able to dissociate the ferroin/sulfonate complex. The exact cause of sulfonate deactivation by crude oil is not known at this time. There does appear to be some correlation between the amount lost and the nature of the crude oil heavy ends. Positive nitrogens in the asphaltene and resin fraction and heavy metal centers are a likely source of complexing (5). The amount of sulfonate lost to various crude oils varies, undoubtedly because of structural differences in the heavy ends. It will likely also vary from one sulfonate to another because of differences in equivalent weight and molecular structure. For purposes of comparing one crude to another, the “sulfonate titration number” (STN) is defined as the amount of a given surfactant (in pequiv) that can be complexed by 1g of crude oil as obtained from a titration of the crude with the sulfonate. The range of STN values for different crudes observed to date is 1 to 44 wequiv/g
(f5-10%). The titration procedure as described above should be used before each series of analyses of sulfonate in a particular crude to obtain the STN of that crude. RSD’s on samples before
and after sulfonate addition will allow one to estimate: (1) the capacity of a particular crude oil to deactivate sulfonate, (2) the amount of free sulfonate in a sample, (3) the amount of complexed sulfonate in the sample. These quantities can be valuable in planning surfactant floods for tertiary oil recovery (5).
ACKNOWLEDGMENT Appreciation is expressed to B. A. Fries of Chevron Research Company, Richmond, Calif., for his assistance in the radioactive method development and to W. E. Gerbacia, Chevron Oil Field Research Company, La Habra, Calif., for many helpful discussions.
LITERATURE CITED (1) (2) (3) (4) (5)
P. I. Brewer, J . Inst. Pet., 58, 41 (1972). C. H. Wayman, USGS Prof. Pap., 450-6, 8117 (1962). W. R. Ali and P. T. Laurence, Anal. Chem., 45, 2426 (1973). C. G. Taylor and J. Waters, Analyst (London), 97, 533 (1972). D. M. Clementz, J. Pet. Techno/., in press.
RECEIVED for review January 10,1977. Accepted April 4,1977.
Simultaneous Determination of Composition and Mass Thickness of Thin Films by Quantitative X-ray Fluorescence Analysis Daniel Lagultton and Willlam Parrish” IBM San Jose Research Laboratoty, San Jose, California 95193
A new method of simultaneous determination of composition and mass thickness of alloy films has been developed. It uses the matrix effect correction by the fundamental parameters method and is performed automatically on a computer by the LAMA program. Only pure element bulk standards are required and no prior knowledge of the thickness of the specimen Is necessary. The iteration method is described, and the results are compared with those of electron microprobe, interferometry, and atomic absorption spectroscopy. The method is rapid, nondestructive, and has an accuracy slmilar to the above methods.
Since its discovery, x-ray fluorescence has been a very fascinating analytical tool, because it is nondestructive, rapid, precise, and potentially very accurate. This latter point, however, has been the limiting factor in the practical development of the method because the concept of the matrix effect correction used to transform experimental fluorescence intensities into weight fractions, involves a large number of fundamental parameters which in many instances are only approximately known. Other methods have been more or less successively developed to overcome the inherent difficulties of the fundamental parameters method (1,2). These include the dilution technique (3),the multiple regression method (4), the alpha or beta coefficient methods (5, 6), and the equivalent wavelength methods (7). Although all these methods could in principle be handled by use of calibration standards to reduce calculations to a minimum, a significant improvement 1152
ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
has been made in their application by the introduction of modern computers. For instance, regression or alpha coefficients can now be generated more easily by a computer (8-1 0). Besides the various simplifications that were necessary, these matrix effect correction schemes were applied only to thick specimens because the preparation of thin f i i standards required special procedures and were difficult to characterize by chemical methods. However, in recent years, the situation has significantly changed and the preparation of thin film specimens has undergone a considerable development as well as the resulting attempts to characterize thin film materials. The determination of fundamental parameters such as the mass absorption coefficients has also made important progress, and the greater availability of computers in research laboratories has made it easier to handle the somewhat complex equations describing the matrix effect correction by the fundamental parameters method (1,2). This paper presents the results of the application of computers to the determination of the composition and the mass thickness of thin f i i s by the fundamental parameters method.
THEORY The equation relating the measured fluorescence intensity of a line to the composition of a thin matrix is given in Equation 1, and the meanings of all symbols used are given in Table I (11-14). In order to cancel the effect of the efficiency of the spectrometer, one usually measures the ratio of the intensity of a characteristic line of the specimen to the intensity of the same line of a standard of known composition. As shown in Equation 1, besides the fundamental parameters which characterize each element, the matrix as a whole is
represented by its density p and its thickness D. The product of these two parameters is commonly designated as the mass thickness of the matrix, expressed in g/cm2.
Ri = R p j
+ Rsi
s
[l - exp(-XDp)]l,(h)dX
Ti(h)
Xsin $,
hmh
hedgej
hmin
with:{
,/ J =
-
Thickness of sample (cm) Exponential function Spectral distribution of primary radiation over interval d h
hedgei
Rpi = KPiwi
Table I. Definition of Symbols
n/2
[
tan ede
1- exp(-X,Dp) XlXZ
I+
1- exp(-XDp j
x2x
Analyzed element Interfering element Natural logarithm Transition probability for considered line of element i Jump ratio of element i for edge of considered line Total counting rate for line of element i Counting rate due to primary excitation for line of element i Counting rate due to secondary excitation for line of element i Irradiated area of sample Weight fraction of element i Integration angle, no direct physical meaning Efficiency of the counting system for wavelength h Wavelength (subscript i indicates wavelength of a line of element i) Minimum wavelength of the primary radiation Wavelength of the considered edge of element i Mass absorption coefficient of the sample for wavelength h (cm*/g) 3.14159. ,
--1-
.
Density of sample (g/cm3) Mass photoabsorption coefficient of element i for wavelength A (cm2/g) Angle between central beam of tube radiation and surface of the sample Take-off angle of measured radiation from
exp(-XDp) X J
specimen
ri - 1 pi = -p i w i i = i , j . . Ti
.
Fluorescence yield for line of element i Detection solid angle
P@i) I P(Xj) X1 = -
sin
$2
cos 0
Any attempt to completely analyze a film by x-ray fluorescence has to include the determination of two parameters, namely the composition and the mass thickness. If Equation 1 is schematically represented by
Ri = f ( M i , W i , PD)
(2) where Mi represents the matrix effect which combines with the values of the weight fraction wi and the mass thickness p D , the system of equations to be solved for the analysis of a film containing n elements can be written:
(3)
Rr7 = fW1, wn7 PD) This system of n equations has n 1 unknowns and is therefore indeterminable. The methods used so far to solve this problem differ according tQ the type of film studied. In cases where it is possible to use an internal standard of element j in the film, Equation 1 can be approximated by
+
Ri = MiwipD
(4)
and therefore the ratio
RiIRj = M
i ~ i / M j ~ j
(5)
is independent of the mass thickness. Mi and MI can be determined by calibration and since wj is known, w, can be
calculated (15). In those cases when the internal standard method could not be used, graphical methods were developed which lead to an approximate compostion and thickness (16, 17). In summary, the x-ray fluorescence analysis of thin films has always been considered as a problem of calibration and standardization. The present method is an entirely different approach which uses modern computer facilities to solve directly Equation 1 with the best values of fundamental parameters. It has been successfully applied to the determination of the composition of thick specimens (2) and to the mass thickness determination of pure element films (18). The necessity of incorporating a term to account for the secondary fluorescence intensity in Equation 1, instead of considering it negligible in thin films is illustrated in Figure 1. It shows the contribution of the secondary enhancement of the Fe K a line to the total fluorescence intensity emitted by iron in iron-nickel alloys of different film thicknesses. The calculation was done using the LAMA program (2) and the experimentally-determined spectral distribution of a tungsten target x-ray tube operated a t 45 kV (19). For example, the secondary fluorescence intensity of an 8000-A thick film is 10% of the total intensity of Fe K a for a FeZ5N&composition, and this proportion increases as the nickel concentration and/or the film thickness increases. Equation 1 in its complete form can only be solved with a computer. There are two ways of solving the system of Equations 3: (a) Measure the intensity of a second spectral line (say KP or Lp) of any of the elements present in the specimen in order to make the number of independent equations equal to the number of unknowns (we have not completely tested this method); (b) Use as the “missing” equation the condition that the sum of the weight fractions must be equal to one. The latter method was used in the ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
1153
,
0.50
,
,
,
,
,
,
,
,
F e Ka i n Fe NI Alloys Tube. W 4 5 k v
0
10
20
30
40
50
Weight
60
70
80
90
100
90 Fe
Figure 1. Variation of the proportion of secondary fluorescence intensity I, to the total fluorescence intensity I, 4- I, emitted by Fe K a in Fe-Ni
alloys of different compositions and thicknesses
present study. The only restriction in this assumption is the case where a light element, such as oxygen, is present in substantial amount and must be analyzed by difference, which requires an assumed stoichiometry. In such cases the assumption that the sum of concentrations is equal to one is used to determine the oxygen concentration and cannot be used for the determination of the mass thickness. Figure 2 is a flowsheet of the calculation scheme used. It is a modification of the hyperbolic iteration method ( I , 20) and includes several original features. 1. The intensity ratios are measured using pure element thick standards whenever available. Although it is also possible to use thin film standards containing several elements, such a choice increases the risks of error since the composition and mass thickness of each standard must be exactly known. 2. In order to obtain a first approximation of the concentrations, it is necessary to normalize the experimental intensity ratios. This is not feasible if the standards are complex or of different thicknesses. T o overcome this difficulty, the LAMA program automatically converts the experimental intensity ratios into pseudo-experimental intensity ratios referring to pure element standards of the same thickness as the specimen, according to the relation:
R ispec Ri pure stand same D
-
R ispec R , stand
X
R istand R j pure stand same D
(6)
These pseudo-experimental intensity ratios are normalizable and no initial knowledge of the specimen thickness is necessary; any value whether it is known or a guess can be used. 3. The hyperbolic iteration is performed until the convergence is obtained. 4. The sum of the concentrations is checked. If it is significantly greater than 1.0 it means that the pseudo-experimental intensity ratios used can be matched only by assuming an excess of elements in the specimen of the assumed thickness D. A new value of D which will be closer to the actual thickness is obtained by simply multiplying the previous assumption of the thickness by the sum of the concentrations. The hyperbolic iteration is then reinitiated with new pseudo-experimental intensity ratios and continued until the sum of concentrations is sufficiently close to 1.0. This procedure is general and can be used in all cases where a simultaneous determination of the composition and the mass thickness of a film is desired. I t should apply as well to other techniques in which the matrix effect correction is thickness dependent (e.g., electron microprobe analysis). The only case where it is not applicable is when an element cannot be di1154
ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
L Rerulf
Collcenlrafani = C Theorel ca Dens t y = W a i i Tn ckneii - p D
Figure 2. Diagram illustrating the iteration procedure rectly analyzed in the specimen. The interferometric measurement of the thickness is then necessary in order to be able to solve the Equation 3, unless a second line is measurable for any of the analyzed elements, in which case composition and mass thickness can still be determined. The theoretical discussion presented above has been applied to the characterization of two series of alloy films and the results are presented in the following. EXPERIMENTAL Procedure. The experimental data were obtained with a Philips universal vacuum spectrometer, automated with an IBM System 7 computer (21),and a Philips FAAQlW tungsten target x-ray tube operated at 45 kV from a Rigaku generator. The geometry of the specimen chamber was IC/1 = 6 6 O and IC/2 = 3 5 O ; the monochromator was LiF (200), and the detector was a scintillation counter with a single-channel pulse height analyzer to ensure good statistical data. A minimum of 5 x lo4counts was recorded at the peak positions, and the background was carefully measured on both sides of the peak to ensure that the correct levels were obtained. The resolving time of the detector and the electronics was 1 ps, and the counting rate was kept below lo4 counts/s t o avoid nonlinearity corrections. Film Preparation. The Gd-Co-Cu series of eight thin films were made by biased magnetron sputtering (22) and deposited on single crystal silicon wafers. The same sputtering target was used, and all the films had about the the same composition and were 2.2 to 3.6 pm thick. Two adjacent companion films were made in each run and were shown to be identical by x-ray measurements. The Fe-Ni series was made by high vacuum evaporation with three adjacent companion films for each composition. One film was used for x-ray fluorescence, another for atomic absorption spectroscopy, and the third for interferometric thickness measurements. Films numbers l to 8 of this series were deposited on silica substrates and numbers 9 to 12 on silicon wafers. RESULTS X-ray Fluorescence vs. Electron Microprobe on GdCo-Cu Films. The Gd-Co-Cu films were analyzed by the
Table 11. XRF and EMP Analysis of Gd-Co-Cu Films X-ray fluorescence analysis Atomic %
Gd
Intensity ratios co
cu
Gd
co
cu
D ( A ) x 100
0.3192 0.3287 0.3056 0.3223 0.3947 0.3480 0.3312 0.3291
0.1767 0.1851 0.1586 0.1834 0.2134 0.1949 0.1949 0.1900
0.1143 0.1220 0.1126 0.1169 0.1346 0.1254 0.1205 0.1216
13.51 13.15 13.78 13.22 13.73 13.30 12.97 13.02
43.19 42.62 41.48 43.42 41.86 42.64 43.89 43.22
43.30 44.23 44.75 43.36 44.41 44.06 43.14 43.76
248 269 227 261 363 295 279 274
42.8 40.6
43.9 44.7
13.3 Averages XRF EMP 14.7
Table 111. XRF and AAS Analyses of Fe-Ni Films Atomic X-ray fluorescence absorption Weight % Intensity Ratio Weight % No. Fe Ni Fe Ni Fe Ni
-
1 2 3 4 5 6 7 8
0.1294 0.0843 0.1051 0.0618 0.0159 0.0289 0.0160 0.0273
0.0127 0.0086 0.0570 0.0340 0.0762 0.1343 0.0751 0.1255
90.83 89.96 62.45 63.04 16.26 15.95 16.56 16.27
9.82 9.77 37.70 36.95 83.57 83.35 83.26 83.46
91.0 90.5 62.0 64.2 19.2 19.3 17.8 17.2
9.0 9.5 38.0 35.8 80.8 80.7 82.2 82.8
method described above using pure element thick standards, and the measured intensity ratios were processed by the LAMA program to obtain the composition and mass thickness of the films. Duplicate measurements of each film by XRF gave highly reproducible results from one specimen to another. A separate electron microprobe analysis was performed on films prepared from the same sputtering target, using the conventional ZAF procedure since the f i i s were all thick enough to be considered as infinitely thick for the electron beam energy used. The microprobe intensity ratios were processed by the MAGIC correction program (23). The results are summarized in Table I1 where all the values are normalized to 100% atomic. The last two rows compare the averages of the normalized values obtained by both methods. X-ray Fluorescence vs. Atomic Absorption a n d Monitor on Fe-Ni Films. The XRF results on Fe-Ni films compared to atomic absorption spectroscopy are shown in Table 111. The XRF results are the values calculated from the intensity ratios. The weights found by AAS were equated to weight percent and the totals are 100%. There is good agreement except for specimen numbers 5 and 6 where the differences are about 3% absolute. It is not evident which method is in error because for the same range of composition, the agreement between XRF and the monitored data is excellent. This is shown in Table IV where the results are given in atomic percent normalized to 100%. The monitored data were derived from the decrease in frequency of a precision quartz piezoelectric plate device placed in the evaporation apparatus in the line-of-sight with the substrates on which the films were deposited to control the composition and thickness. Mass Thickness Determination. The films to be analyzed by atomic absorption spectroscopy were first measured by XRF. The surface areas were carefully measured with a planimeter on a 6X enlarged photograph to calculate the mass thickness from the AAS results. The Tolansky interferometer measurements were made with a He-Ne laser, X = 6328 A. These two non-x-ray methods are destructive in that the
Thickness,
Table IV. XRF and Monitor Analyses of Fe-Ni Films X-ray fluorescence Intensity ratio Atomic % Fe Ni Fe Ni
No. 9 10 11 12
0.0055 0.0056 0.0227 0.0055
0,0189 0.0198 0.0932 0.0277
23.12 22.60 19.06 16.92
76.88 77.40 80.94 83.08
Monitor,
atomic % Fe Ni 23.8 23.8 19.7 17.5
76.2 76.2 80.3 82.5
Table V. Comparison of Thickness Measurements, Fe-Ni Films
H- L/
No.
XRFa
AAS
Int.
Av
1 2 3 4 5 6 7 8
5601 3579 6283 3558 3215 5533 3180 5550
5655 3524 6053 3473 3011 5452 2967 5237
5354 3470 5918 3364 2984 5522 2873 5196
5537 3524 6085 3465 3070 5502 3007 5328
av, % 5 3 6 6 8 1 10 7
837 853 4080 1130
3 1 0 2
Mo n 9 10 11 12
825 858 4090 1117
848 84 8 4070 1142
a XRF, x-ray fluorescence; AAS, atomic absorption spectroscopy; Int., Tolansky interferometer; Mon, evaporation rate monitor; Av, average of measurements; thickness in A .
specimen must be dissolved for AAS and have a very thin aluminum coating for interferometry. In the XRF and AAS determinations, the thickness was calculated from the mass thickness assuming the film density to be equal to that of a thick specimen of identical composition. The data are summarized in Table V. The direct thickness determinations obtained from interferometry are all somewhat lower than those obtained from XRF and AAS, and the assumption of equal thin film and bulk densities may not be exactly correct; the film usually has a lower density and it may not be uniform. The accuracy of the values listed can be judged by the percentages in the last column. T o avoid the impression of five significant figures in the thickness determinations listed in Table 11, the last two digits were dropped and the values should be multiplied by 100 to obtain the actual thicknesses. There are always difficulties in obtaining accurate crosscalibrations between totaJly different methods. The agreement in the results shown in Table V for the four different methods, particularly with the monitor data, is sufficiently close to ANALYTICAL CHEMISTRY, VOL. 49, NO. 8,JULY 1977
1155
demonstrate the practical usefulness and accuracy of the fluorescence method. The x-ray method is rapid and the result is obtained automatically with the composition analysis by the LAMA program. It does not require previous knowledge or even a good estimate of the thickness because any initial value, even if it is wrong by an order of magnitude, will give the correct answer although the computing time will be slightly increased.
CONCLUSION It has been shown that x-ray fluorescence analysis associated with computer calculations can now respond to the growing need of the thin film technology for a rapid, nondestructive, and precise method of determination of the composition and mass thickness of thin film materials. Only thick standards are required and they can be pure element or complex compounds. The accuracy of the analyses is similar to that of atomic absorption spectroscopy or of electron probe microanalysis of thick specimens. The thickness values also compare very well with the interferometry values. If the thickness of a film is known from interferometry for example, the method provides for the calculation of the average density which is an important characterization parameter and may vary from one film to another. ACKNOWLEDGMENT We are grateful to C. R. Guarnieri and R. E. Richardson for thin film specimen preparation and interferometer measurements, J. Eldridge and M. H. Lee for specimen
preparation and rate-monitor data, D.F. Kyser for the electron microprobe results, and B. L. Olsen of the IBM T. J. Watson Research Center, Yorktown Heights, N.Y., for the atomic abosrption spectroscopy results.
LITERATURE CITED J. W. Criss and L. S. Birks, Anal. Chem., 40, 1080 (1968). D. Lagultton and M. Mantler, Adv. X-Ray Anal., 20, in press. F. Claisse, Rep. R.P. 327, Ministry of Mines, Quebec, P.Q., Canada, 1956. B. J. Mitchell and F. N. Hopper, Appl. Spectrosc., 20, 172 (1966). F. Claisse and M. Quintin, Can. Spectrosc., 12, 129 (1967). S. D. Rasberry and K. F. J. Heinrich. Anal. Chem., 48, 81 (1974). R. Tertian and P. Vi0 le Sage, X-Ray Spectrom., 5, 73 (1976). R. Rousseau and F. Claisse, X-Ray Spectrom., 3 , 31 (1974). R. Jenkins, J. F. Croke, R. L. Niemann, and R. G. Westberg, Adv. X-Ray Anal., 18, 372 (1975). C. E. Austen and T. W. Steeie, Adv. X-Ray Anal., 18, 368 (1975). J. Sherman, Spectrochlm. Acta, 7, 283 (1955). J. Sherman, Spectrochim. Acta, 14, 466 (1959). T. Shiraiwa and N. Fujino, Jpn. J. Appl. Phys., 5 , 866 (1966). G. Pollai, M. Mantler, and H. Ebel, Spectrochlm. Acta, Parts, 28, 747 (197 1). F. H. Chung, A. J. Lentz, and R. W. Scott, X-Ray Spectrom.,3, 172 (1974). K. Hirokaw, T. Shimanuki, and H. Got& Fresenius’ 2.Anal. Chem., 190, 309 (1962). Katsumi Ohno, personal communication. D. Laguitton, IBM Rep. RJ 1938 (1977); submitted for publication. J. V. Gilfrich and L. S.Birks, Anal. Chem., 40, 1077 (1968). K. F. J. Heinrich, Anal. Chem., 44, 350 (1972). W. Parrish, T. C. Huang, and G. L. Ayers, Trans. Am. Ciyst. ASSQC. 12, 55 (1976). P. A. Albert and C. R. Guarnieri, J. Vac. Scl. Techno/., 13, 138 (1977). J. W. Coiby, Adv. X-Ray Anal., 11, 287 (1968).
RECEIVED for review February 23, 1977. Accepted April 7, 1977.
Gamma-ray Activity Determination in Large Volume Samples with a Ge-Li Detector Alessandra Cesana and Mario Terrani * Istituto di Ingegneria Nucleare-Politecnico di Milano, Milan, I f a h
A method for the determlnatlon of the y-ray actlvlty of large volume sources is described and dlscussed. The efficiency of the detector Is expressed as the product of an Intrinsic, a geometrlcal, and a self-absorption factor. The first and the second terms are determined experimentally whlle the last Is evaluated theoretlcally. The method has been applied to the determination of the y speclflc activity of natural potassium and natural lanthanum. For potassium a value of 3.21 f 0.01 y / s g of K was obtained, whlle for 13’La the partial half-llves for the photons of 789.1 and 1435.8 keV turned out to be 3.68 f 0.14 X 10” y and 1.99 f 0.03 X 10l1 y, respectlvely.
The main difficulty connected with the measurement of the y activity of large samples is the determination of the counting
efficiency. The use of standards which is the procedure more often encountered, is pratical only when the samples are similar in density and chemical composition (e.g., in the determination of fallout activity) but it can be a problem to find an appropriate set of standards ( I ) when the sample characteristics are widely varying such as, for instance, in the determination of uranium and thorium in rocks. On the other hand, total efficiency calculations are reliable for NaI(T1) detectors, while it is a general opinion that for 1156
ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
Ge-Li detectors the uncertainties on the exact extent of the active volume significantly limit the accuracy. Greater uncertainties are connected to the computation of the peak to total ratio so that full energy peak efficiency (FEP) calculations can easily be wrong by several per cent. Perhaps the more convenient procedures are based partly on measured and partly on calculated quantities (1). The method described below, which is currently used in our laboratory, has proved to be satisfactory. The FEP efficiency eeXt of the extended and self-absorbing source is expressed as: eext =
fF?Pa
where t is the FEP efficiency of a point source situated a t a given position on the axis of the detector; Fg is the ratio between the FEP efficiency of the extended source (supposed non-absorbing) and the point source; and Fa is the ratio between the FEP efficiences of two identical extended sources: absorbing/not absorbing. The first two terms are determined experimentally, while Fa is calculated.
EXPERIMENTAL Counting Device and Sample Dimensions. The y-ray spectroscope is a coaxial Ge-Li detector (32 cm3of volume) coupled to a multichannel analyzer. The detector dimensions are: radius, 1.91 cm; height, 2.98 cm; radius of the p-type core, 0.5 cm. The crystal is enclosed in an aluminum cap 2 mm thick. The distance
