135.60c 1.0000e-24 55137.60c 1.0000e-24
56136.96c 0.000605532
56130.96c 8.17244E-06 56132.96c 7.78695E-06 56135.96c 0.000508233
56134.62c 0.000186347 56137.62c 0.00086597 56138.60c 0.005527809
57139.60c 1.0000e-24 58140.96c 1.0000e-24
c 58141.60c 1.0000e-24
58142.96c 1.0000e-24 58144.96c 1.0000e-24 59141.50c 1.0000e-24
c 59143.60c 1.0000e-24
60142.96c 1.0000e-24 60143.50c 1.0000e-24 60144.96c 1.0000e-24
60145.50c 1.0000e-24 60146.96c 1.0000e-24
c 60147.50c 1.0000e-24
60148.50c 1.0000e-24 60150.96c 1.0000e-24 61147.50c 1.0000e-24
c 61148.50c 1.0000e-24
61148.60c 1.0000e-24 $ ORIGEN_ID 611481
c 61149.50c 1.0000e-24
62147.50c 1.0000e-24 62148.96c 1.0000e-24 62149.50c 1.0000e-24
62150.50c 1.0000e-24 62151.50c 1.0000e-24 62152.50c 1.0000e-24
c 62153.60c 1.0000e-24
62154.96c 1.0000e-24 63151.60c 1.0000e-24 63152.50c 1.0e-24
63153.60c 1.0000e-24 63154.50c 1.0000e-24 63155.50c 1.0000e-24
c 63156.60c 1.0000e-24
64154.60c 1.0000e-24 64155.60c 1.0000e-24 64156.60c 1.0000e-24
64157.60c 1.0000e-24 64158.60c 1.0000e-24 65159.96c 1.0000e-24
66160.96c 1.0000e-24 66161.96c 1.0000e-24
66162.96c 1.0000e-24 $ end_mcode_FP
c 66163.96c 1.0000e-24
c 90232.60c 1.0000e-24
75
c 91231.60c 1.0000e-24
c 91233.50c 1.0000e-24
c 92232.60c 1.0000e-24
c 92233.60c 1.0000e-24
92234.60c 1.0000e-24 $ begin_mcode_ACT
92235.60c 1.163166E-03 $ fuel u-235
92236.60c 1.0000e-24 92237.50c 1.0000e-24
92238.60c 7.685943E-03 $ fuel u-238
c 93236.35c 1.0000e-24
93237.60c 1.0000e-24
c 93238.35c 1.0000e-24
93239.60c 1.0000e-24 94238.60c 1.0000e-24 94239.60c 1.0000e-24
94240.60c 1.0000e-24 94241.60c 1.0000e-24 94242.60c 1.0000e-24
c 94243.60c 1.0000e-24
95241.60c 1.0000e-24
c 95242.50c 1.0000e-24
95242.51c 1.0000e-24 $ ORIGEN_ID 952421
95243.60c 1.0000e-24 $ end_mcode_ACT
m2 6000.60c 4.816981E-05 $C
8016.60c 9.633962E-05 $O
28000.50c 8.898912E-02 $Ni
c ksrc 0 0 0
mode n
kcode 10000 1 10 220
prdmp 220 220 220
76
2. Beginning of life ∆kvoid calculation, mcnp input:
MCNP INPUT DECK FOR MFGR YK_01
c cell cards
1 1 2.926299E-02 -1 2 -3 imp:n=1 tmp= 6.662234E-08
2 2 8.898912E-02 -1 2 3 -4 imp:n=1 tmp= 6.662234E-08
99 0 1:-2:4 imp:n=0
c end of cell cards
c surface cards
*1 pz 50
*2 pz -50
3 cz 150
4 cz 240
c end of surface cards
c Material cards
c Material 1: inner core,Material 2: reflector
c Material 3: reflecter, Material 4: cladding
m1 6000.60c 8.849109E-03 $C
56136.96c 0.000605532
56130.96c 8.17244E-06 56132.96c 7.78695E-06 56135.96c 0.000508233
56134.62c 0.000186347 56137.62c 0.00086597 56138.60c 0.005527809
82000.50c 3.854926E-03 $Pb
92235.60c 1.163166E-03
92238.60c 7.685943E-03
m2 28000.50c 8.898912E-02 $Ni
c tally materials follows (39 ACT + 100 FP)
c Tally Materials
c ----------------------------------------------------------------------
77
c 100 fission products, m701 to m800
c ksrc 0 0 0
mode n
kcode 3000 1.107 5 120
prdmp 120 120 120
78
3. Burnup study, mcode input:
$ MCODE, UC fuel GCR, metal matrix, CO2 coolant, cold condition
TTL test case $ defines title
MCD 1 mcnp.exe Ba2Pb.i ykm.src $ MCNP files def.
$ mcnp cells def.: cell-number type(1=delp.,2=actv.) act-mass(g) vol.(cm3) flux-t#
cross-t#
ORG /usr/local/bin/origen22/origen22 /usr/local/bin/origen22/LIBS DECAY.LIB
GXUO2BRM.LIB
CEL 1 1 1 2.751209912E+07 7.06858E+06 FFTFC.LIB
$ total volume of modeling system (cm3)
VOL 7.06858E+06
$ ORIGEN files def.
$ normalization method, 1=flux, 2=power
NOR 2
$ predictor-corrector (OFF)
COR 0
$ power density, opt: WGU=W/gIHM, KWL=kW/(liter core)
PDE 10.61033475 KWL
$points 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
DEP E 0 5 10 15 20 30 40 50 60 70 80 90 100 120 140 160 180 200
NMD 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40
STA 0 $ starting point
END 17 $ ending point