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i-6713(XC-14 REPORT COLLECTION

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NRC-3

>cay Heat from Products of 235UThermal Fission

by Fast-Response Boil-Off Calorimetry

Issued: September 1977

“)● scientific laboratory

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d LOS ALAMOS, NEW MEXICO 87545

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An Affirmative Action/Equal Opportunity Employet

UNITED STATESENERGY REsEARCH ANO DEvELOPMENT ADMINISTRATION

CONTRACT W-7405 -ENG. 36

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Printedin the United States of America. AvailablefromNationalTechnicalInformationServics

U.S. Departmentof Commerce5285 PortRoyal RoadSpringtleld,VA 22161

Price: PrintedCopy $4.00 Microfiche$3.00

NOTICEThis reportwas preparedas an account of work sponsoredby the UnitedStatesGovernment.Neitherthe UnitedStates nor the

United States Nuclear Regulatory Commission,nor any of their employees, nor any of their contractors,subcontractors,ortheir employees, makes any warranty,express or implied, or assumes any legal liability or responsibility for the accuracy,completeness or usefulness of any information, apparatus,product or process disclosed, or representsthat its usc would notinfringeprivatelyowned rights.

●

✎

10 Iamos

LA-NUREG-6713NRC-3

scientific laboratoryof the University of California

LOS ALAMOS, NEW MEXICO 87S45

Decay Heat from Products of 235UThermal Fission

by Fast-Response Boil-Off Calorimetry

J. L. YarnellP. J. Bendt

I

Manuscriptcompleted: February 1977Issued: September 1977

Prepared for the US Nuclear Regulatory CommissionOffice of Nuclear Regulatory Research

.

●

DECAY HEAT FROM PRODUCI’S OF ‘“’U THERMAL FISSIONBY FAST-RESPONSE BOIL-OFF CALORIMETRY

by

J. L. Yarnell and P. J. Bendt

ABSTRACT

A cryogenic boil-off calorimeter was used to measure the decay heat fromthe products of thermal-neutron-induced fission of 28’U.Data are presentedfor cooling times between 10and 106s following a 2 x lWs irradiation at con-stant thermal-neutron flux. The experimental uncertainty (1 u) in thesemeasurements was = 29o, except at the shortest cooling times where it roseto = 4%. The beta and gamma energy from an irradiated 28’Usample wasabsorbed in a thermally isolated 52-kg copper block that was held at 4 K byan internal liquid helium reservoir. The absorbed energy evaporated liquidhelium from the reservoir and a hot-film anemometer flowmeter recordedthe evolution rate of the boil-off gas. The decay heat was calculated from thegas-flow rate using the heat of vaporization of helium. The calorimeter hada thermal time constant of 0.85s. The energy loss caused by gamma leakagefrom the absorber was s 3?7.; a correction was made by Monte Carlocalculations based on experimentally determined gamma spectra.

The data agree within the combined uncertainties with summationcalculations using the ENDF/B-IV data base. The experimental data werecombined with summation calculations to give the decay heat for White(101’ s) irradiation. For short cooling times, the results are = 7?%below thecurrent American Nuclear Society (ANS) standard. The uncertainty inthese results is significantly smaller than that assigned to the standard.

———. —._ — ____________

I. INTRODUCI’ION

This report describes calorimetric measurementsof the total decay heat from the products of thermal-neutron-induced fission of 2S6U.Data are presentedfor cooling times between 10 and I(Y s following a2 x 104 s irradiation at constant thermal-neutronflux. The experimental uncertainty (1 u) in thesemeasurements was = 2Y0, except at the shortestcooling times where it rose to = 4’%0.

This work was carried out at the Los AlamosScientific Laboratory (LASL) as part of a programsponsored by the U.S. Nuclear Regulatory Commis-sion (NRC) to provide better values and reduced un-certainties for the decay heat source term for use inreactor safety evaluations and, in particular, foranalysis of the Loss-of-Coolant Accident (LOCA).

There have been many measurements of decayheat. Unfortunately, there is considerable scatter in

1

the results of individual experiments. (See, for ex-ample, the review by Perry, Maienschein, andVondy.’) The present American Nuclear Society(ANS) Decay Heat Standardz reflects the state ofknowledge when it was prepared by specifying anuncertainty band of +20Y0, –40Y0 for cooling times< IV s, which are important in LOCA analysis.

Calorimetric measurement have the advantagethat they are relatively simple and straightforward,require only minor corrections, and thus present aminimum opportunity for the introduction ofsystematic errors. Their disadvantages are that theyprovide only integral information (total decay heat,not beta and gamma spectra) and that, in general,they tend to have long time constanta.

Lott et al.’ have reported decay heat measure-ment made with a conduction calorimeter. Thethermal time constant of their apparatus was = 115s, and they estimate the uncertainty in their resultsto be = 5%. The shortest cooling time for which theycould measure decay heat was 70 s. When our ex-periments were undertaken, the results of Lott et al.were the best calorimetric measurements availablefor times pertinent to LOCA analysis.

Our measurements were carried out using acryogenic boil-off calorimeter. In this technique, thedecay heat evaporates a cryogen (in our case liquidhelium) and the evolution rate of the boil-off gas ismeasured with a flowmeter. Since the heat ofvaporization of helium is known, the amount ofdecay heat can be calculated from the boil-off rate,or the system can be calibrated by joule heating.

The idea of cryogenic boil-off calorimetry is notnew. It was first proposed by Sir James Dewar in1894.4 In 1904, Madame Curie reported its use tomeasure the decay heat of radium.a We chose thismethod because it gave us an opportunity todevelop a massive calorimeter with a short time con-

stant.This development involved the construction and

testing of a prototype calorimeter, as well asnumerous auxiliary measurements and calculations.A final model of the calorimeter was designed on thebasis of information thus obtained.’ It was tested ex-tensively to determine its characteristics and to op-timize experimental procedures. It had a thermalconstant of < 1 s, even though it contained a radia-tion absorber that weighed 52 kg. The short response

time was achieved by operating the calorimeter

2

nearly isothermally, and by taking advantage of thelarge decrease in the heat capacity of solids that oc-curs when the temperature is lowered to the boilingpoint of helium (4 IQ.

A preliminary report of our decay heat measure-ments was presented at the Fourth Water ReactorSafety Information Meeting in September 1976.7

II. EXPERIMENTAL DETAILS

A. Samples: Preparation, Irradiation,Transfer

In these measurements, samples of ‘“U

and

wereirradiated in a constant thermal-neutron flux of= 3 x 101’ n/cm* os. The irradiation time of2 x 104s was chosen to be long compared to the timesof greatest interest in LOCA analysis, yet shortenough to be compatible with the single-shift opera-tion of the Los Alamos Omega West Reactor (OWR).The OWR is an 8-MW, tank-type research reactorthat uses 93%-enriched uranium fuel with lightwater coolant and moderator.

To obtain decay heat data at short cooling times,the samples must be transferred to the calorimeterand coded to the temperature of liquid helium asrapidly as possible. In addition, they must producedecay heating rates commensurate with thedynamic range of the calorimeter (= 3400 to 70 mW)and must be provided with a cladding to prevent theloss of gaseous fission products during irradiationand transfer. (During the measurements, the sam-ples were at 4 K and all fission products were solids.)Using the samples and transfer system describedbelow, the samples reached the calorimeter = 1.5safter irradiation; cooldown was essentially complete3 s later.

The samples contained 33-mm-long by 5-mm-wide by 0.02-mm-thick uranium foils that weighed

= 60 mg. The isotopic composition of each foil was0.87 wt% “U, 93.19 wt’% ‘“U, 0.48 wt% ‘W, and5.46 wt% ‘W. The foils were placed in envelopes of0.127-mm-thick aluminum, which were then sealedby electron-beam welding. The completed sampleswere 39 mm long by 8 mm wide by 0.3 mm thick.They weighed = 300 mg. Aluminum was chosen forthe envelopes because of its minimum interference

4

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with the radiochemical procedures used to deter-mine the number of fissions in the sample. Toprovide good heat transfer between the uranium andaluminum, the uranium was electropolished beforebeing inserted in the envelopes, and the envelopeswere carefully flattened after sealing. The low massand large surface area of the samples promotedrapid cooldown when the samples were dropped intothe liquid helium in the calorimeter.

The envelopes were checked for external uraniumcontamination by alpha counting. They were leak-tested before use by immersing them in liquidhelium for 30 rein, followed by rapid warming toroom temperature. Samples that were tightremained flat, whereas those that leaked swelledbecause of the rapid expansion of the helium thatpenetrated the weld. We opened the defective sam-ples and placed the uranium foils in new envelopes.

A dart was used to transport the samples from theirradiation position near the core of the OWR to thesample release chamber above the calorimeter (seeFig. 1). At the start of irradiation, the dart (with en-cased sample) was pushed into position with a long,flexible plastic rod. At the end of the irradiation, thedart was ejected by pressurized helium gas. It tookonly a fraction of a second for the dart to reach andstick in a wooden target in the sample release cham-ber (a distance of = 5 m).

The dart was made of two pieces of aluminum,hinged at the forward end and tapered slightlytoward the rear. The sample was placed between thetwo pieces of the dart, which were held together byan outer steel sleeve. The sleeve was stripped off asthe dart entered the sample release chamber. Whenit struck the wooden target, the dart opened, releas-ing the sample. The sample then fell into a funnelwhere it was guided into a tube that led to the liquidhelium reservoir in the calorimeter.

The irradiation position in the OWR is shown inFig. 2. During an irradiation, the reactor power wascontrolled by a fission chamber adjacent to the sam-ple. The neutron flux at the sample position, whenaveraged over 10-s intervals, was constant to within+0. l% during the irradiation.

Water was circulated through a spiral channel inthe aluminum cylinder ( shown in Fig. 2) to removethe 70 W of fission heat that developed in theuranium foil as well as the gamma heat from thereactor environment. Helium gas circulated around

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Fig. 1.Sample, transport system (dart), and samplerelease chamber used for decay heat measure-ments. During irradiation, the sample is en-cased in the dart. At the end of the irradiation,the dart is blown into the release chumber,where the outer sleeve of the dart is strippedaway, and the sample is freed to fall into thecalorimeter.

the dart and transferred heat to the water-cooledcylinder. The exhaust helium gas passed through anactivated charcoal filter adjacent to a NaI(Tl)radiation detector, which was a sensitive and rapidmonitor of any radioactivity (fission-product gases)that escaped from the sample. Any leakage from asample was discovered within a few seconds afterthe start of irradiation, and the sample was ejectedimmediately into a standby shielded “pig.” All thetubes leading into the reactor port were spiraledaround graphite and brass forms to reduce radiationleakage from the port during the irradiation.

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Fig. 2.Facility used for sample irradiation. The fac;lity is located in one of the 152-mm-diam portsof the 8-M W O WR. The port walls are made of aluminum. The fission chamber a~acent tothe sample was used to control the reactor power during irradiation.

In the neutron spectrum at the irradiation posi-tion, the fission rate per unit mass was determinedexperimentally to be = 10’ times smaller for ‘W

than it was for ‘W. Since the samples containedz 6% ‘aW, the fraction of the fissions that occurredin ZS8Uwas = O.wOA. We calculate that under the

experimental conditions, contributions to themeasured decay heat from neutron capture in fis-sion products and from production of aaW and 2a0Npalso were negligible.

B. Calorimeter and Auxiliary Apparatus

The main features of the calorimeter are shown inFig. 3. The copper Mock, which absorbed z 97% of

4

the radiation energy emitted by the sample, was177.8 mm in diameter, 298.5 mm high, and weighed52.008 kg. The reservoir in the top of the block wasfilled with 1.2 liters of liquid helium. The block wassuspended in vacuum by means of a 10-mm-i.d.thin-wall stainless steel tube that was used totransport the boil-off gas to a flowmeter at roomtemperature. The tube was also used to insert andremove the samples and to transfer the liquidhelium to the reservoir.

To provide a source of electric heating for calibra-tion and testing, a 196-Q coil of Manganin wire waswound in a groove 10 mm from the bottom of theblock. The groove was then filled with Stycast

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Inner wall‘of dewar

Active portion of the boil-off calorimeter.Radiution from the sample was absorbed in thecopper block and was used to evaporate liquidhelium from the reservoir in the top of theblock. Heat leak into the copper block wasprevented by the vacuum jacket and the outerhelium bath.

28501W epoxy* to ensure good thermal contact be-tween the wire and the block. A copper band waspressed over the Mock in the groove area so that thecoil was completely surrounded by copper. This wasdone to ensure that all of the energy produced in thecoil was transferred to the block and none wasradiated directly to the surroundings.

Not shown in Fig. 3 area liquid helium level sen-sor and a germanium resistance thermometer

(GeRT) in the reservoir, and three GeRTs attachedto the block. The GeRTs could detect temperature

changes of 1 mK and had an absolute accuracy of= 5 mK.———‘Manufactured by Emerson and Cuming, Inc., Canton, MA02021.

ToP Of ;j~caltwlmaler

Fig. 4.Upper portion of the boil-off calorimeter show-ing the piping used to transport the boil-off gasto the flowmeter. The ball valve was openedbriefly to permit entry of the sample. Thehelium purge gas and sweep gas prevent airfrom entering the boil-off gas stream.

To prevent heat leak, a copper vacuum jacket im-mersed in an outer liquid helium bath surroundedthe calorimeter block. A commercial liquid-nitrogen-jacketed dewar contained the entireassembly. A level sensor was provided for the outerhelium bath. All electrical leads reaching thecalorimeter block passed through the outer heliumbath, which intercepted heat conducted along theleads from warmer regions.

The calorimeter was assembled by high-temperature brazing in a hydrogen furnace. The up-per portion of the calorimeter system is shown inFig. 4. The irradiated samples fell from the samplerelease chamber into the calorimeter through aremotely operated ball valve. When the ball valvewas closed, the boil-off gas passed through a fast-response flowmeter and was discharged to the at-mosphere. To keep air from entering the system,helium purge gas was injected above the ball valvebefore and during the time it was open, and a cons-tant small flow of helium sweep gas was injecteddownstream of the flowmeter. (Air contamination ofthe boil-off gas would cause incorrect flowmeterreadings.)

The outer helium bath was kept at 15 torr aboveatmospheric pressure by venting it through a bub-bler. This raised its temperature 25 mK above the

5

boiling point of the liquid helium in the reservoir(which was within 1 torr of atmospheric pressure)and prevented the boil-off gas from condensing onthe tube walls after it left the reservoir.

The helium that was evaporated was warmed toroom temperature in a controlled manner. Althoughthe flowmeter was temperature compensated, wefound the accuracy of the flow measurements couldbe improved if the boil-off gas from the calorimeterwas warmed to the temperature at which the flow-meter had been calibrated, The significant precau-tion about warming the helium gas from thecalorimeter was to minimize changes in the tem-perature distribution along the gas transport tube,since such changes varied the gas storage in the tubeand thereby distorted the time profile of the gas flowrate. This precaution was especially important atlow temperatures where the gas density was high.We have dealt with this problem by having long sec-tions of tubing at fixed temperatures and byminimizing the volume of the lengths of tubing be-tween fixed temperatures.

After leaving the copper block, the boil-off vaporfirst flowed through tubing that had good thermalcontact with the outer helium reservoir (Fig. 3). Thevapor next passed through a short length of thin-wall tubing in vacuum, then through a long tube inthermal contact with a liquid nitrogen bath, whichraised the helium temperature above the criticalpoint. The liquid nitrogen was stirred by convectiongenerated by a 20-W heater, which also replacedheat removed by the flowing helium gas, so thatnitrogen was not solidified on the outside surface ofthe gas transport tube. When the helium gasreached the top of the cryostat, it flowed through ahorizontal heat exchanger (see Fig. 4). Water flowedat 4.5 liters/rein at a constant 27°C through theouter jacket of the heat exchanger. The gas enteringthe flowmeter was at a constant 26.5”C. When theflowmeter was calibrated with helium from apressurized tank, using a pressure reducer and nee-dle valve, the bottled gas also flowed through theheat exchanger and emerged at the same tem-perature. The gas temperature was measured by athermocouple in the flow line, just beyond the flow-meter, and was displayed on a chart recorder.

The flowmeter was of the hot-film anemometertype* (Fig, 5). It was sensitive to mass flow and had

Smwr &mf.

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Tamp.C4mp.

Fig. 5.Details of the hot-film anemometer-type flow-meter. The feedback circuit maintaim the hat-film sen.sora corMant number of degrees abovethe temperature of the gas stream. The uottagerequired across the bridge to accomplish this isa measure of the mass flow through theflowmeter.

a time constant of= 1 ma. A smooth venturi placedin the gas-flow stream was designed so that the flowvelocity was uniform over the cross section of thethroat. A sensor, consisting of a platinum filmresistor on a quartz fiber, was located in the venturithroat. Heat was supplied to the film electricallyand removed by the flowing gas. A temperature-compensating resistor was placed downstream of thesensor. The sensor and compensating resistor formedtwo arms of a bridge; a feedback circuit varied the

voltage across the bridge to keep the difference be-tween the film temperature and the gas temperatureconstant (at = 225”C). Under these conditions, the

bridge voltage is represented approximately by theequation

W = A + B(T. - Tc)(pv)”” ,

“Manufactured by Therm o-Systems, Inc., St. Paul, MN 5511.?.

6

where A and B are constants, T. and Tg are the sen-sor and gas stream temperatures, respectively, p isthe gas density and v is its velocity, and l/n is an ex-ponent approximately equal to 1/2. The constantsdepend on the composition of the gas and on theconstruction of the flowmeter. This equation il-lustrates the nonlinear relation between the flow-meter output, V, and the mass flow, pv.

In our decay heat measurements, the bridgevoltage, the primary quantity recorded, wasconverted to heating rate by means of an experimen-tally determined calibration curve rather than bythe above equation. By using an electronic lineariz-ing circuit, the flowmeter also generates a signal ap-proximately linear in (pv). This signal was used tomonitor the progress of the measurements.However, we did not use the linearize output tocalculate any of the final results. The flowmeter wascustom designed to produce the minimum pressuredrop consistent with the required sensitivity. Tostabilize ita temperature, the flowmeter was en-closed in Styrofoam.

The instrumentation used to monitor thecalorimeter and record the flowmeter measurementsis shown as a block diagram in Fig, 6. The bridgevoltage from the mass flowmeter was converted to apulse train of variable frequency by a voltage-to-frequency (V/F) converter,* then counted by a 4096-channel Geoscience Digital Processor* * operated inthe multiscaler mode. In this mode, counts are ac-cumulated for a predetermined time in successivememory channels. During the firat 4095 s of coolingtime, we used l-s-wide channels; at longer times weused 10-s-wide channels. The digital processor had aquartz-crystal-controlled clock that provided thetime base for the measurements. The data were readout onto magnetic tape and processed in a digitalcomputer. Tests at the LASL electrical standardslaboratory showed that the linearity of the V/F con-verter was better than 0.02Y0. Its slewing rate of I&V/s was more than sufficient to follow the l-insresponse of the flowmeter.

The flowmeter output was recorded by three otherinstruments, in addition to the digital processor.The linear output was recorded on two strip chartrecorders, whose gains differed by a factor of 2, toextend the dynamic range. The bridge voltage, after

*Manufacturedby Hewlett Packard Co., Palo Alto, CA 94303.

“*Manut’actured by Geoscience Nuclear, Hamden, CT 06518.

being converted to a pulse train by a V/F converter,was counted by a frequency counter and printed on

paper tape. Also printed on the paper tape was-thetemperature (in millikelvin) of the copper block inthe calorimeter. The counting intervals for the fre-quency counter were determined precisely by an in-ternal quartz-crystal-controlled clock. Although the

printer introduced a dead time of e 0.1 s betweencounts, it caused no errors since the paper tape out-

put was not used for precise timing measurements.The voltage and current supplied to the electric

heater in the copper block during calibrationmeasurements were also converted to a pulse trainby a second V/F converter and printed on papertape. The current was recorded by measuring thevoltage drop across an external 10.004-$2 standardresistance. A transfer standard* provided 1.0000reference volts for calibrating the V/F converters.The temperature of the helium gas passing throughthe flowmeter was recorded continuously on a stripchart recorder. The liquid helium level sensors andGeRTs, shown in Fig. 6, were used in operating theliquid helium calorimeter. Several vacuum gauges,thermometers, gas flowmeters, and a helium leakdetector were also used.

A timing sequencer controlled the transfer of thesample from the irradiation position to thecalorimeter in a reproducible manner. Let t = t. bethe time that the signal to eject the dart was in-itiated, at the end of a 2 x 1(Y s irradiation. Atto – 20s, the flow of helium purge gas above the ballvalve was started and at tO— 5 s, the ball valve wasopened. At to – 0.5 s, the multiscaler was started(using 1-s time channels) so that the center of chan-nel Ooccurred at tO,the center of channel 1 occurredat k + 1 s, and so on. At to + 4s, the ball valve wasclosed. These times were chosen, after trying variouscombinations, because they minimized the distur-bance to the system that followed transfer of thesample. The flow of helium purge gas was set to avalue that had been shown previously to prevent ‘airfrom entering the system through the ball valve.

The fission chamber adjacent to the irradiationposition provided a convenient means of checkingthe timing. When the dart was being irradiated, itdepressed the flux at the fission chamber by e 4%.The 4% rise in fission chamber signal when the dart

●Manufactured by John Fluke Manufacturing Co., MountlakeTerrace, WA 98043.

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Fig. 6.Block diagram of instrumentation used to monitor the boil-off calorimeter and record decayheat data.

left the irradiation position provided an accurate in-dication of the end of the irradiation. The time in-terval between the start of the multiscaler and theend of the irradiation was found to be 0.65 + 0.02s;consequently, the center of the n’th 1-s time channelcorresponded to a cooling time of (n – O.15) s. Thiscorrect ion was applied when analyzing the data.

C. Performance of the Calorimeter

The calorimetric measurement was made asnearly isothermally as possible, in order that nearlyall the radiation energy deposited in the copper ab-sorber would evaporate liquid helium instead of be-ing stored in the form of thermal energy. Suchenergy storage lengthens the response time of thecalorimeter.

Since we had a two-phase system, the tem-perature of the liquid helium was dependent on the

pressure in the reservoir, and could be determinedfrom the saturated vapor-pressure curve,’ Withmaximum helium gas flow, the pressure drop alongthe transport tube and across the flowmeter is S 1torr, and, therefore, the liquid helium temperaturedoes not rise during the measurement by more than1.7 mK. [At one Los Alamos atmosphere (a 598torr), the liquid temperature is x 3.967 K.] The heatcapacity of the 1.2 liters of liquid helium in thereservoir at the start of a measurement was s 550J/K, so the maximum energy storage in the liquidhelium was N 1 J.

The heat capacity of the 52-kg copper block at 4 Kwas only 4.4 JfK, and since the maximum tem-perature rise of the block (measured with a GeRT)during a decay heat measurement was 40 mK,energy storage in the block was only 0.2 J.

The copper block which was made of well-annealed oxygen-free high-conductivity copper hada high thermal conductivity at 4 K. Measurement

.

,

8

with GeRTs located at the top and bottom of theblock indicated a temperature difference of <1 mKwhen 3000 mW was supplied by the heater coil andremoved by the evaporation of liquid helium. Thelarge thermal conductivity and low heat capacity at4 K resulted in a thermal diffusivity of >3000 cm2/sand a thermal time constant ofs 0.16s. (For com-parison, the diffiwivity at room temperature of thecopper block is N 1.1 cm2/s, and the time constant is>400 s.) We conclude that the temperature of thecopper block was uniform (within 1 mK) at alltimes.

The reservoir was made broad and shallow to in-crease the copper-liquid surface area and to reducethe maximum liquid depth above the shelf in thereservoir (56 mm). The 40 mK temperature rise ofthe copper block is the AT necessary to transfers 3 W across the copper-liquid interface. Convec-tion currents in the liquid helium, initiated by ther-

mal cooling of the irradiated sample, provided rapidheat transport to the liquid-vapor interface. We ob-served superheating of the liquid helium only whenit was quiescent. Dropping a thermally hot (x 380K) irradiated sample into the calorimeter alwaysprovided sufficient disturbance to eliminatesuperheating.

When it first evaporated, the helium vapor was atthe same temperature as the liquid; the reservoirwalls however were slightly warmer. Because a smallamount of heat flowed directly into the vapor in-stead of into the liquid, it was not recordedby the flowmeter measurement. The maximumpossible error was (CPAT)/L, where CP was the heatcapacity of the vapor, AT was the temperature riseof the copper block, and L was the latent heat ofevaporation. During decay heat measurements,when the AT was at its maximum value of 40 mK,the maximum possible correction was 1.6~0.However, the actual correction was much smallerbecause of inefficient heat transfer to the vapor. Af-ter calculating the heat transfer by two approximatemethods, we concluded that the correction wasS ().s~o. This was confumed by the good agree-ment between calibration curves, determined fromaccurate knowledge of gas flow and latent heat(which were subject to the correction), and calibra-tions based on electric heating (which automaticallyincluded the correction ).

The heat leak into the copper block was causedmainly by conduction along the thin-wall stainless

steel tube and the electrical leads that connect theblock to the vacuum jacket (which was at the tem-perature of the outer helium bath). The heat leakwas therefore proportional to the temperature dif-ference between the block and the outer heliumbath and was determined experimentally to be 800~W/K. During decay heat measurements, the heatleak varied from +20 pW when the copper block wasat the temperature of the liquid helium in the reser-voir to –12 PW when the copper block was 40 mKwarmer than the helium. This heat leak was sosmall that it was neglected.

The time constant of the calorimeter wasmeasured by making step changes in electric powerto the heater in the copper block while recording theflowmeter output. For changes between power levelsthat were both > 70 mW, the response was wellrepresented by the expression

P(t) = Pi + (Pr – P,) (1 – e-tin) ,

where P(t) is the indicated response t seconds after astep change in input power from PI to Pr and R is theexponential time constant. Ten measurements thatincluded both increases and decreases in inputpower yielded a value of 0,85 + 0.09s for R. Figure 7shows typical response curves for step decreases inelectric power input.

When the input power dropped to zero, the flow-meter response no longer followed a single exponen-tial decay. Below w 70 mW the apparent time con-stant increased as the power decreased, producing along tail on the response curve. The decay heat waschanging very slowly by the time (N 3 x 1(Ys) it hadfallen to 70 mW, so the increased response time inthis power range was not a problem.

Since the thermal time constant of the copperblock was estimated to be < 0.16s, it was clear thatthe calorimeter’s response was dominated by thetime constant of the helium transport and measure-ment system. We verified this by supplying con-stant electric power input to the heater, and thenopening and closing the ball valve. The recoveryshown by the flowmeter when the ball valve wasclosed was similar to its response to a step increasein power, indicating that an important contributionto the response was the time required to build uppressure across the flowmeter. For this reason it wasimportant to select a flowmeter that had a small

9

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L

-.-+__+

Time (s)

Fig. 7.Calorimeter response to step decreases in elec-tric heater power input. The curves are typicalof the response to both increases and decreasesin power (when the minimum power is z 70m W). The curves are well represented by asingle exponential with a time constant of 0.85+ 0.09s. For power decreases to <70 m W, theresponse curve shows a long tail in addition tothe initinl exponential decay.

pressure drop at the desired flow rates. (A secondreason was to minimize the changes in the boilingpoint of the helium in the inner reservoir.)

Since the process of boiling is subject to fluctua-tions, the output signal from the flowmeter con-tained a noise component. The RMS noise,evaluated for a 1-s averaging time, varied froms 0.65% at 100 mW to x 0.25% at 3000 mW. our’method of recording data automatically providesaveraging over 1- or 10-s intervals. Additionalsmoothing was provided in the data analysis.

The charge of liquid helium in the reservoir wasexhausted after 4000 to 6000s, depending on the in-itial filling. At this point the reservoir was refilledand the multiscaler was restarted at a known clocktime, using 10-s time channels. For measurementsout to a cooling time of 105s, a second refill was re-quired. The reservoir was refilled at different timesfor different runs to attain continuous coverage.

D. Calibration of the Flowmeter

Because the relation between the flowmeterbridge voltage and the mass flow of helium gas isgiven only approximately by theory, a calibrationcurve had to be established experimentally. Thiswas done by running two independent series ofmeasurements. In the fwst series, known rates ofelectric heating were supplied to the coil in the cop-per block. This had the advantage of checking theentire helium boil-off and gas-transport system. Inthe second series, the mass flowmeter was checkedwith steady-state flows of helium gas against the in-

tegrated volumes measured with a diaphragm-typetest meter* that had been calibrated by themanufacturer using a one-cubic-foot bottle certified’by the US National Bureau of Standards. Both testxwere repeated each day a uranium sample wasirradiated to determine whether the calibrationchanged between runs. There was no evidence of

changes in calibration, so the same calibration curvewas used to convert all flowmeter bridge voltages,digitally recorded during decay heat measurement,into milliwatts deposited in the radiation absorber.

Electric calibration measurement were taken bydetermining both the voltage, V, and current, I, SUP-

plied to the electric heater, Currents were deter-mined by measuring the voltage drop across an ex-

ternal 1O.OO4-Qstandard resistance. Voltages weremeasured by comparing them to a 1-V FlukeTransfer Standard, which was calibrated against anEpply Standard Cell from the Primary StandardsLaboratory of the Sandia Laboratories. Voltageawere accurate to +0.0020A; currents and electricpower were accurate to &O.01%.

The resistance of the calorimeter heater plus leadsvaried from 194.5 Q at 30 mW to 196.00 at 3 W (at 4K). The resistance of the copper lead wires was= 0.8$2, nearly all of which occurs along parts of thewires in the helium vapor above the liquid level inthe outer helium reservoir. Using an average valuefor the heater resistance, we found that 0.996 of theelectric heat was deposited in the calorimeter; wetherefore used the expression—*Such meters areoften called drytest metemto distinguish themfrom liquid-sealed rotating-drum meters, which are known eswet test meters. Forfurtherdiscuaaionaee the AmericanSocietyfor Testing and Materials Standard D 10’71.

.

I

10

mW = 896 (V” I)l

The gas flow calibration points were measuredwith an American Meter Company Model DTM-115dry test meter.* The manufacturer’s calibrationcurve showed variations from the nominal readingto be < 0.2% over the range of flow rates we used.During calibration measurements, helium gas en-tered the gas transport system just ahead of the heatexchanger (see Fig. 4), and the dry test meter wasconnected to the exhaust side of the anemometerflowmeter. Liters per second of steady-state gasflow, measured at atmospheric pressure and roomtemperature with the dry test meter and a stopwatch, were converted to flow rates at 760 torr and00C using the ideal gas law. Under these conditions,1 mole occupied 22.4136 liters.’

Since about 10% of the vapor evaporated from li-quid helium did not reach the flowmeter, butremained in the reservoir in the volume formerly oc-cupied by liquid, it was necessary to know the “ap-parent” heat of vaporization, L,, in order to convert

the observed gas flow to watts. L. is related to thetrue heat of vaporization, L, by

L = L.(1 – Vfi.) J/mole,

where VL and V~ are the molar volumes of liquidand gas, respectively. The most precise measure-ment of La has been made by Ter Harmsel, vanDijk, and Durieux,’O who also reviewed and com-pared earlier measurement.a.i’,lz Their smootheddata gives a value of L, = 97.91 J/mole (+ 0.13%) at3.967 K, which corresponds to a saturated vaporpressure of 598.3 torr, using the 1958-4He tem-perature scale. Using these numbers, it can bedetermined that a gas flow rate of 1 liter/s at LosAlamos atmospheric pressure corresponds to z 3.15W. (The exact value depends on the temperatureand pressure of the gas in the dry test meter. )

The final calibration curve was a least squares fitof a 10-point cubic spline to 94 gas-flow calibrationpoints and 70 electric-heating calibration points.The uncertainty in the calibration curve was es-timated from the accuracy of the standards( ~ 0.2%) and from an analysis of the deviations ofthe individual calibration points from the fittedcurve. The total uncertainty (1 a) assigned to the———“Manufactured by Singer, American Meter Division,Philadelphia, PA 19116.

fitted calibration curve varied from 0.5% for powers>800 mW to 2.2% at 70 mW. For powers >400 mW(where the calibration is the most accurate), thealgebraic sum of the percent deviations of theelectric-heating calibration points from the fittedcurve was +0.02Y0. The corresponding value for thegas-flow calibration points was –0.01%. We con-clude that there was no significant difference be-tween the two calibration methods.

We took 70 mW to be the lower limit of the usefulrange of the anemometer flowmeter for accuratedecay heat measurements. For power levels < 70mW, where the decay heat was changing slowly(cooling times were >3 x 10’ s), we made integralflow measurements with the dry test meterdescribed above. We estimate a 1% uncertainty inthese measurements, based on discussions with themanufacturer of the flowmeter concerning the ac-curacy to be expected at these (low) flow rates.

III. FISSION RATES

The calorimetric measurements yield the energyrelease rate, in MeV/s, as a function of cooling time.This rate must be divided by the fission rate in thesample during irradiation to obtain the normalizeddecay heat in MeV/s per fissionls (often abbreviatedMeV/fiss).

Since the flux at the sample position was heldconstant (to x 0.1%) during the irradiation, theaverage fission rate was obtained by dividing thetotal number of fissions in the sample by the irradia-tion time, The determination of total fissions wascarried out by the LASL Radiochemistry Group(CNC-11), which has had many yeara experience inconnection with fission yield measurements for theLASL Weapons Test Program.

A. Sample Dissolution

After a calorimetric measurement had been com-pleted and the calorimeter had returned to roomtemperature, the sample was removed from the cop-

per block with a special handling tool and placed ina shielded container. It was later transferred to a hotcell, where it was dissolved in 3 M HC1, to which asmall amount of HN03 was added to ensure dissolu-tion of the uranium. The total volume was made up

11

_ _ .

to 1 liter in a volumetric flask, using additional 3 MHC1. Specimens containing a known fraction of theoriginal l-liter solution were prepared by pipettingand dilution for use in subsequent analyses.

B. Radiochemistry and Beta Counting

In one analytical method, a standardizedradiochemical (RC) procedurela was used toseparate the activity due to a specific fissionproduct, which was then counted in a standard betaproportional counter. The ratio between thecounting rate of this counter (corrected for decay)and the number of fissions in the specimen is knownas the K-factor for that particular activity, counter,and procedure. The K-factors for several fissionproducts have been evaluated in previous experi-ments, as described below.

Using this method, four determinations of ‘Moand two of 140Bawere carried out for each sample.The precision of the determinations, estimated fromthe scatter in the results for identical specimens,was consistent with previous estimates of precisionbased on comparison of measurements made onduplicate specimens.

C. Gamma (hunting

In a second analytical method, the gamma spec-trum of an unseparated specimen was measuredwith a Ge(Li) detector. Six spectra were recordedfrom a specimen from each of the decay heat sam-ples. The Ge(Li) detector was calibrated using li-quid multigamma standards furnished by theNational Bureau of Standards. The geometry usedin the calibration was identical to that used in the

measurements. (The same volume of solution, in thesame kind of container, at the same distance fromthe counter, was used.)

The gamma spectra from the specimens wereanalyzed using a version* of the computer programGAMANAL,’4 which contains a library** of spectrafor individual fission products. The program per-forms a least squares fit of all the gamma rays fromeach selected nuclide and returns the number of——“Mnditied for use on the LASL rornputershy Bruce Erdal.

**The gamma ray librarywas compiled from literature xrurcesby P. (;rant, G. Butler. and B. Erdai.

12

atoms of that nuclide (corrected for decay) presentin the specimen. The fitting program also estimatesthe statistical precision of each determination. Thefinal results are weighted averages from the six spec-tra. The activities “Zr, ‘“Mo, 140Ba-La, “1Ce, and“’Nd were determined using the Ge(Li) countingmethod.

Previous calibrations had established the relationbetween the indicated number of atoms of a par-ticular fission product and the number of fissions inth~sample. In these calibrations, the number of fis-sions was obtained by RC determinations of ‘Me,which are considered to be the most accurate(smallest systematic error).

The final number of fissions for each sample wastaken to be the weighted average of the individualdeterminations. The precision of the weightedaverages was estimated to be $S0.37., where the in-dicated precision is the larger of (1) the value ob-tained from the estimates of precision for the in-dividual determinations or (2) the value obtainedfrom the scatter of the results of the individualdeterminations. Results of the determinations andthe estimated precision (1 u) for the three samplesused in our decay heat measurements are shown inTable I.

D. K-Factor Determination and Uncertainty

The systematic error in the determination of thenumber of fissions in a sample depends on the ac-curacy of the K-factors, which were used for nor-malization in both analytical methods. Here wedescribe how the K-factors were obtained andprovide information on their accuracy. Since the K-factor for ‘Mo is considered to be the most accurateand has been subjected to the greatest number ofchecks, its determination is described in detail.

The K-factor for “MO was determined using afacility (described in Ref. 15) normally used forassay of fissionable materials by comparison fissioncounting. The facility consists of a double fissioncounter inserted in a cavity in the graphite thermalcolumn of a reactor. Two foils are placed back-to-back and simultaneously counted in the sameneutron flux.

To determine the K-factor, a ‘S’U sample wasirradiated between two 2SSUstandard foils in the

b

.

,

TABLE I

DETERMINATION OF THE NUMBEROF F1SS1ONSFOR SAMPLES1, 2, AND 3

.

FiosionProduct

AnalyticalTeehnique

RC and @ ctgRC and 8 ctgGe(Li) TCtgGe(Li) y CtgGa(Li) 7 ctgGe(Li) 7 ctgGa(Li) ‘yCtg

Number ofDetermina- SampIe 1

tions Precision Number ofor Spectra (1 u in %) Fksions

4 det 0.6!! 4,736 X 10U2 det 0.75 4.768 x 10U

6 spec 0.9 4.786 x 101’6 spec 1.1 4.757 x 10106 fl~C 0.4 4.744 x 10”6 spec 1.5 4.755 x 10”6 SpOC 1.9 4.689 x lo”

Weighted Average 4.750x 10”precision of Average 0.27%

double fission counter. The number of fiseions perunit weight in the sample wae taken to be the

average of those in the standard foils on either sideof it. Flux-depression and self-shielding effects wereestimated to be negligible for the sample size (s 2mg) and geometry used for the irradiation.

The sample was then dissolved, and multiplespecimens obtained from it were separated and theOeMo beta activity was counted in a special Propor-

tional counter reserved for this purpose. The ratiosof the weights of the two standard foils to the weightof the original sample were determined by preparinga new foil from the sample solution and counting ittogether with each of the standard foils in the dou-ble fission chamber. The fraction of the originalsolution on the new foil was obtained by tracingwith 2a2U,using a carrier-free procedure. Since thespecific alpha activity for 2S2Uis x 107times higherthan for ‘“’U, alpha counting of the tracer providedan accurate method of determining the yield of theelectrodeposition procedure used in preparing thenew foil.

The K-factor was obtained from the observed‘Mo beta counting rate, the number of fissionscounted on the stnndard foils during the irradiation,and the ratio of the weight of the sample to theweights of the stfindard foils. An advantage of theK-factor method is that it is determined directly byfiesion counting and therefore does not require aknowledge of fission-product yields or decayschemes.

Sample 2

Preeision Number of(1 uin%) Fksions

0.24 4.925 x’lo”0.85 4.889 X“lo”0.87 5.012 x“lO1’1.24 4.952 x’lO1’0.43 4.981 X“lo”1.29 5.005 X“lo’”1.91 4.883 x;1O”

4.941 x 10”0.26%

Sample 3

Precision Number of(1 uin%) Fissions

0.47 4.711 X’lol’0.30 4.679 x“1O”1.06 4.843 X“lo”1.14 4.799 X“lo”0.46 4.752 x“lCI”1.45 4.730 X“lo”2.3 4.857 X“lo”

Z7izzW0.38%

The normalization of the gamma-counting resultswas based on the K-factor for ‘Me. The K-factor forI’”Ba was determined separately, then checkedagainst the factor for ‘eMo.

One source of uncertainty in the ‘nMo K-factorwas the determination of the number of fissions inthe standard foils. The statistical uncertaintycalculated from the number of counts was 0.2%. Ac-tual fission-counting data from the two foile countedin the equipment checkout procedure on 152 dif-ferent days over a 4-yr period had a standard devia-tion of 0.17%, which is consistent with the estimatedvalue.

The standard foils consisted of 0.1 ~g 2“Udeposited on an area of 3.8 cm’. It is estimated that,under the conditions of the measurement, all but2% of the fissions produced pulses that were detec-ted. The 2% correction is believed to be known to10% of its value, thus giving an overall uncertaintyin the correction of 0.2Y0.

According to Ref. 15, the standard deviation ofthe amount of *SW determined to be on another foilby comparison fission counting with a traced stan-dard is 0.46%, and that for a solution asaayed bythis method it is 0.55%. We used 0.55% as the un-certainty in determining the ratio of the weighb ofthe standard foils to that of the sample.

A final source of uncertainty is in the separationand counting of the ‘@Mo activity. The average stan-dard deviation of a single “MO separation andcounting was determined to be 0.96 Ye, based on a

13

study of 348 duplicate or multiple analyses over a3-yr period.” In the original evaluation of the K-factor in current use, six analyses for “MO werecarried out. The standard deviation of the meanwould be expected to be 0.96%/~6 = 0.39~0.

All of the above uncertainties are uncorrelated; itis therefore legitimate to take the overall standarddeviation to be the square root of the sum of thesquares of the individual standard deviations. Thisgives

uK.r.&j~ = (0.2’ + 0.2’ + 0.55’ + 0.399’” = 0,73%.

We will use u = 0,8% as the systematic error in thedetermination of the number of fissions.

The K-factor for ‘Mo in current use at LASL wasdetermined in 1955 using a single bombardment andsix individual ‘9M0 assays, Since then there havebeen 6 additional bombardment and 15 individualassays. A K-factor based on all 21 assays differsfrom the original value by 0.4%, which is well withinthe assigned uncertainty of 0.8%.

In another check on the accuracy of fission deter-minantions using the K-factor method with ‘@Mo,LASL and the Lawrence Livermore Laboratory(LLL) have determined the number of fissions induplicate samples 13 times over the past 11 yr.” Theaverage ratio of the LASL to the LLL determina-tions is 1.007, which is also consistent with an uncer-tainty of 0.8Y0.

E. Interlaboratory Comparison of FissionDeterminations

In connection with the current decay heat studiessponsored by the NRC, LASL prepared duplicatesamples of irradiated *SW that were analyzed atLASL, the Oak Ridge National Laboratory(ORNL), and the Idaho National EngineeringLaboratory (INEL). Details of this comparison are

given in the Appendix, which was prepared by R. G.Helmer and R. L. Heath of the INEL.

Results of the comparisons are summarized inTable II. The good agreement among the fissiondeterminations by the three Laboratories indicatesthat our fission determinations are free of un-recognized systematic error.

TABLE II

RESULTS OF INTERLABORATORYCOMPARISON OF FISSION

DETERMINATIONS

●

Fissionsper ml?ofStandard

Laboratory Solution

LASL (1.179 * 0.009)x 10’”INEL (1.176 + 0.026)X 10’0ORNL (1.184 + 0.018)X 10’0

RelativeNumber of

Fissionsper d

1.0000.9971.004

IV. GAMMA LEAKAGE CORRECTION

Some of the gamma component of the decay heatpenetrates the copper absorber block, and is notrecorded by the calorimeter, On the other hand,< 0.01% of the beta energy is lost. The gammaenergy that escapes must be evaluated separatelyand added to that deposited in the calorimeter toobtain the total decay heat. Our procedure was todetermine experimentally the absolute gammaspectra emitted by the sample for several coolingtimes, and then to calculate the fractions of thesespectra that had escaped the copper block.

A. Measurements of Gamma Spectra

Figure 8 shows a plan view of the spectrometerused to measure the absolute gamma spectra at 10cooling times following a 2 x KY s thermal-neutronirradiation of a thin ‘S5Usample. This spectrometerwas developed for measuring neutron-capturegamma ray spectra. The aluminum-clad ‘W sam-ple was located in an evacuated bismuth-lined

channel that passed transversely through the reac-tor’s graphite thermal column and extended into theconcrete shielding beyond the graphite. Becausethere was no thermal column graphite directlybehind the sample, this important source ofbackground was eliminated. Gamma rays from the

14

*

.’

( /’”/’ -“—”\ ‘“” )

4-’-—--J-+4.. –

NaxW.1’unx

*- ● M

Adiihs

Fig. 8.Plan view of spectrometer used to measure zwu f~sion.product gamma spectra at VariOUS

cooling times following a 2 x 1(7 s irradiation. The spectra were put on an absolute basis bycalibration against hydrogen neutron-capture gammas from a polyethylene sampleirradiated in the same flux and position as the ‘S5Usample.

reactor core were attenuated on entering the ther-mal column by a 76-mm-thick lead shield adjacentto the core and by a 127-mm-thick bismuth shieldjust inside the thermal column. The thermalneutron flux at the target was s 3 x 10IIn/cm%. Thegamma-ray beam was extracted through acollimator, whose viewing area did not include thebismuth walls of the channel. Therefore, to passthrough the collimator, any gamma rays that didnot originate in the sample had to scatter through alarge angle. Thermal neutrons accompanying thegamma-ray beam during irradiation of standardpolyethylene calibration samples were attenuatedby a ‘LiF absorber, which also stopped beta raysfrom reaching the detector.

The detector was a 61-mm-diam by 127-mm-deepNaI(Tl) crystal placed at the center of a 200-mm-o.d. by 300-mm-d.eep cylindrical NaI(TI) annulus,which had a 63.5-mm bore along its axis. The outercrystal was used in anticoincidence with the center

crystal, The gamma-ray beam was 12 mm indiameter at the detector, approximately 6 m fromthe sample. The data were recorded in a 4096-channel pulse-height analyzer, and read out ontomagnetic tape for computer analysis.

A fission counter near the sample positionmonitored the neutron flux and a nearby fissionchamber was used to control the reactor power dur-ing irradiations so that the flux at the sample posi-tion remained constant.

Before irradiating a ‘“U sample, a standardpolyethylene sample was irradiated and the singlegamma ray of E. = 2.2246 + 0.0001 MeV (Ref. 18),resulting from neutron capture in hydrogen, wasrecorded by the spectrometer for a convenient time,At. The number of hydrogen atoms in the sample[composition (CH,).] was determined by weighing.

The ‘W sample, which was also weighed beforebeing sealed in an aluminum envelope, was thenirradiated for 2 x 104 s, after which the reactor was

15

rapidly shut down. (This reduced the thermal fluxby a factor of 106, and effectively ended the irradia-tion.)

The gamma power per unit fission rate I’(E,t) perunit energy interval about E is given at cooling timet by

Gdet(E,t)f(EH) N@H(n,~)r(E,t) ~ EH G

de@I-1) f@) NUou(fksion) ‘

where G~et(EH) is the gamma power recorded by thespectrometer for the hydrogen capture line, andG~e,(E,t) is the gamma power recorded at coolingtime tin the unit energy interval about E. The func-tion f(E) is the relative efficiency of the spec-trometer at energy E. NH and N“ are the number ofhydrogen and uranium atoms, respectively, and@ (n,~) is the capture cross section of hydrogen andau(fiss) is the thermal fission cross section ofuranium. The above equation assumes that thethermal neutron flux was the same during the 2SSUirradiation as it was during the polyethylene irradia-tion.

The relative efficiency f(E) of the spectrometer atenergy E applies to the full-energy peak of the inci-dent gamma ray. However, a single gamma ray ofenergy E contributes to the counting rate at allenergies below the full-energy peak. Before applyingthe above equation for I’(E,t), it is necessary to “un-fold” the observed spectrum to remove the low-energy part of the response function. The unfoldingwas done by a stripping process starting at the highend of the spectrum. Account is taken of the follow-ing processes that occur in the NaI(Tl) crystal: (1) aGaussian-shaped full-energy peak at the energy ofthe gamma ray, (2) electron bremsstrahlung, whichat high energies broadens the distribution on thelow-energy side of the peak, (3) the Compton scat-tering contribution, which is treated as independentof energy and is subtracted from the remaining spec-trum at energies below the peak, and (4) the firstand second pair-production escape peaks, which oc-cur at 511 and 1022 keV below the gamma-rayenergy.

Figure 9 shows the spectrometer response to thesingle (n, ~) hydrogen gamma ray at 2.2246 MeV.The ratio of the area under the peak to the total areais 0.64 for the hydrogen gamma ray. This ratio variesfrom x 0.95 for very low energy gamma rays to s 0.5

t 1mo -

>:600 -

awn

Eg 400 -

200 -

00 300

ktV

Fig. 9.Pulse height spectrum from the ninglehydrogen neutron-capture gamma my at En =2224.6 keV. The first pair-production encapepeak h visible at 1714 keV.

at 10 MeV. The large fraction of the recorded energyin the full-energy peak results from the use of a well-collimated gamma-ray beam incident on the centerof the end of the central NaI(Tl) crystal and an an-ticoincidence annulus around the central counter.This response curve feature makes the we of a sim-

ple stripping procedure for the unfolding processpractical.

In addition to the statistical uncertaintycalculated for sample and background, the un-folding process was assigned an RMS uncertainty of+ 10%, which was included in calculating the totaluncertainty of the gamma power horn fissionproducts.

Gamma spectra at 10 cooling times following a 2 xlW s thermal-neutron irradiation of a ‘SW sampleare shown in Figs. 10 through 19. The data are com-bined into 50-keV energy bins. All experimentalpointa are absolute, except for those shown in Fig.19, which were normalized to a summation calcula-tion because difficulties in background subtractionprecluded the determination of accurate absolute

,

16

.

.

‘.’la 2a 3Q 49 50

MoV

Fig. 10.Gamma spectrum for 70-s mean cooling time.

00-

1 — = calculated* O = Ex*rimental

MeV

Fig. 12.

Gamma spectrum for 388-s mean cooling time.

)Me V

Fig. 11.Gamma spectrum for 199-s mean cooling time.

— = CalculatedO= ?kprrimental

Ma v

Fig. 13.‘ Gamma spectrum for 660-s mean cooling time.

17

‘o

>s

t’o-cm la Za 3* 4Q w)

Gammatime.

MC V

Fig. 14.spectrum for 1524-s mean cooling

1 — = calculated7 0 = experimental

.

MoV

Fig. 16.Gamma spectrum for 3234-s mean coolingtime.

18

I

MoV

Fig. 16.

Gamma spectrum for 2214-8 mean coolingtime.

— = Cekulated0- Experimental

)MaV

Fig. 17.

Gamma spectrum for 5000-8 mean coolingtime.

.

0

.

,

‘o

‘1 — = calculated-y.- 0 = Experimental

d-$i!u-w io 2.0 30 40 k

MoV

Fig. 18.Gamma spectrum for 21 M5-s mean coolingtime.

values. However, earlier results from a pilot experi-ment indicate that the absolute experimental spec-tra in this range of cooling times were within s 10%of the calculated values.

Also shown are spectra calculated at the samecooling times from ENDFfB-IV data.ie The shapesof the spectra were obtained from the 181 fissionproducts whose files contain spectra. These spectrawere normalized to the total gamma release rate forall 711 radioactive species in the files, thenbroadened to match the experimental energy resolu-tion. Table III gives the experimental integratedgamma decay heat, the ratios of experimental tocalculated values, and the percentage of thecalculated gamma energy that is due to the 181nuclides with known spectra.

B. Calculation of the Gamma Energy Leakage

The gamma-ray leakage calculations wereperformed using the Monte Carlo gamma-raytransport code MCG.20 The geometric model in-cluded all of the detail shown in Fig. 20. Since the

PII— = Calculated

O= Experimental

/

●

▼

k~MeV

Fig. 19.

4a ti

Gamma spectrum for 72 550-s mean coolingtime. For this cooling time only, the ex-perimental data were normalized to thecalculated gamma decay heat because of dif-ficulties in background subtraction. However,preliminmy measurements in this region ofcooling time were within = 10% of thecalculations.

fission-product gamma-ray energy spectrum varieswith cooling time, it was necessary to calculate theenergy leakage L(E) as a function of gamma-raysource energy E. Approximately 50000 gamma-rayhistories were tracked for each of 17 source energiesfrom 0.1 to 10 MeV. The results given in Table IVand Fig. 21 are for those cases where L(E) exceeded0.5% of E. In all cases, the Monte Carlo statisticaluncertainty in L(E) is < 0.2% of E. From direct ex-perimentation with different geometric models, weestimate that the uncertainty in L(E) due to themodel is -0.3% of E. For most cases of interest, un-certainty in L(E) is less important than the uncer-tainty in the source energy spectrum.

Combining the measured source spectra with thecalculated leakage fractions gives the total gammaenergy leaking from the calorimeter block, on an ab-solute basis, as shown in Fig. 22. Since spectral

19

MeanCooling

Time(s)

70199388660

1524221432345000

2184572550

TABLE III

INTEGRATED GAMMA DECAY HEAT

ExperimentalGamma

Decay Heat(MeV/fiss)

RatioExp/CalcGamma

Decay Heat

Percentageof Calc GammaDeeay Heat fromNuclides Having

Speetral Data

2.9272,1981.8411.5261.0900.89950.71680.53200.14180.0350 (calculated)

1.078 (1.080)a1.066 (1.069)1.068 (1.071)1.029 (1.032)0.992 (0.995)0.979 (0.983)0.971 (0.976)0.975 (0.981)1.106 (1.121)

87.693.595.596.699.898.799.399.799.8

‘For the ratios in parentheses, the internal conversionenergy haa been excluded fromthe calculated trammadecay heat (forthe 38 nuclidea having internal conversioncoef-ficients in the ENDF/B-IV files). I&emally convertedgammi rayawouldnot be detec-ted by the gamma spectrometerused to obtain tha experimental gamma decay heat.

II t~q”idHe level (Clw3.)

~ =0.129 g/cm3 i

Energy (E)(MeV)

Fig. 20.Geometric representation of the absorber blockused in the Monte Carlo gamma-ray leakagecalculations.

TABLE IV

ENERGY DEPENDENCE OFGAMMA-RAY LEAKAGE

Energy Leakagt#Source Energy

[L(E)fE]

0.42170.56230.74991.0001.3341.7782.3713.1624.2175.6237.499

10.00

0.00560.01080.01960.03200.05060.07280.09460.11080.12170.12310,11970.1056

.

,

.

20

1

ooyL_______l12345678 910

Gamma Energy {MoV)

Fig. 21.Fractional gamma energy leakage from thecopper block in the calorimeter as a function ofinitial gamma energy. These data, obtainedusing the Mo~zte Carlo code MCG, were com-bined with the measured spectra to obtain thegamma leakage confection.

measurements were not made at cooling times< 70s, the average of calculations made with twoother spectra was used as a guide in extrapolatingthe gamma energy leakage to 10 s. The first spec-trum, measured by Dickens et al.,” was from a “Usample irradiated for 100 s, cooled for 100 s, andcounted for 50 s. Because of the short irradiationtime, the Dickens et al. spectrum is expected to beharder than would be obtained fora20000-s irradia-tion time. The second spectrum was calculated us-ing the ENDF/B-IV nuclear data file; this spectrummight be softer than the true spectrum because ofthe omission of (unknown) high-energy gammaswith short decay times. The energy leakagecalculated from the two spectra differed by 15Y&The average leakage fraction for the two spectra wasused at 10 s, and the absolute energy leakage wasobtained from (1) the average leakage fraction, (2)the fraction of the total decay heat that is in theform of gamma radiation (obtained from summa-tion calculations), and (3) the decay heat measuredby the calorimeter at 10-s cooling time.

The gamma leakage decay heat was added to thatmeasured with the calorimeter to obtain the totaldecay heat. An interpolation scheme was used to ob-tain gamma leakage values between cooling timesfor which it had been determined.

o Expcrlmwrtal spcclro

( 8 Oicbna e! 01.(100/100 /!50)

❑ COICUIOtad wctrum; ,.-1.:“=;~

-2 -g 100s50

j10-~-

I 1 0 I10 100 1000 Ioq 10°

Cooling Time (s)

Fig. 22.Gamma leakage from the calorimeter in ab-solute units.

The uncertainty in the gamma correction, arisingmainly from uncertainties in the spectra, was takento be 15% of the correction for tc~l s 15s, falling to10% for tcoo, > 70 s. Figure 23 shows the gammacorrection and its uncertainty, expressed as a per-centage of the total decay heat.

V. CORRECTION FOR INITIAL TRANSIENT

The introduction of the irradiated sample in itaaluminum cladding (which was also activated)caused a disturbance to the calorimeter. Also, thefinite response time of the system distorted the in-dicated decay heat curve. Corrections were made tothe short-cooling-time data for both of these effects.

Figure 24 shows the initial power recorded by the

calorimeter, together with the power recorded whenan all-aluminum dummy sample was irradiated andtransferred to the calorimeter, using the samemechanism and timing sequence used for theuranium-loaded sample. The initial temperature ofthe dummy sample was adjusted to be approx-imately equal to that of the real sample.

To correct for the effects of introducing the sam-ple, the average signal for three irradiated dummysamples was subtracted from the calorimeter powerrecorded when a uranium-loaded sample was used.This correction amounted to 2.3% at 10 s, and to

21

, r I # I I , 1 *

3 -\

I----.. I l-\

E 1’ — Co!culatad correction.

t

‘--- Estimated I u unfxrtaintyz

1

.~10 100 1000 ,.4 K?

Caaling Time (s)

Fig. 23.Gamma leakage from the calorimeter ex-pressed as a percentage of the total decay heat.The estimated 1 u uncertainty band Ls alsoshown.

< 0.l% for cooling times > 400s. The correction in-cludes the effect of the 2.24-m ‘aA1activity producedin the aluminum cladding. This activity was es-timated to contribute x 15 mW at t = O.

The calorimeter had an exponential responsefunction with time constant R = 0.85 s. If the trueinput power is given by

+Tipin= zuie ,

i

where the al and 71are constants and t is the time,then the indicated power is given by

IYTi -tlRa$e —e )

Pout ‘~ (1- R/ri) “

A correction for this effect was obtained byrepresenting the decay heat power (obtained fromsummation calculations) as a sum of exponential,as in the equation for Pi.. The correction was ob-tained by calculating P,n/POu~as a function of cool-

1

ok,.0 50Cooling Time (s)

Fig. 24.Initial power recorded by the calorimeter foran aluminum-clad uranium sample and analuminum dummy sample.

ing time and multiplying the indicated calorimeterpower (after subtraction of the dummy samplebackground) by this ratio. The correction amountedto 1.l% at a cooling time of 10s, and to < 0.1% forcooling times > 200 s.

To test these corrections we used a programmedpower suppy to furnish an exponentially decayingpower to the heatir in the copper block. The ex-ponential time constant was 47.45 s, which is closeto the apparent time constant for the decay heatcurve at a cooling time of 6 s.

A dummy sample was irradiated and transferredto the calorimeter in the normal manner. Approx-imately 1 s after the dummy sample fell into thecalorimeter, the exponential power to the heater wasstarted. (The 1-s delay was needed to prevent gasflow due to the heater power from interfering withthe fall of the dummy sample into the calorimeter.)This test was carried out twice, and the indicatedcalorimeter power for the two runs was averaged.

The corrections described above were applied, us-ing the appropriate expression for Pi”. The corrected

calorimeter power was then compared to the known

.

,

22

,

input power. Between 15 and 70 s the average dif -

ference between the curves, taken at 1-s intervals,

was ( —0.02 + 0.30) ‘A, and the maximum difference

was 0.6%. (The minus sign indicates that the

calorimeter power was smaller than the input

power.) At 10-s cooling time, the calorimeter power

was z 2’%0 below the input power. We feel that thetest substantiates the correction technique for cool-ing times 2 15 s. Although we are not sure whetherthe = 2% discrepancy at 10s was significant for thedecay heat measurements (the small differences intiming could be important at this short coolingtime), we made no further adjustment to the ex-perimental data for the 10-s cooling time.

We estimate the uncertainty in the total short-time correction to be = 50% of its magnitude. Thisvalue includes an allowance for the uncertainty at10 s and is based partly on the results of othermethods of estimating the correction (none of whichagreed as well with the exponential heating test asthe correction actually used).

VI. DATA TREATMENT AND ERRORANALYSIS

A. Data Treatment

The final results are based on experimental runs

on three ‘W samples. For most cooling times, datawere obtained from all three samples. At certaincooling times, data from fewer than three sampleswere obtained. The results at 10, 15, 4000, 7000,25000, and 30000 s are based on two samples, and

those at 4500, 5000, 62183, and 10’ s are based ononly one sample, Figure 25 shows the individualdata points from sample 1 for the first 100 s of cool-ing time.

The data were smoothed to eliminate fluctuationscaused by the boiling process. For times < 200s, thecorrected data for each sample were plotted, and asmooth curve was drawn through each set of points.The decay heat was read from the smooth curves atselected cooling times that were an integral numberof seconds. (This corrected for the 0.15-s displace-ment of the centers of the 1-s mult iscaler channels. )For cooling times from 200 through 4000 s, theaverage of ten 1-s channels was used. For times be-tween 4000 and 30000 s, we took the average for ten

3.0 1 I 1 I ?‘sO U Samp10 no. 1

...

a.o - “e.

~ “..

I

“.“.

“.~ 2.6 - “.

●.

i

“%..%..

i““..

‘%.*W%.**

?..0 - ““%.+.

-%.%*,

“-”----- .

l.ao 1 1 1 I20 40 80 00 100

Fig, 25.Individual data points from a single ‘“U sam-ple. Background from an irradiated aluminumdummy sample kas been subtracted.

10-s channels; for cooling times >30000 s, we tookthe average of 10 timed measurements made with

the dry test meter (carried out over a period of e 30m). The smoothing techniques were chosen becausethey were compatible with the rate of change of thedecay heat at the times involved, and they in-troduced no significant systematic errors in themeasurements.

The data for each sample fell on a relativelysmooth curve, indicating a high degree of correlationbetween measurements made at adjacent coolingtimes. The decay heat curves for the three sampleswere nearly parallel, although the relative valueschanged slowly over long intervals of cooling time.

B. Error Analysis

The RMS scatter in the data at each cooling timewas calculated using

where y, is an individual data point, j is the mean,

and n is the number of data points. When there were

<3 data points, the missing values were estimated

from nearby points on the same curve.

23

For most cooling times, the RMS scatter in thedata was consistent with estimates based on theprecision of the fission determination and the scat-ter of the flowmeter calibration pointa about the fit-ted calibration curve. At. the shortest cooling times,an increased scatter was observed. This might havebeen caused by the variation in the time it took forthe sample to fall from the release chamber to thecopper block, or to some other variation in the in-itial transient. An increased scatter was also obser-ved for cooling times immediately after the heliumreservoir had been refilled for one or more of theruns. This affected the data at cooling times of 6000and 7000 s.

We can use S to estimate the statistical uncer-tainty in the averaged experimental decay heat, ~,provided we take account of the small number (n =3) of individual data points that we used incalculating S and~. If n had been large, the devia-tion of~ from the true mean, m, would be normallydistributed with a standard deviation of s/fin. Whenn is small, ~ –m)/(S/@) has a Student’s t dis-tribution for n –1 degrees of freedom. This distribu-tion involves greater probabilities of large deviationsof ~ from m than does the normal distribution.

For simplicity in combining and interpreting un-certainties, we approximate the deviation of~ fromm by a normal distribution chosen to have a 95~0confidence interval equal to that obtained using theStudent’s t distribution. Such a normal distributionhas a standard deviation of 1.3S.

Other sources of error, discussed earlier, did notcontribute to the scatter in the data from the threesamples. For this reason, we call them systematicuncertainties. They were (1) the systematic uncer-tainty in the fission determination, (2) the uncer-tainty in the flowmeter calibration, (3) the uncer-tainty in the gamma-leakage correction, and (4) theuncertainty in the initial-transient correction. Weassumed that the errors resulting from these uncer-tainties were normally distributed and un-correlated; we therefore equated the totalsystematic uncertainty, aO, to the RMS sum of theindividual systematic uncertainties (see Fig. 26).

The total uncertainty, u, was taken to be theRMS sum of aOand 1.3s. Figure 27 shows a, UO,andS as functions of cooling time.

J===l-------Gamma ●ocapo camctlan

$ I -y___--_____.L. --__,

1- “\.–.–-—-–----”.—.—.------ 1--~k------ ----------- ------ --

1,,,11 \,------

0 , 1,,,,1 , 1,,,,1 1 1,,

10 KM 1000 10’ lo’Caoling TlmO (d

Fig. 26.Estimated individual and RMS totalsystematic uncertainties as functions of cool-ing time. These uncertainties are the same forall samples.

VII. RESULTS AND CALCULATIONS

Let F(t,T) be the decay heat t seconds after anirradiation of T seconds at constant fission rate inthe absence of neutron capture in fission products.Our experimental data may be written in terms ofthis function as F(t, 2 x 1(P). To facilitate com-parison with the present ANS standard and with theresults of others, we extended our data to theinfinite-irradiation case (defined as T = 10i’s) using

F(t,~) = F(t, 2 X 10’) + F(t + 2 X 10’, ~) .

The second term on the right was obtained using theCINDER-10 summation coden with the ENDF/B-IV data base as listed and corrected by England andSchenter.2S Its contribution to the infinite-irradiation decay heat was 16°A at t = 10 s, 51% att = 2500s, and 95% at t = 10’s. It was assigned anuncertainty of 2%, based on the value e8timated bySchmittroth and Schenter24 for a 107 s irradiation.This uncertainty was combined quadratically withthe experimental uncertainty to obtain the uncer-tainty for the extended experimental data.

.

,

24

—- Total uncwtainty ~

u ■ [r: + (1.3s) ]~z

—- - RMS .%xxtw of tha data S

3 ------ Systematic uncwtainty ~a

I$ \s \b2 .\

‘.\

/

t’=. x$ )’

z )).-2 “>..... ,

\\ /.* /’

1,\> \ .“

‘-->- .z -~=--.-- - ---

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

I

010 100 1000 104 10’

Coalmq lima (s1

Fig. 27.Total uncertainty in the data, u, systematicuncertainty, u., and RMS scatter of the data,S, at various cooling times. In calculating u,the value of S was increased by the factor 1.3 tocompensate for a possible underestimate of thetrue scatter in the data, which results from thesmall number (3) of data points considered. At6000- and 7000-s cooling times, where thecurves are dotted, the scatter was larger thunshown because of the disturbances cawed byrefilling the calorimeter reservoir with liquidhelium. Correct values for u are given in Tablev.

The CINDER-10 code and ENDFfB-lV data base

were also used to calculate values of F(t, 2 x 1(Y) and

F(t, m) at cooling times corresponding to those of

the experimental data. The experimental results

and uncertainties, calculated decay heat values,

and the ratios of experiment to calculation are given

as functions of t in Table V.

Figure 28 shows the experimental and calculateddecay heats for 2 x 10’ s irradiations, and Fig. 29shows their ratio.

Caolmg T,ma (s)

Fig. 28.Experimental and calculated decay heat for a2 x 1P s irradiation at constant flux.

t235LJ TIIWmaI thdm , ZS@ t Itradolbn.

I .04 “Cak . CINOER-10 wilh ENDF/S-I!I 4u1o.

I I

-f- A~ 1.02 .

1

.. . . . .

g . / ““● . ..4A=..

“.. “. ●

“.: I.m ———

*“. .

.~ % . . .

.

x 0.98 . . . .6

.“

:a

0.96

0.94 LA AA1lII . _l. A1lulLl A A null__.L-IKt ml 1000 ,.4 lo~

Coding T ima (s]

Fig. 29Ratio of experimental to calculated decay heatfor a 2 x I(Y s irradiation at constant flux.

25

TABLE V

EXPERIMENTAL AND CALCULATED DECAY HEAT FOR THE PRODUCTS OFTHERMAL FISSION OF ‘“U

2 x 104 s Irradiation

ExperimentalCooling DecayTime Heat(s) (?4eV/fiss)

10

15

20

2s

30

35

40

4s

50

5s

60

6S

70

75

80

8S

90

9s

100

110

lpo

130

140

1s0

160

170

180

190

200

2s0

300

3s0

400

450

500

600

700

800

900

1000

26

8.10

7.38

6.933

6.S95

6.335

6.109

5.920

5.758

S.614

S.481

5.358

5.244

5.141

S.047

4. 9S8

4.881

4.806

4.734

4.667

4.s44

4.426

4.339

4.251

4.170

4.092

4.021

3.960

3.899

3.841

3.608

3.419

3.26S

3.13s

3.022

2.920

2.746

2.598

2.474

2.363

2.264

CalculatedOemyHeat Ratio

Experimental using CINDER-10 Exp/CalcUncertain y snd fNOF/B- IV Decay

(1 u in $) (* V/fiss) Heat

4.1

3.0

2.6

2.4

2.s

2.2

2.1

2.1

2.0

2.0

2.0

1.9

1.9

1.9

1.8

1.B

1.8

1.8

1.8

1.8

1.7

1.7

1.7

1.7

1.7

1.7

1.7

1.6

1.6

1.6

1.6

1.6

1.6

1.6

1.6

1.5

1.5

1.s

1.s

1.5

7.780

7.239

6.B42

6.S31

6.276

6.060

5.B73

5.709

5.562

S.429

s .309

5.198

s .097

s .003

4.915

4.834

4.7S8

4.686

4.619

4.496

4. 38s

4.286

4.195

4.112

4. 03s

3.964

3. B99

3.838

3.780

3.s41

3. 3ss

3.20S

3.078

2.969

2.873

2.709

2.S72

2.4S5

2.3S1

2.2s6

1.041

1.019

1.013

1.010

1.009

1.008

1. OOB

1.009

1.009

1.010

1.009

1.009

1.009

1.009

1.009

1.010

1.010

1.010

1.010

1.011

1.009

1.012

1.013

1.014

1.014

1.014

1.016

1.016

1.016

1.019

1.019

1.019

1.019

l.OIB

1.016

1.014

1.010

1.008

1. 00s

1.003

Infinite IrradiationExperimental

Decay HeatExtended byCINOER-10

amdENDF/& XV

(hkV/fiss)

CalculatedOecay Heat Rat h

‘merimental usinl CINDER-10 Exp/CalcUncertsintya and ;NDF/B- IV Decay(1 a in %) (t4ev/f iss) Heat

9.65

8.93

B.4B0

8.142

7.882

7.656

7.467

7. 30s

7.160

7.027

6.904

6.790

6.6B7

6.S93

6.S04

6.427

6.3S1

6.279

6.212

6.0B9

5.971

S.8B4

s. 79s

5.714

S.636

S.S6S

S.S03

S.442

s . 3s4

S.lso

4.960

4. B05

4.673

4.ss9

4.456

4.280

4.130

4.004

3.B90

3.789

3.5 9.327 1. 03s

2.5 8.786 1.016

2.2 8.389 1.011

2.0

1.9

1.8

1.7 7.420 1.006

1.7

1.6

1.6

1.6

1.s

1.s

1.s

1.s

1.4

1.4

1.4

1.4

1.4

1.4

1.4

1.4

1.4

1.4

1.3

1.3

1.3

1.3

1.3

1.3

1.3

1.3

1.3

1.3

1.2

1.2

1.2

1.2

1.2

6.85S 1.007

6.461 1.007

6.164 1.008

S .6SS 1.010

S.323

4.616

4.243

3.984

3.783

1.012

1.009

1. 00s

1.002

TABLE V (Cent).

CoolingTime(s)

2 x 104 s Irradiation

ExpcsirnentalDecayIlcat

@la\t/ f iss)

CalculatedOocay Neat Ratio

Exporimcntalusing CINWR- 10 Exp/CalcUncertainty and EN12F/B- IV Decay[1 a in 2) (NcV/fiss) Heat

1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

2s00

3000

3s00

4000

4s00

sow

6000

7000

8000

9000

10000

1s000

20000

2s000

30000

62133

100000

2.173

2.093

2.020

1. 9s0

1.886

1.827

1.773

1.721

1.671

1.627

1,431

1.283

1,166

1.067

0,9808

0.9111

0.7998

0, 719s

0.6480

0.5886

0, S401

0.3803

0.2918

0.23S9

0.1947

0.0823

0. 04s4

1.s1.s1.s1.s1.s1.s1.s1.s1.s1.s1.5

1.s

1.5

1.s

1.s

1.s

2.5

2.0

1.6

1.6

1.7

1.B

2.0

2.2

2.3

2.2

,3.2

2.174

2.098

2.027

1.962

1.901

1. 84S

1.791

1.741

1.694

1.6S0

1.460

1.311

1.191

1.092

1.008

.0.9362

0.8198

0.7287

0.6S53

0.S948

0.5440

0. 37?8

0.2874

0.2311

0.1923

0.0832

0.04ss

1. I-1oo

0.99B

0.997

0.994

0.992

0.990

0.990

0.989

0.986

0.986

0.980

0.979

0.979

0.977

0.9?3

0.973

0.976

0.987

0.989

0.990

0.993

1.007

1.01s

1.021

1.012

0.989

0.998

Infinite IrradiationExperimental

Decay Neatl!xtcn~cd byCINDER-IO

andEtiDF/B- IV

(NeV/fiss)

3.696

3.614

3.s39

3.467

3.401

3.340

3.284

3.229

3.177

3,131

2.92S

2.768

2.641

2.S33

2.438

2.360

2.231

2.13S

2.049

1.97s

1.912

1.691

1.ss2

1 .4s3

1.37s

1.10s

0.971

Experimental

Uncertaintya(1 o in $)

1.2

1.2

1.2

1.2

1.2

1.2

1.2

1.2

1.2

1.2

1 .s

1.3

1.3

1.3

1.3

1.3

1.s

1.s

1.s

1.s

1.s

1.6

1.7

1.7

1.7

1.9

1.9

Ca lCUI atedDecay NOat Ratiousing CINOER- 10 Exp/Calcand ENDF/B- IV Decay

(14eV/f iss) Heat

3.416 0.996

3.1s4

2.SS7

2.2s1

2.0S6

1.916

1.689

1. S47

0.969

0.993

0.991

0.991

0.997

0.998

1.001

1.003

1.002

-.aCalculated on the assumptions that the calculated infinite ir~iation decay heat curve has 2% uncertainty for

t > z ~ lo4 ~, ~d that this uncertainty is unco~elated with the eqerimental uncertainty.cool -

.

.

10 ~~“$

[,,,,1 I ( 1 1 1 .-r

\“’..,

Z35

k

U Tharmal ft$xon

in hntta (tradmtmn

● Expartmant :eat to inf wrod.)‘$

e‘. — CINOER-tO colcumoan wt!n

‘\ ENOF) a-x data‘.

: ‘. --- ANS standard(1971, lb [9731

o~ “ ‘ “’’”1 ,, 1 I 1 {

10 100 1000 104 IOaCaoq Ttma Is)

Fig. 30.Extended experimental data, summationcalculation-s, and present ANS 5.1 Standardfor an infinite (101’ s) irradiation at constantflux with no depletion or capture. The ANSStandard plus 20% is currently used in reactorsafety evaluations.

Figure 30 compares the extended experimentaldata, the calculated F(t, ~), and the present ANSDecay Heat Standard. It may be seen that the ex-tended experimental data are in good agreementwith F(t, ~) calculated from ENDF/B-IV data, andare % 7°A below the ANS standard at short coolingtimes. Moreover, the experimental uncertainty issignificantly smaller than that assigned to thestandard,

ACKNOWLEDGMENTS

We wish to thank the following for their contribu-tions to this project: E. T. Jurney for measuring thegamma spectra, D. W. Muir for performing the

4 Monte Carlo calculations, G. W. Knobeloch and G.W. Butler for determining the number of fissions, T.R. England and M. G. Stamatelatos for making the

summation calculations, Steven Koczan andGilbert Suazo for supervising the hydrogen-furnace

brazing operation on the calorimeter, J. L. Moorefor helping to build the apparatus and to carry outthe measurements, Frank Newcom for preparing theillustrations, and the OWR personnel for theircooperation and assistance.

We also wish to thank J. K. Dickens, R. G.Helmer, and R. L, Heath for their cooperation inmaking the fission determination intercomparison.

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28

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19. T. R. England and M. G. Stamatelatos, “Betaand Gamma Spectra and Total Decay Energiesfrom Fission Products, ” Trans. Am. Nucl. Sot. 23,493-494 (1976); T. R. England and M. G.Stamatelatos, “Multigroup Beta and Gamma Spec-tra of Individual ENDF/B-IV Fission-ProductNuclides,” Los Alamos Scientific Laboratory reportLA-NUREG-6622-MS (December 1976).

20. E. D. Cashwell, J. R. Neergaard, C. J. Everett,R. G. Schrandt, W. M. Taylor, and G. D. Turner,“Monte Carlo Photon Codes: MCG and MCP, ” LosAlamos Scientific Laboratory report LA-5157-MS(March 1973).

21. J. K. Dickens, T. A. Love, J. W. McConnell, J.F. Emery, and R. W. Peelle, “Fission Product Betaand Gamma Energy Release Quarterly ProgressReport for July—September 1975,” Oak Ridge

National Laboratory report ORNL-TM-5156(November 1975).

22. T. R. England, M. G. Stamatelatos, and N. L.Whittemore, “Decay Heating, Gas Content, andSpectra Calculations for Fission Products,” in “Ap-plied Nuclear Data Research and Development,January l—March 31, 1976, ” Los Alamos ScientificLaboratory report LA-6472-PR (August 1976), p. 60.

23. T. R. England and R. E. Schenter, “ENDF/B-IVFission-Product Files: Summary of Major NuclideData, ” Los Alamos Scientific Laboratory report LA-6116-MS (ENDF-223) (October 1975).

24. F. Schmittroth and R. E. Schenter, “Uncertain-ties in Fission-Product Decay-Heat Calculations, ”Hanford Engineering Development Laboratoryreport HEDL-SA-1 114 (1976) (accepted by NUCLSci. Eng.).

18. G. A. Bartholomew, A. Doveika, K. M.Eastwood, S. Monaro, L. V. Groshev, A. M.

29

APPENDIX

INDEPENDENT MEASUREMENT OF NUMBER OF FISSIONSIN LASL ‘a6U SAMPLE

by

R. G. Helmer and R. L. Heath

Idaho National Engineering LaboratoryEG&G Idaho, Inc.

Two quantities are determined independently inthe decay heat measurements of Yarnell and Bendt’and Dickens.% These are the decay energy releaserate and the fissions rate in the irradiated ‘W sam-ples. In this summary the resulta are given for an in-dependent determination of the number of fissionsin these samples. This work was carried out at theINEL and provides support for the results in thesereports. It should be emphasized that the results atLASL and INEL are completely independent due tothe different methods used. The two methods usedat ORNL are, in part, related to the methods at bothLASL and INEL.

The following intercomparison of the measure-ments of the number of fissions has been carried out.A 63-mg sample of enriched 28’U (93%) wasirradiated for 29 s in a thermal flux in the OmegaWest Reactor at LASL. Except for its duration, thisirradiation was the same as the irradiations for theLASL decay heat measurements. The uraniumsample was dissolved and diluted to 1 liter. Samplesfrom this solution with volumes of 10.0 ml wereshipped to ORNL and the INEL for analysis. A por-tion of the solution also was analyzed at LASL bythe methods used for the decay heat samples anddescribed in Sec. 111.B of Ref. 1.

At the INEL the 10-ml? sample was completelytransferred, a small amount at a time, to a smallpiece of filter paper and dried. The gamma-rayspectrum of this sample was measured in a standardgeometry (at a 10-cm source-detector distance) on aGe(Li) detector. The determination of the efficiencyfor the detection of gamma rays and the dataanalysis methods have been described in Refs. 3 and

4. Four spectra were obtained. In order to determinethe number of fissions in this sample, our methodrequired a knowledge of (1) the absolute gamma-rayintensity, or branching ratio, for each gamma rayused, (2) the half-life for each isotope, and (3) thefission yield from thermal fission of ‘a’U. Therelationship is

A A~T

‘= EoBo Y l-=-AT ‘

where

N = number of fissions,

E = detection efficiency for full-energypeak,

A= area of full-energy peak for a gammaray,

B= gamma-ray branching ratio,T= count duration,r = decay time,Y= fission yield, andA = in 2A’itl, where TIIS = half-life.

The decay scheme parameters, T,,, and B, and fis-sion yields used in this analysis are given in TableA-I. Over the past several yeara we have been in-volved in the Interlaboratory LMFBR ReactionRate (ILRR) Program. As part of this effort we haveprovided an evaluation of decay scheme parametersfor these fission product isotopes. The values inTable A-I are from the latest evaluation;’ previousevaluations for the ILRR Program are given in Refs.6 and 7. The uncertainties quoted in the table are68% confidence level (1 u) values.

.

30

TABLE A-I

PARAMETERS OF FISSION PRODUCT ISOTOPES FOR INEL ANALYSES

Parameter mIjfr ‘OsRu MOBa-14~a

Half-life (days)’ 64.1 + 0.3 39.43 * 0.10 12.789 + 0.006Gamma-ray energy (keV) 724.2 756.7 497.1 1596.2Branching ratio (%)’ 44.1 + 0.5 54,6+ 0.5 89+1 95.40 & 0,08Fission yield (%)

ILRR’ 6.52 + 0.13 3.02 + 0.06 6.22 + 0.12Meelc and Rlderg 6.44 + 0.09 3.15 + 0.06 6.29 + 0.09

The ILRR Program has also involved an in-terlaboratory comparison of absolute gamma-ray in-tensity measurements. In Ref. 3 (Tables VI and VII)counting results are given for similar samples fromour Laboratory and groups at Argonne NationalLaboratory, Hanford Engineering DevelopmentLaboratory, and Atlantic Rlchf3eld Hanford Com-pany. In essentially all cases, the results agree

within the quoted uncertainties, which are about

2%. This provides verification of our counting

methods.

Two sets of thermal neutron fission yields, in

Table A-I, have been used with the results of our

gamma-ray counting. The first set consists of

measured values from the ILRR Programs and the

second set is the evaluated values proposed by Meek

and Ridef for inclusion in the ENDF/B-V data file.

As proposed for the ENDF/B file the latter yieldshave associated codes which indicate a range of un-

certainties. The errors in Table A-1 are the max-

imum values for the ranges quoted. The uncertain-

ties for the ILRR yields include only the contribu-

tion from the fission rates per atom of ‘*8U. These

errora are larger than that of the K-factor quoted in

Sec. 111.D of Ref. 1 because they must relate to a

known mass of 20’U in the fission chamber, whereas

the K-factor depends only on a mass ratio. The

other componeni~ of the error in the final ILRR fis-

sion yields are not included here, since they also oc-

cur in our counting results and will be accounted for

there.

The results flom our counting experiments are

given in Table A-II for each set of fission yields. The

only significant difference is in the value from 1°SRu

which varies by 4~0 causing the averages to differ by1%. The results with the ILRR yields are more con-

sistent; their spread is 2Y. compared to 4% with theMeek and Rider values. This might be expectedsince the ILRR yields are from counting experi-

ments similar to this one. The averages in Table

A-II are weighted averages. “

The various contributions to the uncertainties in

Table A-II are listed in Table A-RI. The uncertain-

ties in Table A-II for the individual gamma rays in-

cluded the contributions in Table A-III except for

the fission yield errors. We have thus assumed that

the yield values are correlated; this is exactly the

case for the ILRR yields. The fission yield error,

2.0% for ILRR and an average of 1.6% for the Meek

and Rider values, is included in quadrature in the

last entry of Table A-II. Since the same gamma-ray

branching ratios were used in measuring the ILRR

fission yields and in our data analysis, this error

cancels and is not included when the ILRR yields

are used.

The results of the LASL analysis of samples from

the same solution are shown in Table A-IV. The

final table entry includes a systematic error of

0.73%, from Sec. 111.D of Ref. 1, in addition to the

precision error in the weighted average.

As can be seen, the LASL result of (1.179+ 0.0Q!3)

x 101° fis/mf is in excellent agreement with the

INEL result of (1.176 + 0.026) x 10’0 fis/ml. It

should be emphasized that these two values are in-

dependent of each other. The only point in common

is the fact that fission chambers are used in the

basic fission rate measurements. Thus an excellent

check is provided on the presence of any significant

31

TABLE A-II

NUMBER OF FISSIONS FOR LASL SAMPLEFROM INEL ANALYSIS

Number of Fissions (lO’”/ml)m

Isotope ILRR Yields Meek and Rider Yields

“Zr-724 1.176 + 0.020 1.186+ 0.023-766 1.165 + 0.020 1.175 + 0.023

‘“’Ru 1.189 + 0.019 1.141 ● 0.022140Ba-ltOLa 1.171 + 0.020 1.158 + 0.020Average 1.176 + 0.010 1.164 + 0.011

1.176 + 0.026b 1.164 + 0.022b

“See text for discussion of error contributions.

bUncertaintiesin fission yielde are added in quadrature to that of the average; eee text.

.

TABLE A-III

UNCERTAINTIES ASSIGNED IN INEL MEASUREMENTS

Uncertainty (70)

Half-Life Branching Deteetor Fission Yield

Isotope counting’ Terms Ratio Efficiency ILRR Meek and Rider

qr 0.5 0.5 1.0 1.5 2.0 1.410~Ru 0.4 0.2 1.1 1.5 2.0 2.0

140Ba.140La 0.8 ~ 0.1 0.1 1.5 2,0 1.4

.

.

.

.

“This contribution includes errore in peak areas and the consistency of the measurements.

32

,

TABLE A-IV

NUMBER OF FISSIONS FROMLASL ANALYSIS

(Results from Ref. 10.)

Fissions PrecisionIsotope (lo’”/ml) (%)

“MO 1.180 0.19‘40Ba 1.171 0.46

Average 1.179 + 0.0031.179 + 0.009’

‘Uncertainty includes contribution of 0.72% from K-factor asdiscussed in Sec. 111.D of IZef. 1.

systematic errors that have not been taken into ac-

count.

One minor restriction on the above comparison

should be noted. The INEL-LASL agreement above

is for the LASL radiochemical analyses of ‘OMo andl’OBaO~ aaociation with the decay heat measure-

ments, the LASL determination of the number of

fissions is based on both the radiochemical analyses

for these isotopes and gamma-ray spectral analyses

for several isotopes. Any systematic difference be-

tween these two types of analyses would confuse the

question of agreement between the LASL and INEL

results. In fact, the values in Table I of Ref. 1 do give

a slightly lower, by 0.3%, value from the

radiochemical analyses than for the average values.

However, even if this bias really exists, the INEL

and LASL analyses still will be in excellent agree-

ment.

From the sample sent by LASL to ORNL, the

ORNL group’ made two sources, one containing

1.00% of sample and the other containing 5.00%.

These samples were counted with the same Ge(Li)gamma-ray detectors as used to determine the fis-sions for the ORNL decay heat measurements. Two

calibration methods were used. The first, called the

absolute method, involves determining the absolute

gamma-ray emission rates and using the gamma-

ray branching ratios and isotopic fission yields to

determine the number of fissions. This is the same

as the INEL method except different isotopes were

used. The second calibration method is the K-factor

technique where a fission chamber is used to deter-

mine the number of fissions in the sample. The

gamma-ray counting rates are determined for the

same, or an identical, sample. Then only relative

gamma-ray counting rates are needed for the un-

known sample. This is, in part, simil~ to the LASL

method.

The values of the gamma-ray branching ratios

and fission yields used by ORNL in the “absolute”

methods have been compared with various evalua-

tions. The agreement is good; in the worst cases, the

variations are about lYo.

After ORNL had completed their counting, the

source containing 5.00% of their sample was sent to

the INEL. If the sample preparations were all

correct, the relative activity of the original INELsample to that of this sample should be 20.00. Thisratio, as measured at the INEL, was 19.97 + 0.14.

This indicates that the preparations were satisfac-

tory.

The results of the ORNL measurement for the

number of fissions in the LASL sample are given in

Table A-V for three isotopes and the two methods

described above. The uncertainties in the six in-

dividual values are quoted in Ref. 2 as 2.5%. We

compute the uncertainty in the final average to be

1.5%, but this depends on the magnitude of the

separate components of the individual errore and

TABLE A-V

NUMBER OF FISSIONS FROMORNL ANALYSIS

(Results horn Ref. 2.)

Fissions (10’O/m.Oa

K-FactorAbsolute Method

Isotope Method (20 cm)

‘Mo 1.172 1.19318zTe 1.178 1.197

@7zr-#7Nb 1.176Average m

1.1901.193

Average 1.184

“Uncertainty in each of the six meaaured values is assigned as2.5%

33

the assumptions” made about their correlations,With this error, the final ORNL value would be(1.184 + 0.018) x 10’0 fis/mL This is in good agree-

ment with the LASL and ‘INEL values of (1.179+

0.009) x 1010 and (1.176 + 0,026) x 10iO fis/ml,respectively. Although one may question whether

these uncertainties are all comparable (e.g., the

LASL value is three times more accurate than the

INEL value), the agreement to better than 1% in the

values is very satisfying and should help place the

associated decay heat measurements on a firm basis.

APPENDIX REFERENCES

1. J. L. Yarnell and P. J. Bendt, “Decay Heat fromProducts of ‘W Thermal Fission by Fast-ResponseBoil-Off Calorimetry, ” Los Alamos ScientificLaboratory report LA-NUREG-6713 (1977).

2. J. K. Dickens, Oak Ridge National Laboratory,personal communication, ApriI 1977.

3. R. C. Greenwood, R. G. Helmer, J. W. Rogers,N. D. Dudey, R, J. Popek, L. S. Kellogg, and W. H.Zimmer, “Nonfission Reaction Rate Measure-

ments,” Nucl. Tech, 2S, 274 (1975).

4. R. J. Gehrke, R. G. Helmer, and R. C.Greenwood, Idaho National EngineeringLaboratory, to be published.

5. R. G. Helmer and R. C. Greenwood, “LMFBRReaction Rate and Dosimetry llth ProgressReport,” to be published as HEDL-TME report.

6. R. G. Helmer and R. C. Greenwood, “EvaluatedDecay Scheme Data,” Nucl. Tech. 26, 258 (1975).

7. R. G. I-Ielmer and R. C. Greenwood, “LMFBRReaction Rate and Dosimetry 9th Progress Report,”

HEDL-TME 74-45 (W. N. McEhoy, Ed.), P. ANC-49 (1974).

8. D. M. Gilliam, “Memorandum for ILRR Partici-pants, ” personal communication, July 1976.

9. N. E. Meek and B. F. Rider, “RecommendedYields for ENDF/B (June 1976),” as quoted in Ref. 8

above.

10. G. W. Knobeloch, Los Alamos ScientificLaboratory, personal communication, November

1976.

34