An improved method for determination of heat production with gamma-ray scintillation spectrometry

l.w‘“D,NC

ISOTOPE

ELSEVIER

Chemical Geology

GEOSCIENCE

130 (1996) 175-194

An improved method for determination of heat production with gamma-ray scintillation spectrometry Richard A. Ketcham University of Texas at Austin, Department

’

of Geological Sciences, Austin, TX 78712, USA

Received 5 April 1995; accepted 17 November 1995

Abstract Gamma-ray

scintillation

spectrometry

is often the method of choice for determination of the heat-producing elements describing modem equipment and proposing revised measurement calculations and error analysis. New equations for calculating HPE concentrations and applicable errors from gamma-ray spectra allow for standards that contain all three HPE’s, rather than requiring that there be only one element in each of three standards. The equations also account automatically for all peak interferences and quantify the error effects of varying counting times. Errors obtained from repeated analyses and distributions of paired analyses compare favorably with those obtained from the equations. The possibility and potential magnitude of secular disequilibrium can be evaluated simultaneously with an analysis by utilizing the low-energy part of the gamma-ray spectrum ( < 0.123 MeV). The factor that is calculated to test for secular disequilibrium also provides a first-order correction for its effects. Repeated analysis of a single sample crushed to varying degrees provides a test of the effects of net sample density on gamma-ray determinations. Uranium and thorium show no variation with sample density in the range studied, but potassium does show a variation, a result that has been observed before. This effect has been explained as a result of source attenuation due to potassium determination utilizing the lowest-energy gamma-rays (1.46 1 MeV), which should be most susceptible to source absorption. However, in the analyses presented here the energy range utilized for thorium is lower (0.916-0.969 MeV), but no source absorption effects are observed. The effect of the potassium variation observed on determination of heat production is negligible, however, and corrections are inadvisable.

(HPE’s) uranium, thorium and potassium. This article updates the procedure,

1. Introduction The use of gamma-ray scintillation spectrometry for determining the concentration of the heat-producing elements (HPE’s) U, Th and K in geologic samples has been summarized a number of times (Hurley, 1956a,b; Bunker and Bush, 1966; Adams and Gasparini, 1970; Rybach, 1971, 1988). Although high-resolution germanium semiconductor detectors (Lewis, 1974) can provide better resolution of the gamma energy spectrum, scintillation detectors are often the instrument of choice for this application, as they provide good results, are less expensive, and are cheaper and easier to maintain. Scintillation detectors also have better counting

’Present address: Department of Geology and Geophysics, Rice University, 0009-2541/96/$15.00 Copyright SSDI 0009.2541(95)00180-8

Houston,

0 1996 Elsevier Science B.V. All rights reserved.

TX 77005, USA.

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RA. Ketchurn / Chemical Geology 130 (1996) 175-194

efficiency than all but the most expensive Ge detectors. There are other analytical methods for determining one or more of the HPE’s (Adams et al., 1958; Hart et al., 1980; Galson et al., 1983; Huntley, 1988), but they do not match gamma-ray analysis for its ease of sample preparation and simultaneous determination of all three elements. Gamma-ray spectrometry utilizes the gamma-rays generated by the normal radioactive decay of unstable isotopes to determine the concentration of the isotopes in a material. Each radioactive isotope undergoing

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Fig. 1. Typical gamma-ray spectra and principal peak nuclides and energies (in MeV) for the three heat-producing elements, obtained by counting IAEA standards RGTh- I, RGU- 1 and RGK-1 for I hr. The energy range represented on the horizontal axis is - 0.01-3.12 MeV, but conversion from channel number to energy is slightly nonlinear.

RA.

Ketcham

/Chemical

2” thick lead enclosure with hinged lid

Geology

130 (I 996)

I75-

I94

177

IBM-compatible computer with analysis software and multichannel analj lzer

Marinelli beaker _ with sample

tube base’ Fig. 2. Schematic diagram of components of the University of Texas at Austin gamma-ray spectrometer.

gamma decay produces gamma-rays at a distinctive energy or set of energies, measured in MeV (or keV). After being generated, gamma-rays tend to lose all or part of their energy by collision with other particles due to the photoelectric effect, Compton scattering and pair production. Discussions of the gamma-ray spectrum and interactions with the detector are numerous; the one provided by Cove11 (1975) is particularly well-written and concise. The typical gamma-ray spectrum from a single isotope will have a peak at the energy of each of its possible gamma-ray energies, plus additional counts spread out over lower energies due to scatter. The peak(s) can be used to identify the isotope, while the total signal is the sum of all counts. Fig. 1 shows the three spectra used for determining the HPE’s. Fig. 2 depicts schematically the gamma-ray scintillation spectrometry system described here. The sample is crushed and sealed in a Marinelli beaker, which maximizes counting efficiency by allowing the sample to surround the detector crystal. The sample and detector are shielded from other potential sources of gamma-rays, such as cosmic rays or local bedrock, in a 2-in-thick (5.08 cm) lead container. Gamma-rays generated by the sample are detected by a 3 in X 3 in (7.62 cm X 7.62 cm) crystal of sodium iodide (NaI) activated with thallium (Tl). Gamma-rays entering the crystal create flashes of light, which are transformed into voltage pulses by a photomultiplier and amplifier. The signal is then sent to a multichannel analyzer, which determines the relative energy level of each gamma-ray and tabulates the events into a series of bins known as channels. Specialized software then allows the user to access and analyze the spectrum. Each radioactive element, either individually or as a part of a decay chain, generates a distinct spectrum. By comparing the spectrum obtained for the sample to spectra obtained from known standards, the concentration of each radioactive element in the sample can be determined.

2. Geological considerations One of the central assumptions in this method is that the uranium and thorium in the rocks being analyzed are in secular equilibrium with their daughter products; in other words, the amount of each radioactive daughter product is determined solely by the amount of its parent through radioactive decay. When a decay chain is in secular equilibrium, the activity (decay events per unit time) of each isotope in the chain is equal (Faure, 1977). All rocks are initially out of secular equilibrium, as the amount of each daughter product is dictated by the circumstances of the rock-forming event rather than the decay of its parent. Subsequently, if the rock remains geochemically undisturbed with respect to all of the elements in the decay chain, it will begin to approach equilibrium. As a rule of thumb, the time required to effectively reach secular equilibrium is six times the longest half-life of any daughter product in the chain, which corresponds to 98.5% replenishment. Table 1 shows the half-lives and gamma-rays for the 238U and 232Th decay chains. The longest-lived daughter in the 238U decay chain is 234U, which has a half-life of 244 kyr. Thus, it takes N 1.5 Myr for the 238U decay chain to be approximate secular equilibrium. The corresponding times for the 235U and 232Th chains are 1.9 Myr and 40 yr, respectively.

RA. Ketchnm / Chemical Geology

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130 (1996)

175-194

Table 1 Isotope

Half-life

y-rays, MeV (absolute intensity,

238U *uTh

4.51 x lo9 yr 24.10 days 6.75 hr 2.47 X lo5 yr 8.0~ lo4 yr 1602 yr 3.8223 days 3.05 min 26.8 min 19.7 min

_

234Pa 234U 230Th 226Ra 2zRn 2’8Po ‘14Pb 214&

2’4Po *“Pb 210Bi 2’OPo ‘06Pb *3zTh “sRa 228Ac 228 Th 224Ra 220Rn *16Po 2’2Pb 2’IBi 2’2Po 208 Tl “sPb

1.64~ 1O-4 s 22.0 yr 5.013 days 138.4 days stable 1.41 x 1o’O yr 6.7 yr 6.13 hr 1.910 yr 3.64 days 55.3 s 0.145 s 10.64 hr 60.60 min 3.04 x IO_’ s 3.10 min stable

Half-lives, gamma-rays, and absolute intensities gamma-rays with intensities 2 3% listed.

%, in parentheses)

0.093(4), 0.064(3.5) _ _ _ 0.186(4) _ 0.242(4), 0.295( 19),0.352(36) 0.609(47), 0.769(5.3), 0.935C3.3). 1.120(16), 1.76(17), 2.20(6), 2.44(2) _

1.26c7.71, l&8.8),

1.73(3.2),

0.047C4.1) _

_ _ 0.129(4.1),

0.270(3), 0.328(4), 0.338(1 I), 0.908(25),

0.960 + 0.966(20)

0.24lc3.7) _ _ 0.23x47), 0.300(3.2) 0.727(7. I) _ 0.277(7), 0.5 11(23), 0.583(86), _ of major members

0.860(12),

2.615(100)

of 238U and 232Th chains,

from Adams and Gasparini

(1970). Only

A rock can be out of secular equilibrium due to either youth or the addition or removal of any member of a decay chain by means other than natural radioactive decay. Examples of interest for heat generation include rocks that have been oxidized by weathering, which preferentially removes uranium, and rocks that have been fractured or disaggregated, which allows radon gas to escape (particularly ***Rn, a decay product of 238U). In this latter case only the decay chain from 222Rn to 2’4Bi need be considered, as daughter products below that oint contribute negligible gamma-ray energy to the spectrum. Within this range, the longest-lived member is P 22Rn, with a half-life of 3.82 days. In this case, re-equilibration takes 3 weeks. This is a maximum estimate, assuming total removal of the daughter product; in most cases radon loss by disaggregation is probably much less than 25% (Hurley, 1956b). The requirement of secular equilibrium has long been the Achilles heel of gamma-ray analysis. Although the use of “fresh, unaltered” rock is often cited as a precaution, it is by no means a fail-safe measure. Due to the ease with which uranium oxidizes into the soluble uranyl ion (IJOg+ 1, and its frequent location on grain boundaries or in metastable radiation-damaged trace phases (Silver et al., 1982), it is very mobile in the near-surface environment (Boyle, 1982). Even samples with little or no visual evidence of weathering can potentially have undergone uranium gain or loss. Thus, verification of secular equilibrium should be an important component of gamma-ray analysis. Existing methods involve utilizing a separate analytical technique to verify uranium determinations (e.g., Adams et al., 1958; Rybach, 1971). Presented below is a method for incorporating the detection of secular equilibrium of uranium into normal gamma-ray analysis. Secular

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Geology 130 (1996) 175-194

179

disequilibrium in equilibrium error.

of uranium should have no effect on determinations of thorium and potassium as long as 226Ra is with its daughter products down to 214Pb, which it will be provided there is no experimental

3. Equipment

and standards

All components of the University of Texas laboratory were purchased premade from commercial sources. The centerpiece of the system is a multichannel analyzer with preamplifier, amplifier, 1024 channels, high-voltage power supply, and digital gain stabilizer, all condensed into a half-sized computer board that can fit into an expansion slot in any IBM-compatible computer, including a portable. Also included is software that controls the board and does some data analysis. The detector is a 3 in X 3 in (7.62 cm x 7.62 cm) NaI(T1) crystal. The Marinelli beakers are polyethylene with polyethylene lids and hold up to 900 ml of material. A set of standards that was specifically created for gamma-ray analysis was obtained from the International Atomic Energy Agency. They are RGU-1, with 400 + 2.1 ppm U; RGTh-1, with 800.2 + 15.8 ppm Th, 6.26 + 0.42 ppm U and 0.02 & 0.01 wt% K; and RGK-1, with 44.8 + 0.3 wt% K (IAEA, 1987). The entire laboratory, including standards, costs approximately US $10,000.

4. Analytical

technique

4.1. Sample preparation Samples are disaggregated in a jaw crusher and then pulverized in a disk mill with the wheels _ 2 mm apart, reducing them to about the grain size of coarse beach sand. This grain size is small enough to ensure even packing of the samples in the Marinelli beakers, both to avoid large grains jamming in the side wells and to have the top surface of the sample in the beaker be relatively smooth and flat, while also being large enough to minimize the problem of settling. This latter effect, in which the sample can change volume due to variable efficiency in packing of grains, increases as grain size diminishes; in practice, a 2-mm-grain-size sample will quickly arrive at a constant geometry by tamping, while an 80-mesh sample will continue settling even after being tamped for 10 min. Although it is recommended by some (e.g., Potts, 19871, a small grain size may present the danger that settling can occur to an extent that the sample geometry will subtly change each time a container is handled. Samples are placed in Marinelli beakers and weighed to + 0.1 -g precision. The beakers are sealed and left undisturbed for 3 weeks in order to re-establish secular equilibrium after possible radon escape. One of the crucial variables in gamma-ray analysis is the geometry of the gamma-ray source (the standard or sample) relative to the detector, as it is one of the factors that determines counting efficiency. To avoid having to utilize correction factors, the samples must fill exactly the same volume in the Marinelli beakers as the standards. The University of Texas laboratory uses two sets of standards: one at 600 ml and one at 250 ml. 600-ml samples are filled to the first graduating line in the Marinelli beakers. 250-ml samples are measured out by filling a 250-ml beaker and then pouring it into the Marinelli beaker. Samples are then visually compared to the standards to verify that they fill the Marinelli beaker to the same level. The main factors influencing mass of sample that fills the beaker are the density of the rock and, more importantly, how finely it is crushed. The mass of 600-ml samples has ranged from 750 to 1050 g, with a mean of - 900 g, while 250-ml samples have ranged from 390 to 460 g.

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4.2. Spectrum acquisition Samples are placed on the detector crystal, sealed in the lead shield, and counted. A typical analysis has a counting time of 1 hr, though counting times can range from minutes to days, depending on the precision desired. High voltage and gain are set so that the channels span the range from roughly 0.01 to 2.0 MeV. Spectra for standards are acquired in the same manner as the spectra for the unknown samples. Temperature changes in the laboratory that houses the detector can cause substantial drift in the electronics (Adams et al., 1958; Gosnold, 1976), resulting in peaks shifting by ten channels or more and leading to substantial errors in subsequent spectrum analysis. In the past, the solution to this problem has been to attempt to keep the laboratory at a constant temperature, or to make frequent energy calibrations. Recent technological advances, however, provide a solution to this problem through the use of a digital gain stabilizer incorporated into the multichannel analyzer board. This device attempts to hold the centroid of one gamma-ray peak at a specific channel. The peak must be present in the spectrum of the sample being analyzed for the gain stabilizer to work, and it must be very distinct, with a high signal-to-background ratio and a sharp apex. In addition, it is also important for it to be in the vicinity of the other parts of the spectrum which are being used in the analysis, for two related reasons. First, in practice the drift in the energy spectrum with temperature is nonlinear with respect to channel number, an effect which has been observed before (Swanberg, 1971). Second, the conversion from channel number to energy may also be slightly nonlinear. An attempt to use the composite 2’2Pb,224Ra, and 2’4Pb peak from the uranium and thorium decay chains at 0.239-0.242 MeV for stabilization failed because minor changes in the position of this peak could propagate into major changes at the higher-energy peaks used in the analysis. The peak now used is the 40K peak at 1.461 MeV, which is very distinct and present in almost all samples. This peak is held at channel 735, and deviations of up to 4 channels are tolerated. In samples with no significant potassium, such as carbonates, spectrum acquisition is bracketed between two other samples known to have potassium, and it is assumed that if the peak position is correct in these two samples then the spectrum is acceptable for the sample in question. Once the stabilization peak is set, it can remain in place for months at a time and through relatively wide temperature variations ( f 5°C). Background counting rates are obtained by analyzing a beaker filled with a nonradioactive material of comparable density to samples, and with the same geometry. The objective is to simulate the shielding effect of a sample on environmental gamma radiation. Background should be measured frequently, as it can be influenced by external factors, such as other samples kept in the laboratory or cosmic rays. An example of the former case was observed when background counts were inflated over a roughly 2-week period during the early calibration stages of the laboratory. This was interpreted as being due to a number of relatively high-radioactivity materials (autunite, uraninite, monazite) which were in the room at that time being used for peak calibration. There was also one incident in which an analysis of a sample that has been measured more than 30 separate times yielded counts up to 30% higher than expected in the low-energy part of the spectrum, with the anomaly diminishing with increasing energy. Other separates of the same rock were measured the same day, and the same sample was measured two days later, with all subsequent analyses giving an “expected” result. The unusual analysis was evidently due to a brief surge in the background, the reason for which is uncertain but probably related to astronomical phenomena. The energy distribution of the surge, which was obtained by subtracting the spectrum of a normal analysis from the spurious one, had the form of a declining convex-downward curve above 50 keV on a log-log plot of counts vs. energy. This form is also seen in gamma-ray bursts (GRB’s) (Teergarden, 1982) and secondary gamma radiation from an extensive air shower (EAS) caused by high-energy (> lOI eV) cosmic ray particles interacting with the nuclei of air atoms and forming an electromagnetic cascade (Trzupek et al., 1993). Of these two possibilities, the latter is a more likely candidate. In general GRB’s are only 5-30 s long (Share et al., 1982), over which time even the most energetic bursts increase background roughly by a factor of 10. Thus the effect of any such event will be subsumed over the course of a long analysis. In contrast, according to computer models, an EAS can create from 10 to lo5 gamma-rays in the I-MeV range observable at sea level for a primary particle energy of lOI to lOI eV

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(Trzupek et al., 1993); primary particles have been detected at least up to the 1019-eV energy level (Wolfendale, 1973). These showers have a very limited area1 extent, with a radius from tens to thousands of meters within which radiation declines geometrically (Wdowczyk, 1973). Gamma-rays can also be generated by cosmic ray particles interacting with other matter, including the shielding around the detector (Adams and Gasparini, 1970). In order to minimize astronomical sources of background a number of preventative measures can be taken, including the use of anticoincidence circuits and locating the laboratory in a basement so that the building acts as a shield (Adams and Gasparini, 1970).

5. Data processing 5.1. Determination

of HPE’s in unknowns

There are two primary methods for utilizing the gamma-ray energy spectrum to determine the concentration of the HPE’s in an unknown: (1) the three-equation method and (2) the least-squares method (Rybach, 1988). In the latter technique, a least-squares solution is used to find the linear combination of standard spectra which best fits the spectrum measured for the unknown (Rybach, 1971). This method requires that there be absolutely no drift, and gives results which are more error-prone and in general not superior to the simpler three-equation method (Lewis, 1974; Rybach, 1988, and references therein). The method proposed here is a modification of the three-equation method. The method is based on the assumption that for any set of channels known as a region of interest (ROI) in a spectrum, the total number of counts observed is equal to the background plus a contribution from each of the gamma-ray emitters in the sample. By specifying one ROI for each radioactive element or decay chain in the sample, it is possible to derive a set of simultaneous equations which when solved will determine the number of counts in each ROI due to each radionuclide. The nine constants required to solve this system for the three heat-producing elements are obtained by measuring the count rates in three ROI’s in each of three standards. The number of counts is directly proportional to the amount of a radionuclide. This conceptual method has been used a number of times (Swanberg, 1971; Rybach, 1988) although the mathematics have varied slightly. In addition, existing sources recommend using standards that each have only one isotope or decay chain. This is in fact not a necessity, as shown below. There are two other major assumptions that are implicit in this method. First, all decay chains must be in secular equilibrium. Fortunately, this property can be tested simultaneously with the analysis, as described below. Second, all major decay chains present in the unknown must be taken into consideration if a significant gamma source is present in the sample or standard and not accounted for in the equations, then all results will be erroneous. In geologic samples generally only the HPE’s are taken into account. Although there are many other elements with naturally occurring radioactive isotopes (e.g., Rb, Sm), in general they are too scarce and/or produce too little gamma radiation in the appropriate energy range to make a difference in this method. In theory, this technique will work regardless of where the ROI’s are, as long as they do not overlap. However, in order to minimize errors the majority of counts in an element’s ROI should come from that element’s decay chain, rather than from other elements or background. This is best accomplished by centering the ROI around a prominent peak in the decay chain’s spectrum, with its width encompassing an area about five channels beyond each edge of the peak. This extra space on each side of the peaks helps to diminish the effects of minor peak drift. The peaks selected for the University of Texas at Austin laboratory are the 1.46 1-MeV peak for 40K (channels 664-809), the 1.765MeV peak of *14Bi for the 238U decay chain (channels 83 l-929) and the three overlapping peaks at 0.911,0.964 and 0.969 MeV of “*AC for the 232Th decay chain (channels 443-543). A more frequent choice for the thorium ROI is the 2.615MeV peak of *‘*Tl, (Rybach, 1971, 1988; Adams and

182

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Geology 130 (1996) 175-194

Gasparini, 1970) which has the advantage of not being in the Compton scatter tail of the 40K peak, and supposedly is less susceptible to source attenuation (Heier and Rogers, 1963; Potts, 1987). However, it was not chosen for this laboratory due its distance from the 40K peak which is used for automated gain stabilization. The problem of attenuation is examined below. Presented here is the derivation of equations for concentrations and error estimates that can be easily calculated with a computer program or spreadsheet. These equations are novel in that they allow any or all of the standards to have each of the three heat-producing elements, rather than requiring that each standard have one and only one radionuclide. They also automatically account for interference among all peaks, including the 2’4Bi peak at 2.44 MeV which is usually ignored in other formulations (Rybach, 1988). The subscripting conventions are as follows: indicates an ROI or the corresponding indicates a standard; and indicates an element.

i j

k

Given the count rate measured

element;

in each ROI for an unknown

Ri=Ci_Bi+6,

(1)

” (where Ri = the background count respectively; and for the count rate

IB

count rate above background in ROI i, in counts per unit time; Ci, Bi = the total and rate in ROI i, respectively; ci, bi = the total and background number of counts in ROI i, t,, t, = the counting times for the unknown and background, respectively) then the equation in each ROI can be written as:

where g, = mass of the unknown for U and Th and wt% for [ R,/X, g], = the count rate in efficiency of counts for element fractional number of counts due These constants are calculated Ri,j

=

Ci,j

-

Bi

in grams; and Xi = the concentration of component i in the unknown, in ppm K; and the constants which must be determined from the standards are ROI i’ per gram of sample per concentration unit of element Xi,; Ef = the i’ in ROI i; for each count due to element i’ in ROI i’, this constant gives the to the same element in ROI i. in a similar fashion. Full spectra are counted for each standard, giving:

b; - fB J

ci j

=

T

(3)

where, similarly, Ri.j = the count rate above background in ROI i for standard j; Ci,j = the total count rate in ROI i for standard j; ci,j = the total number of counts in ROI i for standard j; and fj = the counting time for standard j. Each ROI then produces a set of three equations for each standard:

(4) where X,,j = the concentration of element i in standard j; and gj = the mass of standard j, in grams. Solution of these equations will yield three of the constants necessary for determinations on unknowns; other six constants are similarly calculated using the other two ROI’s.

the

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183

In order to facilitate calculations, the above two-step formulation can be condensed into one step, using the counts and concentrations of the standards directly instead of through efficiencies. The equation to determine a concentration then reduces to:

,$,: [i x,=

j=

'k,jgjDETi.i) 1

(5)

DET

where X,, X,,j = concentration of element k in the unknown or standard j; DET = the determinant of the 3 X 3 matrix of count rate above background for the standards with rows corresponding to standards and columns corresponding to ROI’s; and DETi.j = the determinant of the 2 X 2 matrix of count rate above background obtained by deleting the column for ROI i and the row for standard j from the above 3 X 3 matrix. Once the concentration of each element is known, the equation for heat production is (Rybach, 1988): A = 10-$(952X,

+ 2.56X,,

+3.48X,)

(6)

where A is heat production in p.W/m3; p is density in kg/m3; and concentration units X are in ppm for U and Th and in wt% for K. There are two errors that can be calculated for this method. The precision, or amount of variation expected if an analysis is repeated many times, is based on nuclear decay being a Poissonian process, with the number of gamma-rays emitted from a source in any one time interval having some natural variation (Adams and Gasparini, 1970). The accuracy, or expected amount of deviation from the “correct” answer, is based on every error that can be quantified, including in this case the precision of the count rates in the unknown, standards and background, and the uncertainty of the concentrations of the elements in the standards. All errors here are estimated using the standard equation for error propagation, assuming no cross-correlations (Bevington and Robinson, 1992): ~~~~~(~~+~~(~)*+...+~~(~)

(7)

x,,). The only variables which will change with repeated analyses are the number of where x=f(x,,x,,..., the counts for the unknown and background. Assuming that the errors in these variables are uncorrelated, precision can be estimated in terms of the number of counts: (8) Because nuclear decay can be described by Poissonian statistics, the standard deviations (a’s) can be estimated as the square root of the number of counts in each instance. Extended tests of count variability of standards and background have shown that the square root is a good estimate of the standard deviations, and also that the errors are uncorrelated. The derivatives can be easily calculated from Eq. (1) and Eq. (5), as the counts and backgrounds for each ROI are conveniently separate from the other terms. The result is:

(9) To estimate the accuracy, the estimated precision is combined with individual errors in the concentrations and count rates for the standards. The error from uncertainty in concentrations in standard j is:

( 10)

184

where u,,~ is the published the standards is:

RA. Ketcham / Chemical

uncertainty

Geology

130 (1996) 175-194

k in standard

of element

j. The error from measuring

(1’)

DET4 The Th/U ratio is often used to detect differential for this quantity is:

mobility

the count rate in

of these two elements.

The proper error estimate

(12) This estimate should work well except in cases where the uranium determination is close to zero, in which case the ratio can vary to an extent that may not be well represented by this equation. The precision and accuracy for heat production can be obtained by differentiating Eq. (6) and once again using Eq. (7) and the appropriate errors for each element. As shown below, this procedure probably results in a slight overestimate of the error, as there is an inverse correlation between errors in the different elements. If, for example, the concentration of thorium is underestimated, the number of counts in the ROI’s of potassium and uranium which are attributed to thorium will likewise be underestimated, resulting in a greater chance of overestimating their concentrations. As a result, errors in the calculation of heat production will tend to cancel each other to a limited extent. On the other hand, errors in the Th/U ratio may be magnified. Another potential source of error may come in the form of differences in gamma-ray attenuation owing to source absorption in samples with different matrix materials. The principal way this can alter an analysis is by changing the sample density, as absorption is largely a function of density. The effect of sample density is studied below. 5.2. Detection of secular disequilibrium In order to test for secular disequilibrium, Rybach (1971) suggests utilizing a separate beta-decay detector to analyze the relative gamma and beta activity. Presented here is a sim ler method that does not require additional P equipment and calibrations. Almost all of the gamma energy in the * *U spectrum above 0.25 MeV comes from daughter products below 226Ra in the decay chain. However, in the low-energy range from 0.03 to 0.10 MeV there are a number of gamma-rays produced by 234Th of significant absolute activity (Table 1; Adams and Gasparini, 1970). Although a typical NaI(T1) scintillation detector does not have sufficient resolution to reliably distinguish individual peaks in this region, it is still possible to define an ROI which encompasses this energy range. In most cases it can be safely assumed that 234Th is in secular equilibrium with 238U, as it has a half-life of only 24.1 days. If the uranium decay chain is not in secular equilibrium, 234Th will have a different activity from the post- 226Ra daughter products which are used in the main analysis. By measuring the count rate in this low-energy window and comparing it to count rates from higher-energy peaks, it is in principle possible to estimate whether or not the decay chain is in secular equilibrium. In order to implement this method at the University of Texas laboratory, an ROI is defined encompassing channels l-70, corresponding to an energy range of N 0.010-O. 123 keV. The lower bound is approximate and somewhat misleading, as it is below the detection limit of the apparatus, and zero counts are recorded for the first several channels; however, it is preferable to placing the edge of the ROI on the steep flank of the first peak. The upper bound is once again set in the midst of a relatively flat part of the spectrum, to minimize the consequences of drift. Counts in this ROI are collected simultaneously with the other ROI’s during an analysis.

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185

The expected counting rate in this ROI for a sample in secular equilibrium is predicted using the determinations of U, Th and K as acquired by the method outlined above. The calculation is analogous to Eq. (2): R, = i i=

5 $ 1 i= I[ 1 Rf = g,

Xi

(13)

*

Here the subscript s indicates the ROI used to test for secular equilibrium; and Rf is the count rate in ROI s due to element i. The bracketed constants are once again deduced from the standards, in the same fashion as used in Eq. (4). Solution of the system using determinants gives:

[

DETX,i _ Rs xig 1

(14

DET,

DET, is the determinant of the 3 X 3 matrix of element concentrations in the standards with the rows corresponding to elements and the columns corresponding to standards. DETx,i is the determinant of the same matrix, with row i replaced by the counts per gram per unit time in ROI s in each standard. The test for secular disequilibrium consists of comparing the actual number of counts in ROI s due to the uranium decay chain to the number of counts estimated from the uranium determination obtained by using higher-energy gamma-rays. The former value is obtained by subtracting the estimated counts rates due to thorium and potassium from the observed count rate above background: R&,

= R, - RTh - R,K

(15)

The latter value is simply:

RLt = R;=g,X,

- Rs [ XLJg

1

The most convenient way to utilize these parameters other and look for divergence from unity:

RL

V=c

to test for secular equilibrium

is to divide them by each

(17)

where u is the testing parameter for uranium-series disequilibrium. A value of u above 1 may reflect a recent loss of 238U, or enrichment of 234U or 226Ra. A value of u below 1 may result from youth of the sample, recent 238U enrichment, or recent loss of daughter products at or below 226Ra in the decay chain. It also could indicate experimental error in the form of radon escape, or a cosmic-ray spike, as such an event will inflate low-energy counts relative to high-energy ones (the analysis interpreted above to have been affected by a cosmic-ray event had a u of 0.57). The most common source of disequilibrium in geologic samples is weathering, which commonly leads to overall uranium loss with a preferential loss of 234U. The resulting values of u will vary according to the timing of depletion. Initially u will be above 1, as detectable 234U activity is negligible and thus will not be reflected in Ry,,,, while there is a time lag corres onding to the 8 X 104-yr half-life of 230Th P before depletion of 234U will have an effect on the abundance of 26Ra and its daughter products. As secular equilibrium of 226Ra with 234U is re-established u will fall below 1 due to underestimation of 234Th activity. A final potential source of disequilibrium is systematic and pervasive escape of radon in the decades immediately preceding sample collection, which can cause *“Pb to be out of secular disequilibrium. As the only gamma-ray produced by this isotope is low-energy (0.047 MeV, Table l), these conditions would lead to a smaller number counts in ROI s than normal, which would in turn raise the value of u.

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Assuming that the counting time of the standards is long enough so that the error in determination of the constants in Eq. (14) is minor, the estimated error based on the count rate in the unknown and the relative error of each determination is:

The error in R, is assumed to be Poissonian: b.

2_ -2.1. aR, t*”

(19)

t;

This error estimate is probably conservative in a manner similar to the heat production error, as it does not take into account the inverse correlation of errors in individual element determinations. Once the factor u is calculated, it can also serve as a partial correction for disequilibrium. This is best illustrated by starting with the simplifying assumption that the gamma-ray spectrum of the uranium decay chain can be considered as the sum of the contributions from two subchains (23sU-234Th and 226Ra + daughters), each of which is in secular equilibrium within itself, but not necessarily with the other. In this case, the count rate in ROI s due to uranium can be cast as: R;,,,t = Ryqh -I- RybRaF

(20)

where Rsxv’” is the count rate due to 234Th; RyRa is the count rate due to 226Ra and its daughter products if the entire chain is in secular equilibrium; and F is the fraction of 226Ra that is present relative to the amount necessary for equilibrium. On the other hand, the estimated count rate is: Ry,,,, =

( Rrvh + RrCRa) F

as the estimate R

of activity of 234Th is based on the fraction f'?'"

+

R==%

+

R:~,F

s

u= R;?-h

(21) of 226Ra in the sample. Thus, u becomes:

P (22)

The behavior of this T$uation is linked to the relative efficiency of 234Th to 226Ra and its daughter products in ROI s. If R:‘% -x R, Ra, u approaches 1 in all cases, whereas if RF?‘” x=-RF6Ra then u approaches F. In the latter case, secular-disequilibrium effects on a uranium determination would be entirely corrected for by division by u, whereas in the former case division by u will naturally have no effect. As the true relationship is probably somewhere between these two end-member cases, division by u probably provides a partial correction, as shown below. The actual relationship between these two efficiencies must be determined by an independent calibration. One example of a successful application of secular disequilibrium detection involved a sample of autunite of unknown age, diluted in quartz. It was submitted for four determinations by two commercial INAA (instrumental neutron activation analysis) laboratories, with an average result of 450 ppm U. Gamma-ray analysis gave an answer of only 365 ppm U. The value of u for this sample was 0.836 + 0.003, providing a warning of an incorrect analysis and suggesting the interpretation that the autunite was too young to have reached secular equilibrium. Dividing the uranium determination by u gives a revised value of 437 ppm, which is in much closer agreement with the INAA numbers. The closeness of this value to the desired number suggests that dividing by u provides a good first-order correction for secular disequilibrium. On the other hand, such a correction also introduces an error that is problematic to quantify. There are some additional complexities that inhibit the straightforward application of this calculation, including source attenuation and P-radiation, both of which become important at low energies. Adams and Gasparini (1970) cite problems with calibration and

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reproducibility when using a similar technique to separate 226Ra determination from 238U using the low-energy part of the spectrum. This is particularly unfortunate for heat-production analysis, as it is most sensitive to errors in uranium determination. Thus, while it is appropriate to use this technique to provide a warning of disequilibrium, it should only be used with care as a correction. Further examples are discussed below. 5.3. Choice of counting

time

The above equations allow freedom to select any counting time for measurement of any unknown, standard or background, In general, the longer the counting time, the smaller the error. Because the theoretical error in counts is Poissonian, the error diminishes by a factor that is related to the square root of the number of counts. Assuming a constant counting rate, in order to halve the error the counting time must be increased by at least a factor of four. The precision is also linked to the signal to background ratio and the counting time for measuring background. A shorthand estimation of the effects of these factors can be made if it is assumed that the counts for an element in its own ROI are much greater than the counts for any other element in the same ROI. Then, by dividing Eq. (5) by Eq. (9) and only using the ROI of the element in question, after simplifying we reach the following estimate of the coefficient of variation:

(23) To provide an example, this relationship is examined for uranium, as it is determined using the highest-energy gamma-rays, and thus has the lowest counting efficiency. Assuming a background count rate of 8 counts min- ’ determined by counting for one day, Fig. 3 shows the coefficient of variation as a function of counting time for count rates ranging from 1 to 10 counts min- ’ above background. As a reference, the count rate for uranium measured at the University of Texas lab is close to 5 counts min- ’ ppm- ’, so the count rates in Fig. 3 correspond to roughly 0.2-2 ppm U. It is clear that even for quite low concentrations of uranium the curve quickly levels off. For a 1 ppm U sample, the coefficient of variation is less than 10% after 1 hr, and for 2 ppm U the error falls to just over 5% for the same period. For counting rates with a low peak to background ratio, the error falls slightly more slowly than the square root of time, while for higher rates the square root of time becomes an increasingly good estimate.

Count

rate

above background bsbin)

-1 --_ ... . .

2

... 3

_-_-

5

---

10

0 0

50

100 Counting

Fig. 3. Decline in estimated to 2 ppm U.

precision

200

150

250

time for unknown (minutes)

in uranium determination

with increased

counting

time, corresponding

to sample ranging from - 0.2

R.A.

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It might appear that even samples with very low counting rates can achieve good precision given enough counting time. However, there is some danger to this approach, as non-Poissonian error due to astronomical events are not included in the error statistics, and with increased counting time the chance of such an event occurring during the analysis increases. With sufficient care, such as recording count totals every hour and inspecting each subcount with respect to the entire time series after the analysis is over, it may be possible to recognize unusual spikes and delete them from the calculation. Alternatively, it is easy and good practice to repeat analyses several days or weeks apart to help test whether there may have been a temporary surge in background.

6. Practical tests of the method 6.1. Sample density

The effect of source attenuation due to changing sample density was studied by repeated measurements of a single sample crushed to varying degrees. Note that density here means the mass per volume of the crushed rock in the Marinelli beaker, and not the density of the original rock. The rock selected for this test was sample WC-16a, a dark-gray melarhyolite from the Llano uplift of central Texas. It is very homogeneous, with few faintly visible phenocrysts and very subtle, rare < l-cm layering defined by differing shades of gray. Five determinations by INAA and XRF (X-ray fluorescence analysis) done by three commercial laboratories gave

URANIUM

4.5

u = -5.lEe.Pm

2.5 -1 750

800

850

+ 3.88

900

RI

950

THORIUM

12

0.16

Th= -8.36eSm

loo0

7‘1 750

800

850

900

R = 0,013

950

11

mass (g)

mass (9) POTASSIUM

4.6

+ 9.38

HEAT PRODUCTION

2.2 A=

-2.lle4*m+2.11

R=0.31

4.4 ep d 3 4.2

41 750

800

850

900

mass (g)

950

1000

1.7: ,-, , ( , , 750 800 850 900 massk)

, . 1 950 1000

Fig. 4. Sample mass vs. determination of U, Th, K and total heat production, including fitted regression lines and correlation coefficients. Bars represent precision errors of two standard deviations. Because a constant-volume geometry is used, mass directly correlates with density. Determinations for Th have the least apparent variation with density, despite the fact that they are made using lower-energy gamma-rays than for other elements. There is little overall variation of heat production with sample density, suggesting that a correction is not necessary for most applications.

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uranium concentrations in the range 3.1-3.9 ppm, with a mean of 3.5 &-0.4 ppm, and thorium from 9.0-I 1 .O ppm, with a mean of 10.0 f 1.0 ppm. A single potassium determination by XRF gave 4.09 wt%, and an ICP (inductively coupled plasma) analysis gave 4.33 wt%. A single large specimen was crushed, and then separated out into eight batches by coning and quartering. Different batches were then pulverized with a disk mill to varying degrees, based on the distance between the grinding wheels. Two batches were not milled, two were milled with the wheels 1 mm apart, and the others were milled with the wheels 2, 3, 4 and 5 mm apart. The main effect of the different grain sizes was to alter the amount of sample which could fit into the 600-ml geometry in the Marinelli beakers, with coarser sizes needing less mass to fill the same volume due to less efficient packing. This has the desired effect of changing the average sample density in the beakers, in a fashion similar to a comparable test by Heier and Rogers (1963). The set of samples was repeatedly packed, left to sit for a minimum of 3 weeks, and analyzed by counting for 1 hr. Fig. 4 shows the obtained values of uranium, thorium, potassium and total heat production vs. sample mass. Uranium and thorium determinations show very little variation with mass, with fitted lines having correlations of 0.16 and 0.013, respectively. Both are insignificant, especially with respect to the inherent errors in the analysis. Potassium does show a systematic variation of decreasing apparent concentration with increasing mass,

count rate = -8&k-3*mass + 62.5

I

52.5 750

800

7

I

’

I

850 900 maas (9)

8

R = 0.62

1 950

1 1000

0.8 u = 1.89e-4’mass + 0.849 R = 0.25 0.7, 750

, 800

,

,

850 900 maas (9)

, 950

1000

Fig. 5. a. Count rate in ROI s used for detecting secular disequilibrium as a function of sample mass with constant volume, with fitted line and correlation coefficient. b. u parameter for the same data set, with 20 error bars based on counting statistics.

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130 (1996)

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with a correlation coefficient of 0.46. The potassium determinations are also the only ones that show significantly more scatter than predicted by the relative error calculations. The regression line spans a range of 0.13 wt% over the interval of masses analyzed, and falls to below 0.1 wt% if the two high points are discarded. Total heat production determinations fall slightly with increasing mass, with a correlation coefficient of 0.3 1. The regression line is swamped by the relative errors in the analysis. Raw count rates show similarly inconclusive behavior; count rates in all three ROI’s rise with decreasing density, with the net count rate rising fastest in the potassium ROI, and the rise in count rate as a per cent of the mean being fastest in the uranium ROI. This behavior for potassium has also been observed by Heier and Rogers (1963). They attributed it to the fact that the potassium peak was at a lower energy (1.461 MeV) than the uranium and thorium peaks they used (1.765 and 2.615 MeV, respectively), and thus more susceptible to source attenuation. For the analyses presented here, however, thorium was analyzed using peaks ranging from 0.911 to 0.969 MeV, and yet it shows the least variation, thus casting doubt upon their interpretation of this phenomenon. A simple empirical correction for the apparent attenuation of potassium gamma-rays in this data set would be to subtract out the fitted regression line. However, the effect of this correction on total heat-production determination would be negligible, because potassium is a relatively minor component of heat production. The total 0.13 wt% variation in potassium suggested by Fig. 4 leads only to a 0.01 kW/m3 change in heat production. Based on these data, it is probable that a correction for gamma-ray attenuation is not necessary or advisable for determination of heat production. The low-energy range used for detecting secular disequilibrium is susceptible to source attenuation. Fig. 5 compares the count rate per gram in ROI s and the ratio u to the mass of sample for all of the analyses shown above. There is an obvious negative correlation between mass and count rate for all of the analyses (Fig. 5a). Fig. 5b shows the effect of this variation on the u value. The accuracy of the fitted line was corroborated by a 24-hr analysis of a 946.9-g sample, the u for which was 1.027 + 0.001, whereas the line predicts a value of 1.028. The uranium determination matches well with values from other techniques, and it is unlikely that this rock has had a recent enrichment of uranium as implied by u. Thus, it is evident that not all statistically significant departures of u from 1 necessarily imply secular disequilibrium. However, the variation of u with density is limited to within - 5% of 1.0, so values of u which are statistically (two standard deviations) out of this range are good candidates for secular disequilibrium. These results also imply that the use of u to correct for secular disequilibrium will introduce an error due to source attenuation. Further calibrations are necessary for different materials with different uranium contents to fully establish the behavior of u with sample density. 6.2. Accuracy

of error estimates

Two separate tests were used to verify that the error calculations for HPE determinations presented above are good approximations. The first test consisted of studying the results of repeated analyses of a single sample. A single beaker of WC-16a was analyzed 20 times with a counting time of 1 hr. The actual variability is compared to the calculated relative error in Table 2. In all cases the estimated relative error is very close to the observed error. The largest divergence is for thorium, for which the actual error is less than the estimate. As predicted

Table 2

Estimated relative error (1 a) Observed relative error (I u) Estimated

U

Th

K

n/U

A

II

0.16 0.16

0.41 0.34

0.04 0.05

0.25 0.24

0.05 0.04

0.07 0.06

and observed errors for 20 repeated analyses

of sample WC- I6a.

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191

Table 3 Difference between two analyses, in standard deviations

(o/o)

o-1 l-2 2-3 3-4 4+

51.3 32.7 12.8 2.9 0.3

Estimated

Expected distribution

and observed

distributions

U dist.

Th dist.

K dist.

Th/U dist.

50.7 33.6 9.3 5.7 0.7

51.4 30.0 15.0 2.9 0.7

45.0 40.0 10.0 5.0 0.0

45.0 35.0 11.4 5.0 3.6

of differences

between

ratio

A dist.

v dist.

71.4 21.4 7.1 0.0 0.0

71.9 21.6 6.5 0.0 0.0

I40 paired analyses.

above, the measured relative errors in heat production and u are less than the estimates, probably due to failing to account for cross-correlations. The second test utilized a large suite of rocks that had been analyzed for a different study (Ketcham, 1995). The suite has a wide variety of igneous, metamorphic and sedimentary rocks, with the most common lithotypes being granites and gneisses. 140 of the analyses were duplicated, and these were used to evaluate the precision estimates. If two random samples are taken from a population with a normal distribution, the difference between them (measured in standard deviations) will have a predictable distribution. This distribution was obtained by utilizing a Gaussian random-number generator subroutine (Saupe, 1988). One million simulated pairs of samples were obtained, and in each case the difference between the two was calculated in terms of standard deviations. The resulting distribution is shown in the first column of Table 3. Subsequent columns show the distributions for uranium, thorium, potassium, Th/U ratio, and total heat production. For the three elements, the results are quite close to the expected distribution. The principal apparently systematic difference is that they have a slightly larger number of very divergent analyses (3 or more standard deviations apart) than expected. This may be due to the fact that the precision calculation does not include extra-Poissonian factors such as astronomical sources or experimental error. In the one sample with uranium and thorium errors both in excess of four standard deviations apart, the two determinations had u values of 0.87 + 0.07 and 0.95 k 0.06. The former value suggests the possibility of radon escape, and indicates that further analyses are necessary. The evidently erroneous value was included here both for completeness and as a further demonstration of the utility of the u test. The inverse correlation in element determinations is responsible for error distribution for the Th/U ratio

Table 4 Sample

U (ppm)

BP-902 UP-906 WBH-901 WBH-908 EBH-902 SP-901 EM-906 MBH-905 BM-901 BM-904 BP-901 MBH-904

1.7 4.7 2.2 4.1 1.3 1.2 3.0 1.7 22.9 20.2 I .9 2.3

INAA

gamma * It + * f * f f f f f f

0.3 0.6 0.4 0.4 0.4 0.4 0.4 0.4 0.9 1.1 0.4 0.5

K 2O (wt%o)

Th (ppm)

1.4 4.3 2.1 3.5 0.4 0.9 3.1 0.8 20 20 1.4 2.1

+ 0.2 f 0.7 f 0.3 * 0.6 * 0.1 kO.1 * 0.5 + 0.1 f 3.2 + 3.2 f 0.2 i 0.3

Determinations from gamma-ray analysis compared analyses done at University of Texas at Austin.

gamma 4.8 75.0 12.1 14.3 18.8 15.3 10.8 13.1 75.1 69.8 3.7 12.3

* * + * + * + + f f + +

0.7 2.2 1.0 1.1 1.0 1.0 1.1 1.1 2.4 2.6 0.9 1.3

INAA 4.4 70 11 15 20 14 10 14 79 73 4.9 14

*0.2 It 2.9 + 0.5 + 0.6 + 0.8 + 0.6 + 0.4 f 0.6 f 3.3 * 3.1 f 0.2 f 0.6

with other methods. INAA analyses

gamma

ICP

2.12 f 0.08 5.18 + 0.16 5.26f0.14 5.58 f 0.14 5.49 * 0.13 5.84 f 0.13 6.03 f 0.14 5.84 f 0.14 4.98 f 0.20 4.83 &-0.27 1.96 f 0.13 5.72 kO.20

2.23 * 0.04 5.08 * 0.10 5.40 * 0.11 5.42 f 0.11 5.37 * 0.11 5.72 f 0.11 5.91 * 0.12 5.58kO.11 4.61 f 0.09 4.40 * 0.09 2.12 f 0.04 5.86 + 0.12

done by Activation

Laboratories

Ltd., Canada. ICP

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130 11996) 175-194

Table 5 Analysis method

9.36k0.17 9.29 9.41 kO.14 9.36 f 0.20

Flame photometry XRF Gamma-ray (600 ml) Gamma-ray (250 ml) Potassium determinations by gamma-ray analysis, commercial flame photometry (University of Texas at Austin).

being more susceptible production and u.

7. Comparison

XRF analysis (Geochemical

to large errors than estimated,

Laboratories,

McGill University,

as well as lower than estimated

Canada)

and

errors for total heat

to other methods

In order to help test this apparatus and technique, analyses were made of samples that already had independent determinations of uranium and thorium from INAA by a commercial laboratory and potassium from ICP analysis at the University of Texas (Potter, 1995). Table 4 compares the results obtained for each sample. For each element, the first column is the gamma-ray determination and the second is the determination by the alternative method. Errors reported on gamma-generated numbers correspond to accuracy. Errors on INAA determinations were not provided by the commercial laboratory, and thus are estimated using the coefficients of variation obtained by Potts and Rogers (19861, which are 8.4% for uranium and 2.1% for thorium. Repeated potassium analyses on the University of Texas ICP demonstrate a precision of + 1% (L. Potter, pers. commun., 1994). All errors shown are equal to two standard deviations. The first 9 analyses used 600 ml for the gamma-ray measurement, while the last 3 used 250 ml. Another test of potassium measurements was run using a sample of pegmatite-derived potassium feldspar which had been analyzed by flame photometry (F. McDowell, pers. commun., 1994) and XRF at the Geochemical Laboratories at McGill University. Comparisons of these values to those obtained in the gamma-ray laboratory are presented in Table 5. In the first suite of samples, the matches for uranium and thorium are generally very good, with the greatest disparities coming in samples at the high and low extremes of concentration. The low numbers given by INAA tend to be systematically higher for the gamma-spectrometry analysis. There are also disparities greater than the errors in samples with high thorium (70-80 ppm), although they are not systematic. As for potassium, the matches are also for the most part quite good. The gamma-ray determinations tend to provide slightly higher values, perhaps as a result of incomplete digestion or partial volatilization of alkalis during the ICP analysis. In two of the worst cases, BM-901 and BM-904, the totals for all major elements from ICP were a few percentage points short of 100% (with H,O+ still unmeasured) (Potter, 19951, suggesting systematically low numbers, which would be consistent with the differences observed. The close match between the gamma-ray and flame photometry analysis in Table 5 supports the accuracy of the gamma-ray determinations.

8. Conclusions The three-channel method for gamma-ray scintillation spectrometry presented here has the same theoretical basis as previous formulations, but includes a number of potentially useful enhancements. The advantages of increased flexibility in choice of energy peaks and standards alone may warrant utilizing this approach over others. The demonstrated reliability of error estimates and the ability to detect and potentially correct for secular

RA. Kercham / Chemical Geology 130 (1996) 175-194

193

disequilibrium are additional benefits. The ability to detect secular disequilibrium may even constitute advantage for this technique over others that only determine the amount of uranium in a sample, disequilibrium is symptomatic of recent overall uranium loss which would not otherwise be noticed.

an as

Acknowledgements Funds to purchase the equipment and standards for this laboratory were provided by the University Geology Foundation; I am greatly indebted to W. Carlson and M. Cloos for providing access to these My thanks also go to J. Reese for providing field and research support in collecting sample WC-16a, for lending his samples and sharing his data, and F. McDowell for running the flame photometry Helpful reviews of early manuscripts were provided by D. Blackwell, W. Carlson, C. Chemoff, M. Potter and D. Smith. Finally, I thank P. Morgan for a constructive review. (SB)

of Texas resources. L. Potter analysis. Cloos, L.

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