Study of Neutron Absorptiometry and Its Application to the Determination of Boron DONALD D. DeFORD and ROBERT S. BRAMAN' Department o f Chemistry, Northwestern University, Evansfon, 111. A systematic study of the practical and theoretical aspects of neutron absorptiometry has shown that it possesses many advantages for the determination of elements, such as boron, which have high neutron absorption cross sections. The optimum geometrical arrangement of neutron source, neutron moderator, sample, and neutron detector has been found. Precise determinations of boron can b e carried out in a few minutes with relatively small, safe, and inexpensive neutron sources. The method is nondestructive, the state of chemical combination is immaterial, and there are few interferences. The most serious disadvantages are low sensitivity and the requirement for relatively large samples for highest precision.
arrangement of the apparatus is shonn about 0.003 to 0.01 tiines the rate of in Figure 1. production of neutrons by the source. Sample Cells. The sample cells The high counting efficiency permits used in these studies are listed in the use of small neutron sources (a few Table I. Except for cell G, all were millicuries), and short counting times annular cells, and 7% ere constructed (a few minutes). K i t h the less effiby welding or otherwise sealing a thin cient arrangements described, it was spacer between the inner and outer usually necessary to use powerful members at t h e bottom. The top of neutron sourceh, often as much as several the cell extended a t least 1 inch above curies, to record, in a reasonable time, the moderator. The polyethylene cell, sufficient counts t o permit a precise A , was constructed from standard analysis. The small source is advanwhite polyethylene pipe. All aluminum tageous both from standpoints of cost cells were constructed from Alcoa and radiation hazards. Furthermore, 61ST-6 tubing, 17 gage (Stubs) except when the sample is surrounded by for the 2-inch tubing which was 16 gage. moderator, variations in the scattering properties of the sample have a rela- ' The lime glass cells were constructed from lime glass tubing (Central Scientively minor effect, compared with tific Co., Catalog No. 14076). changes in absorptive properties. More detailed results of this study are available elsewhere ( 5 ) .
A
neutron activation methods have been widely used for chemical analyses, little use has been made of other types of neutron interactions with matter. Taylor. Anderson, and Havens (16) have discussed in detail several ways in which neutrons might be used effectively in chemical analj-sis, but most have not yet been systematically investigated. Onc of the best possibilities, particularly from the viewpoint of siniplicity of the apparatus required, is thermal neutron absorptiornetry. Although no systeniatic study of this method has been reported, several investigators (3, 4, 7-10, 19-14, 17, 18) have described analytical methods based upon the absorption or scattering of thermal neutrons. It became apparent from preliminary experiments that the sensitivity, precision, and selectivity of the neutron absorption method depended largely upon the geometrical arrangement of the neutron source, moderator, sample, and detector. Studies showed that optimum conditions for analysis were realized when the detector tube was completely surrounded by sample solution, and when both the neutron source and the sample were embedded in the moderator. With this geometrical arrangement and Kith no absorber in the sample solution, the counting rate is
ri
LwouGIi
1 Present address, Callery Chemical Co., Callery, Pa.
EXPERIMENTAL
Neutron Moderator. The neutron moderator in all cases was paraffin \\ax poured into a mold while hot and a l l o ed ~ ~t o harden overnight. RIoderator blocks of several shapes and sizes mere constructed to determine the effect of these variables on the neutron absorption method. A typical block m-as about 1 foot square and 6 inches high. Exact dimensions of the block are given for each experiment. A vertical hole, into which the sample cell fitted snugly, n a s drilled or molded in the center of each moderator block. Fiducial marks on the moderator and on the sample cells ensured reproducible placement of the cells for each experin e n t . Vertical holes for the neutron source weie drilled midway between the top and bottom of the moderator block. -1 vertical cross section view of a typical Table 1.
Figure 1 . Typical arrangement of apparatus for neutron absorptiometry M = Moderator S = Source D = Detector X = Somde
Sample Cells
Cross-
Cell 1 I?
Material Polyethylene Aluminurn C Aluminum D Aluminum B Aluminum F Lime glass G Polyethylene a Outside diameter.
Inner Tube 1-in. std. pipe l l / a in.a 11/4 In: 1
1n.a
Outer Tube 2-in..std. pipe l l / z!n." ma 1 3 i a in:
1 1 / 4 in.0 2 in.= 30 mm." 51 mm. l l / s in. I.D. helix of in. I.D. tubing
Sectional Ares, Sq. Cm. 12 72 1.69
3.60 5.57 0 86 10 03 3 28
VOL. 30, NO. 11, NOVEMBER 1958
e
1765
Cell G was a helical coil cell constructed by winding 1/4-inchpolyethylene tubing around a mandrel 11/8 inches in diameter; this coil was then cast into the moderator block. Approximately 13 turns of the coil were embedded in the moderator. The cross sectional area listed for this cell is the average area, calculated from the measured height of the moderator block and the measured volume of liquid required to fill the cell. Neutron Source. The neutron source used in all experiments was a lO-mc., mixed radium-beryllium, fast neutron source. To eliminate any possibility of overexposure to gamma radiation, a wall of lead bricks, 1 1 / 2 inches thick, was placed in front of the moderator. Neutron Detectors and Counting Apparatus. Except as noted, the neutron detector in all experiments was a boron trifluoride counter tube filled t o a pressure of 12 em. of mercury with boron-10-enriched boron trifluoride. This tube was 1 inch in diameter and 27 inches long; the effective counting length was 20 inches. For one series of experiments a similar tube having a 6-inch effective counting length and filled to a pressure of 120 em. of mercury was used. Both tubes were manufactured by Radiation Counter Lab., Inc., Skokie, Ill. The counter tubes were supported by clamps beneath the moderator block, hence, the sample cells could be placed in the apparatus from the top without removing or changing the position of the counter tube. The vertical position of the tube was always such that the center of the effective counting length .\vas approximately a t the center of the moderator. A Nuclear-Chicago Model 182$ scaling unit was used with the low pressure detector tube. The high voltage supply and scaling equipment for use with the high pressure detector tube were made available by the Radiation Counter Lab., Inc. The counting equipment must be operated in the center of both the sensitivity and the counter tube voltages plateaus for stable operation. Counting rates were measured for different settings of both the high voltage supply and the sensitivity adjustment. From these measurements, the value was determined a t which both the sensitivity and the high voltage should be set, so that small changes in either setting would result in minimum changes in the counting rate. The most stable operation was realized when the scaler and the high voltage supplies were left on continuously. Reagents and Solutions. Because of the limited solubility of boric acid and the common borate salts, solutions of triethanolamine borate, which 1766
ANALYTICAL CHEMISTRY
is very soluble in mater, tvere used unless otherwise noted. These solutions were prepared by adding an equivalent amount of technical grade triethanolamine (95%) to weighed portions of reagent grade boric acid and diluting to the desired volume. Solutions containing up to about 5 gram atoms of boron per liter could be prepared in this manner. Experimental Procedure. Before beginning any measurements, the apparatus was assembled and clamped firmly in position, the scaler and high voltage supply were warmed up, and preliminary checks were made t o be sure the counting rates were stable and reproducible. The sample cell was then filled with pure solvent, and the number of counts recorded in a 10-minute counting interval was noted. Boron solutions covering a range of concentrations were placed singly in the sample cell, and the number of counts recorded in a 10-minute counting period was noted for each. Duplicate or triplicate measurements were usually made for each solution. Generally, the range of concentrations studied was from about 0.01 to about 4.0 gram atoms per liter; each solution was usually about twice as concentrated as the next most dilute. A typical series would involve measurements on solutions which contained 0.01, 0.02, 0.05, 0.10, 0.20, 0.50, 1.0, 2.0, and 4.0 gram atoms of boron per liter. The range of concentrations used in each particular study, together with the total number of solutions used, are given under the discussion of that particular study.
4
w
05
io
2b
do
d
zo
Figure 2. period)
Error curves (fixed counting nfN, = 0 nfN, = 0.028 nfN, = 0.1
passed through the sample solution. The value of n is always small in comparison with N o , and may be reduced essentially to zero by proper arrangement of the apparatus. Equation 1 i q similar in form to those derived by Harrington and Stewart ( I I ) , Bleuler and Goldsmith (2), and others for an ideal system. A plot of N us. ( N o - N)/C permits evaluation of the two empirical constants, and makes possible the calculation of boron concentrations from measured values of N , either directly from Equation 1 or from a linear calibration curve of C us. 1/(9 - n). Sometimes experimental results are expressed in terms of the total weight of boron in the sample cell rather than in terms of the concentration of boron. If both sides of Equation 1 are multiplied by the volume of the sample solution, V , in liters, and the atomic R-eight of boron, 10.82, there obtains
RELATIONSHIP BETWEEN COUNTING RATE A N D CONCENTRATION OF NEUTRON ABSORBER
Because of the complex geometry of the system, it has not been possible to formulate and solve the differential equations required to describe the relationship between counting rate and concentration of neutron absorber. Empirically, the concentration of boron n-as related to the number of counts by the relationship No - N No - n
c = c , -N
- n
=
c,- N
-n
-
co
(1)
where C is the concentration of boron,
N is the number of counts recorded in a fixed counting time when the sample cell is filled with a boron solution containing C gram atoms of boron per liter, N , is the number of counts recorded in a counting period of the same length when the sample cell contains pure solvent, and C, and n are constants. The constant n has the dimensions of counts and, as will be evident, apparently represents a background, arising largely from stray thermal neutrons which reach the detector without having
X I O O
C/C"
(2)
where W is the weight of boron in the sample solution and where W,
= 10.82
VC,
(3)
In all of the preceding discussion, a counting period of fixed length was assumed to have been employed. Recording a fixed number of counts in all experiments, and measuring the time required to register this number of counts have two advantages. A more nearly constant precision in the determination of boron over wide concentrations ranges is realized, and an approximately linear relationship exists between the concentration and the measured variable, time. Khen this method of taking experimental data is employed, Equation 1 becomes
where T ois the time required to record a fixed number of counts with pure solvent in the sample cell, T is the time
required to record the same number of counts with a solution containing C gram atoms of boron .per liter in the sample cell, r is the background counting rate, and R, is the counting rate with pure solvent in the sample cell. If the background counting rate, r, can be eliminated, the concentration, C, is then a linear function of the counting period. It is seldom possible to eliminate background counting completely, but it can be made small by proper experimental procedures. and the devintion from linearity is then usually not extremely serious over narrow concentration ranges. THEORETICAL EVALUATION OF THE PRECISION OF ANALYSIS BY NEUTRON ABSORPTIOMETRY
Fixed Counting Period. To evaluate the precision expected in determinations made by neutron ahsorptiometry, the statistical errors involved in counting random events must be considered. Because the standard deviation in counting a large number of random events is equal to the square root of the number of events counted ( 6 ) , the standard deviation of W 2 is constant and equal to +0.50. If N1I2 is plotted as a function of log C for a series of experiments in which a fixed counting period is employed, the percentage standard deviation, uc(%), in the determination of concentration is given by
I n these experiments, factors other than statistical counting errors usually had a negligible effect on the observed precision. If more powerful neutron sources or longer counting periods are used, the counting errors can be decreased to any desired level, and under these conditions, other factors limit the precision. As an alternative to the employment of N112 us. log C plots, the standard deviation in the determination of eoncentration may be expressed as a function of the three constants C, N o , and n of Equation 1 whenever this relationship is valid Although is subject to statistical fluctuations, its average value can be determined precisely by making a large number of determinations, and it may be considered to be a constant. Likewise n is subject to statistical fluctuations if n is a background and not a true constant. However. in the term (iY0- n) an average value of n is used, and the term (Son) is constant. On the other hand the term (S - n) is not, because of the statistical variation in both N and n and the correct value of n in the expression ( K - n) for any given measurement may be different from the average value. If the terms C, and (Yo - n) are treated as constants, and the term (A' - n) is considered subject to statistical variation, then
Figure 3. Typical plot of N'/z vs. log C
ditions. By employing suffciently long counting periods, the standard deviation can be reduced to any desired value. Likewise, for any given counting period, the value of K Ois directly proportional to the strength of the neutron source, and the standard deviation is inversely proportional to the square root of the strength of the source. The optimum concentration, the one at which &(%) is smallest, is equal to 2 C, when n / N , = 0. As n/N, increases, the optimum concentration deapcreases, approaching C, as n,", proaches unity. Throughout the experimental sections the value of uc(O/o) has been tabulated for the point a t which C = 2 C,. This value gives a measure of per cent standard deviation close to the optimum concentration.
L
or
where m is the slope of the curve a t the concentration in question. The optimum concentration-the concentration a t which uc(y0)is a minimum-obviously corresponds to the point of maximum slope in the curve. This method for plotting neutron absorption data is analogous to the method of representing spectrophotometric data in the form of (1 - 2') us. log C plots as recommended by Ringbom (16) and Ayres (1). Such plots are not recommended as working curves for translating observed counts into concentrations, but are useful in estimating the precision expected in an analysis, and for comparing the results under varying conditions. KO particular mathematical relationship between counts and concentration was assumed in deriving Equation 5 ; this equation is valid even though the data cannot be represented by a simple mathematical relationship such as Equation 1. Equation 5 is applicable only for computing the variance in concentration which arises from counting errors, and does not include possible variance which might result from other factors such as random fluctuations in positioning of the sample cell in the apparatus, or drifts in the sensitivity of the scaler.
(7)
where the symbol Y represents the term in the brackets. The effect of changes in the ratios C/C, and n/N, can be seen in Figure 2, in which the value of Y is plotted as a function of C/C, for three different values of n/N,. The analysis error is least when n = 0 and a wide range of concentrations can be determined with high precision. When n/LV, = 0, concentrations in the range between 0.36 COand 23 C, can be determined with a percentage standard deviation which does not exceed twice the standard deviation a t the optimum concentration. The percentage standard deviation increases as n / Y 0 increases; large values of n/N, have a particularly deleterious effect on precision a t high concentrations. reither C/C, nor n/N, depends upon the length of the counting period, but N o is directly proportional to the length of the counting period. Equation 6 shows that the percentage standard deviation in the determination of concentration is inversely proportional to the square root of the counting period for any given set of experimental con-
To evaluate the effect of experimental variables on the sensitivity of the neutron absorption method, it is convenient to employ the standard deviation, in gram atoms per liter, when the concentration is zero. This quantity may be calculated from the expression
Although the standard deviation calculated in this manner is strictly correct only when C = 0, the value calculated is approximately correct (within 107,) for concentrations below about 0.05 C,, and is a good measure of the precision realizable in determining small concentrations of boron. It is sometimes preferable to express this standard deviation on a weight rather than a concentration basis; this standard deviation, uv (W = 0), is equal to uc (C = 0) times Wo/Co. Equations 6 through 8 take account of random counting errors only and represent the precisions expected when all other sources of variance have been eliminated. Table I1 shows a typical set of neutron absorption measurements with the Values of the significant descriptive conVOL. 30, NO. 11, NOVEMBER 1958
* 1767
in this manner. However, from the data given it is easy to predict calibration data, standard deviations, and other similar quantities which would be obtained if this method were employed. With very few exceptions the general principles presented for the method employing a fixed counting period are applicable also to the method in which a fixed number of counts is employed.
Table II. Typical Neutron Absorptiornetry Data
h’,
C,
Run KO. Blank
Gram Atoms per Liter
Counts X
297.0 280.8 254,2 224,8 217.0 169 3 149.6 102.7 65.6 40.65
0 0.01739 0.05277 0.1021 0.1182 0.2362 0.3169 0.6338 1.2677 2.5353
1 2 3 4 5 6 -7
; 9
RESULTS AND DISCUSSION
Descriptive Constants
N O n
CO
wo
ac(%)(C = 2C0) uc(C = 0 ) aw(W = 0 )
Khenever Equation 4 is valid, the percentage standard deviation in the concentration is given by
Moderator Dimensions. To ascertain the effect of the dimensions of the moderator on the significant constants, four paraffin moderator blocks, 2 feet square and 3, 6, 9, and 12 inches high, were constructed. Holes of appropriate size were drilled in the paraffin blocks to house the sample cell, detector, and source. A11 geometric factors other than the dimensions of the moderator block were maintained constant; the source was located inch from the side of the polyethylene sample cell (cell A ) . S i n e boron solutions, varying in concentration from 0.01 to 3.2 gram atoms per liter, were used to obtain the experimental data for each block. Values of the descriptive eonstants for each of the four moderator thicknesses are listed in Table 111. The values of each are plotted as a function of moderator height in Figure 4, and the values of several are plotted as a
,4 comparison between Equations 6 and 10 shows that the precision is more nearly constant over considerably wider concentration ranges when the method employing a fixed number of counts rather than a fixed counting period is used. However, the better precision in the higher concentration ranges with the former method is achieved only by longer counting periods. The concept of optimum concentration is not particularly appropriate when using this method. With this method, as with the method employing a fixed counting period, the best compromise between high precision and reasonable time is realized when C is approximately equal to 2C0. The equations for ac(C = 0) and u W ( K= 0) for this method are identical with those developed for the method employing a fixed counting period if r / R , is substituted for n/Xo and N for LV,. Because the counting equipment used ITas not readily adaptable for measuring the time required to register a fixed number of counts, no data \Yere taken
function of the reciprocal of the moderator height in Figure 5. The value of N o decreases as the height of the moderator is decreased; this decrease is particularly pronounced when the height is reduced to less than about 6 inches. The decreased counting rate as the moderator becomes thinner is t o be expected, because there is insufficient path length to reduce all of the fast neutrons produced by the source t o thermal velocities. It is apparent from Figure 5 that the value of N o is approximately a linear function of the reciprocal of the moderator height. The value of n increases as the moderator height is decreased; the most pronounced change again occurs as the height is reduced to less than about 6 inches. If the quantity n represents a background count, which seems t o be the case, an increase in its value with decreasing moderator height is to be expected. Because many fast neutrons escape from the surface of the thin moderator blocks, some must strike the m-alls of the polyethylene sample
297.0 X lo3 8 . 4 x 103 0.305 0.661 f0.53 f0.58 11.26
counts counts g. atom/liter g. mg. % atom/liter
mg.
Table 111. Effect of Moderator Height Series KO. 1 2 Moderator liejght (in.) 3 6 24 Moderator length and width (in.) 24 125 225 Sample volume (ml.) 129.5 312.1 ATo(counts X 10-3) 8.5 n (counts x 10-.3) 25.8 C, (gram atomhteri 0.392 0.313 ’
\o-
OCi%)(C
~~~- -~ - ~ -
1 28 1 49 2 01
= 2Co)’
uc(C = 0) (mg. atomsjliter) aF(w = 0 ) (mg. boron)
stants calculated as outlined. These measurements were made with a moderator block 12 inches square and 6 inches high; sample cell, A , filled with 200 ml. of the boron-containing sample solutions, was used. The seven descriptive constants listed characterize the particular system under study and provide all the information necessary for a n evaluation of the effects of experimental variables on the neutron absorption method. A plot of Pz us. log C for the data of Table I1 is shown in Figure 3. Fixed Number of Counts. If experimental d a t a are taken by measuring the time required t o register a fixed number of counts, rather than by measuring the counts registered in a fixed time, the equations relating precision to the constants of Equation 4 are different from those developed in the preceding section. The pertinent equations for data taken in this manner are listed. If the logarithm of the time required to register a fixed number of counts, N , is plotted as a function of the log of the concentration of boron, then (9)
where m is the slope of the curve at the point in question. The use of Equation 10 with log T us. log C plots is analogous us. to the use of Equation 5 with 1Y1’2 log C plots as discussed. 1768
ANALYTICAL CHEMISTRY
0 509 0 583 1 42
3 9 24 325 381.3 3.1 0.283
4 12 24 425 417 3
0 434 0 464 1 63
0 403 0 406 1 87
0.0 0,262
0
3
6 Mockator Height
9 (Inches)
12
Figure 4. Effect of moderator height on descriptive constants Ordinates;
Counts X 10 -s Counts X 1 0-3 Gram atoms per liter X l o 3 W. Grams X l o 2 U C ( C = 0) Gram atoms per liter X l o 5 uw(W = 0) Grams X l o 6 uc(%) (C = 2 C 0 ) Per cent X 10’
No n CO
cell above the moderator block, where they may be moderated and counted. (The active length of the counting tube used was 20 inches; hence a large portion of this active length extended above and below the moderator). Likewise many slow neutrons will be lost by diffusion from the surfaces of the thin moderators, and some of these neutrons will strike the counter tube and contribute to the background counting rate. More recent measurements carried out by one of the authors in another laboratory indicate that the value of n does not differ significantly from zero even with moderator blocks 6 inches in height, if a counting tube having an active length of only 6 inches is employed. The value of C, increases as the thickness of the moderator is decreased. Because C, is apparently related to the number of neutrons lost by means other than capture by boron nuclei in the sample solution, and because the number of neutrons lost to the surroundings through the top and bottom surfaces of the moderator increases as the moderator becomes thinner, it is reasonable that C, increases as the moderator thickness is decreased. As the thickness of the moderator is decreased, C, increases, but the necessary sample volume decreases. The value of W,, which is proportional to the product of these two quantities, decreases with decreasing moderator height over the range studied. The actual values of W,, range from 0.53
gram for the 3-inch moderator, to 1.22 grams for the 12-inch moderator. Because the optimum weight of boron is approximately equal to 2 W,, the sample should contain about 1 to 2 grams of boron. The large sample size required is one of the disadvantages of the method. The percentage standard deviation, UC(%) (C = 2CJ, in the determination of concentration in the optimum concentration range increases as the moderator height is decreased. The precision is not seriously impaired unless the moderator height is reduced to less than about G inches. Because the percentage standard deviation is only about *0.5% a t the optimum concentration, the method is one of the most precise available for the deterniination of boron. The standard deviation, UC(C = 0), in the determination of very low concentrations increases as the moderator height decreases, but this effect is not serious unless the moderator height is reduced to less than 6 inches. A measure of the sensitivity of the neutron absorption method is given by the value of the standard deviation, aw(W = 0), in the determination of very small neights of boron. As seen from Figure 4, the value of m~(Tt’= 0) is a minimum nhen the moderator height is about G inches; hence a moderator approximately 6 inches thick is the optimum for the highest possible precision in determining small amounts of boron. The sensitivity of the method is not great, however, even nhen the optimum conditions are employed because aw(W = 0) is about 1-1.3 mg. of boron. This precision could be improved by employing longer counting times. Experiments with moderators varying from 12 X 12 to 24 X 24 inches in horizontal dimensions indicated that there was no significant change in any of the descriptive constants when the horizontal dimensions were altered over this range. For example, the value of NO for a 12 X 12 X 6 inch moderator block was 308.0 X lo3 counts as compared with the value of 312.1 X lo3 counts obtained with the 24 X 24 X 6 inch block. Few experiments were made with blocks less than 12 X 12 inches in horizontal dimensions because the value of N O decreased significantly as these dimensions were further reduced. Values of iv, were approximately 25% less for an 8 X 8 X 9 inch moderator than for a 12 X 12 X 9 inch moderator. While there is some advantage in reducing the moderator height as much as possible because required sample volumes are simultaneously reduced, no advantage is gained in reducing horizontal dimensions. A moderator about 12 X 12 X 6 inches is the optimum for general pur-
Figure 5. Effect of moderator height on descriptive constants Ordinates same as Figure 4
pose use. The greatest sensitivity is realized with a moderator of this thickness. Even when plenty of sample is available, little advantage is gained in using thicker moderators. The very slight advantage realized in using moderators of larger horizontal dimensions is not sufficient in most cases t o aarrant the greater bulk and weight involved in their use. Position of Neutron Source. W t h a moderator block 24 X 24 X G inches and with the other experimental conditions identical n-ith those employed in the preceding section, except that the source was located 23/8 inches rather than 3/8 inch from the cell, values of the seven descriptive constants were found to be 145 0, 5.4, 0.291, 0.708, 0.774, 0.812, and 1.98. These constants are listed in the same order and have the same units as those given in Table I11 and are to be compared with the constants listed under series 2 in Table 111. Placement of the source further from the sample cell sharply decreases the value of AT,, and consequently, values of all standard deviations are about 50% larger when the source is placed 23/8 inches from the sample cell, than nhen placed 3 / / ~ inch away. Values of C, and W , are essentially the same for both source positions. For best results the neutron source should be located as close as possible t o the sample cell. Construction Materials for Sample Cells. The descriptive constants for three series of runs made in a 12 X 12 X 6 inch moderator with the source 3/8 inch from the sample cells, but with different cells are tabuVOL. 30, NO. 1 1, NOVEMBER 1958
* 1769
Table IV.
Effect of Material for Sample Cell Construction
Series No. Sample cell Sample volume (ml.) N o (counts X 10-3) n (counts X C, (gram atom per liter) W , (g. boron) UC(%)(C
= 2CO)
nc(C = 0 ) (mg. atoms/liter)
uw(W = 0) (mg. boron)
Table V. Series No. dnnular space area (sq. cc.) Sample vol. (ml.) N o (counts X 10-3) n (counts X C, (gram atoms per liter) W , (g. boron)
U c ( % ) ( C = 2c 1 uc(C = 0 ) (mg. atoms/liter) UW(W= 0) (mg. boron)
ANALYTICAL CHEMISTRY
30
E
160 264.2
0: 366 0.634 0.507 0.710 1.23
Effect of Annular Space 30 9.86 160.0 264.2
31 5.57 90.4 266.0
0 366 0.633 0.514 0.71 1.23
0 633 0,618 0.515 1.23 1.20
lated (Table IV). Cell A was constructed from polyethylene, cell E from aluminum, and cell P from lime glass. The geometrical factors for the three series were nearly constant, and differences in No, n, W,, and all standard deviations can be attributed largely to the differences in cell material. Nine solutions containing boron in the concentration range of 0.01 to 3.2 gram atoms per liter were used in the measurements for series 6 and 24. Five solutions containing boron in the concentration range of 0.1 to 1.0 gram atoms per liter were used in series 30. The value of n was not evaluated for the last series because the long extrapolation involved did not permit a precise determination of this constant. It b-as clear that n was very small and its value has been considered to be zero for all calculations. The value of N o is significantly higher for the polyethylene cell than for the other cells. This high value of No stems not only from the fact that very few neutrons are absorbed by the cell, but also because polyethylene is an excellent neutron moderator. Although aluminum absorbs very few neutrons, it is a poor moderator, and does not appreciably increase the flux of slow neutrons. Although lime glass contains a low percentage of boric oxide, it absorbs a large number of neutrons, and the value of N o for this cell is less than that for the nonabsorbing cells. The value of the background, n, is also significantly higher for the polyethylene cell. The larger value of n with the polyethylene cell offsets the higher value of N , in improving the precision of analysis; for this reason the precision and sensitivity which can be realized are nearly the same for the polyethylene and aluminum cells. The values of W , are all essentially the same for the two nonabsorbing cells used, but the presence of absorb1770
24 F 200 131.9 0.3 0.642 1.39 0.720 1.77 3.83
6 A 225 308.0 13.6 0.280 0.682 0.539 0.539 1.31
:
32 3.60 58.4 263.4
33 1.69 27.4 262.6
0:9i7
1.76 0.522 0.513 2.90 0.86
0.580 0.513 1. i 9 1 ,13
...
ing nuclei in the lime glass cell causes the value of W , for this cell to be approximately twice that of the nonabsorbing cells. Despite the pronounced changes in both N o and W , which occur when an absorbing cell replaces a nonabsorbing cell, the product of (No n) times W , remains almost constant. Because the precision of analysis a t the optimum concentration is inversely proportional to the square root of N o , the quantity uC(%) (C = 2C,) is only about 50y0 larger for the lime glass cell than for the nonabsorbing cells. The standard deviation, uw(W = 0), in determining very small amounts of boron depends also upon the value of W,. Consequently, the sensitivity of the neutron absorption method is greatly impaired if absorbing cells are used. Sample Height in Sample Cell. Little change in counting rate is observed with changing sample volume, as long as the sample volume is sufficient t o bring the level even with the top of the moderator block, but the counting rate is very sensitive to volume changes if the sample solution does not reach the top of the moderator. In all work reported, the sample volume was always maintained a t a constant value such that the level was a fraction of an inch above the moderator block. Annular Space in Sample Cells. To ascertain the effect of annular space, four aluminum cells, each having inner members of the same size but different annular spaces, were studied (Cells B-E). Geometrical factors other than annular space were maintained as constant as possible, and all cells were filled to exactly the same depth. Five different boron solutions, varying in concentration from 0.1 to 1.0 gram atom per liter, were used for each series. Descriptive constants for the four series of runs are shown in Table V. Because no concentrated solutions were
used in these experiments, the value of n could not be determined precisely because of the long extrapolation involved. consequently no values are listed for n, but in all cases this constant was very small. The tabulated data show that the value of N o is the same for all four cells as was expected. Because the value of U C ( % ) (C = 2C,) depends only upon N o and n, this constant, likewise, is the same for all cells. The most significant information gained is the fact that the value of W , changes only slightly as the annular space is varied. This indicates, a t least for the restricted range of annular spaces used, that the length of the path traversed by the neutrons in passing through the sample solution is of minor importance. Rather the absorption is determined largely by the weight of boron in the sample solution. A given iveight of boron absorbs very nearly the same number of neutrons whether present as a concentrated solution in a thin cell or as a dilute solution in a much thicker cell. By appropriate selection of the annular space, solutions may be analyzed over extremely wide concentration ranges with high precision, provided the total weight of boron in the sample does not differ greatly from the optimum (about 1.0 to 1.2 grams). Helical Coil Sample Cells. Because helical coil cells offer some advantages over annular cells for the continuous analysis of sample streams, cells of this type (cell G) were investigated briefly. The values of the descriptive constants for this type of cell did not differ significantly from those similarly obtained with annular polyethylene cells. Solvents Other Than Water. The value of No varies with the solvent and appears to be approximately a linear function of the concentration of hydrogen nuclei in the solvent. Typical values of iV,, in thousands of counts, for several solvents studied, with the concentration of hydrogen nuclei in gram atoms per liter for each solvent, were: water 303.4, 111.1; methanol 299.5, 98.4; acetone 293.3, 81.8; benzene 289.5, 67.6. Because ‘Tois different for different solvents, the calibration curve for the determination of boron is different for each solvent. Because of the low solubility of the available boron compounds in most organic solvents, complete calibration data were taken only for methanol. For this solvent, the value of C, was larger than when water was employed as the solvent, but the product of Co times (No- n) was the same as that for water. The calibration curfe [C us 1/(S - n ) ] had the same slope as when ivater \vas used, but had a slightly different intercept.
Solvents containing neutron-absorbing nuclei such as nitrogen or chlorine give considerably lower values for X, than those containing only carbon, hydrogen, and oxygen. For example, N o for pyridine was 261.7 X lo3 counts as compared with 289.5 X lo3 for benzene Neutron Detector. When a 6-inch detector tube filled to a pressure of 120 em. of mercury was employed instead of the lo-^ pressure tube under conditions identical to those shown for series 31 in Table V, the values of the descriptive constants, in the same units as those listed in Table V, were 1341.2, -10, 0.854, 0.835, 0.225, 0.736 and 0.720. The most striking difference between these two series of measurements is the value of No,which is about five times larger for the high pressure than for the low pressure tube. The small negative value found for n with the high pressure tube does not differ from zero by an amount greater than the experimental error; no significance can be attached to the fact that a small negative value was obtained. The value of W , is significantly larger for the high pressure tube. The difference between the two values of V, is nearly equal to the difference in the weight of the absorbing nuclei in the two tubes (expressed in units of grams of boron of normal isotopic ratio); this fact lends support to the hypothesis that W , is a measure of the weight of all absorbing nuclei in the system, other than those in the sample solution itself. Because of the higher value of So, all calculated standard deviations are significantly less for the high pressure tube than for the low pressure tube. However, the plateau in the counting rate-applied voltage curve is much shorter and not as flat with high pressure tubes as with low pressure tubes. Consequently, drifts in counter tube voltage or in scaler sensitivity produce more pronounced changes in counting rate with high pressure tubes. Limited experience with the high pressure tube indicates that errors from this source may be as great as those arising from random counting errors. If this is generally true, little or no gain in precision would be realized by using high pressure tubes. Neutron Absorbing Elements Other Than Boron. Although all of the fundamental studies of the neutron absorption method were carried out with boron solutions, other neutron absorbing elements were used in a few experiments. The approximate behavior of these elements may be predicted from the data obtained for boron. The number of thermal neutrons absorbed by a neutron absorbing element is proportional to the product of the concentration of that element times its
Results of Analyses of Boric Acid Solutions Percentage Error Grams of Boron Found Predicted Present Found
Table VI.
Sample No. 1
2
3 4
0.08388 0.08388 0.05388 0.3155 0.3155 0.3155 0 . GOO3
0.6003 0.6003 0.6783
0,6783
5
0.6783 1.123 I.123
0,08528 0.08509 0.08388 0.3126 0.3128 0.3145 0.5983 0.6010 0.5965 0.6823 0.6526 0.6808 1.122 1.121
absorption cross section. If a solution of element X and of concentration Cx gram atoms per liter absorbs exactly the same number of neutrons as a boron solution containing CB gram atoms per liter, then the relationship CXCX = CBUB
(11)
where the sigmas refer to the respective cross sections, is valid. If the cross sections are known, it is possible from this equation to predict the concentration of any other neutron absorbing element which will be equivalent to any given concentration of boron. If identical experimental conditions are employed, the values of Ay0 and of n are the same for all elements. Because the value of C, or of W , for other elements can be calculated from data taken with boron solutions, it is possible to construct an approximate calibration curve for any other element and to predict standard deviations, optimum concentrations, and sensitivities without further experimental work. However, Equation 11 is not valid for elements which exhibit strong resonance absorption peaks in or near the thermal region. The general validity of Equation 11 was verified by experiment. A series of aqueous solutions of hydrochloric acid &-asexamined after calibration data for boron had been obtained. The concentrations of chlorine calculated from Equation 11 agreed with the known values to within ~ t 0 . 0 2gram atoms per liter. Because coneentrated hydrochloric acid (12X) has an absorption equivalent to a solution only 0.5M in boric acid, the agreement between calculated and known values is well within the errors of the method and the uncertainties in the values of the cross sections of the two elements. The concentrations of a series of aqueous cadmium chloride solutions varying from 0.25 to 1.00M, as determined from Equation 11, and a boron calibration curve, differed from the known values by only +5.0 + 1.0%. Because cadmium exhibits a resonance absorption peak
+1.67 $1.43
0.00 -0.92
-0.86 -0.32 -0.33 +o. 12 -0.63 +o. 59 -0.84 +O .37 -0.09
-0.18
11.76
i~0.73 1k0.57
+o
54
10.53
just above the thermal energy region, the agreement found is the best that could be expected. Very few other elements possess cross sections comparable with the high value of the boron cross section. The sensitivity of the neutron absorption method is low even for boron, and the sensitivity for the determination of most other elements is even lower. The insensitivity of the neutron absorption method is a disadvantage, because this restricts its general application to only a few elements, and an advantage, because the problem of interferences from other elements in the sample is minimized. In the determination of boron, nitrogen or chlorine in the sample does not interfere significantly unless the weights of these elements exceed that of boron. If the concentration of the interfering element is known, a correction can be made for the interference through the use of Equation 11 by calculating CB and subtracting this value from the determined concentration. Temperature Effects. S o systematic study of the effect of temperature was made. Although very large temperature changes might cause significant shifts in calibration curves, normal daily variations in room temperature produced no detectable changes. Effect of Isotope Ratio. The neutron absorbing properties of natural boron are due exclusively to the isotope of mass ten. Any deviation of the isotope ratio from its normal value will lead to errors in the determination of total boron by the neutron absorption method, Because significant isotope fractionation occurs in a few reactions involving boron compounds, appropriate corrections must be applied in the analysis of compounds prepared under conditions n-here such fractionation occurs. TYPICAL ANALYTICAL RESULTS
A tabulation of typical results obtained in the analysis of boron-containing solutions is given in Table VI. The VOL. 30,
NO. 1 1 ,
NOVEMBER 1958
1771
calibration data and the descriptive constants for the system employed are listed in Table 11. Solutions for analysis were prepared from the same lot of boric acid used for the preparation of the standards. A counting period of 10 minutes was used in all cases. The weights tabulated in the grams of boron found in column 3 in Table VI were calculated by Equation 2 together Kith the values of W,, No, and n given in Table 11, and the measured value of A‘ for each measurement. The values tabulated in the predicted percentage error column were calculated from Equation 7 with the error curve shown in Figure 2. The errors actually encountered in the 14 separate determinations exceeded the predicted standard deviation in only five instances. Statistical theory predicts that the results of individual measurements will, on the average, exceed the standard deviation in one out of every three cases. Because the calculated standard deviation takes account only of random counting errors, and because the actual errors exceeded this standard deviation in only one third of the measurements made, other sources of error must be very small in comparison with random counting errors. CONCLUSIONS
IYhen the neutron source, neutron moderator, sample, and neutron detector are placed in the proper geometrical arrangement, boron-containing solutions may be analyzed rapidly, using weak and inexpensive neutron sources. Khen the optimum geometrical arrangement is used, the counting rate is related to the concentration of boron by a simple mathematical equation. From this equation and the theory of counting errors, analytical
errors can be predicted and the optimum conditions for analysis established. For best results with the most favorable geometrical arrangement the sample solution should contain about 1.0 gram of boron; the precision which can be achieved under these conditions with a 10-minute counting period, a 10-mc. neutron source, and boron trifluoride detector tube filled to a pressure of 12 cm. is about +0.5%. The error in determining very small amounts of boron under the same conditions is about h1.0 mg. I n both cases the precision can be improved by employing longer counting periods or more powerful neutron sources. Xeutron absorptiometry is particularly suited to the determination of boron because nearly all other elements which are frequently associated Kith boron have very low neutron absorption cross sections, and a separation of boron from other elements in the sample is seldom required. The method is nondestructive and the entire analysis sample may be recovered quantitatively if desired. Because the method is based on a nuclear property, the state of chemical combination is immaterial. Unless a preliminary separation is necessary, the only sample preparation required is dissolution in a suitable solvent. The results depend slightly on the solvent used and the same solvent must be used for both calibration and analysis. The most serious disadvantages of the method are its low sensitivity and the large TTeight of sample required to realize the highest possible precision. ACKNOWLEDGMENT
This research Fas supported by Callery Chemical Co. under a contract from
the Bureau of Aeronautics, Department of the Navy. LITERATURE CITED
(1) Ayres, G. H., ANAL. CHEM.21, 6527 (1949). (2) Bleuler, E., Goldsmith, G. J., “Experimental Xeucleonics,’’ pp. 144-55, Rinehart. New York. 1952. (3) Burger,’ L. L., Rainwater, L., U. S. Atomic Energy Commission, AECD2319 (1948). (4) Crumrine, K. C., U. S. Patent 2,567,057 (Sept. 4, 1951). (5) DeFord, D. D., Braman, R. S., Callery Chemical Co.. ReDt. CCC-1024-TR-243 (1956). ’ (6) Frielander, G., Kennedy, J. W., “Introduction to Radiochemistry,” p. 206, Wiley, New York, 1949. ( 7 ) Govaerts, J., Experientia 6,459 (1950). ( 8 ) Green, M., Martin, G. R., Trans. Faraday SOC.48, 416 (1952). h A L . ( 9 ) Hamlen. R. P.. Koski. W. ‘ CHEM.28; 1631 (1956). ’ (10) Hamlen, R. P., Koski, W. S., i\-uclear Sci. Abstr. 9, 561 (1955). (11) Harrington, E. L., Stewart, J. L., Can. J . Research 19A, 33 (1941). (12) Herzoa, G.. U. S. Patent 2,613,325 . . ‘ (Oct. 7, f952).’ (13) Martellv. J.. Sue. P.. Bull. SOC. chim. ‘ 1946, 103. (14) Ratner, A. P., Rik, G. R., Shebashev, A. A., Primenenie Mechenykh Atomov u Anal. Khim., Akad. iVauk S.S.S.R., Inst. Geokhim i Anal. Khim. 70 (1955). (15) Ringbom. d..Z. anal. Chem. 115,332 A
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I
I
RECEIVEDfor review April 10, 1957. Accepted July 14, 1958. Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, February 29, 1956. Abstracted from the doctoral dissertation of Robert S. Braman, ICorthFestern University, 1956.
Automatic Spectrophotometric Titration of Fluoride, Sulfate, Uranium, and Thorium OSCAR MENIS, D. L. MANNING, and R. G. BALL Analyfical Chemistry Division, Oak Ridge National laboratory, Oak Ridge, Jenn. An automatic, spectrophotometric titration method was applied to the measurement of microgram quantities of fluoride, sulfate, uranium, and thorium. A new indicator, quercetin, was utilized in the estimation of thorium by a titration with (ethylene dinitri1o)tetraacetic acid. Optimum conditions were established for the determination of as little as 6 y of fluoride and sulfate, 12 y of uranium, and 2 y of thorium, with a coefficient
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ANALYTICAL CHEMISTRY
170,
of variation of 4, 5, 3, and respectively. In the case of sulfate, an approximately 1 0-fold increase in sensitivity was obtained by carrying out the titration in 50% isoamyl alcohol. The additions to a Warren Spectracord, which was used in this study, included the time-drive attachment, a titrant-feed assembly, and modifications to permit access to the sample compartment without removing the stirrer and buret tip.
D
the Constituents of reactor fuels, or the by-products of these fuels, is of prime importance in homogeneous reactor studies. The components of interest in this laboratory are sulfate and fluoride, which may occur as impurities in the original fuel; tetravalent uranium, which is a product of the reduction of the higher valent uranium; and thorium, which results from the dissolution of thorium compounds. Although methods exist for ETERhlIKATION O f
