Крючков Фундаменталс оф Нуцлеар Материалс Пхысицал Протецтион 2011

R=240 Pueff (473fis/s ×g)ε 2 exp(-P /τ ) ´

	´[1- exp(-G /τ )]∑P(ν )	ν (ν -1)	(5.22)
			,
		2
	ν

where Р is the pulse count predelay time, G is the coincidence count time; τ is the neutron lifetime in the detector, ε is the neutron detection efficiency,

νis the number of neutron emitted by fission, and P(ν) is the probability of

νneutrons to be emitted by fission.

A schematic of a passive neutron coincidence counter for measurements of small-size samples is shown in Fig. 5.20.

Preamplifier

П

Lids

3Не-counter

П

Cavity Sample

Cadmium

Polyethylene

Fig. 5.20. Schematic of a passive neutron coincidence counter for measurements of small-size samples

The neutrons emitted by the sample are slowed down in the polyethylene and detected by 3Не-counters. The cavity for the samples is cadmium-shielded against slow neutrons, coming back from the polyethylene, to reduce the sample self-screening.

The counter operates in two modes: for thermal and fast neutrons. For fast neutron count, the sample cavity walls are coated with cadmium. Measurements in the fast-neutron mode fit better large-mass samples and thermal-neutron measurements are fit for small-mass samples. Thermalneutron measurements entail a smaller statistical error of small-size sample control. For large-size samples, a great cross-section value leads to the inner space being screened and the result distorted.

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The counter is calibrated to interpret the analysis results. Calibration curves for the fastand thermal-neutron modes differ greatly. The calibration curve for the fast-neutron mode comprises two different segments: a segment with the influence of self-screening present (samples of the mass up to 500 g of 235U), and a further segment with multiplication where the 235U mass is rather large to compensate for the self-screening effect thanks to auxiliary fissions. Calibrating the interval of 150–900 g of 235U requires more than one standard. Each material type needs a special curve (Fig. 5.21).

.

time unit

events Coincidence count rate

500

400

300

200

100

0

0

20

40

60

80

100

Weight of 235U, g

Fig. 5.21. Coincidence count rate depending on the 235U mass for low-enriched U3O8 samples in the thermal neutron detection mode

Table 5.12 gives characteristics of an active well coincidence counter (AWCC).

There is a great variety of instruments based on neutron coincidence count, still all of them have standard electronic components.

Both neutron and gamma ray measurements involve a problem of measuring lengthy NM samples. Passive measurements of lengthy samples require ensuring similar probability conditions for detection of neutrons

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emitted by all sample surface elements, while active measurements additionally require the same irradiation of all these elements by source neutrons. So every effort is made in designing neutron measuring systems to ensure a uniform sensitivity and a uniform field of external source neutrons in the cavity for the samples.

				Table 5.12
Data of active well coincidence counter (AWCC)
Characteristics	Thermal mode			Fast mode
Mass of measured samples	up to 100 g of 235U			100–20000 g of 235U
Coincidence count rate for low-	11 count/(s×g of	235	U)	0.18 count/(s×g of
enriched U3O8 sample				235U)
Absolute measurement error for	0.3 g 235U			18 g 235U
large-size samples for 1000 s

Calorimetry

Calorimetry is a passive nondestructive technique of NM (plutonium and tritium) control based on accurate temperature measurements. Generally, this is a more accurate technique, still it requires good temperature stability and control thereof, and is less fast and handy as compared to other NM nondestructive measurement methods.

Calorimeter is an instrument to measure the heat quantity emitted by an object.

Calorimetry offers an advantage that measurement results do not depend on the sample geometry, the matrix material or the NM distribution inside the sample. No standards identical to samples are required for calibrations. Calorimetric analyses have the accuracy comparable to that of chemical analyses .

Method description

All energy of α-decays transforms into heat. Each α-decay is accompanied by the energy yield of Q = (M 240 Pu − M 236 Pu − Mα )c2 =

Measurements of homogeneous burnt-up Pu samples give the accuracy of 0.1% as in chemical analyses and weighing. Measurements of waste containing Pu of a uniform isotopic composition gives a 1% accuracy.

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5.25578 MeV. b-decay of 241Pu yields Qβ = 20.81 keV, and b-decay yields 3H Qβ = 18.59 keV.

Radioactive decays of 240Pu liberate P = l×N×Q of power, where N is

the number of 240Pu atoms, and l is the 240Pu decay constant. a-decay of 240Pu liberates 0.00707±0.00002 W/g of power. The total power generated by

all plutonium isotopes is Рeff(W/g)=ΣfiPi, where fi is the mass fraction of a single isotope.

Table 5.13 gives an example of the contribution made by some isotopes to Рeff. Рeff increases with the Pu burn-up increase. Burn-up fraction is characterized by the content of 240Pu.

		Table 5.13
Contribution of selected isotopes to Рeff for one of the samples
	Content, mass fraction	Contribution to heat
Isotope		generation, %
238Pu	0.0006	11.0
239Pu	0.8567	53.3
240Pu	0.1211	27.7
241Pu	0.0194	2.1
242Pu	0.0022	0.0
241Am	0.0016	5.9

By measuring the heat generated by a plutonium sample and knowing its isotopic composition, one can find the content of Pu.

The sample-generated heat is recorded by a heat sensor out of a sensitive wire laid in circles around the sample cavity. A double calorimetric bridge with two identical thermostats is shown in Fig. 5.22.

Measurements are done using a potentiometer or a digital voltmeter incorporated in an electric circuit called Wheatstone bridge (Fig. 5.23). The measured voltage is proportional to the difference between the temperature in the sample space and the temperature of the comparison probe, the latter

being in an air or water “bath” with a constant tem perature (maintained within ±0.001 °C).

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	Sample thermostat	Comparison sensor
		thermostat
Resistance bridge
nickel
winding
Heat chamber
wall		Sample
Air		cavity
gap
Plastic		Heat-insulating
end		material

Fig. 5.22. Schematic of a double calorimetric bridge with two identical thermostats

V

Reference arm

Current

source

Reference arm

Reference arm

Test arm

Fig. 5.23. Wheatstone bridge for heat flux measurements

If the temperature in both thermostats is identical, that is there is no sample, the Wheatstone bridge is balanced. When the sample is placed in the thermostat, the temperature changes and the bridge turns unbalanced.

The voltmeter indication is taken some time after the sample is placed in the thermostat. The time needed to have equilibrium reached depends on the sample dimensions and amounts to hours (Fig. 5.24). Preheating of the

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thermostat chamber for the sample helps reach the equilibrium in several times as fast.

To determine the power generated by the sample in the thermostat from the measured potential difference, a sensitivity diagram is normally used.

Equilibrium value

Bridge voltage, V

Time, h

Fig. 5.24. Time-dependent voltmeter indications

To this end, a curve for the thermostat sensitivity to the samplegenerated power is plotted. Fig. 5.25 shows a calorimeter sensitivity diagram option.

V/W
S,			W, W
10	20	30	40

Fig. 5.25. Calorimeter sensitivity diagram

For calibration, the calorimeter is switched on and the potential difference at the bridge ends (ВР0) is measured without a sample or any other heat source. Then a plutonium standard is placed in the sample

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chamber, the equilibrium value for the potential difference ВРs is measured and the calorimeter sensitivity is calculated by the formula:

S = (BPS – BP 0)/WS ,

(5.23)

where WS is the standard-emitted power (not known).

Normally, the quantity S depends slightly on the heat source power. For example, a 1.6% sensitivity decrease was recorded in measurements of samples with the power of 0.1 to 10 W.

As the diagram in Fig. 5.25 shows, sensitivity in the given case is not constant and depends on the sample-generated power.

By and large, the best of the calorimetric analyses have the following

errors: power measurement error <0.1%, effective specific energy release determination error <0.2%.

Typical calorimeter parameters: diameter – 120 mm, height – 275 mm, range – 0–6 W.

Referenced standards or electrical standards (probes) are used to calibrate calorimeters:

1)heat generation standards – 238Pu samples. These feature:

∙small dimensions (enable determination of errors depending on the heat distribution over the chamber);

∙qualification accuracy – 0.02%;

∙decay may be accurately taken into account;

2) electrical heat generation standards. These feature:

∙absence of radioactive radiation;

∙no need for decay to be taken into account;

∙electronics may not depend on the calorimetric system;

∙electronics requires calibration.

The following is taken into account in calorimeter design.

∙Sample size (specifies the sample chamber size). A close samplecalorimeter contact makes it possible to minimize the analysis time. The chamber diameter in existing calorimeters varies form 1 to 30 cm.

∙Sample heat power. High-power samples need low-sensitivity calorimeters with a low heat resistance, and small-power samples require high-sensitivity and highly heat-resistant calorimeters.

∙Graduation techniques. The calorimeter design depends on what heat source is used for graduation (a radioisotope or an electrical one).

∙Capacity. Selection of the calorimeter type depends on the analysis time required.

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∙Accuracy. When the calorimeter type and its operating mode are selected, the analysis accuracy is planned given the time to be spent and other conditions.

∙Application environment. Selection of the calorimeter design depends on the environment and the available workroom area to install it.

5.3. Destructive analyses

Normally, a destructive analysis (DA) includes sample taking, sample chemical treatment and measurement stages. Test material may be a single item or a bulk material. Destructive analysis normally offers a higher accuracy of results than nondestructive measurements. However, DA takes more time to perform and is more costly than nondestructive tests.

Destructive analyses are used to:

∙check nondestructive measurement data;

∙perform critical test measurements;

∙qualify standards.

Sample taking

Destructive analyses have a small portion of controlled material examined and require a representative sample to be taken for analysis. The sample composition should be strictly representative of the average material composition with the sample mass (volume) accurately determined.

If the sample is soluble, it needs to be, generally, dissolved. Sometimes, uranium or plutonium requires separation from interfering elements.

Sample should be taken given a potential heterogeneity of NM, which can be of three types:

∙heterogeneity of material within the container;

∙differences among containers;

∙differences among groups of containers.

Some dispersed and powdered materials, such as ash and roasted scrap, are hard to mix. A number of factors exist that require homogenization of dry powders and dispersed compositions. These are, for example:

∙variations of the composition depending on the particle size and density;

∙differences in the particle forms;

∙cohesion and conglomeration of particles.

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Nuclear industry often deals with insufficiently homogeneous materials, this limiting sample taking capabilities by ladling material to compare from each container batch. Random sampling is so employed, which requires more samples in each case to account for potential differences.

The sample taking method and equipment are chosen given the identity of controlled material, the requirements to the accuracy of results, the material accessibility for sampling and safety of sample taking operations.

Within the nuclear fuel cycle, sample taking and treatment methods differ between sites. There are two categories of sampling-related errors. One should differentiate sample taking error from analytical error:

σ s = (σ t2 − σ a2 )1/ 2 ,

(5.24)

where σs is the random sampling error; σt is the total random deviation of the results for all analyses of all samples; and σa is the random deviation estimated from replicated analyses of each sample.

No replicated analyses with each sample are however performed at some enterprises and no random sampling error is differentiated from the random analytical error. In this case, the sample taking error may be estimated from the spread of the standard analysis results, which is approximately equal to the random analytical error:

σ s = (σ 12 − σ 2st )1/ 2 ,

(5.25)

where σs is the estimated random sampling error; σ1 is the random spread based on single analyses of all samples; and σst is the random spread based on replicated analyses of the standard.

Interpreting the obtained results leads to two conclusions: the solutions in enrichment and conversion processes are fairly homogeneous so representative samples thereof can be obtained through comparatively simple sample taking operations. NM scrap and waste are heterogeneous so large sample taking errors should be expected. This requires prior homogenization with a random sample taking technique to be employed to get a representative result.

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Dissolution of NM samples

One should always try to make so that the inspected material is fully dissolved. Even minor amounts of deposit may cause major losses of the target element. Pure uranium preparations are fairly simple to dissolve.

In the event of plutonium and compounds thereof (thorium as well) there is a potential problem of extremely chemically stable dioxide being formed and disintegrated, having, above other things, an extremely high melting temperature.

Mixed uranium and plutonium dioxides are highly resistant to chemical effects, still they have higher dissolution rates than pure plutonium preparations.

NM extraction from solutions

Uranium can be fairly selectively separated from a solution by extraction thereof into an organic solution other than mixable with the original aqueous solution.

Extraction is an auxiliary analytical chemistry purification process used specifically to identify uranium. Though some elements, including plutonium and thorium, are also extractable, selecting proper conditions for separation helps avoid obstacles caused by these elements at subsequent identification stages. So, by changing the plutonium oxidation level, one can make plutonium extraction quite easily controllable.

The so-called purex-process is the most common spent nuclear fuel treatment technology. This is an extraction process using tributylphosphate (н-С4Н9О)3РО (TBF) solutions in saturated hydrocarbons (hydrogenated kerosene).

Uranium purification of fission products (FP) after three cycles has a factor of around 107, and uranium purification of plutonium has a factor of 3×105.

Ion-exchange separation

Ion-exchange separation is used for selective extraction of the analyzed element from a multi-component mixture. In fact, the whole of the uranium ion-exchange extraction and separation process is run, to the highest extent possible, with plutonium solutions in a hexavalent form. In aqueous solutions, uranium, plutonium and a great deal of other elements may occur as components of cationic and/or anionic complexes.

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