Hyperfine Interactions 92(1994) 1235-1239 1235

A M6ssbauer milliprobe: Practical considerations

Catherine A. McCammon

Bayerisches Geoinstitut, Universitiit Bayreuth, D-95440 Bayreuth, Germany

M6ssbauer spectra of absorbers with diameters smaller than 500 ktm can be recorded using a high specific activity M6ssbauer source. The spectrum quality as defined by the signal/noise ratio has been calculated for 57Fe experiments as a function of absorber composition, thickness and diameter for both conventional and high specific activity source configurations. Results are in excellent agreement with experimental data for sodium nitroprusside, and demonstrate that high quality MOssbauer spectra can be collected for absorbers with diameters smaller than 500 ktm if electronic absorption is low.

1. Introduction

A simple technique for measuring M6ssbauer spectra with a spatial resolution of approximately 500 ~tm has been developed [1], and can be used to study the variation of M6ssbauer parameters within large absorbers (diameter > 1 mm) [2], or to record M6ssbauer spectra of absorbers too small for conventional methods. The technique requires little equipment: a source of high specific activity and a lead plate to restrict gamma rays to the chosen diameter (e.g. 500 ~tm) (further details are given in [1]). Given the range of potential applications, it is appropriate to examine the practical limits of the technique. This paper presents theoretical calculations of spectrum quality as a function of absorber properties (diameter, composi t ion and thickness) for 57Fe experiments, and compares the results with experimental data.

2. T he o ry

The density of 57Co in the source matrix can be increased significantly to provide a high specific activity M6ssbauer source (point source) with a compromise of greater linewidth, reduced recoil-free fraction, and a more rapid increase of 57Fe in the source with time. The latter effect increases the effective thickness of the source, given by ts = crofsn, where cr 0 is the resonance cross section of the transition (=2 .56 x 10 -lg cm 2 for the 14.4 keV 57Fe transition), fs is the recoil-free fraction of the source, and n is the number of 57Fe atoms per cm 2. Figure 1 illustrates a comparison of parameters as a function of time for a conventional and point source.

�9 J.C. Baltzer AG, Science Publishers

1236 C.A. McCammon / A Mi~ssbauer milliprobe: Practical considerations

3.0

2.0

... 1.0

0.0

0.24

~ 0.20 .c:

~0.16

0.12 0.78

sour~--"- ~ polnt

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . n o r m a l s o u r c e .

I I I I i i l i

i i i i

~ 0.74 ~

!o,op I "'062

n u m b e r o f h a l f l i v e s

Fig. 1. Effect of source age on the effective thickness (top), linewidth (middle) and recoil-free fraction (bottom) of a conventional 50 mCi source with 0.1 Ci/cm 2 (dashed line) and a 20 mCi point source with 2 Ci/cm 2 (solid line)

The transmission of gamma rays through an absorber with effective thickness t a is given by the wel l -known transmission integral (see e.g. [3]). The effect of electronic absorption in the absorber reduces transmission by a factor e -/zt', where # is the electronic mass absorption coefficient in cm2/g and t ' is the absorber thickness in g/cm 2. The former can be calculated from ~n fn/.tn, wherefn is the mass fraction of the nth element in the absorber and/.tn is the mass absorption coeff icient for that element (values for # at 14.4 keV are given in [4]). Geometric factors which determine the solid angle of radiation were calculated from [5] based on the source, absorber and detector diameters and their relative spacing. The height of the spectrum is given by D = ( 1 ~ - Io)/I~, where I0 and I** are the on- and off-resonance counts per channel, respectively. The quality of the Mtissbauer spectrum is related to the signal/noise ratio, and can be expressed as the statistical utility U = (C~D2t) / (2 + D) , where C~ is the off-resonance count rate per channel [6]. The statistical utility rate (u = U/t, where t is the measuring time) is independent of time, and can be used to compare the quality of two or more spectra.

C.A. McCammon / A Mi~ssbauer milliprobe: Practical considerations 1 2 3 7

3. Results

The statistical utility rate can be calculated as a function of effect ive absorber thickness for different experimental conditions. Variables include the strength, age, recoil-free fraction and diameter of the source, the composit ion (measured as #) , recoil-free fraction and diameter of the absorber, the background count rate (non- 14.4 keV radiation), the distances between source, absorber and detector, the detector eff iciency, and the number of channels used to collect the data. For old point sources, the thin source approximation (ts << 1) cannot be used (see fig. 1), so the transmission integral was evaluated numerically. To test results of the calculations, M6ssbauer spectra of sodium nitroprusside (Na2 [Fe(CN)5(NO)] �9 2H20) were recorded with a 50 mCi conventional source (age = 1 half-life) and a 20 mCi point source (age = 3.43 half-lives) for different absorber thicknesses. The experiment geometry was chosen to minimise errors due to geometric effects, see e.g. [7], and the background count rate and detector eff iciency were measured experimentally. Measuring times varied from 3 to 73 h. The results are illustrated in fig. 2, which shows that calculated

150

120

�9 ~ 9 0

�9 ~ 60

m 3 0

3

2

1

0 0

i i n o r m a l sou rce "I

I I

point source ~ J

1 2 Effec t ive s a m p l e th ickness

Fig. 2. Comparison for experimental (solid circles) and theoretical (solid lines) results for sodium nitroprusside spectra collected with a conventional source (top) and a point source (bottom).

and experimental data are in excellent agreement for both types of sources. The statistical utility rate of the point source experiment is reduced by a factor of approximately 50 due to the following factors: (1) reduced count rate of an older source (3.43 half-lives for the point source compared to one half-life for the normal source), and (2) increased source thickness due to age which decreases the intensity

1238 C.A. McCammon / A M6ssbauer milliprobe: Practical considerations

of the absorption. The size of the former effect is more than five times the size of the latter effect, and both are negligible in the case of a new point source. Because the solid angle is approximately the same in both experiments (the source-absorber distance can be reduced substantially when the absorber diameter is small), there is little reduction in the statistical utility rate due to the smaller absorber diameter. All sodium nitroprusside spectra collected with the point source were of acceptable quality, and the hyperfine parameters could be reproduced to within at least 1%.

Calculations were extended to illustrate the effect of absorber composition and diameter on signal quality. The source (20 mCi) was assumed to be new; therefore, these results represent the upper limit of possible values. Experimental conditions were assumed to be the same as those above, and the absorber recoil-free fraction was taken to be 0.5. Figure 3 (top) illustrates the effect of absorber composition where # varies from 10 to 100 (for comparison, p = 13.8 cm2/g for Na2[Fe(CN)5(NO)] �9 2H20, while/z = 106.1 cm2/g for FeWO4). Note that the magnitudes of the statistical utility

150

~100

"~ 511

] [ A . = i i J i

Z', 500 ~m-

~ 40 /

0 ~ - - - ~ , , - - - ~ . 0 2 4 6 8 10 Effective sample thickness

Fig. 3. Effect of absorber composition (top) and absorber dia- meter (bottom) on the statistical utility rate obtained with a new 20 mCi point source. The dimensions of /1 are cm2/g.

rate are similar to those for the normal source and large absorber diameter (fig. 2, top). The maximum value of/1 defines the optimum absorber thickness for a given/z, and the results from fig. 3 are in excellent agreement with previous calculations [4]. The effect of the absorber diameter is illustrated for an absorber with # = 25 in fig. 3 (bottom), which demonstrates that absorbers with diameters smaller than 500 [tm still produce high quality spectra if there is low electronic absorption.

C.A. McCammon / A MOssbauer milliprobe: Practical considerations 1239

Acknowledgement

The author is grateful to D.L. Williamson for suggesting the topic of this work.

References

[1] C.A. McCammon, V. Chaskar and G.G. Richards, Meas. Sci. Tech. 2(1991)657. [2] C.A. McCammon, V. Chaskar and G.G. Richards, Nucl. Instr. Meth. B76(1993)428. [3] S. Margulies and J.R. Ehrman, Nucl. Instr. Meth. 12(1961)131. [4] G.J. Long, T.E. Cranshaw and G. Longworth, MOss. Effect Ref. Data J. 6(1983)42. [5] H. Flores-Llamas and R. Zamorano-Ulloa, Nucl. Instr. Meth. B58(1991)272. [6] Z. Kajcsos, C. Sauer and W. Zinn, Hyp. Int. 57(1990)1889. [7] J.J. Bara and B.F. Bogacz, MOss. Effect. Ref. Data J. 3(1980)154.