Quantitative Analysis with the Electron Microanalyzer T. 0. ZIEBOLD and R. E. OGlLVlE Department of MetaIlurgy, Massachusetts Institute o f Technology, Cambridge
The problems in interpreting x-ray spectrometric data taken with the electron microanalyzer are discussed. Theoretical and semiempirical methods for converting x-ray data to chemical compositions are reviewed and the methods now available are tested with data tlgken on the M.I.T. type microanalyzer. It is concluded that calculated corr'xtions cannot generally b e expected to give the 2% accuracy which i s obtained with carefully prepared calibration samples.
0
PAPERS published on the use of the electron microanal>-zer, fen- have given sufficient attention t o the prohlcms of obtaining accurate chemical anal lar t o the difficulty intenqity nieasureinc,nt's into ma.::-\ compositions. Sine(, the electron microanalyzer is being applied to a great varietj- of chemical for a more general niet,hod for correcting . data has beer1 greatly increased. appropriat'e, therefore, to revien1 proceilure.5 now available tlicsir validity with analytical nira~urenient~which have been made. In this paper we present an evaluation of extensive dat'a taken with the 3I.I.'I'. and .Idv:tnced Xetals Researrh microanalyzers to show that intensit>-conversiun formulas available a t this time cannot r,eplace the use of calibration ytandartis for quantitat'ive research. A wmniary of current research a t 1I.I.T. in which tl-e microanalyzer is used as the primar:. analytical tool illustrates the need fo.: accurate quantitat,ive measurements. In the field of solid state diffusion three problems are under study. In one program the cross effect:: of diffusion in the ternary alloy system of copper-silver-gold are being measured. In the fecond, the kinet'ics of preferential oxidation of elements from nickel-platinum alloys and stainless steels are being determined. I n the third, the nature of wcelerated diffusion of zinc along pure edge dislocation boundaries in silver bicrystals is being investigated. Another program, in the field of meteoritics, is seeking to establish the fine structure of composition gradients and interface equilibria. Finally the alteration of the ironvanadium equilibrium diagram under high pressure will be determined by the
F THE: XWY
39,
Mass.
use of diffusion couples. All of this work requires determination of compositions at many data points, and the advantages of the microanalyzer's rapidity and resolution should be apparent. It should also be evident that research of this nature requires that chemical analysis be as precise and reliable as possible. The design and operation of the hI.1.T. instrument has been described elsewhere by Ogilvie ( 2 ) , and many papers are available on the measurement and instrumental correction of x-ray intensities. Consequently, this paper will be limited to a discussion of how x-ray intensities are converted to mass composition. In the following section we present a brief summary of the nature of electron interaction with a solid sample as a basis for interpreting experimental data. The later sections include a survey of calculational corrections, and a compilation and evaluation of experimental calibration curves taken with the ilI.1.T. instrument. PRINCIPLES OF X-RAY PRODUCTION
To interpret x-ray measurements taken with the microanalyzer, it is necessary to understand horn x-rays are produced and what happens to thi. radiation as it emerges from a sample. As high energy electrons penetrate below the surface of a solid sample they interact in several ways; they will in part be scattered back out of the sample, they will produce continuous radiation (bremsstrahlung) , they mill produce heat, and they will produce ionizations leading to the emission of the desired characteristic spectral lines. Figure 1 is a schematic illustration of the penetration of electrons into the sample. I n light elements the electrons penetrate deeply, the distribution resembling a tear drop. In heavy elements the penetration is less and the distribution is more nearly hemispherical as illustrated The effectiveness of a solid in stopping high energy electrons is proportional to the electronic density of the solid. The range of penetration of electrons in a sample is a function of the incident electron energy and the material parameter ( p Z/A) where p , 2, and A are the mass density, the atomic number, and the atomic weight of the target material. Of more importance for probe analysis is the critical range for the production
of x-rays. This is the range of electrons which still have energies in excess of the excitation energy for the particular characteristic line of interest. Approximate values of the critical range for production of K radiation by 30k.e.v. electrons are 5 microns in aluminum and 2 microns in copper. Finally, there is a third range of interest. This is the range within which the incident electrons may be scattered back out of the sample. The fraction of incident electrons which are backscattered depends on the atomic number of the material. Since only a small fraction of the backscattered electrons n ill have produced ionizations before escaping from the sample, these electrons are ineffective in producing the desired x-rays. Because of their shallow penetration they become a n important tool of analysis where a high degree of resolution is necessary. As a first approximation in computing the inteiisity of characteristic lines produced by the incident electrons, it is assumed that the efficiency of electrons for producing x-rays in all elements is strictly proportional to the mass density of the elements. On this basis Castaing (5) has derived that the intensity of a particular line of a given element is proportional to the mass fraction of that element in the sample. Since absolute intensities are difficult t o compare, it is neceqsary to measure intensities relative to a standard, usually the pure element. As a first approximation then, the relative intensity resulting from element A in a mixture of elements is given by
where I' designates the direct primary intensity, that is, the intensity produced within the sample by the incident electrons and neglecting any absorption or secondary fluorescence within the sample itself. I d ' is the direct intensity from element A in the alloy, and IAO' is the corresponding intensity in pure element A . I s a second approximation the efficiency of the elements for attenuating the electrons may be included by computing the relative direct intensity as
where the parameter element i only.
CY;
is a property of
VOL. 35, NO. 6, M A Y 1963
8
621
Area Observed by the X - ray S p e c t r o m e t e r
+,,I
.~~
\ 1/
of the two might be expected to remain essentially constant. I n this case the first approximation for relative intensity would be valid. This is true for alloys of elements with close atomic numbers, but the data reported by Poole and Thomas indicate that this assumption is in error for elements widely separated in the periodic table, copper and gold for example. Figure 2 is a plot of the parameter cy prepared from the backscatter parameter values of Poole and Thomas and the stopping power data of h-elms ( 7 ) . (These data must be used with caution since they are based on only a few measurements.) A recent derivation of the electronic correction is given by .irehard and Mulvey (1). They compute x-ray production from a simplified theoretical model which accounts in limited detail for electron interactions within a solid. The expressions presented by hIulvey and Archard require extensive numerical calculations and cannot easily be used for routine analysis. It is to be hoped that their computation program will lead to parametric curves of sufficient generality to be useful for many systems being analyzed. The second correction t o be considered is the absorption correction. The most widely used approach is that presented by Castaing (4) who developed a theoretical model and determined experimentally the required parameters. For simplicity in the following discussion it is assumed that we are measuring the relative K a intensity of element A in a binary alloy AB. Castaing’s absorption correction for this case is applied to Equation 1 as
iT
, +
J7 -
R - Range of E l e c t r o n R c - C r i t i c a l Range Re- Range of Bockscattered Electrons
+Specimen
- Incident Current - Bockscattered Current i s - Specimen Current iT iB
Figure 1. Schematic of interaction between incident electrons and specimen
It must be emphasized that the relative intensity expressed by Equations 1 and 2 is the intensity produced within the sample and is not the intensity of radiation emitted from the surface of the sample and analyzed by the spectrometer. (It was never proposed that the actual measured intensity ratio should be equal to the mass fraction although this misinterpretation of Castaing’s paper has arisen.) Looking again a t Figure 1, it is apparent that the x-rays must travel through an appreciable volume of material before emerging toward the spectrometer and that the path length within the sample increases as the spectrometer takeoff angle decreases. The radiation produced within the sample is affected in three ways before emerging from the surface. First, the primary intensity is reduced by absorption in the sample. Second, additional ionizations will be produced by the continuous radiation. Third, additional ionizations of element A will be produced by the characteristic radiation of other elements in the sample if the wavelengths of these other lines fall below the absorption edge of element A. These last two effects result in additional components of the emitted intensity of a particular line and are termed secondary fluorescence. The measured intensity will not in general show the linearity given by Equation 1 , but may deviate positively or negatively depending on the composition of the sample and the particular line being measured. Proposals for calculating this deviation are summarized in the next section.
number effects) ; absorption correction; and secondary fluorescence corrections. The first of these, the electronic correction, has been outlined briefly in connection with Equation 2 . As shown by Poole and Thomas (9)) the parameter a, which depends on the electron accelerating voltage, should include the effect of both sample stopping power (electron energy loss per unit depth of penetration) and electron backscatter by the relation 01 = S A (3) where S is the stopping power and A is a parameter which is proportional to the backscattered fraction. These parameters, particularly the latter, are difficult to measure. It is known that S decreases and h increases with increasing atomic number, hence the product
X-RAY INTENSITY CORRECTIONS
From the preceding outline of the nature of x-ray production it is apparent that several corrections must be applied to Equation 1 to relate measured intensity ratios to mass fractions. These corrections may be considered in three parts: namely, electron interaction effects (often referred to as atomic 622
ANALYTICAL CHEMISTRY
Period Period IV
m
IO
Figure 2.
20
Period VI
v
I
I 1
Period
Period
I
50 60 70 ATOMIC NUMBER
30 40
80
1
I
90
100
Electronic correction parameter from Poole and Thomas
(9)
-a
!i! -
2 0.6
-
5?
-
-
R
+
-I
a-0.8-
-
W !-
-
z
0.4 -
a
-
0
v,
0.2 -
-
-
cosec Figure
3.
Absorption correction parameter from Castaing
I A / I A=~ .fAfarA‘/f.4’IA11’ =
(4)
The absorption parameter f~ is a function of
1~here
the mass absorption coefficient is the value for the K a line of element d being atsorbed in the alloy AB. For the biniry alloy this coefficient ii given by (p/p)
The angle 0 is the spectrometer takeoff angle. The value 3f f A a is computed for pure element A . Castaing’s values for the absorption parameter are given in Figure 3. Archard and RIulvey ( I ) have revised the values of Castaing’s absorption parameter with the result that the curve for aluminum is considerably lower than shown in Figure 3 and there is a larger variation with atomic number. Since their curves are computed, whereas Castaing’s are measured, this discrepancy remains unexplained. Other absorption corrections have been proposed by Philibert (8) and by Birks ( 3 ) . Philibert developed an analytical expression for the absorption parameter, namely -
(1 4-
%>
1
(4)
where (fA/fAo) C A
j =
+
-t h
1 -t h (1
+
s>
(6)
is the functional variable and h and u are constants. The constant h depends only on the properties of the sample and the constant u depends only on the incident electron energy. In practice these constants are evaluated by fitting the curve to Castaing’s data, Birks correction is a simplification of Castaing’s data, but in this approach the effect of atomic number on the absorption parameter is ignored. Since Philibert’s and Birks’ absorption corrections are derived from Castaing’s data, their accuracy cannot be expected to differ from that obtained by using Castaing’s parameter. The choice of one method over the others is a matter of personal preference, and we have applied Castaing’s curves t o the experimental data presented in this paper. A third correction which must be added is for secondary fluorescence produced by the continuous spectrum or by other characteristic radiation. An expression for the fractional increase in the K a intensity from element A which is produced by the K a radiation from element B in an AB alloy is given by Castaing ( 5 ) . His expression suffers from some simplifying assumptions which are in disagreement with experimental data. Wittry (10) has recently published a fluorescence correction which corrects some of the shortcomings of Castaing’s derivation. I n addition, Wittry has computed the parameters involved and presented them in graphical form which makes the application of
his correction quite straightforward. Again, however, Wittry’s formula is limited to cases where K radiation is excited by other K radiation, but he has developed the expression for ternary as well as binary systems. The correction for the K a of element A being excited by the K a of element B in a binary mixture is ( I s j / I p j ’ ) ~=
G
= GI (ZB- Za,V) G z ( C A , Z B / Z AG) ~ Z B )( 7 )
Here Ipf’ refers to direct primary intensity (no absorption) and I,, refers to the measured secondary fluorescence (absorption included). The three correction factors are separable functions of the variables indicated; 24 and ZB are the atomic numbers of elements A and B , V is the electron potential, and C A is the mass fraction of element A . Wittry’s fluorescence correction parameters, computed for 30-k.e.v. incident electrons and 15.5” spectrometer takeoff angle, are shown in Figure 4. Birks (3) has also developed a fluorescence correction which is quite simplified. Hoaever, it depends on empirical data for a takeoff angle of 6’, and since it does not include the effect of t h k variable explicitly it cannot be used directly for other geometries. Correction for secondary fluorescence produced by the continuous spectrum is more difficult to obtain. An expression for this correction is given by Castaing (4) but requires empirical data which are not available for other than the few systems which have been measured by Castaing and Descamps (6). Generally one is forced to neglect this correction even though it may not be negligible in the case where the elements differ widely in atomic number. I n conclusion, if one wishes to compute the intensity corrections it is necessary a t this time to use the electronic correction given by Poole and Thomas, the absorption correction given by Castaing or derived from Castaing’s data, and the fluorescence correction given by Wittry. With these factors the fully corrected relative intensity is IA/IAO =
a.,C,] X
[ G A / ~
z
+
[(f G)/fol CA (8) One should keep in mind the limitations of these correction factors and realize that improved models are under consideration. I n the next section we evaluate the accuracy of Equation 8 for several binary systems. EXPERIMENTAL MEASUREMENTS
A compilation of data taken with the iM.1.T. and A.M.R. electron beam microanalyzers is given in the appendix of this paper. The measurements were made on 52 different alloys covering 12 binary systems. The elements VOL. 35, NO. 6, MAY 1963
623
2 4 6 8 ATOMIC NUMBER DIFFERENCE, Z,-Z,
10
I.o
cu c3
& 0.8 W
I-
W
I
2 0.6 i 5 15.5" Take off angle
W
2 0.4 W
analyzed extend from iron to uranium so that these data present a sigriificaiit test of the range of applicability of the proposed correction formulas given in Equation 8. Since the reproducibility of intensity measurements on alloys of known composition is better than 27, (relative standard deviation), we take this figure as a criterioii for judging the suitability of calculated conversions of intensity ratios to mass fractions. The data which we have compiled show that the correct'ions available a t this time do not give better than 5% accuracy except for a few systems, and often do not agree within 10%. It is difficult to assess the correction factors individually since most of the systems reported here have negligible fluorescence effects, and the absorption and electronic correct'ions are about the same magnitude. It is evident in some alloys (Cu-Au, Si-Pt, E O ? , C C ) that the electronic correction of Poole and Thomas reduces significantly the error between measured and true compositions. However, for other alloys (Ag-Zn. W-Ru, K-Rh, 'Pa-Ru) the electronic correction increases the error so that the use of t'he simple parameter a: to account for the atomic number effect is in doubt. One approach to the measurement of the electronic parameter cy is to assume that the other corrections are accurate and to determine the value of a: which will bring the observed composition int'o agreement ivith the true composition. For a binary alloy the ratio of the parameters for the two elements may be computed by rearranging Equation 8 to
0
v, W
8 0.2 3
n-here
-I
.f~' (dF).,= -oI A ___ I A 5.4 GA expresses the measured relative int'eiisity corrected for absorption and secondary fluorescence. By assuming that the values of a: are the same for Os: Ir, Pt, and d u (Figure 1 indicates that they are equal to within 1%), the paranieters for the other elements can be tabulated on a relative scale. The values calculated from our measurements of intensity-concentration curves are listed in Table I. S o t e the close agreement betu-een the values determined from independent line measurements. The only value lacking in this agreement is for silver nhere the published absorption coefficient for AgLa: in Au is in doubt. Dividing the parameter O( by the stopping pon-er value from Selms
+
LL
0
20 40 60 80 WEIGHT PERCENT OF ELEMENT A
1
5- 0.8I-
-
-
-
2 0.6-
-
W
H
?i
-
-
W
0
E 0.4 -
15.5O Take off angle
-
0
m
-
W
5 0.2 -1
-
LL
0
624
20 40 60 80 ATOMIC NUMBER OF ELEMENT B
ANALYTICAL CHEMISTRY
100
4 Figure 4. Fluorescence correction parameters from Wittry (70) for element B fluorescing element A in a binary alloy. (The curves for Gz are for different values of Z,/ZJ
should give the backscatter parameter propwed by Poole and Thomas. Figure 5 is a comparison of our values with those reported prev'ously. There is a close agreement b e t v e i i a linear fit t o our data and the cui've d r a m by Poole and Thomas. Because of the excessive scatter, however, ths: use of the linear function derived frori our data does not impro\-e significantly the accuracy of the corrected iIitensity ratios. It is impossible to say whe1.her this scatter in the calculated CY values is a result of inaccuracies in the absorption correction or whether it ~s due to the fact that the electronic correcbion cannot be expressed as a simple parameter in the maiiner given b>. Castaing's second approximation. The more detailed computations of Archard and hlulvey for the Cu-Au system do not give any better accuracy than the corrections discussed above. Table I1 is a compar~isonof the corrections u&g the d a h of Archard and hlul\-e!- on one liand aiid the data of Caataiiig and Poole aiid Thomas on the ot1ir.r. A further seriou: ob.tacle in attempting to correct intensity measurements for certain alloys is the lack of mass ahsorption coc4icieiits for long war-clcngt,li line-: in heavy elements. For example, the corrections for Ru and R h in IT and T a ( ~ 0 ~ not 1 ~ 3be calculat'ed for lack of dat'a. The correction for rlg I, mcaaurements in ;ig-Au alloys was calculated by estrapolating the absorption coefficient for Ag L in Pt to that in =lu. Thir: apparently is an incorrect value although the estrapolatioii using the cube of the atomic iiumlier should be \.slid in this case. The mpasured intensit'y ratios indicate that the absorption coefficient should be a t leaat twice the w l u e obtained by extrapolat'ion from Pt, A h i l a r difficult:; arises \vhen attenil)ting to compute secondary fluorescence for I , lilies This correction require; knowing the 1-alues of relative inten>itie.s of lines in the I; series, the fluoresct.nc.e yield for L ionizations, and the jump ratios at the L edges. T h e v Iwoperticu are not well knoivn and cstrapolation from the fen. knon-n data 1miiit3 is not satiqfactory for precise a n a l ~ i i s .
13L
E+
Y
w .8
SK
-
(Least
Squares F i t to M I T Data
0. 0. 0
0
-I 0
* w
n
IO
"
20
30
40
50
Poole 8Thomas (Ref. M I T Data Reference Value
60 70
80
90 100
ATOMIC NUMBER Figure 5. Experimental values of backscatter ( 9 )and from data presented in this paper
Table 1.
parameter from Poole and Thomas
Electronic Correction Parameters Calculated from Intensity Measurements CY
Element Fe Xi CU
Zn Ru Rh Ag Ta
Os Ir
Table 11.
(Relative to gold) 1.52 1.56 1.37 1.51 1.26 1.29 1.06 0.95 1.06 1.07 0.50 1.10 1.13 0.93 1.09 0.96
Determined Alloy Fe-Xi Fe-Si Ni-Pt Ki-Pt CU-AU CU-AU Zn-Ag Ru-W Ru-Ta Rh-W
Ag-Au Ag-Au Ta-Os Ta-Os W-Ir
IT-Ir
from
Line FeIi 1-Z NiI< PtL CUI
-
mnJ
Poole 8 Thomas
0
Assumed reference values
Comparison of Proposed Intensity Corrections for Cu-Au Alloys
5 /c K
c 1 -1
79 4
0.994
0.978 59.8 0.967 39.9 20.1 0.965 Au L 20.6 0.738 40.2 0.806 60.1 0.840 79.9 0.914 Corrections used: A-absorption only AE-absorption and electronic
1 059
I , iii
1.161 1.210 0.907 0.925 0.922 0.957
1 059 1.073
1,152 1.208 0.821 0.874
0.887
0.938
1.042
: 1,100 1 085
1.112 1.000 0.993 0.963 0.962
1.001 0.954 0.958 0.931 1.053 1.062 1.016 1 ,003
VOL. 35, NO. 6, MAY 1963
625
Measured and Corrected (l/lo)/C for Binary Alloys
System
Line
Xi-Pt
FiK
CU-AU
CuK
Fe-Ni
Ag-Zn
ZnK
Ag-Au
AgL
Ta-Ru
W-RU
Ru L
Ru L
W-Rh
RhL
Ta-Os
TaL
W-Ir
a
FeK
WL
uoz
UL
uc
UL
True comp.,
~
%
Meas.
Aa
AF"
AFEa
Line
55.1 29.7 16.4 6.5
1.016 1.027 1.012 1.031
1,154 1.249 1.274 1.276
b
1.002 1.010 0.994 0.954
PtL
79.4 59.8 39.9 20.1
0,994 0.978 0.967 0.965
1.059 1.073 1.152 1.208
1.056 1.066 1.137 1.189
1.001 0.954 0.958 0.931
94.8 89.7 84.9 80.7 74.8 63.5 49.7
1.002 1.004 1,015 1.024 1.035 1.047 1.089
1.004 1.005 1.017 1.028 1.041 1.059 1.102
1.000
1.000 0.998 0.991 0.999 1.006 0.999 1.022
7.5 14.6
0.867 0,877
1.026 1.027
b
0.934 0.832
80.1
0.800 0.686 0.634 0.638
b
59.5 40.6 19.6
0.680 0.508 0.404 0.357
0.771 0.639 0.565 0.525
83.5 69.1 56.6 45.6 35.8 19.3 5.9
0.735 0.624 0.498 0.432 0.391 0,347 0.288
E
53.2 56.2 35.5 19.1 5.8
0.685 0.475 0.366 0.319 0,207
C
91.1 68.8 56.4 41 .O 15.3 2.4
0,852 0.618 0.520 0.451 0,451 0,333
c
9.5 29.0 48.8 68.9 89.5
1.189 0,869 1.037 1.067 1.006
1.231 0.897 1.061 1.079 1.010
b
5.7 29.4 43.8 57.9 73.6 94.6
1.I05
b
1.054 1.021 1.036 1.001 0,998
1,140 1.081 1.041 1.050 1.003 1.000
88.1
0.938
0.923
a
1.002
95.2
0.971
0.962
6
0.983
ANALYTICAL CHEMISTRY
KiK
AuL
TaL
WL
Corrections used: A-absorption AF-absorption plus fluorescence AFEabsorption plus fluorescence plus electronic
626
0.998 1.005 1.013 1.022 1.029 1.054
Au L
WL
1.231 0.897 1.061 1.079 1.010 1,087 1.040 1.020
1.031 0.990 1.000
osL
True comp.,
%
Meas.
Aa
Aa
AF5
44.9 70.3 83.6 93.5
0.768 0.825 0.927 0.944
0.835 0.861 0.947 0,952
D
0.987 0.949 1.005 0.972
20.6 40.2 60.1 79.9
0.738 0.806 0.840 0.914
0.821 0.874 0.887 0.938
b
1.053 1,062 1.016 1.003
5.2 10.3 15.1 19.3 25.2 36.5 50.3
0.750 0.670 0.695 0.699 0.698 0.734 0.789
1.173 1,029 1.046 1.036 1.003 1.002 1.011
b
1.192 1.058 1.059 1.051 1.015 1,002 1.011
19.9 40.5 59.4 80.4
0.935 0.985 0.998 0.970
0.915 0,971 0.987 0.964
b
16.5 30.9 43.4 54.4 64.2 80.7 94.1
0.970 0.935 0.947 0.978 0.989 0,991 1.020
1 .ooo
b
0.958 0,966 0.995 1.001 0.998 1 ,024
16.8 43.8 64.5 80.9 94.2
1.071 1.014 1.016 1.020 1.024
1.083 1.022 1.020 1.021 1.024
b
1.226 1,123 1,099 1,042 1.024
8.9 31.2 43.6 59.0 84.7 97.6
0.989 0.981 0.970 0.942 0.961 0,994
1.022 1.003 0,994 0 958 0.968 1.001
b
1.157 1.099 1.071 1,013 0,989 1.001
90.5 71.0 51 2 31.1 10.5
1.006 1.106 1.055 1.016
1.002 1.092 1.037
IrL 94.3
70.6 56,2 42.1 26.4 5.4
0.962
0,999 1.Ol6 1,028 1.021 1.129 1.092
0.990 1,007 1,017 1.004
1.102 1,056
1,133 1.048 1.057 1.051 1,040
1.035 1.043
b
1.002 1,092 1.037 0.994 0,962
0 994
0,990
1.075
1.098 1,072 1.008
i
0.999 1.007 1.040 1.028
1.125 1.092
Negligible secondary fluorescence effect. e
Mass absorption coefficient not available.
although on a more detailed theoretical basis, give no better accuracy than the simpler approach of Poole and Thomas. The electron bei,m microanalyzer is a superb instrument for many research problems, but we can only conclude that accurate measurem1:nts require the use of carefully prepared calibration standards to convert x-ray data to mass compositions. These standards must be chemically homogeneous on a microscopic scale, and tke calibration curves must be measured many times to establish their degrecb of reproducibility. By this approach one should obtain measurements having 27, or better accuracy. We can recommend no other approach when suck accuracy is desired. APPENDIX
Compilation of Measured and Corrected Intensity Data. There are two reasons for including the following data in dt>tail. First, it is clearly shonw what corrections are important for the M e r e n t types of systems and different lines used. Second, it is helpful for th0.e who are working to develop improved correction formulas to have sufficimtly detailed data with which t o test their models. All the data reported here were taken with 30-k.e.v. electrons striking normal to the sample surface. The beam current Jvas held constmt for all measure-
ments within an alloy system and was generally on the order of 0.1 pa. The spectrometer takeoff angle is fixed for all wavelengths a t 15.5’. All data are for fixed time counting. The measured intensities have been corrected for background. High speed counters were used so that instrumental corrections are negligible. The relative standard deviation of the measurements is less than 2% in all cases and less than 1% for many alloys. Measured intensities were corrected in three ways as shown in the tables. For the absorption correction, Castaing’s data were used. For the fluorescence correction, Wittry’s formulas were used. For the electronic correction (interaction effects), the data of Poole and Thomas were used. X o corrections for secondary fluorescence by the continuous spectrum were made. The basic data used for computing the corrections are from two sources. All wavelength values are from “The Handbook of Chemisrty and Physics,” 41st ed. (Chemical Rubber Publishing Co.). All mass absorption coefficients are from a recent compilation which appeared in the Norelco Reporter, MayJune 1962. ACKNOWLEDGMENT
Acknowledgments are made of the following people for supplying data so that the compilation could be as complete as possible: N. J . Koopman, D. M.
Koffman, and J. I. Goldstein of M.I.T. and S. H. Moll of Advanced Metals Research, Somerville, Mass. LITERATURE CITED
(1) Archard, G. D., Mulvey, T., “The Effect of Atomic Number in X-ray Microanalysis,” International Sym-
posium on X-ray Optics and X-ray Microanalysis, Stanford Univ., August 224,1962. ( 2 ) Bakish, R., “Introduction to Electron Beam Technology,” Wiley, New York, 1962. (3) Birks, L. S., J . d p p l . Physics 32, 387 (1961). (4) Castaing, R., “Advances in Electronics and Electron Physics,” Vol. XIII, p. 317, Academic Press, 1960. (5) Castaing, R., “,4pplication of Electron Probes t o Local Chemical and Crystallographic Analysis,” thesis, University of Paris, 1951. (6) Castaing, R., Descamps, J., J. Phys. Radium 16, 304 (1955). (7) Nelms, A. T., N.B.S. CircuZar 577, 1956, supplement. (8) Philibert, J., J. Inst. Metals 90, 241 (1962). (9) Poole, D. M., Thomas, P. M., Ibid., 90,228 (1962). (10) Wittry, D. B., USCEC Report 84204, Univ. of S Calif., 1962.
RECEIVED for review December 26, 1962. Accepted March 6,1963. Eastern Analytical Symposium, New York City, November 1962. Work supported in part by Contract No. AT(30-1)961 from the Atomic Energy Commission.
The Probllem of Determining the Optical Rotation of Highly Scattering Solutions A. L. ROUY, BENJP.MIN CARROLL, and T. J. QUIGLEY Chemistry Department, Rutgers, The State University, Newark, N. 1.
b Reasons are considered for the failure of the conventional polarimeter and photoelectric polarimeter to analyze turbid solutions. The differenceto-sum ratio method described previously is well suited for highly scattering solutions. The qucintitative determination of the opticcl activity suggests that the photoelectri’: polarimeter b e a nonorthogonal type of instrument, and any one of the fallowing analytical procedures may b e used: extrapolation procedures; methods based on an analytical form of the scattering function; or known, angular rotations imposed upon the sample. Details of the two latter procedures are given.
T
URBID S O L ~ I O W ,form a wide class of systems that have been inaccessible to polarimetry in spite of the recent advent of seve*al types of photo-
electric spectropolarimeters. The purpose of this paper is to discuss the nature of this problem and to suggest several methods of approach. Optical activity may be determined in the laboratory with about the same reliability as clear solutions provided that certain experimental conditions are adhered to and that proper theoretical treatment of the data is made. The determination of the optical rotation of turbid solutions presents the experimental problem of obtaining an appreciable light signal through a solution of low transmission-e.g., 10% down to O.l%-and a t the same time the problem of preventing the scattered, depolarized radiation which passes through the analyzer from swamping the signal. Some general aspects of obtaining a polarimetric light signal through a dense medium have been discussed in a previous publication (2).
Thus far the special problems raised by turbid systems have not been considered in the literature. POLARIMETRIC IMPOTENCE OF ORTHOGONAL SYSTEMS FOR TURBID SOLUTIONS
We mag inquire why the conventional visual polarimeter fails when examining turbid solutions. The cause is primarily because of the fact that the visual polarimeter is an orthogonal systemLe., a t the point of balance the angle between the polarized light that has transversed the sample and the optic axis of the analyzer is brought to 90’. Most, if not all, of the photoelectric spectropolarimeters presently available are basically orthogonal systems. The reason for the failure of these instruments becomes apparent from the following considerations. When a beam of linearly polarized VOL. 35, NO. 6, MAY 1963
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