interval specified for computing the calibration characteristics of type KFL-2-1 instruments for a determination error of 4.5%.

The above primolin-stability characteristics make it possible to recommend it as a test- ing means in the excitation range of 365 • 20 nm and the fluorescent range of 475 • 25 nm. Instrument-testlng solutions are prepared by repeated dilution of the 1 �9 10-~-g/ml concen- trations.

LITERATURE CITED

i. D.P. Shcherbov and R. N. Plotnikov, Zavod. Lab., No. 12 (1976). 2. E.A. Bozhevol'nov, Luminescent Analysis of Nonorganic Substances [in Russian], Khimiya,

Moscow (1966). 3. D.P. Shcherbov, Pluorimetry in Chemical Analysis of Mineral Raw Materials [in Russian],

Nedra, Moscow (1965). 4. N.N. Zamysheveskaya et al., Inventor's Certificate No. 466420, Byul. Izobret., No. 13

(1975). 5. N.N. Zamyshevskaya et al., Inventor's Certificate No. 363903, Byul. Izobret., No. ii

(1973). 6. D.G. Konev, et al., Prib. Sist. Upr., No. i0 (1975). 7. V.N. Karalis et al., Opt.-Mekh. Prom-st', No. 7 (1973). 8. P. Pringsheim and M. Vogel, Luminescence of Liquid and Solid Bodies and Its Practical

Application [Russian translation], IL, Moscow (1948). 9. C.A. Parker and W. T. Rees, Analyst, 65 (1960).

CERTAIN METROLOGICAL CHARACTERISTICS OF NEUTRON MOISTURE METERS

A. K. Stroikovskii and A. T. Karmanov UDC 543.818.08:539.125.5

Considerable interest has been displayed in recent years in using neutron methods for measuring the moisture content and other parameters of various materials [I]. Neutron mois- ture meters.are being used in ferrous metallurgy, the building-materials industry, and other branches of our national economy. At the same time the metrological potentialities of neu- tron moisture meters and, in particular, the limiting values of the whole series of their characteristics remain unclear. The basic handbook on the theoretical and practical aspects of neutron moisture meters issued in 1970 by the International Atomic Energy Agency [2] is limited basically to posing problems. Therefore, it has become necessary to determine clearly the basic metrological characteristics of moisture meters and clarify their relationship to the primary-transducer parameters and the measured-material properties.

One of the most important characteristics of neutron moisture meters consists of the volume of materials whose moisture content must be determined in the course of measurements. This is due to the fact that measurements are carried out with an, as it were, automatic sampling of materials subject to measurements and, since the sampling is carried out without adhering to the normal rules which guarantee the required representativeness of specimens, the error can become excessively large when the measurement results are extended to the en- tire volume of materials. Moreover, in measuring essentially nonuniform bulk materials, an unfortunate selection of the prlmary-transducer location will lead to considerable systematic errors due in many cases to the effect of the place where the sample is selected on the mea- sured materials property. This is related in many cases, for instance, to the segregation of bulk materials according to size during their pouring, etc.

The problem of determining the quantity of materials measured with a neutron moisture meter was examined in [3], whose authors based their reasoning on the fact that the radius of the spherical volume of the materials ("influence sphere") measured with the instrument is equal to the radius of a spherical cloud containing 95% of neutrons retarded in the mate- rial. The radius (in centimeters) was determined with the assumption that the neutrons are retarded only by the nuclei of hydrogen contained in the moisture, and the following formula

Translated from Izmeritel'naya Tekhnika, No. 7, pp, 80-82, July, 1978.

1004 0543-1972/78/2107-1004507.50 �9 1978 Plenum Publishing Corporation

evaluation was derived:

where W is the moisture of the material in percentage of its volume.

The formula (I) does not account for the retarding of neutrons by dry materials and the capture of slow neutrons both by the dry-material nuclear elements and water. Moreover, the coincidence of the measured volume with the spherical domain occupied by the slow neutrons is at least doubtful, since in the case of a strong slow-meutron absorption by the measured materials the radius of the sphere which contains the slow neutrons depends on the length of the fast-neutron free path and can be considerable. At the same time, owing to the retarded- neutron absorption, it is hardly probable that the neutrons retarded at the cloud periphery will be able to diffuse through to its center where the detector is located and, therefore, the actually measured volume will be smaller than that determined according to (I).

The "significance sphere" concept of [4] ("indicative sphere" according to [i]), which was introduced in 1965, is determined as the sphere in whose center the thermal-neutron flux density changes by a given value if the entire measured material which lies outside its limits is removed. The two-group diffusion theory was used in deriving the formula for the signifi- cance-sphere radius with the assumption that the variation in the flux of thermal neutrons re- tarded in the measured material does not exceed 5% when all the material outside the sphere limits is removed:

100 R- 1.4+O,1W

It will be seen from the definition that the significance-sphere radius value depends on the retarded neutron flux produced by the material outside the sphere limits. It is not the neutron flux proper that is important for measurements, but rather its increment due to variations in the material moisture content. In other words, evaluation of the measured- material volume on the basis of the "significance sphere" concept in fact leads to replacing the measurement of moisture content by detecting the material located outside the sphere limits. Therefore, the more natural and important characteristic of any measured material portion consists of the degree to which it affects neutron-flux increments registered by the detector when the materials parameters vary within the working range limits.

This characteristic is also important because a neutron moisture meter is characterized, the same as any measuring system, by a certain level of its intrinsic noise. By referring the latter to the instrument input it becomes possible to determine the minimum measured- parameter increment which can be recorded with certainty in a given time interval. For in- stance, the statistical nature of neutron radiation is one of the sources of instrument in- trinsic noise. An example of noise sources of a different type due to external causes con- sists of the random packing of the bulk-material lumps in the measured volume, thus leading to random variations of the neutron flux recorded by the detector.

The neutron-flux increment recorded by the detector and due to small variations of mois- ture or any other measured-materials parameter, for instance, density or chemical composi- tion, can be represented in the form of the sum of two components:

A~ ~ A~p (o, R) + Aq~ (R, ~,),

where A~(O, R) and &~(R, ~) are the neutron-flux increments due to the materials moisture variations inside a sphere with radius R and outside its limits, respectively. Given that

where 0 is the materials measured parameter (in particular moisture content), and assuming that inside the sphere with radius R this parameter does not change, i.e., that A~(O, R) = 0, we obtain

0~ ~q) - ap (R, :~----~ Ap (R, o:) . (2)

In order to be able to measure the retarded neutron-flux increment determined by (2) it is necessary that its value should exceed that of the instrument intrinsic noise by at least a factor of k, i.e., that

1005

By introducing

ap (R, ~-----'~ Ap (R, oo) >/k~n .

a~ laP(R, ~)

which has the meaning of instrument relative sensitivity in measuring the moisture content or other parameters of materials located outside the sphere with a radius R, we obtain

Ap(R, ~) ~n S(R, ~) ~ k - - , (3)

Po ~

where po is the measured-parameter mean value,

The inequality (3) determines the materials spherical volume measured with a neutron moisture meter which has an intrinsic noise level of ~n. In following the existing conven- tion it is possible to call this volume the "measurement sphere."

Let us examine the quantities in (3). The relative sensitivity value S(R, =) can be found most simply by solving the neutron-transfer kinetic equation in accordance with the two-group diffusion approximation (the first group consisting of fast neutrons, and the second one of retarded ones). By using for this purpose the expression obtained in [5] for the neutron flux retarded in a spherically symmetrical double-layer decelerator we find after simple operations that

" i - i 7 . I., o~, o T + ~ j - r - _ :1 ol I i I ~_~, 0~, ,~" T + - - f " •

X Op j L ~ ~ ' L Op t e9 --k"7-"r--~'] D Op d ap e , (4)

where L and D are the fast-neutron lengths and diffusion factor, respectively; Z and d are the same for the retarded neutrons.

Analysis of (4) shows that for a certain value of radius Rms the value of S(R, =) be- comes equal to zero. On the other hand, when the instrument intrinsic noise is equal to zero, the inequality (3) assumes the form

hp (R, oo) S (R, co) > 0,

Po

hence i t f o l l o w s t h a t the volume of t he measured m a t e r i a l s i s bounded by a s p h e r i c a l s u r f a c e w i t h r a d i u s Rme which i s t he r o o t of t h e e q u a t i o n S(R, ~) = 0. Wi th in t h i s volume i t i s in principle possible to record an arbitrarily small measured parameter variation.

The maximum value of the quantity

! Ap(R, oo) ] Pmax--Pmm u P0 ~max P0

where Pmax and Pmin are the maximum and mimimum parameter values determined within the mea- sured range. When the instrument intrinsic noise is not equal to zero, the radius of the measurement sphere is determined from the equation

S(R, co)i. Ap(R,po oo) ]jmax__k q~nq) =0, (5)

where ~ is proportional to the neutron-source power Q in accordance with the expression

Q t ~P= 4ad " L ( L + I ) "

It is obvious that the radius of the measurement sphere decreases with a rising level of the intrinsic instrument noise.

The minimum measured-parameter increment, namely sensitivity threshold value, in which it is possible to record on instruments with a moise level of gn, can be obtained by assum- ing that R = 0 in (5), i.e., that

r- kp(O, co) ] > - - . k q~n L too rain| S {.0, cx~) ~,

1006

~'4ss ~:-45#

#,w #,3s odo #,2s #,m 4/5

#,gs

# 2 6 m m m 2 2 2 6 s o I J I " , I 1 l i R t c l l q

-Nt-

Fig. i

For

S(0,~) [ Ap(0,~) ] ~n > _ _ . k Po max

it becomes altogether impossible to measure with a neutron moisture meter.

This value of S(0, ~) can be obtained from the formula

i 1 ad 2L ~ l OL . L a l ] s(o ,~) :~o - T " ao - - L ( L + O ' 7 - / * Z(L+Z) ap ]'

which is derived from (4).

The measurement-sphere radius computed from the above formulas for carbon with the den- sity of 0.65 g/cm s and the moisture content of 10% (coke dust) has shown that in the ab- sence of noise the value of Rms is equal to 51 cm (see Fig. i). However, as soon as

[ Ap(R,~).] = 2 , - ~ n =0.05, ~ = t PO max

i t d r o p s t o as s m a l l a v a l u e a s 30 cm.

T h u s , a n e u t r o n m o i s t u r e m e t e r h a s a f i n i t e m e a s u r e m e n t r a d i u s e v e n i n t h e a b s e n c e of i n t r i n s i c n o i s e . As t h e n o i s e l e v e l i n c r e a s e s , t h i s r a d i u s d e c r e a s e s w i t h a s i m u l t a n e o u s r i s e i n t h e minimum m e a s u r e d - p a r a m e t e r i n c r e m e n t v a l u e w h i c h c a n be r e c o r d e d by t h e ~ x s t r u - m e n t i n a g i v e n t i m e i n t e r v a l .

l,

2. 3.

4.

5.

LITERATURE CITED

V. A. Emel'yanov, Field Radiometric Moisture and Density Measurements of Soils and Ground [in Russian], Atomizdat, Moscow (1970). "Neutron moisture quakes," Tech. Rep. Ser., IAEA, No. 112, Vienna (1970). C. H. M. Van Bavel, N. Underwood, and R. W. Swanson, "Soil moisture measurement by neu- tron moderation," Soil Sci., 82 (1956). P. L. Olgaard, "On the theory of the neutronic method for measuring the water content in soil," Danish Atomic Energy Commission Riso Report, No. 97 (1965). I. N. Sen'ko-Bulatnyi and R. L. Kharus, Tr. Geofiz. Inst. Akad. Nauk SSSR, No. 2; Geofiz. Sb., No. 3 (1962).

1007