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Determination of H, C, N, O content of bulk materials from neutron-attenuation measurements
ht. /. Appi. Radiat. ht. Vol. 36.No. 3,pp. 185-191.1985 hinted in Great Britain
OEO-708X,85 53.Oil+O.O0 Pergamon Press Lrd
Determination of H, C, N, 0 Content of Bulk Materials from Neutron-Attenuation Measurements J. C. OVERLEY Physics Department, University of Oregon, Eugene, OR 97403, l_J.S.A (Receiced 13
August 1984)
Several bulk samples ranging from chemical compounds to cereal grains have been nondestructively analyzed through neutron-attenuation measurements. A fast-neutron continuum was produced by an accelerator. Attenuations were measured by pulsed-beam, time-of-tight techniques. Average hydrogen, carbon, nitrogen, and oxygen contents were deduced by comparing attenuations to those measured for pure elements. Statistical precisions of 0.3-0.7 atomic percent were achieved for each element in about IOmin. Comparisons with results of other analysis techniques indicate that similar levels of accuracy are possible, even in the presence of small amounts of heavier elements.
1. introduction Determination of the hydrogen (H), carbon (C), nitrogen (N), and oxygen (0) content of bulk organic materials is of great practical importance. The protein content of cereal grains and forage materials, for example, is often inferred from nitrogen content as measured by the wet-chemistry Kjeldahl process. Some of the hydrogen, carbon and oxygen is associated with the protein. The remainder is linked to the carbohydrate, fat, and moisture content which are also of interest. We have been studying a rapid method of analysis for these elements which is nondestructive of bulk materials. It is reminiscent of optical absorption spectroscopy except that neutrons are used instead of light. A pulsed beam of neutrons with a continuous energy distribution is produced by an accelerator and allowed to strike the sample of interest. The energy dependence of neutron attenuation is measured by time-of-flight techniques and is fitted with attenuations measured for pure elements. Projected number densities of each element in the sample are thereby deduced. A related technique termed neutron-resonance transmission analysis has been investigated at the National Bureau of Standards.“) In those studies the energy dependence of attenuation of slow (ev) neutrons was used to deduce the isotopic content of reactor fuel elements. In contrast to the NBS studies, we use fast (MeV) neutrons to determine the light element content of materials. Our interest in the technique stems from using@.” neutrons as an element-sensitive probe in computed tomography. To optimize this application,
.knowledge of how precision of the technique depends on experimental parameters is desirable. In this paper we briefly describe our experimental methods. Results obtained for a variety of samples ranging from chemical compounds to cereal grains are presented. Finally our results are compared to those obtained from other analyses and several factors which can affect precision are discussed.
2. Data Acquisition Neutrons were produced by bombarding a l-mm-thick beryllium-metal target with a 4.5MeV deuteron beam from the University of Oregon j-MV Van de Graaff accelerator. The beam was chopped at 0.5 MHz and klystron-bunched so that beam pulse duration at the target was about 1 ns, full-width at half-maximum (FWHM). Time averaged beam currents were about 0.6pA. Beam location and lateral extent on target were defined by a 2-mm-diameter aperture in a tantalum plate located 25 cm upstream from the target. Neutrons emitted at 0” with respect to the deuteron beam form a continuum with energies up to 9 MeV. Those neutrons were collimated to a beam 2 cm in diameter, 2.3 m from the beryllium target. Samples to be analyzed were placed in the beam at that point. Neutron collimation and extensive shielding around the source target were used to minimize backgrounds caused by neutrons interacting with the sample and the general environment. Neutrons were detected by a proton-recoil specconsisting of a lo-cm-diameter, trometer 2.5cm-thick liquid scintillator coupled to a fast
185
186
J. C. O~ERL.EY
photomultiplier. The detector was located 10 m from the beryllium target in a small room connected to the main target room by a 26cm-diameter tunnel through 3.5 m of earth. Alignment of the neutron source with the colhmators and detector over these long distances was critical. It was established and monitored by reflecting a laser beam through the collimating system from a microscope cover glass mounted at the beryllium target. The neutron source was positioned on the laser line by replacing the beryllium target with quartz and viewing deuteronbeam-induced fluorescence through the cover glass. Timing signals derived from the deuteron-beam pulse and from the photomultiplier were routed to a time-to-amplitude converter (TAC). Resulting pulses were digitized by a IOO-MHz analog-to-digital converter (ADC) and stored by an on-line computer as 1024-channel neutron flight-time spectra. Events corresponding to proton recoil energies of less than 0.3 MeV were rejected at the ADC. Spectra were normalized by integrating the incident deuteronbeam current to a preset level. Compensations for ADC dead times of up to 20% were made by integrating current only when the ADC was able to accept events. Previous publications describe these thicktarget techniques,(4) and detection and shielding systems(5.6)more fully. Figure 1 shows two flight-time spectra; one for neutrons from the 9Be(d,n)‘oB source reaction, the other for neutrons transmitted by a specimen containing HCNO. The width of the prompt y-ray peak in Fig. 1 near channel
1000 indicates
art overall time
resolution of about 2 ns (FWHM). TAC deadtime was reduced by gating the TAC off during 96% of the beam cycles for a 0. l-pus interval centered about the potential arrival time of a prompt y-ray timing signal at the TAC. The y-ray peak height was thus reduced by a factor of 25 without altering the rest of the spectrum. Structure in the source spectrum stems from energy dependence in the neutron-production cross sections and from sharp kinematic edges at the maximum neutron energies for each of the many neutron groups which can be produced. The prom_iient&tTsZiF~ 1 near channels 600 and 740 are examples of these edges. Locations of the edges depend on incident deuteron-beam energy. In the transmitted spectrum, additional structures are observed which correspond to resonances in the total cross sections for elements in the sample. Locations, sizes, and shapes of these features depend uniquely on the elements involved. Backgrounds were investigated by blocking the direct neutron beam with a brass shadow bar at the sample position and also by moving the detector laterally out of the direct beam. Backgrounds were found to be independent of flight time and were therefore determined for each spectrum from the flat region above the highest-energy kinematic edge. The samples investigated fall into three groups. The five samples of the first set were made by dissolving known amounts of urea in water. Number densities of elements in these samples were calculated from mass and volume measurements and were verified in two cases by a commercial laboratory. The
Neutron energy
( MeVl
600
400 Channel
800
1000
number
Fig. 1. Examples of neutron fight-time spectra. The upper curve is the spectrum from the thick target 9Be(d,n)LoBsource reaction. The lower is a spectrum after attenuation by a sample containing HCNO. Each spectrum was obtained with a 43MeV incident deuteron beam and 1.2mC of integrated beam current. Flight time increases to the left at the rate of 0.954 ns/channel. Neutron energy is shown by the upper scale.
Determination
187
of HCN’O content
second set consisted of reagent-grade fructose (C6H,306), melamine (C,H,N,), and urea (CH,NrO). These were selected to produce a range of projected number densities greater than that contained in the first set. Finally, a set of six conveniently available grains and seeds was examined. These were chosen to provide realistic examples. Although they were not well-characterized, they were subsequently analyzed by commercial microanalytical combustion techniques for HCN content. For analysis, all samples were placed in polystyrene boxes with thicknesses in the 3- to 6-cm range. Samples in the first set were used in conjunction with a carbon slab 0.9-cm thick so that the combinations would simulate biological matrices with nitrogen content in the l-10% range by weight. To reduce systematic errors, cross sections measured under present conditions were used in the analyses. Cylinders of carbon and polyethylene were used to obtain carbon and hydrogen cross sections, and normalization factors accurate to + 1% were obtained from cylinder masses and dimensions. Liquid nitrogen and oxygen contained in cylindrical glass-dewar flasks were used to obtain cross sections for those elements, and results were normalized to previously measured(‘) values. Data were collected in increments of 0.4 mC of integrated beam current. Transmission data obtained with empty sample containers were interspersed frequently with sample-in data. Beam focussing and positioning were rarely adjusted and excellent reproducibility was obtained for similar measurements separated by about 1 h. To adjust for drifts over longer times, all spectra were standardized to a common flight-time zero and l.O-ns flight-time bins for a 10-m flight path. All spectra were corrected for background, and in some cases several spectra for a given sample were combined to improve statistical precision.
width of the response function and the interval AE,. In this approximation we define an attenuation. A
J
=
In
NdEj)AE ’ = Zi
a,(Ej)pi
N(Ej)AEj
(3)
as the logarithm of the ratio of sample-out to samplein counts in the jth energy interval. The middle curve of Fig. 2 shows values of A, calculated from the standardized data of Fig. 1. The energy intervals AEj for the attenuations are determined by the 1.O-ns-wide flight-time bins. Linear least-squares techniques can be used to determine “best” estimates pf of projections from the roughly 650 values of Aj calculated for each sample. We use an effective variance method,“’ minimizing
~iOijp:)’ 6: + Zi(Aijp:)' (Aj
x’=C J
-
(4)
with respect to the p:. In this expression Sj and Aij are statistical standard deviations in the .4, and uii, respectively. Figure 2 illustrates values of 4 corresponding to the Aj shown. The fitting is done iteratively with the denominator first evaluated withp: = 0. Resultant values ofp,* are then used in the denominator for the next iteration. This procedure converges rapidly and only one iteration was required. Since the same neutron-source reaction was used for all measurements, Sj and A,’ have similar dependences on j and the major effect of iterating was to reduce values of x2 rather than alter values of p:. Attenuations reconstructed with calculated values of p: and measured cross sections are also illustrated in Fig. 2. Our linear approximation is not strictly valid near sharp resonances in the total cross sections. If errors due to nonlinear “beam-hardening” effects are minor, however, the simplicity of linear techniques should justify their use. If not, nonlinear techniques”) can be used if the experimental response function is known.
3. Data Analysis After correction for background, the number of neutrons detected in energy interval AEj is given by N(E,)AE =
E;) dE
1
dEj,
(1)
where R(E, E,) is an experimental response function which describes detection efficiency and energy resolution in terms of energy E near nominal energy Ej. The response function is convoluted with the product of the incident source spectrum Z,(E) dE and a neutron transmission factor T(E) = exp { --Zai(E)pi}
(2)
in which q(E) is the total neutron cross section for an element of type i with projected atomic-number density pi along the neutron-beam path. The transmission factor may be taken outside the integral signs of equation (1) if it is constant over the
4. Results Analyses for the three types of specimens are shown in Tables 1, 2 and 3. Attenuation data for all three tables were fitted with cross sections measured with 1.2 mC of deuteron-beam charge. Table 1 presents results as projected number densities. For Tables 2 and 3 the samples were assumed to contain only HCNO and results were converted to atomicnumber percent and weight percent, respectively. In each case results of other analyses are given in parentheses. Uncertainties given in all Tables are estimated standard deviations derived from counting statistics alone. A. Statistical prectiion Transmission data for each sample in Table 1 were collected with 1.2 mC of integrated beam current in about 35 min. Roughly 6 x 10’ neutrons were inci-
188
J. C. Onwv Neurron
energy
( MeVl
Fig. 2. Neutron attenuation A, vs flight time. The middle curve is derived from the data of Fig. 1 transformed and standardized to I-ns flight-time bins over a 10-m flight path. The lowest curve represents statistical standard deviations, 4, multiplied by IO. The uppermost curve is a least-squares fit to the attenuations. It has been displaced upward by a constant amount for clarity.
dent on each sample and about 40% of them were transmitted. A value of 0.06% in statistical precision is obtained for an attenuation calculated from the total number of incident and transmitted neutrons detected. In contrast, if the standard deviations in Table 1 are converted to percentages of total projected number densities, results are 0.2, 0.3, 0.3 and 0.15% for H, C, N, and 0, respectively. Uncertainties in attenuation and in the measured cross sections contribute about equally to these values.
Uncertainties due to counting statistics will vary inversely with the square root of the integrated beam current used in acquiring transmission data if other contributions are negligible. Transmission data for each sample in Table 2 were acquired with 0.4 mC of beam charge in lo- 12 min. Percentage uncertainties are roughly twice as large as those for Table 1 and do not depend strongly on composition. They are larger than expected from simple scaling, but this is caused mostly by a larger average transmission of about
Table 1. Projected number densities of elements for samples of carbon, urea. and water. Uncertainties are statistical estimated standard deviations. Values expected from mass and volume measurements are shown in parentheses Projection p: (IF Sample number
atoms/ctG)
H 2.245 c 0.008 (2.261)
C
N
0
XP
0.751 * 0.013 (0.762)
0.000 * 0.013 (0.026)
1.132 = 0.006 (1.119)
4.127 (4.168)
2
2.213 2 0.008 (2.23 I)
0.803 * 0.013 (0.773)
0.035 k 0.013 (0.048)
1.12Oi:O.O06 (1.092)
4.171 (4.144)
3
2.187_LO.O08 (2.234)
0.808 2 0.013 (0.794)
0.074 * 0.013 (0.090)
I.087 ‘- 0.006 (1.072)
4.156 (4.190)
4
2. I74 * 0.008 (2.181)
0.838 t 0.013 (0.826)
0.144 * 0.013 (0.154)
I.034 = 0.006 (1.015)
4.190 (4.176)
5
2. I44 k 0.008 (2.157)
0.859 * 0.013 (0.846)
0.159 20.013 (0.193)
1.010 = 0.006 (0.981)
1.172 (4.176)
I
Determination
of HCNO
content
189
Table 2. Compositions of selected compounds as percentages of total number of atoms. Uncertainties are s:atistical estimated standard deviations. Values expected from s:oichiometry are shown in parentheses Composition (atoma;) Compound
N
0
H
C
Sugar (C,H,:W
49.5 2 0.4 (50.0)
26.0 rt 0.7 (25.0)
Melamine (W&J
39.1 * 0.4 W.0)
2l.OiO.6 (20.0)
40. I * 0.6 (40.0)
-0.2 i: 0.3
Urea (CH,N,O)
50.5 + 0.4 (50.0)
12.9 rt 0.7 (12.5)
23.8 & 0.7 (25.0)
12.7 f 0.3 (12.5)
25.7 _c0.3 (35.0)
-1.3Io.7 (0.0)
(0.0)
Table 3. Compositions of grains and seeds in weight percent. Uncertainties are statistical estimated standard deviations. Values determined through microanalytical combustion techniques are shown in parentheses. Average densities inferred from projection measurements are also given. with values expected from mass/volume measurements given in parentheses Composition (weight Y{) Samule
Density e ‘cm’
H
C
N
0
Barley
6.85 L 0.04 (6.44)
43.2 i: 0.7 (41.12)
1.0 5 0.9 (2.10)
49.0 IO.5
0.80 (0.83)
Bird seed mix
6.96 5 0.04 (7.13)
44.0 f 0.8 (44.05)
1.9* 0.9
47.2 20.5
0.68 (0.66)
Lentils
6.59 5 0.04 (6.79)
43.2 + 0.8 (41.23)
5.48 k 0.9 (3.98)
U.8 5 0.5
0.76 (0.77)
Rolled oats
6.87 & 0.06 (7.01)
43.8 f I.2 (43.3)
3.43 * 1.29 (2.36)
45.9 * 0.7
0.41 (0.47)
Rice
6.71 2 0.04 (6.94)
39.8 2 0.7 (39.61)
1.98 + 0.9 (1.32)
jl.5 * 0.4
0.82 (0.82)
Soybeans
7.45 5 0.04 (7.29)
49.0 = 0.8 (49.84)
8.44 k 0.9 (5.72)
35. I f 0.5
0.77 (0.72)
60%. It has been pointed out previouslyt9) that precision in attenuation is optimized for transmission in the 10-30x range, if other factors are equal. Transmission data for Table 3 were also acquired in IO-12 min per sample. Transmissions were about 60% for oats and 40% for the other materials. When converted to percentage of total weight, the hydrogen content is very precise because uncertainties in number are demagnified by the small atomic mass for hydrogen. In compensation, statistical uncertainties for other elements are roughly doubled. For nitrogen, uncertainties are about 1% of total weight but this should still be sufficient to distinguish between grains with high and low protein content. Statistical precision is enhanced if precise values of cross sections are used to fit attenuations. Hydrogen total cross sections vary smoothly with energy.“” Therefore, measured hydrogen cross sections were least-squares fitted with a power series in the square root of neutron tight time and the results were used in the analyses. The uncertainties Aij in equation (4) for hydrogen were taken to be zero. Statistical’uncertainties for all elements in Table 1 were reduced by 1j-20% by this process. Values of projections and of x’ were not altered significantly. The quality of all fits was such that values of x’ per degree of freedom were always less than 1.1 and usually near 0.8.
(2.12)
Additional uncertainty information is contained in a matrix describing correlations between uncertainties in projections p: and p:. Estimated correlation coefficients derived solely from counting statistics are given in Table 4 for sample 4 of Table 1. The matrix indicates that nitrogen and oxygen are nearly orthogonal in the present weighting scheme and that other elements tend to be anticorrelated. These conclusions do not depend strongly on sample type. Because of anticorrelations, the sum of projections, as given in Table 1, should be more reliable than projections for individual elements. Correlations are affected by the energy domain used in the analysis. The cross sections for hydrogen
Table 4. Correlation matrix for sample No. 4 of Table I. Entries are covariance matrix elements normalized to lie between + 1 (complete correlation) and -I (complete anticorrelation) H H
I .oo
C
N
0
-0.43
-0.42
-0.16
-0.50
-0.37
C
-0.43
1.00
N
-0.42
-0.50
0
-0.16
-0.37
I .oo f0.04
+0.0-J I .oo
J. C.
139
and carbon, for example, have similar energy dependence below 2 MeV. Deleting data below 2 MeV from the analysis decreases the H-C anticorrelation from -0.4 to -0.3, but other correlations increase. Effects of using other data subsets were also investigated with similar results: correlations can be affected slightly, but standard deviations increase. Therefore all results presented are based on the complete dara set, which ranges in energy from 0.6 to 9.0 MeV. Effects of poorer time resolution or shorter flight paths were examined by combining data into 2-, 4and lo-ns bins before calculating attenuations and projections. Results were quite stable. The number of hydrogen atoms decreased smoothly by about 0.5% of the total, but carbon and nitrogen content increased to compensate. Oxygen content was affected least. Standard deviations in all projections increased and correlations were altered, but these effects were slight. The greatest effect was on values of x2 per degree of freedom which doubled to highly improbable values of 2 or more. In poor resolution, beamhardening effects near resonances apparently affect ‘the quality of the fits more than they affect values of projections. B. Systenlatic
errors
The expected HNO contents of the samples summarized in Table 1 are subject to a +0.3’? uncertainty derived from mass and volume measurements and to a systematic error of up to + 1% in sample thickness. Expected carbon content is subject to a systematic error of up to _+0.6% derived mainly from uncertainties in the density and thickness measurements for the carbon slab. Values in Table 1 for HCO content and for the sums of projections almost agree with expectations at the above levels of uncertainty. However, since results from transmission analysis are consistently high for oxygen and low for hydrogen, systematic errors at the several percent level are probably present. Similar conclusions are drawn from Table 2 where expected values are based on stoichiometry of the compounds. Although cross sections used in the fitting could perhaps be justifiably renormalized by a few percent to reduce discrepancies, the problem is probably more complex than a simple normalization error. The total cross sections we deduce for hydrogen are l-2:/, lower than those calculated by Breit and Hopkins (I” from phase shift analyses based on precise measurements. If the latter are used in the fitting, not only are hydrogen projections reduced an additional l-2%, but the amounts of other materials are also altered. This results from slightly different energy dependences in the two sets of cross sections and suggests that errors dependent on energy or cross section are present in our measurements. We do not correct specifically for TAC deadtimes, for example, and scale errors approaching 1% for
OVERLEY
incident-neutron spectra could result. Cross sections calculated from such a spectrum would be in error by a constant amount which could reach several percent at minima in the cross sections. As all attenuations would be similarly flawed, the ultimate effect of such errors would be reduced, but probably not eliminated. A different type of systematic error is suggested by the results for the grains and seeds. The commercial measurements in Table 3 are uncertain by &-194 of total weight for carbon and + 0.6% for hydrogen and nitrogen, with the uncertainties dominated by questions about the degree of homogenization of the samples before analysis. The two sets of hydrogen values agree to within +0.4%. Amounts of nitrogen from transmission analysis, however, are too high in most cases whereas they tend to be too low in Tables 1 and 2. The amounts of HCNO deduced from transmission analysis will be too large, on average, if the assumption that the sample consists only of these elements is incorrect. As likely impurities are heavier than these elements, average densities calculated from projections would then probably be too low. The comparison in Table 3 of mass densities calculated from projections with those from mass;volume measurements is inconclusive, unfortunately, because of large uncertainties due to variable packing of the samples. In an atrempt to compensate for contributions from other elements, attenuations were fitted again with a fifth, fictitious element X included in the analysis. Element X was assigned a constant neutron cross section of 2.0 b. Because heavy elements often have featureless cross sections at high energies this single element might correct for a wide variety of minor constituents. In that case accuracy in projected HCNO number densities would be improved. Conversion to weight percent would still be uncertain, but results in terms of number percent might also be improved since average cross sections do not vary rapidly with atomic weight. The amounts of element X deduced are not tabulated. For the samples of Tables 1 and 2 they were negative in 7 of 8 cases, but differed from zero by less than three standard deviations. Although negative values are not physically realistic they can easily arise from deadtime errors of the type mentioned above. For the grains and seeds of Table 3, on the other hand, projected number densities of element X were positive and ranged from 0.2% of the total for barley to about 2.6”/6 for lentils and soybeans. The latter were nonzero by 4-5 standard deviations. It is in those cases that discrepancies in nitrogen content are also greatest. Projected number densities of hydrogen deduced for all samples were essentially unchanged when element X was included. Oxygen content was altered by less than one standard deviation except for lentils and soybeans, and tended to be correlated with the
191
Determination of HCNO content amount of X. Carbon content, on the other hand was anticorrelated. The largest effect was on nitrogen content, which was also anticorrelated with X with a correlation matrix element of about -0.65. Inclusion of X quantitatively improves agreement for nitrogen content correct
in Table 1 and produces changes in the directions in Tables Z and 3. The extent to which agreement is improved when minor impUritieS are present must await further study with wellcharacterized samples.
evolve, however, and the possibility of producing several neutron beams simultaneously from one machine may reduce this impediment in the future. Acknowledgements-IV. Schildbach, an undergraduate research participant, produced some of the samples and assisted in some data collection. Professor H. W. Lefevre provided constant encouragement. The project was supported by the National Science Foundation under Grant No. PHY-8306683.
References 5. Conclusions Bulk organic materials containing only HCNO can be analyzed for these elements by neutron attenu-
ation analysis. Statistical precisions of a few tenths of a percent by number can be obtained in about 10 min. In many cases, corrections for minor impurities can probably be made without impairing precision. Systematic uncertainties in measured quantities should be reduced below a few tenths of a percent also to take full advantage of the technique. Although nuclear physics experiments at this level of accuracy are difficult, reduction of relative systematic uncertainty is probably the only necessary requirement. This appears feasible. Capital-equipment requirements probably restrict practical application of the technique at the present time. Special-purpose accelerators are beginning to
1. Schrack R. .4., Behrens J. W., Johnson R. and Bowman C. D. IEEE Trans. Nucl. Sci. NS28, 1640 (198 1h 2. Overley J. C. J. Comput. Assist. Tom&r. 7, i17 (i983). 3. Overley J. C. IEEE Trans. Nucl. Sci. W-30, 1677 (1983). 4. Wylie W. R., Bahnsen R. M. and Lefevre H. W. Nucl. Instrum. Methods 79, 245 (1970). 5. Burke C. A., Lunnon M. T. and Lefevre H. W. Phys. Rw. C 10, 1299 (1974). 6. Yu L. L. and Overley J. C. Nucl. Whys. A 324, 160 (1979). 7. Schwartz R. B., Schrack R. A. and Heaton H. T. NBS Monopaph 138, MeV Total Neutron Cross Sections, (U.S. Department of Commerce, Wash. D.C., 1974). 8. &ear J. Am. J. Whys. SO, 912 (1982). 9. Burae E. J. Nucl. Instrum. Metho&. 144. 547 (1977). 10. Ga&el J. L. Fast Neutron Physics Part II, p: 2185. (Eds IMarion J. B. and Fowler J. L.) (Wiley, New York, 1963). 11. Hopkins J. C. and Breit G. Nucl. Data Tables A9, 137 (1971).
OEO-708X,85 53.Oil+O.O0 Pergamon Press Lrd
Determination of H, C, N, 0 Content of Bulk Materials from Neutron-Attenuation Measurements J. C. OVERLEY Physics Department, University of Oregon, Eugene, OR 97403, l_J.S.A (Receiced 13
August 1984)
Several bulk samples ranging from chemical compounds to cereal grains have been nondestructively analyzed through neutron-attenuation measurements. A fast-neutron continuum was produced by an accelerator. Attenuations were measured by pulsed-beam, time-of-tight techniques. Average hydrogen, carbon, nitrogen, and oxygen contents were deduced by comparing attenuations to those measured for pure elements. Statistical precisions of 0.3-0.7 atomic percent were achieved for each element in about IOmin. Comparisons with results of other analysis techniques indicate that similar levels of accuracy are possible, even in the presence of small amounts of heavier elements.
1. introduction Determination of the hydrogen (H), carbon (C), nitrogen (N), and oxygen (0) content of bulk organic materials is of great practical importance. The protein content of cereal grains and forage materials, for example, is often inferred from nitrogen content as measured by the wet-chemistry Kjeldahl process. Some of the hydrogen, carbon and oxygen is associated with the protein. The remainder is linked to the carbohydrate, fat, and moisture content which are also of interest. We have been studying a rapid method of analysis for these elements which is nondestructive of bulk materials. It is reminiscent of optical absorption spectroscopy except that neutrons are used instead of light. A pulsed beam of neutrons with a continuous energy distribution is produced by an accelerator and allowed to strike the sample of interest. The energy dependence of neutron attenuation is measured by time-of-flight techniques and is fitted with attenuations measured for pure elements. Projected number densities of each element in the sample are thereby deduced. A related technique termed neutron-resonance transmission analysis has been investigated at the National Bureau of Standards.“) In those studies the energy dependence of attenuation of slow (ev) neutrons was used to deduce the isotopic content of reactor fuel elements. In contrast to the NBS studies, we use fast (MeV) neutrons to determine the light element content of materials. Our interest in the technique stems from using@.” neutrons as an element-sensitive probe in computed tomography. To optimize this application,
.knowledge of how precision of the technique depends on experimental parameters is desirable. In this paper we briefly describe our experimental methods. Results obtained for a variety of samples ranging from chemical compounds to cereal grains are presented. Finally our results are compared to those obtained from other analyses and several factors which can affect precision are discussed.
2. Data Acquisition Neutrons were produced by bombarding a l-mm-thick beryllium-metal target with a 4.5MeV deuteron beam from the University of Oregon j-MV Van de Graaff accelerator. The beam was chopped at 0.5 MHz and klystron-bunched so that beam pulse duration at the target was about 1 ns, full-width at half-maximum (FWHM). Time averaged beam currents were about 0.6pA. Beam location and lateral extent on target were defined by a 2-mm-diameter aperture in a tantalum plate located 25 cm upstream from the target. Neutrons emitted at 0” with respect to the deuteron beam form a continuum with energies up to 9 MeV. Those neutrons were collimated to a beam 2 cm in diameter, 2.3 m from the beryllium target. Samples to be analyzed were placed in the beam at that point. Neutron collimation and extensive shielding around the source target were used to minimize backgrounds caused by neutrons interacting with the sample and the general environment. Neutrons were detected by a proton-recoil specconsisting of a lo-cm-diameter, trometer 2.5cm-thick liquid scintillator coupled to a fast
185
186
J. C. O~ERL.EY
photomultiplier. The detector was located 10 m from the beryllium target in a small room connected to the main target room by a 26cm-diameter tunnel through 3.5 m of earth. Alignment of the neutron source with the colhmators and detector over these long distances was critical. It was established and monitored by reflecting a laser beam through the collimating system from a microscope cover glass mounted at the beryllium target. The neutron source was positioned on the laser line by replacing the beryllium target with quartz and viewing deuteronbeam-induced fluorescence through the cover glass. Timing signals derived from the deuteron-beam pulse and from the photomultiplier were routed to a time-to-amplitude converter (TAC). Resulting pulses were digitized by a IOO-MHz analog-to-digital converter (ADC) and stored by an on-line computer as 1024-channel neutron flight-time spectra. Events corresponding to proton recoil energies of less than 0.3 MeV were rejected at the ADC. Spectra were normalized by integrating the incident deuteronbeam current to a preset level. Compensations for ADC dead times of up to 20% were made by integrating current only when the ADC was able to accept events. Previous publications describe these thicktarget techniques,(4) and detection and shielding systems(5.6)more fully. Figure 1 shows two flight-time spectra; one for neutrons from the 9Be(d,n)‘oB source reaction, the other for neutrons transmitted by a specimen containing HCNO. The width of the prompt y-ray peak in Fig. 1 near channel
1000 indicates
art overall time
resolution of about 2 ns (FWHM). TAC deadtime was reduced by gating the TAC off during 96% of the beam cycles for a 0. l-pus interval centered about the potential arrival time of a prompt y-ray timing signal at the TAC. The y-ray peak height was thus reduced by a factor of 25 without altering the rest of the spectrum. Structure in the source spectrum stems from energy dependence in the neutron-production cross sections and from sharp kinematic edges at the maximum neutron energies for each of the many neutron groups which can be produced. The prom_iient&tTsZiF~ 1 near channels 600 and 740 are examples of these edges. Locations of the edges depend on incident deuteron-beam energy. In the transmitted spectrum, additional structures are observed which correspond to resonances in the total cross sections for elements in the sample. Locations, sizes, and shapes of these features depend uniquely on the elements involved. Backgrounds were investigated by blocking the direct neutron beam with a brass shadow bar at the sample position and also by moving the detector laterally out of the direct beam. Backgrounds were found to be independent of flight time and were therefore determined for each spectrum from the flat region above the highest-energy kinematic edge. The samples investigated fall into three groups. The five samples of the first set were made by dissolving known amounts of urea in water. Number densities of elements in these samples were calculated from mass and volume measurements and were verified in two cases by a commercial laboratory. The
Neutron energy
( MeVl
600
400 Channel
800
1000
number
Fig. 1. Examples of neutron fight-time spectra. The upper curve is the spectrum from the thick target 9Be(d,n)LoBsource reaction. The lower is a spectrum after attenuation by a sample containing HCNO. Each spectrum was obtained with a 43MeV incident deuteron beam and 1.2mC of integrated beam current. Flight time increases to the left at the rate of 0.954 ns/channel. Neutron energy is shown by the upper scale.
Determination
187
of HCN’O content
second set consisted of reagent-grade fructose (C6H,306), melamine (C,H,N,), and urea (CH,NrO). These were selected to produce a range of projected number densities greater than that contained in the first set. Finally, a set of six conveniently available grains and seeds was examined. These were chosen to provide realistic examples. Although they were not well-characterized, they were subsequently analyzed by commercial microanalytical combustion techniques for HCN content. For analysis, all samples were placed in polystyrene boxes with thicknesses in the 3- to 6-cm range. Samples in the first set were used in conjunction with a carbon slab 0.9-cm thick so that the combinations would simulate biological matrices with nitrogen content in the l-10% range by weight. To reduce systematic errors, cross sections measured under present conditions were used in the analyses. Cylinders of carbon and polyethylene were used to obtain carbon and hydrogen cross sections, and normalization factors accurate to + 1% were obtained from cylinder masses and dimensions. Liquid nitrogen and oxygen contained in cylindrical glass-dewar flasks were used to obtain cross sections for those elements, and results were normalized to previously measured(‘) values. Data were collected in increments of 0.4 mC of integrated beam current. Transmission data obtained with empty sample containers were interspersed frequently with sample-in data. Beam focussing and positioning were rarely adjusted and excellent reproducibility was obtained for similar measurements separated by about 1 h. To adjust for drifts over longer times, all spectra were standardized to a common flight-time zero and l.O-ns flight-time bins for a 10-m flight path. All spectra were corrected for background, and in some cases several spectra for a given sample were combined to improve statistical precision.
width of the response function and the interval AE,. In this approximation we define an attenuation. A
J
=
In
NdEj)AE ’ = Zi
a,(Ej)pi
N(Ej)AEj
(3)
as the logarithm of the ratio of sample-out to samplein counts in the jth energy interval. The middle curve of Fig. 2 shows values of A, calculated from the standardized data of Fig. 1. The energy intervals AEj for the attenuations are determined by the 1.O-ns-wide flight-time bins. Linear least-squares techniques can be used to determine “best” estimates pf of projections from the roughly 650 values of Aj calculated for each sample. We use an effective variance method,“’ minimizing
~iOijp:)’ 6: + Zi(Aijp:)' (Aj
x’=C J
-
(4)
with respect to the p:. In this expression Sj and Aij are statistical standard deviations in the .4, and uii, respectively. Figure 2 illustrates values of 4 corresponding to the Aj shown. The fitting is done iteratively with the denominator first evaluated withp: = 0. Resultant values ofp,* are then used in the denominator for the next iteration. This procedure converges rapidly and only one iteration was required. Since the same neutron-source reaction was used for all measurements, Sj and A,’ have similar dependences on j and the major effect of iterating was to reduce values of x2 rather than alter values of p:. Attenuations reconstructed with calculated values of p: and measured cross sections are also illustrated in Fig. 2. Our linear approximation is not strictly valid near sharp resonances in the total cross sections. If errors due to nonlinear “beam-hardening” effects are minor, however, the simplicity of linear techniques should justify their use. If not, nonlinear techniques”) can be used if the experimental response function is known.
3. Data Analysis After correction for background, the number of neutrons detected in energy interval AEj is given by N(E,)AE =
E;) dE
1
dEj,
(1)
where R(E, E,) is an experimental response function which describes detection efficiency and energy resolution in terms of energy E near nominal energy Ej. The response function is convoluted with the product of the incident source spectrum Z,(E) dE and a neutron transmission factor T(E) = exp { --Zai(E)pi}
(2)
in which q(E) is the total neutron cross section for an element of type i with projected atomic-number density pi along the neutron-beam path. The transmission factor may be taken outside the integral signs of equation (1) if it is constant over the
4. Results Analyses for the three types of specimens are shown in Tables 1, 2 and 3. Attenuation data for all three tables were fitted with cross sections measured with 1.2 mC of deuteron-beam charge. Table 1 presents results as projected number densities. For Tables 2 and 3 the samples were assumed to contain only HCNO and results were converted to atomicnumber percent and weight percent, respectively. In each case results of other analyses are given in parentheses. Uncertainties given in all Tables are estimated standard deviations derived from counting statistics alone. A. Statistical prectiion Transmission data for each sample in Table 1 were collected with 1.2 mC of integrated beam current in about 35 min. Roughly 6 x 10’ neutrons were inci-
188
J. C. Onwv Neurron
energy
( MeVl
Fig. 2. Neutron attenuation A, vs flight time. The middle curve is derived from the data of Fig. 1 transformed and standardized to I-ns flight-time bins over a 10-m flight path. The lowest curve represents statistical standard deviations, 4, multiplied by IO. The uppermost curve is a least-squares fit to the attenuations. It has been displaced upward by a constant amount for clarity.
dent on each sample and about 40% of them were transmitted. A value of 0.06% in statistical precision is obtained for an attenuation calculated from the total number of incident and transmitted neutrons detected. In contrast, if the standard deviations in Table 1 are converted to percentages of total projected number densities, results are 0.2, 0.3, 0.3 and 0.15% for H, C, N, and 0, respectively. Uncertainties in attenuation and in the measured cross sections contribute about equally to these values.
Uncertainties due to counting statistics will vary inversely with the square root of the integrated beam current used in acquiring transmission data if other contributions are negligible. Transmission data for each sample in Table 2 were acquired with 0.4 mC of beam charge in lo- 12 min. Percentage uncertainties are roughly twice as large as those for Table 1 and do not depend strongly on composition. They are larger than expected from simple scaling, but this is caused mostly by a larger average transmission of about
Table 1. Projected number densities of elements for samples of carbon, urea. and water. Uncertainties are statistical estimated standard deviations. Values expected from mass and volume measurements are shown in parentheses Projection p: (IF Sample number
atoms/ctG)
H 2.245 c 0.008 (2.261)
C
N
0
XP
0.751 * 0.013 (0.762)
0.000 * 0.013 (0.026)
1.132 = 0.006 (1.119)
4.127 (4.168)
2
2.213 2 0.008 (2.23 I)
0.803 * 0.013 (0.773)
0.035 k 0.013 (0.048)
1.12Oi:O.O06 (1.092)
4.171 (4.144)
3
2.187_LO.O08 (2.234)
0.808 2 0.013 (0.794)
0.074 * 0.013 (0.090)
I.087 ‘- 0.006 (1.072)
4.156 (4.190)
4
2. I74 * 0.008 (2.181)
0.838 t 0.013 (0.826)
0.144 * 0.013 (0.154)
I.034 = 0.006 (1.015)
4.190 (4.176)
5
2. I44 k 0.008 (2.157)
0.859 * 0.013 (0.846)
0.159 20.013 (0.193)
1.010 = 0.006 (0.981)
1.172 (4.176)
I
Determination
of HCNO
content
189
Table 2. Compositions of selected compounds as percentages of total number of atoms. Uncertainties are s:atistical estimated standard deviations. Values expected from s:oichiometry are shown in parentheses Composition (atoma;) Compound
N
0
H
C
Sugar (C,H,:W
49.5 2 0.4 (50.0)
26.0 rt 0.7 (25.0)
Melamine (W&J
39.1 * 0.4 W.0)
2l.OiO.6 (20.0)
40. I * 0.6 (40.0)
-0.2 i: 0.3
Urea (CH,N,O)
50.5 + 0.4 (50.0)
12.9 rt 0.7 (12.5)
23.8 & 0.7 (25.0)
12.7 f 0.3 (12.5)
25.7 _c0.3 (35.0)
-1.3Io.7 (0.0)
(0.0)
Table 3. Compositions of grains and seeds in weight percent. Uncertainties are statistical estimated standard deviations. Values determined through microanalytical combustion techniques are shown in parentheses. Average densities inferred from projection measurements are also given. with values expected from mass/volume measurements given in parentheses Composition (weight Y{) Samule
Density e ‘cm’
H
C
N
0
Barley
6.85 L 0.04 (6.44)
43.2 i: 0.7 (41.12)
1.0 5 0.9 (2.10)
49.0 IO.5
0.80 (0.83)
Bird seed mix
6.96 5 0.04 (7.13)
44.0 f 0.8 (44.05)
1.9* 0.9
47.2 20.5
0.68 (0.66)
Lentils
6.59 5 0.04 (6.79)
43.2 + 0.8 (41.23)
5.48 k 0.9 (3.98)
U.8 5 0.5
0.76 (0.77)
Rolled oats
6.87 & 0.06 (7.01)
43.8 f I.2 (43.3)
3.43 * 1.29 (2.36)
45.9 * 0.7
0.41 (0.47)
Rice
6.71 2 0.04 (6.94)
39.8 2 0.7 (39.61)
1.98 + 0.9 (1.32)
jl.5 * 0.4
0.82 (0.82)
Soybeans
7.45 5 0.04 (7.29)
49.0 = 0.8 (49.84)
8.44 k 0.9 (5.72)
35. I f 0.5
0.77 (0.72)
60%. It has been pointed out previouslyt9) that precision in attenuation is optimized for transmission in the 10-30x range, if other factors are equal. Transmission data for Table 3 were also acquired in IO-12 min per sample. Transmissions were about 60% for oats and 40% for the other materials. When converted to percentage of total weight, the hydrogen content is very precise because uncertainties in number are demagnified by the small atomic mass for hydrogen. In compensation, statistical uncertainties for other elements are roughly doubled. For nitrogen, uncertainties are about 1% of total weight but this should still be sufficient to distinguish between grains with high and low protein content. Statistical precision is enhanced if precise values of cross sections are used to fit attenuations. Hydrogen total cross sections vary smoothly with energy.“” Therefore, measured hydrogen cross sections were least-squares fitted with a power series in the square root of neutron tight time and the results were used in the analyses. The uncertainties Aij in equation (4) for hydrogen were taken to be zero. Statistical’uncertainties for all elements in Table 1 were reduced by 1j-20% by this process. Values of projections and of x’ were not altered significantly. The quality of all fits was such that values of x’ per degree of freedom were always less than 1.1 and usually near 0.8.
(2.12)
Additional uncertainty information is contained in a matrix describing correlations between uncertainties in projections p: and p:. Estimated correlation coefficients derived solely from counting statistics are given in Table 4 for sample 4 of Table 1. The matrix indicates that nitrogen and oxygen are nearly orthogonal in the present weighting scheme and that other elements tend to be anticorrelated. These conclusions do not depend strongly on sample type. Because of anticorrelations, the sum of projections, as given in Table 1, should be more reliable than projections for individual elements. Correlations are affected by the energy domain used in the analysis. The cross sections for hydrogen
Table 4. Correlation matrix for sample No. 4 of Table I. Entries are covariance matrix elements normalized to lie between + 1 (complete correlation) and -I (complete anticorrelation) H H
I .oo
C
N
0
-0.43
-0.42
-0.16
-0.50
-0.37
C
-0.43
1.00
N
-0.42
-0.50
0
-0.16
-0.37
I .oo f0.04
+0.0-J I .oo
J. C.
139
and carbon, for example, have similar energy dependence below 2 MeV. Deleting data below 2 MeV from the analysis decreases the H-C anticorrelation from -0.4 to -0.3, but other correlations increase. Effects of using other data subsets were also investigated with similar results: correlations can be affected slightly, but standard deviations increase. Therefore all results presented are based on the complete dara set, which ranges in energy from 0.6 to 9.0 MeV. Effects of poorer time resolution or shorter flight paths were examined by combining data into 2-, 4and lo-ns bins before calculating attenuations and projections. Results were quite stable. The number of hydrogen atoms decreased smoothly by about 0.5% of the total, but carbon and nitrogen content increased to compensate. Oxygen content was affected least. Standard deviations in all projections increased and correlations were altered, but these effects were slight. The greatest effect was on values of x2 per degree of freedom which doubled to highly improbable values of 2 or more. In poor resolution, beamhardening effects near resonances apparently affect ‘the quality of the fits more than they affect values of projections. B. Systenlatic
errors
The expected HNO contents of the samples summarized in Table 1 are subject to a +0.3’? uncertainty derived from mass and volume measurements and to a systematic error of up to + 1% in sample thickness. Expected carbon content is subject to a systematic error of up to _+0.6% derived mainly from uncertainties in the density and thickness measurements for the carbon slab. Values in Table 1 for HCO content and for the sums of projections almost agree with expectations at the above levels of uncertainty. However, since results from transmission analysis are consistently high for oxygen and low for hydrogen, systematic errors at the several percent level are probably present. Similar conclusions are drawn from Table 2 where expected values are based on stoichiometry of the compounds. Although cross sections used in the fitting could perhaps be justifiably renormalized by a few percent to reduce discrepancies, the problem is probably more complex than a simple normalization error. The total cross sections we deduce for hydrogen are l-2:/, lower than those calculated by Breit and Hopkins (I” from phase shift analyses based on precise measurements. If the latter are used in the fitting, not only are hydrogen projections reduced an additional l-2%, but the amounts of other materials are also altered. This results from slightly different energy dependences in the two sets of cross sections and suggests that errors dependent on energy or cross section are present in our measurements. We do not correct specifically for TAC deadtimes, for example, and scale errors approaching 1% for
OVERLEY
incident-neutron spectra could result. Cross sections calculated from such a spectrum would be in error by a constant amount which could reach several percent at minima in the cross sections. As all attenuations would be similarly flawed, the ultimate effect of such errors would be reduced, but probably not eliminated. A different type of systematic error is suggested by the results for the grains and seeds. The commercial measurements in Table 3 are uncertain by &-194 of total weight for carbon and + 0.6% for hydrogen and nitrogen, with the uncertainties dominated by questions about the degree of homogenization of the samples before analysis. The two sets of hydrogen values agree to within +0.4%. Amounts of nitrogen from transmission analysis, however, are too high in most cases whereas they tend to be too low in Tables 1 and 2. The amounts of HCNO deduced from transmission analysis will be too large, on average, if the assumption that the sample consists only of these elements is incorrect. As likely impurities are heavier than these elements, average densities calculated from projections would then probably be too low. The comparison in Table 3 of mass densities calculated from projections with those from mass;volume measurements is inconclusive, unfortunately, because of large uncertainties due to variable packing of the samples. In an atrempt to compensate for contributions from other elements, attenuations were fitted again with a fifth, fictitious element X included in the analysis. Element X was assigned a constant neutron cross section of 2.0 b. Because heavy elements often have featureless cross sections at high energies this single element might correct for a wide variety of minor constituents. In that case accuracy in projected HCNO number densities would be improved. Conversion to weight percent would still be uncertain, but results in terms of number percent might also be improved since average cross sections do not vary rapidly with atomic weight. The amounts of element X deduced are not tabulated. For the samples of Tables 1 and 2 they were negative in 7 of 8 cases, but differed from zero by less than three standard deviations. Although negative values are not physically realistic they can easily arise from deadtime errors of the type mentioned above. For the grains and seeds of Table 3, on the other hand, projected number densities of element X were positive and ranged from 0.2% of the total for barley to about 2.6”/6 for lentils and soybeans. The latter were nonzero by 4-5 standard deviations. It is in those cases that discrepancies in nitrogen content are also greatest. Projected number densities of hydrogen deduced for all samples were essentially unchanged when element X was included. Oxygen content was altered by less than one standard deviation except for lentils and soybeans, and tended to be correlated with the
191
Determination of HCNO content amount of X. Carbon content, on the other hand was anticorrelated. The largest effect was on nitrogen content, which was also anticorrelated with X with a correlation matrix element of about -0.65. Inclusion of X quantitatively improves agreement for nitrogen content correct
in Table 1 and produces changes in the directions in Tables Z and 3. The extent to which agreement is improved when minor impUritieS are present must await further study with wellcharacterized samples.
evolve, however, and the possibility of producing several neutron beams simultaneously from one machine may reduce this impediment in the future. Acknowledgements-IV. Schildbach, an undergraduate research participant, produced some of the samples and assisted in some data collection. Professor H. W. Lefevre provided constant encouragement. The project was supported by the National Science Foundation under Grant No. PHY-8306683.
References 5. Conclusions Bulk organic materials containing only HCNO can be analyzed for these elements by neutron attenu-
ation analysis. Statistical precisions of a few tenths of a percent by number can be obtained in about 10 min. In many cases, corrections for minor impurities can probably be made without impairing precision. Systematic uncertainties in measured quantities should be reduced below a few tenths of a percent also to take full advantage of the technique. Although nuclear physics experiments at this level of accuracy are difficult, reduction of relative systematic uncertainty is probably the only necessary requirement. This appears feasible. Capital-equipment requirements probably restrict practical application of the technique at the present time. Special-purpose accelerators are beginning to
1. Schrack R. .4., Behrens J. W., Johnson R. and Bowman C. D. IEEE Trans. Nucl. Sci. NS28, 1640 (198 1h 2. Overley J. C. J. Comput. Assist. Tom&r. 7, i17 (i983). 3. Overley J. C. IEEE Trans. Nucl. Sci. W-30, 1677 (1983). 4. Wylie W. R., Bahnsen R. M. and Lefevre H. W. Nucl. Instrum. Methods 79, 245 (1970). 5. Burke C. A., Lunnon M. T. and Lefevre H. W. Phys. Rw. C 10, 1299 (1974). 6. Yu L. L. and Overley J. C. Nucl. Whys. A 324, 160 (1979). 7. Schwartz R. B., Schrack R. A. and Heaton H. T. NBS Monopaph 138, MeV Total Neutron Cross Sections, (U.S. Department of Commerce, Wash. D.C., 1974). 8. &ear J. Am. J. Whys. SO, 912 (1982). 9. Burae E. J. Nucl. Instrum. Metho&. 144. 547 (1977). 10. Ga&el J. L. Fast Neutron Physics Part II, p: 2185. (Eds IMarion J. B. and Fowler J. L.) (Wiley, New York, 1963). 11. Hopkins J. C. and Breit G. Nucl. Data Tables A9, 137 (1971).