Quantitative Determination OF Crystalline Materials by X-Ray Diffraction S. T. GROSS’
AND
D.
E. MARTIN
University of Illinois, Urbana,
A method is described for using x-ray diffraction patterns for chemical analysis of crystalline compounds. The line intensities, which are recorded b y a suitable microphotometer, are corrected b y means of a simple graphical correction based upon an internal standard, to an arbitrary basis used for all comparisons. The accuracy of the method is limited b y the microphotometer, grain size of the film, exposure relations, possibility of solid solution, etc., and will ordinarily b e within 570 of the observed value. Mixtures of materials are readily analyzed from a single pattern, after standard patterns are taken to determine the characteristic constants. Data are given for several compounds. The method is independent of absorption corrections, sample shape effects, wave-length radiation used, etc.
111.
mum intensity value of the interferences rather thaii integrated intensity. As a result, such determinations may be easily carried through with little calculation and with considerable speed. The method, while not sufficiently accurate for many purpose:,. will serve in some cases, and in certain special applications will enable determinations where no previous methods of analysis could furnish the desired information. Such a case is illustrated in the present paper, the analysis of a rhyolite for quartz. Ordinary chemical analysis permits only determination of total silica, but the diffraction method, which is dependent only on tlir, nature of the compounds present, is not so restricted. THEORY
The intensity of a diffraction line from a given powder sample will vary directly as the mass of the material in the volume irradiated, provided all other factors are considered constant. In case an internal standard is added to a known amount of sample, it becomes possible to determine the amount of any given constituent in terms of the mass of the added internal standard. A single diffraction pattern of a mixture of known composition must be obtained to determine the proper relationship between the inherent intensity values of the two diffraction lines selected for comparison.
M
OST efforts to determine quantitatively the amounts of various constituents in mixtures, using x-ray diffraction patterns, have been concerned largely with efforts to correct for absorption, sample shape, and other quantities tvhich involve considerable calculation. Because of such complications these methods have not found extensive application up to the present time, although considerable use has been made of line comparison methods (1, g). The present investigation shon-s a method of using an internal standard, which serves to give comparative line intensities, enables a direct and simple correction factor to be determined for absorption, sample shape, etc., and also permits use of the maxi-
The intensity of a Debye-Schemer powder diffraction line, neglecting absorption and other effects which accompany the experimental measurement, is given by the relation ( 4 )
* Present address. General Aniline and Film Corporation, Easton, Pa. Mian Martin carried through some of the experimental work in this paper as part of the laboratory course in x-ray diffraction a t the University of Illinois.
I = Io
0.6
0.4
0.3 4
cv N
e6
N
c, 0
0.R
2
8 __-% z
IIII,
0.1
Figure 1 .
L//, Curve for
In
I
Pattern of Mixture
Composition: 40% NaCl 30% CaFz, 30% qua* (pattern 5, Table 11). Croues Indicate value (denrit scale X 10) for ratio IdIs lor each didredion line. NaCl 400 line gives a ratio not in agreement with the rest, probaglv because o f rupedrnposed inlerference kern one of the other constituenb at this point.
95
+
cos* 28) pF’ m2c432rr sin28 cos0
N2e4XV (1
(1)
Z represents the diffracted intensity for a sample havin N unit cells per cubic centimeter wi& a total irradiated volume V. The other symbols have their usual significance. The observed intensity of such a powder diffraction line is not completely expressed by the abore equation, sincr corrections for sample shape (geometrical factors), absorption of the sample, etc., are not considered. If thede corrections, which are all functions of the scattering angle 20, are all summnd into a function .4(d) (expressed in terms of the “interplanar spacing” d given by the Bragg law, X = 2d sin e) n e may write I = Ko(d)A ( d ) ‘c’ = K ( d ) A ( d ) C 12) where A ( d ) represents all corrections for the experimental conditions used in making the diffraction pattern, and K ( d ) all terms from Equation 1 except V , the volume of reflecting material in the irradiated volume of the sample. V is proportional to C, the per cent of the material present in the powder sample investigated. Diffracted intensities for a pure compound in terms of the nhove equation would be
Io = Ko(d) Ao(d) co (3) where CO= loo%, &(d) represents the A ( d ) curve for this particular material and the particular manner in which the pattern is taken, and &(d) involves
96
Vol. 16, No. 2
INDUSTRIAL AND ENGINEERING CHEMISTRY
the quantities indicated in Equation 1 except V , If the sample contained only a portion of this particular standard material, the diffraction intensities would be
1. = Ko(d) C* A ( d ) (4) Z, represents the intensities of the various diffraction lines due to constituent s, C, the percentage of the standard material, s, present, and A ( d ) , since it is independent of everything but quantities dependent upon the size, absorption, and shape of the sample, must be the same for all other materials in the mixture. This permits the evaluation for the observed intensity of diffraction for a given constituent, c, which is to be determined.
but
so that
(5)
We may define a new function, k J d ) = I/K.CoAo(d)
where k,(d) assumes values at various d positions fixed by the scattering properties of the material to be determined and the roperties of the standard material used as an internal standard. gubstitution of this last equation in 5 leads to
c, = c.
IC
(IO/ZJ
(6)
kc@)
k e ( d ) is a constant for any given diffraction line in a pattern, provided a given internal standard, s, is used, and will have different values for the different lines in the pattern. The set of k,(d) values from pattern to pattern, however, is identical. C. is the percentage of the desired constituent in the mixture (including the internal standard material as an ingredient of the mixture). C. is the percentage of internal standard. (Zo/Z,) represents the ratio of the intensity of a given standard line from the reference pattern of the compound used as internal standard, to the same diffraction line from the internal standard in the mixture, This value must correspond to the d value of the line indicated by K,(d). Therefore the ratio (Zo/ZJ is determined for every line due to the internal standard on the microphotometer curve, and plotted against d values. This curve permits interpolation and extrapolation to determine values of the ratio for the particular d values of interest. Z, is the intensity of the diffraction line used for examination. Ze(Z0/Z,) may be regarded as the corrected value of this line. Usually it is desired to express percentages of constituents as they existed in the original mixture before any addition of internal standard is made. Then Equation 6 may be written
C, (in original sample)
value for the specific interference to be used for the analysis; it must be remembered, however, that the constant kc(d) is for a given diffraction line of the material to be estimated, and other diffraction lines even of the same pattern would necessarily involve other constant values. APPLICATIONS
The above treatment has been demonstrated for the circular camera type of pattern, but the same result is obtained for the use of the flat cassette method and the resulting powder halos; even the k,(d) constants will have the same values. The correction curve, Z0/I8, however, will show much greater slope if the standard reference pattern is essentially different in type from that used in the analysis (a-ith consequent loss in accuracy), It is not necessary to specify radiation for the values of the constants, since they are independent of wave length. Radiation sources, however, should be well filtered to permit selection of a smooth background in estimating intensity values. The diffraction cameras should be of such size that good resolution of the diffracted lines is obtained, in order to avoid overlapping of interferences and also to help obtain smooth continuous background values. A film with reasonably small grain size is preferred for the same reason. The sensitivity of the diffraction method of analysis varies considerably as a function of the specific materials concerned. Generally we may assume that about 1% would be the limit detectable in a mixture. In some cases-for example, the determination of platinum in platinized aerogel-quantities extremely minute may be determined, while in other cases, such as the determination of silica in lead oxide, quantities considerably larger
Table
1.
Sodium Chloride Pattern Used as Reference Internal Standard
Line No.
hkl
d,
1.
Relative Demit?
=
where s is weight of internal standard added to w grams of sample. The other terms have the same significance as indicated in Equation 6. With the above expressions it is a simple matter to correct the microphotometer curve of the ordinary powder pattern for computations, since it is only necessary to determine the correction function, Z0/Za, from the diffraction lines of the internal standard, plot the curve, and select the proper
e-& Figure
8 . Microphotometer Tracing for First Sample in Table IV
14.85% NeCl I n k d stendad. Compare with Figure 3, same sample with 19.69% NaCl internal standard. Conditions for two patterns varied over u wide e ranse u feasible In exposure. Internal standard l i n n ( N a U 900 end 920) indlcated by S
A N A L Y T I C A L EDITION
February, 1944
97
LO
Other materials are probably superior to sodium chloride for 0.8 such an internal standard, since the sodium chloride pat(I'l tern has comparatively few0.6 lines and the innermost usable line is rather far removed from the center of the pattern, re03 quiring extrapolation of the E I o / I acurve for many materials. 0.4 It is recommended that the 8 constant values to be used be determined previous to analysis, using the same lot of stand03 ard material (sodium chloride or other standard) which is to be employed in the analysis, in order to obviate errors which ai? might arise through use of various lots of chemicals. Such an error would usually be small. The Io/Zscurves were plotted directly on the microphotometer record, using the density value scale multiplied by Figure 3. Microphotometer Tracing of Pattern for Rhyolite ten. The logarithmic density 19.69% internal standard (see Table IV) scale tends to flatten out the correction curve than 1% would be required. The method permits evaluation and makes it simple to draw a continuous curve through the within the sensitivity of the photographic method; the use of points obtained from the diffraction lines of the internal standard. the microphotometer and film automatically restricts the acThe density values for the five interferences obtained from the curacy of the method to about 5%, and where the amount of sodium chloride are divided into those values given in the referinternal standard does not compare favorably with the amount ence pattern in Table I to obtain correction factors for the posiof the material being determined the error may become somewhat tions corresponding to the particular interplanar spacings listed. greater. The method is adaptable only for crystalline materials, These points are located on the microphotometer paper (see and when colloidal materials or solid solution phenomena are Figure 1) and a smooth curve, Z0/I8 is drawn through them. This present the routine analysis as presented in this paper would have I 0 / Z 8 curve then gives the proper correction value for every posito be considerably modified, and the results would not be so sattion on the pattern, and each interference to be used for calculaisfactory. It is unnecessary to use the integrated intensities tion is corrected by multiplying its observed density value by the (area under the intensity-diflraction angle curve), since the excorrection factor indicated. The microphotometer records and perimental correction function, Zo/Ia,has the property of making correction curves for a known mixture are shown in Figure 1. the required correction, A series of known mixtures containing quartz is shown in Table I1 with a comparison of observed and known percentages. The A modification of the method which enables determinations on sodium chloride was added in knoTn amount, and the percentage a micro scale has been developed and will shortly be published. of sodium chloride in the final sample used is indicated. This particular method permits analysis of alkaloids and other suitable materials in total quantities present of the order of 0.000001 gram. The method could be made even more suitable and accurate by Table II. Quartz in Mixtures Containing the Internal Standard (See Equation 6y using the focusing back-reflection method with its great resoluKnown Mixture Ic(Io/Ia) Quartz tion and almost linear correction curve. The authors have not Patteru NaCl CaFz Rig0 Si02 Quartz Determined done this here, since it was considered advisable to use that type % % % % Clo of pattern which is directly suitable for qualitative identification 1 45 .. 50 0.045 X 1.27 4.95 5.34 ,. 60 0.095 X 0.65 2 45 according to the Hanawalt (3) method, 15.4 ,. 35 15 0.178 X 0.90 3 60 14.8 15 0.224 X 0.69 4 60 . . 35 With slight changes the method permits evaluation, within the 28.7 30 0,277 X 1.35 5 40 30 .. sensitivity of the photographic method, of the absolute intensity a Percentage determined in mixture as given. of powder diffraction lines (except for the corrections brought about by the Debye-Waller temperature factor, etc.) and can be Table I l l . Characteristic Constants for Analysis of Minerals against used to obtain Fourier or other data used in crystal structure a Sodium Chloride Internal Standarda determinations, Mineral d , A. Kc(4 Fu 1'mu 1a 69
;
EXPERIMENTAL
All patterns were made using the wedge method with copper Kalpha radiation filtered through 0.025 mm. (0.001-inch) nickel foil. Exposures were from 2 to 4 hours, using a Phillips Metallix diffraction x-ray tube operated a t 28 kilovolts and 20 milliamperes and a camera with radius of 6.4 cm. The pattern of pure sodium chloride, which was used as a reference internal standard for these experiments, is listed in Table I with density values recorded by a Ileeds & Sorthrup microphotometer.
Cristobalite Fluorite
3.13 3.16 1.65 3.35 4.08
32.0 3.93 8.71 1.92 8.40
SiOz CaFz CaFs
Quartz Si02 Tridymite Si02 0 Determination of tridymite is not satisfactory, since the sodium chloride standard has no lines in the immediate vicinity of the three most important tridymite lines, requiring extrapolation over a rather considerable range, with a larger consequent error than is found in more favorable cases. A standard material other than sodium chloride, chosen so t h a t numerous lines occur in the larger spacings,,would obviate this, di5ioulty, although the diffraction camera should provide suitable resolution.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
98
Table 111lists the characteristic constants for the analysis of several minerals against the given sodium chloride internal standard. One great advantage of the present method of analysis over the usual chemical and physical methods employed for quantitative determination is inherent in the fact that the diffraction method is suitable for any crystalline material, and the patterns obtained are dependent upon the actual structure rather than the chemical composition. It is unnecessary to destroy a compound of interest by solution in solvents as a preliminary step in analysis4.e. analysis of hydrates, polymorphic materials, etc. The method is not indicated for noncrystalline materials such as liquids and glasses, and must be used with caution in the presence of possible solid solutions and of materiak with particle size in the colloidal range. Table IV (and Figures 2 and 3) illustrate the use of the method in analysis of a rhyolite from the extrusion a t Nathrop, Chaffee Co., Colo. The material contains quartz, tridymite, hyalite, cristobalite, spessartite (garnet), hematite, and topaz. The analysis was carried through for quarts. and tridymite. The agreement of tridymite values is probably fortuitous, since an extrapolated correction value over a rather considerable range was used. The present method reduces the number of synthetic specimens which must be employed to a single sample; it is, of course, al-
Table NaCl
IV.
Ie(Io/Ia) Quarts
Partial Analysis“ of Rhyolite Ie(Io/Ia) Tridymite
% 14.85 19.69
0.43 X 1.87 0 . 4 2 X 1.42
Vol. 16, No. 2
0.08 X 2 . 1 8 0.08 X 1.55
Quartz
Tridyrnite
%
%
26.8 25.5 28.1 25.4 Av. 2 7 . 4 25.5 Cristobalite oontent was not determined, since the intensity of the lines was too faint t o permit satisfactory measurement on the patterns obtained. Percentages are expressed for rhyolite before admixture of internal standard.
.
ways advisable to make up a synthetic sample duplicating the results of the analysis after the analysis is completed, at least until the general use of the method has been thoroughly tested for any particular analysis. This pattern could be used to refine the accuracy of the determination. LITERATURE CITED
(1) Ballard, Oshry, and Schrenk, U. S. Bur. Mines, R e p t . Inveuttya-
tron 3520 (June, 1940). (2) Clark, G. L., and Reynolds, D. H., IND.ENG.CHEM..A Y U ~ .ED., 8, 36 (1936). (3) Hanawalt, Rinn, and Frevel, Zbid., 10,457(1938). (4) “Internationale Tabellen zur Bestimmung von Kristallstrukturen”, p. 562, Berlin, Gebroder Borntraeger, 1935.
Determination of Total and Combined Sulfur in Butyl Rubber JOHN REHNER, JR.,
AND
JOSEPH HOLOWCHAK, E s o
A procedure i s described for determining total and combined sulfur in Butyl rubber vulcanizates. M e t h y l ethyl ketone has been found to be a satisfactory and inexpensive extraction solvent. The total sulfur in the vulcanizrte and the combined sulfur remaining after extraction are determined as barium sulfate, following combustion of the samples in the Braun-Shell sulfur apparatus and conversion of the resulting sulfur oxides to sulfate b y means of an alkaline sodium hypobromite solution. Extractable sulfur may b e determined by difference.
I
N T H E course of certain polymer studies in this laboratory, it became necessary to determine the amounts of total and combined sulfur in Butyl rubber vulcanisates. No previously published method of analysis was available for this class of synthetic rubbers. It seemed worth while to disclose the analytical procedure described below, because it may have a wider possible field of application than that for which it was originally developed. Some of the problems that may be studied with the aid of this method are rate of vulcanization, behavior of various acceleratom, sulfur blooming, and factory control. The numerous methods that have been devised for determining total and combined sulfur in natural rubber compositions are adequately described, or referred to, elsewhere (2, 3, 6). A commonly used procedure consists in analyzing the composition for total sulfur by oxidation of the sulfur to sulfate with such reagents as nitric or perchloric acid, followed by determination of the sulfate in the usual manner by precipitation as barium sulfate. Free sulfur is considered to be completely extractable from the vulcanieate, exhaustive treatment with acetone being employed almost universally for this purpose. The sulfur in the acetone extract is commonly determined as barium sulfate, after oxidation with a nitric acid-bromine mixture. The difference between the total and extractable sulfur values is regarded as chemically combined sulfur. No discussion need be given here of the familiar complications sometimes introduced by the presence of inorganic. sulfides and sulfates, some accelerators, and various compoiinding ingredients that contain sulfur.
Laboratories, Standard
Oil Development Co., Elizabeth, N. 1.
Early in this work it was found that the procedure described for natural rubber could not be applied successfully to Butyl rubber. The principal reasons for the difference in behavior appeared to be twofold: the Butyl rubber compositions are less permeable to acetone, and their stability toward oxidizing agents exceeds greatly that of natural rubber. Neither the vulcanizates nor the acetone-extractable materials (which contain small percentages of low-molecular components of the polymer) could be readily oxidized, even after protracted treatment with the hot oxidizing solutions, Furthermore, acetone proved to be a very poor agent for removing extractable sulfur under the conditions employed in this work, It was found, however, that the latter could be completely extracted within 8 hours by means of methyl ethyl ketone. This solvent appears to swell the Butyl vulcanisates sufficiently well to hasten sulfur diffusion very markedly, and its use does not result in the excessive oxidative depolymerization reported by Cheyney (1) for natural rubber. While it is conceivable that the behavior of acetone might be satisfactory in the method of hot extraction recommended for natural rubber by the A.S.T.M. instead of standard Soxhlet extraction as used in this aork, it is believed that methyl ethyl ketone would still prove to be a superior extraction agent, although further experiments would be necessary to verify this point. It was also found that the total sulfur in the original vulcanizate, as well as the combined sulfur remaining after extraction with the ketone, could be readily determined as barium sulfate by burning the sample in a Braun-Shell sulfur apparatus (Braun Corporation, Los Angeles, Calif.), the sulfur oxides formed then being converted to sulfate by absorption in alkaline sodium hypobromite solution. Extractable sulfur is, of course, given by the difference between the total and the combined sulfur values. In view of the ease with which these determinations can be carried out, the excellent results obtained, and the low cost of methyl ethyl ketone, it was considered unnecessary to study the applicability of other ketones, although the use of higher ketones might enable one to reduce still further the time required for cornplete extraction.
