10. R. E. Sturgeon, C. L. Chakrabarti, I. S. Maines, and P. C. Bertels, Anal. Chem. 47, 1240 (1975).

11. L. W. Gamble, and W. H. Jones, Anal. Chem. 27, 1456 (1955). 12. W. G. Wood and J. M. Mathiesen, "Applications of Energy Dispersive X-

Ray Spectroscopy in the Petroleum Industry," in Application Tips, No. P/ M 38 (Finnigan, Corp., May 16, 1974).

13. Symposium on Analysis of Petroleum for Trace Meta l s - Division of Petro- leum Chemistry and Analytical Chemistry, ACS National Meeting, April 6-11, 1975, Philadelphia, PA.

14. J. H. Runnels, R. Merryfield and H. B. Fisher, Anal. Chem 47, 1258 (1975). Contribution of Trace Metals Project Participating Laboratories: Atlantic Richfield Co., Harvey, IL; Chevron Research Co., Richmond, CA; Exxon Research and Engineering Co., Linden, NJ; Mobil Research and Development Corp., Paulsboro, NJ; Phillips Petroleum Co., Bartlesville, OK (refs. 14 to 17).

15. H. E. Knaver and G. E. Milliman, Anal. Chem. 47, 1263 (1975). 16. W. K. Robbins, Anal. Chem. 46, 2177 (1974). 17. W. K. Robbins and H. H. Walker, Anal. Chem. 47, 1269 (1975).

An Auger Electron Spectroscopic Study of the Diffusion of Sulfur and Carbon in s-Iron*

W. E. SWARTZ, JR. and D. M. HOLLOWAY Department of Chemistry, University of South Florida, Tampa, Florida 33620 and Neutron Devices Department, General Electric Company, St. Petersburg, Florida 33733

A u g e r e l ec t ron spec t roscopy h a s been employed to study the diffu- sion of sulfur and ca rbon in a - i r on . In the temperature r a n g e 25 to 500°C ca rbon p re fe ren t i a l ly s e g r e g a t e s to t he sur face . F r o m 400 to 70O°C s u l f u r s eg rega t e s to t he s u r f a c e whi le c a rbon is t h e r m a l l y desorbed. An A r r h e n i u s ana l y s i s o f the sulfur diffusion data yields an ac t iva t ion ene rgy o f 14.5 kca l /mol , wh ich is c o n s i s t e n t wi th a grain boundary diffusion process. The kinetics of ca rbon m i g r a t i o n is compl i ca t ed by t he t h e r m a l desorp t ion wh i ch m a k e s Arrhenius a n a l y s i s impossible. Index Head ings : Auge r e l ec t ron spec t roscopy; Su r face ana lys i s .

INTRODUCTION

Auger electron spectroscopy (AES) has been shown to be most useful in the study of the thermal segregation of bulk impurities to the surface. Harris ~ first employed AES to study the segregation of sulfur in nickel between 600 and 900°C. Jenkins and Chung 2 have reported sulfur segregation to Cu(III) surfaces at 750°C. More detailed studies have resulted in the determination of diffusion parameters. For instance, Kunimori et a l . 3 have deter- mined the activation energy and mechanism for sulfur diffusion in high purity molybdenum.

Interest in the surface segregation of trace impurities in powder of high purity a-iron results from the pyro- technic application of the material . In these applica- tions, the material, in intimate contact with oxidant, experiences temperatures ranging from 25 to 700°C. The thermal segregation of trace impurities to the material surface could influence the pyrotechnic behavior. There- fore, an AES study of the segregation of impurities in high purity iron powder as a function of temperature was initiated. AES was chosen to study impurity segre- gation since the technique gives a direct and quantita-

Received 10 December 1976. * P r epa red for t he U. S. E n e r g y R e s e a r c h and D e v e l o p m e n t Admin -

i s t ra t ion , A l b u q u e r q u e O p e r a t i o n s Office u n d e r Con t rac t No. EY- 76-C-04-0656.

tive measure of the composition of the surface, without excessive manipulation of the specimen. Other tech- niques, e.g., radioactive tracer methods, 4''~ essentially examine bulk diffusion processes rather than surface segregation. Thus any information regarding surface segregation is not explicitly determined. Because AES is truly a surface technique, differences between bulk and surface characteristics can be elucidated. It is the intent of this report to identify the major contaminants which segregate to the surface. Further kinetic analysis of the r a t e s of segregation will be used to define a mechanism for surface segregation.

I. EXPERIMENTAL

The iron powder was obtained from Pfizer Chemical Company and was identified as NXl000, 1972. The iron was analyzed via several analytical techniques. Carbon, sulfur, hydrogen, nitrogen, and oxygen were deter- mined by combustion and inert gas fusion methods us- ing standard Laboratory Equipment Corporation (LECO) apparatus and techniques. Calcium was deter- mined via classical atomic absorption procedures using a Perkin-Elmer 403 atomic absorption spectrometer. Other trace impurities were determined via semiquanti- tative mass spectrometric analysis using a DuPont mass spectrometer on the solid samples. A General Electric XRD-5 diffractometer employing a copper target was used to identify the iron as the a phase.

The apparent particle size of the iron powder was determined to be 3.15 tLm as determined by a Fisher subsieve analyzer. The surface area was determined to be 0.50 m'-'/g via a Quantachrome Corporation Monosorb surface area analyzer which operates using the low temperature gas adsorption (BET) technique. The sam- ples were prepared by pressing the powders into 1/2-in. discs with a hydraulic pellet press at a pressure of 30 000 lb/in 2. The press was thoroughly cleaned prior to contact with the iron powder. The specimens were mounted in molybdenum "baskets" with 1/4-in. windows

210 Volume 31, Number 3, 1977 APPLIED SPECTROSCOPY

for presentation to the Auger electron spectrometer. The Auger electron spectra were recorded with a

Physical Electronics Industries Auger spectrometer. The electron energy analyzer was a single pass cylindri- cal mirror analyzer operated at 3.0 keV, 50/zA sample current with 5 V peak to peak modulation. The sample position was maintained constant with a Varian sample manipulator. This insured that the same area of the specimen was analyzed after each heating cycle.

The samples were heated by bombardment with 2 kV electrons produced by a Physical Electronics Industries electron gun until thermal equilibrium was established. The equilibrium temperature was maintained for con- trolled periods of time such that rates of segregation could be determined. The sample temperature was mon- itored via a chromel/alumel thermocouple that was spot welded to the surface of the disc. The weld was carefully located such that it would not cause complications in data interpretation.

The specimen was sputtered with a Physical Electron- ics Industries argon ion gun operated at 5.0 keV with a current density of approximately 150 t~A/cm ~. Before data collection began, the surface of the specimen was sputtered to remove any extraneous contaminants that may have been introduced during sample preparation.

The residual gas analyses were performed with a UTI model 100-C quadrapole mass spectrometer.

to the surface can be obtained. Fig. 2 is such a plot for sulfur at 400°C. As evidenced by the data, the relation- ship is linear over the time interval shown. The slope of the line can be taken as the rate (V~) of sulfur segrega- tion to the surface. The units of V~ must'necessarily be arbitrary since the exact relationship between the Au- ger peak to peak amplitude and concentration is not known. The rate of sulfur segregation was also deter- mined at 500, 600, and 700°C. The resulting rates are tabulated in Table II.

In order to achieve some understanding of the mecha- nism for sulfur segregation, an Arrhenius analysis of the data was made. By plotting log V~ vs 1/T (K-~), the activation energy (Ea) can be estimated from the Ar-

TABLE I. Bulk analysis of a-iron

Percent Parts per million

Metallic iron Total iron Carbon Calcium Nitrogen Oxygen Sulfur Potassium Chlorine Silicon

94.7 98.5

0.01 0.02 0.004 1.87 0.02

102 170

<340

II. RESULTS AND DISCUSSION

In order to fully characterize the a-iron, chemical analyses of impurities were performed. The results of the bulk chemical analyses are summarized in Table I. The percentages reported are weight percent and the trace impurities determined mass spectrometrically are in parts per million.

The primary contaminant on the surface of high pu- rity a-iron was oxygen. Other minor impurities found on the surface were silicon, sulfur, potassium, chlorine, calcium, carbon, and nitrogen. In the initial studies, it was observed that at low temperatures (150 to 500°C) carbon preferentially segregated on the surface. At higher temperatures (400 to 700°C) carbon dramatically diminished and sulfur segregation dominated. This is shown in Fig. 1. The data plotted are the peak to peak Auger signals for sulfur and carbon "normalized" to that for the 651 eV signal for iron. The ratio X/(Fe + X) is simply viewed as proportional to coverage. The cover- ages by other contaminants were relatively constant as a function of temperature.

In order to determine the specific rate of diffusion at various temperatures, the peak to peak magnitude of the Auger signal for a particular contaminant was mon- itored as a function of time under isothermal conditions. The peak to peak magnitude of the Auger signal was taken to be proportional to surface concentration.

Initially, sulfur segregation was studmd. As shown in Fig. 1, from ambient temperature to 400°C the coverage of the iron surface remained essentially constant. Be- ginning at 400°C, sulfur coverage increased signifi- cantly until a maximum was reached at 700°C. By plot- ting the peak to peak intensity of the Auger signal vs time at a given temperature, the rate of sulfur diffusion

:) 4-

0 ? / / " \, ..d" '\

x , 0 " ' " \

0.3 / '\ • x - s

/ \ o x - c

0., \ . . . . . ~ - - - - - O , ,

~oo 3~o ' ' If® .506 100 900

T (°C)

Fro. i. Fractional coverage as a function of temperature for sulfur • and carbon O.

4-

E -

2-

w 1 < ==

1 ~ I I I J I I I I L I I

]20 3 ~ 6(~ 840 1080 1320 1500

TIME (sec . )

FIG. 2. Rate of sulfur diffusion at 400°C.

A P P L I E D S P E C T R O S C O P Y 2 1 1

rhenius relationship (Eq. (1)).

Ea log V~ - + C (1)

2.3 RT

Fig. 3 shows the Arrhenius plot for sulfur segregation in a-iron. Note the distinct linearity of the plot. From Eq. (1), the slope of the line equals Ea/2.3 R. The activation energy is consistent with a grain boundary diffusion mechanism for sulfur in a-iron. 4' '~

Attempts were made to apply similar kinetic analysis to the low temperature carbon segregation. In all sam- ples examined, the data indicated that carbon segrega- tion invariably commenced at 150°C with maximum coverage occurring at 500°C (Fig. 1). However, unlike the sulfur data, the carbon data, with respect to the rate of segregation, varied significantly from sample to sam- ple. This prevented the accurate determination of diffu- sion parameters.

One explanation for the inconsistency of the carbon data might lie in the desorption of carbon at elevated temperatures. As seen in Fig. 1, at approximately 500°C, the carbon coverage of the surface begins to rapidly diminish. In order to understand this desorption process residual gas analyses (RGA) were performed during the heating cycle. The filament of the electron gun is known to produce considerable amounts of CO (m/e 28) and CO2 (m/e 44) as it is heated. Therefore, the RGA spectra were monitored as a function of electron beam current without sample heating to provide a back- ground condition. Fig. 4 shows that the background is relatively constant with beam current. Since carbon (m/e 12) was the species of interest, the data were plotted as the ratio ofm/e 12 to (m/e 28 + m/e 44). Thus, any growth of m/e 12 resulting from fragmentation of m/e 28 or m/e 44 would not bias the data. When a sample of a-iron was heated, a significant increase in the m/e intensity ratio occurs at approximately 500°C. Note that this is the temperature at which carbon desorption was noted (Fig. 1). The data indicate that carbon desorbs as elemental carbon (m/e 12).

If thermal desorption of carbon is occurring at lower temperatures (note the irregularities at lower tempera- tures in Fig. 4) and varies from specimen to specimen, kinetic analyses would be more difficult.

III. CONCLUSIONS

In pyrotechnic applications, which necessarily in- volve a wide range of temperatures, segregation of im- purities to the surface can be expected to affect the material's behavior. Parameters such as burn rate could be altered by the quantity, nature, and specific segrega- tion rate of impurities in the pyrotechnic material.

The use of Auger electron spectroscopy has indicated that the segregation of sulfur in a-iron between 400 to

TABLE II. Rates of sulfur segregation

T (flC) V~ (Arbitrary units)

400 1.7 x 10 :~ 500 2.0 x 10 :~ 600 9.3 x 10 :~ 700 4.9 x 10 -~

- t 1 -

- 1 9

2-

- 2 . 3

FIG. 3.

I I I f I 1 I I I

• O0°C

600% Q ~

50C°C0 10 400OC

\

T i i i

0.5 1.0 i . ) 2 0

lO00 / I (K 11

Arrhenius plot of sulfur diffusion rate data.

0.3

0.2-

FiG. 4.

• FILAMENT & SAMPLE 0 FILAMENT ONLY

(403) (580} (726) ELECTRON BEAM CURRENT (mA)

Residual gas analysis during heating of a-iron.

700°C occurs via a grain boundary process with an acti- vation energy of 14.5 kcal/mol.

Auger electron spectroscopy has further shown that preferential impurity segregation as a function of tem- perature must be considered. In a-iron, carbon segre- gates between 150 and 500°C while sulfur segregates between 400 and 700°C.

Carbon begins to rapidly desorb as elemental carbon at 500°C as revealed by residual gas analysis as a func- tion of temperature.

It is apparent that Auger electron spectroscopy is more sensitive for studying surface segregation phe- nomena than any other currently available technique (e.g., isotopic tracer techniques).

ACKNOWLEDGMENTS

The authors gratefully acknowledge the support of Sandia Laboratories through Contract ICO 05-1035 issued to the General Electric Company. They also acknowledge W. W. Welbon for many enlightening discussions and M. T.

212 Volume 3i, Number 3, 1977

Esterdahl, R. J. Antepenko, and J. O. Humphries for performing the chemical analyses.

1. L. A. Harris, J. Appl. Phys. 39, 1419 (1968). 2. L. H. Jenkins and M. F. Chung, Surface Sci. 24, 125 (1971).

3. K. Kunimori, T. Kawa, T. Kondow, T. Onishi, and K. Tamaru, Surface Sci. 46, 567 (1974).

4. M. Aucouturier and M. Suzuki, Trans. Iron Steel Inst., Japan 1, 191 (1957).

5. S. J. Wang and W. J. Gravke, Z. Metallk. 61, 597 (1970).

A Nonlinear Least Squares Method of Determining Line Intensities and Half-widths

Y. S. CHANG and J. H. SHAW Department of Physics, The Ohio State University, Columbus, Ohio 43210

A nonlinear least squares method of retrieving line intensities and half-widths from spectra degraded by a finite instrumental resolv- ing power is discussed. Examples of the applications of this tech- nique to obtain the parameters of a single isolated line and of an overlapping pair of lines are presented. Index Headings: Computer, applications; Infrared; Methods, ana- lytical; Techniques, spectroscopic.

INTRODUCTION

Rotation-vibration bands of gases occurring in the infrared region of the spectrum typically consist of many individual lines each characterized by a position, intensity, and shape. Near room temperature and at pressures greater than a few torr, the Lorentz expres- sion is often used to represent the line shape,

S a k (v ) = (1)

where k(v) = absorption coefficient at frequency v, S =

f = k(v ) d r , is intensity, 2a = separation be- the line ~c

tween the frequencies at which the absorption coeffi- cient is k , , ,×/2 , and vo = position of the line center.

This usually gives a good description of the line shape within a few half-widths of the line center, although deviations have been observed at greater distances. 1.2

There have been numerous determinations of line half-widths and intensities since these parameters are required in order to predict the absorptance by gases and they can be used to derive information concerning molecular structure and intermolecular forces.

The measurements typically consist of measuring the absorption spectrum of a known pathlength l of a gas sample containing a partial pressure Pa of the absorbing gas and a partial pressure P~, of a broadening gas. The total pressure P = P~ + P~,, and the amount of the

Received 1 November 1976.

Volume 31, Number 3, 1977

P~l Ko absorbing gas u (atm-cm at STP) = l p- ~ , where Po

and Ko are standard pressure and temperature and K is the temperature of the sample.

A typical spectrum of an isolated line of a homogene- ous gas sample obtained with a grating spectrometer and displayed by using a paper chart recorder, is shown in Fig. 1. The pen deflection is shown as a function of frequency. The observed "spectrum," I(v), is shown as the middle curve, the top curve, I , ( v ) , corresponds to the spectrum which would be obtained with no absorber present, and the bottom curve, O ( v ) , corresponds to the spectrum obtained if the absorber were completely opaque.

Auxiliary experiments, information, or guesses are usually required to estimate both Io(v) and O ( v ) . Once these have been obtained the spectral t ransmittance T ( v ) and absorptance A (v) are given by

I ( v ) - O ( v ) A ( v ) = 1 - T ( v ) = 1

I,,(v) - 0 ( . ) '

where [I,,(v) - O(v)] is proportional to the spectral ra- diant power incident on the sample and [I(v) - O(v)] is proportional to the transmit ted power. If the width of the spectral response function of the spectrometer is much less than the width of the spectral line so that there is no degradation of the line shape then

I ' ( v ) - O ( v ) T ' ( v ) - - e x p [ - k ( v ) u ] , (2)

I , , (v ) - O ( v )

where T ' ( v ) represents the true monochromatic trans- mittance of the sample.

Until recently the widths of the spectral response functions of most spectrometers were greater than the widths of the lines being observed and the appearances of the spectra were modified by the instrument. Inter- ferometers and tunable lasers can now produce spectra in which there is essentially no degradation in resolu- tion and the line widths and intensities can be deter- mined directly from the spectra provided the shapes of I , ( v ) and O ( v ) are known.

APPLIED SPECTROSCOPY 213