THE EFFECT OF MASS IN ELECTRON-SOLID INTERACTIONS AND THE MYSTERY OF THE "HEINRICH KINK"

J.J. Donovan* and N.E. Pingitore Jr.**

*Department of Geology & Geophysics, University of California, Berkeley, CA 94720-4767
**Department of Geological Sciences, The University of Texas at El Paso, El Paso, TX 79968-0555

J. J. Donovan and N. E. Pingitore (1998) The Effect of Mass in Electron-Solid Interactions and the Mystery of the "Heinrich Kink" in: Proc. Microbeam Analysis Society, San Francisco Press, San Francisco (in press)

Is average atomic mass or average atomic number more appropriate to describe backscattered electron (BSE) effects in electron-solid interactions? In electron microprobe literature, either one or both of the terms A and Z may be found utilized in various theoretical models1-3 to describe electron backscattering. Physical theory would seem to favor atomic number averaging, because backscattering ultimately represents an electromagnetic interaction between the electron and the nucleus. At this scale, mass and its associated property of gravity, is 1042 times less powerful than the electromagnetic force. Nonetheless, some empirical results4 show a strong relation between atomic mass and electron scattering, thus endorsing mass averaging.

The periodic table presents an opportunity for distinguishing between these two influences: those pairs of elements for which an increase in Z yields a decrease in average A (e.g., Ar-39.95 and K-39.10; Co-58.93 and Ni-58.71; Te-127.60 and I-126.90) due to natural isotope abundances. For obvious analytical reasons, backscattered electron data are currently available only for the Co-Ni pair. In a careful determination of electron backscatter coefficients (BSC) made 30 years ago by researchers at NBS, a consistent drop in BSC yields from Co to Ni was found5, instead of the typical rise associated with all other pairs studied (with the possible exception of the Mn-Fe pair). We term this observation the "Heinrich kink," a striking deviation in the generally smooth curve of BSC with Z. We have duplicated Heinrich's experiment, by simply measuring the absorbed current in the transition metals from Cr to Cu, and both the Heinrich and our data sets are presented in Table 1. Like Heinrich, we observed a "kink" in BSC or absorbed current vs. Z curves at both the Co-Ni pair, and the Mn-Fe pair. The decrease in the BSC from Co to Ni suggests a mass control, while the dip from Mn to Fe could reflect the small mass difference for this pair (54.94 to 55.85) relative to the typical increase with Z in the transition metals.

Consideration of these data suggests a gedankenexperiment: do two isotopes of the same element share identical backscattering properties? If they do, then atomic number averaging would be appropriate, but if the isotopes exhibit different backscatter yields, related systematically to mass, then use of mass averaging is indicated. A modest review of the literature reveals no direct measurements of backscattering on isotope pairs which might speak to this question.

We therefore conducted various electron and x-ray measurements on natural and enriched isotopes of Ni, Cu and Mo (see Table 2) comparing bulk samples of normal Cu, of mass of 63.54, and 99% enriched 65Cu; normal Ni of mass 58.71 and 99% enriched 60Ni; and normal Mo of mass 95.94 and 95% enriched 100Mo. For each isotope pair no statistically significant difference in either backscatter yield or characteristic radiation was found in t-tests between means. Although the measurement is not easily performed and we are still refining our technique, at present we see no evidence of a causal relationship between mass and backscattering. Since the measurements involve direct isotopic comparison, these data represent a more robust test of mass versus atomic number than the original "Heinrich kink" data.

The mystery of the "Heinrich kink" is at present left unsolved. Although BSC does seem to correlate with the drop in mass from Co to Ni, our isotope experiments argue against causality. The observation that Fe, Co, and Ni are the only three ferromagnetic elements suggest that magnetic induction from the beam, the magnetic lens polepiece, or residual magnetism in the specimens may contribute to the "Heinrich kink." It is worth noting that, because of their crystal structures, Co and Ni exhibit different forms of magnetic contrast in the SEM, although recent measurements6 suggest that this contrast is insufficient to explain the observed anomaly. We are currently studying these magnetic and other effects to determine the exact cause of the "Heinrich kink."

References

1. P. Duncumb and S. J. B. Reed, X-ray Optics and Microanalysis, Eds. R. Castaing, P. Descamps and J. Philibert, Hermann, Paris, (1966) 133.
2. I. B. Borovskii and V. I. Rydnik, Quantitative Electron Probe Microanalysis, Ed. K. F. J. Heinrich, Nat'l. Bur. Standards Spec. Publ. 298, (1968) 35.
3. W. Reuter, Proc. 6th Intl. Conf. X-ray Optics and Microanalysis, Eds. G. Shinoda, K. Kohra, and T. Ichinokawa, Univ. Tokyo Press, Tokyo, (1972) 121.
4. K. F. J. Heinrich, X-ray Optics and Microanalysis, Ed. R. Castaing, P. Descamps and J. Philibert, Hermann, Paris, (1966) 159.
5. K. F. J. Heinrich, Quantitative Electron Probe Microanalysis, Ed. K. F. J. Heinrich, Nat'l. Bur. Standards Spec. Publ. 298, (1968) 5.
6. D. E. Newbury et. al., Advanced Scanning Electron Microscopy and X-ray Microanalysis, Plenum, New York, (1986) 147.

TABLE 1 - The "Heinrich kink" as shown in the original electron backscatter measurements by Heinrich, and also in absorbed current measurements (this work). Conditions for the absorbed current data were ~20 nA, average of 40 points (without a bias voltage on sample holder).

TABLE 2 - Absorbed current and characteristic radiation measurements for several isotope pairs. Conditions were 15 KeV, ~100 nA, average of 40 points (using a 22.5 volt bias on the sample holder) for the absorbed current data and 15 KeV, ~20 nA, 100 seconds, average of 5 points for the characteristic data.