photometric techniques as analytical tools

PHOTOMETRIC TECHNIQUES AS ANALYTICAL TOOLS

Robert Bastian Republic Aviation Corporation, Farmingdale, L . I . , N . Y .

Photometric techniques occupy a rather unusual place in high purity materials analysis in that they have been used to determine major constituents with high precision as well as trace constituents. Major constituent analysis is important not simply from the standpoint of total assay, but in compound materials “purity” may also be taken to mean that the major elements are present in their intended proportions.

In this presentation I have been asked to discuss some recent work that has been performed in our laboratory in developing methods for the determination of major elements in the binary electronic materials gallium arsenide and bismuth telluride, utilizing the very promising technique of indirect spectrophotometry. In addition I have been asked to take a look a t the current place that photometric methods occupy in the trace field.

I n order to preserve continuity in the presentation an attempt will be made to compare the problems involved in major constituent spectrophotometric analysis with those involved in trace analysis. It is hoped that these com- parisons will prove provocative from a practical as well as a scholastic point of view.

Because of the extent of the material to be covered an extensive cata- loguing of reactions, sensitivities or equipment will not be made. I t is assumed tha t most analytical laboratories have a spectrophotometer, and tha t most analytical chemists are familiar with some of the comprehensive books1.’ and review^^.^ on the subject. In addition I shall concentrate on straight absorption spectrophotometry, rather than including the techniques of nephelometry, turbidimetry and fluorimetry. The last of these shows con- siderable promise as a trace

Spectrophotometric methods are almost exclusively solution methods (an interesting exception is the determination of oxygen in silicon and germanium utilizing infrared absorption on a metallic ample)^.^ and from this fact stem some of their advantages and one of their main limitations. Among these advantages are the essential precision, accuracy and ease of standardization. Among the limitations in the trace field is that due to contamination introduced during the solution process and the addition of the necessary reagents.

This presentation will stress both precision and sensitivity since both the major constituent and the trace* field will be considered. Ordinarily the trace

*It is important to define the trace region because rules which apply near ultimate detection limits may not apply elsewhere. In this paper the range is defined as any- where from 100 ppm. downward. As we approach ultimate detectibility sensitive reactions and separations to accommodate them tend to become mandatory; as we approach the other end of the range more flexibility is afforded.

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298 Annals New York Academy of Sciences

analyst is very careful to avoid contamination but does not have to carry out the steps of his analysis with high precision as does the major constituent analyst. There may be cases, however, where the trace analyst can convert additional precision into useful sensitivity and this, among other concepts, will be examined.

Sensitivity and Precision

Expression (1) shows the modern form' of the

A = abc (1)

Lambert-Beer law which governs most direct spectrophotometric systems, t ha t is, systems where the absorbance increases with increasing concentration. Here A is the absorbance, a the absorptivity, b the cell path and c the concentration. Expression (2) gives

Error = Ac/c = AA/A (2)

a form for the error which is the minimum absorbance that can be detected divided by the total absorbance resulting from the absorbing species of interest.

Assuming a given sample size and a given volume for final dilution, to increase the sensitivity in a trace procedure we can do one of three things: choose an absorbing species with a high absorptivity, use a long cell path, or arrange conditions so that, AA, the minimum detectible absorbance, can be made very small. Note that AA is not just the minimum absorbance or difference in absorbance that the instrument is able to detect. I t is estimated by carrying replicate solutions through the entire procedure and must include uncertainties due to factors such as the stability of the absorbing species or inability to develop it exactly the same way each time, the effect of interferences, variations in background absorbance or in a blank which is introduced either from the vessels or reagents or other sources. Often in trace analysis these factors, which will be discussed in more detail later, pre- ponderate, and introduce greater uncertainties than the instrumental error in the final photometric readings. As the uncertainty AA, due to all factors combined, approaches A, we approach the practical detectibility limit.

To increase precision in major constituent analysis expression (2) indicates that we can do one of two things. We can keep the total absorbance somewhere in the vicinity of the theoretical optimum of 0.434, or perhaps a bit higher,* and attempt to lower our AA, or we can allow A to take on much larger values, and maintain the ability of our instrument to detect a constant reasonable difference in absorbance a t the higher values.

*For a complete discussion of the optimum absorbance value in conventional spectrophotometry, taking into consideration various classes of errors, see C a h r ~ . ~

Bastian: Photometric Techniques 299

Because of the problems involved in decreasing AA to very low levels, we have found it more practical to do the latter and this forms the basis for the technique of differential spectrophotometry pioneered by Hiskey" and Bastian""' and reviewed by O'Laughlin and Banks.13 In this method the total absorbance of many systems has been increased to about 2, and samples and standards read differentially against an appropriate reference. The increased light required for this operation is obtained on a spectrophotometer such as the Beckman DU by working a t a wider slit aperature than usual. This lowers the spectral resolution but with many systems used in absorption work this loss is not serious.

Using this technique many workers have obtained rfsults with a precision of between one part per thousand and one part per two thousand. Assuming that we can conduct our chemistry carefully and reproduce readings on the spectrophotometer scale to * 0.2 per cent transmittance (about 0.001 absorbance unit a t very low absorbance scale values) a precision of one part in two thousand may be considered the practical limit of precision of the direct differential method.

Attempts to operate a t values much above an absorbance of 2 do not generally result in an appreciably further increase in precision because the plot of absorbance vs. concentration tends to fall off severely because of the broad slits, and stray light effects in many instruments.

In addition to major constituent analysis a high absorbance reference can also be used when it is desired to determine a trace element in the presence of a large background absorbance. FIGURE 1 illustrates the analogy between the trace and major element determinations. In each of the cases it is

x

MAJOR TRACE CASE CASE

FIGURE 1. Photometry vs. a reference.


assumed that readings are made against a reference having an absorbance equivalent to tha t of constituent X. If we read a small additional amount of X, AX, in the presence of X we have the major element situation; if we determine a small amount of Y in the presence of X we have the trace situation.

The method can be used in the trace field to compensate a large background due to a foreign element, or a large excess of an absorbing reagent provided that these can be held within the required limits of reproducibility. It can even be used t o compensate a reagent blank, although it is preferable that this be reduced as much as possible by prior purification. Note that up to an absorbance of about 2, it is not so much the quantity of the above disturbances that need to cause trouble; i t is the variation which may exist in them, or the variation in absorbance caused by them.

When using a high absorbance reference, in major constituent analysis or trace analysis, it is important tha t all operations must be carried on with sufficient precision to make the final photometry meaningful. For example, if we are trying to detect 0.002 absorbance unit due to a trace constituent in the presence of a background of 2 absorbance units all operations must be carried out to a precision of one part per thousand.

In such cases the trace analyst might consider utilizing practices employed in major constituent differential work. Examples of these are dilution of all samples and standards in a single volumetric flask to avoid the necessity for calibration of volumetric flasks,14 and close attention to the temperature ~oefficient '~ of absorbance of the constituent providing the high absorbance.

In trace spectrophotometry application of the above technique is a case of trading overall precision for effective sensitivity, because we are in effect subtracting two large quantities to obtain a small one. Such procedures are more likely in absorption spectroscopy where we may have the needed precision to trade; in a technique such as emission spectroscopy this would probably not be the case.

While on the subject of differential spectrophotometry much has been written in the literature about the calibration of absorption cells used in the method. In our laboratory we have eliminated the need for this because all samples and standards are read in a single cell against an appropriate reference. This reference can be an attenuator such as wire screen although a solution of similar composition in a similar cell is preferred for uniformity. While the absorbance of the reference should match very closely the lowest standard it need not be identical. The same method is recommended to null out a background absorbance in the trace case, portions of the solution being read before and after addition of the spectrophotometric reagent, both in the same cell.

Bastian: Photometric Techniques

Indirect Spectrophotometry

301

Thus far we have dealt with spectrophotometric reactions in which the absorbance increases as the concentration of the element sought increases. We will next concern ourselves with a class of indirect spectrophotometric reactions in which the element in question bleaches or lowers the absorbance of a given reagent. These are important both in major constituent and trace spectrophotometry because they increase the number of useful reagents. In addition, in major constituent analysis, if appropriate systems can be found, they make possible a potential precision greater than that attainable by direct meth0ds.l'

The manner in which this arises is shown in FIGURE 2. Here have been plotted hypothetical direct and indirect systems with the absorbance vs. concentration curves extrapolated to zero concentration. I t is assumed tha t all readings are made differentially a t A1 to keep the instrumental error in determining a difference in absorbance minimal. The expressions for the errors are shown in the figure.

FIGURE 2. Direct and indirect spectrophotometric systems.

Since A1 in the direct method cannot go much above 2, i t is necessary to reduce AA to 0.001 absorbance unit to obtain a concentration precision of one part in 2000. There are no such limitations on the absorbance which can be bleached, however. As long as we are willing to increase the concentration of the element doing the bleaching and the reagent being bleached, and the absorbance of the reaction products is low, we can make A? - A1 very large indeed.


In recently developing methods for the major elements in bismuth telluride and gallium arsenide, a direct differential method was developed for bismuth, but indirect methods were established for tellurium, arsenic and gallium. Tellurium and arsenic were determined by reacting their appropriate valence forms with dichromate, and gallium was determined by its reaction with EDTA in the presence of copper, appropriately lowering the absorbance of the copper-EDTA system. Calibration curves were established just short of the equivalence points and samples analyzed in terms of appropriate standards treated in identical fashion.

I t was possible to arrange experimental conditions so that A? - A, for the tellurium system was about 48 units, for arsenic 88 units and gallium 166 units, using weight aliquots of these elements corresponding to about 64 to 94 mg. of the element. For a quick visual comparison for a typical direct system, bismuth with excess EDTA (ultraviolet absorption), and an indirect system,

10, , , , , , , , , , , , , 01) R 1

PERCENT CHANGE IN CONCENTRATION

FIGURE 3. Direct and indirect calibration curves.

tellurium-dichromate, FIGURE 3 shows comparative calibration curves plotted in such a way as to normalize them, that is the change in concentration from a fixed point plotted against absorbance scale reading.

A precision of 0.001 absorbance unit on the bismuth curve corresponds to a concentration precision of about six parts in 10,000. (In practice an average precision (std. dev.) of about eight parts in 10,000 was achieved.) In order to obtain a precision of one part in 10,000 on the tellurium curve a repeatability of only 0.005 absorbance units is required, and the requirements are even less for arsenic and gallium. (In actual practice an average precision of 2-3 parts per 10,000 were obtained for tellurium and gallium, and 3-4 parts per 10,000 for arsenic.) Obviously in the indirect procedures the strain is taken off the


TABLE 1 ANALYSIS OF SYNTHETIC SAMPLES

Element No. of Runs

% Recovery (range)

Std. Dev. (range)

AS 2 100.004- 100.012 0.029-0.04 1

Ga 3 99.995- 100.007 0.007- 0.018

Te 5 99.962-100.013 0.012-0.019

photometry and the errors lie mainly in the reproducibility of the chemical reactions involved.

Results obtained for arsenic, gallium and tellurium on synthetic samples of gallium arsenide and bismuth telluride are summarized in TABLE 1. The results have been expressed in terms of the per cent recovery of the given element from a mixture in solution of approximately stoichiometric amounts of the appropriate elements. The recovery errors vary from about -4 to + 1 part per 10,000, the standard deviations from about one t o four parts per 10,000.

Details of the methods and their application to actual high purity samples are given in the final report to Air Force Cambridge Research Laboratories contract AF19(628)-441,17 and the material will also be submitted shortly for publication in Analytical Chemistry.

Indirect spectrophotometric methods of the bleaching type have the ad- vantage over a spectrophotometric titration in that an end point is not sought, so that curvature which may occur near the end point and all other errors in locating the endpoint are eliminated. All solutions in the present work were allowed to stand overnight so that slow reactions (Te-dichromate for example) could proceed to completion. Once the reaction is completed the requirements on measurement of the residual absorbance are not nearly as stringent as in direct work. Thus, if we bleach 99 per cent of the dichromate in a reaction with the element and measure the residual dichromate with a precision of one per cent we will have a potential overall precision of 0.01 per cent. Final dilutions are thus not very critical and temperature coefficients of absorption tend to become negligible.

With an appropriate system, with the chemistry optimized, it is possible that indirect spectrophotometry might be capable of yielding a precision of one part per 10,000 or greater.

FIGURE 4 shows an indirect bleaching reaction in which the complexation constant is not sufficiently large to give a continuous straight line. This is similar to reactions discussed by lot he."^" If the curve has a reasonably flat portion the approximate error a t A, can be obtained by extrapolating a tangent line as shown (it is again assumed that the reading is made against a

304 Annals New Y ork Academy of Sciences

\ ERROR =

CONCENTRATION -D 0

FIGURE 4. Incomplete bleaching reaction.

reference to optimize the instrumental detectibility) although Lothe has given a more detailed treatment of this type of system. For trace purposes note the absorbance vs. concentration curve is steepest where the excess of reagent is greatest which represents a high absorbance situation. For sensitivity in trace analysis one would wish to work in this steep portion of the curve, and make readings against a high absorbance reference, emphasizing the principles stated previously.

I have conveyed the impression tha t photometric methods, properly used, can be made to yield very precise results and perhaps the trace analyst can derive some suggestions from the major constituent analyst. I would now like to comment in more detail on the use of spectrophotometry as a trace tool.

Trace Spectrophotometry

Spectrophotometric methods are hardly a panacea for trace analysis problems. Given a small amount of a difficultly soluble material and an assignment to determine the approximate amounts of several trace elements, spectrophotometry would hardly be the technique of first choice. For multi- element analyses on solid samples the techniques of emission and mass spectroscopy are the choices, and for sheer sensitivity activation methods cannot easily be exceeded.

The utility of spectrophotometry depends on the situation involved. For a truly quantitative result on selected elements in appropriate materials, on a reasonable amount of material (e.g., 0.1 to 1 gram amounts per determination), the method may be the simplest as well as the most economical to use.

We shall now return to a more detailed consideration of the three important factors treated in expressions (1) and (2) as they apply to trace


analysis, namely: the absorptivity or inherent sensitivity, the cell path and finally the minimum useful absorbance, AA, which can be detected.

Were it possible to optimize all of these factors a t once, spectrophotometric methods would provide extremely high sensitivity. In practice it is difficult to do this. Thus, when a reaction is extremely sensitive it may not be specific or the product as stable as that provided by a less sensitive reaction. The limits of minimum detectibility are often provided by the reproducibility of the needed separations or of a reagent blank. In order to place the further considerations in proper perspective i t now seems appropriate to consider a few examples of practical analyses reported in the literature under conditions where high sensitivity was desired.

These examples are taken from the area of semiconductor analysis where the requirements for sensitivity are as severe as any, and appear to justify the generalization that for samples of the order of 1 gram the lower limit of useful determinations in the more favorable cases lies in the range of about 0.1 to 1 ppm. The reported determinations of As, P, Sb and Cu in germanium and germanium dioxide," the determination of boron in silicon2' and sulfur in gallium arsenide" lie within this range. Using 10 to 20 gram samples ChengZ3 found a detectibility limit (1 cm. cell) for the determination of Se in arsenic of 50 ppb. BurkhalterZ4 reported the determination of copper in the parts per billion range using a catalytic type reaction but such sensitivity is exceptional.

Additional examples of work done in the semiconductor area are given by Parker and Rees4 and Adler and Pfaff."

Inherent Spectrophotometric Sensitivities

Spectrophotometric sensitivities are expressed by Sandell' in the practical units of the number of micrograms of the element of interest which when combined with the reagent of interest in a column of solution having a cross section of 1 cm.' gives rise to an absorbance of 0.001. If such a value (referred to hereafter as the "sensitivity value") is multiplied by the volume to which the solution has been diluted (ml.) and divided by the cell path in cm. the result is the total number of micrograms of the element corresponding to 0.001 absorbance unit. Division by the sample weight in grams then gives the parts per million of the element in the original sample corresponding to 0.001 absorbance unit.

I t is interesting to compare the theoretical detectibility limits of a rather insensitive color such as tha t provided by the titanium peroxy complex with the more sensitive spectrophotometric reactions. At 410 my the sensitivity value for the former is given as 0.064 micrograms of T i per cm.' Assuming a dilution to 50 ml., and the use of a 10 cm. cell, 0.32 micrograms of T i will give a reading of 0.001. If a 1 gram sample is taken and we assume our detectibility limit to be 0.001 absorbance unit we could detect 0.3 to 0.4 ppm. of Ti, and we


could determine say 3-4 parts per million with reasonable precision. The sensitivity values for the more sensitive spectrophotometric reactions do not usually exceed 0.001 micrograms per cm.' For such a case under conditions comparable to those assumed above, we could detect 5 parts per billion and determine 50 ppb. While there are some reactions which have sensitivity values better than 0.001 (the reaction between heptavalent Mn and 4.4' tetramethyldiaminotriphenylmethane has 0.001)' these are not common.

Actually since the range of inherent sensitivities usually encountered is less than two orders of magnitude, there may be occasions where a less sensitive reaction of excellent stability, and other desirable characteristics may be preferable to one which is more sensitive, but otherwise undesirable.

Cell Path

Cells in common use on American instruments range from one to ten cm. in cell path and hold from about 3 to 30 ml. of solution. The objective should be to optimize the cell path b for the given volume of solution available, unless one wishes to conserve the solution. One can use a conventional 10 cm. cell if the sample has been diluted in a 50 ml. flask, a 5 cm. cell if a 25 ml. flask has been used, and a 2 cm. cell if a 10 ml. flask is used. The important consideration is the total volume (ml.) to which the solution is diluted divided by the cell path (cm.) and all of the indicated cases give a value of 5 .

If one can concentrate the solution to 10 ml. or less and wishes to obtain a ratio lower than 5 , the micro cells of KochZ5 which hold about 2 ml. and have a cell path of 10 cm. are recommended by Parker and Rees.' In using micro cells it is important to realize that if we are trading off volume for our ability to reproduce photometric readings as well as possible we may not be gaining anything. Capillary cells may fall in this category.

Minimum Absorbance Detectibility (AA)

In this presentation factors affecting AA are divided into three categories based on operations carried out in practice. First, replicate solutions carried through all steps of the procedure prior to photometric reading will show a certain inherent variation in absorbance. Second, there is a n uncertainty in repetitively inserting a given solution in the absorption cell and placing it in the instrument. Finally there is the uncertainty of measuring the absorbance of a given solution once it is placed in the instrument.

A general summary of the principle factors is given below: Solution Preparation. ( a ) Stability, or reproducibility of development, of

absorbing species; ( b ) Interferences or variations due to separation of interferences; (c) Backgrounds; (d ) Blanks.

Absorption Cell. ( a ) Rinsing and handling of cell. ( b ) Positioning of cell. Instrumentation. ( a ) Sensitivity and stability of circuit; ( b ) Light level

striking the detector; (c) Scale length and precision of readibility.


For purposes of clarification we have distinguished between the problems of handling, rinsing and positioning the absorption cell and that in making an absorbance reading once the solution is in the instrument, although these are often considered together.

The trace analyst should use an instrument and technique which enables him to keep the combined effects of the items listed under Absorption Cell and Instrumentation within the uncertainty arising from the items listed under Solution Preparation. If, for example, the actual variation in blanks is * 0.005 absorbance unit, making the instrumental reading to the nearest 0.001 unit will neither give us the overall precision nor the detectibility limit corresponding to that value.

Neither is this an excuse for careless photometry because if we can conduct the reading in such a way as to eliminate i t completely as a source of error we should do so. I n addition, although a small instrumental detectibility limit may not always increase our effective overall sensitivity it can sometimes conserve solution because we may be able to reduce our aliquot in the final stages of an analysis and obtain equivalent sensitivity on the smaller amount.

For general trace analysis an instrument is therefore recommended which is capable of an instrumental reproducibility of 0.2 per cent transmittance, and, by the use of an appropriate reference, such an instrument can be used to detect absorbance differences of 0.001 even in high total absorbance situations.

In the very lowest absorbance range if a good scale expansion device is available (such as the auxiliary 0.0-0.1 absorbance slide wires for the Cary instruments) its use will encourage careful photometry and at least tend to eliminate possible scale (or scale reading) errors encountered in the higher range.

In order to minimize errors due to rinsing and wiping absorption cells some workers have advocated not wetting the outside of the cell surfaces when changing solutions. One interesting way to overcome the problems involved with the cell in special cases might be to develop the color directly in the cell without removing it from the compartment, or bleaching a given color in the cell immediately after reading. This would allow the analyst to take a background on the very same solution which is used to read the color, which would also tend to cut down errors from this source.

The writer conducted an interesting experiment recently on titanium solutions, in which portions of a single stock were inserted in a one cm. rectangular cell in a Cary spectrophotometer. The absorbance was set for zero on each portion using the 0.0 to 0.1 absorbance slide wire and then a drop of 30 per cent hydrogen peroxide added to the cell, the solution stirred momentarily, and read after waiting about 30 seconds. The procedure was repeated nine times. The spread in absorbance values at A = 0.005 was 0.0005 with a standard deviation of +0.0002.

To complete the discussion on instrumental detectibility limits, past literature has described circuits which had reported capabilities of measuring


differences in transmittance of 0.01 per cent or even 0.001 per cent. These have been described by KortiimLG and reviewed by Hiskey.’”

In recent years some interest has been generated in the use of special slide wires to exhaust the electrical sensitivity of modern circuits. Thus, Slavin and Porro” reported the use of a slide wire capable of being read 0.01 per cent transmittance over the full range of a Perkin Elmer instrument, and Nelson and Hawed* have recently utilized a slide wire capable of being read to 0.0001 absorbance even a t 1.0 absorbance unit on a Cary instrument.

A method of expanding the transmittance scale of a spectrophotometer by the technique of zero suppression has been treated by Reilley and Crawford,”’ and the same general principle is involved in work reported by Ringbom and Osterholm. ’‘’

By this method the 0 per cent transmittance end of the scale is made to correspond to a finite amount of light. Attempts have been made to apply this method to both major and trace analysis situations. The general limitations of the approach in both of these areas have been discussed by O’Laughlin and Banks,’ and by Bastian, Weberling and Palilla.3’

Separations

For simplicity photometric methods of trace analysis can be divided into two general classes: those in which separations are required and those in which no separations are required. The bulk of the work in the literature falls in the former category although some examples of the latter can be found. “No separation” examples taken from the semiconductor industry include the analysis of aluminum for copper, silicon and iron in the 0.2 to 50 ppm. range and the determination of iron and copper in gallium.32

In order to try to eliminate or minimize separations both chemical and photometric aids may be employed. Chemical procedures may include the use of complex formers to mask would be interfering elements, the use of organic solvents miscible with water to solubilize otherwise insoluble compounds, or chemical reagents to prevent colloidal materials from settling out. Photo- metric aids may include the use of multicomponent spectrophotometry to turn would-be positive interferences into a method for determining other elements in addition to the given one, and the use of high absorbance reference procedures to compensate backgrounds, or any other factor contributing to high absorbance.

Generally the need for separations are increased as the concentration of trace constituent becomes lower, which accentuates the problem of incomplete recovery.

Among the separation techniques used most may be mentioned volatilization or distillation, precipitation, ion-exchange, electrolysis and extraction. Separation procedures may be classified in two general categories:

Bastian: Photometr ic Techniques 309

(1) those in which the major constituent is separated from the trace and (2) those in which the trace element is separated from the matrix or other traces.

When a clean cut separation of the matrix element is possible the problem of loss of the trace element due to incomplete recovery may not be as acute. Examples of this technique are volatilization of germanium as the chloride,'' and arsenic as the bromide." Generally, precipitation reactions are probably not a good way of removing the matrix, but was able to separate 0.5 gram amounts of nickel as hexamminoperchlorate from 10 to 120 micrograms of cobalt, after which he determined the latter with nitroso R. Of course, methods for separation of traces are very common, with extraction being a very prominently used technique.

Conclusion

Photometric methods in the major constituent area are capable of very high precision. Using indirect (bleaching) photometric techniques a precision in the low parts per 10,000 range has been achieved and an ultimate precision of one part per 10,000 or better is conceivable.

Photometric methods in the trace range are generally used to determine one or a t most a few elements on a single sample. Lower useful working limits for the analysis of samples using the more favorable reactions are in the 0.1 to 1 ppm. range, although there are exceptional cases in which lower amounts may be determined. They are useful in this and higher concentration ranges where truly quantitative results are required.

An interesting possibility for applying photometric methods to the determination of a larger number of elements on a single sample would be to attempt to analyze for both major and trace constituents. I n this case one could justify beginning with a relatively large amount of material which would tend to lessen the effect of any contamination introduced during the original solution process. The resultant solution could then be carefully aliquoted to proceed with the analysis. I t is also true tha t the more information one obtains about the amounts of several elements present in the sample the more one can utilize the information to counteract interferences and employ compensation and multicomponent techniques.

While the trace analyst is properly concerned with blanks he is sometimes reluctant to carry standards through his entire procedure. For the best work standards should always be carried and a combined analysis for both majors and traces might encourage this to be done.

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PARKER, C. A. & W. T. REES. 1964. In Trace Analysis of Semiconductor Materials. J . P. Cali, Ed.: 206-246. MacMillan. New York, N. Y.

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spectrophotometry. Paper presented at Pittsburgh Con. Anal. Chem. Applied Spectroscopy. Pittsburgh, Pa.

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photometric techniques as analytical tools

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