Table 1. Effect of Diverse Group VI11 Metal Ions on Analytical Results for Iridium (0.4 ppm each metal ion added to 3.86 ppm Ir) Ir found Added metal ion (PPm) Error, Ni(I1) as NiCh 3.92 f1.6 Pt(IV) as PtCI, 3.92 f1.6 Co(I1) as CoCh 4.03 +4.2 Fe(I1) as Fe(NH4)2(S04)2 3.77 -2.3 4.07 f5.4 Os(II1) as OsClt Rh(1IJ) as Rh(NO& 4.27 $11 Ru(II1) as RuCI3 4.69 f21
at room temperature and considering the numerous variables which may affect the emission intensity and should be controlled-e.g., temperature, viscosity, oxygen concentration, and pH-it is perhaps remarkable that even 5 average deviation can be achieved by this method. It is anticipated that the lower detection limits for iridium could be reduced by one or more orders of magnitude by using a filter fluorometer with wider band-pass and more intense radiation. The critical chemical and optical parameters appear to have been identified and optimized.
Effect of Diverse Ions. Solutions containing 3.86 ppm iridium and 0.4 ppm of other Group VI11 metal ions were prepared and analyzed. Results are shown in Table I. Rhodium, ruthenium, and (to a lesser extent) osmium are the major interferences. The positive errors are apparently due to ( A * -+ T) luminescence from chelates of these metal ions: the same emission spectra (maximum emission at ca. 440 nm) were observed on blank solutions containing these metal ions. [Although the Ru(I1)-Ter chelate emits a characteristic red A* -+ d luminescence in rigid glassy solution (10, 11), it does not show charge transfer luminescence in fluid solution (4)]. Iron will interfere at higher concentrations because the Fe(I1)-Ter chelate shows intense absorption at 520 nm. ACKNOWLEDGMENT
The authors are grateful to David M. Hercules and Fred
E. Lytle for their generosity in providing the lifetime measurements. RECEIVED for review August 22, 1968. Accepted October 7, 1968. Work supported by the National Science Foundation (Grants GP-5449 and GP-8585). Presented in part at the 155th National Meeting, ACS, San Francisco, April 1968.
A Standardized Inert Dilution Method in X-Ray Fluorescence Analysis Rafael Vera Mige Instituto Central de Fisica, Uniuersidad de Concepcidn, Casilla 947,Concepcidn, Chile This method can be used for the determination of any sample, solid or liquid, which can be diluted, powdered, or melted with a definite inert diluent. The concentrated sample and a dilute sample are measured by X-ray fluorescence and compared with a standard which i s not necessarily related to the sample. A matrix independent relationship i s applied, so that only dilution and intensity ratios are used as variables. A definite constant for the element, standard, and diluent must be determined previously and may be used with any sample. The same samples may be used for the determination of most of the elements in the original sample with the aid of known constants. The errors caused by dead time do not increase with higher counting rates. Absolute X-ray intensities have practically no influence on the results.
THEUSUAL problem in X-ray fluorescence analysis is the dependence of X-ray line intensity on the composition of all the elements in a sample. There are established methods of addition and dilution, some of which require preparation of individual samples for each element to be determined. Others greatly reduce the measured X-ray intensity (I, 2). The ideal is to have a method independent of the matrix of the sample and which does not involve infinite dilutions, chemical compounds, or sample preparation for each element that is to be determined in a sample.
If two sample measurements are made, one in a concentrated sample and the other in a sample diluted with a definite proportion of a standard inert diluent, then a set of two equations can be solved to give a relation independent of the absorption coefficient of the original sample. In this way the matrix influence is eliminated. The equipment variables can be almost completely eliminated by using an external reference standard so that only intensity ratios are involved. This reference standard, which may have a composition very different from that of the sample, can also be used for other samples of entirely different compositions. A particular constant for each element, standard, and diluent must be determined. These constants must remain for the stated composition of the standard and wide range of the equipment variables. Consequently, they can be used in different laboratories. The two samples mentioned above, the original and the dilute, can. be used for the determination of most of the elements, thus saving a great deal of sample preparation.
THEORY It is known that X-ray intensity for a good approximation follows the equation ( 3 ):
-~
(1) Catisha Elis, Bol. Fac. Ing. Agrimensura Montevideo, 7 , 44, 1959. (2) H. A. Liebhafsky, H. G. Pfeiffer, E. H. Winslow, and P. D. Zemany, “X-Ray Absorption and Emission in AnaIytical Chemistry,” John Wiley and Sons, New York, N. Y. 1960.
42
ANALYTICAL CHEMISTRY
(3) Rafael Vera, Internal Report No. 1, I. C. de Fisfca, Universidad de Concepci6n, Chile, 1966.
lois a measure of the X-ray intensity on the sample; Kjis a measure of the average fluorescence efficiency of the element j ; W , is the weight concentration of the element j ; I.( is an effective absorption coefficient of the sample for definite optics. Ratio measurements with the intensity Zs of a standard of known concentrations W , are
The r values for a definite sample and standard are affected only by radical changes of wavelength distributions. If X is the weight fraction of the concentrate in the diluted sample; P d is the effective absorption coefficient of the diluent (prime symbols are used for the diluted sample);
If Zs/Z us. l / W 5 for different concentrations is plotted, a straight line whose slope is C,results. The SID method has the remarkable property (derived below) that the error caused by the dead time of the counting system does not increase with the increase of the absolute counting rate of the sample. The response of the scintillation counter should obey the well known relationship
r is the dead time, Io is the real counting rate if there were no dead time in the counter, and Z is the measured counting rate. Let us make Io = I / To and I = I / T and substitute in Equations 12 and 8. T=To+r
(3) T, TI-T
From Equations 2 and 3 we calculate the absorption coefficient of the original sample.
1 - X P=-.-
x
r'
- rIPd
r
7
TI-T
- R(Z) -
7 ~
T'
- T (14)
By calling E the relative error, as defined below, (4)
With Equations 1 and 4 ;
WSpd 1 - X r r' .w,= .X r-r' PS This expression is the fundamental equation by which the concentration W5 can be calculated in terms of the dilution factor, intensity ratios, and three experimental constants ( W s , Pa, ps). These constants are dependent only on the standard and the diluent employed. It is better to use only one constant defined as:
This error does not depend on the sample measurement and can be kept to a very definite and calculated low percentage. If this intensity can not be kept low, the error calculated by Equation 15 can be added directly to the determined weight percentage. But, if the constant C, has been determined under the same counting rate for the standard, no correction has to be made. The above fact extends the useful counting range of the equipment to a point where double coincidence of the pulses becomes important. EXPERIMENTAL
We define the dilution ratio D ( X ) and the intensity relation R(Z) as follows (7)
r r' z I' R(I) = -= r - r' Is(Z - Z') ~
Thus, the fundamental equation for the standardized inert dilution method (SID) is:
W5 = C j D ( X ) R(Z)
(9)
The constant C5 is almost independent of fluctuations in the X-ray tube voltage and current. For a stated composition of the standard and diluent, this constant can be determined with Equation 9 and the experimental data of a concentrated sample (containing the elementj) and a diluted one. Another way is to use the form invariant of the equation derived below. From Equations 7, 8, and 9:
w, = cj Separating terms :
wj
- W,' . I I' W5' I,(Z - Z')
Apparatus and Procedures. The X-ray equipment used was a Philips Vacuum Spectrograph (Dutch) with a LiF analyzing crystal for Cu, Fe, and Mo determination. A scintillation counter was generally used except in silicon determinations where a gas proportional counter and gypsum crystal analyzer were used (no better crystal was available at the moment). In most of the experiments, the X-ray tube was run at 40 kilovolts and variable current. Three measurements of 256,000 counts each were made for each composition and averaged. Pulse height discrimination was used only in the silicon determinations. Here, a long period of time for each measurement ( 5 to 10 minutes), was necessary. Standard. For stability purposes, the standard reference solution of metal oxides was made up in a borosilicate glass matrix. The fusion of only borax with metal oxides produced a glass unstable to the humidity of the air. After several trials an excellent glass was obtained with the following composition: fused borax, 75 SiOn, 20z, and MgO, The weighed components were mixed with the metal oxides in a mortar grinder. The mixture was placed in a platinum crucible and heated in a muffle furnace at 1 150 O C . Small bubbles were eliminated by turning the crucible about its axis oriented at 45" with the vertical. The melt was poured into a graphite mold with a flat bottom and conical walls. The molds were previously heated at 1 150 O C for 10 minutes in order to avoid bubble formation upon contact of the hot melt with the surface of the mold. Pouring was done with the mold previously heated at about 500 O C under
5z.
z;
VOL. 41, NO. 1, JANUARY 1969
0
43
Table I. Comparison between Chemical and X-Ray Analysis Diluent: sulfuric acid 0.1N. Values in weight per cent A . SYNTHETIC SAMPLES OF SULFATES IN A NORMAL SOLUTION OF SULFURIC ACID Molybdenum Copper Weight Weight A Wt Experimental Calculated Experimental Calculated 2.000 1.304 1.021 0.769
-
Sample lMOl 1MM2 2MM3
1.990 1.309 1,020
0.010 0.005 0.001 0.004
0.765
14.04
1.540 1,822 2.378
0.356 0.347 0.350
0.006 0.003
O.Oo0
a gas burner. Cooling was slow in order to avoid stresses and embrittlement of the glass. The standard was ground and polished. In special cases, plastic pellets with embedded power have been used. The grain size must be controlled exactly in order to have good reproducibility. Some absorptive diluent can be used if the peak-to-background ratio must be increased. Each standard is labeled and its C j constant determined experimentally for a definite diluent. The reference number, analytical line, kilovoltage, and diluent are tabulated with the Cj values. An internal record is made with the complete specification of each standard. The Sample. For liquid samples the standard diluent may be any liquid or even a soluble solid substance. Water may be the usual standard diluent. Normalized acid solution may be used for samples that precipitate by hydrolysis. Some solid salt can be added to reduce the background in the diluted sample. Weight concentrations must be used. For solid samples, the dilution can be done by mixing with a powdered standard diluent. The powders must be fine enough so that further grinding does not produce any variation in the measured X-ray intensity. This grinding factor becomes less critical with the use of harder exiting radiation and a diluent with an absorption coefficient similar to that of the sample. In some cases it is necessary to mix the sample with starch or some organic plasticizer in order to avoid sample cracking. This additional substance can be taken as part of the sample or as part of the diluent. In the first case, the ratio between plasticizer and original sample must be the same in the two pellets. In the second case, the constant C j must be de44
3.147 1.037 0.347 0.112
OF COPPER IN LEACHING SOLUTION OF MINERALS FROM CHUQUICAMATA, CHILE B. DETERMINATION Solutions from Ore Oxidized Mixed Weight Weight Experimental Calculated A Wt Sample Experimental Calculated 1.020 1.024 0.004 Conc. 0.718 0.725 1,325 1.328 0.003 Wash. 1 0.174 0.177 1.441 1,431 0.010 Wash. 2 0.078 0,078
Table 11. Influence of Matrix Composition in the SID Method Solutions with constant concentration of copper (0.350 %) and variable concentration of ferrous ammonium sulfate. D ( x ) = 2.000 Wt, experimental ("412 Wt, Fe(S04h. TITS calculated 6HzO secisec cu A Wt 1.259 0.350 O.OO0 0.00 3.51 7.02
3.131 1.044 0.348 0.112
ANALYTICAL CHEMISTRY
A Wt 0.016 0.007 0.001
O.Oo0
A wt 0.007 0.003
O.Oo0
termined with the same per cent of organic binding substance. If the pulverized sample technique does not give accurate and precise results, the solid solution method is used. Borax is a very good diluent for this purpose because it has no elements that interfere with the elements to be determined and has no absorption edges in the usual range of analysis. Lithium tetraborate is also a good solvent especially for determining sodium. Metals sulfides do not dissolve directly in borax, but they can be oxidized earlier or simultaneously with melting. For instance, the dissolution of copper sulfide minerals was made with a mixture of borax and sodium perborate. When the original sample is heterogeneous, two homogeneous samples can be prepared, one with a minimum amount of fused borax or lithium tetraborate and another more dilute. The technique for sample preparation is similar to the one described for the reference standard. It may be that in some samples an appreciable weight of some other element or compound can volatilize at high temperatures. In this situation, a test sample is melted and a correction factor applied. Dilution Ratio. Statistical and practical considerations ( 4 ) were made in order to calculate the optimum dilution ratio. The best intensity reduction factor I ' j I for minimum error is between and Thus, the usual dilution ratio D ( X ) , for a diluent of similar absorption coefficient to the one of the sample, must be between 1 and 4. Two has been selected for most of the experiments. For lighter or heavier diluents, greater or lower dilution rates can be taken accordingly. For practical purposes, whole numbers are preferred. The above estimations were made from a compromise among the several counting techniques generally used. RESULTS AND DISCUSSION
Results for samples of differing natures are summarized in Tables I, 11, and 111. Table I shows the results for several liquid solutions made with variable concentrations of one element. The samples in part A are synthetic solutions. The samples in part Bare industrial leaching solutions from copper minerals. They have variable concentrations of sulfuric acid, Cu, Fe, Zn, Ca, Mn, Co, Ni, As, and Br, and were taken from different stages of the leaching cycle of minerals from Chuqicamata, Chile. (4) C. Trautmann, Internal Report No. 3, 1. C. de Fisica, Universidad de Concepcih, Chile, 1967.
Table 111. Powdered Samples A . FERRIC oxmE IN
SODIUM CARBONATE
Weight Experimental
Calculated
A Wt
D(X)
5.0 10.0 20.0 40.0
4.9 10.1 20.0 40.0
0.1 0.1 0.0 0.4
0.5 1.0 2.0 4.0
B.
Sample Fagergreen-tail Mill-Head 1 Mill-Head 2 Mill-Head 3
COPPER IN MINERALS FROM
T
T’
T.
97.49 48.52 50.59 52.07
193.94 141.58 149.53 152.06
17.90 17.63 17.90 17.90
Table I1 shows the results of a test to indicate the lack of response of this method to differences in matrix composition. The solutions were made with identical concentrations of copper sulfate but with increasing concentrations of ferrous ammonium sulfate. With the addition of approximately 14% ferrous ammonium sulfate, the counting time is about doubled, but the calculated concentrations show no appreciable variation. Table IIIA shows the results of pulverized synthetic samples of iron oxide mixed with sodium carbonate as diluent. Table IIIB shows the results of pulverized minerals in copper sulfide samples from Sewell, Chile (5). The fagergreen sample has a heavy matrix (54% Fe, 3% Ca, 6 % Si02). The Mill-head samples are of lighter matrix (5% Fe, 1 % Ca, 57 % SiOz . , . ). The diluent was silica and the dilution ratio D ( X ) was 3.00. The number of counts was 64,000 (three measurements). The standard has 1 % Cu (as CuO) in a matrix of the standard composition described above. The constant C j is equal to 3.25%:. The samples were finer than 100 mesh and nickel filter was used to slightly decrease the grain size effect. The standard deviation in the calculated percentages was 1 %. Determinations of very light elements-eg., alumina and silicon- with pulverized samples did not work. Nevertheless, compared with the simple ratio method some improvement was observed. Silicon in samples of natural quartz, glass, and clinker has been determined with better accuracy and precision in spite of the high matrix differences (6). Here, in order to avoid the grain size effect, the diluted samples were made by fusion with borax. To illustrate the method, a sample calculation is given using the data of the sample Mill-head 2. We have Equations 7 and 9 and the relation I = NJT. (No is the fixed number of count, T is the counting time corrected for background.) By using the Ci and D ( X ) data for these experiments (see above), the practical formula for the calculations is :
R.Campos, Internal Report No. 2, I. C. de Ffsica., Universidad de Concepci6n, Chile, 1967. (6) M. Campos, Internal Report No. 4, I.C. de Fisica, Universidad de Concepcih, Chile, 1968. (5)
EL TENIENTE, CHILE Weight Experimental Calculated 1.82 1.83 1.77 1.75
A wt 0.01 0.02 0.01 0.00
1.81 1.85 1.78 1.75
W5 = 3.25 X 3 X R(I) = 9.75
I * I’ I*(Z - I f ) T, 9.75 T’ - T
Taking the data from Table IIIB X 17.90 w5 = 9.75 = 1.77x 149.5 - 50.9
If the constant C5 is known for one standard, the constant C5‘ for a standard of different composition can be calculated by using the simple ratio of their X-ray intensities under the same experimental conditions. To show this, let us use the following identity valid for measurements with the same sample and different standard.
The concentration W5’ of the new standard can be different from W,, so that the duplicate may have a different useful concentration range. In practice, one standard may have one or several elements for reference. Also, one of these reference elements can be used as reference for other elements of close excitation voltage. If j is the element to be determined, and k is the reference element, then the constant Cjkcan be determined experimentally. In this case, kilovoltage must be clearly specified because two elements behave differently at different voltages. If C5’ is known for one standard, C5kcan also be determined by using equations similar to 16 and 17. For stabilized equipment in routine measurements, the intensity of the standard may be omitted as a variable and included in the constant C5 in order to make faster calculations. This new constant should be checked periodically by measuring the intensity of the standard. The true constant, C,, does not need to be controlled unless the superficial composition of the standard is altered. RECEIVED for review June 11, 1968. Accepted September 23, 1968.
VOL 41, NO. 1, JANUARY 1969
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0
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