Generation of a BroadGroup HTGR Library for 

Use with SCALE

Office of Nuclear Regulatory Research

NUREG/CR-7106

ORNL/TM-2011/298
DISCLAIMER: This report was prepared as an account of work sponsored by an agency of the U.S. Government. 

Neither the U.S. Government nor any agency thereof, nor any employee, makes any warranty, expressed or

implied, or assumes any legal liability or responsibility for any third party’s use, or the results of such use, of any

information, apparatus, product, or process disclosed in this publication, or represents that its use by such third

party would not infringe privately owned rights.

AVAILABILITY OF REFERENCE MATERIALS

IN NRC PUBLICATIONS

NRC Reference Material

As of November 1999, you may electronically access

NUREG-series publications and other NRC records at

NRC’s Public Electronic Reading Room at 

http://www.nrc.gov/reading-rm.html. Publicly released

records include, to name a few, NUREG-series

publications; Federal Register notices; applicant,

licensee, and vendor documents and correspondence;

NRC correspondence and internal memoranda;

bulletins and information notices; inspection and

investigative reports; licensee event reports; and

Commission papers and their attachments.

NRC publications in the NUREG series, NRC

regulations, and Title 10, Energy, in the Code of

Federal Regulations may also be purchased from one

of these two sources.

1. The Superintendent of Documents

 U.S. Government Printing Office

 Mail Stop SSOP

 Washington, DC 20402–0001

 Internet: bookstore.gpo.gov

 Telephone: 202-512-1800

 Fax: 202-512-2250

2. The National Technical Information Service

 Springfield, VA 22161–0002

 www.ntis.gov 

 1–800–553–6847 or, locally, 703–605–6000

A single copy of each NRC draft report for comment is

available free, to the extent of supply, upon written

request as follows:

Address: U.S. Nuclear Regulatory Commission

 Office of Administration 

 Publications Branch

 Washington, DC 20555-0001

E-mail: DISTRIBUTION.RESOURCE@NRC.GOV 

Facsimile: 301–415–2289 

Some publications in the NUREG series that are 

posted at NRC’s Web site address

http://www.nrc.gov/reading-rm/doc-collections/nuregs 

are updated periodically and may differ from the last

printed version. Although references to material found

on a Web site bear the date the material was accessed,

the material available on the date cited may

subsequently be removed from the site.

Non-NRC Reference Material

Documents available from public and special technical

libraries include all open literature items, such as

books, journal articles, and transactions, Federal

Register notices, Federal and State legislation, and

congressional reports. Such documents as theses,

dissertations, foreign reports and translations, and

non-NRC conference proceedings may be purchased

from their sponsoring organization.

Copies of industry codes and standards used in a

substantive manner in the NRC regulatory process are

maintained at—

The NRC Technical Library 

Two White Flint North

11545 Rockville Pike

Rockville, MD 20852–2738

These standards are available in the library for 

reference use by the public. Codes and standards are

usually copyrighted and may be purchased from the

originating organization or, if they are American

National Standards, from—

American National Standards Institute

11 West 42nd Street

New York, NY 10036–8002

www.ansi.org 

212–642–4900

Legally binding regulatory requirements are stated

only in laws; NRC regulations; licenses, including

technical specifications; or orders, not in 

NUREG-series publications. The views expressed

in contractor-prepared publications in this series are

not necessarily those of the NRC.

The NUREG series comprises (1) technical and

administrative reports and books prepared by the

staff (NUREG–XXXX) or agency contractors

(NUREG/CR–XXXX), (2) proceedings of

conferences (NUREG/CP–XXXX), (3) reports

resulting from international agreements

(NUREG/IA–XXXX), (4) brochures

(NUREG/BR–XXXX), and (5) compilations of legal

decisions and orders of the Commission and Atomic

and Safety Licensing Boards and of Directors’

decisions under Section 2.206 of NRC’s regulations

(NUREG–0750).
Generation of a BroadGroup HTGR Library for 

Use with SCALE

Manuscript Completed: August 2011

Date Published: June 2012

Prepared by: 

R.J. Ellis, D.J. Lee*, D. Wiarda, M.L. Williams, U. Mertyurek

Oak Ridge National Laboratory

Managed by UT-Battele, LLC

Oak Ridge, TN 37831-6170

*Formerly of Oak Ridge National Laboratory

Don Algama, NRC Project Manager

NRC Job Code N6841

Office of Nuclear Regulatory Research

NUREG/CR-7106

ORNL/TM-2011/298

iii

ABSTRACT

With current and ongoing interest in high temperature gas reactors (HTGRs), the U.S. Nuclear Regulatory 

Commission (NRC) anticipates the need for nuclear data libraries appropriate for use in applications for 

modeling, assessing, and analyzing HTGR reactor physics and operating behavior. The objective of this 

work was to develop a broad-group library suitable for production analyses with SCALE for HTGR 

applications. Several interim libraries were generated from SCALE fine-group 238- and 999-group 

libraries, and the final broad-group library was created from Evaluated Nuclear Data File/B Version 

ENDF/B-VII Release 0 cross-section evaluations using new ORNL methodologies with AMPX, SCALE, 

and other codes. Furthermore, intermediate resonance (IR) methods were applied to the HTGR broadgroup library, and lambda factors and f-factors were incorporated into the library’s nuclear data files. A 

new version of the SCALE BONAMI module named BONAMI-IR was developed to process the IR data 

in the new library and, thus, eliminate the need for the CENTRM/PMC modules for resonance selfshielding. This report documents the development of the HTGR broad-group nuclear data library and the 

results of test and benchmark calculations using the new library with SCALE. The 81-group library is 

shown to model HTGR cases with similar accuracy to the SCALE 238-group library but with 

significantly faster computational times due to the reduced number of energy groups and the use of 

BONAMI-IR instead of BONAMI/CENTRM/PMC for resonance self-shielding calculations.

v

FOREWORD

In recognizing the need for nuclear data appropriate for HTGR applications, a robust and versatile broadgroup nuclear data library for use with SCALE was generated for the U.S. Nuclear Regulatory 

Commission. An HTGR-appropriate 81-group energy structure was selected with energy boundaries that 

are a subset of the standard SCALE 238-group structure. This nuclear data library is intended for HTGR 

applications. The final broad-group library was generated directly from ENDF/B-VII files using the latest 

methodology, and the intermediate resonance parameters, lambda factors and f-factors for important 

nuclides were included in the new library.

vii

CONTENTS

Page

ABSTRACT ...............................................................................................................................................iii

FOREWORD............................................................................................................................................... v

CONTENTS ..............................................................................................................................................vii

LIST OF FIGURES.................................................................................................................................... ix

LIST OF TABLES...................................................................................................................................... xi

ACKNOWLEDGMENTS ........................................................................................................................xiii

ACRONYMS AND ABBREVIATIONS.................................................................................................. xv

1. INTRODUCTION.................................................................................................................................. 1

2. PROCEDURES AND METHODOLOGY FOR GENERATING HTGR LIBRARIES........................ 3

2.1 INTRODUCTION TO LIBRARIES ............................................................................................... 3

2.2 ISSUES RELATED TO HTGR NEUTRONICS AND NUCLEAR DATA ................................... 3

2.3 CODES AND TECHNIQUES......................................................................................................... 3

2.3.1 RIML .................................................................................................................................. 4

2.3.2 Creating a Multigroup Library............................................................................................ 4

2.4 GENERATION OF LIBRARIES FROM ENDF/B-VII FILES ...................................................... 5

2.5 INTERMEDIATE RESONANCE CONSIDERATIONS ............................................................... 8

2.5.1 IR method ........................................................................................................................... 8

2.5.2 Library generation............................................................................................................... 9

2.5.3 Library testing................................................................................................................... 11

2.6 TESTING OF BONAMI-IR DURING IMPLEMENTATION INTO SCALE............................. 11

2.7 SUMMARY OF LIBRARY GENERATION METHODS ........................................................... 13

3. NUCLEAR DATA LIBRARIES ......................................................................................................... 15

3.1 INTRODUCTION ......................................................................................................................... 15

3.2 GENERATING BROAD-GROUP LIBRARIES .......................................................................... 17

3.3 DESCRIPTION OF THE BROAD-GROUP LIBRARIES ........................................................... 19

3.3.1 Library 81A....................................................................................................................... 19

3.3.2 Library 81B....................................................................................................................... 39

3.3.3 Library 81B2..................................................................................................................... 40

3.3.4 Library 81B3..................................................................................................................... 40

3.3.5 Library 81C....................................................................................................................... 40

4. COMPARISON OF RESULTS WITH THE SCALE BROAD-GROUP LIBRARIES ...................... 41

5. SUMMARY AND RECOMMENDATIONS ...................................................................................... 45

6. REFERENCES..................................................................................................................................... 47
viii

APPENDIX A DESCRIPTION OF INTERMEDIATE RESONANCE METHOD IN SCALE ...........A-1

A.1 Intermediate Resonance Approximation.....................................................................................A-3

A.2 Computation Of Hydrogen-Equivalent Lambda Factors.............................................................A-4

APPENDIX B INPUT FILE FOR RADIAL CORE MODEL 999-GROUP (VHTR) MODEL............B-1

APPENDIX C INPUT FOR GENERATING CENTRM POINTWISE FLUX WEIGHTING 

 FUNCTIONS.................................................................................................................. C-1

APPENDIX D INPUT FOR TEST2R3_MG: SAMPLE JAPANESE HTTR BENCHMARK CASE ..D-1

APPENDIX E SCHEMATIC DIAGRAMS OF THE HTTR BENCHMARK CASE........................... E-1

APPENDIX F IR F-FACTOR................................................................................................................. F-1
ix

LIST OF FIGURES

 Page

Figure 2.1. Work flow for AMPX master library creation. ......................................................................... 5

Figure 2.2. AMPX sequence for producing neutron multigroup data.......................................................... 6

Figure 2.3. Comparison of CENTRM pointwise flux weighting functions for the HTGR temperatures. ...8

Figure 3.1. Comparison of HTGR spectra in 999-group calculations for a range of temperatures. .......... 15

Figure 3.2. Comparison of HTGR spectra in 238- and 999-group calculations. ....................................... 16

Figure 3.3. Comparison of HTGR spectra (238 group and 999 group) in the 1 to 10 eV region. ............. 17

Figure 3.4. HTGR spectra in the 10 to 100 eV region: comparison of fine-group solutions.................... 18

Figure 3.5. HTGR spectra in the 10 to 100 eV range for broad and fine group libraries. ......................... 18

Figure 3.6. HTGR 238-group spectrum in the 10 to 100 eV region: broad-group comparisons. ............. 19

xi

LIST OF TABLES

Table 2.1. Background cross sections for Bondarenko factors of 

Page

238U...................................................... 10

Table 2.2. Assessing the IR-methods improvement to the library: HTR pin-cell test problem................ 11

Table 2.3. Infinite homogeneous medium of 1.26% enriched LEU and H; background 

 XS ~ 100 b and temperature 300K............................................................................................ 12

Table 2.4. Infinite homogeneous medium of 1.26% enriched LEU and H; background 

 XS ~ 50 b and temperature 300K.............................................................................................. 12

Table 2.5. Infinite homogeneous medium of 1.26% enriched LEU and H; background 

 XS ~ 25 b................................................................................................................................... 12

Table 2.6. Simplified PWR pin cell 3.34% enriched UO2

12

, pitch = 1.44 cm; pellet 

 OR = 1.44 cm; temperature 300K .............................................................................................

Table 2.7. Double-het HTR pin cell and temperature 300K...................................................................... 13

Table 3.1. Neutron energy group structure comparisons for 999-, 238-, and 81-group............................. 20

Table 4.1. keff comparisons for MG KENO homogeneous cell HTGR model .......................................... 41

Table 4.2. keff comparisons for homogeneous 1-D radial model............................................................... 41

Table 4.3. keff results for HTTR benchmark case 1 ................................................................................... 42

Table 4.4. keff results for HTTR benchmark case 2 ................................................................................... 42

Table 4.5. keff results for HTR-10 pebble unit cell (1200K fuel, 900K coolant)....................................... 43

Table 4 6. keff results for HTR-10 pebble unit (300K)............................................................................... 43

Table 4.7. keff results for HTR-10 full core ............................................................................................... 44

xiii

ACKNOWLEDGMENTS

This project was supported by the U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory 

Research. The authors are grateful for the assistance and support of Don Algama of the NRC Office of 

Nuclear Regulatory Research. The authors are grateful for the support and guidance of ORNL project 

managers Mike Dunn and Steve Bowman. The authors thank Harold Smith, Germina Ilas, and Matthew 

Jessee of ORNL and Don Carlson of NRC for their technical reviews. Also, thanks are extended to Angie 

Alford and Debbie Weaver for their efforts in preparing this manuscript for publication.

xv

ACRONYMS AND ABBREVIATIONS

1-D one dimensional

2-D two dimensional

3-D three dimensional

AMPX Analytical Methods Nuclear Cross-Section Processing Computer Code System

ASME American Society of Mechanical Engineers 

CE continuous energy

CENTRM Continuous Energy Transport Module

DCS data control system

ENDF evaluated nuclear data file

ENDF/B-VII.0 evaluated nuclear data file version VII

HTGR high temperature gas reactor

HTR high temperature reactor

HTS heat transport system

HTTR High Temperature Engineering Test Reactor

HX heat exchanger

IR intermediate resonance

LWR light-water reactor 

MOC method of characteristics

MWd/te U megawatt-days per metric ton of uranium

MWt megawatt thermal

NGNP next generation nuclear plant

NPP nuclear power plant 

NR narrow resonance 

NRC U.S. Nuclear Regulatory Commission 

OE operating experience

ORNL Oak Ridge National Laboratory

P&IC pressure and inventory control

PBR pebble bed reactor

pcm parts per hundred thousand (cent mille)

PSA probabilistic safety assessment

PW pointwise

PWR pressurized water reactor

RB reactor building

RG regulatory guide

SAS1X SCALE Shielding Analysis Sequence 

SDC shutdown cooling

1X

SF spent fuel

VHTR very high temperature reactor

WR wide resonance

XML extensible markup language

1

1. INTRODUCTION

Analyses and simulations for high temperature gas reactor (HTGR) models require appropriate nuclear 

data libraries. In order to perform timely production calculations, a suitable broad-group neutron energy 

structure is required. Calculations using the broad-group library need to provide results comparable to 

calculations performed with fine-group libraries or continuous energy calculations.

Until now, most broad-group libraries have been prepared or generated with the intention of being 

suitable for light water reactors (LWRs). In this work, it is the goal to generate a broad-group nuclear data 

library for use in the Oak Ridge National Laboratory (ORNL) SCALE code system [1,2] for HTGR 

applications. Several broad-group HTGR cross-section libraries were produced with SCALE modules 

(e.g. MALOCS) or through the use of AMPX [3,4] modules. The selection of a suitable broad-group 

neutron energy structure resulted from analysis and assessment of HTGR neutron spectra and features of 

neutron resonances and reactions. The final HTGR 81-group library produced in this work was generated 

directly from ENDF/B-VII nuclear data files using ORNL library generation techniques and procedures.

In addition, intermediate resonance (IR) treatment methods were applied to generate intermediate 

resonance (IR) parameters (including lambda factors and f-factors) that were added to the library. 

Furthermore, some additions and augmentations were made to the SCALE code software (in particular, 

BONAMI-IR) to implement the capability to utilize the IR parameters. The 81-group library is expected 

to be released in SCALE 6.2.

This report provides details of the process in which the broad-group structure of neutron energy group 

boundaries was determined. In addition, testing of model scenarios and benchmark calculations were 

completed using SCALE for a range of representative HTGR-related models. The results from SCALE

calculations using the new HTGR broad-group libraries were compared with similar calculations using 

fine-group and ultra fine-group libraries and also with continuous energy KENO and MCNP [5] model 

results.

3

2. PROCEDURES AND METHODOLOGY FOR GENERATING HTGR 

 LIBRARIES

The methodology for producing a broad-group nuclear data library for HTGR applications in SCALE 

modeling and simulation utilized AMPX and SCALE software modules in conjunction with analysis and 

interpretation of calculated relevant neutron spectra.

2.1 INTRODUCTION TO LIBRARIES

For this work, the main goal was to create an efficient and effective broad-group nuclear data library that 

would be suitable for use with SCALE HTGR models for production cases ranging from room 

temperature to 2000 K. The standard SCALE ENDF/B-VII cross-section library for reactor analysis

contains 238 neutron energy groups. Recently, a fine-group library was generated, using a HTGR 

weighting function, with nuclear data in 999 neutron energy groups. An HTGR broad-group library with 

81 energy groups was produced from this 999-group library. The libraries discussed in this report are all 

based on ENDF/B-VII nuclear data files.

2.2 ISSUES RELATED TO HTGR NEUTRONICS AND NUCLEAR DATA

HTGRs operate under conditions quite different from LWRs and pressurized heavy water reactors 

(PHWRs) for which many nuclear data libraries have been generated. The nuclear data libraries for 

HTGRs generally need to be suitable for the higher temperatures and characteristic neutron flux spectra 

that are generated in these reactors. There are special neutron resonances and material concerns associated 

with HTGR neutronics. Usually, fine group structure is needed in the nuclear data libraries so that all the 

neutron absorption, capture, and fission processes are appropriately simulated.

In order to generate a broad-group nuclear data library suitable for HTGR models, careful establishment 

of neutron energy boundaries is required such that major resonances and reactions will be treated 

properly. Various broad-group neutron energy structures were considered and assessed in this work, with 

reference to earlier broad multigroup libraries. The results of SCALE model scenarios with broad-group 

nuclear data libraries were compared against cases utilizing fine-group SCALE nuclear data libraries (238 

and 999 groups). These cases were also compared against MCNP and KENO continuous energy 

simulations to assess the appropriateness of the broad-group libraries.

2.3 CODES AND TECHNIQUES

SCALE was used in this work in conjunction with AMPX [3,4] and other nuclear data codes, such as 

RIML [8]. Monte Carlo calculations with MCNP and SCALE/KENO were used in addition to 

deterministic neutron transport simulations. Representative HTGR pin cell and full core models were 

analyzed. Furthermore, a series of HTGR benchmark model scenarios were assessed with the different 

nuclear data libraries to test the suitability of the newly generated broad-group nuclear data libraries. In 

addition to using ENDF/B-VII data files with appropriate weighting functions to generate broad-group 

nuclear data for use with HTGRs, appropriate nuclide-dependent Bondarenko IR f-factors and lambda 

factors were implemented with the nuclear data. Necessary modifications to implement the IR 

methodology in SCALE were performed and used in the analyses.
4

2.3.1 RIML

RIML [8] is a code for generating IR parameters, self-shielded cross sections, subgroup levels and 

weights, and the associated AMPX master libraries. RIML is a control module composed of three 

separate programs: RILAMB, IRVING, and SUBGR. RILAMB generates IR parameters for the 

homogeneous mixtures and self-shielded cross sections as a function of background cross section for the 

homogeneous and heterogeneous geometries. Self-shielded cross sections are converted into the 

Bondarenko factors and into the resonance integral table. IR parameters and Bondarenko factors are to be 

included or replaced in the master AMPX library using IRVING. SUBGR uses the resonance integral 

table created by RILAMB to generate the subgroup levels and weights. These subgroup data can be used 

in a transport lattice code, such as DeCART, which uses the subgroup method to self-shield resonance 

group cross sections.

The wide and the narrow resonance (NR) approximations have been combined [10], together forming an 

IR approximation that is good for the resonance range from a few electron volts up to 100 keV. IR

parameters can be used to interpolate between the narrow and wide resonance approaches. Because nearly 

all deterministic transport codes use multigroup cross sections, utilizing between 30 and 300 groups, it is 

very important to use the appropriate approximations to estimate the effective group self-shielded cross 

section. 

Many kinds of methods have been developed for the resonance treatment in this energy range. However, 

in many cases the basic approach for the resonance treatment is similar. The self-shielded cross sections 

are tabularized in advance as a function of some parameter such as background cross section by using 

various methods. One of the typical methods is to obtain the self-shielded cross sections by solving the 

continuous or ultrafine group slowing-down equation and to obtain the corresponding background cross 

section to complete the self-shielded cross-section table.

The CENTRM/PMC codes are used to estimate the self-shielded group cross sections by solving the 

slowing-down equation with the continuous energy cross sections and integrating the continuous energy 

flux and cross section over each group. These effective self-shielded group cross sections are used in 

SCALE multigroup/transport codes (e.g. NEWT, KENO) directly. The SCALE CENTRM/PMC codes 

can be used to obtain the self-shielded group cross-section table through a slight modification and a 

combination with a module to generate the corresponding background cross section.

The program RILAMB (Resonance Integral and Lambda) has been developed to compute IR parameters 

and self-shielded cross-section tables using the results from CENTRM/PMC in the SCALE system. IR

parameters are generated for a set of homogeneous mixtures, and self-shielded group cross-section tables 

are generated for the specified homogeneous and heterogeneous geometries. The program IRVING uses 

the self-shielded cross-section tables to generate Bondarenko factors and resonance integral tables. 

IRVING replaces the original NR Bondarenko factors in the master AMPX library and adds the IR 

parameters.

2.3.2 Creating a Multigroup Library

A flow diagram is presented in Figure 2.1 to illustrate the automated procedure to generate the AMPX 

master library from ENDF/B evaluations.
5

Figure 2.1. Work flow for AMPX master library creation.

2.4 GENERATION OF LIBRARIES FROM ENDF/B-VII FILES

In this ORNL process, the input files are generated automatically using extensible markup language 

(XML) templates. The general flow of creating the nuclear data in this methodology is depicted in Figure

2.2. The AMPX modules and utility codes employed in this process are described below and shown in 

the flowchart.
6

Figure 2.2. AMPX sequence for producing neutron multigroup data.

The following AMPX modules are used in the process to produce a neutron multigroup library.

POLIDENT: Creates pointwise cross-section data at 0 K from the ENDF/B-VII data files. For resonance 

nuclides, POLIDENT contains a procedure that determines a point energy mesh in the resolved resonance 

region and calculates the cross sections on that energy mesh. The pointwise data are stored as x-y values 

on a linear-linear grid.

TGEL: When all of the cross-section data are produced on a linear-linear grid, the sum of a group of 

linear functions is itself linear; however, simply linearizing the data that are given in an evaluation does 

not lead to this consistency. To ensure consistency, the total cross section and other “redundant” reactions 

(e.g., fission, inelastic) are formed by summing the partial values. This module is used to ensure that all 

redundant reactions are equal to the sum of the partial reactions. 

BROADEN: This module is used to Doppler broaden the cross-section data.

PRUDE: For nuclides with unresolved resonance data, this module is run to produce point averaged 

cross sections that are a function of temperature and background cross section (background cross sections 

are discussed in more detail in Section 2.5). The background cross section is simply defined as the 

cross section per unit atom of a nuclide of the mixture (other than the nuclide itself) in which the nuclide 
7

is mixed. In the sequences that were prepared, temperatures of 293, 900, and 2100 K were chosen, along 

with background values of 10-6

, 1, 10, 100, 1000, 104, 105, 106, and 108 barns. 

FABULOUS: For all nuclides, the point data from PRUDE (if applicable) and POLIDENT are passed to 

this module with the weighting spectrum file. FABULOUS uses the same temperatures and background 

cross sections described for PRUDE to numerically Doppler broaden the functions exterior to the 

unresolved region, after which the functions are spliced together with the appropriate unresolved 

functions. These spliced functions are then used in a numerical scheme that calculates Bondarenko factors 

for all nuclides for elastic scattering, capture, fission, and total cross sections. 

UNITAB and SIMONIZE: These modules are used to combine partial master libraries generated by 

FLANGE6, FABULOUS, and X10 into a cohesive AMPX MG master library for a given evaluation. The 

module combines the data into one AMPX MG master library after recalculating and renormalizing the 

data.

JERGENS: This module is used to generate the flux used to collapse point-wise data to MG format.

Y12: This module reads an ENDF/B evaluation and produces tabular double-differential collision 

kinematics data for all reactions. The functions it produces tell what particles are produced and at what 

energies and directions when a reaction is encountered at some source energy point. The output from Y12 

is an AMPX tabular kinematics file.

X10: The weighting spectrum, the point data from BROADEN, and the kinematics data from Y12 are 

passed to X10. X10 produces a group-averaged AMPX master library.

FLANGE6: This module is used to produce thermal scattering matrices at 293, 600, 900, 1200, and 

2100 K based on the free-gas scattering model.

RADE: This module is used to perform internal consistency checks on the AMPX master library. 

To generate the 999-group library, we used the AMPX JERGENS module to generate a smooth weighting 

spectrum that has the form of a Maxwellian–1/E–fission spectrum–1/E above 10 MeV. For the 81-group 

library 81B3 and 81C, we used a custom flux as the weighting function. Figure 2.3 shows the pointwise 

flux generated in CENTRM (from the HTGR prismatic fuel SCALE input case listed in Appendix C) for 

two representative temperatures. The pointwise flux data (approximately 16,000 data points) at a 

temperature of 1800 K was chosen to be the weighting function for the generation from the ENDF/B-VII 

nuclear data files [11] of the 81-group library.
8

Figure 2.3. Comparison of CENTRM pointwise flux weighting functions for the HTGR temperatures.

2.5 INTERMEDIATE RESONANCE CONSIDERATIONS

This section is a summary of the new methods and data that were added as an IR treatment in the new 

library. The resonance data in SCALE 6.1 and all earlier versions of SCALE were based on the neutron 

spectrum from the narrow resonance approximation. With the new IR methods applied for selected 

isotopes (e.g., 238

2.5.1 IR method

U), new Bondarenko factor tables were generated based on a more rigorous neutron flux 

spectrum. In addition, IR parameters (lambda factors) have been added for the evaluation of background 

cross sections in the resonance treatment with the IR approximation.

The effective shielded cross section in a resonance group g can be written [10] as

∫

∫

∆

∆

=

g

g

u

u

x

x g

u du

u u du

( )

( ) ( )

,

φ

σ φ

σ .

where ∅ = �lux and u = lethargy.

In the narrow resonance (NR) approach, the neutron spectrum is simply inversely proportional to the total 

cross section:

( )

constant ( )

t u

u

Σ φ = .

In a more sophisticated IR method, the flux spectrum can be written as
9

a b

b

u

u

σ σ

σ φ

+ = ( ) ( )

where a background cross section is defined as

, 1 = ∑ , i=all

i i p i

r

b N

N

σ λσ

Nr is the atomic number density of the resonance nuclide, Ni is the atomic number density of isotope i, 

λi is the IR parameter of isotope i, and σ p,i is the potential cross section of isotope i. In case of 

heterogeneous problems, the background cross section can be adjusted as below using the equivalence 

theory:

σ b → σ b +σ e

where σ e is the escape cross section,

, 1 (1 )

l

a c

Nr

e

− σ =

in which a is the Bell factor, c is the Dancoff factor, and l is the mean chord length of fuel region.

2.5.2 Library generation

As shown above, in order to apply the IR method, the resonance integrals of isotopes selected for IR 

treatment need to be recalculated either by using the IR definition of flux spectrum or using a neutron 

slowing-down solver such as CENTRM. The lambda factors also need to be generated for implementation 

in a new library to allow for the application of the IR method in the BONAMI-IR module in SCALE.

New Bondarenko factors

The Bondarenko factors of given resonance materials are computed using a pointwise (PW) flux spectrum 

for an infinite homogeneous mixture of the resonance nuclide combined with hydrogen. The hydrogen 

concentration in the mixture is varied to obtain the desired σb values corresponding to different degrees of 

self-shielding for the particular resonance material. The temperature of the resonance material is also 

varied to account for the impact of Doppler broadening on self-shielding. CENTRM was used to calculate 

the PW flux in the homogeneous media for each hydrogen concentration (i.e., σb) and resonance Doppler 

temperature, for each resonance nuclide of interest. PMC was used to compute the corresponding selfshielded cross sections. The Bondarenko factor is the ratio of the self-shielded cross section from PMC 

divided by the infinitely dilute (unshielded) cross section in the library. For example in the case of 238U, 

CENTRM/PMC was run for three Doppler temperatures of 293, 900, and 2000 K and 93 different 

hydrogen concentrations. This corresponds to 3 X 93 = 279 CENTRM/PMC cases. The Bondarenko 

factors at the desired background cross section values (σb ) in the library were interpolated from these 

results. Table 2.1 shows the final background cross section values for which 238U Bondarenko factors are 

tabulated in the library. The Bondarenko factors for other resonance materials were generated similarly, 

but different hydrogen concentrations may have been used.
10

Table 2.1. Background cross sections for Bondarenko factors of 238U

Background cross section

(barns)

Background cross section

(barns)

Background cross section

(barns)

1.00E-06 1.20E+02 1.00E+05

1.00E+00 1.60E+02 1.00E+08

1.00E+01 3.20E+02

1.50E+01 6.40E+02

2.00E+01 1.00E+03

3.00E+01 2.00E+03

4.00E+01 5.00E+03

6.00E+01 1.00E+04

8.00E+01 2.00E+04

From the CENTRM/PMC outputs of these cases, the effective cross sections of 238

, ( , ) ( , )

, ,

, ,

,

∞

=

x g

x g eff f b

x g f b

T

f T

σ

σ σ

σ

U have been collected 

and converted to Bondarenko factor tables using the following definition:

where f is the Bondarenko factor, Tf σ x,g,eff is the fuel temperature, is the effective cross section of type 

x, andσ x,g,∞ is the infinitely dilute cross section. These factors have been tabulated in the library at three 

temperatures (293, 900, and 2000 K) and 19 background cross sections (1 × 10-6

, 10, 15, 20, 30, 40, 60, 

80, 120, 160, 320, 640, 1000, 2000, 5000, 10,000, 20,000, 1 × 106

, and 1 × 108

Lambda factors

barns). Before this 

modification to the process, the original library had Bondarenko factors for only nine background cross 

sections.

Lambda factors are also called hydrogen equivalence parameters and are calculated in the following 

procedure:

1) Compute a 238 σ a,g table as a function of 238 σ b,g by changing the particle number density of hydrogen for a 

homogeneous mixture at the fixed 238U (N238

2) Compute the slowing-down calculation for a mixture of 

) particle number density. The calculation of the effective 

cross sections has been done in CENTRM/PMC and RIML has been used for the processing of the 

data.

238U (N238), 1

H (N1) and a target nuclide x 

(Nx 238 σ a,g ), and obtain a new (CENTRM/PMC).

3) Read the corresponding 238 σ b,g from the prepared 238 σ a,g table (RIML). 

4) Calculate the hydrogen equivalence parameter of the isotope x using the following equation (RIML), 

where σp

x

p

x

x b g g p g p

g N

N N N

σ

σ λ σ λ σ

λ

238 238 238 238 238 1 1 1

, − − =

is the potential cross section (refer to Appendix A).

.
11

The above procedure has been applied to all the isotopes in the old library, and the calculated lambda 

factors have been added to a new library at MT=2000. The lambda factors have been generated for a 

single fuel temperature of 300K. 

2.5.3 Library testing

A simple HTGR pin cell has been used for testing the implemented method. In the model, the fuel kernels 

in the compact have been homogenized with graphite. The calculated k-effective values are summarized 

in Table 2.2 as a function of pin pitches. The fuel temperature used for testing is 900 K to match the 

cross-section data for the continuous energy calculations with KENO. NR and IR results from XSDRN 

are compared with continuous energy KENO (CE KENO), which is considered the reference solution in 

lieu of measured data, and with CENTRM, which is the reference method for generating the IR factors. In 

other words, BONAMI-IR results cannot be expected to be better than the CENTRM results. Note that 

the large differences between NR and CENTRM/CE KENO are expected. They demonstrate the 

inadequacy of the NR methodology for thermal systems, which is the reason for developing the IR 

method.

The results presented in Table 2.2 and the following tables in this section are based on preliminary 

investigations in the development of the IR methodology. The calculated results for the final method in 

Section 4 provide validation of the 81-group library for real world HTGR applications.

Table 2.2. Assessing the IR-methods improvement to the library: HTR pin-cell test problem

Pitch 

(cm) CE KENO

238-Group KENO

BONAMI-NR

∆k (pcm)

vs. CE 

KENO

BONAMI-IR

∆k 

(pcm)

vs. CE 

KENO

CENTRM 

(n2d=0,ibr=3)

∆k (pcm)

vs. CE 

KENO

NR vs. 

CENTRM

∆k (pcm)

IR vs. 

CENTRM

∆k (pcm)

1.5 0.97725 1.17518 19793 0.97398 -327 0.97587 -138 19931 -189

2.0 1.21413 1.39732 18319 1.20669 -744 1.20919 -494 18813 -250

2.5 1.38634 1.53469 14835 1.37588 -1046 1.37967 -667 15502 -379

For the 238-group library, the nuclear data library with IR treatment is significantly improved over the old 

library with the NR approach.

2.6 TESTING OF BONAMI-IR DURING IMPLEMENTATION INTO SCALE

As part of the process of implementing IR treatment into BONAMI (also called BONAMI-IR), several 

comparisons were made between BONAMI-IR, standard BONAMI (BONAMI-NR), CENTRM, and 

continuous energy KENO. The BONAMI-IR calculations used a new IR-relevant 238-group library 

(238ir) that was generated using the HTGR CENTRM weighting function. The results presented in Tables 

2.3–2.5 were calculated with XSDRN for an infinite homogeneous medium of very low enriched uranium 

(LEU) and hydrogen with different background cross sections. Table 2.6 presents results for a simplified 

PWR pin cell, and Table 2.7 compares results for a doubly heterogeneous HTGR pin cell. The agreement 

between the BONAMI-IR and the CE KENO results is generally on the same order as the CENTRM 

results and significantly better than that of BONAMI-NR, with the exception of Table 2.6. The 

discrepancy between MG KENO/CENTRM and CE KENO for LWR pin cells has been previously 

observed with the standard SCALE V7-238 library and is under investigation. Note that the BONAMI-IR 

and CENTRM results are consistent. The fact that the BONAMI-NR result is better for this case is most 

likely due to a cancellation of errors.
12

Table 2.3. Infinite homogeneous medium of 1.26% enriched LEU and H; background 

 XS ~ 100 b and temperature 300K

Code BONAMI

method

MG XS 

library Eigenvalue

∆k (pcm)

Diff from

CE KENO

CE KENO − − 1.09394 ± 0.00021 −

CENTRM IR 238ir 1.09508 114

BONAMI IR 238ir 1.09648 254

BONAMI NR 238 1.10282 888

Table 2.4. Infinite homogeneous medium of 1.26% enriched LEU and H; background 

 XS ~ 50 b and temperature 300K

Code BONAMI

method

MG XS 

library Eigenvalue

∆k (pcm)

Diff from

CE KENO

CE KENO − − 1.05673 ± 0.00019 −

CENTRM IR 238ir 1.05855 182

BONAMI IR 238ir 1.05560 -113

BONAMI NR 238 1.06525 852

Table 2.5. Infinite homogeneous medium of 1.26% enriched LEU and H; background XS ~ 25 b

Code BONAMI

method

MG XS 

library Eigenvalue

∆k (pcm)

Diff from

CE KENO

CE KENO − − 0.95583 ± 0.00020 −

CENTRM IR 238ir 0.95861 278

BONAMI IR 238ir 0.95812 229

BONAMI NR 238 0.96553 970

Table 2.6. Simplified PWR pin cell 3.34% enriched UO2, pitch = 1.44 cm; pellet OR = 1.44 cm; 

Temperature 300K

Code BONAMI

method

MG XS 

library Eigenvalue

∆k (pcm)

Diff from 

CE KENO

CE KENO − − 1.35578 ± 0.00022 −

MG KENO/CENTRM IR 238ir 1.34903 ± 0.00018 -675

MG KENO/BONAMI-IR IR 238ir 1.34714 ± 0.00019 -864

BONAMI/ XSDRN NR 238 1.34948 -630
13

Table 2.7. Double-het HTR pin cell and temperature 300K

Code MG XS 

library Eigenvalue

∆k (pcm)

Diff from 

CENTRM double-het

XSDRN/CENTRM 238ir 1.29596 −

XSDRN/BONAMI-IR 238ir 1.29797 201

2.7 SUMMARY OF LIBRARY GENERATION METHODS

Several methods of nuclear data library generation were employed in this work. The MALOCS utility 

module in SCALE was used to condense existing SCALE nuclear data libraries into appropriate broadgroup energy structures using HTGR case-calculated weighting functions (based on case neutron flux 

distributions). This procedure was used in the creation of the interim broad-group libraries 81A, 81B, and 

81B2. The other major methodology for creation of a nuclear data library is to generate it directly from 

ENDF/B data files, using continuous energy (pointwise) weighting functions, such as generated with 

CENTRM. This process was used to generate the recent 999-group library for SCALE (with independent 

weighting function) and was used in generating a new IR-relevant 238-group library using the HTGR 

CENTRM weighting function. The 81B3 broad-group library was also generated in this manner, using the 

neutron energy group structure of 81B2, but with the CENTRM generated weighting function rather than 

the neutron flux from 999- and 238-group SCALE HTGR model calculations.

To provide additional computational efficiency by removing the need to use CENTRM/PMC for unit cell 

calculations, the final broad-group libraries were enhanced and augmented with IR lambda factors and ffactors. These IR-enhanced nuclear data libraries were used in case calculations for HTGR models using a 

developmental version of SCALE in which the new IR features can be accessed and used in cases as 

discussed in the following section.

15

3. NUCLEAR DATA LIBRARIES

3.1 INTRODUCTION

The SCALE 6.1 code system includes both pointwise (PW) and multigroup (MG) libraries processed 

from ENDF/B-VII nuclear data files using SCALE and the AMPX code system. The PW data are used for 

two distinct functions in SCALE. First, they are used for three-dimensional (3D) continuous-energy (CE) 

Monte Carlo calculations with KENO. Second, they are used in the one-dimensional (1-D) CENTRM CE 

discrete ordinates code to compute pointwise flux spectra for generating self-shielded MG cross sections. 

The PW nuclear data are stored on a very fine energy mesh so that the value at any energy can be linearly 

interpolated with an error of less than 0.1%. 

Figure 3.1 presents a comparison of neutron spectra calculated with SCALE for a representative HTGR 

homogeneous prismatic fuel model case input, “vhtr” (listed in Appendix B), using a 999-group ENDF/BVII library at three different representative temperatures of 300 K, 900 K, and 1700 K. In addition, the 

999-group HTGR neutron spectrum at 1700 K is compared with a 238-group spectrum at the same 

temperature in Figure 3.2. The 238-group ENDF/B-VII library is the most current and generally 

recommended library in SCALE 6.1. The 999-group library has been developed and used internally at 

ORNL for various studies [6]. This 999-group library allows calculations to be performed with an ultra

fine neutron energy mesh, allowing multigroup calculations that more closely resemble continuous energy 

representations. Note that the 238-group structure is a subset of the 999-group structure, i.e., the 

boundaries of the 238-group structure align with boundaries in the 999-group structure.

Figure 3.2 compares the 238-group and the 999-group neutron flux spectra calculated for the SCALE vhtr 

input model (listed in Appendix B) at a temperature of 1700K. As seen in the figure, the spectra are very 

similar for the main characteristics. However, the 999-group spectra, by virtue of its near-continuous 

energy fine group aspects shows more detail and structure in the resolved and unresolved resonance

regions.

Figure 3.1. Comparison of HTGR spectra in 999-group calculations for a range of temperatures.

0.0E+00

2.0E-02

4.0E-02

6.0E-02

8.0E-02

1.0E-01

1.2E-01

1.4E-01

1.0E-09 1.0E-07 1.0E-05 1.0E-03 1.0E-01 1.0E+01

Normalized flux per lethargy

Neutron energy (MeV)

vhtr model: 999g, 300K

vhtr model: 999g, 900K

vhtr model: 999g, 1700K
16

Figure 3.2. Comparison of HTGR spectra in 238- and 999-group calculations.

In this report, neutron flux spectra are plotted in two ways, with the y-axis for both methods representing 

the neutron flux level divided by the lethargy of the energy group bins (the natural log of the ratio of the 

bin upper energy to the bin lower energy). The first plotting method (used in Figure 3.1) plots the flux per 

unit lethargy against the average bin neutron energy. The other plotting method is to use histograms for 

the full neutron energy bin with each bin ranging from its lower to higher neutron energy limits. 

Figure 3.3 provides more detail of the neutron spectra calculated with SCALE using 238- and 999-group

nuclear data libraries in Figure 3.2 over the energy range of 1 to 10 eV, which includes the large neutron 

capture resonance at 6.7 eV for 238U reactions. The agreement in this large neutron capture resonance 

between the 238-group and the 999-group neutron flux representations with SCALE is quite good for 

HTGR simulation cases. Small differences are evident between the solutions due to the much finer 

neutron energy group structure in the 999-group nuclear data library. Note that the broad peak between 2 

to 3 eV in this and other figures is not physical. It is caused by truncation of the thermal scattering at 3 eV 

in the SCALE multigroup (MG) libraries. This phenomenon is more noticeable for graphite. The impact 

on calculations is typically negligible, because there are no important resonances at this energy. The 

SCALE team has plans to address this problem in the near future.

0.0E+00

2.0E-02

4.0E-02

6.0E-02

8.0E-02

1.0E-01

1.2E-01

1.4E-01

1.0E-09 1.0E-07 1.0E-05 1.0E-03 1.0E-01 1.0E+01

Normalized flux per lethargy

Neutron energy (MeV)

vhtr model: 999g, 1700K

vhtr model: 238g, 1700K
17

Figure 3.3. Comparison of HTGR spectra (238 group and 999 group) in the 1 to 10 eV region.

3.2 GENERATING BROAD-GROUP LIBRARIES

In this project, a number of interim broad-group nuclear data libraries were generated in 81 neutron 

energy groups; a previous study of the efficacy of nuclear data libraries for use in modeling VHTRs 

considered broad-group libraries with 72 and 79 groups [7]. Several broad-group neutron energy 

structures were devised by adding several judiciously placed energy bins to the library energy structure

starting with that of the 72-group structure. The first 81-group broad-group library (81A) was a subset of 

the 999-group ultra fine group library with the neutron energy boundaries selected to capture the 

important resonances and features in the HTGR spectrum. The second broad-group structure (81B3) was 

established by shifting energy group boundaries in 81A that did not align with the 238-group structure so 

that the energy boundaries in 81B are a subset of the standard SCALE fine-group 238-group library 

energy bin boundaries. 

Figure 3.4 compares the fine detail in the 238- and 999-group flux solutions for the HTGR prismatic fuel 

case for the 10 to 100 eV neutron energy range in the spectra. As can be seen, the 999-group flux solution 

shows deeper flux dips in the narrow resonances followed by increases in flux level at the lower energy 

side of the resonances, which is consistent with the somewhat reduced cross section that would be in 

effect. This is clearly evident for the 36 eV (3.6 × 10-5 MeV) neutron resonance region seen in the middle 

of Fig. 3.4.

5.0E-03

1.0E-02

1.5E-02

2.0E-02

2.5E-02

3.0E-02

3.5E-02

4.0E-02

4.5E-02

5.0E-02

1.0E-06 1.0E-05

Normalized flux per lethargy

Neutron energy (MeV)

vhtr model: 999g, 1700K

vhtr model: 238g, 1700K 6.7 eV 

resonance 

in 238U
18

Figure 3.4. HTGR spectra in the 10 to 100 eV region: comparison of fine-group solutions.

In Figure 3.5, histograms representing the 81 group neutron flux spectra solutions for the 81A and 81B3 

nuclear data libraries in the 10 to 100 eV neutron energy range are displayed in addition to the spectra 

from Fig. 3.4 to show the applicability of the chosen group energy structures to the resonances and details 

of the calculated multigroup neutron spectra.

Figure 3.5. HTGR spectra in the 10 to 100 eV range for broad and fine group libraries.

1.0E-02

1.5E-02

2.0E-02

2.5E-02

3.0E-02

3.5E-02

4.0E-02

4.5E-02

5.0E-02

1.0E-05 1.0E-04

Normalized flux per lethargy

Neutron energy (MeV)

vhtr model: 999g, 1700K

vhtr model: 238g, 1700K

1.0E-02

1.5E-02

2.0E-02

2.5E-02

3.0E-02

3.5E-02

4.0E-02

4.5E-02

5.0E-02

1.0E-05 1.0E-04

Normalized flux per lethargy

Neutron energy (MeV)

vhtr model: 999g, 1700K

vhtr model: 238g, 1700K

vhtr model: 81B3, 1700K

vhtr model: 81A, 1700K
19

Recall that the energy structure in library 81A is a subset of the 999-group library energy structure, while 

the 81B3 energy structure is a subset of the 238-group SCALE fine-group library (which is also a subset 

of the 999-group library). As would be expected, the flux dips in the 81A spectrum agree more closely 

with the 999-group spectrum while the 81B3 spectrum is similar to the 238-group spectrum. The 

comparison in Figure 3.5 is illustrated in a different way in Figure 3.6 by using a fine-group histogram for 

the 999-group solution in the 10 to 100 eV range.

Figure 3.6. HTGR 238-group spectrum in the 10 to 100 eV region: broad-group comparisons.

In Figure 3.6 the 999-group fine-group spectrum plotted in histogram format shows the details also seen 

in the curves in Figs. 3.4 and 3.5. Although differences can be seen between the 81A and 81B3 spectra, 

the energy boundaries for both 81-group libraries are adequately positioned to address the major HTGRrelated resonances for prismatic and pebble bed fuels.

3.3 DESCRIPTION OF THE BROAD-GROUP LIBRARIES

3.3.1 Library 81A

Library 81A was developed by condensing the new 999-group library with the SCALE module MALOCS 

using a 999-group neutron flux solution as a weighting function. The neutron-energy structure for 81A 

was selected from the available 999 neutron energy group boundaries, with care taken to select 

boundaries that surround major resonances and neutron spectrum features for HTGRs. Table 3.1 

compares the energy group boundaries for the 999-group, the 238-group, and the various 81-group 

libraries.

1.0E-02

1.5E-02

2.0E-02

2.5E-02

3.0E-02

3.5E-02

4.0E-02

4.5E-02

5.0E-02

1.0E-05 1.0E-04

Normalized flux per lethargy

Neutron energy (MeV)

vhtr model: 81B3, 1700K

vhtr model: 81A, 1700K

vhtr model: 999g, 1700K
20

Table 3.1. Neutron energy group structure comparisons for 999-, 238-, and 81-group 

 

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

2.000E+07 1 1 1 1

1.964E+07 2

1.900E+07 3

1.845E+07 4

1.790E+07 5

1.733E+07 6 2

1.691E+07 7

1.649E+07 8

1.608E+07 9

1.568E+07 10 3

1.530E+07 11

1.492E+07 12

1.455E+07 13 4

1.419E+07 14

1.384E+07 15 5

1.350E+07 16

1.317E+07 17

1.284E+07 18 6

1.252E+07 19

1.221E+07 20

1.191E+07 21

1.162E+07 22

1.133E+07 23

1.105E+07 24

1.078E+07 25

1.051E+07 26

1.025E+07 27

1.000E+07 28 7

9.753E+06 29 2

9.512E+06 30

9.278E+06 31

9.048E+06 32

8.825E+06 33

8.607E+06 34

8.395E+06 35

8.187E+06 36 8 2

7.985E+06 37 3

7.788E+06 38

7.596E+06 39

7.408E+06 40

7.225E+06 41

7.047E+06 42

6.873E+06 43

6.703E+06 44

6.592E+06 45

6.434E+06 46 9 3

6.376E+06 47 4

6.219E+06 48
21

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

6.065E+06 49

5.916E+06 50

5.770E+06 51

5.627E+06 52

5.488E+06 53

5.353E+06 54

5.221E+06 55

5.092E+06 56

4.966E+06 57

4.882E+06 58

4.800E+06 59 10 4

4.724E+06 60

4.607E+06 61

4.493E+06 62

4.398E+06 63

4.304E+06 64 11

4.183E+06 65 5

4.066E+06 66

3.965E+06 67

3.867E+06 68

3.772E+06 69

3.679E+06 70

3.588E+06 71

3.499E+06 72

3.413E+06 73

3.329E+06 74

3.247E+06 75

3.166E+06 76

3.080E+06 77

3.000E+06 78 12 5

2.932E+06 79 6

2.865E+06 80

2.794E+06 81

2.725E+06 82

2.658E+06 83

2.592E+06 84

2.535E+06 85

2.479E+06 86 13 6

2.466E+06 87 7

2.385E+06 88

2.365E+06 89

2.354E+06 90 14 7

2.307E+06 91 8

2.231E+06 92

2.176E+06 93

2.123E+06 94

2.070E+06 95

2.019E+06 96

1.969E+06 97

1.921E+06 98

1.850E+06 99 15 8
22

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

1.827E+06 100

1.782E+06 101

1.738E+06 102

1.695E+06 103

1.653E+06 104

1.612E+06 105

1.572E+06 106

1.536E+06 107

1.500E+06 108 16

1.461E+06 109 9

1.423E+06 110

1.400E+06 111 17 9

1.356E+06 112 18

1.317E+06 113 19

1.287E+06 114

1.250E+06 115 20

1.225E+06 116

1.200E+06 117 21

1.165E+06 118

1.136E+06 119

1.108E+06 120 22

1.100E+06 121

1.070E+06 122

1.040E+06 123

1.010E+06 124 23

1.003E+06 125

9.800E+05 126

9.616E+05 127

9.400E+05 128

9.200E+05 129 24

9.072E+05 130 10

9.000E+05 131 25 10

8.874E+05 132

8.750E+05 133 26

8.611E+05 134 27

8.506E+05 135

8.403E+05 136

8.301E+05 137

8.200E+05 138 28

8.100E+05 139

8.002E+05 140

7.904E+05 141

7.808E+05 142

7.730E+05 143

7.653E+05 144

7.576E+05 145

7.500E+05 146 29

7.427E+05 147

7.335E+05 148

7.244E+05 149

7.154E+05 150
23

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

7.065E+05 151

6.926E+05 152

6.790E+05 153 30

6.700E+05 154 31

6.622E+05 155

6.545E+05 156

6.468E+05 157

6.393E+05 158

6.313E+05 159

6.235E+05 160

6.158E+05 161

6.081E+05 162

6.000E+05 163 32

5.891E+05 164

5.784E+05 165

5.730E+05 166 33

5.672E+05 167

5.614E+05 168

5.557E+05 169

5.500E+05 170 34

5.432E+05 171

5.365E+05 172

5.299E+05 173

5.234E+05 174

5.173E+05 175

5.113E+05 176

5.054E+05 177

4.995E+05 178 35

4.920E+05 179

4.845E+05 180

4.772E+05 181

4.700E+05 182 36

4.650E+05 183

4.601E+05 184

4.553E+05 185

4.505E+05 186

4.452E+05 187

4.400E+05 188 37

4.349E+05 189

4.299E+05 190

4.249E+05 191

4.200E+05 192 38

4.138E+05 193 11

4.076E+05 194

4.000E+05 195 39 11

3.938E+05 196

3.877E+05 197

3.829E+05 198

3.782E+05 199

3.735E+05 200

3.688E+05 201
24

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

3.643E+05 202

3.597E+05 203

3.553E+05 204

3.508E+05 205

3.465E+05 206

3.422E+05 207

3.379E+05 208

3.337E+05 209

3.300E+05 210 40

3.264E+05 211

3.228E+05 212

3.192E+05 213

3.157E+05 214

3.122E+05 215

3.088E+05 216

3.053E+05 217

3.020E+05 218

2.985E+05 219

2.972E+05 220

2.945E+05 221

2.909E+05 222

2.873E+05 223

2.837E+05 224

2.802E+05 225

2.767E+05 226

2.732E+05 227

2.700E+05 228 41

2.670E+05 229

2.641E+05 230

2.612E+05 231

2.584E+05 232

2.555E+05 233

2.527E+05 234

2.500E+05 235

2.472E+05 236

2.442E+05 237

2.411E+05 238

2.381E+05 239

2.352E+05 240

2.323E+05 241

2.294E+05 242

2.265E+05 243

2.237E+05 244

2.209E+05 245

2.182E+05 246

2.155E+05 247

2.128E+05 248

2.102E+05 249

2.076E+05 250

2.050E+05 251

2.024E+05 252
25

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

2.000E+05 253 42

1.962E+05 254

1.926E+05 255

1.902E+05 256

1.878E+05 257

1.855E+05 258

1.832E+05 259

1.809E+05 260

1.786E+05 261

1.764E+05 262

1.742E+05 263

1.721E+05 264

1.699E+05 265

1.678E+05 266

1.657E+05 267

1.637E+05 268

1.616E+05 269

1.596E+05 270

1.576E+05 271

1.557E+05 272

1.538E+05 273

1.519E+05 274

1.500E+05 275 43

1.481E+05 276

1.463E+05 277

1.445E+05 278

1.426E+05 279

1.409E+05 280

1.391E+05 281

1.374E+05 282

1.357E+05 283

1.340E+05 284

1.323E+05 285

1.307E+05 286

1.291E+05 287

1.283E+05 288 44

1.269E+05 289 12

1.255E+05 290

1.241E+05 291

1.228E+05 292

1.213E+05 293

1.197E+05 294

1.183E+05 295

1.168E+05 296

1.153E+05 297

1.139E+05 298

1.125E+05 299

1.111E+05 300

1.096E+05 301

1.082E+05 302

1.068E+05 303
26

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

1.054E+05 304

1.040E+05 305

1.027E+05 306

1.013E+05 307

1.000E+05 308 45 12

9.804E+04 309

9.652E+04 310

9.502E+04 311

9.355E+04 312

9.210E+04 313

9.067E+04 314

8.926E+04 315

8.788E+04 316

8.652E+04 317

8.500E+04 318 46

8.374E+04 319

8.250E+04 320

8.200E+04 321 47

8.074E+04 322

7.950E+04 323

7.835E+04 324

7.722E+04 325

7.610E+04 326

7.500E+04 327 48

7.399E+04 328

7.300E+04 329 49

7.200E+04 330

7.081E+04 331

6.965E+04 332

6.851E+04 333

6.738E+04 334

6.641E+04 335

6.545E+04 336

6.451E+04 337

6.358E+04 338

6.267E+04 339

6.177E+04 340

6.088E+04 341

6.000E+04 342 50

5.912E+04 343

5.826E+04 344

5.740E+04 345

5.656E+04 346

5.551E+04 347

5.448E+04 348

5.347E+04 349

5.248E+04 350

5.200E+04 351 51

5.099E+04 352

5.000E+04 353 52

4.905E+04 354
27

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

4.812E+04 355

4.721E+04 356

4.631E+04 357

4.565E+04 358

4.500E+04 359 53

4.446E+04 360

4.393E+04 361

4.340E+04 362

4.288E+04 363

4.237E+04 364

4.186E+04 365

4.136E+04 366

4.087E+04 367

4.042E+04 368

3.998E+04 369

3.955E+04 370

3.912E+04 371

3.869E+04 372

3.827E+04 373

3.786E+04 374

3.744E+04 375

3.704E+04 376

3.663E+04 377

3.624E+04 378

3.584E+04 379

3.545E+04 380

3.507E+04 381

3.468E+04 382

3.431E+04 383

3.367E+04 384

3.304E+04 385

3.243E+04 386

3.183E+04 387

3.136E+04 388

3.090E+04 389

3.045E+04 390

3.000E+04 391 54

2.962E+04 392 13

2.924E+04 393

2.887E+04 394

2.850E+04 395

2.812E+04 396

2.774E+04 397

2.737E+04 398

2.700E+04 399 14

2.653E+04 400

2.606E+04 401

2.580E+04 402

2.552E+04 403

2.520E+04 404

2.500E+04 405 55 13
28

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

2.479E+04 406 15

2.450E+04 407

2.418E+04 408

2.388E+04 409

2.358E+04 410

2.314E+04 411

2.271E+04 412

2.229E+04 413

2.188E+04 414

2.139E+04 415

2.092E+04 416

2.045E+04 417

2.000E+04 418

1.965E+04 419

1.931E+04 420

1.900E+04 421

1.870E+04 422

1.841E+04 423

1.812E+04 424

1.783E+04 425

1.755E+04 426

1.727E+04 427

1.700E+04 428 56 14

1.674E+04 429

1.649E+04 430

1.623E+04 431

1.599E+04 432

1.574E+04 433

1.550E+04 434

1.527E+04 435

1.503E+04 436

1.476E+04 437

1.450E+04 438 16

1.424E+04 439

1.398E+04 440

1.373E+04 441

1.348E+04 442

1.324E+04 443

1.300E+04 444 57 15

1.266E+04 445

1.234E+04 446

1.202E+04 447

1.171E+04 448

1.142E+04 449

1.114E+04 450

1.086E+04 451

1.060E+04 452

1.031E+04 453

1.003E+04 454

9.763E+03 455

9.500E+03 456 58 16
29

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

9.307E+03 457

9.119E+03 458

8.975E+03 459

8.834E+03 460

8.694E+03 461

8.557E+03 462

8.422E+03 463

8.289E+03 464

8.159E+03 465

8.030E+03 466 59

7.908E+03 467

7.787E+03 468

7.669E+03 469

7.552E+03 470

7.437E+03 471

7.323E+03 472

7.212E+03 473

7.102E+03 474

6.954E+03 475

6.809E+03 476

6.667E+03 477

6.528E+03 478

6.392E+03 479

6.258E+03 480

6.128E+03 481

6.000E+03 482 60

5.879E+03 483

5.761E+03 484

5.645E+03 485

5.531E+03 486

5.400E+03 487

5.250E+03 488

5.100E+03 489

4.960E+03 490

4.850E+03 491

4.740E+03 492

4.620E+03 493

4.500E+03 494

4.400E+03 495

4.307E+03 496

4.202E+03 497

4.099E+03 498

3.998E+03 499

3.900E+03 500 61

3.819E+03 501

3.740E+03 502 62

3.707E+03 503 17

3.616E+03 504

3.527E+03 505

3.440E+03 506

3.355E+03 507
30

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

3.272E+03 508

3.191E+03 509

3.112E+03 510

3.035E+03 511

3.000E+03 512 63 18 17

2.935E+03 513

2.871E+03 514

2.808E+03 515

2.747E+03 516

2.679E+03 517

2.613E+03 518

2.580E+03 519 64 18

2.532E+03 520 19

2.485E+03 521

2.435E+03 522

2.386E+03 523

2.337E+03 524

2.290E+03 525 65 19

2.249E+03 526 20

2.200E+03 527 66 20

2.158E+03 528 21

2.116E+03 529

2.075E+03 530

2.035E+03 531

2.004E+03 532

1.973E+03 533

1.943E+03 534

1.914E+03 535

1.885E+03 536

1.856E+03 537

1.828E+03 538

1.800E+03 539 67 21

1.772E+03 540

1.744E+03 541

1.716E+03 542

1.689E+03 543

1.662E+03 544

1.636E+03 545

1.610E+03 546

1.585E+03 547

1.550E+03 548 68

1.525E+03 549

1.500E+03 550 69

1.482E+03 551

1.464E+03 552

1.446E+03 553

1.429E+03 554

1.411E+03 555

1.394E+03 556

1.377E+03 557

1.361E+03 558
31

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

1.344E+03 559

1.328E+03 560 22

1.312E+03 561

1.296E+03 562

1.280E+03 563

1.265E+03 564

1.249E+03 565

1.234E+03 566

1.213E+03 567

1.191E+03 568

1.171E+03 569

1.150E+03 570 70

1.137E+03 571

1.125E+03 572

1.112E+03 573

1.100E+03 574

1.087E+03 575

1.075E+03 576

1.063E+03 577

1.051E+03 578

1.040E+03 579

1.028E+03 580

1.017E+03 581

1.005E+03 582

9.940E+02 583

9.829E+02 584

9.720E+02 585

9.611E+02 586

9.555E+02 587

9.500E+02 588 71 22

9.360E+02 589

9.221E+02 590

9.085E+02 591

8.950E+02 592

8.818E+02 593

8.688E+02 594

8.559E+02 595

8.433E+02 596

8.308E+02 597

8.185E+02 598

8.064E+02 599

7.945E+02 600

7.827E+02 601

7.712E+02 602

7.598E+02 603

7.485E+02 604

7.400E+02 605

7.316E+02 606

7.232E+02 607

7.150E+02 608

7.069E+02 609
32

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

6.988E+02 610

6.909E+02 611

6.830E+02 612 72

6.765E+02 613

6.700E+02 614 73

6.585E+02 615 23

6.471E+02 616

6.359E+02 617

6.250E+02 618

6.142E+02 619

6.036E+02 620

5.932E+02 621

5.830E+02 622

5.745E+02 623

5.662E+02 624

5.581E+02 625

5.500E+02 626 74 23

5.435E+02 627

5.370E+02 628

5.306E+02 629

5.243E+02 630

5.180E+02 631

5.118E+02 632

5.057E+02 633

4.997E+02 634

4.937E+02 635

4.879E+02 636

4.821E+02 637

4.763E+02 638

4.706E+02 639

4.650E+02 640

4.595E+02 641

4.540E+02 642

4.470E+02 643

4.400E+02 644

4.332E+02 645

4.265E+02 646

4.199E+02 647

4.134E+02 648

4.070E+02 649

4.007E+02 650

3.944E+02 651

3.883E+02 652

3.823E+02 653

3.764E+02 654

3.705E+02 655

3.648E+02 656

3.591E+02 657

3.536E+02 658

3.471E+02 659

3.408E+02 660
33

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

3.345E+02 661

3.284E+02 662

3.224E+02 663

3.165E+02 664

3.107E+02 665

3.050E+02 666 75

2.999E+02 667

2.948E+02 668

2.899E+02 669

2.850E+02 670 76

2.801E+02 671 24

2.754E+02 672

2.707E+02 673

2.661E+02 674

2.615E+02 675

2.571E+02 676

2.527E+02 677

2.484E+02 678

2.442E+02 679

2.400E+02 680 77 24

2.367E+02 681 25

2.333E+02 682

2.301E+02 683

2.269E+02 684

2.237E+02 685

2.206E+02 686

2.175E+02 687

2.145E+02 688

2.122E+02 689

2.100E+02 690 78 25

2.088E+02 691 26

2.075E+02 692 79 26

2.036E+02 693 27

1.999E+02 694

1.962E+02 695 28

1.925E+02 696 80 27

1.892E+02 697

1.860E+02 698 81 28

1.835E+02 699

1.811E+02 700

1.786E+02 701

1.763E+02 702

1.739E+02 703

1.716E+02 704

1.693E+02 705

1.670E+02 706

1.650E+02 707

1.625E+02 708

1.600E+02 709

1.575E+02 710

1.550E+02 711
34

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

1.525E+02 712

1.500E+02 713

1.475E+02 714

1.450E+02 715

1.425E+02 716

1.400E+02 717

1.375E+02 718

1.350E+02 719

1.325E+02 720

1.301E+02 721

1.280E+02 722

1.260E+02 723

1.240E+02 724

1.220E+02 725 82

1.205E+02 726 29

1.190E+02 727 83 29

1.170E+02 728 30

1.150E+02 729 84 30

1.130E+02 730

1.105E+02 731

1.080E+02 732 85

1.063E+02 733 31

1.038E+02 734

1.013E+02 735

1.000E+02 736 86 31

9.750E+01 737

9.500E+01 738

9.250E+01 739

9.000E+01 740 87

8.800E+01 741 32

8.600E+01 742

8.400E+01 743

8.200E+01 744 88 32

8.100E+01 745 33

8.000E+01 746 89 33

7.945E+01 747

7.889E+01 748

7.745E+01 749

7.600E+01 750 90

7.400E+01 751

7.200E+01 752 91

6.975E+01 753 34

6.750E+01 754 92 34

6.625E+01 755 35

6.500E+01 756 93 36 35

6.322E+01 757

6.144E+01 758 37

6.122E+01 759

6.100E+01 760 94 36

6.000E+01 761

5.900E+01 762 95 37
35

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

5.620E+01 763

5.340E+01 764 96

5.270E+01 765

5.200E+01 766 97

5.130E+01 767

5.060E+01 768 98

4.990E+01 769

4.920E+01 770 99

4.875E+01 771

4.830E+01 772 100

4.808E+01 773

4.785E+01 774

4.743E+01 775

4.700E+01 776 101

4.610E+01 777

4.520E+01 778 102

4.460E+01 779

4.400E+01 780 103

4.320E+01 781

4.240E+01 782 104

4.170E+01 783 38

4.100E+01 784 105 38

4.030E+01 785 39

3.960E+01 786 106 39

3.935E+01 787 40

3.910E+01 788 107 40

3.855E+01 789 41

3.800E+01 790 108 41

3.763E+01 791 42

3.727E+01 792

3.713E+01 793

3.700E+01 794 109 42

3.625E+01 795 43

3.550E+01 796 110 43

3.505E+01 797

3.460E+01 798 111

3.418E+01 799

3.375E+01 800 112

3.350E+01 801

3.325E+01 802 113

3.250E+01 803

3.175E+01 804 114 44

3.150E+01 805

3.125E+01 806 115

3.063E+01 807 44

3.000E+01 808 116

2.951E+01 809

2.902E+01 810

2.826E+01 811

2.750E+01 812 117

2.625E+01 813
36

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

2.500E+01 814 118

2.375E+01 815

2.250E+01 816 119

2.175E+01 817 45

2.100E+01 818 120 45

2.050E+01 819 46

2.000E+01 820 121 46

1.950E+01 821 47

1.900E+01 822 122

1.875E+01 823

1.850E+01 824 123 47

1.805E+01 825

1.760E+01 826

1.730E+01 827

1.700E+01 828 124

1.650E+01 829

1.600E+01 830 125

1.555E+01 831

1.510E+01 832 126

1.475E+01 833

1.440E+01 834 127

1.408E+01 835

1.375E+01 836 128

1.333E+01 837 48

1.290E+01 838 129 48

1.240E+01 839

1.190E+01 840 130

1.170E+01 841

1.150E+01 842 131

1.109E+01 843 49

1.068E+01 844

1.034E+01 845

1.000E+01 846 132 49

9.550E+00 847

9.100E+00 848 133

8.708E+00 849

8.315E+00 850

8.208E+00 851

8.100E+00 852 134

7.625E+00 853

7.150E+00 854 135

7.075E+00 855 50

7.000E+00 856 136 50

6.875E+00 857 51

6.750E+00 858 137 51

6.625E+00 859 52

6.500E+00 860 138 52

6.375E+00 861 53

6.250E+00 862 139 53

6.000E+00 863 140

5.850E+00 864
37

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

5.700E+00 865

5.550E+00 866

5.400E+00 867 141

5.250E+00 868

5.044E+00 869

5.000E+00 870 142 54

4.875E+00 871 54

4.750E+00 872 143

4.500E+00 873

4.300E+00 874

4.150E+00 875

4.000E+00 876 144

3.928E+00 877

3.830E+00 878

3.730E+00 879 145

3.620E+00 880

3.500E+00 881 146

3.300E+00 882

3.150E+00 883 147

3.050E+00 884 148 55

3.000E+00 885 149 55

2.970E+00 886 150 56 56

2.920E+00 887 57

2.870E+00 888 151 57

2.820E+00 889

2.770E+00 890 152

2.720E+00 891

2.670E+00 892 153

2.620E+00 893

2.570E+00 894 154

2.520E+00 895

2.470E+00 896 155

2.425E+00 897

2.380E+00 898 156

2.340E+00 899

2.300E+00 900 157

2.255E+00 901 58

2.210E+00 902 158 58

2.165E+00 903

2.120E+00 904 159

2.060E+00 905

2.000E+00 906 160

1.970E+00 907

1.940E+00 908 161

1.900E+00 909

1.860E+00 910 162

1.815E+00 911

1.770E+00 912 163

1.725E+00 913

1.680E+00 914 164

1.635E+00 915
38

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

1.590E+00 916 165

1.545E+00 917 59

1.500E+00 918 166 59

1.450E+00 919 167

1.400E+00 920 168

1.350E+00 921 169

1.300E+00 922 170

1.250E+00 923 171

1.225E+00 924 172

1.200E+00 925 173 60

1.175E+00 926 174 60

1.150E+00 927 175

1.140E+00 928 176

1.130E+00 929 177

1.120E+00 930 178 61

1.110E+00 931 179 61

1.100E+00 932 180

1.090E+00 933 181

1.080E+00 934 182

1.070E+00 935 183

1.060E+00 936 184

1.050E+00 937 185

1.040E+00 938 186

1.030E+00 939 187

1.020E+00 940 188

1.010E+00 941 189

1.000E+00 942 190

9.750E-01 943 191 62 62

9.500E-01 944 192

9.250E-01 945 193

9.000E-01 946 194

8.764E-01 947

8.500E-01 948 195

8.000E-01 949 196

7.500E-01 950 197

7.000E-01 951 198

6.826E-01 952

6.500E-01 953 199

6.250E-01 954 200 63 63

6.000E-01 955 201

5.500E-01 956 202

5.316E-01 957

5.000E-01 958 203

4.500E-01 959 204

4.140E-01 960 64

4.000E-01 961 205 64

3.750E-01 962 206 65 65

3.668E-01 963 66

3.500E-01 964 207 66

3.250E-01 965 208 67 67

3.000E-01 966 209
39

Upper neutron 

energy (eV)

999-group 

structure

SCALE

238-group 

structure

81A groups

81B3,C groups

2.750E-01 967 210 68 68

2.500E-01 968 211 69 69

2.250E-01 969 212 70 70

2.000E-01 970 213 71 71

1.840E-01 971

1.750E-01 972 214

1.500E-01 973 215 72 72

1.250E-01 974 216

1.000E-01 975 217 73 73

9.000E-02 976 218

8.000E-02 977 219

7.000E-02 978 220 74 74

6.000E-02 979 221

5.000E-02 980 222 75 75

4.000E-02 981 223 76 76

3.000E-02 982 224 77 77

2.530E-02 983 225 78 78

2.100E-02 984 79

1.850E-02 985

1.450E-02 986

1.000E-02 987 226 79

7.500E-03 988 227 80 80

5.000E-03 989 228

4.000E-03 990 229

3.000E-03 991 230 81 81

2.500E-03 992 231

2.000E-03 993 232

1.500E-03 994 233

1.200E-03 995 234

1.000E-03 996 235

7.500E-04 997 236

5.000E-04 998 237

1.000E-04 999 238

3.3.2 Library 81B

Because the energy boundaries chosen for 81A did not always coincide with the energy boundaries used 

in SCALE’s 238-group libraries, it was decided to make minor adjustments to the 81A-group structure so 

that it would align with the 238-group neutron energy group definitions. This alignment allows for easier 

comparisons between the broad-group and fine-group libraries. The 81B broad-group library (Table 3.1) 

was generated from the SCALE 238-group V7-238 library using a weighting function based on an HTGR 

238-group neutron flux solution. The HTGR model used to calculate the neutron flux solution weighting 

function is listed in Appendix B. The 81B energy boundaries were selected to minimize differences with 

the 81A library energy boundaries. 
40

3.3.3 Library 81B2

The broad-group library 81B2 used the same neutron energy group structure that was used in the 

generation of library 81B, but the library was generated using SCALE/MALOCS by condensing from the 

999-group fine-group library using an appropriate 999-group HTGR neutron flux solution as the 

weighting function. This library should better represent the HTGR solution as it is based on the much 

finer detail of the SCALE 999-group master library and the ultra fine neutron flux solution in 999 groups.

3.3.4 Library 81B3

Broad-group library 81B3 was generated directly from ENDF/B-VII nuclear data files using an HTGR 

weighting function (flux solution) calculated with the CENTRM module in SCALE. The SCALE input 

case used to calculate the CENTRM flux weighting function is listed in Appendix C. The same neutron 

energy boundary structure was used with library 81B3 as with libraries 81B and 81B2.

Section 2.4 discusses the methodology employed in generating broad-group libraries directly from 

ENDF/B-VII nuclear data files. The SCALE input file listed in Appendix C was used to calculate the 

1800K HTGR weighting function based on the CENTRM pointwise flux. This weighting approach is 

different from the method used in the generation of the generic 999-group fine-group library from the 

ENDF/B-VII files. The 999-group library was generated using the same weighting spectrum as all 

previous multigroup SCALE libraries, consisting of 

1. Maxwellian spectrum (peak at 300 K) from 10−5 to 0.125 eV, 

2. a 1/E spectrum from 0.125 eV to 67.4 keV,

3. a fission spectrum (effective temperature at 1.273 MeV) from 67.4 keV to 10 MeV, and 

4. a 1/E spectrum from 10 to 20 MeV.

The use of a weighting function that is based on the CENTRM pointwise flux from a representative 

HTGR model simulation is a new technique developed at ORNL during this work. The temperature 

(1800K) considered in the calculation of the pointwise weighting function was considered appropriate for 

the high-temperature operation of an HTGR. This corresponds to a representative temperature of 1527°C, 

or 2780°F.

The initial version of this library (81B3i) created from the ENDF/B-VII data was then processed and 

enhanced with new IR f-factors and lambda factors for 238U. The IR factors can be used with the new 

BONAMI-IR module to produce results that are generally equivalent to results with CENTRM/PMC, thus 

removing the need to run CENTRM/PMC for each unit cell. Thus, the IR capability can result in 

significant speedups in computer runtime compared with the traditional resonance self-shielding methods 

in SCALE.

3.3.5 Library 81C

The final broad-group nuclear data library, 81C, is based on the testing and improvements to library 

81B3. This library is the ultimate result and includes new f-factors for 238U and other actinides (App. F) 

and lambda factors for all nuclides. The neutron energy group boundaries are the same as the broad-group 

library 81B3. Broad-group library 81C, in addition to having all the necessary IR treatment factors 

implemented, also uses the new nuclide identification naming convention that has been developed to 

remove the maximum mixture number limit of 2147 in SCALE.
41

4. COMPARISON OF RESULTS WITH THE SCALE BROAD-GROUP 

LIBRARIES

Tables 4.1–4.3 summarize simplified model results with SCALE using various fine- and broad-group 

nuclear data libraries. The final 81C library is intended for use in production runs with SCALE. This

broad-group library can model HTGR scenarios adequately, with similar accuracy to fine-group library 

runs but with considerably less computational time for resonance self-shielding of the cross sections. In 

the results presented in this section, BONAMI-IR and the 81C library ran 35 to 100 times faster than 

CENTRM/PMC with the same library.

Table 4.1 shows the results for a series of KENO MG cases for a homogenous HTGR pin cell model that 

is representative of a prismatic NGNP design. These results are compared with the 999 group library

eigenvalue solution. The results obtained with the various 81-group libraries compare quite favorably

with respect to the 238-group KENO result. The cases in Table 4.1 all use CENTRM cross-section 

processing with white boundary conditions at a temperature of 300K.

Table 4.1. keff

Libraries 

comparisons for MG KENO homogeneous cell HTGR model

k Δk relative to 999-group

result (pcm) eff

81A 1.25766 ± 0.00039 -300 ± 81

81B 1.25746 ± 0.00040 -320 ± 83

81C 1.25586 ± 0.00040 -480 ± 82

238 1.25769 ±0.00041 -376 ± 88

999 1.26066 ± 0.00042 N/A

Table 4.2 shows results of a very simple XSDRN 1-D homogeneous HTGR core model at 300K and 

1200K. Results using BONAMI-IR and the 81C Library are compared with cases using CENTRM with 

the 81C, 238-group, and 999-group libraries. Note that the CENTRM cases use a triangular pitch lattice 

cell that produces homogenized number densities for the 1-D XSDRN model. This simple model is not 

as precise as the benchmark cases that follow.

Table 4.2. keff

k

comparisons for homogeneous 1-D radial model

eff T(K) CENTRM Δkeff (pcm) BONAMI-IR a Δkeff (pcm)

81C

a

300 1.25214 -378 1.24397 -1195

238 300 1.25434 -158 N/A N/A

999 300 1.25592 − N/A N/A

81C 1200 1.11115 -364 1.10665 -814

238 1200 1.11279 -200 N/A N/A

999 1200 1.11479 − N/A N/A

 a

 

Difference from CENTRM case with 999 groups at same temperature.
42

The High Temperature Engineering Test Reactor (HTTR) [12,13], which is the first HTGR in Japan, is a 

prismatic fuel graphite-moderated and helium-cooled reactor with a thermal output of 30 MW and a 

maximum outlet gas temperature of 950 °C and has the capability to demonstrate nuclear process heat 

utilization using an intermediate heat exchanger. The construction of the HTTR was decided by Japanese 

Atomic Energy Commission (JAEC) in 1987 and started in March 1991 by the Japan Atomic Energy 

Research Institute (JAERI) to establish and upgrade the technology basis for an HTGR. The HTTR was 

intended to serve as a potential tool for new and innovative basic research on high temperature 

technologies.

Calculations were performed in this work with two of the HTTR benchmark cases (case 1 and case 2) 

from the SCALE HTGR validation report [14]. The case 2 input file is listed in Appendix D, and both a 

cross-sectional and a vertical view of this HTTR model are shown in Appendix E. The calculated keff 

results,and the relative Δk values with respect to the CE KENO results are tabulated in Table 4.3 and 4.4. 

The results obtained with the 81C library and BONAMI-IR show good agreement with both the 238-

group library and the CE results.

Table 4.3. keff

Library

results for HTTR benchmark case 1

Cross-section 

processor

k Δk eff eff

81C

(pcm) 

relative to CE

BONAMI-IR 1.21629 ± 0.00024 -305 ± 49

81C CENTRM 1.21661 ± 0.00022 -273 ±47

238 CENTRM 1.21887 ± 0.00025 -47 ± 50

999 CENTRM 1.21807 ± 0.00023 -127 ± 48

CE N/A 1.21934 ± 0.00025 −

Table 4.4. keff results for HTTR benchmark case 2

Library Cross-section processor keff Δkeff

81C

(pcm) relative to CE

BONAMI-IR 1.20799 ± 0.00027 -374 ± 52

81C CENTRM 1.20659 ± 0.00029 -514 ± 54

238 CENTRM 1.20930 ± 0.00023 -243 ± 48

CE N/A 1.21173 ± 0.00025 −

The performance of the 81C library for analyses of pebble bed reactor (PBR) configurations was assessed 

using two test cases: (1) a pebble unit cell with fuel representative of the HTR-10 reactor at full power 

and (2) the first critical core of HTR-10. The models that were used for testing are described in detail 

elsewhere [14]. The model for the pebble unit cell is a 1-D SCALE/XSDRN model. The model for the 

first critical core of HTR-10 is a full 3-D SCALE/KENO-VI model that has been developed using 

benchmark specifications included in the IRPhE Handbook [15]. The double heterogeneity of fuel is 

modeled in SCALE using the DOUBLEHET option for multigroup cross-section processing.

The results obtained with SCALE for the pebble unit cell at operating temperature (1200K for fuel and 

900K for coolant) are presented in Table 4.5, as obtained using the 81C HTGR library and the standard 

238-group ENDF/B-VII transport library in SCALE. The 81C library was used with both CENTRM and 

the new BONAMI-IR for cross section self-shielding. Also shown in Table 4.5 is the result obtained with 

MCNP5 continuous energy ENDF/B-VII data for the same configuration. The MCNP5 model explicitly 
43

represents the fuel particles inside the fuel pebbles using a lattice representation that ensures the fuel 

particles do not intersect the interface of the graphite matrix with the pebble shell [14]. The result 

obtained with the 81-group library and BONAMI-IR is within 146 pcm of the SCALE result for the 238-

group library and within 271 pcm of the MCNP result.

Table 4.5. keff

Code

results for HTR-10 pebble unit cell (1200K fuel, 900K coolant)

Library Cross-section processor keff ∆keff (pcm) ∆k d eff (pcm)e

MCNP CEa ENDF/B-VII NA

1.60822

b (σ=0.00021)

c − -125

SCALE 238-group ENDF/B-VII

81C

81C

CENTRM

CENTRM

BONAMI-IR

1.60936

1.60783

1.61082

125

-28

-271

−

-153

146

a CE = continuous energy.

b NA = not applicable.

c Standard deviation from the Monte Carlo transport calculation. d Difference in keff is calculated using the MCNP result as reference; 1 pcm=10-5

. e Difference in keff is calculated using the SCALE 238-group ENDF/B-VII with CENTRM result as reference.

To assess the effect of the temperature on library performance, the same pebble unit cell was calculated 

with 300K temperature in both fuel and coolant. The corresponding results are presented in Table 4.6. If 

the SCALE result for the 238-group library is used as the reference for comparison, the result obtained 

with the 81-group library is within 148 pcm when using CENTRM and within 338 pcm when using 

BONAMI-IR. 

Table 4 6. keff results for HTR-10 pebble unit (300K)

Code Library

Cross-section 

Processor keff Δkeff (pcm)d Δkeff (pcm)e

MCNP CEa ENDF/B-VII NA

1.69040

b (σ=0.00014)c − 110

SCALE 238-group ENDF/B-VII

81C

81C

CENTRM

CENTRM

BONAMI-IR

1.68930

1.68782

1.68592

-110

-258

-448

−

-148

-338 a CE = continuous energy.

b NA = not applicable.

c Standard deviation from the Monte Carlo transport calculation. d Difference in keff is calculated using the MCNP result as reference; 1 pcm=10-5

. e Difference in keff is calculated using the SCALE 238-group ENDF/B-VII with CENTRM result as reference.

The results obtained for the HTR-10 first core (full core 3-D model) are shown in Table 4.7. There is an 

excellent agreement between MCNP and SCALE when using the 238-group ENDF/B-VII library. The 

result obtained with the 81-group library and BONAMI-IR is within 357 pcm of the 238-group library 

result with CENTRM. This difference is consistent with the difference seen in Table 4.6 for the pebble 

unit cell at the same temperature (300 K).
44

Table 4.7. keff

Code 

results for HTR-10 full core

Library Cross-section processor keff Δkeff (pcm) Δk d eff (pcm)c

MCNP CEa ENDF/B-VII NA

1.01473

b (σ=0.00021)c − 54 ± 85

SCALE 238-group ENDF/B-VII

81C

CENTRM

BONAMI-IR

1.01419

(σ=0.00082)

1.01062

(σ=0.00087)

-54 ± 85

-411 ± 89

−

-357 ± 120

a CE = continuous energy.

b NA = not applicable.

c Standard deviation from the Monte Carlo transport calculation. d Difference in keff is calculated using the MCNP result as reference; 1 pcm=10-5

. e Difference in keff is calculated using the SCALE 238-group ENDF/B-VII with CENTRM result as reference.

The calculated results with BONAMI-IR and the 81C library for the HTTR and HTR-10 reactor 

benchmarks demonstrate the capability to produce accurate results for actual operating HTGRs, both with 

prismatic and pebble bed fuels. These results show good agreement with CE and 238-group calculations. 

Although further verification and validation of BONAMI-IR and the 81C library are desirable, these 

results presented here provide confidence that this library can be useful for HTGR analyses.
45

5. SUMMARY AND RECOMMENDATIONS

The final 81-group library allows for the modeling of HTGR cases with SCALE with sufficient accuracy

and faster CPU times than the V7-238 library. Further processing to include intermediate resonance 

features provides an additional improvement by reducing computational times for resonance selfshielding (up to 100 times faster) without loss of accuracy.

We observed that

1. HTGR broad-group libraries need more groups than LWR broad-group libraries.

2. In HTGRs, the average neutron flux distribution in the vicinity of fuel is more important for 

neutronics and self-shielding considerations than the flux within the fuel.

3. Fine-group libraries with many groups (such as the new 999-group library) properly show details of 

the increase in flux at the lower end of resonances, due to the self-shielding of the resonance and the 

reduction in cross section at the lower energy.

4. The use of flux values from the average flux distribution of an HTGR model is an appropriate 

weighting function for use in the generation of broad-group libraries.

The effectiveness and correctness of a broad-group nuclear data library is quite sensitive to the neutron 

energy boundary structure and to the weighting function (usually a fine-group neutron flux solution) that 

is used in generating the library from ENDF/B files or through condensation from a fine-group master 

library.

Based on the results presented in this report, the choice of the broad-group energy boundaries for 81C

library allows SCALE to model HTGR cases with reasonable accuracy and significantly faster CPU times 

than fine-group or CE calculations. The new 81C library includes new lambda factors for all nuclides and 

f-factors for 238U and other actinides. It also contains high-temperature data consistent with HTGR 

operation and modeling. The 81C library requires the BONAMI-IR module in SCALE to fully utilize data

in the library. When the IR data are processed with BONAMI-IR, accurate results can be obtained with 

significantly reduced computational runtimes.

47

6. REFERENCES

1. SCALE: A Comprehensive Modeling and Simulation Suite for Nuclear Safety Analysis and Design, 

ORNL/TM-2005/39, Version 6.1, Oak Ridge National Laboratory, Oak Ridge, Tennessee, June 

2011. Available from Radiation Safety Information Computational Center at Oak Ridge National 

Laboratory as CCC-785.

2. S. M. Bowman, “SCALE 6: Comprehensive Nuclear Safety Analysis Code System,” Nucl. Technol. 

174(2), 126-148 (May 2011).

3. N. M. Greene, J. L. Lucius, L. M. Petrie, W. E. Ford, III, J. E. White, and R. Q. Wright, AMPX—A 

Modular Code System to Generate Multigroup Neutron‐Gamma Cross Sections from ENDF/B,

ORNL/TM‐3706 (AMPX‐1), Union Carbide Corporation (Nuclear Division), Oak Ridge National 

Laboratory, 1976.

4. M. E. Dunn, N. M. Greene, “AMPX-2000: A Cross-Section Processing System for Generating 

Nuclear Data for Criticality Safety Applications,” Trans. Am. Nucl. Soc. 86, 118 (2002).

5. MCNP—A General Monte Carlo N-Particle Transport Code, Version 5, LA-CP-03-0245, 

Los Alamos National Laboratory, April 2003.

6. D. Wiarda et al, “AMPX Cross-Section Processing Status”, Presentations at the 2009 and the 2010 

Cross Section Evaluation Working Group (CSEWG) and U.S. Nuclear Data Program (USNDP) 

Annual Meetings, National Nuclear Data Center, Brookhaven National Laboratory.

7. M.L. Williams, Kang-Seog Kim, and D. F. Hollenbach, Generation of Multigroup Cross Sections for 

the Very High Temperature Reactor, Final Report – Department of Energy Generation IV Nuclear 

Energy Systems Initiative Program, VHTR Advanced Modeling and Simulation Project, Oak Ridge 

National Laboratory, September 25, 2009.

8. Kang-Seog Kim, M. L. Williams, D. F. Hollenbach, “RIML: A Program to Generate Intermediate 

Resonance Parameters, Self-Shielded Cross Sections, Subgroup Levels and Weights, and Associated 

AMPX Master Library,” Oak Ridge National Laboratory, October 2, 2009

9. “The Numerical Nuclear Reactor for High Fidelity Integrated Simulation of Neutronic, ThermalHydraulic and Thermo-Mechanical Phenomena,” Final Report of US/ROK International Nuclear 

Energy Research Initiative Project Number 2002-010-K, Argonne National Laboratory, Korea 

Atomic Energy Research Institute, Purdue University, and Seoul National University, March 2005.

10. R. Goldstein and E. R. Cohen, “Theory of Resonance Absorption of Neutrons,” Nucl. Sci. Eng. 13,

132 (1962).

11. National Nuclear Data Center (NNDC) at Brookhaven National Laboratory (BNL), website 

http://www.nndc.bnl.gov

12. IAEA, Evaluation of High Temperature Gas Cooled Reactor Performance: Benchmark Analysis 

Related to Initial Testing of the HTTR and HTR-10, IAEA-TECDOC-1382, International Atomic 

Energy Agency, Vienna, November 2003.
48

13. International Handbook of Evaluated Reactor Physics Benchmark Experiments, NEA-1765, 

IRPHE2009-HANDBOOK; HTTR-GCR-RESR-001, CRIT-SUB-REAC-COEF-KIN-RRATE (new), 

“Evaluation of the Start-Up Core Physics Tests at Japan's High Temperature Engineering Test 

Reactor (Fully-Loaded Core),” March 21, 2009.

14. G. Ilas, D. Ilas, R.P. Kelly, and E.E. Sunny, Validation of SCALE for High Temperature Gas-Cooled 

Reactor Analysis, ORNL/TM-2011/161 (2011).

15. W. K. Terry, L. M. Montierth, S. S. Kim, J. J. Cogliati, and A. M. Ougouag, “Evaluation of the Initial 

Critical Configuration of the HTR-10 Pebble-Bed Reactor,” International Handbook of Evaluated 

Reactor Physics Benchmark Experiments (IRPhE) Handbook, Nuclear Energy Agency (March 2009).
A-1

APPENDIX A

DESCRIPTION OF INTERMEDIATE RESONANCE METHOD IN SCALE

A-3

A.1 INTERMEDIATE RESONANCE APPROXIMATION

The intermediate resonance (IR) approximation was proposed in the 1960s as an extension to the narrow 

resonance (NR) and wide resonance (WR) approximations, which are used in solving the slowing-down 

equation to obtain an analytical flux expression for computing multigroup (MG) cross sections. The NR 

approximation is used to represent elastic scattering sources of nuclides for which the neutron energy loss 

is large compared to the practical width of resonances for the absorber materials of interest. This 

approximation tends to be more accurate for light nuclides (e.g., moderators) and for higher energy 

ranges. Conversely, the WR approximation is used to represent elastic scattering sources of nuclides for 

which the neutron energy loss is small compared to the practical widths. This approximation tends to be 

more accurate for heavy nuclides (e.g., the limit of infinite mass is usually assumed) and for lower energy 

ranges. Since most resonance absorption in LEU thermal reactors occurs in 238U, this material is usually 

used as the basis to determine if a nuclide is a NR or a WR scatterer.

Many materials cannot be treated accurately by either the NR or WR methods. The IR method provides a 

more generalized approach in which the scattering source is represented by a linear combination of NR 

and WR expressions; i.e., for scatterers with slowing-down properties intermediate between NR and WR 

scatterers. This is done by introducing an IR parameter usually called lambda factors, for which NR 

scatters have λ=1, WR scatters have λ=0, and fractional λ’s are for intermediate scatterers. Codes have 

been developed by ORNL to determine group-dependent lambda values for all materials, using the 

procedure described in Section A.2. Lambda values are included in the HTR 81-group library.

Applying the IR approximation and neglecting resonance overlap effects in the slowing-down equation, 

the following analytical expression is obtained for the flux spectrum near a resonance of nuclide “r”:

(r)

IR

(r) (r)

(r) p 0

0 (r) (r)

t 0

(E; )

1

(E) E

σ +σ

σ

σ +σ

Φ =

   

 

where (r) (r) (r) σ (E), σ , σ t p0 are the total, potential, and background cross sections for resonance material “r”.

The background cross section in Eq. 1 depends on the lambda factors and is equal to

(r) (j) (j)

0 p (r)

1

σ

N j r

λ

≠

= Σ ∑

Equation 2 is appropriate for a homogeneous medium, but a similar expression also can be used for 

heterogeneous lattices by including an additional constant called the escape cross section. Eq. 1 shows 

that the IR method allows the flux energy spectrum to be parameterized in terms of the single variable (r)

0 σ

, which indicates the degree of resonance self-shielding. The value of (r)

0 σ can vary by multigroup, but it is 

not a function of energy within a group.

Energy-dependent spectra for weighting MG cross sections of an arbitrary resonance material “r” are 

obtained by solving the slowing-down equation with the pointwise code CENTRM for a homogeneous 

mixture composed of “r” plus hydrogen. The hydrogen concentration is varied to produce the desired 

background cross sections in a predetermined set that spans the expected range of self-shielding for the 

resonance material, so that a set of MG data are computed at varying degrees of self-shielding. These are 
A-4

converted into group-dependent self-shielding factors parameterized versus (r)

0 σ , which are stored on the 

AMPX master library.

During a reactor physics calculation with TRITON, for example, the background for the system of

interest is computed using eq. 2 with problem-specific materials and concentrations, and the 

corresponding shielding factor is found by interpolating from the set of background cross sections on the 

library. This is done by the SCALE code BONAMI, which has been modified to use the IR expression for 

the background cross section. The self-shielded cross section for the particular system is equal to the 

product of the interpolated shielding factor and the unshielded (i.e., infinitely dilute) cross section, which 

is also stored in the master library. The BONAMI IR procedure for computing self-shielded cross sections 

is very fast since only data interpolation is required. 

A.2 COMPUTATION OF HYDROGEN-EQUIVALENT LAMBDA FACTORS

An important component of the IR method is to have reasonable values for the IR lambda values. ORNL 

computes these values using the “hydrogen equivalence” approach based on 238U resonances. In this wellestablished method, it is assumed that hydrogen is a true NR material (λ=1) since a neutron can lose 

essentially all of its energy in single elastic collision. A table of self-shielded cross sections versus 

background cross sections is generated for mixtures of 238U and hydrogen with varying concentrations, 

using CENTRM calculations as described in the previous section. To obtain lambdas for nuclides other 

than hydrogen, a portion of the hydrogen number density in the mixture is replaced by another nuclide 

“j”. If a one-to-one exchange of hydrogen atoms with atoms of “j” is done (i.e., number of hydrogen 

atoms removed equals the number of j added), the shielded cross section for the mixture will be different 

than the corresponding mixture containing only hydrogen, since the slowing-down properties of j are 

different. However instead of one-to-one replacement, the number of j atoms is modified to obtain the 

same shielded cross section as obtained with hydrogen. This is called the hydrogen equivalent number 

density of j, and from this value the corresponding lambda value for nuclide j can be found. The 

procedure is repeated for each multigroup to obtain group-dependent lambdas. The lambda factors are not 

very sensitive to temperature and thus have been generated only for the nominal fuel temperature of 

1500 K in the HTR 81-group library.
B-1

APPENDIX B

INPUT FILE FOR RADIAL CORE MODEL 999-GROUP (VHTR) MODEL

B-3

Presented here is an input file for the radial_core_model-999grps (VHTR) model.

=shell

cp ~xxx/SCALE6/HTR_multigroup_proj/older_csas_decks/v7_999 v7_999

end

=csas1x parm=centrm 

homog (no double het) fuel unit cell for ngnp prismatic lattice

v7_999

read comp

'

'

' This case does not collapse to 23-Groups

'

'

'

'

' homgenized channel 

u-238 1 0 7.99688E-4 300.0 end

u-235 1 0 7.23460E-5 300.0 end

o 1 0 1.30805E-3 300.0 end

graphite 1 0 5.85220e-2 300.0 end

graphite 1 0 3.77085E-3 300.0 end

si 1 0 3.77085E-3 300.0 end

'

' graphite moderator

graphite 7 den=1.74 1.0 300.0 end

'

' helium coolant

he-3 8 0 3.71220e-11 300.0 end

he-4 8 0 2.65156e-5 300.0 end

'

' carbon steel for PV

carbonsteel 91 end

'

' S.S. for structure

ss316 92 end

'

' graphite reflector

graphite 93 den=1.74 1.0 300.0 end

b-11 93 0 1.0e-8 300.0 end

b-10 93 0 0.2e-8 300.0 end

'

end comp

read celldata

 lattice triangpitch pitch=1.8796 7 fuelr=0.6225 1

 gapr=0.6350 8 cellmix=40 end

 centrm data 

 ixprt=1 ipbt=1

' reflected BC in CENTRM

 ibr=1 iup=20 demin=2.0E-5

 end centrm

end celldata

end 

=shell

rm ft02f001
B-4

rm ft03f001

rm ft42f001

rm ft81f001

end

=xsdrn

Radial model of VHTR, with homo 999 grp XSs (no double het).

' this case collapses over 3 zones: inner refl, core, and outer refl

'

' ige izm im ibl ibr mx ms sn isct ievt iim icm iclc ith 

'1$$ 2 3 334 1 0 2 11 8 3 1 20 60 30 0 e

1$$ 2 3 334 1 0 2 11 8 3 1 20 600 500 0 e

'

' iprt id1 ipbt isx isen idm2 nbands ifsn 

'2$$ -2 -1 1 1 0 0 -2 0 e

2$$ -2 -1 1 1 0 0 -4 0 e

'

' ifg iqm ipm ifn itmx idat1 ipn idfm iaz iai ifct 

'3$$ 1 0 0 1 0 0 3 0 4 1 1 e

3$$ 0 0 0 1 0 0 3 0 4 1 1 e

' 

' icon igmf itp ipp 

4$$ 0 999 0 0 e

'

' eps ptc xnf ev evm bf dy 

'5** 1.0e-4 1.0e-5 1.0 a7 813.0 e

5** 1.0e-4 1.0e-6 1.0 a7 813.0 e

T

'

' << M I X I N G T A B L E >>

'

' mixtures: mix-1=homo fuel block ; mix-2=graphite reflector

13$$ 10r1 2

'

' nuclide iDs for cell-homogenized fuel XS ; reflector

14$$ 1092238 1092235 1008016 1006312 1014028 1014029 

 1014030 7006312 8002003 8002004 93006312

'

' homo fuel atom densities ; and reflector

15** 3.18E-04 2.88E-05 1.093E-02 2.48E-02 1.38E-03 7.01E-05 

 4.65E-05 5.12E-02 5.99E-13 4.28E-07 8.73211E-02

T

'

' fission density guess

34## f1.0

T

' radial intervals

35** 146i0.0 32i147.62 32i180.31 27i213.01 92i241.32 334.40

' 

' zone numbers by interval

' -inner refl- -- 3 fuel rings -- -- outer refl --

' ------------ -------------------- ----------------

36$$ 144r1 1 1 1 2 2 2 88r2 2 2 2 3 3 3 90r3

'

' mixture by zone

39$$ 2 1 2

'

' transport method by group, for iclc outers
B-5

46$$ 148r0 f1

'

' activity materials

49$$ 1092238 1092235 1092235 93006312 

'

' activity mts

50$$ -102 -18 1452 -2 

'

' was: collapsed group structure. set to 23 groups

' 51$$ 11r1 6r2 17r3 10r4 5r5 8r6 17r7 69r8 22r9 14r10 5r11 6r12

' 4r13 8r14 2r15 2r16 2r17 2r18 3r19 1r20 2r21 5r22 17r23

'51$$ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

'25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

'48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

'71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93

'94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 

'113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129

'130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146

'147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163

'164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180

'181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197

'198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214

'215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231

'232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 

'249 250 251 252 253 254 255 256 257 258 259 260 261 

T

end

'=shell

'rm ft04f001

'mv ft03f001 ft04f001

'end

=xsdrn

Radial model of VHTR, with full 999 grp XSs (no double het).

' uses 999-grp XSs collapsed over 3 zones (innr refl,core,outr refl)

'

' ige izm im ibl ibr mx ms sn isct ievt iim icm iclc ith 

1$$ 2 3 334 1 0 3 12 8 3 1 20 300 200 0 e

'

' iprt id1 ipbt isx isen idm2 nbands ifsn 

2$$ -2 0 0 0 0 0 -3 0 e

'

' ifg iqm ipm ifn itmx idat1 ipn idfm iaz iai ifct 

3$$ 0 0 0 1 0 0 3 0 4 1 1 e

' 

' eps ptc xnf ev evm bf dy 

5** 1.0e-4 1.0e-6 1.0 a7 813.0 e

T

'

' << M I X I N G T A B L E >>

'

' mixtures: mix-1=homo fuel block ; mix-2=graphite reflector

13$$ 10r1 2 3

'

' nuclide iDs for cell-homogenized fuel XS ; reflector

14$$ 21092238 21092235 21008016 21006312 21014028 21014029 

 21014030 27006312 28002003 28002004 193006312 393006312

'
B-6

' homo fuel atom densities ; and reflector

15** 3.18E-04 2.88E-05 1.093E-02 2.48E-02 1.38E-03 7.01E-05 

 4.65E-05 5.12E-02 5.99E-13 4.28E-07 8.73211E-02 8.73211E-02

T

'

' fission density guess

34## f1.0

T

' radial intervals

35** 146i0.0 32i147.62 32i180.31 27i213.01 92i241.32 334.40

' 

' zone numbers by interval

' -inner refl- -- 3 fuel rings -- -- outer refl --

' ------------ -------------------- ----------------

36$$ 144r1 1 1 1 2 2 2 88r2 2 2 2 3 3 3 90r3

'

' mixture by zone

39$$ 2 1 3

'

' transport method by group, for iclc outers

46$$ 8r0 f1

'

' activity materials

49$$ 21092238 21092235 21092235 193006312 

'

' activity mts

50$$ -102 -18 1452 -2 

'

 T

end
C-1

APPENDIX C

INPUT FOR GENERATING CENTRM POINTWISE FLUX WEIGHTING 

FUNCTIONS

C-3

Presented here is an input file for generating a temperature-dependent CENTRM pointwise flux 

weighting function (this example for 1800 K).

=csas1x parm=centrm 

homo (NO double-het) fuel unit cell for ngp prismatic lattice

V7-238

read comp 

' homgenized channel 

u-238 1 0 7.99688E-4 1800.0 end

u-235 1 0 7.23460E-5 1800.0 end

o 1 0 1.30805E-3 1800.0 end

graphite 1 0 5.85220e-2 1800.0 end

' c 1 0 3.77085E-3 1800.0 end

graphite 1 0 3.77085E-3 1800.0 end

si 1 0 3.77085E-3 1800.0 end

'

' graphite moderator

graphite 7 den=1.74 1.0 300.0 end

'

' helium coolant

he-3 8 0 3.71220e-11 300.0 end

he-4 8 0 2.65156e-5 300.0 end

end comp

read celldata

lattice triangpitch pitch=1.5 7 fuelr=0.6225 1

 gapr=0.6350 8 end

centrm data ixprt=1 ipbt=1 nprt=1 iprt=-1 id1=2

' reflected BC in CENTRM

isn=10

n2d=0

ibr=3

iup=20

demin=2.0E-5

end centrm

moredata szf=0.5 end

end celldata

end 

D-1

APPENDIX D

INPUT FOR TEST2R3_MG: SAMPLE JAPANESE HTTR BENCHMARK 

CASE

D-3

Presented here is input for the Test2r3_Mg: sample Japanese HTTR benchmark case

=shell

cp /home/xxx/newlib_htgr/81B3/tst8_IR_Master ft34f001

ln -sf /home/xxx/SCALE6_100204/Linux_x86_64/bin/csas6 ./csas6

ln -sf /home/xxx/SCALE6_100204/Linux_x86_64/bin/bonami ./bonami

end

=ajax

0$$ 88 e

1$$ 1 t

2$$ 34 0 t

end

=csas26 parm=bonami 

Volkan's test# 1: 5 rings of 6.3% enriched fuel blocks + 1 reflector ring

ft88f001

' -----------------------------------------------------------------------------

' --- References:

' [1] John D. Bess, Nozomu Fujimoto: Evaluation of the Start-up Core Physics Tests

' at Japan's High Temperature Engineering Test Reactor (Fully-Loaded Core),

' Revision 0, March, 2009

' -----------------------------------------------------------------------------

' --- Materials ---------------------------------------------------------------

read comp 

' Material References:

' --------------------

' m=7 CFP fuel atom densities from Table 3.1, pag. 195 of [1]

' m=13 Buffer atom densities from Table 3.2, pag. 196 of [1]

' m=14 IPyC atom densities from Table 3.2, pag. 196 of [1]

' m=15 SiC atom densities from Table 3.2, pag. 196 of [1]

' m=16 OPyC atom densities from Table 3.2, pag. 196 of [1]

' m=17 Overcoat atom densities from Table 3.2, pag. 196 of [1]

' m=18 Compact atom densities from Table 3.3, pag. 196 of [1]

' m=19 Sleeve atom densities from Table 3.4, pag. 196 of [1]

' m=20 IG-110 atom densities from Table 3.6, pag. 197 of [1]

' by multiplying with 1.005

' m=21 Helium coolant from 3.1.3.10, page 199 of [1]

' m=22 Disks atom densities in BP pins from Table 3.5, pag. 197 of [1]

' m=24 BP atom densities (2.5%) from Table 3.5, pag. 197 of [1]

' m=25 PGX Graphite from Table 3.9, pag. 199 of [1]

'

' ==============================================================================

' --- Fuel Kernel, 6.3% enrichment: 

 U-234 7 0 1.1293E-05 300.00 end

 U-235 7 0 1.4783E-03 300.00 end

 U-238 7 0 2.1699E-02 300.00 end

 O-16 7 0 4.6343E-02 300.00 end

 B-10 7 0 1.7276E-07 300.00 end

' --- Buffer:

 C-graphite 13 0 5.5153E-02 300.00 end

 B-10 13 0 1.8290E-08 300.00 end

' --- IPyC:

 C-graphite 14 0 9.2758E-02 300.00 end

 B-10 14 0 3.0761E-08 300.00 end

' --- SiC:

 C-graphite 15 0 4.8061E-02 300.00 end

 Si 15 0 4.8061E-02 300.00 end

 B-10 15 0 5.3208E-08 300.00 end

' --- OPyC:

 C-graphite 16 0 9.2758E-02 300.00 end

 B-10 16 0 3.0761E-08 300.00 end

' --- Graphite overcoat:

 C-graphite 17 0 8.5237E-02 300.00 end
D-4

 B-10 17 0 2.8267E-08 300.00 end

' --- Graphite compact:

 C-graphite 18 0 8.5237E-02 300.00 end

 B-10 18 0 1.5452E-08 300.00 end

' --- Graphite sleeve:

 C-graphite 19 0 8.8747E-02 300.00 end

 B-10 19 0 7.2596E-09 300.00 end

' --- IG-110 Graphite:

 C-graphite 20 0 8.8243E-02 300.00 end

 B-10 20 0 7.8036E-09 300.00 end

' --- Helium coolant:

 He 21 0 2.4616E-05 300.00 end

' --- Graphite disks:

 C-graphite 22 0 8.8747E-02 300.00 end

 B-10 22 0 7.2596E-09 300.00 end

' --- Burnable poison (2.5wt%):

 C-graphite 24 0 8.7995E-02 300.00 end

 B-10 24 0 4.9882E-04 300.00 end

 B-11 24 0 2.0078E-03 300.00 end

' --- PGX Graphite:

 C-graphite 25 0 8.6134E-02 300.00 end

 B-10 25 0 3.6372E-08 300.00 end

' --- Homogenized graphite compact (inner and outer helium embeded):

' Obtained by volumetric homogenization of materials 18 and 21

 He 28 0 4.6313E-06 300.00 end

 C-graphite 28 0 6.8834E-02 300.00 end

 B-10 28 0 4.7270E-09 300.00 end

end comp

' -----------------------------------------------------------------------------

' --- Cell data ---------------------------------------------------------------

read celldata

doublehet fuelmix=10 end

 gfd=0.06 7

 coatr=0.036 13

 coatr=0.039 14

 coatr=0.0415 15

 coatr=0.046 16

matrix=28

numpar=12987 end grain

rod triangpitch right_bdy=white left_bdy=reflected

pitch=5.15 20 fuelr=1.3 fuelh=3.9 gapd=3.4 19 cladd=4.1 21 end

moredata iropt=1 end

end celldata

' -----------------------------------------------------------------------------

' --- Parameters --------------------------------------------------------------

read parm 

 gen=110

 npg=100000

 nsk=10

 tba=100

 htm=no

 flx=yes

 fdn=yes

end parm

' -----------------------------------------------------------------------------

' --- Geometry ----------------------------------------------------------------

read geom

' Dimensions for block and pin details based on Figure 1.52 page 68 of [1]

' Counting of pins starts at the lower left corner, going horizontally and

' then vertically
D-5

' Dimensions for grain cells based on Figure 3.1 page 176 of [1]

'

' Numbering scheme for cells that make up fuel block units:

' zlb1 fuel grain

' zlb2 BP pin

' zlb3 fuel pin

' zlb4 central hole

' zlb5 empty pin

' zlb6 graphite

' zlb block

'

' Block numbering (Fig. 3.15, page 190 of [1]):

' Each block is numbered according to the scheme 100*z+10*l+b, where:

' z=1,...,8 zone number

' **Fuel: z=1,2 for zones 1 and 2, respectively

' z=3,5 alternatively as one goes counterclockwise

' for zone 3, z=4 for zone 4

' **Replaceable Reflectors in fuel columns follow the same

' pattern as fuel blocks, but with different l: l=1,2,8,9

' **CR: z=6 for "C" (b=1) and "R1" (b=2,...,7)

' z=7 for "R2" and "R3" (b=1,...,9, going 

' counterclockwise)

' **Instrumentation Blocks have z=8 (b=1,2,3)

' l=1,...,9 layer number from top to bottom

' (fuel blocks in layers 3 to 7 from top)

' b=1,...,bmax(z) block number (starting from pozitive x, counterclockwise)

' bmax(1)=...=bmax(5)=6

' bmax(6)=7, bmax(7)=9

' bmax(8)=3

' Replaceable Reflector (RR) blocks that are not in fuel columns are assigned

' block# 900

' Graphite blocks to make up the Permanent Reflector are assigned block# 100

'

'================ Graphite Block =================

unit 10

 hexprism 1 18. 29. -29.

 media 25 1 1

 boundary 1

'================ Void Block =================

unit 20

 hexprism 1 18. 29. -29.

 media 0 1 1

 boundary 1

'================ Central handling hole =================

unit 1114

 cone 1 2.5 29. 1.5 20.

 cylinder 2 1.5 20. 14.

 cylinder 3 2.25 14. 4.

 cylinder 4 2.505 29. -29.

 hexprism 5 2.575 29. -29.

 media 21 1 1

 media 21 1 2

 media 21 1 3

 media 20 1 4 -1 -2 -3

 media 20 1 5 -4

 boundary 5

'================ Graphite =================

unit 1116

 hexprism 1 2.575 29. -29.

 media 20 1 1

 boundary 1

'================ Empty BP pin location =================

unit 1315
D-6

 cylinder 1 0.75 25.2 -24.8

 cylinder 2 0.75 29. -29. 

 hexprism 3 2.575 29. -29.

 media 21 1 1

 media 20 1 2 -1

 media 20 1 3 -2

 boundary 3

'================ 2.5 wt% BP pin =================

unit 1412

 cylinder 1 0.7 5.2 -4.8

 cylinder 2 0.7 25.2 -24.8

 cylinder 3 0.75 25.2 -24.8

 cylinder 4 0.75 29. -29. 

 hexprism 5 2.575 29. -29.

 media 22 1 1

 media 24 1 2 -1

 media 21 1 3 -2

 media 20 1 4 -3

 media 20 1 5 -4

 boundary 5

'================ Block 241 =================

unit 2413

 cylinder 2 1.3 27.3 -27.3

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 10 1 2

 media 19 1 4 -2

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 110

 rhexprism 1 17. 29. -29.

 array 241 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

unit 11

 hexprism 1 18. 29. -29.

 hole 110 rotate a1=30

 media 20 1 1

 boundary 1

'================ Global Geometry =================

global unit 1

 rhexprism 1 176.669182 29. -29.

 array 1 1 place 7 7 1 0.0 0.0 0.0

 boundary 1

end geom

' -----------------------------------------------------------------------------

' --- Boundary conditions -----------------------------------------------------

read boun

surface(1)=vacuum

surface(2)=vacuum

surface(3)=vacuum

surface(4)=vacuum

surface(5)=vacuum

surface(6)=vacuum

surface(7)=reflect

surface(8)=reflect

end boun

' -----------------------------------------------------------------------------

read array

 ara=1 nux=13 nuy=13 nuz=1 typ=hexagonal
D-7

 fill

 20 20 20 20 20 20 20 20 20 20 20 20 20

 20 20 20 20 20 20 10 10 10 10 10 10 20

 20 20 20 20 20 10 10 10 10 10 10 10 20

 20 20 20 20 10 10 11 11 11 11 10 10 20

 20 20 20 10 10 11 11 11 11 11 10 10 20

 20 20 10 10 11 11 11 11 11 11 10 10 20

 20 10 10 11 11 11 11 11 11 11 10 10 20

 20 10 10 11 11 11 11 11 11 10 10 20 20

 20 10 10 11 11 11 11 11 10 10 20 20 20

 20 10 10 11 11 11 11 10 10 20 20 20 20

 20 10 10 10 10 10 10 10 20 20 20 20 20

 20 10 10 10 10 10 10 20 20 20 20 20 20

 20 20 20 20 20 20 20 20 20 20 20 20 20

 end fill

' --- Fuel block arrays -------------------------------------------------------

 ara=241 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 2413 2413 2413 1315 1116

 1116 1116 1116 2413 2413 2413 2413 2413 1116

 1116 1116 2413 2413 2413 2413 2413 2413 1116

 1116 1412 2413 2413 1114 2413 2413 2413 1116

 1116 2413 2413 2413 2413 2413 2413 1116 1116

 1116 2413 2413 2413 2413 2413 1116 1116 1116

 1116 2413 2413 2413 1412 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

end array

' -----------------------------------------------------------------------------

' --- Energy splitting --------------------------------------------------------

read energy

 2e7 1.01e6 0.625 1e-5

end energy

' -----------------------------------------------------------------------------

' --- Plot cros-section -------------------------------------------------------

read plot

ttl='z=25 cm'

 TYP=XY

 XUL=-205.0 YUL=205.0 ZUL=25.

 XLR=205.0 YLR=-205.0 ZLR=25.

 NAX=640 end

ttl='Vertical View of the HTTR Core'

 TYP=XZ

 XUL=-205. YUL=0. ZUL=30.

 XLR=205. YLR=0. ZLR=-30.

 UAX=1.0 WDN=-1.0 NAX=640 end

end plot

end data

end

' -----------------------------------------------------------------------------

' --- End input deck ----------------------------------------------------------

E-1

APPENDIX E

SCHEMATIC DIAGRAMS OF THE HTTR BENCHMARK CASE

E-3

Presented here is a schematic diagram of the HTTR benchmark case (Test2r3_Mg).

F-1

APPENDIX F 

IR F-FACTOR

F-3

Nuclides for which IR f-factors are applied

Am-241

Am-242

Am-242m

Am-243

Am-244

Am-244m

Bk-249

Bk-250

Cf-249

Cf-250

Cf-251

Cf-252

Cf-253

Cf-254

Cm-241

Cm-242

Cm-243

Cm-244

Cm-245

Cm-246

Cm-247

Cm-248

Cm-249

Cm-250

Es-254

Es-255

Fm-255

Np-235

Np-236

Np-237

Np-238

Np-239

Pa-231

Pa-232

Pa-233

Pu-236

Pu-237

Pu-238

Pu-239

Pu-240

Pu-241

Pu-242

Pu-243

Pu-244

Pu-246

Ra-223

Ra-226

Th-227

Th-228

Th-229

Th-230

Th-232

Th-233

Th-234

U-232

U-233

U-234

U-235

U-236

U-237

U-238

U-239

U-240

U-241

BIBLIOGRAPHIC DATA SHEET

(See instructions on the reverse)

NRC FORM 335

(12-2010)

NRCMD 3.7

U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMBER

 (Assigned by NRC, Add Vol., Supp., Rev.,

 and Addendum Numbers, if any.)

NUREG/CR-7106

3. DATE REPORT PUBLISHED

MONTH

June

YEAR

2012

4. FIN OR GRANT NUMBER

N6841

2. TITLE AND SUBTITLE

Generation of a Broad-Group HTGR Library for Use with SCALE

5. AUTHOR(S)

R. J. Ellis, D. J. Lee, D. Wiarda, M. L. Wiliams and U. Mertyurek

6. TYPE OF REPORT

Technical Report

7. PERIOD COVERED (Inclusive Dates)

8. PERFORMING ORGANIZATION - NAME AND ADDRESS (If NRC, provide Division, Office or Region, U.S. Nuclear Regulatory Commission, and mailing address; if contractor,

Oak Ridge National Laboratory

9. SPONSORING ORGANIZATION - NAME AND ADDRESS (If NRC, type "Same as above"; if contractor, provide NRC Division, Office or Region, U.S. Nuclear Regulatory Commission, 

Division of Systems Analysis

provide name and mailing address.)

and mailing address.)

10. SUPPLEMENTARY NOTES

n/a

11. ABSTRACT (200 words or less)

With current and ongoing interest in high temperature gas reactors (HTGRs), the U. S. Nuclear Regulatory Commission (NRC)

anticipates the need for nuclear data libraries appropriate for use in applications for modeling, assessing, and analyzing HTGR

reactor physics and operating behavior. The objective of this work was to develop a broad-group library suitable for production

analysis with SCALE for HTGR applications. Several interim libraries were generated from SCALE fine-group 238-group and

999-group libraries, and the final broad-group library was created from Evaluated Nuclear Data File/B Version and other codes.

Furthermore, intermediate resonance (IR) methods were applied to the HTGR broad-group library, and lambda factors and

f-factors were incorporated into the library's nuclear data files. A new version of the SCALE BONAMI module, named

BONAMI-IR, was developed to process the IR data in the new library and, thus, eliminate the need for the CENTRM/PMC

modules for resonance self-shielding. This report documents the development of the HTGR broad-group nuclear data library and

the results of test and benchmark calculations using the new library with SCALE. The 81-group library is shown to model HTGR

cases with similar accuracy to the SCALE 238-group library but with significantly faster computational times due to the reduced

number of energy groups and the use of BONAMI-IR instead of BONAMI/CENTRM/PMC for resonance self-shielding

calculations.

12. KEY WORDS/DESCRIPTORS (List words or phrases that will assist researchers in locating the report.)

HTGR, SCALE 14. SECURITY CLASSIFICATION

13. AVAILABILITY STATEMENT

unlimited

(This Page)

unclassified

(This Report)

unclassified

15. NUMBER OF PAGES

16. PRICE

NRC FORM 335 (12-2010)

Managed by UT-Batelle, LLC

Oak Ridge, TN 37831-6170

Office of Nuclear Regulatory Research

US Nuclear Regualtory Commission

Washington, DC, 20555-0001


UNITED STATES 

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

--------------------

OFFICIAL BUSINESS
NUREG/CR-7106 Generation of a Broad-Group HTGR Library for Use with SCALE