tivity i> approximately 37,000 a t 325
w. Precision. D a t a were obtained on 0.5-7 amounts of nickel, about the normal cQntent of 10 ml. of whole blood. The standard deviation on 10 replicate samples was 0.02 7 or i%.
Interference from Diverse Ions. Analyses were carried out o n individual synthetic solutions containing, except in t h e case of zinc. a t least t h e amount of each ion normally expected in 10 ml. of whole blood. Values for the metals present in n-hole blood gii-en by dlbritton ( 1 ) . together with \-slues made available hj- the Pratt Trace Analysis Laboratory, ivere used in tlie preparation of the solutions. An aLqohance greater than ‘0.010 1‘s. a l h i i k vias arbitrarily chosen to indicate interference. As shonn in Table I. iron, copper, and lead interfere. The concaentration of zinc in whole h h d is a t least ten times greater than i q iiidicat’ed in the table. €Ion-ever. zinc will not interfere because it is separated in the ion exchange procedure ( 1 1 ) . Other ions, not listed in Table I. which might be present in human blood do not interfere. Thiq was established by analyzing spectrographicall!- tlie isoamyl alc~~!io! ex-
tracts obtained from the analysis of several whole blood samples. RESULTS
The results of the analysis of a synthetic blood-ash solution and of human blood samples are given in Tables I1 and 111. Sickel was determined in the synthetic samples with an average deviation of 0.005 p.p.m. The average deviation calculated from the blood data in Table I11 is 0.009 p.p.m. The concentration of nickel determined in human whole blood ranged from 0.025 to 0.067 p.p.m.; the average concentration in blood from eight patients !vas 0.041 p.p.m. I n one sample of plasma the nickel concentration \vas 0.012 p.p.m. LITERATURE CITED
( 1 ) Albritton, E. C., “Standard 1-alues in Blood,“ p. 117, W. B. 8:iiindrw
Co., Philadelphia, 1952. ( 2 .\lrsander, 0 . It., Godar, 1,;. lI,, I,inde, S . J., ISD. EXG. CtrEx.. AS.^,. ED. 18, 206 (1946). ( 3 I Bell, G. H., Davidson, J. S., Scarborough, H., “Textbook of Physiology and Biochemist1 D. 80. E. & S. Livineston. Ltd.. 1
Edinburgh, 1953.
-
( 4 ) Beitrand, G , Nakamwa, H , Rtili soc chzn,. btol 16, 1366 (1934) ( 5 ) Bode, H , 2 anal L‘hent 142, 414
(1954).
END
(6) Everett, hl. R., “hledical Biochemistry,” 2nd ed., p. 608, Paul B. Hoeber, Inc., New York, 1944. ( 7 ) Feigl, F., “Chemistry of Specific, Selective and Sensitive Reactions,” p. 89, Academic Press, New York, 1949. (8) Ibid., p. 174. ( 9 ) Ferguson, It. C., Banks, C. L-., A S A L . CHEM. 23, 1486 (1951). (10) Koch, H. J . , Jr., Smith, E. R., Shimp, 1.F., Conner, J., Cancer 9, 499 (1956). (11) Kraus, K. A , , lIoore, G. E., J . Ani. Chem. SOC. 75. I460 11953). (12) Kraus, K. -$., kelsonj F., I b i d . , 76, 981 i19-54) 984 (1954). r a n S ,K. A , , Selson, F., iroorp, Krans, lIoorp, (13) ~ G.. E., I b i d . , 77,3972 (1955). G (14) lIiddleton, G., Sttickey, R . E., Analyst 79, 138 (1954). 1 15 i lIonacelli. It.. Tanaka. H.. Tiocl. J. H., ’Clin,’ (‘him. Acta ’1, 577 (1956). (16) l l o o r e , G. E., Kraus, K. A , , J . A m . Chem. SOC.72,5792 (1950). 117 1 Siistinen. R.. Tamminen. V.. Suotrieri \----I.
ScJlson, F., I i t , a d , K.’ A , , J . -3 m. (‘hrm. SOC. 76,5916 (1954). Shprwood, It. ll.,Chapman, F F. K., ,Jr., .4sar,. CHEJI.27, 88 (19: (1955). Thirrs, R. E., Killiiims, J. F., Toe, J. H.. Ibid.. 27. 1725 (1955). Thiers.’R. E.: Y&. J. HI..SOC.d ~ o l . Spe&oscopy B d i . 5 , 8 11951). ( 2 2 ) I-oP, ,J. H., Wirsing, F. H., J . A m . Clfelfl S O C . 54, 1866 (1932). .
I
RECEIVEDfor rrvien l r n r c h 11, 19.57. .\ccrptrd Julv 10, 1957.
OF SYMPOSIUM
Efficient Use of the IBM File of ASTM Powder X-Ray Diffraction Data THOMAS
E. BEUKELMAN
Jackson Laboratory, E. 1. du Pont de Nemours & Co., Inc., Wilmingfon, Del.
b The use of the IBM file of powder x-ray diffraction data compiled and published b y the Joint Committee on Chemical Analysis b y X-Ray Diffraction Methods of the American Society for Testing Materials is discussed. A sorting procedure based upon the statistical distribution of holes in the IBM punched card i s described for the qualitative analysis of multicomponent samples. The method i s also applicable to use of IBM files of infrared and ultraviolet absorption data.
T
powder x-ray diffraction (data publibhed by the Joint Coniniittee on Chemical Analysis by S-R:i>. Diffraction Methods of the ;Inierican Society for Testing llnterial. have long &ice proved their usefulness for HE
the identification of unknon n niaterials by their x-ray diffraction patterns. However, the I R M punched card file of these data as originally developed by the Wyandotte Chemicals Corp. ( 2 ) has not been aq n idely used. This may be partially the reiult of the more elaborate equipment needed for the handling of punched cards. but milalso be caused t)? an incomplete appreciation of their urefulnew in x - r q diff ractioii anall-sis. The file of 3 X 5 inch cards of powder diffraction data, familiarly knov n as the A S T l I file, or even the Numerical Indexes ( 1 ) furniqhed in book form to the users of the A S T l I file is normally adequate for the identification of singleconiponent samples. The greateqt utility of the I R l I file i. in the analysis of multicomponent samples, where each of
the three qtrongest cliffraction inasinia may arise from different conipounds. I n this case the usual practice of match. ing by searching for a single roinpound containing all three strongest diff riwtion riiaxima will proliubly fail. Another difficulty is the rhance coinc.itlence of minor tiiffraction imtziino of tn-o o r more components. \vhic*h leads to :i niasiniuni irliose intensit!. may lie out of proportion to tlie diffraction Ixrtterns of any of the component.. I n bhis case, too, the extensive cross-indexing possible n-ith punchetl i.:ircl techniques may lie used t o full ad\-antage. The method described here is not a rapid o r shortcut method. I t is a method for searching all of the availahle data in a comprehensive imnner and should be used only after niore rapid methods have failed. VOL. 29, NO. 9, SEPTEMBER 1957
1269
Figure 1.
Distribution of punches in columns 1 to 35
Darkest holes a r e mast frequently punched, lightest ones a r e least frequently punched
DESCRIPTION OF WYANDOTTE SYSTEM
The Wyandotte system for coding powder x-ray diffraction data makes use of the standard I B M punched card divided into several fields or regions ( 2 ) (Figure 1). Columns 1 through 35 are used to code the interplanar spacings of the diffraction maxima. Columns 36 and 37 contain a code number which refers to the Hanawalt classification. Columns 43 through 50 contain the elements present in the compound to which the card refers. Columns 51 through 62 contain information concerning the chemical groupings or radicals present. There are fields for coding the melting point of the compound in question and for a literature reference. Columns 75 through 79 contain a reference to the number of the 3 X 5 inch card in the ASTLL file. The last column contains a code that designates the card as one bearing x-ray powder diffraction data. Although the fields containing chemical classifications are extremely useful, this paper is concerned only with the use of the coded powder diffraction data (columns 1 through 35). It mill be noted from Figure 1 that the punching resolution is not always the same. For interplanar spacings from 0 to 3.5 A., the resolution is 0.01 A. From 3.5 to 10.0 A. the punching resolution is 0.1 -4. Spacings from 10 to 30 A. have a resolution of only 1 A. Row 9 of column 35 is punched for all spacings greater than 29 A. KO diffraction maximum is punched into the card unless its relative intensity is greater than 9, where the strongest maximum is assigned the value of 100. The only other intensity information indicated on the card is the designation
1270
ANALYTICAL CHEMISTRY
of the strongest diffraction maximum through the coded Hanawalt group. As only the strongest maximum is indicated, the usual procedure of matching by the three strongest maxima normally used with the 3 X 5 file is not possible with the IBLI cards. It is not even 1-ery desirable. as the IBLI cards would have very little advantage over the 3 X 5 file if used in this manner. It has been recommended to the committee responsible for the preparation of the IBLI file that Hanawalt groups based on the second and third strongest maxima be coded into columns 38 through 41, not for matching, but for use in rejecting undesired cards. The rejection of undesired cards is based on the fact that if the strongest diffraction maximum of a standard pattern is not present in the unknown pattern, i t is highly improbable that the compound is present in the unknown sample. The same statement may be made of the second and third strongest maxima, with perhaps a slightly lesser degree of improbability. An experimental deck with the above modifications has been in use in the author’s laboratory for some time with good results. SORTING PROCEDURE
The general procedure used in this laboratory for the analysis of the diffraction pattern of a multicomponent sample follows five main steps. 1. Reduction of the diffraction pattern-powder, photograph, or diffractometer recording-to numerical data. T h a t is, reduction to a list of interplanar spacings and their relative intensities. 2 . Removal from the general IBM file of cards that may be rejected on the basis of prior chemical knowledge.
This should be done with care, lest the very card sought be rejected as being improbable. 3. Removal from the remaining file of those cards carrying the Hanawalt designation of a region in which no diffraction maxima occur in the unknon-n pattern. If the analyst is interested only in major components, he may also reject those cards in which the Hanawalt group lies in a region where there are only very small diffraction maxima. 4. Searching for the most probable matches. It is with this step that this paper is mainly concerned. 5 . Checking compounds chosen by the IBhI sorter as probable against the complete diffraction patterns on the ASTM 3 X 5 cards. It might be hoped that this final step, which requires the attention of a person trained in powder diffraction work, could be avoided through the use of modern decisionmaking machines. Unfortunately, it is not possible with the incomplete data carried b y the IBhI powder diffraction file. Even if the file were more complete, i t would be difficult to devise a clear-cut mathematical criterion of what does or does not constitute an identification. The task of finding the most probable matches (step 4) is the most timeconsuming step. I n general, compounds having the greatest number of diffraction maxima matching the unknown are considered “most probable.” This very general statement requires a little explanation. A compound nhich has only one of its diffraction maxima in common with the unknown pattern would not be considered a likely candidate. On the other hand, a compound which has ten or more diffraction maxima in common with the unknown pattern would be considered a very
used as a simple guide. For example, the deck currently in use in this laboratory consists of the original deck plus the first four supplements less the deletionb iecommended with the fifth supplement. It contains about 4300 cards with an average of 13.4 holes per card. Only the section of the card concerned with the coding of diffraction maxima is considered here. On the average, two holes are used to include the region of a single diffraction maximum and there is a possibility of about 340 holes. Under these conditions Formula 2 reduces to
Orlglnnl Deck
Figure 2.
Schematic diagram of sorting procedure
Numbers in boxes refer to number of individual matches in that particular deck
likely candidate. It is in this sense that the term “most probable” is used here. However, the simple correspondence of a large number of maxima is not sufficient for a positive identification. Comparison with the complete diffraction pattern is always necessary. The sorting technique used in this laboratory to select the most probable matches may be broken down into a number of steps. First, those cards that have diffraction maxima where the unknown pattern has its largest maximum are selected. This divides the deck into tivo portions; one has the unknown pattern’s strongest maximum and the other has not. Kext, the second strongest maximum in the unknown pattern is used as a basis for the further separation of each deck. This leads to four decks, one with both of the two strongest maxima, one with neither of the t n o strongest maxima. and two decks each r i t h one of the two strongest maxima. These last two decks are comlined, leaving three decks. The third strongest maximum is then treated in the same manner, leading to six decks which :ire then recombined as shown in Figure 2 to give four decks. one of which has none of the three maxima, one of which has any one of the three, another which has any t n o of the three, and one n-hich h:is all three. The procedure is illustrated diagrammatically in Figure 2. b s the process continues, the cards are distributed into groups according to the number of individual matches to the unknown diffraction pattern. The group or deck with the most matches will be the most probable cards. Only in the case of a single-component sample may any card be found t h a t has all the diffraction maxima of the unknown. Usually the most probable cards will have fewer maxima than the number sought. Since the final decision on a n identification must be made on the basis of comparison with the complete dif-
fraction pattern, i t is the author’s practice to stop the sorting procedure, a t least temporarily, whenever the deck of most probable cards contains few enough cards, perhaps two or three, so that their complete diffraction patterns may be hand checked. If no identification is made, the sorting procedure is continued. Occasionally a single sort will lead to the identification of all the components present. Generally, however, a situation arises, wherein i t is necessary to repeat the entire procedure, using a corrected diffraction pattern after each component is identified.
PUNCHING DISTRIBUTION
-4s a rough guide to the number of sorting steps t h a t might be required, i t may be noted that the probability t h a t a particular card contains a certain diffraction maximum is p = -Nq
R
ivhere S is the average number of holes per card (including only that region of the card used for coding diffraction data), q is the number of holes used to include a single maximum, and R is the total possible holes per card, Therefore the number of cards that may be expected to contain any particular n diffraction maxima is
where -11is the total number of cards. These formulas are very approximate. They assume a random distribution of holes in the IBXI card which, of course. is not the case. They contain other approuimntions, hut may he
Thus it would be expected that about 344 cards would contain any one par-. ticular maximum but only about 26 cards ~ o u l d contain a n y particular pair of maxima. The number of cards containing three particular maxima would be expected to be only 2 . I n other words, sheer chance will give about two matches to any pattern of three diffraction maxima. No particular significance can be attached to these t n o chance matches. Only when the number of individual matehey greatly exceeds that expected by chance does the event become significant Thus, if a card has five particular diffraction maxima it should be seriously considered as a possible identification, qince the odds of such a n occurrence happening by chance are about 14 in 1000-that is, the chances of finding one card out of 4300 that has five particular diffraction maxima is about 14 in 1000. Even if such a circunid a n c e is encountered, the coincidence is improbable but not impossible. I n the analysis of a multicomponent sample i t is probable that no card will contain all of the maxima in the unknown pattern. Therefore i t is of interest to know the number of cards that would be expected by chance to have any particular number of maxima out of a group. For example, it may be desirable to know how many cards would be expected to contain three out of any particular ten maxima. The number of cards t h a t would be expected to contain exactly r out of a particular group of s maxima is equal to
nhere -VI is the total number of cards and p is the probability that a particular card contains a certain maximum. If Jf = 4300, s = 10, r = 3, S = 13.4, q = 2, and R = 340 (the parameters which apply to the author’s current deck), it would be expected VQL. 29, N O . 9, SEPTEMBER 1957
1271
that there would be approximately 140 cards containing three out of any particular ten diffraction maxima by chance alone. Thus the distribution of cards sorted in the manner previously described may be predicted n i t h an accuracy limited only by the deviations from random distribution of holes and the corresponding uncertainty in the value of p , the probability. Figure 1 shows the actual distribution of holes in the deck in use in this laboratory. The blackest holes are most frequently found, while those that are lightest in shade are most rare. For eyample, 16.5% of the cards have a hole in column 27 row 6, but only 0.5% have holes in column 33 row 9. The distribution is far from random. HOKever, the regions of the card n-hich have the greatest number of holes are also the regions where one hole covers a wider range of Bragg angles, thereby allowing the use of feiver holes t o include a particular diffraction maximum. Although those particular holes are more probable, a smaller value of Q would be used, and the tm-o effectp tend to cancel one another. The range used to cover a particular maximum should not be made too narrow. illthough the diffraction data being analyzed may be of the greatest accuracy, the same cannot always he said of the ASTM file of powder diffraction data. So to avoid missing a possible identification, it is wise to regard data as no more accurate than the ASTM file. A particularly difficult case arises when one of the components of the unknown has few diffraction maxima. For example, consider a case where the diffraction pattern of the unknon n multicomponent sample has 20 diffraction maxima, but one of the components has only three. I n this case, according to Equation 4 about 600 cards out of a deck of 4300 would contain three of the 20 diffraction maxima. It is therefore often necessary to reduce the number of maxima under consideration before a component with few maxima may be located. Thus if one of the components is identified and accounts for 10 of the 20 maxima. the sorting process should be started over again with only the remaining maxima being considered. Only about 140 cards out of 4300 will contain three out of the 10 maxima. EXAMPLE
A mixture of phosphates gave a diffraction pattern with 43 maxima in the region from 0” to 60”. After re-
1272
ANALYTICAL CHEMISTRY
inoval of those cards carrying the Hanawalt codes of regions in which the pattern of the mixture contained no maximum with a relative intensity greater than 7 (chosen arbitrarily), the IB11 file was reduced to 687 cards. KO attempt was made to reduce the file on the basis of chemical knowledge. After sorting through the nine strongest maxima in the manner previously described, the distribution of cards was as follows: Sumher of Matches 0 1
2 3 4
5 6-9
Found
Expected
278 242 105 47 13 2 0
266 266 118 31
5 1
0
The “expected” distribution \vas calculated from equation 4 using the value of 0.10 for p as being a more correct value for the deck of 687 than the previous value of 0.08 which applied to the full deck. The deviations between “found” and “expected” represent the departures from randomness. The complete diffraction patternq of the two cards with five matches were checked against the unknown pattern. One of them was an obvious mismatch, as it had a maximum with a relative intensity of 75 where the pattern of the mixture had no maximum. The other card was potassium dihydrogen phosphate. This compound accounted for 11 of the 43 maxima. These 11 were removed from further consideration, and the process was repeated starting with the strongest of the remaining maxima. After sorting through 12 of them the distribution was: Sumber of IZatches 0 1 2 3
4 5 6-12
Found
Expected
254 242 121 48 16 4 0
194 259 158 50 15 3 0
Of the four cards with five matchep, only the card for Zn3(PO&.4Hz0 was consistent n-ith the data. After elimination of the maxima accounted for by the two identified compounds, 19 remained unaccounted for. The process was repeated starting with the strongest of the remaining maxima. After sorting through seven of them the distribution n aq:
Nunihcr of
1Iatches
Found
Expected
0
308 259 91 21 2 0
329 256 85 16 2 0
1
3 3 4 5-i
O t the trio cards with four matches, only the card for sodium dihydrogen phosphate n as possible. After elimination of the maxima accounted for by the thiee identified compounds only eight maxima remained. The Ytrongest had a relative intensity of 15 based on the original pattern, and the average relative intensity was 5 . Therefore, the three identified components account for the major portion of the unknonn diffraction pattern. The m a l l r e d u a l s may be due to inaccuracies in the experimental pattern or in the *tandard pa t tern
