agrees within experimental error with that measured for nickel-iron alloys containing 20 to 50% iron by weight (10). A least squares fit of the difiusion coefficient data for the twophase alloy [0.0057 cm2 sec-l exp (10.8 kcal mole-l/RT), Table 111 pooled with diffusion data for hydrogen in pure tungsten over the temperature range of 900 t o 2000 “C ( 2 ) resulted in no significant change in Do, Q, or their standard deviations. This agreement may be taken to indicate that hydrogen difuses through the tungsten particles. Since both alloys have the same activation energy (Q) for hydrogen diffusion, the rate of diffusion through the tungsten particles relat i w to diffusion through the matrix is difficult t o establish. A simple estimate of the effective diffusion coefficient for hydrogen through the matrix of the two-phase alloy based on the additional distance the hydrogen must travel around the tungsten particles and the reduced cross-section through which the hydrogen must diffuse, i.e., the matrix phase consists of -1-pm tilm between 40-pm tungsten particles, yielded a reduction in Do of a factor of five from that of the matrix alloy if no diffusion occurred via the tungsten particles. The observed Do for the two-phase alloy was lower than that for the matrix alloy by a factor of 1.9. The precision with which diffusion coefficients were determined by this technique is surprisingly good considering the number of simplifying assumptions that have been made. The cylindrically shaped sample, having a diameter-to-thickness ratio of 2.5 would not appear to be a n infinite plate, however, the square of that ratio (6.2) gives a better estimate of the diffusion rate along the axis of the cylinder relative to that along the radius of the cylinder. The solution of the diffusion equations [Ficlc’s laws ( I ! ) ] for a n infinite plate of thickness d at a constant temperature with a uniform hydrogen concen-
tration in the plate and zero hydrogen concentration a t the sample surface for t 2 0 predicts that the rate of hydrogen evolution from the plate would be given by m
J
=
exp (-nZrI2Dt,Id)
AD n=l
where A is a constant (7). After approximately 90% of the hydrogen has evolved from the plate, only the term for n = 1 is not negligible and J can be described as a simple exponential decay having a rate constant given by IT?D/d. These equations were solved numerically while allowing D to be temperature-dependent and the plate temperature to change in time as shown in Figure 3. This reduced the effects of the higher order terms but was not sufficient to prevent J from tending to a t t = 0. It also did not explain the experimentally observed exponential decay which started after approximately 50% of the hydrogen has been evolved. A more plausible explanation is that a desorption process prevented the achievement of zero hydrogen concentration at the sample surface a t the beginning of the exponential portion of the hydrogen evolution curves. This phenomenon certainly occurs a t low temperatures as evidenced by the delay in hydrogen evolution during the early stages of a n analysis and by hydrogen remaining in the metal at room temperature. 0)
ACKN0U’LEDG;LIEW
The author is indebted to M. Reeves, 111, and J . J. Beauchamp, Oak Ridge National Laboratory, for consultation concerning the solutions of the diffusion equations and t o C. Cook, Jr., and H. L. Tucker, Oak Ridge Y-12 Plant Laboratory, who performed most of the analyses.
__ (10) W . Beck. J. O’M Bockris, and M. A. Genshaw, Met. Traris., 2, 883 (1971). ( 1 I ) A. Fick. Poggi A/i/i.$94, 59 (1855).
RECEIVEDfor review May 1, 1972. Accepted July 31, 1972. Work performed at Oak Ridge Y-12 Plant under Contract W-7405-eng-26 with the U.S. Atomic Energy Commission.
Electron Probe Microdetermination of Carbon in Ferrous Alloys J. S. Duerr’ and R. E. Ogilvie Depurtnietir of Metallurgy and Materials Science, ikfassachusetts Institute of Teclinologj,, Cambridge, Mass. 02139
Low-level analysis of light.elements using the electron probe microanalyzer is discussed with particular emphasis on the microanalysis of carbon i n ferrous alloys. Necessary equipment modifications a r e described including a gas jet for decontaminating the analyzed area of the sample and an automated stepping system to allow a step-delay-count sequence of operations. Examples given a r e the measurement of the carbon profile associated with the case hardening of steel and the determination of t h e carbon concentration at various points within the taenite lamellae in metallic meteorites.
ANALYSIS OF CARBON and other light-element characteristic X-rays with the electron probe microanalyzer presents a number of problems beyond those associated with analysis of elements heavier than neon. The necessary equipment modifications have been studied and developed, partially by Present address, Bettis Atomic Power Laboratory, West Mifflin, Pa. l512?
Henke (I), and the possibility for analysis of carbon in ferrous alloys has been shown by Ong ( 2 ) . Some special techniques are nevertheless required to ensure high precision and accuracy along with a reasonable degree of convenience for low-level light-element analysis. This paper summarizes the appropriate techniques and equipment modifications for light-element analysis in general and for low-level carbon analysis in ferrous alloys in particular. Experimental Setup. The MIT electron probe microanalyzer with a n X-ray take-off angle of 15.5” is used for the light-element analysis. A commercial Norelco vacuum spectrometer, installed for a study of the distribution of fluorine in teeth (3), is used with little modification. An (1) B. L. Henke, A d m i . X-rczy A i d . , 7, 360-88 (1961). ( 2 ) P. S. Ong, in “X-ray Optics and .Microanalysis,” R. Castaing, J. Deschamps, and J. Philibert. Ed.. 1966, pp 181-92. (3) A . J. Saffir, Ph.D. Thesis, Massachusetts Institute of Technology. Cambridge, Mass.: Feb. 1970.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972
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Figure 1. Variation of peak intensity and figure-ofmerit with accelerating potential
auxiliary pumping system and an isolation valve allow the spectrometer to be separately evacuated and maintained under vacuum at all times. When the main column is evacuated, the valve can be opened to provide a clear vacuum path to the detector with only the necessity of a small permanent magnet to act as a trap for backscattered electrons. The dispersive crystal is lead stearate-Pb(C18H3502)2-deposited directly on the standard Philips continuously-bent mica crystal by the Langmuir-Blodgett technique. By using this technique, monolayers of a fatty acid can be successively deposited with accompanying improvement in wavelength resolution until the thickness (almost 100 layers for lead stearate) becomes so great that the X-rays which are diffracted from the bottom layers are absorbed before reaching the surface. Lead stearate has the widest wavelength range, the highest diffracted efficiency, and the best wavelength resolution of the large number of such fatty acids which have been tried and which are commercially available. Typical 20 scans over the carbon Kcu X-ray peak gave a full width a t half the maximum peak (FWHM) of 2.0’ which corresponds to 1.6 A at the peak position of 44 A. The X-ray detector must be designed for high efficiency and good energy resolution. The detector window is a few thousand-angstrom-thick layer of collodian supported by a 200-mesh ( 7 0 z transmission) grid. A few drops of collodian are floated on water and picked up on a wire loop. Four layers are used to improve strength and vacuum seal in spite of the increased absorption. The conventional detector gas PI0 (10% methane-90Z argon) is increased in methane content to P75 (75z methane-25z argon) which decreases absorption of long wavelengths and allows those low energy photons to get further into the detector. The increase in methane content increases the separation between noise and the energy peak on a pulse height distribution curve but also necessitates an increased detector voltage. For studies, where the aim is to measure small concentrations of a light element, it is important to pick operating con2362
ditions that give a low detectability limit. Ziebold ( 4 ) has shown that for the analysis of a n element in a particular matrix with a known counting time, the detectability limit is directly proportional to the ratio d Z / ( P - B ) where B and P are the background and peak intensities for some concentration of the element in that matrix. Since the ratio varies with accelerating voltage, the reciprocal of its square, (P-B)y/ B, can be used as a figure-of-merit to determine the optimum accelerating voltage for low-level microanalysis. Generally, increasing the voltage above the excitation potential increases the effective penetration depth of the electrons which increases the number of X-rays produced. The measured X-ray signal similarly increases until enough of the X-ray generation is so deep in the sample that absorption becomes important and the measured signal decreases. This turning point depends greatly on the absorption coefficient and, therefore, the atomic number of the matrix atoms. For carbon in ferrous alloys, the minimum detectability limit occurs about 3 kV as shown by the curves in Figure 1 which give the variation with accelerating voltage of the peak X-ray intensity and the figure-of-merit for carbon in an iron matrix. The optimum accelerating voltage for measuring low levels of carbon in ferrous alloys is still about 3 kV; however, the practical working voltage may be higher. In this study a voltage of 10 kV was used because it gives a reasonably low detectability limit while still maintaining stability of the electron beam and producing a measurable level of iron Xrays, which are measured on a second spectrometer, for checking over-all stability. In addition, the IO-kV accelerating voltage excites only a low intensity of iron-K radiation. Therefore, the pulse height analyzer can completely eliminate the iron-KU (fifth order) line which diffracts from the mica substrate just 0.5” in 28 from the angle at which the carbon-Kcu line diffracts from the lead stearate. Decontamination Methods. Soft X-ray analysis is hampered by the persistent problems of sample contamination. As soon as the electron beam hits the sample, a contamination spot-composed basically of carbon (but also containing oxygen, silicon, and a little of everything else in the vacuum system)-begins to build up. For the short wavelength Xrays from heavy elements, the main effect is a reduction in signal due to absorption of incident electrons by the contamination layer (5). For light elements a second effect is the absorption of the low-energy X-rays by the contamination which further reduces the signal. For measurements of carbon X-rays, a third and predominant effect is introduced since the carbon signal will increase steadily with time as the contamination spot grows thicker. For low-level carbon analysis, the contamination spot is intolerable and even at higher levels will be a serious source of error. The contamination spot grows because of the interaction of the electron beam with the adsorbed film on the sample. Basically, hydrocarbons in the system migrate to the incident beam where they are decomposed into gases which are pumped away and carbon, which remains. The film has four sources, all of which can be minimized but not eliminated. The sources and preventative measures are as follows: ROOMAIR. Minimize time between polishing the sample and analyzing it, and keep it in a desiccator during any necessary delay. (4) T.0. Ziebold, ANAL.CHEM.. 39, 858-861 (1967). ( 5 ) A. J. Campbell and R. Gibbons in “The Electron Microprobe,” T. D. McKinleq, K. F. J. Heinrich. and D. B. Wittry, Ed.. 1966, pp 75-82.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972
OUTGASSING OF SAMPLE,MOUNT,AND COLUMN. Porous samples or mounts should be prepumped; mounting materials that decompose under the beam should be protected or avoided; and all parts of the column, specimen chamber, and vacuum system must be kept immaculate by frequent cleaning and by venting with dry nitrogen. DIFFUSION PUMP BACKSTREAMING. Use as small a pump as practical and one of modern low-back-stream design; use a water-cooled or preferably a liquid-nitrogen-cooled baffle; and use a very low vapor pressure pumping fluid that does not contain silicon such as CVC Convalex-10 or Monsanto Santovac 5. MECHANICAL PUMPBACKSTREAMING. Again, use a small pump, have separate pumps for roughing the column and backing the diffusion pump so that the hot oil vapors of the continuously-running backing pump d o not have direct access to the column during roughing, use a pump oil like CVC Convoil-20 instead of the conventional mechanical pump oils, and install zeolite traps on the mechanical pumps (the zeolite should be heated regularly to keep it from saturating with oil). The above suggestions should reduce the rate of contamination to some extent depending on how many could conveniently be applied to a particular microanalyzer. A number of techniques have been used with varying degrees of success tn eliminate contamination completely. The techniques and comments on their effectiveness are as follows: ULTRA-HIGH-VACUUM. Required vacuums are on the order of Torr or lower which can be achieved only with considerable increase in cost and loss in flexibility and cannot be achieved by modification of an existing conventional microanalyzer. Furthermore, there is no decontamination effect so that initial contamination or spots too close together would contribute to errors. COLDTRAP. An efficient cold trap can effectively create a local ultra-high vacuum a t the sample surface, but to be effective it must have a very large area near the sample which is hard t o reconcile with the necessity of measuring backscattered electrons, secondary electrons, and three channels of X-rays. Again, little or no decontamination is possible. ZERO-TIMEEXTRAPOLATION. Contamination causes the carbon signal to rise with time along a straight line so successive counts over a period of time can be extrapolated back to zero-time. Here, there is no decontamination effect and very long counting times and extrapolation periods would be necessary for low-level analysis. BEAMFOCUS.Some reports indicate that at high sample current, e.g. >1 NA, a focused beam will heat the sample enough locally to drive offsome of the contamination while at low current, e.g.
