man No. 39170) and a platinum inlay electrode (Beckman KO.39273). Procedure. A 1.0-1.5 meq. sample, weighed to the nearest 0.1 mg., is added to an electrolytic beaker and dissolved in 150 ml. of methanol. Then 10 ml. of 70y0perchloric acid is added and the solution is titrated immediately with standard ferric chloride reagent. DISCUSSION AND RESULTS
An acidified solution of alkyl ferrocene turns blue upon standing, indicating the presence of ferricinium ion. It was also observed that the longer the delay before titrating the acidified solution the lower the assay. To overcome the oxidation of the sample, the titrations were conducted immediately after addition of perchloric acid. The presence of ferrous ion in ferrocene does not affect the determination. This was demonstrated by adding several drops of 1% ferrous ammonium sulfate to the ferrocene solutions. Titration of the samples was the same as if ferrocene alone were present. However, ferric ion as a contaminate will
lower the assay. Addition of ferric ion to the sample is equivalent to adding the titrant. Carbonyl substituted ferrocenes do not titrate with ferric chloride. Investigated compounds include; ferrocene-1,l ’-dicarboxylic acid, ferrocenoyl propionic acid, acetyl ferrocene, 1,l’-diacetyl ferrocene, 1,l’dibutanoyl ferrocene, and hexanoyl ferrocene. By making use of the difference in reactivity, it is possible to determine the amount of alkyl ferrocene in a mixture with alkyloxo ferrocene. An experiment was conducted where a mixture was prepared from weighed portions of alkyl ferrocene and its keto counterpart. A purity correction, as determined in Table I, was applied, and the mixture was titrated. The composition of the mixture and the results are found in Table 11.
LITERATURE CITED
(1) Baun, W. L., ANAL.CHEX 31, 1308
(1959). (2) Behum, J. D., Talanfa 9, 83 (1962). (3) Clancv, D. J., Spilners, I. J., ANAL. 2 ).
ACKNOWLEDGMENT
The authors thank R. C. Olberg for synthesizing and donating the compounds used in this study.
RECEIVEDfor review Augusb 20, 1964. Accepted October 27, 1964. Published by permission of the Aerojet-General Corp.
Computational Aids for Identifying Crystalline Phases by Powder Diffraction LUDO K. FREVEL Chemical Physics Research laboratory, The Dow Chemical Co., Midland, Mich.
b A comprehensive computer program has been devised to carry out the entire searching-and-matching process of phase identification by powder diffraction. The input information consists of the powder data and elemental data of a sample. The output of the program is in the form of a report listing the experimental diffraction data in juxtaposition to the 10 most intense lines for each matched standard.
D
two decades the Joint Committee on Chemical Analysis by Powder Diffraction (20) has made available a file of some 8000 powder patterns and several index books for these tentative standards. Many analytical laboratories have found this compendium useful in the qualitative identification of corrosion products, the phase study of fluxes, the detection of inorganic fillers in plastics, the analysis of minerals, the recognition of polymorphs, and generally in the phase identification of crystalline substances in unknown mixtures. For this type of analysis it is tacitly assumed “that the URIKG THE PAST
same substance always gives the same pattern; and that in a mixture of substances, each produces its pattern independently of the other, so that the photograph obtained with a mixture is the superimposed sum of photographs that would be obtained by exposing each of the components separately for the same length of time” (11). Unfortunately these statements are not unequivocally true for any of the powder diffraction methods (9, 18). Moreover, the most crucial assumption that the powder pattern yields a chemical analysis of a sample is theoretically unsound (21). VALID INFERENCES FROM POWDER DIFFRACTION
An x-ray powder pattern of a crystalline solid consists of diffraction lines usually listed in descending order of interplanar spacings measured in angstroms. The intensity of a diffraction line is generally recorded as peak intensity measured in arbitrary units. Thus the measured data can be represented conveniently by a paired set { d v , I v ] . For a mixture of crystalline
phases the set of interplanar spacings { d v ) corresponds to the sum of the observed spacings for each crystalline phase present, i.e. {dvl
=
c
(1)
( 4 P
where { d ) designates the set of interplanar spacings for phase p . The d’s for any particular phase, however, are not totally independent of each other but are related functionally according to expression 2 d-2
=
h2a*2
+ k2b*2 + 12c*2 +
2klb*c*cos a*
+ 21hc*a*cos p* + 2hka*b*cos y*
,
(2)
where a*, b*, c*; a*,8*, and y * are the reciprocal cell constants. From Equation 2 it is seen that the d-data for any crystalline phase can be accounted for by no more than six independent cell constants. The only valid information deducible from the spacings data pertains to the geometry of the unit cells of the various crystalline phases present. Each powder reflection, however, yields not only a &value b u t also a V O L 37, NO. 4, APRIL 1965
471
Table 1.
Comparison of Powder Diffraction Data of Metallic Phases
Metal bead
2.26 1.96
l.OO(75) 0.53 .~
1.384
0.40
~
200
2.265 1.962
1.00 0.53
1.000 0.467
220
1.387
0.31
0.253
111
1.180 0.30 311 1.130 0.15 222 a = 3.916 f 0,005 A. Al-Type
I
=
1.1826 1.1325
0.33 0.12 a = 3.9231 A. Al-Type ASTM 40802
+
cos2 28 sin2 e cos 8
*jhkl'
the various symbols being defined as follows: 28
= angle between incident and diffracted x-ray beams h,k,l = indices for a particular reflection jhbI = multiplicity factor for reflection
hkl f, = scattering factor for atom Z, e - M a = temperature factor for atom Za
= atom coordinates for atom Z, A(@,e,r) = absorption correction factor (1, 41 26, p = linear absorption coefficient r = radius of powder specimen.
zy,z,,
From the above intensity expression,
it is seen that the composite diffraction pattern for a particular crystalline phase yields implicit information about the 3dimensionally periodic electron density withinhhat phase. In general, however, the complete crystal structure for an unknown phase is not directly determinable; hence no explicit determination can be made of the number and kinds of atoms in the unit cell of an unknown phase. Since no positive identification of either elements or compounds can be deduced from the diffraction pattern of an unknown solid, one may naturally question the validity of a chemical analysis by the fingerprint match. I n practice this empirical
472
0.267 0.076
2.775 0.12 2.265 1.00 1.962 0.65 1.602 0.03 1.387 0.35 1.241 0.01 1.183 0.45 1.133 0.20 a = 3.9239 A. E2t-Type ASTM 7-46
peak intensity in arbitrary units.
corresponding intensity profile determined by the arrangement of the atoms in the unit cell and by the dimensions and orientations of the crystallites. For a randomly oriented powder the integrated intensity of a Debye-ScherrerHull line on a cylindrical film is proportional to
1
MnsZnC
Pt
0
ANALYTICAL CHEMISTRY
method involves the quantitative matching of the d-values of the unknown with the d-values of one or more standards and the qualitative agreement between corresponding relative peak intensities. The complications encountered in its use were described in 1944 (7) and attributed to the lack of uniqueness of a n established standard pattern. Isotopic substitution, solid solution, isomorphism, or isotypism can affect the validity of a match between the pattern of the unknown and the standard patterns matched. For example if two or more isomorphous cubic substances, with lattice constants al and a,, form a continuous solid solution, it is always possible to match precisely an intermediate lattice constant a by an appropriate solid solution the composition of which can be calculated closely from Vegard's rule: a = (1
- r,)a,
+ 2,a,
(4)
where 2, is the mole fraction of the a t h isomorph. Likewise, it is possible to match the scattering power of a particular atom Z by a solid solution in which two or more atoms Z1 and Z, are substituted according to Equation 5 Z = (1
- ru)Z1
+
ZuZa
(5)
where the Z's refer to atomic numbers and the 2's to mole fractions. To illustrate these complications two representative cases are described briefly. Case 1. The first case concerns the analysis of a n unknown submitted in the form of small spherical metallic beads. Powder data from filings of one of the beads are given in Table I, and refer to filtered CuK, radiation with a G. E. camera of 71.6 mm. radius. Using the ASTN Index (16) one finds potential matches with Pt (XSTM card 40802) , MnaZnC (card 7-46) , and PtaZn (card 6-0584). Although a satisfactory match is realized with Pt, an x-ray fluorescence analysis is required to confirm or reject the phase identification because the following solid solutions have unit cells practically identical with that of Pt and possess
the -41 structure: Pd gSn 13 (16), Pd.8Ag z (6,I+$), Pd J g i - 4 I~ (I+$),P t 9Ag 1 (IS). Indeed the element analysis gives the composition unambiguously as 83.5 wt. % Pd and 16.5 wt. % Ag. Case 2. This sample, prepared from two known powders, was exposed to CuKa1 radiation in an AEG Guinier double cylinder camera (114.7mm. diameter) to obtain more precise d-data than for routine Debye-ScherrerHull patterns. A small portion of the finely powdered sample was dusted onto a 0.008-mm. A1 foil coated with a very thin layer of petrolatum. The excess powder was removed gently by tapping the sample holder and by delicately stroking the powder surface with a piew of cleansing tissue. The randomly oriented layer of powder _ ( R ) . This latter test is optional and frequently is omitted in the program. After these two criteria are met successfully, the second strongest reference line of the potential candidate is matched according to the condition
ddl
- 6) 5
(dZ)Zsn
Iddl
+ 6)
(7)
where d, is any spacing of the subset {&,}. A similar match is tried for the third stronBst reference line of the potential candidate, provided the previous match was acceptable. Having successfully passed the { Z } , { R ] . and { D]-tests, the potential candidate is located in the standard pattern file { Z , n ) which starts with Z = 3 for a i i tLe lithium-containing phases and ends with Z = 93 for all the neptunium-containing substances of the ASTN file. The standard pattern file lists only the 10 most intense lines for each standard and its ASTM card number (see Table VI). These data are then made available for comparison with the powder data { Y , d,, I,,] of the unknown. The matching of the ten most intense lines of the standard pattern {d,, 102(Z/ZJa} is accomplished according to Equation 8 dv(l
- 6 ) I d6 I
d,(l
+ 6’
(8)
If a match is found then the calculated intensity of the strongest line of the identified phase is computed automatically from the quotient Z v / ( Z / Z J a . After matching the 10 most intense lines of the standard (a minimum match of three lines is always assured), the computer averages the 10 (or less) values for the calculated intensity of the most intense line and calculates the difference between the observed and calculated intensity for each matched d-value :
fl
where is the averaged value of the most intense line of the identified phase, If AZ is greater than a specified value, the d-spacing for this particular reflection is retained as a possible superposed line with intensity AZ. The completed match for the first identified phase is then printed in the form shown in Table VII. The entire process is then iterated until no more candidates are found under any of the Z D files searched, or until three or more (specified by stop number) failures to match a d, are encountered, or until a minimum intensity is reached. Only a search under the ZD1 file has been described. However, if there are no successful ZRD VOL. 37, NO. 4 APRIL 1965
475
Table V.
-
3302 -
3301
vi
n
13 33 26 25 14 12 33 28 27 26 16 33
. . . .
. . . . 82 29 16 33 47 16 33 47 33 27 20 33 82 16 33 82 16 33 5 33 47 16 33 25 20 12 11 33 33 22 33
. .
1
2 3
1RJ
99 823 1221
. .
72 73 74 75 76
di, A.
dn, A.
da, A.
77
io:
79 80 81 82
1.43 1.688 1.710
3.44 1.89 2.673 1.511 2.51 2.30
82 16 19 19 3
33 33 33 33
. .
215 96 94 50 54 253 98 97 120 205 88
4.82 2.97 2.95 2.54 2.57 8.95 2.98 2.97 3.08 4.20 2.89
2.70 2.73 2.73 2.75 2.77 2.77 2.785 2.80 2.80 2.80 2.82
4.00 2.32 3.59 2.68 2.72 1.486 2.606 2.47 2.07 2.78 2.02
3.12 3.13 3.14
2.98 1.95 47.21 .3
3.16 3.17 3.17 3.19 3.19 3.20 3.20 3.20 3.21 3.21 3.21 3.21 3.24
3.85 4.44 2.93 2.94 3.95 3.11 2.26 2.64 2.72 2.93 4.62 2.99 2.541
3.78 3.79 3.82 3.84
3.72 3.30 2.15 3.34
3.85 2.48 2.504 3.08 3.60 3.52 2.388 3.28 1.65 3.52 2.48
16 33 1.749 82 16 33 3.27 1.639 11 33 3.59 28 33 3.39 27 33 2.947 26 20 33 1.688 25 20 33 3.18 47 29 16 33 1.35 38 33 50 12 33 1.879 19 33 1.82
3.16 3.17 3.17 3.18 3.18 3.19 3.19 3.195 3.20 3.20 3.21 3.22 3.22 3.22 3.220 3.228 3.23
3.06 2.63 3.58 1.95 1.96 2.22 2.630 6.394 2.58 3.00 1.96 1.859 1.97 3.53 3.578 3.991 2.634
2.96 29 17 11 33 257 99 3012 9.81 2.91 82 33 164 91 3.35 4.93 29 33 182 99 823 3.56 3.59 1.66 29 33 186 99 823 1.69 30 33 156 91 3012 3.24 1.82 19 17 33 66 2.622 1.610 82 33 166 91 3.39 2.541 16 33 223 5.40 2.93 29 33 262 3012 10.2 2.72 83 33 162 99 3.28 1.67 33 192 3.70 2.87 30 33 200 98 4.00 1.68 47 16 33 83 2.82 3.10 82 29 33 130 99 823 3012 3.14 2.080 11 33 227 91 3012 5.9 2.124 27 33 234 99 3012 6.69 2.530 53 19 33 67 2.644
823
823 3012
823
. .
194 195 196 197
. . .
. . . 93 93 99
3.74 3.77 3.81 3.89
3.00 2.97 2.98 4.09
2.70 2.00 2.00 3.64
82 16 92 3 92 19
90 99 99 823 99 3012 99
*
(1
searches under the ZD1 file, the program continues to the ZDl%le and then to the ZDS file before searching under another specified element. After exhausting all potential searches the program prints out the entire analysis in the form of a report. The time to process the digitized powder data of an unknown requires from 2 to 5 minutes on the Burroughs 5000 computer using magnetic tape storage. PERFORMANCE
The practicality of the described program was tested by key-punching and storing on magnetic tape ZD-files for 25 different elements ranging in Z from 21 to 70; tabulating, keypunching, and storing on tape the 10 most intense
-
ANALYTICAL CHEMISTRY
. .
33 33 33 33
168 246 167 254
.
.
. .
92 3.55 2.96 11.9 99 823 83 29 33 269 2.46 3.57 99 823 3012 12.0 83 29 33 270 92 56 2.46 4.48 99 3012 12.1 29 33 271 26 14.9 7.47 2.70 38 25 23 20 11 33 272 3012 92 29 3.33 8.65 99 823 3012 17.6 26 13 33 273 2.97 29 20 14.1 99 823 3012 28.0 29 20 33 274 ( Z } = Set of elements spectroscopically detectable in a standard substance; substance.
476
3.4 2.98 1.00
. .
dz, A .
. .
. * . . . .
30 11 33 78 33 30 3 33
2.72 2.74 2.743 2.75 2.75 2.752 2.76 2.76 2.77 2,771 2.79
* . 27 33 138 101 82 29 33 139 99 11 33 140 96 51 33 141 32.30 33 142 82 16 33 143 35 19 33 144 33 145 82 26 33 146 99 30 33 147 99 51 33 148 29 16 33 149 51 33 150 99 29 33 151 99 53 33 152 55 33 153 93 35 33 154 2015
. . . .
d2, A. 0.79 1.15 1.21
(Ki
I
. . 99 99 3012
28 4 29
di, A. 2.09 1.80 2.09
n
( ZI
Triple Index File
.
99 2033 3012
3.43 8.59 3.42 9.14
176 99 2015 2033 3.53 8.62 3.29 210 4000 4.39 8.82 5.03 184 99 2033 3012 3.57 8.89 5.03 244 4000 8.54 9.96 5.02 189 99 2033 3012 3.60 1 0 . 3 5.07 274 99 823 3012 28.0 14.1 2.97 n = ordinal number locating a reference pattern in
33 33 33 33 33 33
lines for 1359 standard patterns selected from the ASTM card file ( l a ); and then running some 20 cases which proved tedious or fruitless by the conventional identification procedures. By way of introduction, a simple case will be cited to elucidate the more important features of the program. A mixed powder was prepared from 102 mg. of arsenic metal and 107 mg. of selenium (Eimer and Amend labeled amorphous precipitate) , and the intimate mixture was exposed on 4 1 foil in a n AEG Guinier camera. The film was read on a precision comparator and the measurements were computer-processed t o give the interplanar spacings listed under d, in Table VIII. Diffraction lines arising from the internal standard were obviously excluded from the input
-
99 2033 3012
data (explanation for missing number in column 1 of Table VIII). Several entries on the data input sheet require some explanation. The total number of pertinent diffraction lines are entered in (v)MAX. No entries under ( R o ) automatically Since x-ray eliminates the {Rf -test. fluorescence analysis confirms that -4s and Se are the chief elements detectable in the sample, searches are prescribed for Z = 33 and 34 (the order of searching is immaterial). Provision is made to test if any two standard substances listed in the {Z, n} file are present in the unknown- sample by specifying Z1-nl and Zz-nz under Match. If only zeros are entered here the option is by-passed. The Stop Number determines the number of unsuccessful
Table VI. Standard Patterns for Arsenic and Hexagonal Selenium
for Z = 33 (Arsenic)"
33Da
di, A. 2.07 2.09 2.22
dz, A.
da, A.
3.4 1.21 1.28
0.79 1.00 1.11
4.32 2.57 2.82 3.20 3.61 4.84 3.10 4.20 3.02 3.25 2.55
3.09 2.77 3.21 3.00 2.95 3.41 3.07 2.80 3.30 7.90 2.48
2.71 2.72 2.72 2.72 2.73 2.76 2.77 2.78 2.79 2.79 2.84
3.48 3.00 2.238 5.56 2.46 2.76 6.58 10.4 4.00 6.65 6.7 2.74 8.42 8.76 3.53 4.85 8.59
2.46 2.82 2.97 4.44 4.45 3.28 2.98 4.04 2.62 1.677 3.01 2.48 3.63 3.71 8.62 4.55 3.79
3.13 3.14 3.15 3.16 3.17 3.18 3.18 3.18 3.19 3.22 3.24 3.27 3.27 3.28 3.29 3.29 3.30
6.7 3.43 3.24 3.15
3.99 3.78 3.16 5.40
3.70 3.72 3.85 3.86
n
26 29 36
47 30 33 30 3 33 48 33
. .
. .
209 54 83 147 190 216 123 205 107 157 52
91 3012
19 33 47 16 33 82 16 33 26 33 29 33 47 16 33 28 33 29 28 27 33 30 33 27 33 27 33 47 16 33 92 11 33 92 29 33 92 33 30 33 92 33
171 104 37 226 46 79 232 265 199 233 235 73 242 248 176 217 246
91 3012
26 33 82 16 33 30 33 33
236 168 156 136
20 27 47 16 30
33 33 33 33 11 33 24 33 20 12 33 50 12 33 81 33 30 33 28 33
.
.
99 3012 96 99 99 3012 99 99 3012
34-50 Se (hexagonal) ASTM 6-0362
33-81 AS ASTU 5-0632
2.771 3.52 1.879 2.050 1.556 1.768 1,757 1,199 3,112 1.658
100 26 26 24
3.010 3.780 2.070 1.998 1.766 2.184 1.637 1.503 1.650 1,429
11 10
7 7 6 6
100
53 35 21 21 16 12 10 9 9
. .
. . . .
99 3012 99 823 99 3012 3012 98 99 3012 99 3012 99 99 99 99 99
. .
2033 2033 2015 2015 2033
. .
3012 3012 2033 3012
99 3012 91 3012 93 2015
.
.
3.59 99 823 3.14 7.21 186 29 33 5.34 99 823 3012 2.83 7.37 222 29 33 17.6 99 823 3012 3.33 8.65 273 26 13 33 6.79 99 3012 7.50 237 8.97 26 33 6.83 99 3012 7.06 9.01 238 26 33 2015 3.27 2.646 9.31 160 53 33 standard pattern file; ( R = set of codified polyatomic groups present in a standard
exhaustive searches tolerated before the searching process under the chief elements is terminated. Usually this number varies between 3 and 7. Before any of the Z D files are searched, the upper and l%er bounds for the most intense line of subset (d1-m) = (2.770, 3.006, 3.781, 1.879, . ., di3 = 3.516, . , , , 1.115 A.) are computed as 2.770 (1 - 6) = 2.763 A. and 2.770 ( 1 6) = 2.777 A. A search under the 3301 file (refer to Table V) reveals only two potential candidates:
.
+
2'763 A'
'
2'77 A'
(,771
A.)
5 2.777 A.
The ( Z J - t e s t eliminates the first candidate, 33-80, because { 25, . 20,
12, 11, 331 i s n o t a subset (34, 33). The second 33-81, passes the (21-test; no (R]-test is requested, is applied successfully : d13(1
-
of (Zo) = candidate, and, since the D-test
6) =
3.507 A.
5 3.52 A. 2 3.525 A. dd1
=
+ 6)
-
d4(1 6) = 1.874 A. 2 1.879 A. 2 1.884 A. =
+ 6)
A search in the arsenic file, (33, n ) , identifies the successful candidate, 33-81, as As (see Table VI). The final programmed match between the first identified phase and the matched standard is
printed out as shown in Table VII. The averaged value for the calculated intensity of the strongest line of As is 4/.26 computed as 1/9(53/1.00 11/.26 6/.24 6/.11 5/.10 5/ 3/.06 4/.06) = 47.59. I , for .07 the second strongest line of As follows obviously as 47.59 X 0.26 = 12.37. Elimination of the identified lines leaves the new subset {3.006, 3.781, 6.407, 3.198,2.073, 2.770,. . ,dm = 1.318A). in which d6 = 2.770 A. is rated with an intensity of 5.41 (see AI column of Table VII). Iteration of the described process with dl = 3.006 A. leads to no potential candidates in files 33D1, 33D2, or 33D3 because the ( Z ] - t & fails in ea& case, thus indicating that the 3.006 A. spacing does not belong to a listed As-containing phase. Consequently, a search is made under 34D1 (Table IV) by applying the ZRD-test yielding the successful candidate, 34-50; namely, hexagonal Se. Again the match between the second identified phase and the matched selenium standard is printed in tabular form (see Tabule VII). Surprisingly, a third phase is encountered and identified as --1s203. The last step of the program is the printing of the analyst's report reproduced in completed form in Table IX. The analyst refers to the three ASTM cards of Table VI1 and completes the matching of the remaining unidentified lines beyond the first 10 lines for As, Se, and Xs203~Inspection of the last column of the report reveals the presence of any unidentified residuum and precludes sloughing off any unaccounted data. I n the case of the (As Se) sample, the presence of a few weak unidentified lines warrants a closer inspection of the individual components. A 10-hour exposure of the Se powder in the AEG camera yielded 15 weak reflections belonging to a-Ses ( 2 ) not listed in the h S T M file. To explore the capabilities of the ZRD Search-Match program, powder
+
+
+
+
+
+
+
+
.
+
VOL 37, NO. 4, APRIL 1965
0
477
Table VII. V
dv,
A.
Iv
&, A.
2.771 47.59 3.520 12.37 1.879 12.37 2.050 11.42 1 556 5.23 1.768 4.76 ... 1.757 I. 199 3.33 3.112 2.86 1.658 2.86 ASTM 5-0632
9 4 21 17 26 22
2.770 3.516 1.879 2.048 1.555 1.769
53 4 11 6 6 5
37 7 23
1 i98
5 3 4
..,
3.113 1.656
8 3 16 19
Phase 2 d v , A. 3.006 3.781 2.073 1.997
13 25
2 i53 1.638
V
..
:
Print-Out of Matched Diffraction Dataa
As
Phase 1
...
Y
..
d,, A.
1 10 9 20
... 3 2
AI 15.4
..
..
14 12
...
As208
d,, A.
3
...
2:i31 2.260
1 1
IC 9.19 5.79 3.49 2.57 2.48
3.195 6.394 2.541 2,768 1.957
5.4 2
...
I, =
IC 1.503 2.26 1.650 2.03 1.429 ... ASTRl 6-0362
I” 6 6
AI
2.83
...
1,561
1.670 ... 2.132 1.56 2,262 1.10 1.442 ... ASTM 40566
...
...
..
3.62 2.71
Se d., A.
...
Phase 3 d v , A. 3.198 6.407 2.543 2.770 1.957
V
6
IO 22.60 11.98 7.91 4.75
3.010 3.780 2.070 1.998 1.766 2.184 1.637
...
1.67 1.14
Se
I” 38 12 6 3
-
Phase 2 (cont’d.) dv, A. I” 28 1.503 2 24 1.653 3
AI 5.41
IC
...
4 (I/Il),
Values of AI, less than or equal to minimum intensity specified, are not printed. (Negative values of AI arise from poor intensity data, preferred orientation, or pronounced superposition of two or more strong lines.)
Table VIII.
Deck
829
Input Data Sheet for ZRD SEARCH-MATCH
Project
372
Prob.
Date 091164
250
Charge
Name of Customer
For
Card #I
+
‘‘
(Sample Description) As Se 60 spaces
I11
Card #2, 3, __(,)MAX
34
6 = 0.0025,
I
Punch zeros if blank Elements
(&I
Groups
(Rol
Search
33
---I--.--.-’-l-l-f-
,
,
~ 33 _1
’1 ,
Match
34
34_
1
, _
p I’-
DELTA I
MINIMUM
1
_
7
, , _
_
-, I 1 ,
I
_I
~
(Do not punch dash) StopNumber
3
Cards 4 etc. V
1
3 4 5 6 7
t
8
9 10 12 13 14 15 16 17 19 20
478
ANALYTICAL CHEMISTRY
t
-d v 6.407 3.781 , 3.516 , 3.347 * 3.1982; 3.1126, 3.0062, 2.7698, 2.5433, 2.2604, 2.1831, 2.1306, 2.1046, 2.0734, 2.0481, 1.9973, 1.9567,
Y
21 22 23 24 25 26 27 28 30 31 32 33 34 35 37 38 40
, , , , , ,
;
, , , , , , , ,
-dv __I” 11 1.8793, 1,7692, 5 4 1.6564, 3 1.6533, 2 1.6382, 6 1.5552, 2 1.5145. 2 1.5031; 5 1.3847, 2 1.3675, 1 1.3520, 2 1.3176, 2 1.2892, 2 1.2835, 5 1.1982, 2 1.1776, 3 1.1152,
I
_
1
_
_
~
~
~
Print-Out of Programmed Report for Sample: As
Table IX.
v
1
3 4 5 6 7 8 9 10 12 13 14 15 16 17 19 20 21
22 23 24 25 26 27 28 30
31 32 33 34 35 37 38 40
Sample dv 6.407A. 3.781 3.516 3.347 3.198 3.113 3.006 2.770 2.543 2.260 2.183 2.131 2.105 2.073 2.048 1.997 1.957 1.879 1.769 1.656 1.653 1.638 1,555 1.515 1.503 1.385 .1.367 1.352 1.318 1.289 1.284 1.198 1.178 1.115
Sample: As
I, 6.0 12.0 4.0 2.0 6.0 3.0 38.0 53.0 3.0 1.0 3.0 1.0 2.0 6.0 6.0 3.0 2.0 11.0 5.0 4.0 3.0 2.0 6.0 2.0 2.0 5.0 2.0 1.0 2.0 2.0 2.0 5.0 2.0 3.0
Se Phase 2 D , A. I C
As Phase 1 D,A. I C
3.520
12.4
3,112
2.9
2.771
47.6
As203 __Phase 3
D , A.
I,
Phase 4 D, A. I ,
+ Se5
Phase 5 D , A. I C r
Phase 6 D , A. I ,
1.4
1.879 1 .768 1.658
2.4 4.8 2.9
1.556
2.9 1.9
1.289 1.284
2.4
1,199
2.4 3.3
1.1158
1.9
C(lc)n I;
3.010
22.6
2.184
3.6
2.070
7.9
1.998
4.7
1.766
4.7
1.650 1.637
2.0 2.7
-0.7
12.0
6.394 5 . 8
2.768 2 . 6 2.541 3 . 5 2.262 1 . 1 2.132 1 . 6
1.957 2 . i
1.1
1.0
0.8 (2.0) 0.4 -0.3 (5.0) 2.1 (2.0) 0.1 1.0 (2.0) 0.9 (2.0) -0.4 (2.0) -0.4 1.7 (2.0) 0.9 (3.0) 1.1
5.2
1.586 1.367
-
0.2 0.0 -8.4 2.0 -3.2 0.1 15.4 2.8 -0.5 -0.1 -0.6 -0.6 2.0 -1.9 -5.4 -1.7 -0.5 -1.4 (0.2) -4.5
3.780
3.195 9 . 2
2.050
I,
1.5127
1.6
1.503
2.3
1.3170
1.1
1.1769
1.1
+ Se
Date Received: 091064
Origin: C P R L
Sample was examined by x-ray powder diffraction and data processed by computer program ZRD-Search-Match. Following crystalline phases were identified: As, Se (hezagonal), and Asz03. Analyst: L . K . F.
Date: 091164
Report: X R D
Charge: 1280
Comments: Lines 6, 16, and 32 unidentijied. X-rayjluorescence analysis: As, Se chiefekmats; M n .70%, Fe .26%, Te .04%, Z n .OS% a
All data filled in by analyst are printed in italics.
patterns were taken of various mixtures prepared from substances listed among the 1359 standards in the ( 2 ,n ) file. A11 samples were analyzed by x-ray fluorescence and/or optical emission spectroscopy to confirm the chief elements present. The combined data were then processed by the program as described above. Rather than report on the pedestrian successes encountered with simple mixtures, it is thought more enlightening to describe two rather difficult cases which required the judgment of the analyst. The first such case involved a sample prepared by grinding together 100 mg. of A&03, 100 mg. of SeOn,70 mg. of of PbSe04, and 70 mg. of AgdS04. When the complex pattern from this sample was analyzed by the film-matching technique (practiced competently in this laboratory for over two decades), no identification
--
could be made even though three capable analysts tried diligently to find a match by our established procedures (8). On the other hand, processing the ZD-data by the ZRD program gave two satisfactory matches, namely PbSeOI and iisZo3.The other two initial phases were not detected because the selenium dioxide hydrated and reacted with Ag&04 and possibly some As203 to form one or more unlisted phases. As our starting PbSeOc had been synthesized from very pure reagents it was decided to compare its powder pattern with the ASTM data. Table X exemplifies the typical shortcomings of most ASTM patterns of biaxial phases: poor accuracy for dvalues greater than 3 A., low resolution for closely spaced reflections, and lack of exhaustive and correct indexing of patterns. I n up-dating our Z-D files
and {Z, n ) files the more accurate data for P&e04 were included. Another interesting comparison between the performance of the ZRD program and the capability of the filmmatching technique was afforded by the analysis of a light-gray powder labeled U-3.6. Treated as an unknown, this sample was partially identified by our routine method as a mixture of “a rare earth oxide & 0 3 (pattern almost identical with YzOa), Asz03, or Sb2O3,and KH,As04. There were several additional weak lines which were not identified.” X-ray fluorescence revealed Y, As, Ag, Pb, Se, and K as dominant elements. Optical emission spectroscopy substantiated this analysis except for Se to which the particular method is not sensitive. Consequently {ZO)was entered as 182, 47, 39, 34, 33, 19) along with the diffraction data VOL. 37, NO. 4, APRR 1965
479
tional Table X.
ASTM 11-534
Dow d, A.
d, A.
" 1 ::: 5.5
30
102
(')11
obad
5.529 5.073 5.000 4.429 4.385 3.772 3.701 3.482
16 30 30 9 19 21 71
11
3.74 3.49
50 25i
3.38
5
3.387
18
3.28
100
3.268
100
3.16
20
3.150 3.111 3.079
29 7 74
3.060
50
2.762 2.654 2.622 2.587 2.536 2.517
43 2 28 28 7
2.488 2.366
22 3
2.318 2.307
12 32
281
3.08{
g5i
2.78
25
2.61 2.59
30 15
10
2.49
2.31(
25{
1
2,27{
25i
2.255
2.21
15
2.2141(
4
2.1490
4
2.1010 2.0706 2.0561
40 4 5
40 25{
2.10 2 . oi{
2.0172r 2.0025 1,991
6( 8
1.9885{
39r Lattice constants for a-PbSeOd: a ='7.147 A., b = 7.400 A., c a t 23°C. Space group P2,lrn. a
cited in columns 2 and 3 of Table XI. Since our list of 25 test elements excluded Pb, Ag, and K, the search under the Z D files had to be restricted to 39, 34, and 33. Notwithstanding this limitation, the Z R D program identified and matched four phases: Y203, AszO~, A4g&.04, and KH2AsO4. The printout, as received by the analyst, listed these phases but also recorded a large number of unidentified lines (see Table XI). Incompleteness of the analysis was also evident to the analyst by the absence of any Se-containing phase(s)
.
480
ANALYTICAL CHEMISTRY
A.
hkl
6.961 6.778 5.522 5.070 4.998 4.425 4.385 3.772 3.700 3.481 3.428 3.389 3.362 3.267 3.248 3.150 3.110 3.081 3.074 3.061 2.845 2.828 2.807 2.761 2.656 2.625 2.587 2.535 2.515 2.499 2.488 2.366 2,325 2.320 2,318 2.308 2.259 2,2555 2,2533 2.2522 2.2363 2.2141 2.2127 2.2033 2.1925 2.1609 2.1558 2.1499 2.1280 2.1022 2.0698 2,0571 2.0451 2.0189 2.0125 2,0022 1.9943 1.9931 1.9887 6.959 A., p =
100 001
doa1cd.r
=
As-containing phases besides and KH2ds04. The print-out of the report was completed by filling in the less intense lines for the 5 identified phases and adding the signed comments. Sample C-3.6 actually was prepared by mixing and grinding together 38 mg. of Yz03,23 mg. of KHzAsOa, 28 mg. of PbSe04, 47 mg. of Asz03,and 23 mg. of Lig&jo4.
AsZ03, Ag&04,
Comparison of PbSe04 Powder Patternv
io1
110
011
111
101
111
020 200
201 002 io2 120 021 210 211
Q12 121 Ti2 201 121 102 202 211 112 212 220 22 1 022 -122 301 130 300 03 1 io3 003 22 1 311 131 122 310 222 113 202 413 302 -131 203 212 312
301
213 103 230 231 032 321 132 103'5.7'
Failure to identify a Se-containing phase could be accounted for either by the lack of a suitable standard in the 3 4 0 files or by an over-subtraction suffered by a superposed reference line of the sought standard. To circumvent the latter possibility an exhaustive ZRDsearch was made only under the 3 4 0 files by utilizing the original powder data of U-3.6 and setting the Stop Number a t 15. The fifth phase was thus identified as PbSeOl (see Table XII). A similar exhaustive search under the 3 3--0 files revealed no addi-
SCOPE
Although the full potential of the Z R D program will not be realized until precise certified standard patterns become generally available, several pertinent conclusions and plausible predictions can be stated a t this time: The present ASTM file of standards can be used effectively with the described Z R D program. Mixtures with more than three components, however, will yield some accidental matches which usually can be spotted by a random mismatch of d-values (rather than by a uniformly larger set or smaller set of d-spacings) and by a very poor match of intensities. I t is assumed that the diffraction data of the unknown are registered with monochromatic CuKal radiation and with an internal standard to yield precision d-values, thereby eliminating essentially half of the error of matching interplanar spacings. The various options of searching will prove useful to the analyst. Searching exhaustively for the phases containing a particular element is only one of several optional selections. For example, the option to search for any potential selenates or selenites is exercised by specifying ( E o ]= { 1211, 12121 and searching in the 3 4 0 files. The more restricting the specifications of the search, the greater can be the tolerance factor 6 to allow for possible solid solution phases. Supplemental information from an infrared split mull, an optical absorption curve, or a spot test can furnish input data for a restricted search. It should be noted that all organic substances, which do not contain elements detectable by optical emission or x-ray fluorescence, are listed under carbon (2 = 6), and all ammonium salts as well as hydrazine compounds are classified under nitrogen
(2 = 7). The ability to detect minor phases in the presence of major unidentifiable phases is unique to the Z R D program. The advent of fully digitized output of diffraction data-e.g. (a@,, ZJ-in the form of punched cards or tape will speed up the analysis and will introduce a quantitative aspect to the intensity data. The programmed report will raise the
Table XI.
Sample A.
Y
dv,
1 2
7,066 6.788 6.397 5.258 5.224 5.070 5.001 4.816 4.477 4.430 4.330 4.146 3.814 3.705 3.482 3.382 3.269 3.243 3.212 3.198 3.152 3.079 3.061 2.984 2.938
3 5 6 7 8 9
10 11 12 13 16 19
21 22
24 25 26 27 28 30 31
32 33 34 35 36 37 38 39 40 41 42 43 45 46 50 51
52 53 54 55 56
2.919
2.852 2.767 2.741 2.696 2.650 2,622 2.612 2.587 2.576 2,540 2.502 2.316 2.308 2.259 2,211
2.131 2.100 2.078 2.000 58 1.988 59 1.966 60 1,958 61 1.874 66 1,863 67 1.852 68 1.845 69 1.817 70 1.789 71 1.769 73 1.719 76 1.715 77 1.704 78 1.700 79 1.692 80 1.668 81 1.638 82 1.620 83 1.598 85 1.563 87 1.549 88 1.532 89 1.491 92 1,442 93 Sample: U-3.6
yzo3
I"
0 0 0 0 0 0 5 0 4 0 7 0 7 0 7 0 6 0 17 0 3 0 10 0 10 0 15 0 3 0 11 0 45 0 10 0 12 0 58 0 34 0 3 0 3 0 8 0 11 0 45 0 4 0 10 0 4 0 3 0 4 0 3 0 13 0 28 0 3 0 3 0 8 0 3 0 8 0 6 0 5 0 12 0 5 0 4 0 10 0 18 0 3 0 4 0 3 0 3 0 3 0 4 0 3 0 3 0 11 0 11 0 3 0 6 0 16 0 4 0 13 0 4 0 5 0 6 0 4 0 5.0
Phase 1 D,A. I,
Completed Print-Out of Programmed Report for Sample U-3.6" AS203 AgaAsOc KHzAs04 PbSe04
6 5 38 14 14 3
Phase 2 D,A. I,
Phase 3 D,A. I,
Phase 4 D,A. I,
Phase 5 D,A. I,
I,
Phase 6 D,A. I,
6.0 5.0 13.1 14.0 -5.5 (3.0) -1.8 ( 5 . 0 ) -1.9
6.394 2 4 . 9 5.210
19.5 6.073 6.000
4.429
4.340 1 4 . 5 3.810
4.2 7.9
4.0
7.0 (7.0) -7.5 6.0 -13.0 (3.0) (10.0) (10.0) (15.0) 3.0 11.0 5.5 (10.0) (3.0) (-32.6) 8.5 3.0 3.0 8.0 (-0.1) -4.5 -5.0 -17.2 (4.0) (3.0) (4.0) 3.0 -2.0 -5.6 3.0 (3.0) (0.8) 3.0 1.3 (6.0) -5.9 -9.0 (5.0)
7.9
30.0 3.701 6.0 3.482 1 8 . 8 3.387 4 . 8 5:26'8 26.4
3.195 39.5 3.078
3.060 90.6
3.066
2.768 11.1
12.3
2.743 49.5
2.652 27.2
2.541 15.0 2.500
6.3
2.261
7 . 2 2.262
4.7
2.132
6.7
2.980
2 . 7 6 2 11.4
9.0
2.610
1.8
2.000 0.7 9.4
1.846
8.0
2.818
1.8
1.720
4.6
1.770
1,670
8.3
3.6
1.599 28.1 1.699 1.563 6 . 3 1.551 1.631 4 . 5
4.0
1.442
4.7
7.4
2.687
7.4
8.307
8.6
8.101
10.6
21 .o
1.989 1.966
10.3 4.6
1.863 1.862
6.9 7.4
-B.O -8.8 6.8 -11.4
8.3 -16.6
-58.1
-11.6
-3.4 1.8 -3.4
-6.6 -3.9
-4.6 -6.3
-0.5 -0.7 (-23.7) -26.1 (3.0) -3.9 (4.0) -3.4 (3.0) 1.0 (3.0) 1.2 3.0 -1.4
1.707
(3.0) 3.0 5.6 0.6 (3.0) -2.3 (2.1) (4.0) (-15.1) -2.3 -3.7 1.5
5.4 1.691
6.9
1.639 13.9 1.622
4.2
1.4966
3.9
8.7
1.533
-0.9
(4.0)
5.4
1.701 1 0 . 4 1.636
2.682
2.504 27.2
2.080 10.9
1.957 1.874 41.7 1.873
5.160 7 . 7 9 . 0 3.079 19.6 3.060 1 3 . 2 25.5
2.697
-C(Ic), D
4.5
-1.6
-3.9 -1.6 -0.2 -19.1
(4.0)
0.3 Origin :
Date Received:
0.1
Sample was examined by x-ray powder-diffraction and data processed by computer program ZRD-Search-Match. Following crystalline ~, KHzAsOi, and PbSeO4. phases were identified: YzOS, A s z ~ AgaAsOl, Analyst: L. K. F.
Date:
Report:
Charge:
Comments: 16 weak unidentified lines indicate presence of several minor phases. X - r a y fluorescence analysis of U-3.6: Y , A s , Ag, Pb, Se, and K are chief elements detected. The pronounced superposition of the strongest line (3.061 A . ) raises the affected calculated intensities unduly and accounts for the larger negative values in the last column. All data filled in by analyst are printed in italics. 0
~~
VOL. 37, NO. 4, APRIL 1965
481
Table XII.
Identification of Se-Containing Phase in Sample U-3.6
Phase 5 d v , A. 3.269 3.079 3.482 3.061 2.767 2.100 1.988 2.308 5,001 4,430
V
24 30 21 31 36 55 59 51 8 11
PbSeOl I” 15.0 12.0 10.0 58.0 11.0 6.0 5.0 3.0 5.0 7.0
quality of diffraction analysis and provide numerical records. The prospect of programmed quantitative diffraction analysis will be feasible if the powder data are coupled with quantitative elemental analysis. Lastly, the ZRD program will free the diffractionist from the fatiguing task of searching and will allow him time to concentrate on the textural information revealed in a diffraction pattern and to attempt matching the structure of an unidentified phase by comparison with tabulated isomorphs. ACKNOWLEDGMENT
The author is grateful to Miss Carole Engbrecht of the Dow Computations Laboratory for writing the ALGOL 60
d., A. 3.268 3.079 3.482 3,060 2.762 2.101 1.989 2.307 5,000 4.429
I C
26.41 19.54 18.75 13.20 11.36 10.56 10.30 8.45 7.92 7.92
AI
44.80
program for the Burroughs 5000 digital comuuter to handle ZRD Search-Match. LITERATURE CITED
(1) Bradley, A . J., Proc. Phys. SOC.(Lond o n ) 47, 879 (1935). (2) Burbank, R. D., Acta Crust. 4, 140
(1951). (3) “Chemical Abstracts,” 56, 80N-86N (1962). (4) Claasen, A., Phzl. Mag. 9, 57 (1930). (5) Coles, B. R., J . Znst. Metals 84, 346 (1956). (6) Donnay, J. D. H., Donnay, G., Cox, E. G., Kennard, O., King, SI. V., “Crystal Data Determinative Tables,]’ 2nd Ed., ACA &lonograph N o . 5, American Crystallographic Association, 1963. ( 7 ) Frevel, L. K., IND. ENG.CHEM.,ANAL. ED. 16,209 (1944). (8)Hanawalt, J. D., Rinn, H. W., Frevel, L. K., Ibid., 10, 457 (1938).
(9) Hargreaves, A., “X-ray Diffraction by Polycrystalline Xaterials,” H. S. Peiser, H. P. Rooksby, and .4.J. C. Wilson, eds., p. 298, The Institute of Physics, London, 1955. (10) Hofmann, E., Jagodzinski, H., 2. Metallk. 46, 601 (1955). (11) Hull, A. W., J . Am. Chem. SOC.41, 1168 (1919). (12) “Index (Inorganic) to the Powder Diffraction File (1963),” ASTRI Special Technical Publication 48-M2,PhiladelDhia. Pa. (13) Johannsson, C. H., Linde, J. O., Ann. Phys. L p z . (5) 6,458 (1930). (14) Kuznetsov, V. G., Zzv. Zekt. Platzny, dkad. ?;auk. SSSR, N o . 20, 5 (1946). (15) Nial, 0..Svensk Kem Tidskr. 59. 172 (1947). (16) Paalman, H. H., Pings, C. J.,J . 9 p p l . Phys. 33,2635 (1962). (17) Smith, D. K., “A Fortran Program for Calculating Powder Patterns from Atom Coordinates,” Amer. Crvst. Assoc. Annual Meeting, March” 28-30, 1963; paper E l l . ( ( (18) Stokes, A. R., X-ray Diffraction by Polycrystalline Materials,” H. S. Peiser, H. P. Rooksby, and A. J. C. Wilson, eds., p. 409, The Instituteof Physics, London, 1955. (19) Taylor, A., Sinclair, H., Proc. Phys. SOC.57, 108 (1945). (20) The American Society for Testing and Materials, The American Crystallographic Association, The (British) Institute of Physics, and The National Association of Corrosion Engineers. (21) Warren, B. E., J . A m . Ceram. SOC. 17, 73 (1934). (22) Wyckoff, R. W. G., Posnjak, E. W., J . Wash. Acad. Sei. 13,393 (1923). RECEIVED for review December 14, 1964. Accepted February 8, 1965.
An Integrating Analog Computer for Atomic Absorption Spectrometry E. A. BOLING Medical Service and Research laboratory, Boston Veterans Administration Hospital, and the School o f Medicine, Tuffs University, Boston, Mass.
b An integrating analog computer is described which permits atomic absorption spectrophotometry in analytical situations ordinarily too noisy for satisfactory analysis. Speed and precision for routine analyses are markedly improved. The Beer-Lambert equation is solved by the computer and concentration in the undiluted specimen is given directly in digital form for each reading. O p erator fatigue is reduced. The stand= 1.0 ard deviation for the ///, setting for calcium when collecting data for 10 seconds is typically *0.0003. The relative detection limit for calcium using this apparatus is less than 0.003 p.p.m. Serum calcium analyses may be performed using as little as 5 PI. of sample. The absolute detection limit for calcium is about 1 0 - 8 gram. 482
ANALYTICAL CHEMISTRY
R
EADOUT SYSTEMS for atomic absorp-
tion measurements are usually one of two types. Meter readout in % transmission is convenient for singlebeam instruments (2). Null-point voltage dividers are typically employed for double beam applications and might be used in single beam instruments if automatic operation or digital readout were desired. Many atomic absorption analyses tend to be somewhat noisy, and for some, noise seriously limits analytical precision. For any analysis, noise increases the time needed to reach a given level of precision. This has the indirect effect of increasing the amount of sample which is required, since the sample must be atomized continuously while each decision is being made. Noise also plays a basic role in setting detection limits.
We have constructed an improved data readout system for use in atomic absorption spectrophotometry. Integrators are used for data collection, because they act to increase signal/ noise ratios and also to permit shortterm storage of the result, which conserves the sample. Servo-operated voltage dividers compute the signal ratios. I n addition, the Beer-Lambert equation is solved by a nonlinear potentiometer plus a second servodriven divider so that concentration is given directly in digital form. We have found that the device increases speed and accuracy for any analysis. Since the instrument automatically indicates the result for each sample as it is atomized, all operators analyzing a given sample should obtain identical results for any trial. Furthermore, operator fatigue is markedly re-
