ANALYTICAL CHEMISTRY, VOL. 51, NO. 13, NOVEMBER 1979 * 2297
EXPERIMENTAL Data. In order to test the efficacy of the new algorithms, a training set pool of 13614 low resolution mass spectra of monofunctionalcompoundswere drawn from the NIH/EPA/MSDC mass spectral data base of 25 560 spectra, leased from the Office of Standard Reference Data, National Bureau of Standards. For each of 5 categories of compounds (selected from those listed in Table I), training sets of 200 spectra were chosen. The training sets were constructed so as to contain equal numbers of class and nonclass spectra. For example, the training set for recognition of the ether function was comprised of the spectra of 100 ethers and 100 additional spectra were chosen from among the other 10 categories listed in Table I. For training with each category, the 60 most frequent m / e peak positions were chosen as the features to be used. Computations. Super-modified Simplex (SMS) and Improved Super-modified Simplex (ISMS) programs were written in Fortran IV and all computations were done using an IBM 360/65 computer. Spanning constants used were the same for both SMS and ISMS calculations. The extrapolation factor used was 50% of the distance between the worst vertex and its reflection about the centroid of remaining vertices and the safety factor was 5% of the same distance.
RESULTS AND DISCUSSION Table I1 summarizes the data relevant for comparison of the SMS and ISMS simplex pattern recognition speed and performance in development of weight vectors for recognition of each of the 5 categories chosen for testing. When total computation times are compared, it is seen that the improved algorithm described here was, on the average, 14 times faster in locating an optimal weight vector. Recognition performance of the vector thus produced was generally as good as,or better than, those obtained using the SMS method. Closer ex-
amination of the tabulated data shows that this speed improvement derives primarily (as expected) from the ability of the ISMS technique to complete many more iterations in a given amount of time. The total number of iterations carried out with each of the methods was approximately the same. Because the dot products of the vertices must be stored when the ISMS method is used, memory requirements are somewhat greater than with the SMS technique. In the present instance, the program size increased from 150 Kbytes to 200 Kbytes when the ISMS technique was implemented. However, this modest memory increase is more than compensated by the additional computational speed obtained.
LITERATURE CITED Spendley, W; Hext, G. R; Himsworth, F. R. Technometrics 1962, 4 , 441. Nelder, J. A; Mead, R. Comput. J . 1965, 7, 308. Emst, R. R. Rev. Sci. Instrum., 1966, 3 9 , 998. Deming, S . N; Morgan, S. L. Anal. Chem. 1973, 45, 278A. Long, D. E. Anal. Chim. Acta 1969, 46, 193. Deming, S. N; Morgan, S. L. Anal. Chem. 1974, 46, 1170. Johnson, E. R.; Mann, C. K; Vickers, T. J. Appl. Spectrosc. 1976, 30, 415. Routh, M. W. Swartz, P. A; Denton, M. 8 . Anal. Chenr. 1977, 49, 1422. Rtter, G. L; Lowry, S. R; Wilkins, C. L; Isenhour, T. L. Anal. Chem. 1975, 47, 1951. Brunner, T. R; Wilkins, C. L; Lam, T. F; Soltzberg, L. J; Kaberline, S. L. Anal. Chem. 1976, 4 8 , 1146. Lam, T. F; Wilkins, C. L; Brunner, T. R; Soltzberg, L. J; Kaberline, S. L. Anal. Chem. 1976, 4 8 , 1768. Kaberline. S . L; Wilkins, C. L. Anal. Chim. Acta 1978, 103, 417. Ritter, G. L; Lowry, S. R: Isenhour, T. L; Wilkins. C L., submitted for publication in J . Chem. Inf. Comput. Sci. Duda, R . 0; Hart, P. E. "Pattern Classification and Scene Analysis", Wiley-Interscience: New York, 1973; p 141.
RECEIVED for review June 25,1979. Accepted August 10,1979. The support of the National Science Foundation under grant CHE-76-21295 is gratefully acknowledged.
Quantitative Analysis of Silicates by Instrumental Epithermal Neutron Activation Using (n,p) Reactions Ernest S. Gladney" and Daniel R. Perrin University of California, Los Alamos Scientific Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545
Instrumental epithermal neutron activation (IENA) involves the use of a neutron filter to screen out the thermal portion of the reactor neutron energy spectrum. Both Cd and B are efficient neutron filters. The former is essentially opaque to neutrons with kinetic energies of less than 0.4 eV, while the absorption cross section of the latter follows a l / v relationship and reaches a small value a t approximately 280 eV (1). The advantages of epithermal over conventional thermal neutron activation for elemental analysis of geological materials have been well summarized by Steinnes ( 2 ) . The principal advantage is that the most common rock forming elements, which activate strongly with thermal neutrons (e.g., Na, Al, P, K, Fe, and Sc), have their activities suppressed, relative to elements which have cross-sectional resonances in the epithermal energy region. T h e reduction in activity from common (n,y) products permits the observation of activation products from the lower cross section (n,p) reactions. Elements with potentially useful (n,p) reaction products are shown in Table I. Cross-sectional data are taken from Steinnes ( 2 )and Erdtmann ( 3 )and are presumably for Cd filtered epithermal fluxes. The energy threshold values are from Howerton et al. (4). Only "Mn and =Co are commonly observed in spectra of thermal neutron activated geological samples. The remainder are usually obscured by the background caused by those species that are 0003-2700/79/0351-2297$01 .OO/O
produced in greater abundance by thermal neutron capture. The threshold energies for (n,p) events are also shown in the table. For most of the reactions, neutrons with 0.5 MeV kinetic energy or more are required. When the thermal component of the flux is absorbed, neutrons of this energy become a much more prominent part of the remaining spectrum. Steinnes has carefully explored the (n,p) reaction for Ni determination in silicate rocks ( 5 ) ,and Ni measurements in geological materials using this reaction have been reported by other investigators (6-9). The determination of Si through the 28A1reaction has been reported in bulk iron ore samples (10) and in lymph node samples (11). The quantitative study of the application of (n,p) reactions to the analysis of geological materials is the subject of this paper.
EXPERIMENTAL One-gram samples of various silicate standard reference materials were encapsulated in polyethylene vials and irradiated in the Los Alamos Omega West Reactor epithermal facility. The epithermal neutron flux is boron filtered and is described in detail elsewhere (12). The flux is approximately 5 X 1O1O n/cmz/a. Samples may be pneumatically transferred in a few seconds from the reactor to the counting room. Each irradiation is monitored by use of a known amount of an Au solution pipetted onto filter paper disks lodged in the rabbit caps. These monitors may be 0 1979 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 51, NO. 13, NOVEMBER 1979
Table I. Epithermal Neutron (n,p) Reactions isotopic energy abun- activa- (n,p) cross threshtarget dance, tion section, old, nuclide % product mb MeV(3)
half-life
prominent y-rays, keV
"F
100
190
1.35
EQ
27
23Na 24Mg
100 79 100
23Ne 24Na Z7Mg
1.5 1.53 4.0
3.76 4.93 1.90
38 s 15 h 9.4 m
92.2
28A1
6.4
3.99
2.2 m
1779
4.7
29Al
560
3.00
6.5 m
1273
31Si
36
0.72
2.6 h
1266
2 7 ~ 1
"Si 29Si 31P
100
46Ti
8.0 7.5
46Sc 47sc
10.5 16.3
1.62 E
84 d 3.4 d
73.7 5.8
48sc 54Mn
0.27 82.5
3.27 E
43.7 h 312 d
4 9 3
48m
S4Fe 58Ni
193
s
68.3
'To
113
E
71 d
439 1368, 2754 844,1013
epithermal cross sections of interfering reactions, mb
interfering reactions and y rays, keV la,( n,y)I9O 22Ne(n,Lu)I9, 26Mg(n,ol)23Ne 3Na(n,y)24Na "Mg(n,y )"Mg 30Si(n,or)27Mg 847-keV 56Mn
0.070 0.056 0.027 290 13 0.155
-
180 0.118
889, 1021 I60 983,1037,1312 835 811
1268:keV 28A1 single escape 30Si(n,y)31Si 34S(n,~)31Si 1268-keV "A1 single escape 45Sc(n,y)46Sc "V( n,n)47Sc 46Ca(n,y )47Ca(p+) 47sc 51V(n,ol)4aSc 834 keV72Ga 55Mn(n,2n)54Mn SgCo(n,2n)saCo
-
47 22
-
10,700 1.5 320 0.022
-
0.258 0.72
Exothermic. Table 11. Concentrations in Various Standard Reference Materials Fe, %
Ti, P P ~
material USGSAGV-1 BCR-1 G-2 GSP-1 PCC-1 GXR-1 GXR-2 GXR-3 GXR-4 GXR-5 GXR-6 NBSSRM 91 120 633 635
IENA (n,p) 5500 12600 2900 3900 90 650 2800 1000
2600 2100 5000
