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Anal. Chem. 1987, 59,822-826
Computation of Determination Limits for Multicomponent Chromatograms W. L. Creten* Laboratorium voor Experimentele Natuurkunde, liniversiteit Antwerpen, RUCA, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium L. J. Nagels Laboratorium voor Organische Scheikunde, Universiteit Antwerpen, RUCA, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
A new method Is presented for the computatlon of determination ilmlts In the chromatographic anaiysls of complex samples. The determlnation lbnlt DLeWIs the mlnhnum relative abundance of a component in an extract, necessary so as to have a probablllty w to do a determlnation on which the error is smaller than e. Matrbr interference (peak overlap) is taken into account as the main source of determlnatlon error. The method is valid for those analyses for which the frequency distribution of observed peaks Is quasi-exponential. The resuits are compared wlth determinatlon limits obtalned from computer-slmuiatedchromatograms. Crltlcai resolution and crltical dlstance between two adlacent peaks are discussed for chromatograms wlth quasi-exponential frequency dlstrlbutions for observed or component peaks.
Organic trace analysis in complex (mostly biological) matrices is a challenge to modern chromatographic methods. It is very difficult to evaluate and predict the extent of peak overlap (or “matrix interference”) phenomena in this type of analyses. This is so because the samples are composed of a large and unknown number of components which are present in apparently unpredictable ratios. In a series of papers, Davis and Giddings (1-4) developed a statistical model of peak overlap in multicomponent chromatograms, based on the assumption that the retention times of single-component peaks are distributed randomly over the separation space, according to a Poisson process. Large peak capacities seem to be needed to resolve even relatively simple mixtures. In two of the papers (3, 4), they introduced a procedure that should make it possible to estimate the number, m, of single-component peaks in a chromatographic recording from the number of observed peaks, n. The method was tested by using computer-generated chromatograms in which the different parameters were widely varied ( 3 ) . For the amplitudes of the single-component peaks, three types of distributions were used: uniformly randoni between a minimum and a maximum value, exponential, or constant. Parallel to the work of Davis and Giddings, but with a different approach, the present authors developed a model describing peak overlap in chromatographic analysis of complex biological samples ( 5 ) . The model is based on the assumption that the distribution of retention times of chromatographic peaks is random (each retention time has an equal probability to occur), and it takes into account a quasi-exponential distribution of relative peak areas (or relative component responses). The latter distribution was based on data derived from the analysis of 65 different plant species with gradient HPLC/UV methods. Starting from a frequency distribution of relative pe ik areas observed in these chromatograms, FDO, a computer-simulation program was used in an iterative procedure to estimate the frequency distribution of component peaks, FDC. The validity of the quasi-expo-
nential distribution of relative peak areas was confirmed by later investigations (6, 7) in which hundreds of plant extracts (total extracts and subfractions) were analyzed with gradient HPLC chromatography with UV, EC, and fluorometric detection (for these systems only positive peaks were detected). There are also indications in the literature that the frequency distributions of relative peak areas observed in plant analyses are comparable with distributions observed in the analysis of totally different types of complex samples (8, 9). The assumption that chromatographic peaks are randomly distributed over the t o t d separation space is not always valid in real analyses. Nonrandom distributions were measured and discussed for gradient HPLC analysis of plant extracts (total extracts and subfractions such as “acids”, “bases”, ...; data from 134 different plant species) in ref 10. It seemed more appropriate however not to include these realistic features in our model in order to avoid over-complication a t this stage. The distribution function FDC was used ( 5 )to simulate a large number of chromatograms (e.g., lOOO00) and to compute the probability PC, that a component peak is determined with a relative error smaller than e. This probability is a function of the relative response of the component in the sample and of the peak capacity of the chromatographic system. The relative response for which PC, equals the probability w was then proposed as the determination limit DL,”. For HPLC determinations of UV absorbing substances, this relative response is expressed in percent absorbance units, the absorptivity of the whole extract being considered as 100%. It was shown that even for highly efficient techniques (total separation space Soou), the determination limit DLo,P9was as high as 12%. The practical usefulness of determination limits for the evaluation and optimization of organic trace analysis in biological samples was explored and proved in our subsequent papers (6, 10-12). The computation procedure described above requires the simulation of large numbers of chromatograms and is thus extremely time-consuming. The aim of the present work is to compute the above-mentioned probabilities PC, and determination limits DL,” on a purely statistical basis. The formerly used computer-simulation method ( 5 ) will serve as a control. In the past, statistical work on the derivation of detection and determination limits in trace analysis has always been devoted to interferences caused by background noise with Gaussian amplitude distribution (13 ) . Background noise is very important in organic trace analysis of simple mixtures. It is not taken into account in the present study because its contribution to determination error is negligible in comparison with matrix interference, when complex biological samples are analyzed. THEORY The following assumptions will be valid throughout this study: (a) For the separation of complex samples, a separation
0003-2700/87/0359-0822$01.50/0@ 1987 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 59, NO. 6, MARCH 15, 1987
space X (Xis some multiple of the peak width parameter u) is available, and all component peaks have the same width. Such a situation can be met in gradient chromatography. (b) The retention times of the peaks me randomly distributed over the separation space. This is mostly an over-simplification of the situation in real analyses as it corresponds to an ideal spreading of the sample components over the separation space. (c) The relative responses provoked by the sample components (Le., the relative peak areas) are distributed according to a quasi-exponential frequency distribution FDC which was derived from real measurements (frequency distribution of component peak areas, cf. Glossary and ref 5). Frequency distributions of the relative peak areas of observed peaks, FDO, can be obtained from real, recorded chromatograms. Because of peak overlap phenomena (an observed peak can be a cluster of component peaks), FDO’s contain much more of the larger peaks than FDC’s. The higher the peak capacity of the analytical system, the more the FDO distribution will resemble the underlying distribution of component peaks FDC. For the above conditions, the probability PC, was defined ( 5 ) as the probability that a component peak is determined with a relative error smaller than e. Therefore, the area of the component peak is compared to the total area of the observed peak (which can be a cluster of overlapping peaks) to which it belongs (5). The true value (area of the component peak) and the measured value (area of the observed peak) are then used to calculate the relative error e on the measurement. For any method of analysis, probabilities PC, will become progressively smaller with decrease in the content of component to be determined. The dependence between the probability to determine the component accurately, PC,, and the relative response of the component, was called the “determination characteristic” by Liteanu and Rica (ref 13, p 337). Such determination characteristics were obtained by the authors ( 5 ) for the chromatographic determination of components in complex mixtures, using computer simulation. The component’s relative response for which PCo,lequals, e.g., 0.9, was then called the “determination limit” DLo,pg. We now want to express PC, in another way using simple probability theory, i.e., by combination of the so-called addition rule (incompatible outcomes) and product rule (independent outcomes). Let us therefore consider a component peak selected at random out of the collection of all possible component peaks of the chromatogram and define two critical zones left and right of the center of the peak considered. When an interfering peak falls in one of these two zones, it will form a cluster with the original component peak, and the integration algorithm will recognize this cluster as a single peak. The width of each of these zones equals the critical distance
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component’s relative response in the mixture. Equation 2 is the mathematical description of the determination characteristic. The computation of both probabilities 0 and P, is discussed separately in the following sections. Equation 2 is in fact a simplification of the exact mathematical expression where P, is replaced by aP, + (1- a)Pl. In this expression a is the probability that the contamination either consists of one or more contaminating component peaks all falling in the same critical zone (single-zonecontamination) or that the contamination consists of two or more peaks falling in both critical zones but summing up to a total contamination showing only one maximum (double-zone-one-peak contamination). The factor (1 - a ) is the probability that the contamination consists of a double-zone contamination summing to a result showing two (or exceptionally three) maxima. P,‘ is then the probability that the sum of such a double-zone two-peak contamination is so small as to achieve that the relative error is smaller than e. Experimental assessment of both parameters a and P,‘ is very difficult if not impossible. Analysis of computer-simulated chromatograms however proved that a >> (1- a ) and that P, and P,‘ were very similar. Anyway one can use the simplified eq 2 if maximum errors not larger than 15% are allowed. As discussed below, these errors only occur in the less important sections of the PC curves (see Figure 3).
RESULTS A N D DISCUSSION P e a k Overlap a n d Critical Resolution. In our further computations we need a good estimate of the critical resolution Rs. If each maximum in the chromatogram is defined as a peak, Snyder (14) already stated that the critical resolution between components of the same amplitude is 0.5, while for a peak-height ratio of 16/1 the critical resolution is approximately 1.0. In chromatographic analyses of complex biological samples such as UV-absorbing substances in plant extracts, there are no fixed relative amplitudes for adjacent component peaks. This means that a fixed, constant critical resolution is nonexistent. Only a mean critical resolution can be determined experimentally. Giddings (15) mentions optimal empirical resolutions calculated from weighted least-squares analyses of counted peak maxima in 48 computer-simulated multicomponent chromatograms. All simulations were based on the assumption that component width was constant in a given simulation and that all components gave Gaussian responses. The simulations were done with five possible peak capacities; the amplitudes of the components in these simulations fell randomly within an l8-fold range, while the component number was fixed a t 80, 160, or 240. The empirical resolutions Rs ranged from 0.427 to 0.515. These values however are not realistic for chromatograms built up with unequal component amplitudes (14).
being the minimum distance between two Gaussian peaks so that an integrator algorithm is able to identify them as two distinct peaks. Rs is the critical resolution and u the standard deviation of a single-component peak. The probability PC, that a component peak will be determined by the integrator with a relative error smaller than e is now given by
PC, =
+ (1- 02)P,
We therefore tested the Davis and Giddings model on our simulations (5). In these simulations the component amplitudes obeyed the distribution FDC; the number of components was not fixed beforehand because the generation of peaks only stopped when the sum of their areas reached 100%. In the Davis and Giddings model, the critical resolution can be written as (see ref 1, eq 25 and 29)
(2)
(3)
In this equation 0 is the probability that no contamination (consisting of an other single peak or a cluster of one or more components) falls in a critical zone. The probability that both critical zones remain unoccupied is then given by 02. Obviously, the probability that a contamination occurs in one of the two critical zones is then 1 - 8’. P, is the probability that the contamination, if it occurs, is so small as to achieve that the relative error is smaller than e. P, is a function of the
where X is the total separation space, ( m ) the mean component number, and q the number of peaks detected. Empirical critical resolutions were determined by application of eq 3 on chromatograms simulated following the Nagels et al. procedure (5)with the frequency distribution of component peaks FDC as valuable for HPLC determinations of UV-absorbing substances in plant extracts. The critical resolutions
02
ANALYTICAL CHEMISTRY, VOL. 59, NO. 6, MARCH 15, 1987
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Table I. Different Distributions of Component Peaks Used in Chromatogram Simulations as Described by Nagels et al. (5)
peak area: class boundaries, %
0.00-0.05 0.05-0.10 0.1-0.3 0.3-0.5 0.5-0.7 0.7-0.9 0.9-1.1 1.1-1.3 1.3-1.5 1.5-1.7 1.7-1.9 1.9-2.3 2.3-2.7 2.7-3.1 3.1-3.7 3.7-4.5 4.5-5.; 5.7-7.0 7.0-9.0 9.0-11.0 11.0-20.0 20.0-30.0 30.0-40.0 40.0-50.0 50.0-60.0 60.0-65.0
cumulative frequency distributions of component peaks, % FDC(a) FDC(p)" FDC(b) 10.5 23.00 50.00 62.00 70.00 75.00 79.00 82.00 84.50 86.20 87.50 90.00 91.50 93.00 94.20 95.50 96.70 97.70 98.40 98.85 99.60 99.81 99.92 99.97 99.99 100.00
16.00 28.39 57.38 71.32 79.40 84.11 87.48 89.49 91.52 92.91 93.86 95.04 96.02 96.50 97.28 97.91 98.35 98.69 99.18 99.37 99.64 99.82 99.92 99.97 99.99 100.00
41.00 56.00 75.00 82.00 86.00 88.50 90.20 91.50 92.50 93.30 94.00 95.00 95.70 96.30 97.00 97.50 98.10 98.50 98.90 99.20 99.60 99.81 99.92 99.97 99.99 100.00
Table 11. Estimates of the Critical Resolution R from the Maximum Number of Detected Peaks in Simulated Chromatograms, Simulations with Different Distributions of Component Peaks distribution
no. of
separation
of
space (no. of
detected
std devs)
component peaks FDC
simulated chromatograms
peaks
RS
90 140 140 100 188 260 110 150 188
FDA (a) FDC (a) FDC (P)" FDC (PI FDC (p) FDC (p) FDC (b) FDC (b) FDC (b)
123000 70 000 58 000 96 500 126500 107300 46 000 57 000 67 500
30 43 44 33 57 75 35 47 57
0.75 0.81 0.80 0.76 0.82 0.87 0.79 0.80 0.82
max no. of
"FDC (p) is the cumulative relative frequency distribution of UV absorbing components in plant extracts (HPLC determinations). I
1
1
'
1
I
I
I
l
l
I
I
I
1
-
probability
f
0.6
"FDC (p) is the cumulative relative frequency distribution of UV absorbing components in plant extracts (HPLC determina-
0.4
I
0
FOC ( p )
A
FDC ( b )
i
i
/-
0 FDC ( a )
1 -I
1
tions). obtained ranged from 0.39 for X = 188u to 0.57 for X = 2300~. These results again are not realistic for chromatograms built up with unequal component amplitudes (14). Alternatively one can compute the critical resolution if the real peak capacity n, = X / x , can be estimated for a given distribution of peak amplitudes. We must remember that the peak capacity is defined as the hypothetical maximum number of peaks that can be packed into a chromatogram with total separation space X. The exact number of components and the exact configuration of peaks in a single simulated chromatogram cannot be predicted as the position and amplitude for each component peak are random. Only the mean number of components for the entire set of chromatograms is fixed and determined by the distribution FDC. The number of detected peaks will thus vary due to the varying number of component peaks, their position in the coordinate space X, and their relative amplitudes. Our approach for the estimation of the real peak capacity is based on the idea that, if the number of simulated chromatograms is great enough, it will happen that the total separation space is filled "ideally" and that the number of detected peaks reaches its maximum possible value. This maximum number of detected peaks will tend to the real peak capacity n,. An estimate of the empirical critical resolution is then obtained from
1 roparation rpace 0
10
I
I
I
1
1
100
I
I
I
l
l
1000
1
I
I
x
I 3
0
Figure 1. Probability t? that a critical interval remains unoccupied as a function of the total separation space X . Results for different cumulative frequency distributions of component peaks.
(4)
it must remain possible to fill it with generated component peaks. Results are summarized in Table 11. The obtained empirical critical resolution ranged from 0.76 to 0.87. It is remarkable that the results are relatively independent of the distribution of component peaks used. On that account a mean estimate Rs = 0.8 for the critical resolution is assumed for all further computations. Probability That a Critical Interval Remains Unoccupied. With the empirical value Rs = 0.8 of the critical resolution, a mean critical spacing for peaks with quasi-exponential amplitude distributions is assumed as xo = 3 . 2 ~ .The probability that such an interval remains unoccupied (by a top of a peak) is investigated using chromatogram simulations. The influence of both the value of the total separation space X and the distribution of peak amplitudes FDC is studied. For each set of simulated chromatograms, the mean number of detected peaks ( m )was computed. The probability that an interval x o remains unoccupied is given by
Computer simulations were done for different values of the separation space X and for different distributions of component peaks FDC. Several distributions were used for the simulations. Extreme distributions FDC(a) and FDC(b) (Table I) were characterized respectively by much less and much more components with small amplitudes than the distribution found for UV-absorbing components in plant extracts FDC(p). In these simulations, the choice of very large values for the separation space was not opportune because
The results are presented in Figure 1. As expected, the probability that a critical interval remains unoccupied increases as the total separation space increases. The results are fairly independent of the distribution of component peaks FDC. This was checked particularly for X = 188u, for which several other distributions of component peaks FDC were
Rs = X/4unC
"r
ANALYTICAL CHEMISTRY, VOL. 59, NO. 6, MARCH 15, 1987
,/P
0.4
C(0.5)
825
l-r
0.8
L
0.6-
0.4 -
0.4
0.2peak area , % 0 0.1
1
10
I
4 I
,,,I
,
I
,
peak area,% I , I I I I
,
I
1 1 1 1 1 1
100
Flgure 2. Probabilities PC0.5 and PCo,las functions of the relative peak area of component peaks. They are respectively the probabilities that a component peak is measured with a relative error smaller than 0.5 and 0.1. Total separation space X = 188a. The solid line was obtained through computer simulation of chromatograms (5);the dashed line is the result of the actual computations. used, all lying within the limits fixed by FDC(a) and FDC(b). The resulting values for 8 were all found in the interval (0.27-0.34) being the values found for FDC(b) and FDC(a), respectively. In fact a mean value (8) = 0.30 with a standard deviation of 0.03 was found for X = 188a. We can conclude that for each value of X , an acceptable value of 8 can be determined by using the graph of Figure 1 (full line). The probability that an interval remains unoccupied could also have been derived experimentally from chromatographic recordings. This would however have been much more timeconsuming than the simulation approach used here, without improving the reliability of the results. Estimation of the Probability P,. The probability P, that the relative area of a contaminating peak or a cluster of peaks is smaller than a given value (i.e., provokes a relative error smaller than e ) ,can be derived from the frequency distribution of observed peaks FDO. Therefore the experimentally obtained FDO is extended with small area peaks (proportional areas smaller than the detector threshold value) whose abundance is estimated by extrapolation. Then this completed frequency distribution is converted to a cumulative relative frequency distribution (such a distribution was used already in our first paper ( 5 ) as FDFE). The cumulative relative frequency distribution of observed peaks gives the probability that the relative area of the contaminating cluster is equal to or smaller than a given value. The maximum relative area that can be tolerated for the contaminating cluster is computed for the relative area of the actual component peak and from the admitted error e. By use of the maximum relative area, the probability P can now be read off directly from the cumulative relative frequency distribution of observed peaks. This distribution depends strongly on the peak capacity of the chromatographic system. Computation of Probabilities PC, and Determination Limits. By use of the cumulative relative frequency distributions derived from FDO distributions at different values of the total separation space X , probabiliities PC, were computed with eq 2 and compared with results from chromatogram simulations as reported in our first paper (5). Results for PCol and PCo,5for X = 1 8 8 are ~ ~ given in Figure 2 and for X = 480a in Figure 3. For X = 188a, the FDO distribution of the relative areas of observed peaks was obtained from chromatograms of 62 plant extracts ( 5 ) ;for X = 480a and X = 800u,FDO was computed from simulated chromatograms based on the FDC for phenolic compounds (5). Note that the FDO distributions obtained from simulated chromatograms contain no other input information than the fixed FDC dis-
0.1
L h 0
200
400
600
800
x, 0
Flgure 4. Determination limits DLO,,'.' and DLo,cg as functions of the total separation space X . The solid line is obtained by redrawing the results from computer-simulated chromatograms (5);the dots are the results of the actual computations. tribution valid for the analysis of all plant extracts (phenolic compounds) and the fact that Gaussian peaks are distributed uniformly over the entire separation space X . For separation spaces of 480a and higher, the accordance of both probability curves is less for those parts of the curves, corresponding to lower probability values. For the higher probability sections of the PC, curves, necessary for the deduction of the determination limits DL,", the accordance is fairly well for X values up to 1500a. Herman, Gonnord, and Guiochon proved that in crowded random chromatograms, in which local regions of high peak density occur, a greater number of peak maxima can be observed than is predicted by the theory for any arbitrarily chosen degree of separation: it is possible to observe several peak maxima from summed Gaussians whose distances between consecutive tops are less than 2a (16). This fact, together with the unavoidable inaccurateness of the extrapolation of FDO and restrictions concerning the validity of eq 2 , can be responsible for discrepancies between the actual computed PC, curves and the exact results obtained through chromatogram simulations. In Figure 4, the determination limits DL0.50.9 and DL0,10.9 obtained for X = 188a,480u, and 8000 are compared with the results previously obtained from computer-simulated chromatograms (5). The model was further tested for other distributions FDC and for higher values for the separation space X. We can conclude that, if one allows errors up to 20% on
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Anal. Chem. 1987, 5 9 , 826-828
determination limits, the easy and fast computation as presented above is possible for separation spaces X up to 1500~ and for distributions of component peaks lying between the extreme distributions FDC(a) and FDC(b) as given in Table I.
CONCLUSIONS The probability PC,, that a component present in a complex biological sample can be determined chromatographically with a relative error smaller than e , is computed as a function of the relative response of the component in the sample. Matrix interference is taken into account by using (quasi-exponential) frequency distributions FDO of observed peaks. The probabilities PC, depend on the component's relative response and on the peak capacity of the chromatographic system (or the width of the separation space X). The relative response for which PC, = 0.9 is called the 90% determination limit. The presented description of determination characteristics uses input from real HPLC analyses of plant extracts. Computer-simulation data are used only to estimate the critical resolution Rs and to obtain FDO distributions for those peak capacities which were difficult to realize experimentally. The equation for the calculation of PC, is thoroughly tested by computer simulation. It can be applied provided the complex samples under study have quasi-exponential FDC distributions comparable to plant extract FDC's. GLOSSARY FDO frequency distribution of observed peaks FDC cumulative relative frequency distribution of component peaks FDFE cumulative relative frequency distribution of observed peaks PC, the probability that a component peak is determined with a relative error smaller than P
DL,"
determination limit: the minimum relative abundance of a component in the extract, which is necessary so as to have a probability w to do a determination with a relative error smaller than
RS (m) nc
resolution parameter mean component number peak capacity number of detected peaks total space in c units over which the computation applies critical distance standard deviation of a pure component peak
e
4
X XO
u
LITERATURE CITED (1) Davis, J. M.; Giddings, J. C. Anal. Chem. 1983, 55,418. (2) Davis, J. M.; Giddings, J. C. J . Chromatogr. 1984, 289, 277. (3) Davis, J. M.; Giddings, J. C. Anal. Chem. 1985, 57,2168. (4) Davis, J. M.; Giddings, J. C. Anal. Chern. 1985, 57,2178. (5) Nagels, L. J.; Creten, W. L.; Vanpeperstraete, P. M. Anal. Chern. 1983, 55,216. (6) Nagels, L. J.; Creten, W. L. Anal. Chem. 1985, 57,2706. (7) Nagels. L. J. Postdoctorial Thesis, University of Antwerp (UIA), in press. (8) Martin, M.; Guiochon, G. Anal. Chem. 1985, 57, 289. (9) Herman, D. P.; Gonnord, M. F.; Guiochon, G. Anal. Chern . 1984, 56, 995. (10) Nagels, L. J.; Creten, W. L.; Parmentier, F. I n t . J . Environ. Anal. Chem. 1988, 25, 173. (11) Nagels, L. J.; Creten, W. L. Anal. Chim. Acta 1985, 169,299. (12) Nagels, L. J.; Creten, W. L.; Van Haverbeke, L. Anal. Chirn. Acta 1985, 173, 185. (13) Liteanu, C.; Rica, I . Statistical Theory and Methodology of Trace Analysis; Wiley: New York, 1980. (14) Snyder, L. R., J . Cbromatogr. Sci. 1972, 10,200. (15) Giddings, J. C.; Davis, J. M.; Schure, M. R. ACS Syrnp. Ser., in press. (16) Herman, D. P.; Gonnord, M.-F.; Guiochon, G. Anal. Chem. 1984, 56, 995.
RECEIVED for review June 2 , 1986. Accepted November 10, 1986.
Effect of X-rays on the Polycarbonate Substrate of X-ray Calibration Standards Gerald A. Sleater* Center for Analytical Chemistry, National Bureau of Standards, Gaithersburg, Maryland 20899
John M. Crissman Institute for Materials Science and Engineering, National Bureau of Standards, Gaithersburg, Maryland 20899
Jimmy C. Humphreys Center for Radiation Research, National Bureau of Standards, Gaithersburg, Maryland 20899
Peter A. Pella Center for Analytical Chemistry, National Bureau of Standards, Gaithersburg, Maryland 20899
The effect of X-rays on the polycarbonate film substrate of X-ray calibration standards is described. Tenslle measurements of polycarbonatespecknens indicate that deterioration of the polycarbonate is proportlonal to the X-ray energy to which the film is exposed.
In a new type of X-ray calibration standard issued by the National Bureau of Standards (NBS), thin uniform layers of silica-based glasses containing certified amounts of specific
elements were deposited by ion beam coating on a polycarbonate (PC) film substrate (I). The PC substrate was selected primarily because it was essentially free of trace elements. This substrate was stable when exposed to lowintensity X-rays from secondary target emitters in energy dispersive (EDX) spectrometers. However, PC films irradiated with primary X-rays in a wavelength dispersive (WDX) spectrometer showed radiation damage, such as color changes in the film (from milky white to brown), embrittlement, and, in some cases, splitting along the parallel striations visible on one side of the film.
This article not subject to U.S. Copyright. Published 1987 by the American Chemical Society
