AlllDD ‘nME7S

NBSIR 81-2236

Measurements and Standards for

Nuclear Materials Safeguards

. N8S

B. S. Carpenter and F. E. Jones

National Measurement Laboratory

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

March 1981

Annual Report, Fiscal Year 1980

(October 1 , 1 979 - September 30, 1 980)

Prepared for Division of Siting, Health and Safeguards Standards

Safeguards Standards Branch

ffice of Standards Development

.S. Nuclear Regulatory Commission

nder Contract No. AT(49-25)-9009

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APR 7 1981

NBSIR 81-2236

MEASUREMENTS AND STANDARDS FOR

NUCLEAR MATERIALS SAFEGUARDS

B. S. Carpenter and F. E. Jones

National Measurement Laboratory

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

March 1 981

Annual Report, Fiscal Year 1980

(October 1 , 1 979 - September 30, 1 980)

Prepared for Division of Siting, Health and Safeguards Standards

Safeguards Standards Branch

Office of Standards Development

U.S. Nuclear Regulatory Commission

Under Contract No. AT(49-25)-9009

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U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
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PREFACE

This report was prepared for the U.S. Nuclear Regulatory Commission,

Office of Standards Development, under Interagency Agreement No. AT(49-25) -9009.

1
TABLE OF CONTENTS

Page

ABSTRACT iii

IN'T’RODUCTION iv

PROGRESS OF TASKS

TASK I: STANDARDIZATION OF NON-DESTRUCTIVE ASSAY (NDA) METHODOLOGY

FOR NUCLEAR MATERIALS 1

Sub-Task A: NDA Reference Materials Research 1

Sub-Task B: Reference Method Development 6

TASK II: STANDARDIZATION OF DESTRUCTIVE ANALYTICAL CHEMISTRY

METHODOLOGY FOR NUCLEAR MATERIALS 14

Sub-Task A: SRM Research and Reference Methodology .... 14

Sub -Task B: Support of Measurement Assurance Programs . . 15

TASK III: STANDARDIZATION OF BULK MEASUREMENT METHODOLOGY IN

NUCLEAR FUEL CYCLE PLANTS 16

Sub -Task A: Process Tank Volume Measurements

Standardization 16

Sub-Task B: UFg Mass Measurement Implementation 16

TASK IV: APPLIED MATHEMATICS FOR NUCLEAR SAFEGUARDS 17

Sub-Task A: Statistical Methods in Nuclear Material

Accounting 17

Sub-Task B: Statistical Support for Other NBS Safeguards

Tasks 19

TASK V: USERS GUIDE, FACILITY ENGINEERING FOR SAFEGUARDS

MEASUREMENT INSTRUMENTS 19
ABSTRACT

This report is a review of the progress made during Fiscal Year 1980

(October 1, 1979, through September 30, 1980) of a long-term NBS program

sponsored by the Nuclear Regulatory Commission (NRC) to upgrade national

measurements and standards capability for nuclear materials safeguards. This

is the last report to NRC for this program, since NRC has terminated support to

NBS as of September 30, 1980. The NRC-sponsored program at NBS was a synergistic

part of the overall NBS program in this area which is sponsored jointly by the

NRC, the Department of Energy (DOE) , and the Department of State through the

International Safeguards Project Office (ISPO)

A summary of the progress for each of the five NRC-supported Tasks in the

project is given. The first Task is concerned with the standardization of NonDestructive Assay (NDA) methodology - work in this Task includes development of

a series of low-enriched UaOe NDA Gamma Spectroscopy NBS SRMs; the calibration

of plutoniiara heat source reference materials for calorimetry; the establishment

of a test facility for resonance neutron radiography (a possible NDA reference

method) and the completion of experiments confirming the scientific validity of

the method; effort toward using resonance neutron tomography (another possible

NDA reference method) with reactor-produced neutrons for high- accuracy measurements

and for the establishment of reference standards; and improvement of the accuracy

of detectors to lead to more accurate measurement on the capture cross section of

gas.

The second Task involves the standardization of analytical chemical methodology - work in this Task includes: the development of a "spike” SRM for

isotope dilution mass spectrometry; determination of the uranium content and

isotopic composition of samples from the Safeguards Analytical Laboratory Evaluation (SALE) Program; and research to improve uranium mass spectrometry measurements.

The third Task involves the standardization of bulk measurement technology - the work in this Task includes: the standardization of tank volume measurements

and the transfer of the technology to the field; the completion and laboratory

testing of a prototype dynamic volume calibrator intended to make tank volume

calibration more convenient, less time-consuming and less subject to operator

error; the characterization of pressure transducers; the implementation of a Measurement Assurance Program (MAP) to improve in- facility weighing of large UFs

cylinders; and field testing of a mobile flow prover for calibration of nuclear

facility flow measurement systems at a nuclear facility.

The fourth Task applies mathematics and statistics to nuclear safeguards - the work in this Task includes: development and description in detail of a design

for an improved measurement system and the associated statistical analysis of

the resulting data; and recommendation of the appropriate statistical models for

all currently used passive gamma, active gamma and passive neutron NDA measurement

systems.

The fifth Task involves the development of a Users Guide to provide specific

recommendations on how facilities should be designed to accommodate the necessary

measurements to meet the SNM accountability goals of the safeguards program - the

work in this Task includes the preparation of a review draft and preparation of

the final version of the Users Guide for publication.
INTRODUCTION

An adequate measurement and accounting system is necessary for the detection

of and protection against unauthorized removal of special nuclear materials by

persons having authorized access to facilities. The sensitivity of this type of

detection depends directly on the uncertainties of measurement. The NBS program

will assure the availability of the certified reference materials, reference

measurement methods, reference data and quality assurance methodology for the

adequate standardization of measurements for nuclear safeguards. Domestic and

international dissemination is required.

The goal of the NBS program is

To assure that measurement standards exist for the timely measurement

of special nuclear material throughout the fuel cycles so that measurements can be performed at reasonable cost with accuracy sufficient for

the safeguarding of nuclear material. These measurements of enriched

uranium, plutonium, and related materials need to be made domestically

by NRG and DOE inspectors, government facilities, and the industry. In

addition, these measurements need to be made by other countries and the

International Atomic Energy Agency (IAEA)

The overall NBS program is currently funded by NRG, DOE, and the Department

of State through the International Safeguards Project Office (ISPO) . NRG funding

terminated on September 30, 1980. The program may be viewed as consisting of

three related parts: (1) development of capability, including calibration standards,

reference measurement methods, sampling schemes, statistical treatment of data,

data generation; (2) dissemination mechanisms to transfer the standards and reference

methods and data to the users; and (3) mechanisms to directly assist inspectors and

the nuclear industry to ensure that their measurements are of sufficient accuracy.

In order to carry out the tasks assigned to NBS in a timely manner, NBS must

continually assess the advancing needs for national and international measurement

standards. NBS has received substantial guidance and input from NRG as to

standards needs.

The NBS Measurements for Nuclear Safeguards Program is broadly organized into

five Tasks: non-destructive assay; chemical and isotopic measurements; bulk

measurmeents ; statistics, sampling and error analysis; and the development of a users guide for design of facilities to accommodate accountability instrumentation.

Gonsideration for needed reference data is included in each of the first four

Tasks. The research is being carried out in six line organizations at NBS:

Genter for Radiation Research, Genter for Applied Mathematics, Genter for

Materials Science, Genter for Thermodynamics and Molecular Science, Genter for

Analytical Ghemistry, and Genter for Mechanical Engineering and Process Technology.

Researchers with backgrounds in analytical chemistry, mass and volume measurement,

nuclear and radiation physics, thermodynamics, mechanics, etc., are part of the

program team. NBS is also supplying a substantial amount of equipment, both

previously existing and new, that is needed to carry out the program.

NRG supported an important portion of the total NBS program on measurements

for nuclear safeguards in all of the above-mentioned Task areas.

IV
TASK I: STANDARDIZATION OF NON-DESTRUCTIVE ASSAY (NDA)

METHODOLOGY FOR NUCLEAR MATERIALS

The objective of this Task is to provide a common and accurate basis for

the non-destructive assay of nuclear fuels and disseminate to industry.

Government, other countries and the IAEA. This Task is divided into three

components (Sub-Tasks): A - NDA Standard Reference Materials Research. The

effort in this Sub-Task is directed toward the development of primary (facilitiesindependent) NBS-certified reference materials to be used for the calibration of

NDA instruments. These SRMs will be used by others for the evaluation and

development of NDA methods and for the production of NDA secondary or working

reference materials. B - Reference Method Development. The effort is directed

toward the development of reference methods to be used for the characterization

of NDA reference materials.

Sub-Task A : NDA Reference Materials Research

A major portion of the effort in this Sub-Task has been on the development

of a series of low-enriched UsOa NDA Gamma Spectroscopy SRMs. This is a cooperative project involving NBL, LASL, NBS and Euratom Labs. NBS provided

collaborative support to the Central Bureau for Nuclear Measurements (CBNM) on their design of a suitable aluminum container for the reference materials and

helped to finalize the specifications for the UaOe materials. Specifications

were required for a number of parameters including: chemical assay, enrichment,

chemical and isotopic homogeneity, and radioactive impurities.

Study of 20 pre-experiment samples of UaOe prototype reference materials was completed to prepare the results for the Joint Collaborators' meeting scheduled

in Geel, Belgium, 5-6 November 1979. The meeting consisted of representatives

from all of the laboratories or organizations involved in this joint collaborative

project: ESARDA, JRC-Geel, JRC-Ispra, Euratom Inspectorate, IAEA, KfK, NBL, LASL

and NBS. The results, tabulated in Table 1, presented at the meeting consisted of:

« the homogeneity of each enrichment set (0.298%, 0.720% and 2.95%),

e the effects of varying packing density on a given enrichment (2.95%),

« the determination of ^^^U enrichment.

f» the problems associated with container design, and

• the problems associated with gamma spectroscopy, i.e., peak area

evaluation, pulse pile-up, dead-time and collimation.

The results indicated that the material was homogeneous within each set and

that there were no interfering impurities present. The variation in the packing

density was found to have no effect on the enrichment measurements when the 186 keV

line of ^^^U was used. In all of the gamma spectroscopy data presented, consideration had to be given to, or corrections made for, pulse pile-up, dead-time, and

variation in the window thickness of the cans. Finally, a new aluminum container

design was approved (see Figure 1) which would protect the thin window from scratches.

A purchase order has been dispatched to British Nuclear Fuels, Ltd., to

acquire the 4.5% enriched U 3 O 8 .

1
Table 1

Enrichment Da+-a on U 3 O 8 NDA

Sample n

Test Samples

% Enrichment (Declared) Measured Value

Depleted 5 0.298 0.2979 + 0.0002

Natural 6 0.720 0.720 + 0.001

Enriched 4 2.95 2.950 + 0.002

Enriched with

varying density 4 2.95 2.950 + 0.003

The final design for the aluminum cans was given to the NBS Shops to mass produce 900 containers. Six of the first 20 cans produced were sent to Geel

for tolerance evaluation by ultrasonic techniques. The Shops produced the cans in three phases: the inner plug, the outer can, and then the hollowing of the

interior of the can. Figure 2 shows an array of outer cans and the inner plug

being inserted into one of the outer cans. All 900 cans have been completed and

shipped to CBNM-Geel for filling. At present, CBNM has taken 13 samples ('vl g

each) from the four batches of material (0.32%, 0.72%, 1.94% and 2.95% enrichment)

that are being shipped to NBS for homogeneity and isotopic measurements. An

additional 20-g sample from each batch is being shipped for chemical assay and

for determining the concentration by gamma-ray spectrometry. CBNM has also

begun canning the 0.32% U 3 O 8 material and will continue in order of increasing

enrichment.

Another major effort of this Sub-Task was devoted to studying the contribution of daughter products (^^**Pa and ^^‘*’"'*Pa) to the 185.7-keV gamma-ray peak

observed from low-enriched samples. The purpose of this study was to provide

additional information in certifying the proposed low-enriched U 3 O 8 NDA standards,

as well as to aid in accurately measuring the Since the protactinium gamma

rays have energies at 185 ^ 1 keV which cannot be resolved from the 185.7-keV

gamma-ray line of a small non-linear error is introduced in NDA enrichment measurements. According to the work of H. Ottmar at Kemforschungszentrum

Karlsruhe GmbH, the contribution of Pa gamma rays to the 186-keV region is

negligible (<0.1%) for enrichments at 1%, and is 'vo.5% for depleted uranium samples.

Our study was performed on previously prepared counting standards made from

NBS uranium isotopic SRMs (see Table 2) . These standards contained approximately

300 mg of U 3 O 8 and were counted on a high-purity Ge detector for long periods of

time such that errors due to counting were smaller than the effect being studied.

Unfortunately, the sample sizes were too small to provide reasonable counting

periods necessary for the accurate measurements needed.

In order to increase the accuracy of the measurement and reduce the counting

time needed, larger sample sizes ('^^11.5 g) were prepared. Gamma-ray spectrometry

has been performed on 11.5-gram samples whose isotopic abundances have ranged

from 0.0004% to 0.7198%. This isotopic range was chosen because the contribution

from ^^**Pa and ^^‘*"'Pa is significant.

2
3

Figure

1.

New

Aluminum

Container

Design

Drawings
jj0

i Kt

i***-"*' lil'iSiM^

StT*--***

4

Figure

2.

An

Array

of

Outer

Cans

and

the

Inner

Plug

Being

Inserted

Into

One

of

the

Outer

Cans
Table 2

Previously Prepared Counting Standards

Made From NBS Uranium Isotopic SRMs

SRM % %

23 8u

U-0002 0.01755 99.9823

U-005 0.4895 99.504

U-010 1.0037 98.984

U-015 1.5323 98.443

U-020 2.038 97.933

U-030 3.046 96.915

U-050 5.010 94.915

950a 0.7198 99.2711

U-238 0.004 99.995

In addition to the gamma-ray spectrometry, these samples are to undergo

chemical separation, since secular equilibriiim exists. The uranium is separated

from its daughter decay products of thorium and protactinium. After separation,

the two fractions (uranium and thorium-protactinium) are then measured by gammaray spectrometry. By measuring the uranium fraction, there is an indication of

the 186-keV gamma-ray line build-up from protactinium, while the thoriumprotactinium fraction provides quantitative information on the actual amount of

interference being contributed.

The investigators for this Sub-Task are B. S. Carpenter and T. Mitlehner.

NDA Calibration Methodology

Major steps were taken in FY 80 to realize the NBS goal of providing

traceability to national standards for calorimetric measurements made in the

industrial assay of plutonium-bearing solids. These included (1) further

testing of a Mound-designed heat-flow calorimeter, together with an automated

data-acquisition system (this included power measurements on two Mound-fabricated,

encapsulated plutonium heat standards) ; (2) design and start of construction of an NBS heat-flow calorimeter; and (3) preparation of an NBS ’'General Reference

Material” certificate to accompany Mound- calibrated plutonium heat standards.

The twin-bridge, heat-flow calorimeter obtained previously on loan from

the Mound facility was tested in measuring the total decay power of two calibrated plutonium heat sources (nominal powers 0.25 W and 4.0 W, respectively).

The sources were loaded automatically and calorimeter data were recorded with

an automated data acquisition system built around a Hewlett-Packard 9835* desktop

computer. The NBS power data for both sources had a range of 20 ppm and a standard deviation of about 10 ppm. They agreed with the Mound predicted powers

for these sources within the combined measurement uncertainties of NBS and Mound.

*Identification of commercial equipment, instruments, or materials does not

imply recommendation or endorsement by the National Bureau of Standards.

5
Design specifications for an NBS twin-bridge, heat-flow calorimeter were

developed, using our experience with the Mound calorimeter as a guide. While

the gross physical features and operating principles of the NBS calorimeter

follow the Mound design, some changes in construction materials (as use of

stainless steel for all submarine parts and use of 0-rings instead of gasket

seals) were used to improve the reliability. In addition, the calorimeter was designed to be symmetrical, so that either of its two sensing chambers could be

used as a reference chamber. The main calorimeter body has been completed, and

we are presently constructing the thermal sensing elements, including heaters

and resistance thermometers.

In order to establish traceability to national standards for calorimetric

heat-flow measurements in assaying radioactive materials, we are proposing a service similar to the one offered by NBS to the radiopharmaceutical industry:

essentially a Measurement Assurance Program (MAP) in which traceability to

national standards is established through a programmed exchange of measurement

artifacts between major suppliers (in this instance, of calibrated radioactive

heat sources) and NBS. As a first step in this direction, we have carried out

power measurements on three Mound- calibrated heat standards in an NBS ice

calorimeter, and have determined that the NBS- and Mound-measured powers are in

agreement within their combined uncertainties for all three standards. We are therefore, together with the Office of Standard Reference Materials, preparing

a "General Reference Material" certificate (GM-10) that documents these NBS/Mound

intercomparisons. Mound will be authorized to distribute this certificate (together with its own calibration certificate and data) along with each newlycalibrated source it provides. A copy of the NBS certificate for GM-10 appears

in Figure 3. As soon as the NBS heat-flow calorimeter is operational, a formal

MAP between Mound and NBS, covering calibrated plutonium heat standards, will be

started.

David Ditmars, the staff member whose measurements were used in the preparation of Special Reference Material Report, GM-10, "Encapsulated Plutonium Heat

Source", also serves as a member of INMM 8.4, "Calibration Techniques in the

Calorimetric Assay of Pu-Bearing Solids", and the NBS Pu Steering Committee.

The investigators for this portion of the Sub-Task are D. A. Ditmars and J. Colwell.

Sub-Task B : Reference Method Development

Resonance Neutron Radiography

Work continued on improving experimental appratus and methods of data

reduction for resonance neutron radiography as an NDA technique. Having

established the scientific validity of the method, we have been actively engaged

in reporting our results at several conferences. Our preliminary tests to

develop the resonance neutron radiography technique involved the nondestructive

examination of a defective silver braze. These results have been finalized and

prepared for publication.

Experimental gas-filled position-sensitive proportional counters (PSPCs) are used in the development of the resonance neutron radiography technique.

For this application, "area" PSPCs having submillimeter spatial resolution for

neutrons in the epithermal energy range are needed. Through the NBS collaboration with Oak Ridge National Laboratory (ORNL) , a "linear" PSPC was built having

6
Figure 3.

special ^Material Report

GM 10

Encapsulated Plutonium Heat Source

Introduction

The enclosed encapsulated plutonium heat source provides a convenient, measured standard for calorimeter

calibration [1] in the calorimetric assay of plutonium-bearing solids. This report summarizes the NBS

measurements made on this reference material. The reference is produced and certified by the Mound Facility*,

Monsanto Research Corporation, Miamisburg, Ohio.

Description of Source

This heat source, fabricated and calibrated at the Mound Facility, consists of a doubly encapsulated sample

of plutonium-oxide. The sealing of both inner and outer capsules has been carried out using documented and

reproducible welding procedures. Nondestructive testing (radiography and He leak tests) has been conducted

to ensure the integrity of each capsule. Since the active materials are largely alpha-particle emitters, helium gas

will accumulate within the inner capsule. The capsules have a conservative design life of five years. The lack of long-term compatibility and creep data for the materials of construction precludes the assignment of longer

working lifetimes to the sources at this time. Therefore, it is strongly recommended that this source be returned

three years from the date of receipt to the Mound Facility for reevaluation and recertification. This source

should be handled with the normal precautions for alpha-particle emitters and stored in the container provided

when not in use.

Certification

This source has been calibrated at the Mound Facility using Mound heat-flow calorimeters and electrical standards traceable to the National Bureau of Standards. A separate certificate issued by the Mound Facility

accompanies this reference material. Selected Mound plutonium heat sources similar to the one accompanying

the Mound certificate have been independently measured in a precision Bunsen ice calorimeter at NB.S. riie calibration results accompanying that certificate are in the form of computer printout and microfiche giving

the decay power calculated from these measurements. day-b>-day. for a threc->ear period after the calibration.

Also included arc the physical parameters of the source including materials of construction and measured

radiation dose rates.

•Mound l-'ucilily is operated by Monsanto Koscarch Corporation for the U.S. Department of Energy tinder Contract No. DE-AC04-76-

DP00053.

7
-igure 3 (cont'd.)

NBS Measurements on Mound-Encapsulated Sources

Each measurement in a precision Bunsen ice calorimeter reflects the average (unweighted) of at least 10 independent determinations of heat flux (power) for a single source. Three such measurements were carried out on Mound sources of nominal power, 0.23 \V, 1.5W, and l.OW, and are summarized below. The first two are documented extensively in [2]. Mound Source Designation

0.23WB 1.5WB l.OWK

Mound Predicted Power*[W] 0.22544 1.44942 0.97027

NBS-Measured Power^ [W] 0.22517 1.44936 0.96996

Number of NBS Measurements 16 19 11

sn,” m 0.00005 0.00004 0.00034

Estimated NBS Overall Uncertainty' [W] 0.0003 0.0007 0.0014

"individual data for each source calculated for a single time mid-way through the measurements scries for that source.

^Sm = Computed standard deviation of the mean. 'Sum of maximum conceivable systematic errors and 99^? confidence limits for the mean.

At NBS measurements were carried out by D. Ditmars of the Chemical Thermodynamics Division and at Mound Facility by K. C. Jordan, Senior Research Specialist.

Packaging and reshipment of this source to the Mound Facility for testing and recalibration must follow all applicable Department of Transportation, U.S. Department of Energy and/or U.S. Nuclear Regulatory

Commission regulations. All shipments should be addressed to:

C. L. Fellers, Group Leader

Safeguards Research and Development

Monsanto Research Corporation

Mound Facility

P.O. Box 32

Miamisburg, Ohio 45342

[1) ANSI Standard N 15.22-1975, “Calibration Techniques for the Calorimetric .Assay of Plutonium-Bearing

Solids Applied to Nuclear Materials Control*', available from American National Standards Institute,

1430 Broad\v;iy, New York, New York lUOlS.

[2] D. Ditmars, Inti. J. Appl. Raduit. Isotopes 22. 469 (1976).

8
a spatial resolution o£ about 1 mm. High spatial resolution area PSPCs have now been built to replace the linear PSPC. These area PSPCs contain 3 atm. ^He,

11.5 atm. Xe, and 0.5 atm. CO2 . -The sensitive area is 50 x 50 mm^, and the

spatial resolution is 1.5 x 1.5 mm^. Work continued on improving this design

and implementing the new detector for use on the linac. Preliminary runs have

verified resolution of about 1 mm. The counter gas has been modified to increase

the amount of ^He gas by a factor of 5 to increase the detector sensitivity.

Modifications have been made in the voltage divider chain to allow operation at

20% lower bias potential to avoid gas breakdown. Tests of the effects of these

changes are now underway.

A sample of spent fuel is now being acquired to determine the radiographic

technique sensitivity to the fission products and plutonium isotopes present.

Work on unirradiated fuel pellets was reported in the Annual Report for FY 1979

in a paper presented at the American Nuclear Society Topical Meeting, November

26-30, 1979, Kiawah Island, SC, published in the Proceedings for the meeting

(Safeguards Reference Measurement System Utilizing Resonance Neutron Radiography,

by R. A. Schrack, J. W. Behrens, C. D. Bowman, and A. D. Carlson).

The neutron radiography detector system has been used in a pin-hole camera

system to image the distribution of neutrons from a spatially extended source

(see Figure 4) . The source in this case was the neutron-producing target used

with the NBS electron linac. Adjacent to the target was a l/16”-thick cadmium

sheet with a **V" cutout. In the experiment the low-energy (E <0.3 eV) neutrons

emerging from the V were imaged. To image the V we placed a l/16"-thick cadmium

sheet, containing a 2-mm diameter hole in the center, at a flight distance of 4

meters from the neutron target. A one -dimensional PSPC was placed horizontally

at 4.5 meters and could be remotely positioned in the vertical direction. The

PSPC, designed and built in collaboration with the Instrumentation and Control

Division of ORNL, had a sensitive length of 50 mm and a spatial resolution of

'^ 1.2 mm. The results of this measurement were presented at the June 1980 ANS

meeting in Las Vegas, Nevada.

In Figure 5 the results are shown. A total of nine horizontal slices were

required to image the V. The circle in Figure 5 represents the field-of-view

imposed by our flight path collimation. The pixel size and the resolution are also indicated.

Calculations were carried out to determine the degree of non-homogeneity

of an absorber that can exist within a pixel without degradation of assay accuracy.

The ability to tolerate greater pixel inhomogeneity allows quicker measurements

because larger areas can be covered in a single measurement. The computer

calculations have shown that inhomogeneities in sample thickness that would

cause large errors in assay of constituents can be compensated for and the

error reduced by a factor of about 20 by shape analysis of the resonance line

in the absorption spectrum. With this philosophy in mind, two samples of spent

fuel have been measured treating the whole 1-cm diameter slice of fuel as one analysis area. Analysis of the data is now underway, but a cursory examination

shows quite obvious differences in isotopic composition between the two samples.

The two samples are from the same fuel rod. One sample is taken from the end of

the rod where the neutron flux is relatively low, and one cut is taken from the

center of the rod where the neutron flux is greater. It is clear that the

transuranic isotope buildup is greater in the center cut and, conversely, the

depletion of the is less on the end cut. This technique should be a valuable tool in spent fuel analysis for the safeguards program to determine

reactor history and fuel rod composition.

9
Fig. 4. Experimental arrangement for neutron pin-hole camera

COLLIMAl

PIXEL RESOLUTION

Fig. 5. Pin-hole camera image of the "V” obtained

with low-energy neutrons

10
A different type of two-dimensional detector has been developed in cooperation with Surface Science Corporation. A small detector about 2.5 cm in diameter,

having a resolution of about 0.1 mm, has been developed that utilizes a multichannel plate electron amplifier. Plans for testing the device are now underway.

The following papers were written during this fiscal year:

J. W. Behrens, R. A. Schrack, A. D. Carlson, and C. D. Bowman, "Resonance

Neutron Radiography for Nondestructive Evaluation and Assay Applications", presented at Conf. on Nuclear Cross Sections for Technology, Univ. of Tenn.,

Knoxville, TN, Oct. 22-26, 1979, Proceedings published as NBS Special Publication 594, September 1980.

R. A. Schrack, J. W. Behrens, C. D. Bowman, and A. D. Carlson, "Safeguards

Reference Measurement System Utilizing Resonance Neutron Radiography", presented

at Conf. on Measurement Techniques for Safeguards and Materials Control, Kiawah

Island, SC, Nov. 26-30, 1979, NBS Special Publication 582, June 1980.

J. W. Behrens, R. A. Schrack, and C. D. Bowman, "Nondestructive Examination

of a Defective Silver Braze Using Resonance-Neutron Radiography", Nuclear

Technology 51 , No. 1, pp. 78-82, November 1980.

The investigators for this portion of the Sub-Task are R. A. Schrack, J. W, Behrens,

A. D. Carlson, C. D. Bowman and R. G. Johnson.

Resonance Neutron Tomography

The effort on the resonance neutron tomography portion of this Sub-Task during

FY 1980 was devoted to two areas: (1) the continuing development of software

programming and the library data set; and (2) the finalizing of the design of

the reactor-based resonance neutron safeguards experimental system and the making

of provisions for its use. The major effort was concentrated on the second area.

In the first area, a mathematical analysis has been conducted and a computer

code v/ritten for solving multiple non-linear equations relating fission detector

response to fissile sample thickness. The cross-section data library has been

further upgraded; this has helped to improve the sensitivity for the self-indication

effect.

The detail design of the reactor-based resonance neutron safeguard experimental system was completed in April and has been approved by the NBS Reactor

Hazards Evaluation Committee. The NBS Shops Division is responsible for the

construction of the system and the letting of bids to private contractors.

Three U-235 fuel pellets of different enrichments were acquired and are being

fabricated into 1-mm thick discs for use in the initial resonance neutron transmission experiments. An experiment is scheduled in early September to utilize

these discs to verify and implement our theoretical predictions.

In addition, glovebox provisions are being made to the SRM Shop to permit

the handling of SRM U 3 O 8 powders of various enrichments for the fabrication of

transmission cells.

In order to verify the resonance neutron self-indication effect with the NBS

reactor facility, an experiment was conducted to quantitatively determine the U-235

and U-238 contents in three nuclear fuel pellets supplied by General Electric

Wilmington Manufacturing Department. The known information is in Table 3.

11
Table 3

Knovm Characteristics of Three Nuclear Fuel Pellets

Supplied by General Electric Wilmington Manufacturing Department

Isotopic U-235

^ y enrichment %°

3.9572 88.15

2.5174 88.168

1.194 88.14

Density Length

95.9243 0.432"

96.56 0.4395"

95.52 0.434"

Diameter

0.410"

0.410"

0.410"

A horizontal neutron beam of 1/4" (0.635 cm) -diameter was extracted from

the NBSR core on port BT-7. The thermal neutron portion of the beam was removed

by using a 0.04" (0.102 cm) -thick Cd sheet as filter. The filtered beam was then transmitted through the fuel pellet and detected by NBS double fission

ionization chamber detectors [Grundl, J. A., Gilliam, D. M., Dudey, N. D., and

Dopek, R. J., Nuclear Technology 25, 237 (1975)].

The experimental setup and fuel pellet holder are shown in Figure 6. The

holder was made with a lucite block approximately 15 cm long, 5 cm wide and 1 cm

thick. Four holes were drilled to accommodate the three fuel pellets and a blank

reference hole. The three fuel pellets, along with the blank hole, were scanned

by the neutron beam and detected with U-235, Pu-239 double fission chamber detectors and then with U-235, U-233 detectors. The reason for using Pu-239 and

U-233 detectors was that the fission cross section for U-238 was very small. A

count rate of > 1000 cps was obtained using very thin fission foil in all detectors,

thus no corrections were made for detector dead- time, self-absorptions, and background noise. A total count of > 50,000 was accumulated for each data point.

Table 4 lists the measured U-235 and U-238 contents in grams in the third

pellet as compared to the known quantities.

Table 4

Measured U-235 and U-238 Contents, in Grams,

in the Third Pellet as Compared

to the Known Quantities

Known Measured with Measured with

quantities* U-235, Pu-239 detectors** U-233, U-235 detectors**

U-235 0.2174 0.185 0.03 0.193^^0.03

U-238 5.2764 5.581 + 0.05 5.476 + 0.49

*Corrected for 1/4" neutron beam size.

**Errors were estimated second order effects.

The measured U-235 content in the third pellet is about 11% of the known

U-235 quantity when the U-233 and U-235 detectors set are used, and about 15%

with the U-235, Pu-239 set. The accuracies for the measured U-238 content in

the third pellet are 4% and 6%, respectively, for the two sets of detectors.

12
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13
The fact, that all neutrons with energies below 0.5 eV were filtered out in the

beam caused the Pu-239 detector to perform less satisfactorily relative to

U-233 and U-235 detectors, since 60% of the resonance strength for Pu-239 lies

in the 0.3 eV region. Nevertheless, the results indicate that a reasonably

accurate estimation of U-235 and U-238 contents can be obtained in a very short

time (< 1 min.) with the self-indication method with counting statistics of 0.1%.

In summary, it would require approximately one day to characterize a nuclear

waste container approximately the size of a gallon paint can for use as a reference material or to verify field methods. This conclusion asstimes that it

would require 110,000 transmission measurements with a resolution of 4 mm and 3%

counting statistics. The assumption is made that the container will be scanned

at 64 points in a plane orthogonal to its axis. The container will be rotated in

two-degree increments following each orthogonal 64-point scan. Following each

complete 180® rotation cycle, the container will be stepped axially and the process

repeated for a total of 20. The amount of time needed for the entire interrogation,

together with resolution and counting statistics, can be greatly improved by incorporating a linear series of detectors and a reactor power of 20 MW.

The investigators for this portion of the Sub-Task are D. A. Garrett, Y. T. Cheng,

and M. Ganoczy.

TASK II: STANDARDIZATION OF DESTRUCTIVE ANALYTICAL CHEMISTRY

METHODOLOGY FOR NUCLEAR MATERIALS

The goal of the Destructive Analytical Chemistry Task is to provide standardization for wet chemical and mass spectrometric methodology used for the assay of

nuclear materials. This Task is divided into two Sub-Tasks: A - Standard

Reference Material (SRM) Research and Reference Methodology; and B - Support

of Measurement Assurance Programs (MAPs)

Sub -Task A : SRM Research and Reference Methodology

The goal of this Sub-Task is certification of a ^^^U "spike” SRM for both

uranium elemental concentration and isotopic composition. This material is

intended as a spike for mass spectrometric determination of the isotopic and

elemental composition of uranium in the full range of materials found in the

nuclear fuel cycle. With this material, a single analysis can be used to obtain

both the elemental concentration and the isotopic composition of uranium.

Approximately 400 ampoules of the ^^^U "spike", SRM 995, were prepared con- taining 5 mg U in 10 mL of HNO3 (1 + 19). Before ampouling, the uranium was purified by anion exchange chromatography to remove ^^®Th and other daughter

products. All analytical measurements and an extensive statistical evaluation

of the SRM were completed.

The concentration of uranium in the ampoules of the SRM were determined by

thermal ionization isotope dilution mass spectrometry following a sampling plan

supplied by the NBS Center for Applied Mathematics: eight ampoules were chosen

for use in the assay of the SRM. Separate aliquots from each of the ampoules were spiked with known amounts of ^^^U (SRM 993) and uranium metal (SRM 960, assay

standard). In addition, eight aliquots of SRM 993 were spiked with SRM 960 as a cross-check on the assay of these materials. Thus, all three SRMs have been

assayed against each other.

14
The statistical design of the experiment allowed for the assessment of

the following parameters: ampoule-to-ampoule variations among the

samples, sample-to-sample variations among the and natural uranium metal

spikes, inconsistency in the concentration previously assigned to the

spike SRM, and finally the measurement error in the concentration of the

spike SRM. No ampoule-to-ampoule or sample-to-sample variations were detected

from the statistical evaluation of the data. The concentration of spike

(SRM 995) was found to be 489.93 yg U/g with an uncertainty at the 99% confidence

interval of ^0.037%. This uncertainty can be divided into a 0.011% random error

component and a ^0.026% possible systematic error. The isotopic composition of

SRM 995 was also determined mass spectrometrically using both Faraday cage and

ion counting detection systems. The content of the SRM was found to be

99.9245 _+ 0.0006 atom percent.

One member of the NBS staff visited the New Brunswick Laboratory, Argonne,

Illinois, for the purpose of observing their methods for small sample assays of

uranium. It is a goal of the NBS laboratory to try to determine uranium (assay)

at a very small sample size while retaining as much of the accuracy as possible.

Certification of the absolute isotopic composition of uranium SRMs requires the

mixing of pure separated isotopes to produce calibration standards of known

isotopic composition. High accuracy assay techniques for small samples are needed to minimize the irreversible use of high purity uranium separated isotopes. The NBL laboratories have been routinely analyzing 50 mg samples of

uranium with a precision of _+0.05% or better. Preliminary studies at NBS indicate

that the titration itself may yield precisions of j^O.01% at a sample level of 50 mg.

A visit was made also to the Central Bureau of Nuclear Measurements in Geel,

Belgium, where experiments on the use of the Davies-Gray titration method in the

assay of small uranium samples are being carried out. In this laboratory, 250-

300 mg samples were being titrated to an automated end point with a precision of

0.01%. A contributing factor to this improved precision was a higher purity of

starting material.

With the arrival of a printing digital pH meter, some efforts have been

made to scale down the Davies-Gray titration. At a level corresponding to 100 mg

of U metal, it is possible to titrate dichromate manually to a precision of better

than ^0.01%. The dichromate titration itself may be useful at a level equivalent

to 10 mg uranium. Future experiments will center around miniaturizing the DaviesGray chemistry to these levels while retaining as much precision as possible.

Sub-Task B : Support of Measurement Assurance Programs

High precision and high accuracy measurements are made at NBS to support

MAPs by providing the "true value" for uranium elemental concentration and

isotopic composition of reference samples distributed in selected national and

international evaluation programs.

Atomic weights of depleted and enriched SALE samples were computed based upon

the isotopic analysis of these materials completed by the mass spectrometry group.

Using the calculated value for the depleted SALE sample, the correct assay values

for the depleted SALE samples were calculated. The results previously reported

were based upon a natural uranium atomic weight and were subject to revision

pending the true atomic weight calculation.

15
The assay of the enriched SALE samples was determined and reported based

upon the NBS calculated atomic weights. During these assays, a major problem

was found with contamination of the sample from beakers previously used for

other uranium assays. A procedure was developed to positively control the

uraniiam blank problem.

The investigators for this Task are J. D. Fassett, E. L. Gamer, J. W. Gramlich,

H. M. Kingston, L. A. Machlan and J. R. Moody.

TASK III: STANDARDIZATION OF BULK MEASUREMENT METHODOLOGY

IN NUCLEAR FUEL CYCLE PLANTS

This Task provides standardization for bulk measurements (mass, volume,

density, flow, pressure and temperature) of nuclear fuels. Bulk measurements

play a very important role in the accountability of SNM and in the safeguarding of SNM against diversion. The standardization provided by this Task will

assist inspectors and licensees in implementing efficient measurement systems

and will allow licensees and inspectors to make the measurements traceable to

national standards.

Sub -Task A : Process Tank Volume Measurements Standardization

The final testing on the automated tank calibration apparatus was completed.

The final report on the development and testing of the apparatus was presented at

the American Nuclear Society Topical Conference on Measurement Technology for

Safeguards and Material Control, Kiawah Island, South Carolina, November 26-29,

1979 ("Automated Accountability Tank Calibration", by D. Cooper, P. Baumgarten

and B. Robertson). The apparatus has been moved to the scale house at NBS in

preparation for demonstration of its use (in the first quarter of FY 81) in

calibrating a 3000- liter tank which had previously been calibrated using volumetric test measures.

A paper, "In-Tank Measurement of Solution Density", by F. E. Jones, R. M.

Schoonover and J. F. Houser, was presented at the Kiawah Island meeting. A

modified version of the paper appeared in J. Res. Nat. Bur. Stand. (U.S.) 85 , No. 3, May-June 1980 (219-221).

Two papers are undergoing editorial review. These relate to volume calibration of tanks using bubbler tubes. The titles for the two papers are:

(1) Time Dependence of Pressure in a Bubbler Tube; and (2) The Dependence of

Pressure in a Bubbler Tube on Liquid Properties. A. Gaigalas and B. Robertson

are the authors of the first paper, and A. Gaigalas is the author of the second.

Sub -Task B : UFe Mass Measurement Implementation Program

The objective of this Sub-Task is the improvement of in-facility weighing

of large UFe cylinders. The effort involves the implementation of a Measurement

Assurance Program (MAP) for the measurement of the mass of UFe cylinders, filled

with UFe or empty. The MAP provides continually verifiable evidence of performance of the mass measurement process, giving timely and quantitative uncertainty

statements for the mass measurements.

16
A draft Standard Operating Procedure was sent to participating organizations

for comment.

The 308 Replica Mass Standard (RMS) was first shipped to Oak Ridge to be

used in calibrating the Oak Ridge In-House Standards. The RMS cylinder was then

shipped from Oak Ridge to the General Electric Co. (G.E.) facility at Wilmington,

NC, where it was used to recalibrate the G.E. In-House Standards, and then on to

the Combustion Engineering Co. facility at Hematite, MO, and used to calibrate

In-House Standards. The measurement data were sent to NBS for analysis.

The investigators for this Task are J. R. Whetstone, D. G. Cooper, G. P. Baumgarten,

B. Robertson, A. K. Gaigalas, J. F. Houser, and E. Johnsen.

TASK IV: APPLIED MATHEMATICS FOR NUCLEAR SAFEGUARDS

This Task applies mathematics and statistics to the nuclear safeguards

mission of NRC. The work in this Task consists of the preparation and publication of reports in five specific areas (Sub-Task A) , and statistical support for

other nuclear safeguards Tasks (Sub-Task B)

.

Sub-Task A : Statistical Methods in Nuclear Material Accounting

Assessing Errors Related to Characteristics of the Items Measured . A paper,

"Assessing Errors Related to Characteristics of the Items Measured", by W. S.

Liggett, appeared in Nuclear Materials Management IX, No. 1, 78-82 (1980). This

paper (Report #1 of this Sub-Task) presents some problems in safeguards measurements that require further research. The abstract for the paper follows:

Errors that are related to some intrinsic property of the items

measured are often encountered in nuclear material accounting.

An example is the error in nondestructive assay (NDA) measurements caused by uncorrected matrix effects. Such errors cannot

be assessed by remeasurement of the items, and they cannot be

fully assessed by measuring standards, although standards that

span the range of the item characteristics might give upper and

lower bounds. Nuclear material accoimting requires for each

material type one measurement method for which bounds on these errors can be determined. If such a method is available, a second method might be used to reduce costs or to improve precision.

If the second method is less expensive than the first, then

cost might be reduced by substituting the second method for

the first in the measurement of some items. If the measurement

error for the first method is longer-tailed than Gaussian, then

precision might be improved by measuring all items by both methods.

Some Effective Statistical Approaches for Presenting Interlaboratory NDA

Enrichment Measurements . In order to realistically evaluate measurements on prototype and primary standards measured by several different nondestructive

assay (NDA) labs, it is necessary to distinguish real differences between

laboratory findings and artificial differences, such as those caused by artifacts of peak area calculations. The first draft of Report #2 of this Sub-Task,

"Empirically Calculated Weights for Finding Peak Areas in Gamma Spectroscopy",

17
by C. Spiegelman, provides guidance for locating and assessing the magnitude

of these peak area artifacts. In particular, it provides a variety of algorithms for linear peak area computations which make the standards appear either

most or least homogeneous under a variety of statistical criteria. The criteria

include the usual F statistics, as well as the standardized range.

Robust Inference for Items Measured a Few Times . Estimation methods that

de-emphasize the measurements that appear to be most in error offer the possibility of improved performance. This possibility, which occurs when the

measurement error is non-Gaussian, is explored for some measurement designs

not covered by previous work on robust methods. In these designs, each item in

a collection of somewhat dissimilar items is to be measured two or three times,

and the total for the entire collection is to be estimated. The methods are based on the assiimption that the measurement errors for different items are from the same population. A method is proposed for each of three cases: three

replicate measurements on each item, two replicate measurements by one method

and one measurement by another method on each item, and two replicate measurements on each item. All the methods use the differences between the measurements

on the same item to obtain a scale estimate by which the size of the measurement

errors is judged. How the methods adjust the measurements differs from case to

case. When there are three measurements per item, the most dissimilar of the

three is downweighted. When there are only two measurements per item, the measurements for the entire collection are used to judge which measurements to

downweight. The methods include estimates of the uncertainty due to measurement

error, which are also obtained from the differences between the measurements on the same item. A report discussing these methods will be Report #3 of this SubTask.

The following is a preliminary abstract of Report #4 of this Sub-Task, which

is in preparation:

Inventory Difference Calculations: Problems and Possibilities . The origin,

development, and termination of the "error study" task funded by the Nuclear

Regulatory Commission at the National Bureau of Standards is presented in this

report. Other reports which grew (at least partially) out of this study are listed and related to the intent of this study.

A general approach to the calculation of Inventory Difference (ID) and its

Limit of Error (LEID) was devised and refined through visits to a selected fuelfabrication facility. This approach is discussed, with emphasis on the importance

of having measurements "under control" and on the possibility of automating the

computations. The concepts of "measurement process" and "Measurement Assurance

Program" are also discussed and their importance shown. Possible problem areas,

both those observed at the studied facility and others, are given, along with

possible directions for resolution. Finally, new approaches to the calculation

of ID and LEID being developed elsehwere are described and their relation to the

approach being considered herein elucidated.

The following is the abstract of a report which is available as NBSIR 80-2151,

and which has been submitted for publication in Technometrics:

A New Method of Assigning Uncertainty in Volume Calibration . This paper

presents a practical statistical overview of the pres sure -volume calibration

curve for large nuclear materials processing tanks. It explains the appropriateness of applying splines (piecewise polynomials) to this curve, and it presents

an overview of the associated statistical uncertainties. In order to implement

these procedures, a practical and portable FORTRAN IV program is provided, along

18
with its users’ manual. Finally, the recommended procedure is demonstrated on actual tank data collected by NBS.

The work with ASTM C26.06, the subcommittee on statistics of the committee

on the Nuclear Fuel Cycle, included assumption of the chairmanship of the

subcommittee by an NBS staff member. Two meetings were held to revise the

draft standard on sampling nuclear materials in preparation for the July subcommittee meeting. At a meeting at Kiawah Island, SC, November 28-30, contributions were made to the revision of ANSI Standard N-15. 22-1975 , Calibration

Techniques for Calorimetric Assay. Also, one staff member participated in the

November 1979 meeting of the SALE Program Executive Committee and the general

meeting of the participants.

Sub -Task B : Statistical Support for Other NBS Safeguards Tasks

Consultation, including two trips to Geel, Belgium, and preparation of an experimental design for the mass spectrometer measurements, was provided in

support of the U 3 O 0 SRM.

Mass spectrometer measurements on the SRM were analyzed, and the

results were presented for inclusion on the SRM certificate.

Analysis of the first set of data from the UFe cylinder Mass Measurement

Assurance Program was accomplished.

Investigators for this Task are W. S. Liggett, J. A. Lechner, and C. Spiegelman.

TASK V; USERS GUIDE, FACILITY ENGINEERING FOR

SAFEGUARDS MEASUREMENT INSTRUMENTS

The primary objective of the Users Guide is to provide specific recommendations on how facilities should be designed to accommodate the necessary measurements to meet the SNM accountability goals of the safeguards program. The Guide

will discuss how the measurement instruments and accountability systems should be

installed and will outline the supporting services required. The Guide will also

discuss facility design considerations so that the instruments can be efficiently

calibrated, operated and repaired, either manually or remotely.

The preliminary draft of the Guide, which was completed during the previous

fiscal year, was revised to reflect certain directives from the NRC. Discussions

were held with the persons at Mound Laboratories who are preparing a Handbook of

Nuclear Safeguards Measurement Methods . The purpose of these discussions was to assure that the two documents would be complementary.

The first rough draft of the Guide was completed and copies sent to con- tributors for comment and/or correction. In its draft form, the document had

a length of approximately 18,000 words.

After the cut-off date for comments. May 30, 1980, the Guide was rewritten

into its final form. It is now undergoing editorial review.

The investigator for this Task is E. Johnsen.

19
NBS-K4A (REV. 2«eo) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publication Date REPORT NO.

NBSIR 81- 2236 NBSIR 81- 2236 1981

4.

TITLE AND SUBTITLE

Measurements and Standards for Nuclear Materials Safeguards

5.

AUTHOR(S)

B. Stephen Carpenter and Frank E. Jones, Editors

6.

PERFORMING ORGANIZATION (If joint or other than NBS. see fnstruct/onsj 7. Contract/Grant No. national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

NRC AT(49-25)-9009

8. Type of Report & Period Covered

Annual/FY 1980

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Division of Siting, Health and Safeguards Standards

Safeguards Standards Branch, Office of Standards Development

U.S. Nuclear Regulatory Commission, Washington, DC 20555

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

This report is a review of the progress made during Fiscal Year 1980 (October 1,

1979, through September 30, 1980) of a long-term NBS program sponsored by the Nuclear

Regulatory Commission (NRC) to upgrade national measurements and standards capability

for nuclear materials safeguards. This is the last report to NRC for this program,

since NRC has terminated support to NBS as of September 30, 1980. The NRC-sponsored

program at NBS was a synergistic part of the overall NBS program in this area which

is sponsored jointly by the NRC, the Department of Energy (DOE), and the Department

of State through the International Safeguards Project Office (ISPO) . A summary of

the progress for each of the five NRC-supported Tasks in the project is given. The

first Task is concerned with the standardization of Non-Destructive Assay (NDA)

methodology. The second Task involves the standardization of analytical chemical

methodology. The third Task involves the standardization of bulk measurement technology. The fourth Task applies mathematics and statistics to nuclear safeguards.

The fifth Task involves the development of a Users Guide to provide specific recom- mendations on how facilities should be designed to accommodate the necessary measurements to meet the SNM accountability goals of the safeguards program.

t 12. KEY WORDS (S/x to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

analytical chemistry; annual report; bulk measurements; facility measurements guide;

non-destructive assay; Nuclear Regulatory Commission; nuclear safeguards; standards;

statistical support

'13. AVAILABILITY 14. NO. OF

PRINTED PAGES

[TQ Unlimited

[ 1 For Official Distribution. Do Not Release to NTIS

1 1 Order From Superintendent of Documents, U.S, Government Printing Office, Washington, D.C. 20402.

20

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