or less, other uses for the electron probe microanalyzer suggest themselves. For instance, in many problems of determining very low concentrations, the specimen preparation could consist of diffusion with an element that selectively precipitates with the impurity. The electron probe would then be merely the end-point tool in the analysis. zone refinement techniques can be used to concentrate impurities
to a sufficiently high local level that the electron probe could perform the analysis. Extensive development work will be required to establish optimum conditions for such analyses, but the feasibility has been demonstrated with the precipitates in diffusion zones.
(2) Birks, L. S.,
J. A p p l . Phys. 32, 387
(1961). (3) Birks, L. S., Seebold, R. E., J. Nuclear ~~~~l~ 3, 249 (1961). (4) HansEn, M., “Constitution of Binary Alloys, McGraw-Hill, New York, lg5*.
RECEIVEDfor review October 5, 1961.
LITERATURE CITED
S.,ANAL. CHEY. 32, 19 A (September 1960).
(1) Birks, L.
Accepted October 24, 1961. Presented in part before the International Union of Pure and Applied Chemistry, Montreal, Canada, August 1961.
X-Ray Absorption Edge Analysis HARRIS W. DUNN Analytical Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tenn.
b Although the determination of some elements by ordinary methods is difficult, from previous work it appeared that the x-ray absorption edge method could determine some of these elements quickly and accurately. The method is relatively free from interferences, a number of elements can b e determined in the same solution, the solution is not contaminated or consumed, and only a small amount of solution is required (0.2 to 2 ml.). All but the elements of very low atomic number can be determined. Good mechanical and electrical stability is required to achieve accurate results. For most elements, a limit of error (95% confidence level) of about 1% can be achieved for concentrations down to 1 mg. per ml., and about 5% for concentrations down to 0.2 mg. per ml. The method is essentially free of matrix effects. Most determinations require about 30 minutes.
T
HE determination of some elements by ordinary methods is difficult. From published work, it seemed that xray fluorescence or x-ray absorption could determine some of these elements quickly and accurately. At first, x-ray fluorescence seemed more versatile, as either solids or liquids could be analyzed, and either semiquantitative scans or complete quantitative determinations could be made. However, x-ray fluorescence is subject to three major interferences: direct x-ray emission line interferences, selective absorption interferences, and excitation interferences. These disadvantages limited the usefulness of this method for nonroutine samples, since they necessitated a considerable amount of chemical work on each sample, and new working curves and
116
ANALYTICAL CHEMISTRY
correction factors had to be worked out for each change in matrix. ADVANTAGES
Work done during 1950-52 had shown that the x-ray absorption edge method had several advantages over most other methods (6). It is relatively free from interferences. The only serious interferences occur when there is a direct overlapping of absorption edges or when the absorption edge of the element being analyzed falls very near the short wavelength side of the absorption edge of one of the contaminating elements. These occur in only a few cases. When there is a direct overlapping of absorption edges, it is usually possible t o determine one of the constituents by using another absorption edge: The remaining constituent can then be determined by difference. If the absorption edge of the element being analyzed falls just on the short wavelength side of an absorption edge of one of the contaminating elements, a correction can be applied to the data, or the contaminating element can be removed chemically. (This will be discussed in more detail later.) There are other interferences, but they are of low magnitude and usually can be eliminated or corrected. (These will be discussed later.) The precision and accuracy are good, even though the matrix may change. The parameters for the determination of a given element can be used over a wide range of matrix compositions, thus eliminating or minimizing development work needed for determining a given element in a new type of sample. Small amounts of solution (0.2 to 2 ml.) are used. This is an advantage when there is only a small amount of material or when it is best to use a small sample, as in the case of radioactive material. The sample is not
contaminated or consumed during the analysis. As with x-ray fluorescence, a number of elements can be determined in the same solution. Preliminary investigation indicates that elements from Cr up in the periodic table can be determined without using special atmospheres. If powders were used, lower atomic number elements could be determined. DISADVANTAGES
X-ray absorption shares with x-ray fluorescence the disadvantage that elements of very low atomic number cannot be determined. Excellent stability of all mechanical and electrical components is required. THE METHOD
In the x-ray absorption edge method, the sample is irradiated with the continuous or white x-ray radiation emitted by the x-ray tube. The x-rays which pass through the sample are analyzed by a conventional crystal-goniometer arrangement. The absorption coefficient of an element undergoes abrupt changes a t the excitation potential of the K spectrum and a t the three excitation potentials of the L spectrum. These abrupt changes are referred to as the absorption edges of the element. The position of each edge is different for each element; the magnitude of the break is a function of how much of the element is present. By determining the transmitted x-ray intensity on both sides of the absorption edge, it is possible to make a quantitative determination of the element. A typical x-ray absorption curve near the absorption edge of an element is shown by the solid line in Figure 1. The absorption edge is sharp, being,
I
~
I I
TRANSMITTED X-RAY
1
A2
xE
'I
>
WAVEL E N GT H 'E
WAVELENGTH
Figure 1. edge
Figure 2.
' 2
X-ray absorption curve
>
~
Typical x-ray absorption curve near absorption
theoretically, almost a vertical line (see dashed line a t AB in Figure 1). However, with the slits normally used to obtain high counting rates, the edge is spread out as shown by the solid line in Figure 1. EQUATIONS
The basic equation for x-ray absorption is
M here Z is the x-ray intensity after passing through the sample, Zo is the incident intensity, e is the base of natural logarithms. pim is the mass absorption coefficient, 1 is the cell thickness, and C is the concentration of the element. 2pm,ZC, is the sum of the absorption a
effects of all of the absorbing matter in the x-ray path. This equation describes mass absorption only, and does not deal nith the abrupt changes which occur a t the excitation potentials of the elerrmts. To calculate the mass absorption coefficient of an element in a solution a t a particular wavelength A, the equation may be written in the form
a here C is the concentration in mg. per ml., 1 is the cell thicknc JS in centimeters, li is the x-ray intensity a t wavelength h for the sample, and z b x is the x-ray intensity a t the same wavelength for a blank containing everything in the solution except the element for which the mass absorption coefficient is being determined. To calculate Apm, the difference between the absorption coefficient a t the short wavelength and long wavelength side of the absorption edge, the equation may be written in the form (3)
where Z x E L is the x-ray intensity on the long wavelength side of the absorption edge and ZxES is the x-ray intensity on the short wavelength side of the absorption edge. Theoretically, I x E L and IxEs are a t essentially the same wavelength (see dashed line a t X E , Figure l),so it is not physically possible to obtain these values directly. It is therefore necessary to obtain Z A E L and Z X E by ~ extrapolating to X E from the long and short wavelength sides of the Z vs. X curve, respectively. Because the line is curved as shown in Figure 2, data will have to be taken a t three points on each side of the absorption edge and extrapolated to the respective values. However, this is too time-consuming for routine determinations, so a faster method of obtaining those extrapolated values is given below. For all solutions tested so far, it has been found that in a blank samplei.e., one in which the element having an absorption edge between XI and As is not present (see Figure 2)-10g10 Z x z can be obtained mathematically from data taken a t a point on either side of the absorption edge by using the formulas
+ log,o Ix, +
loglo IxEs = ml log10 Ix,
a1
(4)
log10 IxsL =
a2
(5)
m2
where Zx, is the x-ray intensity a t a point on the short wavelength side of the absorption edge, ZxE (ZxBs or Z X E L ) is the x-ray intensity a t the position of the absorption edge, and Zx, is the x-ray intensity a t a point on the long wavelength side of the absorption edge. The parameters m,, m2 mul, and u2 are constant for a given set of wavelengths X1,XE, and hz-i.e., for the element being determined-and are essentially independent of matrix composition. A method of experimentally determining ml, mz, ul, and u2 will be given below. By determining Zx, and Z x , for a sample containing the element which
has its absorption edge a t AB, the extrapolated intensities I x E X and Z x s L (see Figure 1) may be obtained by using Equations 4 and 5. For convenience in calculation, Equations 3, 4, and 5 may be combined and put into the form C =
2.303 X 1000
A d [ml loglo Tx,-
1n2
loglo Tx, - a1
(6)
n-hich gives the concentration of the element sought. Tx, is the time for a specified number of counts a t X1 and Tx,is the time for the same number of counts a t X2. Under these conditions, 2.303 X lOOO/Ap, X 1 is a constant for the element in a cell of thickness 1. ESTABLISHMENT OF PARAMETERS FOR DETERMINING A GIVEN ELEMENT
Selection of XI and Xz. The absorption edge is not a clean break, but has fine structure associated with it. Compton and Allison (1) say that this fine structure may extend back 200 volts from the edge. Although the fine structure is not resolved with the slits and crystal we are using for routine determinations, it may change the slope of the white radiation curve. For this reason, it is necessary to select, XI far enough from the short wavelength side of the absorption edge t o clear this fine structure. \Ye select X2 about the same distance from the long wavelength side of the absorption edge. The wavelength (or goniometer angle) of X1,XE, and X2 may be obtained by using the well known Bragg equation nX = 2d sin 0
( 7)
where n is the order number, d is the interplanar spacing of the crystal, and 8 is the angle of incidence or diffraction of the x-rays from the crystal. (The goniometer usually reads 28.) The relation of energy (or volts) to Wavelength is given by the equation
where E is in kilovolts and A is the wavelength of the x-rays in Angstrom units. VOL. 34, NO 1, JANUARY 1962
117
Experimental Determination of m,, m2, and a (or a1 and U Z ) . To obtain m,, mz, and a (or a1 and a,) for the
+
determination of a given element, a series of blank solutions is prepared containing various concentrations of any absorbing material likely to be encountered, but not containing the element to be determined (see Figure 2). Each solution is placed in the absorption cell and data are taken a t X,I XE, and At. The data must be corrected for resolving time loss in the equipment. (This will be discussed later.) The equation used to correct for resolving time loss is Tc = To - N T ,
Y
- YI
=
m ( z - 21)
the slope, m, between the various points can be obtained. Let the y’s be the logloof the x-ray intensities IxEand 2’s be the loglo of the x-ray intensities Ix, or Ix?,depending on whether ml or mz is being determined. We use an average of the slopes between various points for our values of ml and m?. These values may then be substituted into Equations 4 and 5 to obtain a1 and a?. The sum a1 a2gives us a in Equation 6. I t is sometimes easier to calculate a
+
Table I. Effect of Chemical Cornposition of Matrix Elements on Analyses
Av. a with X S 0 4 solutions Ay. a n-ith HZS04plus Xi foils Difference in a
0.09981 0.09973
0.00008
Element
Av. ml
AI Ki
I , 049 1.050 1.048 1.047 1.050 1.049
Ag
Sn
AU
Av . 118
ANALYTICAL CHEMISTRY
0.0
+o. 1
-0.1 -0.2 +o. 1
/
I
I
I
I
I
I I
1
INTENSITY AT A , OR A, Figure 3. Correclion of x-ray intensity at theoretical value at absorption edge, X E
in Equation 6 from data taken with a blank solution in the cell. With this blank solution in the cell, concentration C in Equation 6 will be zero, so the term (mllog10 Tx,- m2 loglo Tx,) must equal
-
Instead of using blank solutions as described above, it is sometimes easier to use the cell with H 2 0 or dilute acid and to add varying amounts of metal foils to obtain the desired total absorption. The foils should be placed between the collimator and crystal to prevent the scattering of fluorescent radiation into the detector tube. Foils may be used, because the chemical state of the contaminant will not affect the results. To prove this, a series of NiSOc solutions was prepared. Data were taken a t the XI and X2 positions of Zr with these solutions and also with HzS04 in the cell and Xi foils added to equal approximately the concentration of Ni in the solutions. The average value of a as determined from each set of data using Equation 6 is shown in Table I. This difference in the value of a is well within our limit of error. To show the effect of matrix composition on the analysis, data were taken a t the XI and X2 position of K b with HzO plus varying amounts of Al, Nil Ag, Sn, and ilu foils in the beam. A summary of the data for each element is shonm in Table 11. From these data it appears that the atomic number of the contaminating element will have no effect on slopes ml and m2. The atomic number may have a slight effect on the constant, a. However, since we have not claimed better than 1% limit of
II.
A1
or Xz to
error to date, me have had no detectable interference from elements with an atomic number less than 50 (Sn). If a large amount of heavy element is present, it mould be necessary to make a correction to the data or chemically separate the heavy element before making the determination. Since the error appears in the constant term a (column 6, Table 11), the percentage effect on the analysis of the element (Yb) is a function of the concentration of the element (in this case S b ) being determined (see column 8, Table 11). To illustrate, a Iarge amount of Au would cause an error of only 1.5% in a 10 mg. per ml. Nb solution, but it would cause a 15% error in a 1 mg. per ml. S b solution. Measurement of Ap,,, for an Element. If the solution measured contains the element whose absorption edge is located a t XE, Equations 4 and 5 will give different values of login I x E . In terms of Figure 1, extrapolation from X1-i.e., use of Equation 4-gives IxBs, and extrapolation from X2-i.e., use of Equation 5-gives I x E L . Substituting these in Equation 3 gives A@,,,.
a.
Table
% Variation from Av.
I
LOG 10 OF TRANSMITTED X-RAY
( 9)
!There T , is the correct time for accumulating N counts, T ois the observed time for accumulating N counts, Ar is the number of counts accumulated, and T , is the resolving time of the system. To obtain a constant limit of error, we operate on a preset count basis. Under these conditions, the resolving time correction is easily made. The values of mland a1 in Equation 4 are obtained by plotting the log,, 1x88 values for the various solutions in this series against the corresponding loglo Ix, values; a similar plot gives m2 and az in Equation 5 (see Figure 3). The same information can, of course, be obtained analytically from any pair of points in Figure 3. Using the formula from analytic geometry
I
COMPARISON OF GRAPHICAL EXTRAPOLATION WITH CALCULATED EXTRAPOLATION
To determine whether the Apm obtained by graphical extrapolation of three points on each side of the absorption edge to the absorption edge would be the same as the Apm obtained by the calculated extrapolation described above, the loglo of x-ray intensity was plotted against wave-
Effect of Atomic Number on Analyses
Av. m2 0.954 0.956 0,954 0,955 0.959 0,956
% Variation from Av. -0.2 0.0 -0.2 -0.1 +0.3
a
0.1578 0.1584 0.1589 0.1594 0,1637 0.1586
70Variation from Av. -0.5 -0.1 +0.2 +0.5 +3.2
Error in Terms
of h4g./Ml. Nb 0.023 0.006 0.009 0.023 0.145
\X-RAY
IL
5
TUBE
1
3.5 -+METAL FOIL
i
33.31
Zr SOLN. I
I
I
I
0.65 0.66 0.67 0.68 0.69 0.70 0.7f
I
0.72
WAVELENGTH IN ANGSTROMS-
Figure 4. Effect of high Zr concentration on shape of absorption curve near Zr K absorption edge
Figure 5.
X-ray absorption equipment
tion, depending on the matrix composition. length in Angstrom units for a 25 mg. per ml. Zr solution. The points mere tlien extrapolated to the absorption edge (see solid line, Figure 4). By graphical extrapolation, a value of 87.57 was obtained for Apm, while calculation , ~ 84.67 for the 25 mg. per gnvc a A ~ J of ml. Zr solution. For a 0.200 mg. per ml. Zr solution, however, calculation gave a value of 87.04 for Apm. The reason for these differences is shown by the broken line in Figure 4. This broken line was obtained by using the absorption cell b-ith HzO and adding metal foils until the x-ray intensity was as near as possible to that of the 25 mg. per ml. Zr solution. Different numbers of foils rvere used to match the x-ray intensity approximately on the tu o sides of the absorption edge. The slopes and shapes of the two curves on the long wavelength side of the absorption edge are the same. However, on the short wavelength side of the absorption edge, the slopes and shapes of the curves are slightly different. To date we have neglected this difference. By using a mean value of 85.12 for Apm we obtained the data shown in Table 111; these data are m-ithin the 1% limit of error (9570 confidence level) we claim for concentrations above 1 nig. per ml. Zr. (These data will be discussed in more detail later.) For more accurate work, especially a t high concentrations, 3 correction would have to be made for the disagreement in slope shown in Figure 4. ROUTINE PROCEDURE
To determine the concentration, C, of an element, the sample solution is placed in the absorption cell. The time required for the accumulation of a fixed number of counts a t XI and X2 for the element is measured. Using the ml, m2, and a values previously determined for the element in question, the required concentration is calculated from Equation 6. It usually requires about 30 minutes for each determina-
INSTRUMENTATION
The instrument is essentially the same as that used for x-ray diffraction, with a single crystal replacing the powder sample and the absorption cell mounted in the beam a t the collimator (see Figure 5 ) . Our basic instrument is a General Electric Co. XRD-5. The timer and scaler !\ere designed and made at Oak Ridge National Laboratory. The single-channel analyzer and amplifier (DD2’i were also designed a t this laboratory, but are now available commercially. X-ray absorption edge analysis requires some modifications of equipment which are not usually required for x-ray diffraction. Both voltage and current must be well regulated. In the equations, the counting rates, or times for a specified number of counts, appear as logarithmic functions. To obtain an accurate analysis, it is necessary to accumulate a large number of counts. We usually accumulate lo7counts on each side of the absorption edge. To obtain an analysis in a reasonable length of time, it is necessary to use high counting rates. On some samples, our counting rates are as high as 40,000 counts per second, which makes it necessary to correct for resolving time losses. The resolving time of the system should be as low as possible, since this decreases the magnitude of the correction. The type of resolving time correction usually made assumes the counts to be randomly distributed. When raw full-wave rectified voltage is applied to the anode of the x-ray tube, however, this is not the case, for no xrays of wavelength X are excited until the excitation potential for that wavelength is reached. The x-ray intensity then increases approximately as the square of difference between the voltage and the excitation potential. (This relationship does not hold if the voltage is over five times the excitation poten-
tial.) With full-wave rectified voltage applied to the anode of the x-ray tube, the x-ray intensity varies from zero to some maximum value and back to zero 120 times per second, so that average counting rates observed under these conditions cannot be used to correct for resolving time losses. If a constant potential is applied to the x-ray tube, however, the observed average counting rates can be used to correct for resolving time losses in the equipment. A constant potential filter has therefore been included in the high voltage power supply. When it is used, the voltage on the x-ray tube is loner than that indicated on the meter. The actual voltage on the x-ray tube can be determined by scanning with the goniometer and recorder. To do this, one begins scanning near zero and scans to higher 28 values. The x-ray intensity will remain fairly constant up to a point, then will increase rapidly with increasing values of 20. The exact 28 reading where the x-ray intensity first begins t o increase corresponds to the excitation potential of that particular wavelength of x-rays, which will be the same as the voltage applied to the x-ray tube. Substituting the corresponding value of e into Equation 7 , the n-ai-elength of the xrays may be determined. Substituting this wavelength into Equation 8 11-ill give the voltage of the x-ray tube. To obtain accurate results, narrow slits should be used. Second-order radiation must be eliniinated. To date, n e have done this by keeping the voltage on the x-ray tube below the excitation potential of the second-order radiation. Xork published by Lublin (4) indicates that a Si or Ge crystal could be used to eliminate the second-order radiation. If a good proportional counter tube is used, it may be possible to eliminate the secondorder radiation with differential discrimination or a single-channel analyzer. If the energy of the radiation entering the proportional counter tube is higher than the excitation potential of the gas in the counter tube, the fluorescent VOL. 34, NO. 1, JANUARY 1962
119
x-ray radiation of that gas is excited. This causes the counter tube to emit a pulse whose energy does not correspond to the position of the goniometer (5). This is referred to as the escape peak of the proportional counter tube. In some cases this can be eliminated with a discriminator. When it cannot be eliminated, a correction must he applied to the data. We have found a xenon-filled proportional counter tube to be the best for general use. A similar interference is encountered with a scintillation detector when the fluorescent iodine radiation is excited in the NaI crystal of the scintillation detector. Another instrumental difficulty was due to variation of the temperature of the coolimg water for the x-ray tube. Small changes caused errors in the
analysis. After taking our instrument off the building water supply and installing a General Electric Co. radiator cooliig system (replacing the connecting hoses furnished with copper tuhing), we had no more difficulty from this source. The cell mount should reproducibly locate the absorption cell between the collimator and the crystal. If the absorption cell were located between the crystal and the detector, the fluorescent radiation from the eel would scatter into the detector and cause an error in the analysis. The cell is constructed with a flange on the side to facilitate handling and mounting in the beam. This flange slides behind spring clips on the cell mount. Polystyrene is used for the
n.04n
Error
%
0.038
0.200 1.001 5.007
O.O( O.O( 0.01 0.03 0.13
0.205
1.011 5.040
24.91 0 Based on counting statktiea only. Because of Low counting rate, not as m Zr solution as for other solutions. 25.04
Table IV. Effect of Impurities an Determination of Zirconium
(1.001 mg./ml. Zr present) Zr ImOb-
purity, served, Impurity Mg./Ml. Mg./Ml. None None None None None
%
Error.'
Al Al
AI AI
SP SP On_
uu.
Ni Nb Nb Hf
Hf Pt
u
U
-',"
Foilb 9.96 9.96 6.53 6.53 8.11 15.03 15.03 7.52
0.992 1.007 1.007 1.019 1.016 1.018 1.092 1.090 1.045
-0.9 +0.6 +0.6
+1.8 +1.5 +1.7 9.1 8.9 4.4
U a Expected error, 2.2%, based an statistioal evaluation of ure Zr solution data (95% . .. confidence Evel). 1-em. cell used. b Al foils added t o equal approximately 43.20 mg./ml. and Ni foil8 added to equal 19.27 me./ml. amroximatelv ..Standard"lO1e staid& steel containing Fe, Cr, Ni, Mn, Mo, and traces of other elements. 0
120
ANALYTICAL CHEMISTRY
5.0 2.5 1.0 0.7 0.5
Expected Error. Mg./ml. % 0.007 0.007 0.007 0.007 n.011
...
X-ray absorption cells
used to obtain the high counting rates for the x-ray absorption edge analysis. (We use a 1" collimator slit, a 0.05" detector slit, and a NaCl crystal for routine determinations.) It is necessary to use a lithium fluoride or higher
Table Ill. Accuracy of Zircor m Determination with 1 -Cm. Cell
ZI.. MK./Ml. . KnoWll Obsd.
Figure 6.
24.7 4.9 1.0 0.2 0.lb
DATA
counts were accumuiatea tor zo.1~4 mg.iml. I
.
successful, as it has good radiation stability, does not flow under pressure, and machines well. The windows are also made of thin (about 0.010-inch) polystyrene and are sealed by O-rings and screw caps (see Figure 6). For organics, the cells are made of steel with gold plating over the steel. Thin microscope cover glasses are used for windows in these cells. To wash the cell, a water lime is inserted into the cell, water is flushed through it until it is thoroughly washed out, and it is then rinsed with alcohol and dried by pulling air through it with a vacuum. Although a 1-em. cell is adequate for a large number of elements, we have cells from 0.2 to 2 em. thick, and, in some cases, even the 2-em. cell is not adequate. Calculations by Dodd ($) indicate that the efficient determination of some elements would require a cell 6 em. thick, in which case it would be necessary to modify the collimator of the XRD-5. As was mentioned above, the absorption edge has fine structure associated with it. This fine structure is a function of the chemical state of the element and can be used to determine the chemical state of the element. However, it requires very high resolution to resolve the fine structure. It is not resolved with the slits usually
Table I11 shows data obtained from Zr solutions made up in 5% H2S04. Most of these data were obtained by accumulating 10,000,000 counts on each side of the absorption edge. The excepted errors were based on counting statistics only, which are normally the predominant errors in the determin& tion. Some exceptions are discussed below. The errors obtained for the higher concentration are greater than would be expected from counting statistics. This is probably due to the change in shape of the white radiation curve on the short wavelength side of the absorption edge that was discussed earlier. If a correction were made for this, these data would probably be within the expected error. However, we claim only 1% limit of error (95% confidence level) for concentrations above I mg. per ml. Zr, and 5% for concentrations from 0.2 to 1 mg. per ml. Zr. All these data fall within these limits of error. Table IV shows data that were obtained from 1 mg. per ml. Zr solutions that were contaminated with impurities as shown. The expected errors (95% confidence level) were calculated from the pure solution data that were taken a t the same time the impure solution data were being taken. These data therefore include all the errors that were present a t the time these determinations were made. There was an instability in the iustrnment a t the time these data were taken. If the instrument had been perfectly stable, the data should have been within 1.5%. The Zr K absorption edge is very near
the short wavelength side of the uranium LIII edge. As was discussed above, there is a change in the slope of the white radiation curve near the short wavelength side of an absorption edge. Because of this change in slope, uranium causes an error in the determination of Zr. This same type of interference is present whenever the absorption edge of the element being determined falls near the short wavelength side of the absorption edge of a contaminating element. The elements that will cause such interferences can easily be determined from tables such as those published by the General Electric Co. ( 3 ) . This type of interference does not occur very often, and when it does a correction can be applied to the data or the interfering element can be chemically removed. CONCLUSION
The x-ray absorption edge method of analysis has been used a t the Oak Ridge National Laboratory for about two years and has proved to be satisfactory. We have routinely determined Zr, h’b, RLo, Th, and U with an approximate
limit of error (95% confidence level) of 1% for concentrations above 1 mg. per ml. and 5% for concentrations from 0.2 to 1 mg. per ml. This has been achieved in the presence of a variety of matrix elements, including Al, Cr, Fe, Ni, Y, Zr, Kb, Mo, Sn, Hf, Pt, Th, U, and NH4, and with a variety of anions and organics. We have also determined Hf and W; the limits of error being approximately twice those of Zr. Because of the lower x-ray intensity a t Hf and W; we do not accumulate as many counts for these elements. If we did, limits of error for Hf and W would be approximately the same as they are for Zr. By keeping the instrument stable and applying the corrections as stated above, the expected errors listed in Table I11 could probably be achieved. If more counts were accumulated, even better precision and accuracy could probably be achieved. The absorption edge method has been used in a routine laboratory a t the Y-12 plant in Oak Ridge for several years and has proved satisfactory there also (7, 8 ) .
ACKNOWLEDGMENT
The author thanks Cyrus Feldman for his help and encouragement on this project and for his help in preparing this manuscript. LITERATURE CITED
H.. Allison. S. K.. lLX-Rcys-& Theory‘ and Experiment,” Van Nostrand, New York, 1935. ( 2 ) Dodd, C. G., Division of Analytical Chemistrv. 138th Meeting, ACS, New York, N.-Y., September 1980. (3) General Electric Co. X-Ray Department, “X-Ray Waveiengths of Spectrometer,” Catalog No. A4961DA. (4) Lublin, Paul, “A Novel Approach to Discrimination in X-Ray Spectrographic Analysis,” S lvania Research Labor& tories, BaysiJe, N. Y . 15) Parrish. W.. Kohler. T. R.. Rev. Sci. . ,In&. 27,’795’(1956). ‘ (6) Peed, W. F., Dunn, H. W., U. S. At. Energy Comm., Rept. ORNL-1265 (April 1952). ( 7 ) Stewart, J. H., Jr., ANAL. CHEM. 32, 1090 (1960). (8) Wright, W. B. Barringer, R. E., U. S. At. Energy bornm., Rept. Y-1095 (August 1955). (1) Comnton. A. \-I
’
RECEIVEDfor review May 29, 1961. Accepted November 7 , 1961.
X-Ray Method for Determining Liquid Densities at High Temperatures and Pressures N. A. KROHN and R. G. WYMER Oak Ridge National laboratory, Oak Ridge, Tenn.
b A method for measuring liquid densities at high temperatures and pressures is based on x-ray determinations of the position of the liquidvapor interface in a calibrated pressure vessel. Densities of a 35.270 uranyl sulfate solution were measured from room temperature to 300’ C. as a demonstration of the method.
To Recorder Sio!ted Po
I.
C. Thermocouple
and $.I. capillary
Shxtter\
*‘ 7 F In Caiielle
Lead
..-
Carr oge .c__-------
L
densities a t high temperatures have been determined by observing volume changes in sealed fused silica ampoules (6) and by buoyancy methods ( 2 ) . Sealed ampoules have been used primarily with aqueous systems where high vapor pressures are involved. Shortcomings of this method are that chemical attack of the silica may be severe, leading to weakened vessels and contamination; that somewhat arbitrary corrections for end effects must be made, even when capillary tubing of uniform bore is employed; and that vapor pressures cannot be measured. Buoyancy methods have
====+--I I
’
Norelco MG X-roy Unit Target
300
1
IQUID
Trock
I
loa cm
9 c71
I
1
f Figure 1.
Diagram of apparatus
been used with stable fused salt systems where vapor pressures are not significant. Use of this method for precise work requires a knowledge of surface tensions of the liquids being studied, so that corrections from apparent to true buoyancy can be made. The method described consists of
determining the liquid volume of a weighed solution of known composition in an autoclave of suitable material. An x-ray photograph shows the position of the vapor-liquid interface in a calibrated section of the autoclave. By using the weight of solution and the volume obtained from the location of VOL. 34, NO. 1, JANUARY 1962
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