Direct Quantitative Diffractometric Analysis P. P. WILLIAMS Dominion laboratory, Wellington, New Zealand
F A modification of the absorptiondiffraction method of quantitative xray analysis is proposed. A numerical constant, P, is obtained for the analyte from the intensity of the analytical peak corrected for absorption and finite sample thickness. These corrections are obtained by mounting the sample on a metal surface and measuring the intensities of a reflection from the metal, with and without the sample in place. Analyses of sodium fluoride and quartz mixtures are accurate to about 4~4% of the total weight of the mixture. The limitations and advantages of the method are discussed.
T
H E USE of any method of quantitative diffractometric analysis that does not involve an internal standard requires a knowledge of the absorption coefficients of the analyte and the sample to be analyzed. The theory has been presented by Alexander and Klug
(1).
Previous methods have required a plate of sample of infinite thickness. The method described here uses a sample of finite thickness mounted on a metal specimen holder. Absorption corrections are obtained from the intensity of a reflection from the specimen holder. The relationship between the concentration of analyte and the intensity of the analytical peak is derived using a power sample of n components, containing a weight fraction 21of component 1, in the form of a thin layer on a metal surface. For the geometrical conditions in a diffractometer (a) I1 =
where I I is the intensity of a reflection due to component 1 a t a glancing angle el; p , ~.r,and 1 are the bulk density, linear absorption coefficient, and total thickness of the power, respectively; A is the cross-sectional area of the incident beam, and (IJ1the intensity diffracted by unit weight of 1 under conditions of nonabsorption. If the interstices do not absorb, )&* =
Ir/P
then, I,- =
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0
ANALYTICAL CHEMISTRY
If a reflection occurs from the metal under the sample at a glancing angle Or, T,,and T, are the intensities of this reflection with and without the sample in place, respectively. Then 21 (- sin eh whence (2)' = exp (- 21
T. = T. exp
p*p)
where
T
=
p*p),
sin eh sin e,
(3)
Putting Equations 3 and 4 in Equation 2, and assuming the layer of powder is uniform with area B,so that p = W / V = W / B t , Equation 5 is obtained. I1 =
Put PI= (ZJIA/B and rearrange Equation 5
In Equation 6, PI is a constant for the particular analyte if the incident radiation and A and B are constant. It must always be positive for its logarithm to be negative, as T J T , is less than unity. P has dimensions quanta per gram second or quanta per gram if integrated intensities are used. EXPERIMENTAL
Metal specimen holders were machined from l-inch diameter soft copper rods of fairly small grain size, to fit the rotating specimen attachment for the Norelco wide angle Gei er goniometer. Flat ends were m a c k e d on a piece of rod about 2 cm. long and a flatbottomed circular recess, 2.22 cm. in diameter, was cut in one end. The depth of this sample recess varied according to the sample. The moat convenient depth was about 0.025 cm. and this was used for most of the work. The x-ray generator was a Norelco unit with stabilized potential and anode current, used with a Geiger mractometer and scaling circuit. The x-ray output was sufficiently constant to allow a close comparison of results obtained on m e r e n t days. Operating conditions were 35 kvp. and 18 ma., using nickel-filtered copper radiation. The scanning rate of the difiractometer
was '/a" or '/do 28 per minute. Integrated intensities were measured by counting the quanta diffracted while scanning over a peak and subtracting the background count, found by counting for half the total scanning time on either side of the peak and adding the two counts. The quartz used was ground to less than 5 microns by ball milling. No particular care was taken to reduce the particle size of the other materials used, but usually it was not greater than about 10 microns. A uniform layer of sample was difficult to obtain if the sample recess in the copper holder was very shallow. Successful work was done with a sample thickness of only 0.005 cm., but for many materials this proved too small. The use of a greater depth of sample necessitated reduction of the absorption coefficient, and this waa achieved by dilution with gum tragacanth. The extent of dilution necessary depends on the sample, and an overall mass absorption coefficient of about 20 cm.2 gram-' gave a value of about 0.1 for T J T , using a specimen 0.025 cm. thick. If T./T. is less than 0.1, the accuracy of the analysis is reduced. For the exploratory work described here, the sample was mixed with gum trsgacanth by hand grinding in an agate mortar for 10 minutes and mounted in the metal holder by putting a small amount a t a time into the recess and spreading it by pressing down firmly with a slab of plate glass. RESULTS
Although the expression for P in Equation 6 looks formidable, it is calculated fairly rapidly and easily with four-figure logarithms, or with su5cient accuracy for most purposes on a good slide rule. If many determinations of the same type are to be made-Le., if r is c o n s t a n t i t is useful to plot
against T./T,. The usefulness of the technique aa a means of analysis depends on the reproducibility of P for a given analyte under given conditions. Table I illustrates the results that can be obtained. Ten determinations of P have been made for the 19.4' e peak of sodium fluoride. Four M e r e n t concentrations in gum tragacanth were used, the angle 0, was varied, and in determination 9 the scanning rate was half that of the others.
The value of P for this determination is consequently twice the other values. The application of the method to fairly rapid analysis of a simple mixture is shown in Table I1 which includes all the experimental data n e c m y for the analysis. Mixtures of sodium fluoride and quartz were made up containing 20, 40,60,and 80% of sodium fluoride. These mixtures were then diluted with an equal weight of gum tragacanth, and the total 100 mg. of mixture was mixed by hand grinding for 10 minutes. The values of TJT,for each determination are given, and from these are calculated the F values for each of the components. The peaks used were the 21.64" e peak for copper, and the 19.43' and 13.32' e peaks for sodium fluoride and quartz, respectively. From the calculated value of xP,z is obtained by dividing by the value previously obtained for P . For sodium fluoride, this value was taken as the mean of those given in Table I-Le., 342.0 quanta per mg., which were obtained using the same specimen holder (0.025-cm.) as the one used for these analyses. The P value for quartz was taken as 371.6 quanta per mg.,and this was obtained using pure quartz in a specimen holder 0.002 inch deep. These two holders, the 0.00% and the 0.010-inch, were constructed with the same area so that resulta obtained with one were transferable to the other. The results are accurate to within about *4% of the weight of the quartzsodium fluoride mixtures, which is about the accuracy predicted by estimation of errors in the measurements. DISCUSSION
A practicable method of diffractionabsorption analysis haa been described by h r o u x , Lennox, and Kay (6). These authors used a layer of sample of infinite thickness for their diffraction measuremcnts, and then turned the sample block at right angles to the main beam to measure the absorption of the sample with the direct unmonochromated beam. Thus the diflraction and absorption measurements were made with x-rays of different wave lengths, and although this did not prove a serious difficulty for the samples originally studied, t h e authors pointed out that the method is inapplicable if the sample contains an element with an absorption step between the two wave lengths. In a later paper, Leroux (4) demonstrated that somewhat better results were obtained by using monochromatic molybdenum K U radiation. The method described in the present paper uses monochromatic radiation effectively,as all intensity measurements are made on d8ract.d beams. Furthermore, the measurement of integrated intensities in this work accounts to a
advantages only when materids with low absorbing power are to be analyzed Analysis of highly absorbing materials necessitates either dilution of the eample with an amorphous low absorber, which involves tedious weighing and mixing, or reduction of sample thickness to a stage where the problem of obtaining a fairly uniform layer of sample becomes very difficult. This defect is a result of using copper radiation, and it is expected that the use of the more penetrating molybdenum radiation will increase the range of materials that can be analyzed. Further work on these lines is in progress. The techniques described here have been applied in this laboratory to the very rapid approximate estimation of a component in a series of similar samples The samples, which are ceramics containing quartz, were ground to about 10 microns, and the intensity of the quartz peak was measured on an infinitely thick layer of each samplc and of pure quartz. Then TJT. was measured for one of the samples and for pure quartz in a 0.005cm. copper specimen holder Then
Table 1.
P for Sodium Fluoride (Glancing angle, Bh, 21.6; scanning rate, l/kn 2B/minute) z P No. 1 2 3 4 5 6 7 8a 9b 10
0 6 0.6 0.5 0.5 0.5 0 3 0.3 0.3 0.3
335 9 341.6 340.9 346.4 335.7 337.3 342.8 347.0 688.5 340 I
0.1 Glancing angle, 25.2. Scaming rate, I/)' %/minute.
certain extent for the scattering of the diffracted beam from the holder by the sample. This problem had not been discussed by Leroux, Lennox, and Kay. All measurements in this work were made on a sample rotating in its own plane. This was done primarily to eliminate the effects of large grain size in the metal on T,and T,. However, rotation of the sample has also been observed to improve the reliability of diffracted intensities. Legrand and Nicolas (9) have shown that rocking a nonrotating sample through a small angle about the axis of the diffractometer improves the reliability of intensity measurements, and precisely the sam? effect is obtained by rotating the sample in a divergent beam. P has been measured for a variety of materials, from beryllium oxide (p*=9.2) to thorium oxide ( ~ * = 2 9 9 ) The beryllium oxide was mounted pure in a 0.050- or 0.025-cm. holder; thorium oxide was diluted to 7% with gum tragacanth and mounted in a 0.025 cm. holder. When copper radiation is used, accurate measurement of P for highly absorbing material is limited to peaks with very high P values, because the necessary dilution makes the measured intensity of the peak too small for high accuracy. The method described here offers
Table II.
as the correction term for finite sample thickness is unity for an infinite sample, and the factor sin cancels out if the same copper peak is used for both mcasurements. By assuming that all thc samples in the series had approximately the same absorption, application of one factor to all the values of I,unpls/Jquartl gave quartz concentrations very quickly. Analysis of eight samples received as blocks was completed in about 3 hours. CONCLUSION
The method presented hew gives direct analytical results without reference to an internal standard, avoiding mme problems of grinding and mixing. The measurements of absorption of
Experimental Data for Calculating Compositions of Standard Sodium Fluoride-Quartz Mixtures, Equations 6 and 7
Integrated intensities were obtained from a single scan over the peak
0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.4 0.4 0.4
0.4 0.4 0.3 0.3 0.3 0.2 0.2 0.2 0.1 0.1 0.1
0.0976 0.0932 0.1147 0 1060 0.1093 0.1328 0.1060 0.1241 0.1227 0.1340 0 1259
0.4031 0.4084 0.3813 0.3916 0.3880 0.3620 0.3916 0.3708 0.3721 0.3591 O r3692
0.3811 0.3882 0.3570 0.3693 0.3646 0.3364 0.3693 0.3461 0.376 0.3353 0.3440
6375 6387 13950 13701 13983 21946 22698 21805 32257 31600 30668
29901 30241 24461 25084 24597 17639 18124 18182 10102 10409 lo004
79.4 79.7 77.4 81.9 80.5 80.7 82.2 80.1 87.3 85.4 57 8
0 095 0.096 0.201 0.192 0.197 0.288 0 317 0.296 0.403 0.389 0.378
VOL 31, NO. 1 1, NOVEMBER 1959
0 386 0 396 0 303 0304
0300 0 198 0 219 0 21: 0 108 0 !1@ 0 1Wi
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the sample are made in the same way as the diffraction measurements, without moving the sample, which is an advantage over the method proposed by Leroux, Lennox, and Kay (6). Furthermore, in all respects the method gives the results predicted by theory, without the need for determining an empirical correction factor as was found necessary by Leroux et al. When using copper radiation, the
method is restricted to a certain extent to the analysis of materials of fairly low absorption, and the lower limit of concentration that can be estimated is rather high. However, the use of molybdenum radiation should eliminate both these defects somewhat.
(2) Brindley, G . W., “X-ray Diffraction
by Polycr stalline Materials,” Peiser, Rooksby Wilson, p. 159, tech. eds., Inst. Phys., London, 1955. (3) Legrand, C., Nicolas, J., Bull. sue. jranc. ceram. 38, 29 (1958). (4) Leroux, J., Nurelco Reptr. 4, 107 (1957). (5) Leroux, J., Lennox, D. H., Kay, K., ANAL.CHEM.25,740 (1953).
LITERATURE CITED
(1) Alexander, L., Klug, H. P., ANAL. CHEM. 20,886 (1948).
RECEIVEDfor review October 27, ,1958. Accepted July 9, 1959.
Determination of Blood Urea with p-dimethy laminobenzaldehyde HAROLD H. BROWN’ The Memorial Hospital, Pawtucket, R. 1.
bA
simple, rapid, accurate procedure
i s described for the routine determination of urea in protein-free filtrates of blood plasma or serum with an acidified solution of p-dimethylaminobenzaldehyde in ethyl alcohol. More than 1000 plasmas were analyzed; only sulfa drugs interfered. A simple screening technique to detect contaminated filtrates is described and a procedure to circumvent the contamination is given. The effects of such variables as concentrationsof reagents, temperature, and time are discussed. The standard curve is linear to 100 mg. of urea nitrogen per 100 ml. Higher values may b e determined by dilution with the reagent.
T
colored solution formed by urea and a reagent consisting of pdimethylaminobenzaldehyde (PDAB) in ethyl alcohol and hydrochloric acid has been introduced as a colorimetric procedure for the determination of urea in samples containing urea, hydrazine, semicarbazide, and ammonium ion (6). A similar reagent was used to determine urea in an enzymatic, urea-synthesizing system (4). This report describes a procedure for the routine determination of urea in protein-free filtrates of blood serum or plasma with a pdimethylaminobenzaldehyde reagent. HE
REAGENTS
Reagents are analytical grade unleas otherwise indicated. Zinc Sulfate, 10%. Dissolve 100 grams of zinc sulfate heptahydrate in distilled water and dilute to 1 liter. Sodium Hydroxide, approximately 0.5N. Dilute a saturated solution of 1 Present address, Harrisburg Polyclinic Hospital, Harrisburg, Pa.
1844
ANALYTICAL CHEMISTRY
carbonate-free sodium hydroxide to provide 1 liter of approximately 0.5N sodium hydroxide. The zinc sulfate and sodium hydroxide solutions should be balanced as follows: Dilute 10 ml. of the zinc sulfate solution to about 50 ml. with water and titrate slowly with the sodium hydroxide to the phenolphthalein end point. Ten f 0.05 ml. should be required. If necessary, dilute the stronger solution with water and titrate again. p-Dimethylaminobenzaldehyde - Sulfuric Acid Solution. Dissolve 5 grams of pdimethylaminoben~aldehyde(Eastman No. 95) in 95% ethyl alcohol (U.S.P. or reagent grade) and dilute to 100 ml. with 95% ethyl alcohol. Most lots of PDAB were used as received; occasionally however, a lot would produce such a high blank that it had to be recrystallized (I). In every instance the alcoholic solution had to be filtered to make it clear. Slowly add 5 ml. of concentrated sulfuric acid to about 50 ml. of the PDAB solution in a 1Wml. volumetric flask, mix, and allow to cool to room temperature. Dilute to the mark with more of the solution. This reagent has a fairly intense yellow color. It is stable for many weeks a t room temperature. Alcoholic Buffer Solution. Dissolve 10 grams of sodium acetate trihydrate and 1 gram of (ethylenedinitri1o)tetraacetic acid, disodium salt, dihydrate (disodium EDTA) in about 50 ml. of water in a 1Wml. volumetric flask. Add 30 ml. of 95% ethyl alcohol and dilute to the mark with water. The pH should be approximately 6.8. Urease Solution. Add 20 ml. of the alcoholic buffer solution to 0.5 gram of defatted jack bean meal (Sigma Chemical Co.) in an Erlenmeyer flask. Shake for 5 minutes and filter. A sediment forms on standing, but the supernatant fluid may be used. This urease retains its activity for several days, if stored in a refrigerator.
r’
WAVE LENGTH (m)c) Figure 1. Absorption spectra of p-dimethylaminobenzaldehyde reagent A. Urea equivalent to 50 mg. of urea N/100 ml. 6. Urea equivalent to 25 mg. of urea N/100 ml. C. Sulfathiazole equivalent to 2 mg./100 rnI. Blank salution was equal volumes of water and color reagent
Urea-Free Plasma. Pooled plasma (or serum) free of urea is required for a blank of the unknowns. The following preparation hss been found convenient: Pool several plasmas that have normal urea concentrations and do not contain sulfa drugs to obtain about 5 ml. Add 3 or 4 drops of the urease preparation, cover, and allow to stand overnight a t room temperature. (The presence of sulfa drugs can be detected as described in the procedure.) Standard Urea Solutions (50 mg. of urea nitrogen per 100 ml.). Dissolve 107 mg. of urea in water in a 1Wml. volumetric flask and dilute to the mark. Prepare other standards as required by diuting aliquots of the standerd with water. APPARATUS
A Beckman DU spectrophotometer with l-cm. Corex cells and a Bausch & Lamb Spectronic 20 SpectrophotoIseter with O.binch round cuvettes were used.
