they do not exist. However, the proposed separation was tested in the presence of different amounts of high purity nickel and the results were found to be satisfactory. A comparison between the proposed method and several other analytical techniques for three nickel oxides is given in Table VII. The NBS nickel oxides are spectrographic standards but they are not certified for their lead content. At this laboratory they were analyzed using the optical emission spectrograph and atomic absorption. The two emission procedures use the dc arc for the direct determination of lead in the oxide as well as a determination of lead after its coprecipitation by iron(II1) hydroxide. The agreement of the polarographic, spectrophotometric, emission techniques, and the methyl iso-butyl ketone (MIBK) solvent extraction separation of lead with the manganese(1V) oxide separation is excellent. The data in Table VI11 contrast the coprecipitation technique with MIBK solvent extraction of lead and bismuth in nickel metal, The MIBK procedure extracts the iodides of lead and bismuth from a 5 hydrochloric acid solution containing an excess of potassium iodide (31). After the extraction, the organic material is destroyed and the remaining salts are taken up in a small volume of acid for analysis by atomic absorption. The extraction procedure could not be applied to the deter(31) C. L. Luke, Anal. Chirn. Acta, 39,447 (1967).
mination of antimony and tin. Again the results are satisfactory. The procedure has been applied t o various types of nickel, Table IX. None of the materials listed have been certified for antimony, bismuth, lead, or tin. They are used as emission spectrographic standards to obtain calibration curves. These secondary standards are commercially available, except for the P D M R L standards; however, they are not certified for antimony, bismuth, lead, or tin. The precision of the method is given for several samples. The limit of detection can be decreased and the precision improved by adjusting the sample weight and final volume. For instance for a material containing 5 ppm lead, a 5-gram sample is carried through the procedure and concentrated into a 5-ml volume. This gives a precision of 5.7 f 0.3 ppm with a coefficient of variation of 5 %. ACKNOWLEDGMENT
The author wishes t o thank Emil Stumpp for his assistance in obtaining the data.
RECEIVED for review May 20, 1970. Accepted August 21, 1970. Presented at the 160th National Meeting, ACS, Chicago, Ill., September 1970.
A Critical Examination of Computer Programs Used in Quantitative Electron Microprobe Analysis D. R. Beaman The Dow Chemical Co., Midland, Mich.
J. A. Isasi Westinghouse Electric Corporation, Steam Turbine Division, Lester, Pa. Forty computer programs have been written since 1963 for use in quantitative electron microprobe analysis. In this investigation, all of these programs have been studied and their important characteristics tabulated to facilitate program selection by the analyst. The content of an ideal program is proposed and the 40 programs were critically examined with respect to accuracy, content, and versatility. Programs by Mason, Frost, and Reed; Duncumb and Jones; Shaw; and Colby were found to be outstanding. The last was recommended for use in metallurgical applications and the others for use in both metallurgical and geological applications. COMPUTER PROGRAMS are needed in the conversion of electron probe X-ray intensity ratios, k , to chemical compositions, C, primarily because some of the correction parameters are functions of concentration and, hence, make successive approximations necessary. While the analytical expressions normally used are not complex, a total correction formula is lengthy and iteration in multicomponent systems makes hand computations formidable. The existence of 40 programs by authors from Canada, England, France, Germany, Italy, Japan, Sweden, and the United States attests to the need for a good correction program. In this investigation all published and many unpublished computer programs, used in quantitative electron microprobe analysis, have been examined and critically evaluated with the following objectives: to list in one location the features and capabilities of all available programs; to critically examine each program with respect t o accuracy, content, and versatility; and to establish what a program 1540
should and should not contain in an attempt t o diminish duplication and the proliferation of inadequate programs. Fulfillment of the first two objectives should allow each analyst to select the program most suitable for his needs based upon the type of problem he normally encounters, the computer facilities at his disposal, his interest in evaluating correction procedures, etc. The validity of the third objective is supported by an extrapolation of a plot of the number programs available as a function of time which indicates that, at our present production rate, at least 150 programs should be available by 1975. The 40 programs described and dissected herein were all written between 1963, when the first published program appeared, and June 1970, when the latest program became available. It is important to mention that this work could not have been completed without the willing cooperation of the program authors. Most authors completed data sheets, made test computations, provided examples of experimental input and computer output, and examined the tables herein t o ensure their accuracy. PROCEDURE
Program listings, published articles, and company reports obtained from the different authors were studied and a description of each program was written and sent to the author for his comments. The data collected were reduced t o tabular form and returned t o the authors for their final approval. Each author was also asked t o use his program to correct measured X-ray intensity ratios, using supplied
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
physical data, for atomic number, absorption, and characteristic fluorescence effects in Ti-Nb, Fe-Cr, and Cr-Co-Mo alloy systems. The 40 programs are listed as references (1-39), appear in the tables in chronological order with the (1) J. Henoc, private communication, to be published by NBS; J. Henoc, C.N.E.T.-P.E.C.,3Avenue de la Republique, 94-Issy Les Moulineaux, France, or K. F. J. Heinrich, Spectrochemical Analysis Section, Analytical Chemistry Division, U. S . Dept. of Commerce, National Bureau of Standards, Washington, D. C. 20234. (2) J. L. Solomon and R. MacQueen, private communication; J. L. Solomon, IBM/FSD, MA5/001-1, Oswego, N. Y. 13827. (3) J. Rucklidge and E. L. Gasparrini, Geology Department, Report “EMPADR VII,” University of Toronto, Toronto (1969); J. Rucklidge, Dept. of Geology, University of Toronto, Toronto, Ontario, Canada. (4) D. G. W. Smith and M. C. Tomlinsom, State Geological Survey, The University of Kansas “Computer Contributions” Series; D. G. W. Smith, Dept. ofGeology, University ofAlberta, Edmonton, 7, Canada. (5) P. Duncumb and E. M. Jones, Company Report, Tube Investments Research Laboratories, 1969; P. Duncumb, Tube Investments Research Laboratories, Hinxton Hall, Nr. Saffron Walden, Essex, England. (6) J. Bomback, private communication; J. Bomback, U. S. Steel Research Center, Monroeville, Pa. 15146. (7) D. M. Gast and E. D. Glover, private communication; E. D. Glover Dept. of Geology and Geophysics, University of Wisconsin, Madison, Wis. 57306. (8) G. L. Fisher and W. G. Wickersty, Jr., in Proc. Fourth Natl. ConJ Electron Microprobe Analysis, July 16-18, 1969, Pasadena, Calif., Paper No. 28; G. L. Fisher, Paul D. Merica Research Laboratory, International Nickel Company, Sterling Forest, Suffern, N. Y. 10901. (9) F. Borile, F. Kunz, and E. Eichen, private communication; E. Eichen, Ford Motor Company, Box 2053, 2oooO Rotunda Drive, Dearborn, Mich. 48124, or C. N. R., Via Induno 10, 20092 Cinisello B., Milano, Italy. (10) R. H. Packwood, private communication; R. H. Packwood, Dept. of Energy, Mines and Resources, 568 Booth St., Ottawa, Ontario, Canada. (11) P. K. Mason, M. T. Frost, and S. J. B. Reed, National Physical Laboratory, I.M.S. Report 2, April 1969; M. T. Frost, Geology Dept., Imperial College, Prince Consort Road, London, S.W. 7, England. (12) P. K. Mason, M. T. Frost, and S . J. B. Reed, National Physical Laboratory, IMSReport 2,1969; R. F. Braybrook, I.M.S. Division. National Physical Laboratory, Teddington, Middlesex, England. (13) J. L. Shaw, Atomic Energy Research Establishment Report AERE-R6071 (1969); J. L. Shaw, Dept. of Mining and Mineral Technology, Royal School of Mines, Imperial College, Prince Consort Road, London S.W. 7, England. Cards and listing are available from B. W. Mott, Solid State Division, Atomic Energy Research Establishment, Harwell, Berkshire, England; the approximate cost is S150. (14) L. J. Gray, Ph.D. Thesis, University of Illinois, Urbana, Ill. (1969); J. B. Woodhouse, B67 Materials Research Laboratory, University of Illinois, Urbana, Ill. 61801. (15) S . Kimoto, M. Sato, and H. Ohyi, Company Report XA69023, Japan Electron Optics Laboratory, 1968; M. Sato, Japan Electron Optics Laboratory, Ltd., 1418 Nakagamicho, Akishima-shi, Tokyo, Japan. (16) B. Pascal, in “Fifth International Congress on X-ray Optics and Microanalysis,” G. Mollenstedt and K. H. Gaukler, Ed., Springer-Verlag, Berlin, 1969, p 135; B. Pascal, Electricite de France, Service National, Direction des Etudes et Recherches, 12, Place des Etats-Unis, Paris XVI. (17) K. F. J. Heinrich, private communication; K. F. J. Heinrich, Spectrochemical Analysis Section, Analytical Chemistry Division, u. S . Dept. of Commerce, National Bureau of Standards, Washington, D. C. 20234. (18) W. Reuter, private communication; W. Reuter, Thomas J. Watson Research Center, P. 0. Box 218, Yorktown Heights N. Y. 10598. (19) J. Moriceau, PCchiney Internal Report No. 10043, Centre de Recherches Pechiney (1968); J. Moriceau, Centre de Recherches PCchiney, B. P. 24, 38 Voreppe, France. (20) C. Zeller, These FacultC des Sciences, Nancy, France (1968); also C. Zeller, J. Babkine, J. C. Reithler, J. Bolfa, and F. Zeller, Bull. Acad. Soc. Lorraines Sci., 8, 122 (1969); also C. Zeller and
F. Zeller, in “Fifth International Congress on X-Ray Optics and Microanalysis,” G. Mollenstedt and K. H. Gaukler, Ed., SpringerVerlag, Berlin, 1969, p 132; C. Zeller, Laboratoire de Minerolgie et Cristallographie, FacultC des Sciences, 54-Nancy, France. (21) J. Colby, in Adaan. X-Ray Anal., 11 287 (1968); J. Colby, Bell Telephone Labs., Inc., 555 Union Blvd., Allentown, Pa. 18103. (22) J. I. Goldstein, in Trans. Third Natl Conf. Electron Microprobe Analysis, July 31-August 2, 1968, Chicago, Ill., Paper No. 6; also J. I. Goldstein and P. A. Comella, Report No. X-642-69-115, Goddard Space Flight Center, Greenbelt, Md., 1969; J. I Goldstein, Dept. of Metallurgy and Materials Science, Whitaker Laboratory, Lehigh University, Bethlehem, Pa., or P. A. Comella, Goddard Space Flight Center, Greenbelt, Md. (23) L. R. Woodyatt and R. J. Henry, in Trans. Third Natl. Conf Electron Microprobe Analysis, July 3 1-August 2, 1968, Chicago, Ill., Paper No. 7; L. R. Woodyatt, Homer Research Laboratory, Bethlehem Steel Co., Bethlehem, Pa. (24) F. R. Boyd, L. W. Finger, and F. Chayes, Carnegie Institute, Washington, D. C., Yearbook, 67, 210 (1968); F. R. Boyd, Geophysical Laboratory, 2801 Upton St., N. W., Washington, D. C. 20008. (25) A. E. Bence and A. L. Albee, J. Geol., 76, 382 (1968); A. L. Albee, Division of Geological Sciences, California Institute of Technology, Pasadena, Calif. 91109. (26) S . S . So and H. R. Potts, J. Electrochem SOC.,115, 65 (1968); IBM Program Information Dept., Hawthorne, N. Y., Reference NO. 360D-17.1.001. (27) R. Tixier and J. Philibert, IRSID Report N. Met. Phy. 370; R. Tixier, IRSID, 185 Avenue President Roosevelt, 78 Saint Germain en Laye, France. (28) M. H. Beeson, Open File Report, U. S . Geological Survey, 1969; M. H. Beeson, U. S . Geological Survey, 345 Middlefield Road, Menlo Park, Calif. 94025. (29) G. Springer, Fortschr. Mineral., 45, 103 (1967); G. Springer, Falconbridge Nickel Mines Ltd., Metallurgical Laboratory P. 0. Box 900, Thornhill, Ontario, Canada. (30) M. G. Hobby and G. W. Wood, Metallurgia, 85, 143 (1967); M. G. Hobby, UKAEA Culham Lab. nR. Abingdon, Berkshire, England, D5/29. (31) J. Rucklidge and E. L. Gasparrini, Geology Dept. Report “EMPADR,” University of Toronto, Toronto (1968); also, J. Rucklidge, J. Geol., 75, 126 (1967); J. Rucklidge, Dept. of Geology, University of Toronto, Toronto, Ontario, Canada. (32) D. R. Beaman, Microkhim. Acta 1969 117; also Dow Chemical Co. Report (1967); Algol programs from D. Beaman, The Dow Chemical Company, 241 Bldg., Midland, Michigan 48640; Fortran-4 program from R. Lewis, Bell and Howell Company, Electronic and Instruments Group, 360 Sierra Madre Villa, Pasadena, Calif. 91016. (33) R. E. Hanneman and E. Lifshin, Trans. Met. SOC.AIM€, 236, 1503 (1966); also G.E. Research Laboratory Report No. 6642-250 (1966); E. Lifshin, General Electric Company, Distribution Unit, Building 5, Room 345, Research and Development Center, P. 0. Box 8, Schenectady, N. Y.12301. (34) J. Brown, ANAL.CHEW,38, 890 (1966); also U. S. Department of the Interior Bureau of Mines Report No. 6648 (1965); J. Brown, Faculty of Engineering Science, University of Western Ontario, London, Ontario, Canada. (35) J. Z. Frazer, R. W. Fitzgerald, and A. M. Reid, Scripps Institution of Oceanography Report 66-14, University of California at La Jolla, Calif., June 1966; J. Frazer, Scripps Institution of Oceanography, University of California, La Jolla, Calif. 92037. (36) G. R. Lachance and R. J. Traill, Can. Spectrosc., 11,No. 2 and 3 (1966); G. R. Lachance, Geological Survey of Canada, 601 Booth Street, Ottawa, Ontario, Canada. (37) C. I. Helgesson, in “X-ray Optics and Microanalysis,” R. Castaing, P. Deschamps, and J. Philibert, Ed., Hermann, Paris 1966, p 284; C. I. Helgesson, Forsvarets Forskningsanstalt, Research Institute of National Defense, Dept. 43, S-104, 50 Stockholm 80, Sweden. (38) J. W. Criss, U. S. Naval Research Laboratory Report, Washington, D. C., 1965; also J. W. Criss and L. S . Birks in “The Electron Microprobe,” T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry, Ed., John Wiley and Sons, Inc., New York (1966), p 217; J. W. Criss, Department of Navy, Naval Research Laboratory, Washington, D. C. 20390. (39) V. G. Macres and R. G. Wolf, Dept. of Material Sciences, Report No. 63-18, Stanford University, Stanford, Calif., 1963; R. G. Wolf or V. G. Macres, Materials Analysis Company, 1060 E. Meadow Circle, Palo Alto, Calif.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
0
1541
most recently written program listed first, and are identified by the name of the principal author. Following each reference is the name and address of the person who will supply the program upon request. A concerted effort was made to obtain information from all possible sources and t o our knowledge there is only one general correction program which is not included because the author (40) was unable to provide the necessary information. Throughout the discussion, the following terminology will be used. The chemical composition, Coalo,is calculated, unless otherwise indicated, from the measured X-ray intensity c
ratio, k , using the common ZAF expression Ccalo= k(ZAF) or
where the three terms in brackets represent the atomic number, absorption, and characteristic fluorescence correction factors, respectively. The superscripts, prime and zero, refer to the unknown and standard material, respectively. f ( x ) is the fraction of generated intensity that is emitted,
i.e.,
f(x)
=
F(x)/F(O);
x
is csc
+
( P / ~ ) ~ Awhere C% %=A
+
is the spectrometer take-off angle, (pip)%”the mass absorption coefficient for the analyzed radiation ( A ) by element i, and n the number of components; Ij’ is the X-ray intensity emitted by a n unknown due t o characteristic fluorescence and I,’ is the intensity emitted by a n unknown as a result of direct excitation by the electron beam; y is the ratio If’/Ip‘. The first portion of this report lists the characteristics of the different programs in a condensed but meaningful manner. This is followed by a section on the requirements of a good program. The ideas presented therein are based upon what was found in previously published programs and upon the needs of the analyst. Finally, a rating of the programs is presented and recommendations are made. PROGRAM FEATURES
Some comments concerning specific aspects of certain programs are necessary before beginning the general description of the programs. The program by Gray (14) is a modified version of the M A G I C I1 program written by Colby (21). The Packwood (10) program is patterned on an earlier program by So ( 2 6 ) . A program by Gurney and Bonizewski (41) has not been included, at the authors’ request, because they believe it to be obsolete. Hoff and Gregory ( 4 2 ) have written a specialized program used to obtain diffusion data from concentration-penetration curves. Theirs is not a general program for quantitative analysis and is not included in the evaluation. Mason, Frost, and Reed (11, 12) have written two programs. M K 1 is a short program that can be used on small computers. M K 2 is a versatile program requiring considerable core storage; it contains data handling routines and a large amount of permanent input data that M K 1 does not. To differentiate between the two in the tables, M K 1 is listed as Mason-MK1 and M K 2 as Frost-MK2. The program by Tixier and Philibert ( 2 7 ) is a modified version of an earlier program by C. da Casa. These authors (40) R. Coy-yll, private communication; R. Coy-yll, Ecole Polytechnique, University of Montreal, Quebec, Canada.
(41) T. R. Gurney and E. Bonizewski, British Welding Research Association Report MISC/6/66 (1966); T. R. Gurney, The Welding Institute Research Laboratory, Abington Hall, Abington, Cambridge, England. (42) W. D. Hoff and B. Gregory, Metahrgia, 72, 99 (1965). 1542
( 2 7 ) also have a separate program available for thin specimen corrections which is not included herein as it is an application outside the scope of the present evaluation, Le., quantitative correction in bulk samples. The program by Woodyatt and Henry (23) is no longer available; these authors now use Colby’s MAGIC I1 program. The Lachance program is one which solves a series of simultaneous equations. The Bence and Albee ( 2 5 ) and Gast and Glover ( 7 ) programs make use of the empirical expression developed by Ziebold and Ogilvie and are intended for making corrections in geological systems. Henoc (1) has written two programs, one which corrects for continuous fluorescence effects in multicomponent systems and is labeled Henoc-cf in the tables. Henoc’s (1) other contribution is a general correction program, but it differs from the other programs in that the intensity ratio is obtained from calculated values of the absolute intensities for the unknown and standard. This program is labeled Henoc in the tables. Because Rucklidge and Gasparrini (3, 31) have just issued (12/69) a new program (EMPADR VII) (3), which is an expanded form of their earlier program (EMPADR) (31), their programs appear twice in each table. The most significant change is a n improvement in the absorption and atomic number corrections. While the features, or lack therof, of each program listed in Tables I-IX are in some cases self-explanatory, a complete description of each table heading is provided for the sake of clarity. The desirability of a particular feature or method is discussed in some detail in the computer programming section. Throughout the tables “na” means not applicable. Table 1. Program Availability and Computer Characteristics. This information should make it possible to ascertain if a particular, available program will run o n the users’ hardware. The approximate cost of computation is listed. COLUMN 1-Author-indicates the principal author; collaborating authors are listed in the references. COLUMN 2-Datemonth and year of publication; if unpublished, date program was completed. COLUMN 3-Ref-reference number. COLUMNS 4-6-Availability-Listing, Cards, and Instructionsindicates whether the author will provide upon request, a listing, and/or punched cards, and/or instructions for program usage. COLUMN 7-Language-the computer language in which the program was originally written. COLUMN 8Machine-the computer used in developing the program and in some cases other machines on which the program has been run. COLUMN 9-Time Share-indicates if the program has been run remotely from a time sharing station. COLUMNS 10, 11-Core Storage-Words and Bytes/Word-the number of words of core storage required in the computer listed in column 8 and the approximate number of bytes per word for that equipment. COLUMN 12-Time in Seconds to Compileis the computer time in seconds required to compile the program excluding any input, output, and/or calculations. COLumn 13-Time in Seconds to Calculate (# e l e m e n t s t i s the processor time in seconds required to perform complete calculations for the number of elements indicated in parentheses. COLUMN 14-Cost-# per element-is the approximate cost of using the program in cents per calculated concentration and is based on the programmer’s experience and/or the times in columns 12 and 13. The cost/element factor is useful because it serves as a normalizing factor by eliminating the differences in hardware. The wide range in compiling times is insignificant because, once compiled, the program can usually be stored o n disk o r tape (generally less expensive) as an object file.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
m
o
4
N
I
I
o N
0 r
I
prolnom
0
LO
i I . .
o m m b m
riw
L O m
I
m N
ri
4ln
N
-m o
e,
br4d
Nln I
h
rim
W ri
4 0
0
- v u
v u
v
-no
0
ul
-I
m
1
0 4
4
h-
m o
xv 2m m
0
m
b
'0
-mw
e4Jrid
l n m
n
....
ri
m
p.
m o o o d o
0
w
E d p r
d 0 r i W
m
W
V
u
pr prN
N
rl
o
o w
P O
mm
rl
trl
w
lnLnN
mrl0
pro W
09 \9
00
0
Wm
N
0 8 - ri .d m a a 0 0
Ln
rid
m\-d
O N 0
- W d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ~ 0 00 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
ooooovo
oooriooooo
mmtnmmrim ~
N
m
P
m
~
r
l
NmOrnprw-U~m m N mpr N
m o o o o o -$mmoco~? wm 4
m m m m
m
fflm
m
omomoooooa,oooooommma,oma,oaJ h e C c C C h C C c, G C c h h h h C h h C >1
fi h C
m o o O N 0
m m m r-mrl e VI
030
pro 0 0 Nr(
rJri
a m
0 0 0 0
G
bi
0 0
N N
d m
mffl
o o m o o o u ~ o o 0 0 0 C C h C c d h h c d d C k
5 OD
0 0 0
m w m o w 0
r-rib
zez
mmm
H H H
rid
ri
d
ri
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
1543
Table 11. Data Handling Features. This Table indicates the ability of a program to statistically examine measured intensity values and convert them to experimental probe ratios corrected for deadtime, drift, and background. Such a data reduction capability is essential when the probe is to be 2,3--Statistical Evalinterfaced with a computer. COLUMNS uation-Is There Any? and If So, What-column 2 indicates whether or not statistical calculations are performed and the coding in column 3 indicates what is done. “u-m, k or C” means that the standard deviation (u) is calculated for a series of measured X-ray intensity values, m, and/or X-ray intensity ratios, k, and/or calculated compositions, C. “u-m, a’’ means that u is calculated for a series of X-ray intensities and compared to (fl)l’z where fiz is the mean intensity. “a-m; rej.” means that this same comparison is made and if u >~ ( a ) the~data ’ ~ are rejected; s is generally in the range of 1-6 and is part of the experimental input. COLUMNS 4, 5Deadtime Correction-Is There One? and What Inputindicates if there is a deadtime (7)correction, and, if so, what input is required or what constant 7 value is included in the program. “fixed” means a constant T value is incorporated in the program. All 7 values are in psec. All programs in which a correction is performed d o so using the expression n = m / ( l - m r )where n and m are the true and measured intensities respectively. COLUMNS 6, 7-Drift Correction-Is There One? and Method-indicates whether or not a drift correction is performed and, if so, how. “linear” means that linear drift in time is assumed between the initial and final intensity measurements o n a standard; standard intensities are then calculated corresponding to each measured unknown intensity. COLUMNS 8, 9-Background Correction-Is There One? and Method-indicates if a background correction is made and, if so, how. “k-input” means that the experimental probe ratio is part of the input and the correction is made outside the program. ‘‘input” means that background intensities measured in any manner are part of the experimental input and are subtracted from the peak intensities within the program. “calc” means that the unknown background intensity, BA’, is not measured but is calculated using
where BA is the background from a pure A target usually measured off spectral peak and Bi is the intensity measured at the spectral peak for A with a pure i target. Table 111. Computation Characteristics. The information in this Table provides some insight into a program’s computational methods, limitations, and versatility. COLUMN 2Number of Components-is the maximum number of components allowed in any given system. COLUMN 3-Take-off Angle-indicates possible take-off angles in degrees. 38.5 is one effective take-off angle used in MAC probes with nonnormal electron beam incidence (+ = 33.5’, 6’ = 62.5’). COLUMN 4-Atomic No. Limitations-indicates that in some cases only the concentrations of elements with atomic num,hers, z , greater than some minimum value can be computed. COLUMN 5-Calculation Procedure-“sequence” means that the correction is completed sequentially, e.g., according to a Z A F scheme where the probe ratio is adjusted for characteristic fluorescence before the absorption and atomic number corrections which follow (2 or 3 steps per iteration). “complete” means the correction is a one-step-per-iteration process in which all quantities that are functions of concentration are 1544
a
calculated and then Coalois determined in a single step using Equation 1. COLUMN 6-Convergence Method-indicates either the expression or the name of a common technique used to promote convergence during successive iteration. C,, C,-], and C,A are the new estimate of the concentration, the last calculated concentration, and the last estimated concentration, respectively. “simple” means C, = Cn-.l, 7, 8“average” means C , = (Cn-1 C,-2)/2. COLUMNS Iteration-Max. No. and Stopped-indicate the maximum number of iterations allowed and the criterion used to discontinue iteration. “input” means the maximum number of iterations is part of the experimental input. “6” means iteration stops when C , - C,-l < 6 where 6 is the indicated value. “6=input” means 6 may be part of the experimental input. COLUMN 9-Element by Diff.-“yes” means that a probe ratio is assumed for a single missing element, this element is assumed to be present in the calculation of all other elements, and the concentration of the element is calculated in the normal manner. “yes :atomic number” means that only the element(s) with the indicated atomic number(s) can be calculated by difference. “yes*” means that more than one element can be calculated by difference if the unknowns are present in a fixed ratio or if there are known stoichiometric relationships between unmeasured and measured elements. “no” means that the author requires that all probe ratios be experimentally determined. Most programs include the take-off angle, +, as part of the experimental input (input that is required with each experimental determination). Any such program can be used to handle nonnormal electron incidence by using a n effective take-off angle (E) as part of the input. This angle is given by E = csc-l(sin 6’ csc +) where 6’ is the acute angle between the incident beam and the specimen surface. Duncumb and Jones ( 5 ) state that the accuracy of such a procedure is unknown. Green (43) and Brown ( 4 4 ) have questioned such a simple relationship between f ( x ) and 6’. Bishop (45) has found that the factor (1 - 0.5 cos2 0) accounts for the observed variation of f(x) curves with the incident angle 6’. In this case E is given by: E = csc-l{(l- 0.5 cos2 6’)csc +}, Bishop (46) was not able to use this simple relationship to account for the f(x) variation with 0 obtained from Monte Carlo calculations. Abelmann and Jones ( 4 7 ) found both expressions for E inadequate. Colby, Wonsidler, and Conley (48) reported that experimental probe ratios, measured in two instruments (one with normal and one with nonnormal incidence), were correctable, using a specific correction scheme, to the same value within experimental error and no bias was observed. Colby et al. (48) used e = csc-Ysin 6’ csc +) and made measurements in three alloy systems. Duncumb (49) expects negligible effects in quantitative corrections, using an effective take-off angle, as long as 6’ is more than 45”. Experimental f ( x ) and backscatter data (R) will help to establish the range of validity of the simple expressions for E.
+
(43) M. Green, Proc. Phys. SOC.83, 435 (1964). (44) J. D. Brown, Ph.D. Thesis, University of Maryland, College Park, Md., 1966. (45) H. E. Bishop, Proc. Phys. Soc., 85, 855 (1965). (46) H. E. Bishop, Brit. J. Appl. Phys., 1, 673 (1968). (47) R. A. Abelrnann and R. Jones, J. Appl. Phys., 37,4507 (1966). (48) J. W. Colby, D. R. Wonsidler, and D. K. Conley, in Proc. Foiirtk Natl C012f Electroiz Microprobe Analysis, July 16-18, 1969, Pasadena, Calif., Paper No. 9. (49) P. Duncumb, J . Sci. Z/istrum. Series 2, 2, 553 (1969).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
.
v1
E
a JZ
u
a c e o
3 .i
2
o u Llu
ma,
XLl
u u mo m u Ll
a, P.
Azo H e 0 H
UI
23 EW Fr
o r no o o o o o o a , om a , m o o am ,L o~ o o mo cLo i o o o 0In o oL a o Q mJ o am, o o am , o ma m, am , a , o orno 0 c c h h c e c h G c c h e h h c c c c c c cL=-lcxchcX F C x c h h h c c c h
a 4
2P H H
w
3
H
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
1545
Table IV. Correction Scheme. This Table lists the correction schemes used (50-74) and indicates cases where the program author has modified (m) the published correction procedure. The complexity of the correction process led early investigators to make simplifying assumptions and to develop simple analytical expressions [Belk (75), Birks (65)] which facilitated hand calculations. Because of the wide availability of high speed computers, this era appears t o have passed. Most computer programs now utilize complete physical expressions derived, more or less, from basic principles. The Pascal (16) program is the first program written for general quantitative analysis which is based upon Monte Carlo calculations (54). The distribution in depth of primary
(50) P. Duncumb and P. K. Shields, in “The Electron Microprobe,” T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry, Ed., John Wiley and Sons, New York, 1966, p 284. (51) K. F. J. Heinrich, in Adrian. X-Ray Anal., 11,40 (1968). (52) P. Duncumb and S. J. B. Reed, in “Quantitative Electron Probe Microanalysis,” National Bureau of Standards Special Publication 298, K. F. J. Heinrich, Ed., U. S. Government Printing Office, Washington, D. C., 1968, p 133. (53) H. E. Bishop, Thesis, Cambridge University, 1965. (54) H. E. Bishop, in “X-Ray Optics and Microanalysis,” R. Castaing, P. Deschamps, and J. Philibert, Ed., Hermann, Paris, 1966, p 112. (55) H. A. Bethe, Ann. Plzys. (Leipzig), 5, 325 (1930). (56) J. Philibert, in “X-Ray Optics and X-ray Microanalysis,” H. Pattee, V. Cosslett, and A. Engstrom, Ed., Academic Press, New York and London, 1963, p 379. (57) J. Philibert and R. Tixier, in “Quantitative Electron Probe Microanalysis,” National Bureau of Standards Special Publication 298, K. F. J. Heinrich, Ed., U. S. Government Printing Office, Washington, D. C . , 1968, p 13. (58) R. Castaing, Thesis, University of Paris, O.N.E.R.A. l’ubl. No. 55 (1951). (59) S. J. B. Reed, Brit. J . Appl. Phys., 16, 913 (1965). (60) D. B. Wittry. University . of Southern California, USCEC ‘ Report No. 84-264, 1962. (61) D. B. Wittry, Adcan. X-Ray Aml., 7, 395 (1964). (62) J. F. Smith, J . Geology, 73, 830 (1965). (63) D. M. Poole and P. M. Thomas, J. hist. Metals, 90, 228, (1961-62). (64) T. 0. Ziebold, in “The Electron Microanalyzer and Its Applications,’’ Lecture notes for summer program at the Massachusetts Institute of Technology, Suppl. (1965). (65) L. S. Birks, “Electron Probe Microanalysis,” Interscimce, New York, 1963. (66) G. Springer, Neues Julirb. Mitzeral. Abk., 106, 241 (1967). (67) J. Henoc, in “Quantitative Electron Probe Microanalysis,” National Bureau of Standards Special Publication 298, K . F. J. Heinrich, Ed., U. S. Government Printing Office, Washington, D. C., 1968, p 197. (68) P. M. Thomas, UKAEA Report, AERE-R-4593 (1964). (69) J. Ruberol, M. Tong, and C . Conty, presented at the Groupement pour I’Avancement des Methods Spectroscopiques (G.A.M.S.), Conference in Paris, France, June 8, 1966. (70) C. A. Andersen and D. B. Wittry, Brit. J . Appl. Phys., 1, 529 (1968). (71) M. Green, in “X-Ray Optics and X-Ray Microanalysis,” H. Pattee, V. Cosslett, and A. Engstrom, Ed., Academic Press, New York and London, 1963, p 361. (72) J. W. Criss and L. S. Birks, in “The Electron Microprobe,” T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry, Ed., John Wiley & Sons, Inc., New York, 1966, p 217. (73) J. Henoc, F. Maurice, and A. Zemskoff, in “Fifth International Congress on X-Ray Optics and Microanalysis,” G. Mollenstedt and K . H. Gaukler, Ed., Springer-Verlag, Berlin, 1969, p 187. (74) J. Henoc, C.N.E.T.-P.E.C.,3 Avenue de la Republique, 94Issy Les Moulineaux, France, private communication, 1969. (75) J. A. Belk, in “X-Ray Optics and Microanalysis,” R. Castaing, P. Deschamps, and J. Philibert, Ed., Hermann, Paris, 1966, p 214. 1546
X-radiation, +(pz), is determined from the primary electron distribution, and the emergent X-ray intensities for unknown and standard materials are calculated and compared with the experimental probe intensity ratios. Helgesson (37) expresses the Philibert (56)and Tong (37)F(x)functions as cubic equations which are solved using the Newton method. In the Lifshin (33) program the indicated procedures are used to complete calibration calculations (calculate k for an assumed C) which provide k us. C values at 1 intervals. A linear least squares fit to a C/k us. C plot yields a coefficients which may be used in the Ziebold and Ogilvie (76) empirical expression
(3) to convert measured k values to compositions. This program (also Beaman’s) then can provide a coefficients which may be used externally in binary systems or to calculate a A B . . . n for use in multicomponent systems. The Lachance (36) program is used to solve a group of j ( j = 3 to 10) simultaneous equations each involving k , C , and a. Depending on what is known, these may be solved for C, k , or a. Generally, k is measured and C is sought, thus the a coefficient must be calculated or experimentally determined for each set of operating conditions (Eo and +). The success of the empirical approach (using experimentally determined a values) has been good in many binary systems and Ingersoll et al. (77) and Ziebold and Ogilvie (76, 78) have obtained good results in some ternary systems. In addition, Bence and Albee (25) have been successful in applying the technique to complex geological samples and this approach is the basis of their program and the one by Gast and Glover (7). The Henoc-cf program uses the expression developed by Henoc (67) to correct for continuous fluorescence effects, In Henoc’s general correction program ( I ) , the primary generated intensity (not ratio) is calculated from expressions for the ionization cross section and energy loss. The integral,l( Q:(dE/dx))dE, is evaluated in the manner of Philibert and Tixier (57) using either J = 1 1 . 5 ~or J = 9 . 7 6 ~ 58.5 z(-O, 19) for the mean ionization potential. The backscatter coefficient is calculated using the polynomial expression developed by Duncumb (79) to fit the experimental data of Bishop (53). f ( x ) is evaluated using the Philibert (56) expression with the Duncumb and Shields (50) value for u as modified by Heinrich (51). The contribution to the intensity from characteristic fluorescence is calculated using the technique of Henoc and Maurice (73, 74) with the Criss (72) expression for ~ ( p z ) ;the constants, u iand bi,are obtained from the Philibert (56) expression and are listed in the paper by Criss (80). The continuous fluorescence contribution is calculated using the Henoc equation (67). This approach is fundamentally good, but, because of the absence of the usual ratios and the inclusion of a continuous fluorescence correction, a considerable amount of additional input is required.
+
(76) T. 0. Ziebold and R. E. Ogilvie, ANAL.CHEM.,36, 322 (1964). (77) R. M. Ingersoll, J. E. Taylor, and D. H. Derouin, in Aduan. X-Ray Anal., 9, 273 (1966). (78) T. 0. Ziebold and R. E. Ogilvie, in “The Electron Microprobe,” T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry, Ed., John Wiley & Sons, Inc., New York, 1966, p 378. (79) P. Duncumb, Tube Investment Research Laboratories, Hinxton Hall, Nr. Saffron Walden, Essex, England, private communication, 1969. (80) J. W. Criss, in “Fifty Years of Progress in Metallographic Techniques,” ASTM STP430, Philadelphia, 1968, p 291.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
z
d
4 m
z
0 0 0
x
N r i d
m
x
(nom
\, N 0 0
rl
m
rd
u
u
H E+
u u u
m
‘ai
H
a w €+
3 4
z
U
5H H
2
3
20
U
U
I
H H H
w I=
m
3
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
1547
TABLE I V .
CORRECTION SCHEME
A b s o r p t i o n a n d A t o m i c Number Author Henoc Solomon Ruck 1i d g e Smith Duncumb Bomback Henoc-cf Borile Packwood F r o s t -MK2 Mason-MK1 Shaw Gray
Kimoto Pascal Heinrich Reuter Mor i c e a u
A t o m i c Number St R P-F ( x ) DR DR DR DR St R DR DR DR DR QR DR Poole-Thomas, Monte-Carlo-m DR-m SI R Si R
H
H DS H H
DS H H H H , P-corn. DR
Zeller
SI
Colby Go I d s t e i n Woodyatt Boyd
R , PT DR Ziebold DR P-F (XI PT DR Springer P-F (XI RL T o n g , Thomas D R , PT, Z i e b o l d Poole-Thomas Thomas J i Si R Tong, P-F(x) T h o m a s , Thomas-m none
so
Tixier Beeson Springer Hobby Rucklidge Beaman Lifshin Brown Frazer H el g e sson Criss Wolf
Secondary Fluorescence
Absorption
H DS H
Zeller-R
DS, P Monte-Carlo-m H
P H I DS H H H DS, P H DS H DS DS DS P Andersen-W , G r e e n DS, H , P DS DS, P H Tong, P - / ( x )
Criss P
*
Characteristic
Continuous
Henoc-Maurice Reed-a Reed-e Reed-a Reed-a Reed-e none Reed-a Reed-a Reed-a Reed-a Reed-a Reed-e C , Reed-a Reed -a-m Reed a ;m Reed-e Reed-e Reed-e Reed-e Reed-e C , Reed-a, B i r k s , W Reed-e C , Reed-e, B i r k s Reed-a C -w Reed-e Reed-e Reed-e C , R e e d - a l e , Reed-m
Henoc none none none none none Henoc none S p r i n g er none none none none none Henoc-m none none none none none none none none none none none Springer none none none
Reed-e Reed-e,
none Henoc none none none Castaing
-
C,
c-w
none Criss
w
W , W-m
* t h e a b b r e v i a t i o n s are a s s o c i a t e d w i t h r e f e r e n c e numbers a t t h e b o t t o m o f t h i s t a b l e . m.........modified by t h e program a u t h o r DS........Duncumb and S h i e l d s u v a l u e i n t h e P h i l i b e r t e x p r e s s i o n (C=2.39; n=1.5) H... . H e i n r i c h ' s u v a l u e (C=4.5 o r 4.25; n=1.65 o r 1 . 6 7 ) u s e d i n P h i l i b e r t $ ( r , ) DR Duncumb a n d R e e d R.........Backscatter c o e f f i c i e n t from Bishop S, R......stopping power, S , from B e t h e and b a c k s c a t t e r , R, from Bishop J, S, R...same a s S , R e x c e p t u s e D R v a l u e s f o r J , t h e mean i o n i z a t i o n p o t e n t i a l P.. .Philibert P-com.....uses t h e c o m p l e t e P h i l i b e r t e x p r e s s i o n w i t h DS 0 PT........Philibert and T i x i e r C.........Castaing Reed-a....Reed's approximate expression Reed-e.. .Reed' s e x a c t e x p r e s s i o n W.........Wittry C-W C a s t a i n g formula u s i n g W i t t r y v o l t a g e dependence RL.. .Reed-Long; F ( O ) = ( z / A ) ( 4 . 7 + 0 . 9 l n ( E o - E c ) - l n z ) ( 1 / R ) l)........uses P ~ ~ z 2 .r 4a t h e r t h a n Reedk v a l u e of 4 . 2 2).. k i s c o r r e c t e d f o r c o n t i n u o u s f l u o r e s c e n c e u s i n g t h e Henoc-cf program
..... ........
$(x)
......
. ....... .....
......
references: D S ( 5 0 ) ; H ( 5 1 ) ; DR(52) ; R ( 5 3 , 5 4 ) ; S ( 5 5 ) ; P ( 5 6 ) ; P T ( 5 7 ) ; C ( 5 8 ) : R e e d ( 5 9 ) ; W(60,61); R L ( 6 2 ) ; Poole-Thomas(63); Z i e b o l d ( 6 4 ) ; B i r k s ( 6 5 ) ; S p r i n g e r ( 2 9 , 6 6 ) ; FIenoc(67); Thomas(68); Tong(69); Andersen-W(70); G r e e n ( 7 1 ) ; C r i s s ( 3 8 , 7 2 ) ; H e n o c - M a u r i ~ e ( 7 3 ~ 7 4 ) .
1548
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
Table V. Characteristic Fluorescence Correction (81-92). The completeness of, the ease in performing, and the constants used in the characteristic fluorescence correction are indicated in this Table. COLUMN 2-Fluorescence-KL, LL, and LKindicates that KL(Ka excites La) etc., fluorescence can be corrected for; all programs containing a fluorescence correction procedure (see Table IV) can treat KK fluorescence. COLUMN 3-Fluorescence-K/3 and LP-indicates whether o r not fluorescence excitation by KP and/or LP lines can be corrected for. COLUMN 4-Fluorescence-Bypass-indicates whether o r not the fluorescence correction can be omitted, generally by an input instruction. COLUMN 5-FluorescenceDecision-indicates if the decision as t o the need for a fluorescence correction is made within the program (internal) or by the analyst (external). I n multicomponent systems, the determination of the possibility of characteristic fluorescence can require many minutes with wavelength tables and preparing the input can require several more minutes. Thus, it is important t o know if fluorescence is ascertained internally or externally. COLUMN 6-Fluorescence-a-indicates whose expression for u [one of the fitting parameters appearing in the Philibert expression for f ( x ) ] is used in the characteristic fluorescence correction, notwithstanding that used in the absorption correction: P = Philibert; D S = Duncumb and Shields; H = Heinrich; LB = Lenard and Becker. This u is not to be confused with the standard deviation. COLUMNS 7-10-Source of w(K), w(L), r(K), and v(L)-indicate, respectively, the source of the values used for the K fluorescence yield, L fluorescence yield, K absorption jump ratio, and L absorption jump ratio. Table VI. Compound Standards and Calibration Capability. This Table is concerned with the programs ability t o handle compound standards and perform calibration calculations in which an expected probe ratio is calculated from 2-5-Compound Stana n assumed composition. COLUMNS dards-columns 2 through 5 indicate, respectively, whether or not compound (nonpure) standards can be used, the number of such standards that may be used in a single system analysis, the maximum number of elements a standard may contain, and whether or not the program will correct for characteristic fluorescence of the analytical line in the standard. COLUMNS 6, 7-Calibration Calculations (C + k)-
(81) P. Lenard and A. Becker, in “Handbuch der Experimental-
physik,” Kathodenstrahlen, Akad. Verlagsges, Leipzig, 1927 XIV, p 178. (82) J. W. Colby, USAEC Report NLCO-917 (1964). (83) R. W. Fink, R. C. Jopson, H. Mark, and C. D. Swift, Reo. Mod. Phys., 38, 513 (1966). (84) J. Laberrigue and P. Radvanyi, J. Plzys. Radiirm, 17, 944 (1956); C. R . Acad. Sci., 242, 901 (1956). (85) J. Laberrigue-Frolow, P. Radvanyi, and M. Langevin, J. Pliys. Radium, 17, 530 (1956). (86) E. H. S. Burhop, “The Auger Effect of Other Radiationless Transitions, “Cambridge University Press, London, 1952. (87) H. L. Hagedoorn and A. H. Wapstra, Nucl. Phys., 15, 146 ( 1960). (88) M. Green, in “X-Ray Optics and X-Ray Microanalysis,” H. Pattee, V. Cosslett, and A. Engstrom, Ed., Academic Press, New York, 1963, p 185. (89) B. Lindstrom, Acta. Radio/. Suppl., 125, 39 (1955). (90) J. Frazer, S.I.O. Reference No. 67-29, Institute For the Study of Matter, University of California at La Jolla, Calif., 1967. (91) K . F. J. Heinrich, in “The Electron Microprobe,” T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry, Ed., John Wiley & Sons, Inc., New York, 1966, p 296. (92) M. A. Listengarten, Izc. Akad. Naak. SSSR, Ser. Fiz., 24, 1041 (1960); 26, 182 (1962).
indicates whether or not the probe ratio can be calculated from a n assumed concentration and, if so, whether or not the data can be plotted out as k us. C in a binary system. Table VII. Excitation Potentials and Mass Absorption Coefficients refs. (93, 94). I n this Table the values used for E, and pip and the ease with which they may be altered are indicated. COLUMN2-Mass Absorption CoefficientsStored-“yes” means that either (pip) or c and n (using (p/p) = cX“) values are stored. A number following “yes” indicates that p/p values are stored for this number of elements only. “no” means p/p values are part of the experi3-Mass Absorption Coefficientsmental input. COLUMN Author-indicates the literature source of the stored pip values and whether they are tabulated values (T) or calculated 4within the program (C) using pip = cX”. COLUMN Mass Absorption Coefficients-Experimental Input-indicates whether or not the experimental input may contain p / p values selected by the analyst that will override any perma5-7-Range of Excitation nently stored values. COLUMN Potentials Used-K, L, and M-indicates the range in atomic numbers of the analyzed line for which K, L , or M excitation is assumed. “x-ray line input” means that all E, values are stored within the program and the analyst indicates the use of a K, L, or M line in the experimental input. “input E,” means the excitation potential of the analyzed line is part of the experimental input. COLUMN8-Alteration of E,“perm” means that E, can be changed only by altering the value in the permanent data file and “expt.” means that E, can be changed by including it, along with a n instruction, in the experimental input. Some programs limit the choice of the analytical X-ray line by fixing the value of E , within the program; column 8 indicates the facility with which this limitation may be overcome. Table VIII. Experimental Input Requirements. These are the quantities that must be input every time a correction is performed. The greater the number of these, the greater will be the chance of error and the longer the time required to prepare the input. I n cases where a program contains a separate data handling routine, the experimental input requirements may be substantially reduced if the investigator chooses to use the intensity ratio as input. I n the Table, each quantity which is required in the experimental input, as differentiated from parameters permanently stored within the program, is indicated by a 0 . Table IX. Computer Output. These are the quantities that are printed out by each program. The user bewarethe more is not always the better. Each quantity which appears in the computer printout is indicated by a . I t would be impossible to list all input and output parameters which have been encountered. We have tried t o list the most important quantities and also those that are common to several programs. In addition t o the output indicated in the Table, the Pascal program prints out the distribution in energy and depth of primary electrons, ~ ( p z )and , the range. Some programs designed for use in geological applications include structural information and weight per cent oxide as part of the output (see Table XII). The Henoc-cf program includes in its output: the emergent intensities from an alloy and standard due t o continuous fluorescence; the emergent intensity from a standard due t o excitation of the primary electron beam, Heinrich’s u (51), Duncumb’s (79) R and f(x).
(93) T. K. Kelly, Trans. Inst. Mitring Met., B75, 59 (1966). (94) R. Theisen and D. Vollath, “Tables of X-Ray Mass Attenuation Coefficients,” Verlag Stahleisen mbH., Dusseldorf, 1967.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
1549
a >e h
ld
c
0 N
m
LI h
$4
a
m
z 0
H
I3
i a
- 0
m~
m m
0
U
wU z
w
U
e,
cr)
w a
0 3
0 c G* k 3
m u m
4 rJ4
A d
U
V
m
H
I3 (r]
H
e: w I3
3a:
3: U c c
3
w4
m
a: I3
-
m X
r c
00
N r i
m!d!d
1550
0
C 0
d
c
0
rn K O * m m m m m a, 0 0 a, 0 0 0 a, a, a, a, 0 0 a 0 0 0 0 0 a m 0 0 0 0 c3 0 u al a, 0 a, rn he c h C c C hhhhc C he C C C c C C G x C hx h C hx
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
TABLE V I .
Author Henoc Solomon Ruck l i d g e Smith Duncumb Bomback Gas t Henoc-cf Borile Packwood F r o s t-MK2 Mason-MKl Shaw Gray Ximoto Pascal Heinrich Reuter Moriceau Zeller Colby Go Ids t e i n Boyd Bence so Tixier Beeson Springer Hobby Rucklidge Beaman Lifshin Brown Frazer Lachance Helgesson
COMPOUND STANDARDS AND CALIBRATION CAPABILITY
Compound S t a n d a r d s Elements/ Fluorescence i n Number Standard Standard 5 ves any 7 no 15 103 Yes 20 any Yes 8 8 no
10
10
10 12
10 12 10
10 8
8
8
2
10
10
any any 12 8
any 10 12
na
C a l i b r a t i o n C a l c u l a t i o n s (c+k) G r a p h i c a l Output
no yes no no yes’ no no no no no no no no no no no no no no no
2
no
9
no no no Yes yes no no no no Yes
9 20
20
any
11
8 14 see 2
14 10
15
15
10 18 any
10 18 3-10
8
Criss Wolf
no
no Yes no no no no
1) some hand c a l c u l a t i o n s r e q u i r e d : 2 ) t h e maximum=the number of components; 3 ) f i v e e l e m e n t s p e r i n t e r n a l s t a n d a r d and t e n e l e m e n t s p e r e x t e r n a l s t a n d a r d : t h e r e a r e s i x t e e n p e r m a n e n t l y s t o r e d ( i n t e r n a l ) s t a n d a r d s c o n t a i n i n g f i v e e l e m e n t s o r l e s s ; 4 ) i n t h e c o r r e c t i o n program which d o e s n o t c o n t a i n d a t a h a n d l i n g f e a t u r e s ; 5 ) i n a s e p a r a t e program.
Table X. Input-Output. Listed here are some important input-output features and, in addition, some evaluation of the input and output capabilities. COLUMN 2-Data Fileindicates whether or not there is a file of permanent input data containing all of the required physical constants ( p i p , z, A , E,, R, S , J , W , r , X, etc.). The number indicates that data are supplied for that number of elements. “all” means data are stored for all atomic numbers. COLUMN 3-Experimental Input-Format-“free” indicates the use of free field input without any column restrictions and with the decimal included in the input; “fix-D” indicates the use of a fixed field with the decimal unspecified, i.e., appearing anywhere within the field; “fixed” indicates fixed field with specified decimal, i.e., the decimal is not normally input; however, if it is, the format is usually overridden. COLUMN 4-Experimental Input-Easeis an indication of the ease with which the experimental input can be prepared, The relative scaling factor ranges from 1 for easy to 5 for difficult. COLUMN 5-Computer OutputIndividual Corrections-indicates that in some manner the magnitude of all of the individual corrections (absorption, atomic number, characteristic fluorescence) can be determined from the output. COLUMNS 6, 7-Computer Output-Complete and Clarity-are relative ratings, in the first case indicative of the completeness and in the latter of the output clarity. The completeness factor ranges from 1 for abundant
to 4 for limited and the clarity factor ranges from 1 for clear 8-Computer Output-Normalizedto 4 for vague. COLUMN indicates whether or not the final calculated concentrations are normalized. “yes” means that the concentrations before and after normalization are provided. This completes the description of the programs which, brief as it is, hopefully will provide sufficient information t o allow the analyst t o select the particular program that best meets his requirements. COMPUTER PROGRAMMING
Before presenting the overall program evaluation, several aspects of the programming of microprobe corrections will be discussed, and a concept of the content of a good program should emerge. To the extent that an existing program contained or lacked the features encountered in this discussion, it was ranked relatively high or low. This information should be of use t o any investigator wishing to make a program selection or develop a new program. Computational Aspects. Hand calculations are simplified by performing in order the fluorescence, absorption, and atomic number correction ( Z 2 F ) (57) and some programs function in this manner (sequence). With a computer, once a composition is assumed, all the quantities that are functions of concentration, such as 7 , f ( x ) ’ , and F(O)’, should be cal-
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
1551
.!J
a X
a!
..
"
..
. , 6.
0
m
d
m
ul
c
CJ
m
N
m I m r-
\D
V V
A
A I A\
w
m I m
0
m
moo
a, ul
N
I
03
m
CO
a
d
a,
e H
.. -em
N
c
1 !-!
e V m a,
s
4J
.d
3
4J
0
I N r l
%I %I
mrl r
m m V
l
v)m m m
v/ v/
In
m I
c a, m .d
a,
c
H
-.. m m h
7
Y
c
d
m
x
a
m
v
cm
rl
a,
.
9
'd a,
4J V a,
rl
a, ul
rl v
h
m k u
..
h
a, Q 4J v)
rl
m
v
.c V
1
.d
4J
4.J
.d
a,
.c
a, 5:
E
rn
m
m
c
4J
V .d
w w
a, 0 U
h
4J
Iv
B H B V H
e
0
.d
4J
a !-!
0
2
uu c V
B H
c c v u
V
c
a,
E
rl
!-! a, N
Id !-I
F
a,
e V m
c"
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
c
-.. 0
m
Y
h a,
m
k h
a,
v)
h 0
w
v
rl rl
v)
w
0
v)
m
k
m
! !
d31NMOUf 3lOA
I
SSI tl:
! ! I ! I ! ! ! ! ! I ! ! ! I ! ! ! I ! ! I I ! ! ! ! ! !
NOSS3Dl3 t 33NVH3V" tl3ZVtl:
NMOtlg NIHSJI' NVWV31
39011)13nt AEEOt U3DNltld! NOS33t
natxti
0
0
!
4
I I ! I
! ! ! ! ! ! ! ! ! ! ! I ! I
I
! ! ! ! ! ! ! ! ! ! ! I ! ! ! AVUE ! MVHI ! ! 1 XW - NOSVH ! ! z Y W - ison. I ! I 000MY3Vr ! ! ! aiitloE ! ! 33 - 30N3C ! ! U3HSIJ ! lSVE ! ! ! mvawoa ! ! ! I I ! I ! ! ! I I I ! !
0 . 0 0 .
0
I
!
! ! !
! ! !
! !
I
! I
!
!
I
4
!
! I
! ! I
! !
! ! !
! ! !
! ! !
I I
! ! !
!
!
! !
! ! !
I
!
!
I
I
! ! !
!
!
J
1
?
ii
I
Y
U J
L
Y
C
ij
2
U
2 > > L
W CT K
Y
i
5
, 1
J
2
f
J
?
! 2
r:
2
1
2
; g
i C
I ?
J
;2
ii I
5
>
I
1
t
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
1553
i-tt JlON
!
ssin:
! I
!
I I
!
!
!
I
0 0 8
~
!
!
I
$I
I
I
! !
0
I
I
! ! !
!
! !
I
!
I
!
!
I
!
! !
I
!
! I I
! !
m
!
! I
B
!
! !
! !
!
!
! ! ! !
!
o!
y
A
m
La
C
u
I
4
1
i
!
P
1 /
2
z
L
1
:
1
I
a
,1554
i e
r
5
5
I
?
i
E
I
ANALYTICAL CHEMISTRY, VOL. 42,
NO. 13, NOVEMBER 1970
TABLE X.
INPUT-OUTPUT Computer Output
Experimental I n p u t Author Henoc Solomon Rucklidge Smith Duncumb Bomback Gast Henoc-cf Borile Packwood Frost-MK2 Mas on -MK 1 Shaw Gray Ximoto Pascal Heinrich Reuter Mor i c e au Zeller Colby Goldstein Woody a t t Boyd Bence
so
Tixier Beeson Springer Hobby Rucklidge Beaman Lifshin Brown Frazer Helgesson Criss
Wolf
Data F i l e yes-41 yes yes-18 yes-all yes-82 Yes yes-10 yes-13 no yes-16 yes-all yes-all yes-z>lO yes-all no Yes no no yes-85 no yes-all yes-all Yes yes-47 yes-11 no yes-25 yes-73 yes-all Yes
yes-18 yes-all no no yes-all no no no
Format fixed free fixed free fix-D fixed fixed fixed fixed free fixed fixed free fix-D free free fix-D free free free fix-D fixed fix-D fixed fix-D fixed free free fixed free fixed fix-D fixed fixed
Ease
Individual Corrections
Complete
Clarity
1
2
1 1
Normalized no Yes no Yes no
2
1
1
2 2
4
Yes
4 4 5
4
3
5
2 1 1 1 1
1 1 1
3
1
1
2
2
3
3
2’ 2
1
3
3
1
4 2 1 5 2 5
3 3 4
3
3 1
2
3
3
1
4
3
3
3
4 1 1
1
1
2 2 1
3 3
2 3 1
5
1 3
1 1
3
3 1 4
1
3
3 4
1 4
2‘
3
3
2 4
2
1 1
2
5
4
2 5 5
2
2 2
4
3
J.
no no no no
Yes Yes
no no Yes Yes
no no no Yes no no yes no no no no no no no Yes no no Yes no
no
1) more d i f f i c u l t i f element i s n o t i n t h e s e t of 18 elements: 2 ) atomic number f a c t o r only: 3 ) f l u o r e s c e n c e f a c t o r only: 4 ) a b s o r p t i o n f a c t o r only: 5) some hand c a l c u l a t i o n r e q u i r e d ; 6 ) only normalized v a l u e s
are printed out.
culated and the calculated composition obtained in a single step (complete) from Equation 1 (seeTable 111; column 5 ) . Some programmers calculate the concentration of element A , assuming concentrations for all others; then do the same for element B, and so on until C, is obtained. Very often the calculated value of CA is not used in the determination of C ,, etc. Any calculated value of concentration should be used in some manner (e.g., a new estimate based on the latest guess and calculated value) in later calculations of other elements, and then the entire sequence repeated [as in the Bomback (6) program]. The proper method for estimating the concentrations for use in any calculation should be established. We are presently studying the differences in concentrations and sums of concentrations obtained using different methods of calculation within a constant correction scheme. The simultaneous determination of all compositions appears t o be most suitable. The Lachance (36) program, utilizing an empirical approach, is one that provides the solution to n simultaneous linear equations of the type:
simultaneous determination of concentrations. They assume that the concentration variables are separable and write GU = Z’A’F’/ZoAo exp(1n G,O)
where G, is the G value for the standard and equals one for a pure material. The Z A F factors are given in the paper by Zeller (20), are not functions of concentration, and are calculated by the first of two programs. Z ’ , A ’ , and F’ are calculated for an infinitely dilute ij alloy (C, .-,0, Cj-+ l), an approach used previously by Ziebold and Ogilvie (76) in the calculation of a coefficients for use in Equation 3. The backscatter correction R is calculated in a manner developed by Zeller who claims good agreement with experimental ratios in the range 12 < z < 30. The stopping power is calculated in the usual manner but uses an expression for the mean ionization potential derived by Zeller. The fluorescence and absorption factors are based on the expressions of Reed (59) and Philibert (56) [modified by Heinrich (51)], respectively. The second program uses the Gij values t o solve a set of n simultaneous equations relating k , C, and G where n
In k c - In C iThis approach is mathematically appealing, but the accuracy is affected by the assumptions made in calculating aAn (assumed constant) and the extrapolation required in multicomponent systems. Zeller et al. (20) have also developed a technique for the
C, In Gc5 = 0 3=1
Since the G, values are not functions of concentration but depend only on the elements present and instrumental parameters (take-off angle and EO), they may be retained and used in the same manner as a coefficients are used. It is
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
1555
unfortunate that these authors were unable to use their program to correct the data in the three test systems. The convergence method used in estimating new concentration values should prevent divergence and provide efficient convergence (see Table 111, column 6). Reed and Mason (95) have thoroughly examined iterative techniques in binary and ternary systems and found that simple iteration (uses calculated value from preceding cycle) infrequently leads to divergence in cases of a severe absorption correction, Averaging (average of last two cycles) and hyperbolic worked better, but not as well as Aitkens delta-squared or Wegstein (96), the Wegstein method being preferred because it required the fewest iterations. Our own experience in comparing the averaging and Wegstein techniques confirms this. Correction in ten AlM g alloys required 65 and 35 iterations for the averaging and Wegstein techniques, respectively; however, the total processor times involved were 48 seconds for averaging and 50 seconds for the more complex Wegstein formulation. The Wegstein technique is still preferred, notwithstanding this small time difference, because it generally avoids divergence. Colby (97) has reported divergence with the Wegstein method in some extreme cases. A maximum number of allowed iterations of 20 (Table 111, column 7) is more than adequate with the Wegstein technique. We have never encountered a case involving over ten iterations, Consequently, having the number of iterations be part of the input appears unnecessary. Iteration should continue until successive approximations differ by less than a n amount which is part of the experimental input. Setting (Cn-l - C,-2)/C,-l in the range of 0.1 to 1.0% seems appropriate in view of present experimental and correctional precision, while a fixed value of 0.01 (Table 111, column 8) would lead to additional iterations with no additional information. Testing for convergence should be carried out after each iteration t o avoid unnecessary computations. The number of components should be a variable, preferably without limit; however, a maximum of 20 will certainly be sufficient in most systems regardless of discipline (Table 111, column 2 ) . Many program users prefer that in any particular system the number of elements for which corrections are t o be made be variable, i.e., in a system of n components corrections for 1 through n elements should be possible, the common case being the correction of n. Even though many of the correction procedures have innate atomic number and acceleration potential (Eo) limitations, such limitations should not be programmed into any future programs because, as improved correction techniques become available, it will be necessary to use the program a t lower z and kV values (Table 111, column 4). It is particularly disconcerting to be unable to correct a heavy element in a system which contains a n unallowed element. The analyst, however, should be aware of the limitations of the different correction procedures and the difficulties encountered in the analysis of low atomic number elements, e . g . , uncertainty in p i p at long wavelengths, contamination, chemical bonding effects on peak shape, intensity, wavelength, etc. Duncumb et al. (98) suggest the Duncumb and Reed correction be used for z 2 11. (95) S. J. B. Reed and P. K. Mason, in Trans. Second Natl Conf. Electron Microprobe Analysis, July 14-16, 1967, Boston, Mass., Paper No. 12. (96) R. H. Cavett, Amer. Petrol. Znst. Proc., 43 (111), 57 (1963). (97) J. W. Colby, open discussion at Fourth National Conference on Electron Microprobe Analysis, July 16-18, 1969, Pasadena, Calif. (98) P. Duncumb, P. K. Shields-Mason, and C. da Casa, in, “Fifth International Congress on X-Ray Optics and Microanalysis,” G. Mollenstedt and K. Gaukler, Ed., Springer-Verlag, Berlin, 1969, p 146. 1556
ANALYTICAL CHEMISTRY, VOL. 42,
In some applications it is desirable to measure different elements at different acceleration potentials (Table XII). In geological applications, operation at about 15 kV is common with higher voltages used only for atomic numbers above 22 to 25, The assumption that k does not vary significantly with EO is often employed in determining compositions. This procedure is not rigorous and should be used with caution based upon experience. In a binary system, kB is not required in the calculation of Ca so the two elements can be studied at different acceleration potentials and a rigorous determination of composition made. It should be possible to determine at least one unmeasured element by difference (Table 111, column 9). The probe ratio for this element can be estimated and must be used in the computations. More than one element can be determined by difference if the elements are present in a fixed ratio or are stoichiometrically related to other measured elements. It is obviously not acceptable to measure two elements in a ternary system, make the calculations in the binary system, and assume that (100 - CA - C), is the concentration of the missing element. Since most geological samples contain large amounts of oxygen, an element often not amenable to accurate analysis, it is usually necessary to determine oxygen by difference. The relationship between the elements in the unknown and the oxide forms in which they exist should be included in the program o r as part of the experimental input. Elements that exist in more than one oxide state require special handling (as in the Frost-MK2 program). Any new program should be thoroughly checked for computational accuracy before it is distributed. This can be accomplished by hand computation or by comparison with the results of earlier investigators. Upon request the authors will provide the physical constants and experimental conditions for the three test systems used herein and indicate which results in Table X I were obtained using these constants. Experimental Input. The importance of this aspect of a correction program has been neglected by many authors (Table VIII). I t is the nearly unanimous opinion of the users encountered that none of the programs they have used possess simple input; however, in some cases familiarity with the program has established the essential ease of input. If routine correction is to be made, it is mandatory that the necessary physical constants be contained within the program or permanently stored on disk o r tape (Table X, column 2 ) . This file should be accessible for truly easy modification as is usually the case in time sharing systems. If the investigator must look up and input physical constants in a multicomponent system, errors are likely and boredom and a reduction in the amount of quantitative work he engages in is a certainty. The argument that the investigator should possess a knowledge of the required constants is negated by providing output options that reveal the constants used. Serious efforts should be made to be certain that this permanent data file contains those physical constants which represent the best values at the time the program is written (Table V, columns 7-10; Table VII, column 3). Input options are required. The standard input should be one which consists of identification of the components and the analytical X-ray line for each, take-off angle, acceleration potential, experimental probe ratios, and several simple instructions indicating the type of calculations desired. Such input will accommodate most metallurgical systems. Input options which would add to the complexity of the input are required for problems in geology, whenever compound standards are used, and if data reduction is desired. The
NO. 13, NOVEMBER 1970
TABLE XI.
CALCULATED' CONCENTRATIONS OBTAINED IN
THREE ALLOY SYSTEMS
USING DIFFERENT COMPUTER PROGRAMS A l l o y s Sys tems Element Experimental Concentration True Chemical Concentration Author Henoc
Solomon Rucklidge* Smith* Dun cumb * Bomback* Borile* Packwood* Frost-MK2 Mason-MK1 * Shaw* Gray* Kimoto Pascal Heinrich* Reuter
*
Moriceau Colby Goldstein*
so Tixier Beeson Springer Hobby R u c k li dge Beaman* Brown Frazer Olsen
a/c
Ti-Nb
authors
Mo
-
Ni -
79.7
7.7
49.4
52.5
80.6
9.4
43.6
56.6
63.5 64.9 63.8 65.3 65.8 64.5 66.1 63.3 63.3 64.4 65.5 65.7 64.7 64.3
Calculated Wt.% 10.5 80.8 9.6 9.8 80.7 10.4 10.3 80.6 9.9 10.4 80.7 9.9 10.3 80.7 9.9 10.6 80.8 10.0 10.3 80.9 10.1 10.5 81.4 9.3 80.7 10.2 9.9 80.7 10.2 9.9 10.2 80.7 9.8 80.3 10.2 10.3 10.1 80.0 9.8 10.0 80.5 9.5 10.5 80.8 9.6 10.4 79.8 9.8 10.5 80.9 9.9 10.4 80.7 9.6 10.1 80.7 9.9 81.3 10.0 9.4 79.2 10.9 9.1 80.7 10.0 10.0 81.1 10.0 9.4 81.4 10.7 9.3 10.2 80.6 9.7 81.0 9.9 9.9 10.4 81.3 9.2 81.1 9.8 11.8 80.2 10.4 10.8
45.1 43.6 45.0 45.5 45.0 45.3 45.0 44.3 45.0 45.1 45.0 45.0 43.8 44.1 45.1 44.0 38.7' 4 5 .O 44.4 44.0 45.1 46.2 44.2 44.7 44.8 44.7 44.7 46.0 46.1
56.1 56.9 56.0 55.9 55.9 56.3 56.3 56.7 55.9 55.9 55.9 55.0 56.1 55.9 56.1 56.0 55.9 56.1 56.0 56.5 54.2 56.1 57.4 56.8 56.1 56.7 56.7 54.6 55.9
65.0 1..o 1.5
10.3 0.4 3.8
80.7 0.5 0.6
9.8
44.8 0.6
56.1
0.3
3.1
1.5
10.3 0.2 1.9
80.8 0.2 0.2
9.9 0.2 2.0
45.0 0.3 0.7
-
co -
32.6
62.0
11.7
35.0
65.0
9.9
36.1 32.3 34.9 .34.7 34.7 34.9 35.3 35.4 34.6 34.6 34.7 34.3 34.0 35.1
64.0 68.0 65.0 65.7 65.3 65.4 65.4 65.6 65.4 65.5 65.1 65.0 66.0 64.3
36.5 35.8 36.0 34.7 33.5 33.3 34.3 35.4 36.5 34.4 35.3 34.6 35.8 35.3 34.9 0.9 2.6 34.8 0.3 0.9
F e -N i
Cr-Co-Mo Nb -
Ti
Cr
65.3 0.2 0.3 1 ) c a l c u l a t i o n s made f o r t a k e - o f f systems a n d 2 5 kV i n Fe-Ni s y s t e m ;
-
Fe
0 ..6
1.1
56.0 0.4 0 -7 angle=52.5', 2 0 kV i n Ti-Nb a n d Cr-Co-Mo 2 ) o m i t t e d i n c a l c u l a t i n g t h e mean and
standard deviation. * A u t h o r s u s i n g s i m i l a r c o r r e c t i o n s c h e m e s ( D R , DS, H, R e e d ) .
use of free field input (Table X, column 3) would reduce significantly the possibility of input errors and simplify the investigator's work ; however, the programmer is restricted by available hardware. The take-off angle, 9,should be part of the input or alterable with an override instruction (Table 111, column 3). This will allow the investigator t o use data taken from the literature and to study the effect of variations in 9. A program without this feature would be useless to investigators using probes in which the take-off angle varies with Bragg angle. If the investigator has to alter 9 or csc $ within the program, he will only be able t o run using a single value of in any particular instance; however, if he has only one type of instrument and no particular interest in the data of others, such an arrangement would be satisfactory. Because of the uncertainty in pip and the continuing appearance of "improved fits," the option to input selected pip values, thcieby overriding those stored within the system, must be available (Table VII, column 4). At the present time the most popular and satisfactory (complete and good fit t o best available data) list appears t o be that of Heinrich (91).
Some redetermination of the c and n ( p i p = cX") values is needed in ranges where new experimental values have become available (99, 100). J. Colby is presently preparing a new ( p / p ) tabulation. A single system input is required when a large set of data points are t o be collected in the same alloy system, e . g . , in diffusion or phase diagram work (Table XII). The user should not have to provide complete input information for each data point. Likewise, in the performance of calibration calculations, a single system input should be used for the entire composition range of interest and for any desired compositional increment. Since it is a nuisance to have to input E, values, as in ten programs, the ideal situation is where all values of E, are stored ( K , L , M> and the program selects the proper value based upon an indication of the X-ray line
(99) G. D. Hughes, J. B. Woodhouse, and I. A. Bucklow, Brit. J. Appl. Phys., Ser. 2 , 1, 695 (1968). (100) P. Lublin, P. Cukor, and R. Jaworowski, Aduan. X-Ray Anal., 13, 632 (1970).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
1557
used in the experimental input, as in nine programs (Table VII, columns 5-7). Correction of Intensity Data. With any new program it should be possible to correct intensity data for background, drift, and deadtime (Table 11). Such capability should exist as an option and not as a procedure that must be utilized in every problem, as in some programs. I n view of the sophistication now existing in quantitative probe analysis, it is surprising that these “simple” experimental corrections are not uniformly applied. Consider the background correction. In some programs it is not possible to correct for background using off spectral peak measurements, which is certainly the most satisfactory method. In some cases the backn
ground intensity in the analytical line is given by i=A
CtBi
where Bt is the background intensity measured at the spectrometer setting for element i using, as a target, a n element with an atomic number close to that of element i. Such a procedure is not always accurate, e.g., using a 1120 quartz crystal the mean off peak intensity for C r K a was 2.1 cps while the intensity from M n at the C r angle was 0.7 cps. It is well known that peak to background ratios can vary significantly depending upon the technique used for measuring background. Some programs plot B , us. atomic number or specimen current and then use the observed specimen current or a mean atomic number to calculate the unknown background. The technique expressed by Equation 2 is the most popular. Some programmers calculate the background only once using normalized probe ratios for Ct while others calculate it during each iteration using the calculated concentrations for C,,the latter approach being preferred. The primary reason for the use of these expressions is presumably due to the fact that in complex materials interfering spectral lines make it difficult t o select a n appropriate location for measuring off spectral peak backgrounds. Recent crystal improvements help to alleviate this problem; however, the validity of the approximations involved in these expressions needs to be determined experimentally because in some cases such estimates are necessary (phase analyzer, energy dispersive spectrometers, concentration mapping, geological applications). The most satisfactory correction is obtained when it is possible to measure off spectral peak intensities in the unknown and standard and this type of input must be accommodated. A deadtime correction should be applied using the proper expression. F o r measured intensities below 30000 cps and 7 values below 3 psec, the Ruark (101) expression (m/n = ljl n ~ may ) be used; however, Beaman, Isasi, and Lewis (102) have shown that this expression does not always apply. They found that when the amplifier pulse width was greater than the P H A pulse width, the counting efficiency was given by m/n = ecnr where T is the amplifier pulse duration. Since T depends on the electronic components whose characteristics may alter with age, are often repaired and/or replaced, it would appear best to have T be part of the experimental input o r a t least have a n override possibility. Approximate expressions, such as n = m (1 mr), need not be used. The correction for instrumental drift is not an easy one to perform because the cause of drift is difficult to establish and often differs from instrument to instrument. Most authors measure the peak intensity on the standard at the beginning and completion of the measurements o n the unknown, as-
+
+
(101) A. E. Ruark and F. E. Brammer, Phys. Reu., 52, 322 (1937). (102) D. R. Beaman, J. A. Isasi, and R. Lewis, in Proc. Fourth Natl Con5 Electron Microprobe Analysis, July 16-18, 1969, Pasadena, Calif., Paper No. 13. 1558
0
sume the drift to be linear in time, and use the following expression to make a correction. m i o(drift corrected)
=
+ (mzo- m I c )( t i a t )
mIc
where mt O is the standard intensity at time t when the unknown measurement is made, mIo is the standard intensity at the beginning of the experiment when t = 0 and m20 is the standard intensity measured after a time interval A t . Unless some independent experiment has shown the instrument to have linear drift, this approach may be invalid o r at best inaccurate. A few authors monitor only the beam o r specimen current. This also is inadequate since drift in the spectrometer setting, specimen stage (transverse or height), crystal temperature, detector pressure, etc., will not be detected. Monitoring the specimen current is not effective because it varies with the mean atomic number of the target and is, therefore, rather sensitive to such things as oxide formation or removal, carbon deposition, subsurface second phases, etc. Topography and pulse amplitude shifts cause intensity variations that could be mistaken for current drift. The best procedure is to have an instrument in which careful measurements of stability have been made and any problems rectified. Then, in the measurement sequence, the standard intensity should be measured frequently and the closest (in time) value used with each unknown intensity to calculate the intensity ratio. Ferguson (103) provides a unique approach t o the drift problem encountered in trace analysis. Because of the difficulty involved in isolating drift effects, the advisibility of making such a correction within a program is questionable. Consequently the drift correction must be an option, Le., a simple override instruction should eliminate it. Statistical evaluation of measured intensities, m, X-ray intensity ratios, k , and compositions, C, is desirable; however, data rejection must be carefully conceived (Table 11, columns 2 and 3). In a recent evaluation of six commercial probes, it was found that u = s d % , where s varied between one and three (104). Any rejection of intensities must be based on a careful experimental determination of s for the instrument and instrumental conditions utilized. If data rejection o r reliability is not the aim, calculations of u would seem irrelevant. A few programs do provide some statistical evaluation of probe data, but only two programs utilize this information as a guide to data rejection. If data are rejected by the program, the output must indicate what and why points have been rejected. Our own experience has indicated that rejection of k values is useful. When precise k data are sought, several k values are measured on 2-5 different days and in well characterized systems, it is found that u x / k = 0.005-0.01 when k > 0.1. A user is generally interested in the corrected composition and, therefore, in the experimental standard deviation in composition. Only two of the existing programs provide such information (Table 11, column 3). The importance of the statistical evaluation of data makes statistical options essential. It is difficult to design a data handling procedure that will be applicable to all problems encountered. The requirements in the study of a mineral, a diffusion couple, o r a simple alloy system differ considerably. Consequently, the data handling problem could be best treated by providing several input options. Before using or writing a data handling routine, the investigator should be well aware of the experimental errors encountered in microprobe analysis. These (103) L. A. Ferguson, Adaan. X-ray Anal., 9, 265 (1966). (104) J. A. Isasi, Westinghouse Electric Corporation Engineering Report EM-1050, July 1969.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
are thoroughly discussed in recent papers by Heinrich (105), Poole and Martin (106), and Sweatman and Long (107). Many programmers use as input an experimental probe intensity ratio which is corrected for deadtime, background, and drift outside the program either by hand or by using a separate data handling program such as that written by Fisher and Wickersty (MANIP), So and Potts (EPMPl), Rucklidge (DATRAN subroutine), Frazer, Fitzgerald, and Reed (EMX), Boyd, Finger, and Chayes (CONE), Gast and Glover (COMPAR), Shaw, and Bence and Albee. The first of these is quite useful in metallurgical systems; however, it cannot be used in geological applications because it cannot handle nonpure standards. It would be feasible, but not necessarily easy, for an analyst t o complement a program lacking data handling features with one designed specifically for data handling. Separation of the data handling and correction function is desirable in some cases t o avoid the accumulation of vast amounts of concentration information of nebulous value. If an analyst requires data handling, a program containing that capability should be selected. Intensity correction capability is a requirement when the probe is t o be interfaced with a computer. Ingram (108) has designed a workable and inexpensive system for interfacing an ARL EMX-2 probe and Linc-8 computer. More recently Eichen, Kunz, and Matthews (109), Wolf and Saffir (IZO), and Chambers (111) have reported on computerized electron microprobes. Most of the above mentioned data reduction programs will accept punch paper tape input. Output. The complexity of the output (Tables IX and X) of many existing programs is surprising in view of the ease with which it may be programmed. Obviously, all output information should be clearly labeled. Several output options, selected by an input instruction, should be available. The first should consist simply of the system identification and the calculated concentration; this will be the most commonly used option and should not be cluttered with unneeded and unwanted information. Another should consist of, e.g., system identification, the individual correction factors ( Z , A , and F), indication of any fluorescence corrections, EO, probe ratios, and the computed concentrations. It is extremely important that the magnitude of the individual corrections be part of the output (Table X, column 5). Another output option should permit the display of all input data and the physical constants selected by and used in the program. An option to print out the quantities involved in the data reduction option should exist. Just as a separate input is required in geological applications so is a separate output option. Many of the programs studied herein print out the results at each iteration step. If an iteration scheme is selected which avoids divergence, the value of such output is questionable. Correction Scheme. Within the concept of a Z A F scheme, corrections for absorption, atomic number, and characteristic fluorescence effects must be made (Table IV). Omission of any of these effects would greatly limit the usefulness of the (105) K. F. J. Heinrich, in Aduan. X-ray Anal., 11, 40 (1968). (106) D. M. Poole and P. M. Martin, Met. Rev., 133, 61 (1969). (107) T. R. Sweatman and J. V. P. Long, J. Petrology, 10, 332 (1969). (108) F. D. Ingram, in Proc. Fourth Nut1 Conf. Electron Microprobe Analysis, July 16-18, 1969, Padadena, Calif., Paper No. 27. (109) E. Eichen, F. Kunz, and G. Matthews, in Proc. Fifth Nut1 Conf. Electron Probe Analysis, July 22-24, 1970, New York, N. Y., Paper No. 5. (110) R. Wolf and A. J. Saffir, ibid., Paper No. 6. (111) W. F. Chambers, ibid., Paper No. 7.
program. The continuous fluorescence correction has received some attention recently (66, 73, 112, 113). Springer (66), using his own expression for continuous fluorescence, has found the correction to be generally small, usually less than 1 % of the measured intensity ratio, and concludes that neglecting it is usually, but not always, justified. Springer and Rosner (114) reported significant improvements in some computed concentrations when applying the Springer (66) continuous fluorescence correction, but found the correction negligibly small in most cases. Brown et al. (122) in their TEP work, have reported a significant improvement in some of their results when a correction was made. In limited experience with the Henoc-cf (1) program, we have not encountered a correction greater than 0.5 wt %. Kirianenko (115) et al. reported absolute corrections of less than 0.4% in several U alloys. Henoc et al. (73) have illustrated remarkable and significant effects at phase boundaries. Brown (113) has found the correction negligible for K lines if z < 20, and for L lines if z < 50 (71) or for X > 2.1 A. Notwithstanding the magnitude of the correction, future programs should include the correction because improvements in experimental results and other phases of the correction will increase the significance of this effect. In correcting for continuous fluorescence, k in Equation 1 is replaced by ( k - klkz)/(I - ks) where k l = Icr'iIcr" and k2= Zc,o/(Zcr" I D o )IC,' ; is the emitted intensity due to continuous fluorescence in an unknown; IC," is the same for a pure standard; 1,' is the emitted intensity due only to primary electron excitation in a pure standard. The output of the Henoc-cf program includes k l , k 2 ,I,', Zero, and IC,'. Presently we (32) make corrections neglecting continuous fluorescence, calculate k l and kl with Henoc's program using the previously calculated concentrations, replace k with ( k - k l k 2 ) / ( 1- k 2 ) , and then recompute the concentrations. Such a procedure is acceptable only if the correction is small. Since the Henoc program is well conceived and accurate, future programmers might do well to incorporate it as a subroutine with optional use in their own program. Even though such incorporation may not be simple, it would seem that attempting to write a subroutine based on the Henoc (67, 116) expression would represent an extensive duplication of effort and the chances of producing a program as good as Henoc's would appear remote. Brown (113) has reported on a program which contains both the Henoc (67) and Springer (66) expressions. Incorporation of this program, when it becomes available, would allow comparison of the two techniques. The program by Springer (29) is not only of interest as a correction program but also offers an opportunity to study the effectiveness of the atomic number and continuous fluorescence correction procedures proposed by Springer (66). The additional input information required when correcting for continuous fluorescence should be stored within the program. The question as to whose correction procedures should be included in the program (by implication the best available) is
+
(112) D. B. Brown, D. B. Wittry, and D. F. Kyser, J. Appl. Phys., 40, 1627 (1969). (113) J. D. Brown, in Proc. Fourth Nut1 Conf: Electron Microprobe Analysis, July 1 6 1 8 , 1969, Pasadena, Calif., Paper No. 11. (114) G. Springer and B. Rosner, in "Fifth International Congress on X-Ray Optics and Microanalysis," G. Mollenstedt and K. H. Gaukler, Ed., Springer-Verlag, Berlin, 1969, p 170. (115) A. Kirianenko, F. Maurice, D. Calais, and Y. Adda, in X-Ray Optics and X-Ray Microanalysis, H. H. Pattee, V. E. Cosslett, and A. Engstrom, Ed., Academic Press, New York, N. Y., 1963, p 559. (116) J. Henoc, Thesis, University of Paris, 1962, translation by H. Yakowitz, NBS, Washington, D. C.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
0
1559
not easily answered. Table IV indicates the most popular techniques a t this time. The characteristic fluorescence correction proposed by Reed (59) is the most commonly used procedure and the superiority of this technique has been reported (117). It allows for KK, L L , L K , and K L fluorescence, and for excitation by KP and L/3 radiation (Table V, columns 2 and 3). In the expression for y, Reed uses the multiplier P i j (i excitingj) to allow for other than KK fluoresappears because in deriving the expressions for y cence. Pi,. the ratio of the primary intensities, IJZj, is used. Reed measured IL and by comparing it with calculated values obtained the following: PKK = P L L = 1 ; PLK = 4.2, and PK& = 0.24. Heinrich (105) has suggested that PLKshould be 2.4. Brown and Criss (118) confirmed the 4.2 value. Further experimental work is needed. The work of Criss (80) offers a n opportunity for improvement in the characteristic fluorescence correction, an area where improvement would be welcome (117, 119-121). His n
analytical expression for p(pz)
{ p(pz)
= i. = .1
a i exp (- bipz)}
can be used to carry out the integration required in evaluating the expression for If’. Criss (122) has also derived a n expression for (1 y) in terms off()() without using p(pz) and is presently adding it to his program. The Philibert (56) absorption correction modified by Duncumb and Shields (50) is the commonly used absorption correction; note, however, that Duncumb et al. (98) have suggested that the Heinrich (51) values for C and n, where u = C(lO)j/(E,” - E,”), are better than those originally suggested by Duncumb and Shields (50). Beaman (123) has found this to be true in a series of alloys and Boyd et ai. (24) have reported improvement in the sums of calculated concentrations when using the Heinrich constants. Sweatman and Long (107) report marked improvement in the analysis of silica with Heinrich’s CT. Heinrich has published two sets of values for C and n: C = 4.25, n = 1.67 (51)and C = 4.5, n = 1.65 (124). Duncumb et al. (98) have studied 450 binary alloys and silicates and recommend that the latter be used and that no further improvement is to be expected by varying C and n. O n the basis of these reported results, inclusion, in the Philibert expression for f(x), of the Duncumb and Shields u, as modified by Heinrich, is a necessity and probably sufficient at the present time. Monte Carlo techniques are discussed later. It should also be noted that Beaman (123) has obtained good results with the Andersen-Wittry (70) absorption correction. At low atomic number, some authors (69,
+
117, 125) have reported obtaining good results with the modified Tong absorption correction, e.g., this technique worked unexpectedly well in the calculation of F in fluorapatite. The Duncumb and Reed (52) atomic number correction is the most popular correction and Duncumb and Reed (52), Beaman (123), and Duncumb, Mason, and da Casa (98) have all reported excellent results with this procedure in systems where the atomic number correction predominates. Heinrich (105) has found this procedure to be superior to that of Thomas (68). Philibert and Tixier (57) have evaluated, for both pure and complex targets, the integral
SEo
Q,ii(E)dE 1 - dEld(PX) s
where QaiA ( E ) is the ionization cross-section of A atoms for the j level and dE/d(pX) is the energy loss per unit path length, X. They use the expressions for Q and dE/d(pX) of Bethe (55) and Bethe, Rose, and Smith (126) and integrate l/S in terms of a logarithmic integral function. This avoids the earlier assumptions made to avoid the integration where the variables were considered separable-Le., dE/d(pX) = S(z) ./cn(E). fcn(E)and S(z) were evaluated at a mean energy, (Eo E,)/2. Such an approach should improve the atomic number correction. Walitsky and Colby (127) have found that the Philibert and Tixier procedure gave better results than the Duncumb and Reed procedure in the analysis of Cu in three Cu-Au alloys; they used the Berger and Seltzer (128) expression where J = 9.762 5 8 . 5 ~ - O , ~ ~In. the systems studied by Beaman (12.9, the Philibert and Tixier procedure did not provide quite as good results as that of Duncumb and Reed; however, it was significantly better than that of Thomas (68). Note, however, that Philibert and Tixier use J = 11.5 z. Poole (129) reported good results with the Thomas procedure as did Beaman (117). At the present time, inclusion of the Duncumb-Reed and the PhilibertTixier atomic number correction seems advisable. On the basis of the success of the existing techniques in a large number of more or less well characterized systems (97, 105,117,120,123,129), the minimum requirement in a classical correction scheme at this time would include: the DuncumbReed atomic number correction, the Philibert-DuncumbShields-Heinrich absorption correction, and the complete (all possible conditions of fluorescence) Reed characteristic fluorescence correction with access to the Henoc program for the continuous fluorescence correction. Inclusion of the Philibert-Tixier expression and Criss’s expression for (1 y ) would also be desirable. With the exception of the program by Pascal and those based on the empirical approach (761, the programs written for general correction purposes studied herein use classical expressions containing empirically adjustable parameters and separate correction terms (ZAF). The necessity and validity
+
+
+
(117) D. R. Beaman, ANAL.CHEM., 39,418 (1967). (118) D. B. Brown and J. W. Criss, presented at The Fifth International Congress on X-Ray Optics and Microanalysis,Tubingen, Germany, September 9-14, 1968. (119) L. S. Birks, J. V. Gilfrich, and H. Yakowitz, in “Fifty Years of Progress in Metallographic Techniques,” ASTM STP 430, 1968, p 343. (120) J. W. Colby and D. K. Conky, in “X-Ray Optics and Microanalysis,” R. Castaing, P. Deschamps, and J. Philibert, Ed., Hermann, Paris, 1966, p 263. (121) D. R. Beaman and T. P. Schreiber, in Trans. Third Natl Cotlf: Electroiz Microprobe Anufysis, July 31-August 2, 1968, Chicago, Illinois, Paper No. 49. (122) J. Criss, in “Quantitative Electron Probe Microanalysis,” U. S. Dept. of Commerce, National Bureau of Standards Special Publication 298, K. F. J. Heinrich, Ed., U. S. Government, Printing Office, Washington, D. C., 1968, p 53. (123) D. R. Beaman, Mikrochim. Acta, 1969, 117. (124) K. F. J. Heinrich, in Trans. Second Nurf Conf; Electron Microprobe Amlysis, June 14-16, 1967, Boston, Mass., Paper No. 7. 1560
(125) M. Tong, J. Microsc. (Paris),8, 276 (1969). (126) H. A. Bethe, M. E. Rose, and L. P. Smith, Proc. Amer. Phil. Soc., 78, 573 (1938). (127) P. J. Walitsky and J. W. Colby, in Proc. F i f h Natl C o d Electron Probe Analysis, July 22-24, 1970, New York, N. Y., Paper No. 19. (128) M. J. Berger and S. M. Seltzer, Nut. Acad. Sci.-Nut. Res. Couiic Publ., 1133, 205 (1964). (129) D. M. Poole, in “Quantitative Electron Probe Microanalysis,” U. S. Dept. of Commerce, National Bureau of Standards Special Publication 298, K. F. J. Heinrich, Ed., U. S. Government Printing Office, Washington, D. C., 1968, p 53.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
of this separation have been discussed by Criss (122) and Brown (130). The failure of this approach to provide accurate quantitative results in all materials under a variety of operating conditions led t o the use of the transport equation program (TEP, 131) and Monte Carlo, (MC, 45, 132, 133) techniques. Both approaches require detailed fundamental information concerning the interaction of primary electrons with the atomic nucleus (elastic scattering) and atomic electrons (inelastic scattering). Theoretical expressions are required for electron scattering, energy loss, and the ionization cross sections. This need for good fundamental data is rewarded by extremely useful output: the distribution in energy and depth of primary electrons, &z), f(x), distribution in energy of backscattered electrons, range, etc. Ogilvie and Brown (134) have demonstrated the use of TEP in obtaining “limiting/(x) curves” for A in A and a trace of A in B-Le., the two curves necessary for analyzing A in a n A B alloy. It is now apparent that the results from M C and T E P calculations are about as good as the existing experimental data. Brown, Wittry, and Kyser (112) compare T E P results, and Bishop (132) and Brown (130) compare M C results with experiment. Brown (130, 135) and Brown et al. (112, 118, 131) have demonstrated the use of T E P in making practical corrections while Bishop (132) has done the same with M C results. Pascal (16) has shown that M C techniques can be successfully and economically incorporated into a programmed correction scheme, e.g., in this program, if the intensities for the standards have been previously calculated and stored, 10 (n 1) seconds are required to carry out the calculations in a n-component system. It is safe to assume in view of this past work that the use and success of M C and T E P will increase as more and better fundamental data become available. While these computer methods of direct calculation are relatively expensive at the present time, it is probable that they will ultimately be used in general correction programs. It is certain that M C and T E P calculations will provide information that will permit improvement in the classical expressions. Hopefully information will be forthcoming in the range of low z where the classical expressions have provided rather dismal results. Any complex and complete program should be written so that future developments can easily be incorporated, as the actual calculation process would comprise a small portion of a program providing total capability. The geologist o r mineralogist often uses large numbers of complex standards with compositions close t o the unknown in order to minimize the absolute magnitude of the correction-sometimes a n advisable procedure in view of the complexity geologists normally encounter. This use of complex standards in conjunction with a classical correction scheme, a technique originally proposed and empirically modified by Smith (62), has recently been challenged by a n empirical technique using as end members pure oxides rather than pure elements. This technique proposed by Bence and Albee
+
(130) D. B. Brown, ibid., p 63. (131) D. B. Brown and R. E. Ogilvie, J. Appl. Phys., 37, 4429, (1966). (132) H. E. Bishop, ibid., 18, 703 (1967). (133) M. Green, Proc. Phys. Soc., 82, 204 (1963). (134) R. E. Ogilvie and D. B. Brown, in “X-Ray Optics and Microanalysis,” R. Castaing, P. Deschamps, and J. Philibert, Ed., Hermann, Paris, 1966, p 139. (135) D. B. Brown, presented at The Fifth International Congress on X-Ray Optics and Microanalysis, Tubingen, Germany, September 9-14, 1968.
(25, 136) avoids some of the problems associated with the
complex standards used heretofore-namely, inhomogeneity and inaccurate chemistry. Bence and Albee (25) have experimentally determined the a correction parameters for ten elements in the corresponding oxides; however, the values are applicable only to Eo = 15 kV and $ = 52.5”. The results presented in their paper are good. An excellent and thorough comparison of the two techniques was recently completed by Knowles, Smith, Bence, and Albee (137). The Gast and Glover ( 7 ) program utilizes the Bence and Albee approach and data. I n a comprehensive study, Sweatman and Long (107) recently concluded that accurate corrections could be made in complex geological systems using the classical expressions ( D R H Reed) and pure oxide or metal standards. While this last approach is the ultimate aim of microanalysis, each of the three (Smith, Bence and Albee, Sweatman and Long) approaches has provided good results in selected test systems. Computer. Since the vast majority of computers in the United States have Fortran compilers, programs should be written in Fortran IV or a language easily convertible to Fortran IV (Table I, column 7). While Algol is more commonly used outside the United States most installations also have Fortran compilers. Because of the increasing availability and usefulness of time sharing, the program should be compatible with time sharing systems. This should not pose any serious problems; e . g . , we were able to transfer a 12000word Algol batch program to the Algol time sharing system o n a Burroughs 5500 computer in four hours. I n view of the amount of core storage (Table I, column 10) required for a complete program and its permanent input data, some thought should be given to core storage and rhe cost of running the program. Existing programs were found t o cost (Table I, column 14) from about $0.01 to $1.50 per corrected element, the cost usually decreasing as the number of elements per run increased. Core storage requirements generally increase with program versatility. Using classical correction procedures, it should be possible to maintain the cost in the range of 1 to 5 cents per corrected element, even in a fairly elaborate program. This may be facilitated by calculating quantities such as w / p and u rather than storing (Table VII, column 3) the values. Colby, for example, uses the Burhop (138) formula for calculating the fluorescence yield where (w/l - w)1’4 = A Bz Cz3. Colby (139) has evaluated A , B , and C using the data of Fink (83), which is presently the best available. It is not advisable to carry out integrations in the program (e.g., R data) but rather to perform the integration and find a polynomial fit to the calculated values as Duncumb (79) has done with the R data of Bishop (53, 54). Duncumb et al. (98) have developed an analytical expression for J / z . Perhaps even more important is the use of efficient constructs which can be provided by experienced programmers. The means of accessing charges in a computer center can also significantly affect cost. Standards. A major advantage of electron microprobe analysis over other analytical techniques is that pure element standards aIe used in most quantitative analysis; however, compound standards which are sometimes useful in metallur-
+ +
+ +
(136) A. E. Bence and A. L. Albee, in T r a m Secorid Nail Corzf: Electron Microprobe Aiialysis, July 14-16, 1967, Boston, Mass., Paper No. 32. (137) C. R. Knowles, J. V. Smith, A. E. Bence, and A. L. Albee, J . Geol., 77, 439 (1969). (138) E. H. S . Burhop, J. Phys. Radium, 16, 625 (1955). (139) J. W. Colby, Adca/?. X-Ray A d . , 11, 287, (1968).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
1561
gical applications are essential in most geological and some biological applications (Table VI, columns 2-5). I n typical geological studies, 3 to 10 compound standards are used since it is common to use more than a single standard in establishing the concentration of a given element. While oxides and sulfides are common standards, some standards contain 3 to 5 and, less commonly, 10 elements per standard. Programs lacking this multielement/multistandard capability are of limited value in many geological applications. Because the probe has found its widest use in metallurgical applications, some authors have not included the capability for treating compound standards (Table VI, column 2). It should be possible to correct for characteristic fluorescence of the analytical line in the standard. Availability. Before a programmer announces his program to the public, he should be prepared to provide, upon request, at least a program listing with thorough and lucid instructions o n how to use the program (Table I, columns 4-6). This minimum is essential but considerably less than desirable. A complete description of the program content and examples of labeled input and corresponding output would be most helpful (Table XII). Written program descriptions should include a list in which all terms used in the program are clearly defined. The cost of producing a paper tape from an original tape is about $2.00 per tape (100,000 characters at 0.002& character). In view of this small cost and the relatively high cost and difficulty involved in producing punched cards from an often illegible listing, one would hope that the author would offer tapes of the program t o truly interested users. Experience at our own installation has revealed that reproduction of a single 3000 card deck (1 1000 Algol words) from magnetic tape, paper tape, or cards costs about $4.00. This tape can be reproduced using the tape reader and punch on a data communications terminal (time sharing system). Desirable Options. Any program should be capable of performing calibration calculations (Table VI, column 6). Such information is of considerable value if a large amount of work is to be carried out in a particular system and also in the examination of standards. This capability should be extendable to a range of compositions, Le., construction of a calibration curve. Graphical output (Table VI, column 7) of such data is desirable and, if a k us. C array for a binary system is constructed by the program, it is relatively easy to add existing plot routines t o the program. A routine to provide the variation of k with take-off angle at constant C would be desirable. Once k us. C information is available, theoretical a values can be determined from a linear least squares fit to the C/k us. C curve (Equation 3). These a values are useful in comparison with experimentally determined a values and have been found to be particularly useful in calculating expected limits of detection, C(LOD), using the Ziebold (140) relationship, C(L0D) = 3.29 a / ( N t P 2 / B ) 1 ’ 2 , where N is the number of determinations, t the counting time per determination, and P and B are the peak and background intensities, respectively, for the pure solute. It has been found that the C(L0D) calculated from this expression agrees within a factor of two with experiment, the experimental values being lower (141). This expression o r most others for C(L0D) can be easily programmed (Table IX, rows 40, 41). In addition to questions concerning detectability, the analyst must daily answer questions concerning penetration and reso(140) T. 0. Ziebold, ANAL.CHEM.,39, 859 (1967). (141) D. R. Beaman, in Trans, Third Nail Conf: Electron Microprobe Analysis, July 31-August 2 , 1968, Chicago, Ill., Paper No. 14. 1562
lution. The expressions proposed by Castaing (142), Duncumb (143, or Reed (144) may be used to make approximate estimates of X-ray resolution; however, the former tends t o underestimate the lateral spread at high E O . Colby (21) uses an experimentally confirmed (139) expression to calculate penetration. An important problem particularly in geology is that of the peak shift accompanying changes in chemical bonding. To date, no programmer has attempted to incorporate a routing that would correct for this effect. Subroutines or procedures to be used in homogeneity problems (121, 1 4 9 , diffusion studies [Bomback (6) and Lifshin (33) programs, and 421, and in the determination of possible spectral interferences would be welcome. Separate programs are needed for use in energy dispersive analysis with multichannel analyzers; E. Lifshin (146) is developing such a program. The ability to determine the effects of errors in the acceleration potential, take-off angle, mass absorption coefficients, etc., on the computed concentrations would be quite useful in establishing reliability in the computed concentrations. The programmer is referred to the series of papers by Heinrich and Yakowitz (147-149). The Mason-Frost-Reed programs calculate the error in concentration due to the expected errors in the correction factors. CRITICAL EVALUATION
The manner in which the programs performed in the correction of data for three test systems was of prime importance in the evaluation since it provided a n excellent means of assessing the accuracy of computation and the input/output characteristics of each program. Table XI is a tabulation of the results of the calculations in the three test systems. There are several reasons for the observed differences: incorrect mathematical calculations; use of different physical constants (the authors were provided with a complete set of physical constants but many were unable to incorporate them into their program); use of different correction schemes and/or inconsistent applications of the total correction, e.g., some authors applied and some did not apply a n atomic number correction in the Fe-Ni and Cr-Co-Mo systems; use of different test criterion in the termination of computations; use of different convergence methods; incorrect programming of proposed correction procedure, e.g., the improper calculation of S and R in the Duncumb and Reed correction. In the calculation of the concentration of element A , the excitation potential &(A) should be used in obtaining the values of Sa, SB. . . .S, which are used to calculate Sa’. Some programs [subsequently corrected by two programmers ( I S O ) ] use E,(B). . . .Ec(n)in calculating SB and S,, Le., they assume (142) R. Castaing, Advan. Electron. Electron Phys., 13, 317 (1960). (143) P. Duncumb, in “Proceedings of the Second International
Symposium on X-Ray Microscopy and X-Ray Microanalysis,” Elsevier Publishing Company, Amsterdam, 1960, p 365. (144) S. J. B. Reed, in “X-Ray Optics and Microanalysis,” R. Castaing, P. Deschamps, and J. Philibert, Ed., Hermann, Paris 1966, p 339. (145) H. Yakowitz, D. L. Vieth, K. F. J. Heinrich, and R. E. Michaelis, U. S . Dept. of Commerce, Nut1 Bur. Stand. ((1. S.) Misc. Pub/. 260-10 (1965). (146) E. Lifshin, G. E. Research Laboratory, Schenectady, N. Y., private communication, 1969. (147) H. Yakowitz and K. F. J. Heinrich, Mikrochim. Acta, 1968, 182. (148) K. F. J. Heinrich and H. Yakowitz, ibid., p 905. (149) K. F. J. Heinrich and H. Yakowitz, in Proc. Fourth Nut1 Conf: Electron Microprobe Analysis, July 1618, 1969, Pasadena, Calif., Paper No. 12. (150) We are grateful to E. Glover of the University of Wisconsin, who found that two programs contained this deficiency.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
that S, values are dependent only on the characteristics of element n and Eo. This neglects the fact that the quantity of interest is the stopping power of element n for electrons that have sufficient energy to excite element A , notwithstanding the excitation potential of element n. The same is true for the backscatter correction, RA’, Le., a loss of ionization only occurs when E > E,(A). It is worth noting that in evaluating the integralJ (Q/S)dE, the energy range of interest is Eoto E @ ) . In the evaluation, every calculated value was examined and the reason for any serious discrepancies determined. It is not possible t o comment on the accuracy (Table X I and XII) of programs that were not used to correct the supplied data. Only one author (20) whose program could make the corrections failed to d o so. The results of Olsen (151) are included as an example of the use of the complete Ziebold and Ogilivie expression (64); unfortunately the program is proprietary and unavailable. The completeness and correctness of the computations were heavily weighted in the evaluation, notwithstanding the fact that it would be much easier to correct a computational error than to add a data reduction capability. The data in Table X I indicate that the selection of an accurate correction scheme is vital. The results obtained by thirteen authors (indicated by a n asterisk in Table XI) using similar correction schemes (DR, DS, or H, Reed) show good agreement. The 1% relative accuracy (a/c) stated by Poole and Martin (106) may still be somewhat optimistic, particularly for lower compositions, but may apply under optimum conditions to a careful analyst using a good instrument and correction scheme. It is unfair t o subject some of the early programs to the rigors of such a n evaluation, but they have been included for the sake of completeness and because they d o contain useful concepts. The first published program by Wolfe and Macres (39) was remarkably complete containing features that some programs published years later lacked. Criss (38, 152) is presently upgrading his program which will ultimately include his own characteristic fluorescence correction, a continuous fluorescence correction (TEP), a permanent data file, and compound standard capability. Lifshin’s (33) series of programs are extremely useful in binary systems and include: the determination of diffusion activation energies, Q, and frequency factors, Do; interdiffusion coefficients by Matano analysis; diffusion profiles in uniaxial diffusion couples; theoretical and experimental a coefficients; and intensity cs. thickness calibration curves for thin films obtained using the method of Cockett and Davies (153). Helgesson’s ( 3 7 ) program was written only to compare the Tong ( 3 7 ) and Philibert (56) correction procedures. The programs by Frazer et al., and Brown are the first general correction programs useful in multicomponent systems and they were written at a time when the atomic number correction was still a n emotional issue. The most appropriate way t o evaluate a computer program is t o actually use i t ; however, this is not feasible when 40 programs are involved. Because we have been able to actually run only a limited number of the programs, the present evaluation is to some degree subjective. I n addition, the rating of a program is probably influenced to some degree by the programmers cooperation is providing the requested in(151) R. H. Olsen, 1969, private communication. The Boeing Co., Organization 6-8856, Mail stop 23-29, Seattle, Wash. (152) J. Criss, U. S. Naval Research Laboratory, Washington, D. C., private communication, 1968. (153) G. H. Cockett and C. D. Davies, Brit. J. Appl. Phys., 14, 813 (1963).
formation because when data are unavailable, the inclination is to assume that the program lacks the capability in question. Because user’s needs vary considerably, it is possible that features deemed relatively unimportant herein may be of considerable importance t o a particular user. Hopefully, the descriptive material provided will help to eliminate any inadvertent bias appearing in the evaluation and allow the analyst to make his own evaluation without resorting to the accumulation and assimilation of vast amounts of information. The programs were evaluated primarily o n the basis of data in Tables I-XI11 and the extent to which they contained the desirable features previously discussed. A weighting procedure was used since it is obviously considerably more important that a program contain an atomic number correction than be able to correct for fluorescence by K/3 and LP lines. The following is a list of the major aspects considered in program evaluation and they are listed in order of decreasing importance : mathematically correct, complete correction scheme, quality of results in the three test systems, inclusion of correction techniques of proved value, number of components, listing availability (a program that is not available is certainly of limited value, e.g., the programs by Reuter, Olsen, and Solomon are proprietary), the lack of limitations in the selection of the acceleration potential, ability to correct for other then KK fluorescence, simplicity of experimental input, a determination of one or more elements by difference, completeness of permanent data file, ease of using any chosen p i p values as input, the lack of atomic number limitations, calibration capability, availability of a data reduction routine, variable X-ray line selectivity, ability to utilize other than pure standards in metallurgical applications, the number of such standards and elements per standard, computation sequence, completeness and clarity of output, variable take-off angle as input, correction for fluorescence excitation by K/3 or LP lines, reports from users concerning the quality of the program, program language, availability of useful options, convergence technique, selectivity allowed in choosing a correction scheme, and the availability of punched cards or paper tape. In addition, programs designed for use in geology were further evaluated to establish the ease and versatility with which complex geological systems could be handled. Particular emphasis was placed on the following: number and type of compound standards that could be used, ability to determine one or more elements by difference utilizing known stoichiometric relationships, possibility of assuming all elements oxidized, inclusion of weight per cent oxide in output, standard data stored within program, possibility of assuming known concentrations which are used in the computation scheme, ability to make corrections for different analyzed elements at different acceleration potentials, calculate structural formulas, and ability to input different oxide forms. Tables XI1 and XI11 list some specific limitations and outstanding features of each program. These tables are incomplete but should be useful to prospective users and were helpful in arriving at a ranking. The negative comments combined with Tables I-X could be somewhat misleading since they d o not indicate the degree of any particular handicap; however, in the final evaluation this was taken into account by the weighting scheme. Most of the programs are degraded by the reduction to tabular form, but such reduction is essential to present large amounts of information in limited space. In the overall evaluation a concerted effort was made to consider each program as a whole entity with its own merits and limitations.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
1563
TABLE XII.
OUTSTANDING FEATURES O F THE PROGRAMS
-
Henoc a c c u r a t e c o r r e c t i o n ; c o n t a i n s c o n t i n u o u s f l u o r e s c e n c e c o r r e c t i o n ; e x c e l l e n t c o r r e c t i o n scheme; d a t a h a n d l i n g : good f l o w s h e e t s , d e s c r i p t i o n and i n s t r u c t i o n s f o r u s e ; p r o v i d e s check s y s t e n s ; warniiig messages when i n p u t d a t a i s i n c o m p l e t e ; c a n choose one of s e v e r a l e x p r e s s i o n s f o r J; o x i d e w t . % i n c l u d e d i n o u t p u t ; c o n t a i n s i n p u t and o u t p u t o p t i o n s .
- w r i t t e n i n APL l a n g u a g e . R u c k l i d j e - a c c u r a t e c o r r e c t i o n ; d a t a h a n d l i n g ; i-,eglects d r i f t C o r r e c t i o n i f v a r i a t i o n ; c a l c u l a t e s a homogeniety i n d e x ( a s i n B o y d ( 2 4 1 ) ; c a l c u l a t e s P/B Solamon
l e s s t h a n 1%i n t e n s i t y r a t i o ; accepts large amounts o f d a t a t a k e n d i r e c t l y from p r o b e ; some c o n t r o l on o u t p u t ; c a n assume a known c o n c e n t r a t i o n f o r any number o f e l e m e n t s : d a t a f o r 1 6 common s t a n d a r d s s t o r e d i n program; good h a n d l i n g o f g e o l o g i c a l s t a n d a r d s ; c o m p l e t e l i s t i n g ; permanent d a t a and i n s t r u c t i o n s s u p p l i e d ; c a l c u l a t e s w t . % o x i d e ; can c o r r e c t d i f f e r e n t e l e m e n t s a t d i f f e r e n t kV; c a n assume a l l e l e m e n t s o x i d i z e d ; c a n a s s i g n G i f f e r e n c e t o two o r iiiore unanalyzed e l e m e n t s e x i s t i i i g i n a f i x e d r a t i o .
-
Smith a c c u r a t e c o r r e c t i o n ; works i n b o t h d i s c i p l i n e s ; d a t a h a n d l i n g ; good d r i f t c o r r e c t i o n ; known c o n c e n t r a t i o n s c a n b e u s e d i n c a l c u l a t i o n o f unknowns: u s e s a c o n v e r s a t i o n a l l a n g u a g e , APL; provides varied output.
-
Duncumb a c c u r a t e c o r r e c t i o n : c a n c o r r e c t d i f f e r e n t e l e m e n t s a t d i f f e r e n t kV; c o n t a i n s i n p u t and o u t p u t o p t i o n s ; u s e s p o l y n o m i a l f i t t o Bishop e x p e r i m e n t a l b a c k s c a t t e r c o e f f i c i e n t s ; c a n u s e two colciplete (u/p j daka f i i e s ; e x c e l l e n t l i s C i n g - - c o r i t a i i l s l a r g e niimber of comments; w i l l r u n on s m a l l and l a r g e machines; c o n t a i n s ari o u t p u t e r r o r code which i n d i c a t e s i t e m s i n e r r o r ; e a s y t o use d i f f e r e n t s t a n d a r d s : good i n s t r u c t i o n s ; w i l l c o n v e r t c a l c u l a t e d c o n c e n t r a t i o n s t o w t . % o x i d e and l i s t o x i d e : c a n u s e d i s k s t o r a g e o r c a r d s f o r permanenc d a t a ; o x i d e forms a r e iriclucied i n program; e a s i l y a s s i m i l a t e d by o t h e r computers.
-
Bomback p l o t s c o n c e n t r a t i o n v s . d i s t a n c e ( d i f f u s i o n p r o f i l e ) ; good convergence t e c h n i q u e , i . e . , l a t e s t C v a l u e s a r e used i n each c a l c u l a t i o n ; good o u t p u t p r e s e n t a t i o n ; d a t a h a n d l i n g .
G a s t - u s e s Bence and Aibee t e c h n i q u e ; c a n a c c e p t l a r g e amounts o f d a t a , e . g . , up t o lG0 v a i u e s p e r unknown; e x t e n s i v e s t a t i s t i c a l c a l c u i a t i o n s ; s t r u c t u r a l a n a l y s i s f o r o r t h o p y r o x e n e , c l i n o p y r o x e n e , o l i v i n e , s p i n e l and
amphibole; e x c e s s oxygen,H20 and OH by d i f f e r e n c e ,
-
Fisher d a t a r e d u c t i o n program; o p e r a t e s i n s t e p s c a n mode; p r o v i d e s c o r r e c c e d i n t e n s i t y vs. distance data.
-
Renoc-cf Borile
-
provides accurate c o r r e c t i o n f o r continuous fluorescence: useful output.
d e s i g n e d f o r t i m e s h a r i n g s y s t e m ; a c c u r a t e c o r r e c t i o n ; c o n t a i n s a homogeniety c o m p u t a t i o n .
-
s h o r t program; good o u t p u t p r e s e n t a t i o n ; o u t p u t f o r e a c h combination o f c o r r e c t i o n s , + a t o m i c number, and a b s o r p t i o n + a t o m i c number -+ c h a r a c t e r i s t i c f l u o r e s c e n c e ; c o n t a i n s c o n t i n u o u s f l u o r e s c e n c e c o r r e c t i o n ; e a s i l y a s s i m i l a t e d by o t h e r computers.
Packwood
i . e . , absorption only, absorption
-
Frost-MK2 a c c u r a t e c o r r e c t i o n ; good o u t p u t p r e s e n t a t i o n ; d a t a h a n d l i n g ; can c o r r e c t d i f f e r e n t e l e m e n t s a t d i f f e r e n t kV; o u t p u t o p t i o n s ; c a l c u l a t e s a b s o l u t e e r r o r i n c o n c e n t r a t i o n b a s e d on e x p e c t e d e r r o r s i n c o r r e c t i o n f a c t o r s ; c a l c u l a t e s Uk/k based on x-ray c o u n t i n g s t a t i s t i c s ; two ( H e i n r i c h and T h e i s e n ) complete p/p d a t a f i l e s ; c a n have a l l p h y s i c a l c o n s t a n t s p r i n t e d o u t w i t h a s i n g l e i n s t r u c t i o n ; can r e d u c e s i z e o f permanent d a t a d e c k ; when e r r o r a p p e a r s , program d o e s n o t always t e r m i n a t e b u t p r o c e e d s t o n e x t d a t a s e t ; a common d a t a s e t can be used f o r s e v e r a l a n a l y s i s i n t h e same system: s e v e r a l c a l c u l a t i o n modes--can a s s i g n d i f f e r e n c e t o two o r more u n a n a l y z e d e l e m e n t s e x i s t i n g i n a f i x e d r a t i o : can a s s i g n d i f f e r e n c e t o oxygen, assume a l l e l e m e n t s o x i d i z e d and c a l c u l a t e o x i d e c o n c e n t r a t i o n s ; s e p a r a t e programmed r o u t i n e s f o r o l i v i n e s , f e l d s p a r s and p y r o x e n e s ; c a l c u l a t i o n s b a s e d on FeO and Fe2O3 i n a g i v e n sample a r e p o s s i b l e ; can u s e a known c h e m i c a l c o n c e n t r a t i o n f o r one o r more e l e m e n t s : can assume t h a t t h e c o n c e n t r a t i o n s of an i d e n t i f i e d b u t unmeasured c o n s t i t u e n t i s g i v e n by: l - ( s u m of unmeasured e l e m e n t s o f known c o n c e n t r a t i o n ) ( c o n c e n t r a t i o n s o f measured e l e m e n t s ) : c o r r e c t i o n f a c t o r s f o r any e l e m e n t i n a s t a n d a r d c a n be o b t a i n e d i n a c a l i b r a t i o n c a l c u l a t i o n and a r e a u t o m a t i c a l l y s t o r e d i n 5 kV i n c r e m e n t s f o r t h e r a n g e 5 - 4 0 kV: good program d e s c r i p t i o n : c a l c u l a t e s s t r u c t u r a l f o r m u l a e : p r o v i d e s f i v e t h o r o u g h example p r o b l e m s ; can a s s i g n a d i f f e r e n t t a k e - o f f a n g l e t o e a c h a n a l y z e d e l e m e n t .
-
Mason-MK1 a c c u r a t e c o r r e c t i o n ; good o u t p u t p r e s e n t a t i o n ; can c o r r e c t d i f f e r e n t e l e m e n t s a t d i f f e r e n t kV; c a l c u l a t e s e x p e c t e d e r r o r i n c o n c e n t r a t i o n due t o e r r o r s i n c o r r e c t i o n f a c t o r s ; same d i f f e r e n t c a l c u l a t i o n methods l i s t e d u n d e r F r o s t ; can change c o n s t a n t and e x p o n e n t a p p e a r i n g i n e x p r e s s i o n f o r u i n t h e i n p u t ; p r i n t s o u t a warning message i f U>20; p r o v i d e s n i n e thorough example problems.
-
Shaw a c c u r a t e c o r r e c t i o n ; d a t a h a n d l i n g ; complete D e x c i t a t i o n ; a c c e p t s punched p a p e r t a p e : c a l c u l a t e s P-B/P r a t i o s f o r sample and s t a n d a r d ; c a l c u l a t e s d e t e c t i o n l i m i t s i n ppm f o r e a c h e l e m e n t a s a f u n c t i o n o f s i x c o u n t i n g times ( 3 - 1 0 0 0 s e c . ) ; c a l c u l a t e s e x p e c t e d p e n e t r a t i o n .
Gray
-
d a t a h a n d l i n g ; Woodhouse i s a d d i n g compound s t a n d a r d s ; good o u t p u t p r e s e n t a t i o n .
Ximoto
- designed
Pascal
-
t o o p e r a t e in c o n j u n c t i o n w i t h a s m a l l computer.
makes s u c c e s s f u l u s e o f Bishop Monte-Carlo t e c h n i q u e ; a c c u r a t e c o r r e c t i o n ; D e x c i t a t i o n .
H e i n r i c h - can c o r r e c t d i f f e r e n t e l e m e n t s a t d i f f e r e n t k v ; d e s i g n e d f o r t i m e s h a r i n g s y s t e m ; c a n c a l c u l a t e Unmeasured e l e m e n t s usingknown s t o i c h i o m e t r i c r e l a t i o n s h i p s .
(Continued on next page)
1564
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
Table XII. (Continued) Reuter - convergence t e c h n i q u e (minimize C(k/k-kcalc); t o Duncumb a n d S h i e l d s b a c k s c a t t e r d a t a .
-
Moriceau
u s e d on t i m e s h a r i n g s y s t e m ; p o l y n o m i a l f i t
c o r r e c t s d i f f e r e n t elements a t d i f f e r e n t kV; program s e l e c t s optimum Eo f o r e a c h e l e m e n t .
-
Zeller i n c l u d # i s a new ( a u t h o r ' s ) b a c k s c a t t e r c o r r e c t i o n ; s i m u l t a n e o u s d e t e r m i n a t i o n o f a l l c o n c e n t r a t i o n ; ; u s e s a u t h o r ' s own e x p r e s s i o n f o r mean i o n i z a t i o n p o t e n t i a l ; c a n c o r r e c t d i f f e r e n t e l e m e n t s a t d i f f e r e n t kV.
-
Colby c a l c u l a r e s p e n e t r a t i o n , Z i e b o l d ' s C(LOD) and s e n s i t i v i t y ; d a t a h a n d l i n g ; w i d e l y used w i t h good s u c c e s s ; r and w c a l c u l a t e d i n program; i n d i c a t e s when a b s o r p t i o n c o r r e c t i o n e x c e e d s 2 0 % ; c a l c u l a t e s P/U r a t i o s ; 20 i n k and C f o r a s e r i e s o f measurements; a c c u r a t e c o r r e c t i o n . G o l d s t e i n - d a t a h a n d l i n g ; good i n s t r u c t i o n s f o r u s e ; m u l t i - d i s c i p l i n a r y a p p l i c a t i o n ; c a l c u l a t e s oxygen a s s o c i a t e d w i t h e a c h e l e m e n t ; t o t a l oxygen g i v e n i n o u t p u t ; c a n u s e more t h a n one s t a n d a r d p e r a n a l y z e d e l e m e n t ; o x i d e forms i n c l u d e d i n program; c a n u s e known C v a l u e s i n t h e c a l c u l a t i o n s .
-
p r i n t s o u t a n a r r a y o f Reed f u n c t i o n s i n d i c a t i n g f l u o r e s c e n c e ; compatible w i t h probe o u t p u t ; c a l c u l a t e s P/!3 r a t i o ; c a l c u l a t e s C ( L 0 D ) ; compares c a l c u l a t e d C ( L 0 D ) w i t h measured c o n c e n t r a t i o n i n t r a c e a n a l l y s i s ; e x c e l l e n t d a t a h a n d l i n g ; c a n c a l c u l a t e two e l e m e n t s o f known a t o m i c r a t i o by d i f f e r e n c e ; , c a l c u l a t e s a homogeniety i n d e x u s i n g a m = s (m)4 -- i f s > 3 sample judged inhomog e n e o u s ; o x i d e forms a r e i n c l u d e d i n program; c a n c o r r e c t d i f f e r e n t e l e m e n t s a t d i f f e r e n t kV, c a n assume a l l e l e m e n t s a r e o x i d i z e d ; o x i d e w t . 9 i n c l u d e d i n o u t p u t .
-
Bence u s e s e m p i r i c a l a p p r o a c h e f f e c t i v e l y i n g e o l o g i c a l a p p l i c a t i o n s ; c a n h a n d l e l a r g e amounts of d a t a ; d a t a h a n d l i n g ; c a l c u l a t e s s t r u c t u r a l f o r m u l a e ; f a v o r a b l e comments from u s e r s .
So -
d a t a h a n d l i n g ; good o u t p u t p r e s e n t a t i o n ; p l o t t i n g r o u t i n e i n c l u d e d .
-
Tixier c o n t a i n s P h i l i b e r t and T i x i e r a t o m i c number c o r r e c t i o n ; c a n a s s i g n a d i f f e r e n t t a k e - o f f a n g l e t o e a c h e l e m e n t i n a s y s t e m ; c a n c o r r e c t d i f f e r e n t e l e m e n t s a t d i f f e r e n t k v ; c a n u s e any J v a l u e t o o v e r r i d e J = 1 1 . 5 z i n t h e program; w i d e l y used i n F r a n c e ; t r e a t s t h i n s p e c i m e n s i n s e p a r a t e progir.sm; c a n assume a l l e l e m e n t s a r e o x i d i z e d ; o x i d e w t . % i n c l u d e d i n o u t p u t ; o x i d e f o r m s a r e i n c l t J d e d i n program.
-
Beeson good i n i j t r u c t i o n s ; good d a t a h a n d l i n g c a p a b i l i t y ; d i r e c t l y c o m p a t i b l e w i t h o u t p u t o f ARL and MAC p r o b e s , : c a n assume a l l e l e m e n t s a r e o x i d i z e d ; o x i d e w t . % i n c l u d e d i n o u t p u t .
-
Springer c o n t a i n s c o n t i n u o u s f l u o r e s c e n c e c o r r e c t i o n ; s h o r t program; c o m p l e t e i n t e g r a t i o n f o r a t o m i c number e f f e c t ; u s e s p o l y n o m i a l f i t t o Bishop e x p e r i m e n t a l b a c k s c a t t e r c o e f f i c i e n t s ; r and w c a l c u l a t e d :..-I program; c a n c o r r e c t d i f f e r e n t e l e m e n t s a t d i f f e r e n t kv. Hobby
- Xp
excitation.
-
Rucklidge dat'3 h a n d l i n g ; i n e x p e n s i v e ; o x i d e w t . % i s i n c l u d e d i n t h e . o u t p u t ; e a s i l y h a n d l e s l a r g e amounts o f d a t a ; can c o r r e c t d i f f e r e n t e l e m e n t s a t d i f f e r e n t kV; c a n assume a l l e l e m e n t s oxidized.
-
Beaman c a l c u l a t e s c1 and C ( L 0 D ) ; v a r i a b l e t e c h n i q u e s e l e c t i o n ; a c c u r a t e c o r r e c t i o n ; c a n u s e d i s k s t o r a g e or c a r d s f o r permanent d a t a ; p l o t t i n g r o u t i n e i n c l u d e d .
-
Lifshin c a l c u l a t e s t h e o r e t i c a l and e x p e r i m e n t a l c1 v a l u e s ; c a l c u l a t e s d i f f u s i o n a c t i v a t i o n e n e r g y , a n d f r e q u e n c y f a c t o r s , Do; d a t a h a n d l i n g ; X 3 e x c i t a t i o n ; v e r y c o m p r e h e n s i v e and u s e f u l i n s t r u c t i o
-
Brown contain::. c o n t i n u o u s f l u o r e s c e n c e c o r r e c t i o n ; d a t a h a n d l i n g ; R e x c i t a t i o n ; c o m p r e h e n s i v e i n s t r u c t i o n s €or use.
-
Frazer e x c e l l k f i t d a t a h a n d l i n g c a p a b i l i t y ; d a t a r e j e c t i o n ; f a v o r a b l e comments from u s e r s ; good i n s t r u c t i o n s f 3 r u s e ; o u t p u t o p t i o n s ; p l o t t i n g r o u t i n e ; c a n assume a l l e l e m e n t s a r e o x i d i z e d ; o x i d e w t . % i s p a r t o f o u t p u t ; S i c a n be h a n d l e d i n same manner a s 0. Lachance Helgesson
-
e x t r e m e l y e a s y t o u s e ; simple i n p u t ; u , C o r k as o u t p u t .
-
c o m p a r e s Tong and P h i l i b e r t e x p r e s s i o n s .
C r i s s - u s e s d p z ) = C a . embiPz ; 6 excitation: Wolf - d a t a hanAling.
The need for a substantial number of experimental measurements on compound standards in geological applications often leads t o exy.Nerimenta1 input requirements that are burdensome in mos t relatively simple metallurgical systems. The need to make computations peculiar t o geological problems also adds complexity to a simple metallurgical system. Because of this, the ratings have been divided into the two disciplines, metallur,yy and geology, with some programs
working well in both categories. Because of the somewhat subjective nature of such an evaluation, only the programs that most closely met the requirements of an ideal program are mentioned (referred to as class I programs). Class I1 programs would be class I programs except for input and/or output complexity. Some programs that were for the most part quality programs, but were downgraded for reasons that would be important to most users but not to all, are not
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
1565
TABLE XIII.
SPECIFIC LIMITATIONS OF THE PROGRAMS
Henoc - o n l y 4 1 e l e m e n t s p r e s e n t l y i n d a t a f i l e ; m u s t
i n p u t d a t a f o r compound s t a n d a r d s .
-
Solomon p r e s e n t l y p r o p r i e t a r y ; p/p n o t i n p e r m a n e n t d a t a f i l e : l i m i t e d d a t a h a n d l i n g : u s e s P-F(Xj--poor T i - N b r e s u l t s ; h i g h Mo; C+k i s i n a s e p a r a t e program.
-
Rucklidge 1 8 e l e m e n t s i n d a t a f i l e - - t h e e l e m e n t s a r e 0 , Na, Mg A l , S i , S , C 1 , K , C a , T i , C r , Mn, F e , Co, N i , Cur Zn and A S ; program d e s i g n e d t o a c c e p t a maximum of 2 0 e l e m e n t s i n p e r m a n e n t d a t a f i l e ; d e s i g n e d f o r m i n e r a l o g i c a l a p p l i c a t i o n s ; oxygen a l w a y s assumed t o be p r e s e n t ; t h e e x t e n s i v e output could be clearer.
S m i t h - no C+k; z>10; f i x e d Y; no M l i n e s . Duncumb - no d a t a h a n d l i n g ; o n l y f o r z>10; n o f l u o r e s c e n c e c o r r e c t i o n i n s t a n d a r d s . Bonback - f i x e d p/p v a l u e s : no C+k; o n l y p u r e s t a n d a r d s ; o n l y f i v e i t e r a t i o n s a l l o w e d . Gast - f i x e d c o u n t t i m e f o r a l l m e a s u r e m e n t s ; o n l y good f o r ARL p r o b e s o p e r a t e d a t 1 5 kV s i n c e u s e s Bence a n d ' A l b e e d a t a ; f i x e d i n e a c h c h a n n e l : d a t a h a n d l i n g program o n l y h a c d l e s a 'I
maximum of t h r e e e l e m e n t s a t a time; o n l y u s e f u l i n g e o l o g i c a l a p p l i c a t i o n s .
-
Fisher c o r r e c t e d i n t e n s i t i e s b u t n o t k as o u t p u t : o n l y p u r e s t a n d a r d s ; one c o u n t time o r i n t e g r a t e d c u r r e n t ; w r i t t e n t o l i n k w i t h Colby p r o g r a m o n l y .
-
program c o r r e c t s o n l y f o r c o n t i n u o u s f l u o r e s c e n c e ; 1 3 e l e m e n t s i n d a t a f i l e ; no d a t a Hen'oc-cf h a n d l i n g : complex i n p u t .
-
Borile n o p e r m a n e n t d a t a f i l e ; no d a t a h a n d l i n g ; no C+k; v a r i a b l e l i n e s e l e c t i o n d i f f i c u l t ; complex i n p u t ; o n l y p u r e s t a n d a r d s .
-
Packwood c o n s i d e r a b l e amount o f i n p u t r e q u i r e d ; s e p a r a t e i n p u t r e q u i r e m e n t s f o r k+C and c + k ; m u s t c a l c u l a t e s t a n d a r d c o r r e c t i o n f a c t o r s s e p a r a t e l y and i n c l u d e them i n e x p e r i m e n t a l i n p u t ; c a n n o t u s e k as i n p u t .
-
Frost-MK2 a f e e i s c h a r g e d f o r t h e p r o g r a m E 3 5 = $ 9 0 + s h i p p i n g ) ; o n l y f o r z>10: E . r e s t r i c t i o n s b a s e d o n R e e d ' s f l u o r e s c e n c e c o r r e c t i o n ; Eo)5; d i f f i c u l t y i n i n c o r p o r a t i n g w i t h o t h e r c o m p u t e r s . Mason
Shaw -
- only f o r
a fee i s c h a r g e d f o r t h e program ( a b o u t $ l 5 0 ) ; m u s t i n p u t d a t a f o r compound s t a n d a r d s ; z>10.
-
Gray
z>10; no d a t a h a n d l i n g ; l i m i t e d p e r m a n e n t d a t a ; e x t e n s i v e i n p u t ; ~ ~ ) 5 .
small p r o b l e m w i t h a b s o r p t i o n c o r r e c t i o n ( p e r h a p s i n p / p ) ;
Kimoto
l o w N i and T i ; no C+k; f i x e d u / p .
-
l i s t i n g n o t available: u s e s P o o l e and Thomas atomic number c o r r e c t i o n b u t h a s r e c e n t l y a d d e d DR; T i - N b r e s u l t s i n f e r i o r ; n o p e r m a n e n t d a t a f i l e ; complex i n p u t ; o n l y p u r e s t a n d a r d s .
-
Pascal a fee i s c h a r g e d f o r t h e program (20,OSO f r a n c s = $ 3 6 0 0 d e p e n d i n g on e x c h a n g e r a t e ) ; n o d a t a handling.
- n o permanent d a t a f i l e ;
Heinrich
-
no d a t a h a n d l i n g , e x t e n s i v e i n p u t ; o n l y p u r e s t a n d a r d s .
program l i s t i n g n o t a v a i l a b l e ; atomic number c o r r e c t i o n a p p e a r s i n a d e q u a t e ; i n f e r i o r Reuter Ti-Nb r e s u l t s ; no p e r m a n e n t d a t a f i l e ; c a l c u l a t i o n s n o t c o m p l e t e l y a u t o m a t e d ; f i x e d Y ; m u s t c a l c u l a t e s t a n d a r d c o r r e c t i o n f a c t o r s s e p a r a t e l y and i n c l u d e them i n e x p e r i m e n t a l i n p u t .
-) sf oi lmee;t hni no gdwrong w i t h f l u o r e s c e n c e c o r r e c t i o n ( F e ) ; KK a t a h a n d l i n g ; some i n p u t d i f f i c u l t y .
Moriceau v
p
f l u o r e s c e n c e o n l y ; o i l l y 30 e l e m e n t s
-
Zeller
n o p e r m a n e n t d a t a f i l e ; complex i n p u t ; z>ll; KK f l u o r e s c e n c e o n l y ; o n l y a v a i l a b l e i n A l g o l ; must c a l c u l a t e s t a n d a r d c o r r e c t i o n f a c t o r s s e p a r a t e l y and i n c l u d e them i n e x p e r i m e n t a l i n p u t .
Colby
-
f i x e d u/p v a l u e s ; no C+k; b i n a r y compound s t a n d a r d s o n l y ; low N b v a l u e .
Goldstein
- some i n p u t d i f f i c u l t y i n s i m p l e s y s t e m s ;
requires the generation of a sta'idard f i l e .
Bo d - f i x e d c o u n t t i m e ; o n l y f o r g e o l o g i c a l a p p l i c a t i o n s ; c a n a n a l y z e -k corrected s e p a r a t e l y , i . e . , g e n e r a t e a f i l e o f s t a n d a r d s .
z=ll t o 56; s t a n d a r d s m u s t
B e n c e - see Gast. s o - u s e s P a t o m i c number c o r r e c t i o n ; Ti-Nb r e s u l t s i n f e r i o r ; no permanent d a t a f i l e ; complex i n p u t . T i x i e r - low T i , and N i c o n c e n t r a t i o n s ; no f l u o r e s c e n c e c o r r e c t i o n i n s t a n d a r d ; n o d a t a h a n d l i n g ; m t e d d a t a f i l e ; some i n p u t c o m p l e x i t y ; no C+k. Co
Beeson
-
f l u o r e s c e n c e c o r r e c t i o n problem--highest
F e v a l u e ; KK f l u o r e s c e n c e o n l y ; Nb h i g h f o r
DR-DS c o r r e c t i o n ; c a n n o t s e p a r a t e t h e i n d i v i d u a l c o r r e c t i o n s ; must c a l c u l a t e s t a n d a r d c o r r e c t i o n
f a c t o r s s e p a r a t e l y and i n c l u d e them i n e x p e r i m e n t a l i n p u t .
-
Springer low N b ; N i v a l u e s l i g h t l y h i g h f o r DS a b s o r p t i o n c o r r e c t i o n ; f i x e d u/p v a l u e s ; no d a t a h a n d l i n g ; f i x e d 1 ; o n l y a v a i l a b l e i n A l g o l ; must i n p u t d a t a f o r compound s t a n d a r d s .
(Continued on next page)
1566
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
Table XIII. (Continued)
-
Hobby u s e d P h i l i b e r t F ( x ) w i t h DS U f o r a t o m i c number c o r r e c t i o n ; Ti-Nb r e s u l t s i n f e r i o r ; K K a n d LL f l u o r e s c e n c e o n l y ; no p e r m a n e n t d a t a f i l e ; kV l i m i t a t i o n s ; l i m i t e d d a t a h a n d l i n g ; no C+k; f i x e d Y; complex i n p u t ; o n l y p u r e s t a n d a r d s ; o n l y a v a i l a b l e i n A l g o l .
-
Rucklidge u s e s P a b s o r p t i o n c o r r e c t i o n ; o n l y 1 8 e l e m e n t s i n d a t a f i l e ; complex i n p u t f o r o t h e r t h a n t h e s e 1 8 : m u s t r u n a t 1 0 , 1 5 , 2 0 , 2 5 , o r 30 kV; oxygen a l w a y s assumed p r e s e n t u n t i l r e p l a c e d by t o t a l o f o t h e r c o n c e n t r a t i o n s . Beaman y / p v a l u e s f o r 41 a b s o r b e r s o n l y ; no d a t a h a n d l i n g ; v a r i a b l e l i n e s e l e c t i o n d i f f i c u l t ; fluorescence input d i f f i c u l t y ; only pure standards. Lifshin - uses Poole o n l y ; no p e r m a n e n t
a n d Thomas a t o m i c number c o r r e c t i o n ; b i n a r y s y s t e m s o n l y ; K K f l u o r e s c e n c e d a t a f i l e ; complex i n p u t ; o n l y p u r e s t a n d a r d s .
-
Brown o n l y h a s Thomas a t o m i c number c o r r e c t i o n ; no p e r m a n e n t d a t a f i l e ; complex i n p u t ; d o e s n o t p r o v i d e u n n o r m a l l z e d c o n c e n t r a t i o n s a l t h o u g h t h e y c a n b e hand c a l c u l a t e d from o u t p u t ; m u s t c a l c u l a t e s t a n d a r d c o r r e c t i o n f a c t o r s s e p a r a t e l y and i n c l u d e them i n e x p e r i m e n t a l i n p u t .
-
Frazer C r c o r r e c t i o n wrong d i r e c t i o n ; h i g h e s t C r ; h i g h Fe; l o w N i ; KK f l u o r e s c e n c e o n l y ; z > 1 2 ; f i x e d p/p v a l u e s ; f i x e d '4; m u s t c a l c u l a t e s t a n d a r d c o r r e c t i o n f a c t o r s s e p a r a t e l y a n d i n c l u d e them i n experimental input.
-
Lachance R e q u i r e s knowledge o f k and a o r k and o n l y one c a l c u l a t i o i l p e r run.
c
or
c
a n d a ; w i l l n o t c a l c u l a t e t h e o r e t i c a l a;
-
H e 1 esson L a c k s c h a r a c t e r i s t i c f l u o r e s c e n c e c o r r e c t i o n ; d o e s n o t c o n t a i n DS o r H a b s o r p t i o n *ion; b i n a r i e s o n l y ; no p e r m a n e n t d a t a f i l e ; no d a t a h a n d l i n g ; no C+k; complex i n p u t ; only pure standards.
- d e p e n d s on Thomas a t o m i c number c o r r e c t i o n ; no p e r m a n e n t d a t a f i l e ; no d a t a h a n d l i n g ; complex i n p u t ; o n l y p u r e s t a n d a r d s .
Criss
Wolf -
l a c k s a t o m i c number c o r r e c t i o n ; c o n t a i n s P h i l i b e r t a b s o r p t i o n a n d W i t t r y c h a r a c t e r i s t i c f l u o r e s c e n c e c o r r e c t i o n ; c o r r e c t s o n l y CuK i n Co-Cd a t 30.5 kV; no d a t a f i l e ; f i x e d Y; o n l y pure standards.
mentioned (class 111 programs). In the event that a user has a specific interest in an unmentioned program, the authors will provide upon request the overall ranking (class I through class VI) of that program. The following four programs were rated unequivocally as class I programs: Mason, Frost, and Reed's M K 2 ; Duncumb and Jones; Shaw; and Colby; the first three recommended for both disciplines, the last for metallurgical applications only. The availability of a program is important and the Colby program appears to be the most readily available and widely distributed program at the present time. The complete program by Henoc would also be in class I if the input/output were simplified; while it is of considerable theoretical value, its use as a routine correction program will depend upon the final form of the input. The MasonMK1 program, also has extensive input requirements. These two programs, in their present state, and the Goldstein program are ranked (class 11) just behind the four already mentioned. All three programs can be used in either geology or metallurgy. The following is a list of good programs that have specific areas of application which are indicated in parentheses: Henoc-cf (continuous fluorescence correction); Gast (uses Bence and Albee empirical approach to geological problems); Pascal (practical M C correction scheme); Lifshin (useful metallurgical calculations in binary systems). The Pascal program definitely requires further evaluation and should be tested in a larger number of alloy systems. For geological applications, the programs of Boyd, Packwood, Rucklidge, and Smith were rated just below those listed above. If a prospective user has limited core storage a t his disposal, he will have to bypass the more elaborate programs and use one of the shorter ones. Short programs that ranked high in the rating were those by Duncumb (requires disk monitor), Mason-MK1, Packwood, and Smith. Authors who failed to
provide core storage requirements could not be rated on this basis. The program by Beaman was not considered in the overall ranking in order t o eliminate the possibility of any bias. This program is the only complete correction program that includes several of the more effective correction procedures. Because there are fine programs available which are easy to use on a routine basis for performing quantitative corrections in metallurgical and geological systems, we recommend that before a n analyst decides to write his own program, he should seriously consider using one of these published programs unless, of course, he plans on eliminating many of the deficiencies discussed herein. The addition of another incomplete program to the burgeoning list of existing programs would certainly be of limited value. Major modification of a program by a user (changing input-output format, adding permanent data files) is always a possibility, but we have found it is considerably easier to contemplate such a modification than to carry it out. The most desirable situation is t o entice the program author into performing the required change or addition. Minor modifications (changing takeoff angle or the expression for deadtime) are not difficult. With only three exceptions, the authors of the recommended programs will at no charge, willingly provide sufficient material so that a prospective user can begin using the program. The Frost, Pascal, and Shaw programs can be purchased. When one makes a critical evaluation, it is necessary to rank; and once a ranking exists, inferiority is implied. We want to emphatically state that we believe most of the programs have been carefully conceived and have contributed significantly to the advance of quantitative analysis. The fact that a program appears low in the ranking does not imply that it is or was not good but usually only that, as time pro-
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
* 1567
TABLE XIV. Smith........add
continuous fluorescence correction; statistical evaluation.
Bomback......compaund GaSt.........add
standards; element by difference.
structural formulae to Output; limit o f detection StatlStlCS.
Fisher.......camputatian Borile.....
PLANS FOR ADDITIONAL CAPABILITY*
of corrected x-ray intensity ratios.
..compound standards; Philibert-Tixier atomic number correction; modify program for use on-line with a PDPB computer; data handling.
Packwood... ..incarporate v a l u e s ; drift correction; inprove the instruct1ar.s for use. Frost..,,....add
Springer continuous fluorescence correction.
Gray.........compaund standards--8 standards containing up to 8 elements each by J. Woodhouse. Reuter.......add
Philibert-Tixier atomic number correction.
Moriceau.....improved
Colby......
characteristic fluorescence correction.
..continuaus fluorescence correction; step scan analysis: diffusion calculatlans; t h i i films.
Goldstein....continuaus Tixier.......add
fluorescence correction.
data handling and punch paper tape capability; plan to rewrite program to provide more flexlbillty.
Beeson.......make each correction separate option; add hamageniety index; run at different kv; separate background readlng f o r each data set. Springer... ..improved iteration pracedlre; fi excitation; use better v/p values. Bearnan.......link with Fisher’s data handling program; add new Tong correction; add Criss’ characterlstic fluorescence corrcction. Brown........add
Duncumb and Reed atonic number carrectiqn.
criss........use transport equation solution to calculate d 3 2.1 and fluorescence by continuum: perrranent data file: add characterISt2C f l u o r e s c e n c e correction of Criss; compound Standards. *Authors n o t listed have ro p l a n s to alter their programs.
gressed, more elaborate and useful programs have been written. Most early authors have contributed significantly to the work of later investigators. As expected, and fortunately, there has been a consistent improvement in the computer programs over the years, the later published programs being generally superior to the earlier ones. Since many authors have plans (Table XIV) t o improve or upgrade their programs, this evaluation must, of course, be a temporary one. Perhaps this evaluation in itself will motivate some useful additions and improvements. As new programs appear and changes or additions are made in old ones, the authors will attempt t o update the evaluation. Prospective users are encouraged to ask for additional information as it becomes available. In addition, attempts will be made t o actually test run as many as possible of the most promising programs. To date, we have run or been involved in the running of twelve of the programs. It seems reasonable to expect that an all inclusive program based on the classical approach will appear during the next year. In addition, progress is certain in M C and TEP calculations. What was yesterday’s impossibility, is today’s absolute limit-and tomorrow will be commonplace (154). RECENT DEVELOPMENTS Many changes have been made in several existing programs as a result of distribution of this report to the program authors in an attempt to ensure the accuracy of the data presented. The input requirements of the Pascdl(l6) program have been (154) Hart Ski Co., St. Paul, Minn., from a film entitled “Ski The Outer Limits.” (1969).
1568
greatly simplified and the cost of running reduced to 18# per analyzed element when standard intensities have been previously calculated. The Boyd (24) program has been expanded to include elements in the interval z = 11-56 and correction for KL, LL, and LK fluorescence is now possible. Several authors have removed serious computational errors, Packwood (IO)has added the Springer (66) continuous fluorescence correction. A new version of the Frost program called MK-5 is now available. The earlier EMPADR program by Rucklidge and Gasparrini(31) has been replaced by EMPADR VI1 (3) and is no longer being distributed. The program by Gurney and Bonizewski (41) has been translated into Fortran IV by J. S. Miller (155). Myklebust and Heinrich (156) have added an output option written in Fortran V to the Henoc ( I ) program. A large amount of data has been added to the permanent data file which has been expanded to include 41 elements. Consequently, the experimental input requirements have been simplified considerably. A program based on the use of the TEP (112, 131) written by D. Brown (157) has just become available and is being evaluated. This Fortran program written for use on a C D C 3800 computer is, in its present form, not a general purpose program for use in routine quantitative analysis as it lacks many of the essential features described herein, e.g., one cannot iterate from a series of measured concentrations to a series of calculated concentrations and there is no permanent data file. The input is extensive but easy to prepare once the data are accumulated. The output of the program i s most exciting and should be carefully studied by anyone seriously interested in the advancement of quantitative microanalysis. Where w is the fluorescence yield, f i s the fraction of the relevant ionization resulting in the line of interest, and W is E/Eo the program output includes: emitted intensity/w/f (fluorescence neglected) ; generated intensity/w/f(fluorescence neglected); total emitted intensitylwlf (including characteristic and/or continuous fluorescence contribution); the energy distribution of backscattered electrons (dq/d W us. E is also displayed on a lineprinter graph); ~ ( p z is ) displayed on a lineprinter graph; y ; R; f ( x ) 5s. x. Lucid instructions for use are provided as are three example problems (Cu-Au, UOn,Zr-0) and a complete listing. ACKNOWLEDGMENT The assistance provided by the many program authors is gratefully acknowledged. Without it, this report would not have been possible. We must especially acknowledge the very willing cooperation of J. Woodhouse who provided us with the information of the program written by L. Gray. Thanks are also due C. R. Knowles and E. Glover for their helpful comments on geological applications.
RECEIVED for review May 22,1970. Accepted July 8, 1970. (155) J. S. Miller, British Steel Corporation Group Research Report SNW (C) Y.2/1, Scottish and North West Group; also U. S. Department of Commerce, Nut. Bur. Stand., PB 187 826
(1969); The Reports Section, BISRA, 24 Buckingham Gate, London S. W. 1, England. (156) K.F.J. Heinrich, private communication, 1970. (157) D. B. Brown, private communication, D. B. Brown, Code 7680, Naval Research Laboratory, Washington, D. C. 20390.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
