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Conversion electron surface imaging
Nuclear Instruments and Methods in Physics Research A 425 (1999) 390—402
Conversion electron surface imaging G.M. Irwin *, J. Green, A. Wehner Department of Physics, Lamar University, P.O. Box 10046, Beaumont, TX 77710, USA Idaho State University, Pocatello, ID 83209, USA Utah State University, Logan, UT 84322, USA Received 30 June 1997
Abstract A method of imaging the Mo¨ssbauer absorption over the surface of a sample based on counting conversion electrons emitted from the surface following resonant absorption of gamma radiation is described. This Conversion Electron Surface Imaging (CESI) method is somewhat analogous to Magnetic Resonance Imaging (MRI), particularly chemical shift imaging, and similar tomographic reconstruction techniques are involved in extracting the image. The theory behind the technique and a prototype device is described, as well as the results of proof-of-principle experiments which demonstrate the function of the device. Eventually this same prototype device will be part of a system to determine the spatial variation of the Mo¨ssbauer spectrum over the surface of a sample. Applications include imaging of variations of surface properties of steels and other iron containing alloys, as well as other surfaces over which Fe has been deposited. 1999 Elsevier Science B.V. All rights reserved.
1. Introduction The Mo¨ssbauer Effect (ME) [1] has found many applications in the study of materials, particularly those containing iron. The gamma-ray absorption spectrum one obtains is uniquely sensitive to the local environment of the iron nucleus (specifically Fe, the active isotope). The hyperfine effects on the spectrum are due essentially to three effects: (1) the electric monopole interaction, due to the local charge density at the nucleus, (2) the electric quadrupole interaction, due to the interaction of the quadrupole moment of the nucleus with the local
* Corresponding author. Tel.: #1 409 880 8243; e-mail: [email protected].
electric field gradient, and (3) the magnetic dipole interaction, due to the possible presence of a magnetic field on the nucleus. All of these hyperfine effects are sensitive to the crystal structure and magnetic properties of a given material. We propose a technique for analysing surfaces of materials based on the detection of conversion electrons emitted from nuclei in the surface of the sample following ME absorption, which we call Conversion Electron Surface Imaging (CESI). The technique is based on the Conversion Electron Mo¨ssbauer Spectroscopy (CEMS) method, in which the conversion electrons following resonant absorption of gamma radiation are counted. The conversion electrons emitted have a range of only 200—300 nm, making the technique truly surface sensitive. Even a monolayer of Fe can be
0168-9002/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 1 3 7 4 - 6
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detected using the CEMS method [2]. The CESI technique utilizes a specialized detector in which the sample is mounted on a rotating platform (the device is described in more detail below). Using the specialized detector and a conventional ME spectrometer system, one may obtain the ME spectrum as a function of position on the surface of the sample. The technique makes use of the same type of tomographic reconstruction methods used in MRI and X-ray CT, although one is not looking in the interior of a sample, rather on its surface. Nonetheless, one may consider the proposed technique to be a tomographic form of ME spectroscopy. The need for spatially resolved ME spectra has been identified by researchers studying properties of quenched metallurgical slags [3]. They used a “brute force” method, using a small (0.5 mm) collimator and a very intense, point-like gammaray source. By moving a prepared cross-sectional specimen across the collimator, they were able to obtain the ME spectrum as a function of depth from the surface in a sample. The variation in the spectrum as a function of depth indicated effects of the rapid quenching. However, the spatial resolution of the technique is limited by the size of the collimator. Such data is of great interest in the study of rapidly solidified “splats” and ribbons in which the details of the rapid quenching process are poorly understood. It is known, for example, that variations in the relative amounts of austenite and martensite in surface and bulk occur when steels are formed into rapidly solidified ribbons [4]. The proposed technique would allow one to image the variation of properties of the surface and of cross sections internal to samples, giving important information concerning the formation of the material. For example, the percentage of retained austenite in a rapidly solidified sample of stainless steel could be imaged, giving information regarding cooling rate over the surface of the sample. Also variations in the direction of surface magnetism due to surface stresses are known to affect the ME spectrum [5], and these properties could similarly be imaged, e.g. in welds. However, unlike the technique described in Ref. [2], the spatial resolution of the proposed technique is not limited by any sort of collimation.
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Besides the aforementioned studies of rapidly solidified materials, the proposed technique has a variety of other potential applications. One may group these applications in a few broad categories: 1. materials containing natural iron (about 2% Fe), 2. materials enriched with Fe, 3. surfaces over which a thin film of Fe has been deposited, 4. generalization to other Mo¨ssbauer effect isotopes, such as Sn and rare earths. Other specific applications might include analysis of geological specimens such as meteorites, including both surfaces and cross sections of samples. The sensitivity of the ME technique to the oxidation state of the iron (e.g. Fe>, Fe>) would allow one to image such variations of a sample or cross section of a sample. Such data is of interest, e.g. in the study of vitrification of radioactive waste [6], in which the oxidation state of the glass is important in maintaining the integrity of the material for such uses. ME spectroscopy has provided an alternative to wet chemical analysis, and the spatial resolution of such effects could not be obtained using wet-chemical techniques. The sensitivity of the Mo¨ssbauer absorption spectrum to the magnetic properties of a surface suggest several applications. Both the magnitude and direction of the surface magnetization affects the ME spectrum. The proposed technique could be used to image magnetic domains in ferromagnets, perhaps providing an alternative to the Bitter method [7], and imaging the magnetization in magnetic recording media and thin films. In addition, the penetration of the conversion electrons emitted by the nuclei following resonant absorption will also affect the observed count rate at different positions, providing unique possibilities for contrasting different regions of a sample. Mo¨ssbauer Imaging has been suggested in transmission geometry, and simple one-dimensional demonstration experiments have been performed, but with little apparent application [8]. The conversion electron surface imaging system proposed here is centered around a specialized conversion
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electron counter, described in detail below, in which the sample is mounted on a rotating platform. As described below, the device has been tested utilizing a conventional ME spectrometer system in a constant acceleration mode, and it has been shown to function as predicted. The principle of operation is similar to MRI: in Nuclear Magnetic Resonance (NMR) one obtains resonant absorption as a function of magnetic field strength. Thus by imposing a magnetic field gradient across a sample spectral information is converted to spatial information. In Mo¨ssbauer Effect Spectroscopy one obtains resonant absorption as a function of relative source-to-absorber velocity. Thus by imposing a velocity gradient across a sample (e.g. by rotating), spectral information is converted to spatial information. In either MRI or the proposed technique, conventional tomographic reconstruction techniques are used to obtain an image of the sample. The technique proposed here is the direct analog of chemical shift imaging in NMR [9], in which the NMR spectrum is obtained as a function of position in the sample. The specialized detector is based on a commercially available conversion electron counter for ME spectroscopy [10]. The sample rotates within the conversion electron counter chamber at an angular frequency X. The source makes an angle a with respect to the axis of rotation. The conversion electrons are counted as a function of source velocity v and the rotational phase h of the sample (a rotating notched wheel and LED-detector pair provide a synchronization signal). Using standard tomographic reconstruction techniques, the ME spectrum is obtained as a function of the position on the sample. For a narrow line spectrum such as austenite (FWHM C+0.5 mm/s), the spatial resolution of the technique is d+C/X sin a (a is the angle between the gamma-ray direction and the normal to the sample surface), which can be as small as 1 lm for angular velocities of 100 revolutions per second. Note that no arrangement of collimating slits is used to obtain this fine resolution. We begin with a discussion of the theory of CESI. We then describe the prototype device and the system used for proof-of-principle experiments, which involve “test patterns” of Fe-enriched foil.
These initial experiments do not allow for tomographic image reconstruction, primarily due to limitations of the available ME spectrometer system, but illustrate the function of the device. Finally, we describe a proposed system incorporating the prototype device into a state-of-the-art ME spectrometer which will allow for the full tomographic surface imaging, including the extraction of the ME spectrum as a function of position on a sample surface.
2. Principle of conversion electron surface imaging As described in the introduction, the principle behind CESI is essentially the same as Magnetic Resonance Imaging (MRI). In CESI, a velocity gradient is obtained on the sample by rotating the sample, analogous to the magnetic field gradient in MRI. The essential geometry of the concept is illustrated in Fig. 1a. The circular sample is mounted on a rotating platform, which is inside the conversion electron counter (not indicated in Fig. 1). The normal to the sample surface makes an angle a with the direction of the gamma-ray beam. The gammaray source (e.g. Co) is mounted on a standard Mo¨ssbauer velocity transducer, which we will assume for the moment is run in a constant velocity mode, with source velocity v . Let us suppose for the moment that the sample material consists of a narrow-line material (linewidth C) which is present on the surface of the sample in some pattern. As the sample rotates at a given angular velocity X, absorption can occur over a narrow strip of width d"C/X sin a at a position y"!v /X sin a as in dicated in Fig. 1b, due to the doppler effect on different portions of the rotating sample (note that it is necessary to have the sample oriented at the angle a: for a"0 the width of the strip diverges, giving no spatial information. Of course a"90° gives the best resolution, but the source does not illuminate the sample). This strip of absorption is essentially analogous to the plane of absorption one obtains in MRI for a given orientation and field strength. Thus by varying the velocity of the source, the sample is “scanned” along the y-axis. By counting the conversion electrons resulting from the resonant absorption of the gamma radiation as
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a three-dimensional set of data which will give the Mo¨ssbauer spectrum at the point (or pixel) at (x,y). This three-dimensional imaging scheme is analogous to chemical shift imaging in MRI in which the NMR spectrum is obtained as a function of position in the sample, as described in Ref. [9]. A unique quality of this technique is that the resolution of the method, as given by d, is not related to some arrangement of collimating slits. The entire sample is “bathed” in the gamma radiation at any given time. It is the doppler effect resulting from the relative velocity of the source and a given point on the rotating sample which determines the resolution. As the angular velocity X of the sample is increased, the resolution improves. Of course, the practical resolution obtainable in an actual device is signal-to-noise limited. Let N(v , h) be the number of counts obtained with source velocity v and sample phase h. This can be represented as a kind of integral transform of the absorption M(x,y) on the sample surface:
N(v ,h)"
Fig. 1. Geometry of CESI. (a) indicates the rotating sample and the source moving with velocity v at an angle a with respect to the sample normal indicated by vector X. (b) Absorption profile over the sample surface with the source moving with velocity v . Here a narrow-line absorbing material is assumed, resulting in the Lorenztian absorption profile.
a function of the angular phase h of the sample rotation and the source velocity v , one can use standard tomographic reconstruction algorithms to obtain the Mo¨ssbauer absorption as a function of position (x,y) on the sample. This two-dimensional imaging scheme gives the integrated absorption at the point (or pixel) at (x,y), which depends on the pattern of Mo¨ssbauer-active material on the sample. By obtaining data also as a function of the angular velocity X of the sample, one can obtain
M(x,y)n(v ,h;x,y) dx dy,
(1)
where the integration extends over the dimensions of the sample surface. The function n(v , h; x, y) ex presses the overlap between the absorption profile and the density of absorbing material on the sample. Consider, for example, a single small spot of absorbing material, with a narrow-line spectrum, on an otherwise non-active substrate. In the v , h plane this spot traces out a sine-wave (sometimes called a “sinogram” in conventional tomography), with a velocity profile given by a Lorentzian of width C at each angle h for a narrow-line material. The equation of the resulting sine-wave, indicating the position of the peak of the Lorentzian is v (h)"!oX sin a sin(h! )
(2)
for a spot at polar coordinates o, (x" o cos , y"o sin ) on the sample. Thus we can write the function n(v ,h; x, y) as n(v , h; x, y)"P (v, v , C), *
(3)
where P (v, v , C) is a Lorentzian distribution with * mean v and full-width C. Fig. 2 shows a plot of the
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surface n(v , h; x, y) for a spot at x"R/2, y"0. Here v "RX sin a is the maximum speed needed
to scan the complete circular sample, and the linewidth of the Lorentizan is taken as v /10. For
differential area elements at other positions x, y, the sine wave Eq. (2) would be shifted by angle and would have an amplitude o X sin a. Fig. 2 illustrates a symmetry in N(v , h): the second half from p to 2p is a mirror image of the first half from 0 to p, or N(v , h#p)"N(!v , h).
(4)
Thus the data can be reduced by “flipping” the second half about v "0 and adding it to the first half. This process is similar to “folding” conventional velocity spectra obtained with a trianglewave modulated source to eliminate parabolic baseline distortion. Extraction of the image M(x, y) from the data essentially involves inverting Eq. (1), for which many tomographic reconstruction algorithms have been developed for X-ray CT, MRI, etc. For a more complex spectrum, e.g. iron metal, several lines would occur as a function of velocity at each value of h. As the angular velocity of the sample drive is increased, however, the six-line spectrum is “squeezed” into a smaller spatial width, giving the same result as the single line material for
Fig. 2. The function n(v , h; x, y) indicating the count rate of conversion electrons as a function of v and h for a differential element of a narrow-line Mo¨ssbauer-active material at x"R/2, y"0, as indicated in the inset.
a large enough X. The lower angular velocities are of interest for imaging in spectroscopy mode, in which the spatial variation of the ME spectrum is extracted from the data.
3. Prototype device We describe here the prototype device which has been constructed and the proof-of-principle experiments which indicate the proper functioning of the device. 3.1. Device description The prototype CESI device was built around two commercially available devices: (1) A Ranger Scientific, Inc. model SD-300 conversion electron detector designed for ME spectroscopy, and (2) an Oriel Corporation model 75154 variable frequency open chopper motor which was altered to provide the sample rotation. The conversion electron detector is a gas-flow proportional counter with a gas mixture of helium with 4% methane, with a flow rate of 1 cc/min. A pre-amp for the detector is contained in the same housing, resulting in a compact device. A LED/Detector pair on the chopper was used with a notched wheel to provide a synchronization signal. The Co source was mounted on a Technical Measurements Corporation model 305 ME transducer with a model 306 drive unit. This transducer was capable of modulating the source with either triangle or ramp waveforms. The transducer could not be driven reliably for speeds greater than 30 mm/s, nor could it be driven in a constant velocity mode. This significantly limited the scope of proof-of-principle experiments to test the function of the device. Also the low activity of the available source (&1 mCi) limited signal-to-noise in the present measurements. The samples are mounted on a 5.0 mm radius aluminum peg which mounts with set screws to the motorized platform and notched synchronization wheel. The whole CESI device is mounted on an optical bench oriented to make an angle a"16.0° with respect to the gamma-ray beam direction. The sample is set inside the gas counter chamber which
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Fig. 3. Diagram of the prototype CESI system. The two sync signals are used to trigger the MultiChannel Scaler (MCS) for the two types of proof-of-principle experiments.
contains two anode wires, and the gas simply flows past the sample and out a small annular gap between the rotating peg and a hole in the counter. Fig. 3 shows a diagram of the prototype CESI system. Here the two synchronization signals are used to trigger the mutichannel scaler in the two types of proof-of-principle experiments to be described in Section 3.3 below. Not indicated in the diagram are the high voltage and low voltage power supplies for the conversion electron detector. 3.2. Numerical simulation of the cesi prototype Numerical simulations were performed to illustrate the theoretical performance of the CESI prototype. In these simulations it was assumed that a sample having a single narrow absorption line (e.g stainless steel) was present on the sample surface in a particular pattern. The simulation then calculated assuming a particular number n;n of pixels in the matrix N(v , h)"N . Fig. 4 shows IJ various absorber patterns (a) expressed as a discrete matrix M . The theoretical matrices N for these GH IJ patterns are shown in (b). Darker shades indicate
higher values of M and N . The vertical velocity GH IJ scale for N runs from !v to #v , where IJ
v "R X sin a is the maximum velocity needed to
completely scan the absorber. The horizontal angular scale runs from 0 to p, indicating that the folding operation has been performed. Numerical simulations were also performed to extract the matrix M from N using tomographic GH IJ reconstruction algorithms developed by the authors [11]. The algorithms used to extract the image are based on minimizing chi-squared between the given N data and the transform of the IJ extracted image, as calculated with a discrete form of Eq. (1). These algorithms were performed by assuming a particular noise level on top of the theoretical N , to simulate real data. Fig. 5 shows IJ the results for a “quadrant” absorber pattern. Fig. 5a indicates the absorber pattern, and Fig. 5b indicates the theoretical N matrix. The scales of IJ the axes are the same as in Fig. 4. Fig. 5c shows the results of the tomographic reconstruction algorithms assuming random noise of 5% of the peak signal added to the N in 5b, and Fig. 5d shows the IJ results with 8% noise. The algorithms used are not
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Fig. 4. Simulated CESI data. (a) Assumed sample patterns, where dark areas indicate the presence of Mo¨ssbauer-active material; (b) indicates the resulting N matrices, where darker shades indicate higher conversion electron count rate. The velocity scale (vertical) runs IJ from !v to v , and the horizontal (angular) scale runs from 0 to p.
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Fig. 5. Example of tomographic reconstruction algorithms. (a) Assumed M absorber pattern. (b) Simulated N matrix. (c) ReconstrucGH IJ ted image with 5% noise added to N . (d) Reconstructed image with 8% noise added to N . IJ IJ
necessarily the best, but they indicate the process by which the sample image can be obtained from experimental data. 3.3. Proof-of-principle experiments Two types of proof-of-principle experiments were performed to test the operation of the prototype detector and compare with theoretical predictions. These experiments involve: 1. triggering the multichannel scaler (MCS) with the source velocity sync signal (with source in
a triangle, or constant acceleration mode) and ignoring the sample drive sync, and 2. triggering the MCS with the sample drive sync with the source at rest. The second measurement amounts to obtaining the central row in N(v ,h), while the first involves sum ming the rows in N(v ,h) giving a kind of integral result. These preliminary experiments were limited by the available source strength (+1 mCi), and the rather old ME spectrometer system used (a 30 year old Technical Measurements Corp. model 305 transducer and model 306 Mo¨ssbauer Drive Unit).
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These experiments with the current system are not able to reconstruct the image of the sample surface, but indicate that the device, in conjunction with a modern MES system, can be used to obtain all data necessary for 2-dimensional image reconstruction. Samples used to test the prototype device consisted of Fe-enriched iron foils. The enriched foils allowed data acquisition in reasonable times with the rather weak Co source which was available. The use of Fe foil complicated the analysis of the data due to the six-line spectrum. The use of Feenriched stainless steel foil would have been more suitable for the proof-of-principle studies, but the Fe-foil was available. Samples were made by placing masks of plastic tape over a uniform sample of Fe-enriched foil, thus blocking the conversion electron emission from those regions of the sample. This allowed a number of patterns to be studied with a relatively small amount of the expensive enriched foil. The sample patterns used in the proof-of-principle patterns are shown in Fig. 6. Black areas indicates the mask, and light areas indicate the Fe foil. For the experiments of type 1 described above, samples with no angular dependence were used, including a “full” absorber (no mask) and a “hole” absorber (small circular mask in the center), as indicated in Fig. 6a. For the experiments of type 2 (zero source velocity), samples with no radial dependence to the pattern were used, as indicated in Fig. 6b. It should be noted that the results obtained are not unique to the patterns shown in Fig. 6: any patterns in addition to those in Fig. 6a having the same average radial dependence will give the same results in type 1 measurements. Similarly, any patterns in addition to those in Fig. 6b which have the same average angular dependence will give the same results in type 2 measurements. Obviously, more than just two measurements are necessary to obtain enough information to extract the image of an arbitrary absorber pattern. 3.3.1. Type 1 experiments with triangle-wave source velocity The first type of proof-of-principle experiment involves counting conversion electrons as a function of source velocity v with the source transducer
Fig. 6. Sample patterns used in the proof-of-principle experiments. (a) “Full” and “Hole” absorber patterns for the type 1 velocity scan experiments. (b) “Quadrant” and “Octant” absorber patterns for the type 2 angular experiments. All of these absorbers were made by placing plastic adhesive tape masks (indicated by dark areas) over the “Full” absorber to block conversion electron emission.
run in a constant acceleration mode with a triangle waveform. By using a triangle waveform the solid angle effect which results from the varying distance between source and sample can be eliminated by folding the data, as in a typical Mo¨ssbauer experiment. The multichannel scaler (MCS) is triggered on the motion of the source, and the sample rotational phase is ignored. This essentially gives an integral measurement, which can be expressed as
p
N(v , h) dh (5) Q which amounts to a sum for discrete data, as is obtained from the multichannel analyser. For zero angular velocity, one simply obtains a conventional Mo¨ssbauer spectrum. As the angular velocity of the sample X is increased, the spectral lines broaden in a way that is dependent on the spatial distribution of the absorbing material on the sample (that is, the pattern of the sample). This type 1 experiment thus gives information related to the radial dependence of the sample, as averaged over the sample rotation. Fig. 7 shows the results obtained from the prototype device with the “full” absorber, a uniform circular sample of Fe-enriched iron foil. Indicated
N (v )"
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Fig. 7. Results of the type 1 velocity scan experiments with the “Full” absorber, showing N (v ) as a function of v . The rotational period ¹"1/f"2p/X are indicated for the various scans.
in Fig. 6 is the period of sample rotation ¹"2p/X for each spectrum. At a given ¹, the resulting data can be represented by a convolution of the six-line pattern (e.g. ¹"R, X"0) with an elliptical function. This elliptical function would be the result from a similar circular sample of material with a single very narrow line. Fig. 8 shows the results obtained with the “hole” absorber, consisting of a 4 mm diameter circular mask placed over the center of the 10 mm diameter “full” absorber. In this case the six-line spectrum is convoluted with an elliptical function with a smaller elliptical “notch” removed in the center. Clearly the effects due to the different spatial distribution of iron foil on the two samples is evident. Similar results were obtained using stainless steel absorbers with natural abundance of Fe, but with poorer statistics.
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Fig. 8. Results of the type 1 velocity scan experiments for the “Hole” absorber, showing N (v ) as a function of v . The rota tional period ¹"1/f"2p/X are indicated for the various scans.
The total width of the velocity scans in Figs. 7 and 8 can be written ¼"¼ #2R X sin a, (6) where ¼ is the width from the six-line iron spec trum alone (X"0). The spacing of the outer peaks is 10.65 mm/s (this value was used to calibrate the velocity scale). The width of the X"0 spectrum was taken to be 10.65 mm/s plus two linewidths (C+0.4 mm/s here) for a value ¼ "11.45 mm/s. The experimental widths of the scans at various values of X were compared with Eq. (6) with the values R"5.0 mm and a"16.0°. Fig. 9 shows the results. Filled circles indicate the widths for the “full” absorber, and open circles indicate the widths for the “hole” absorber. The experimental widths are seen to be in reasonable agreement with the theoretical predictions.
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Fig. 9. Comparison of the widths of the velocity scans in Figs. 7 and 8 with theoretical prediction. Filled circles correspond to the “Full” absorber pattern and open circles correspond to the “Hole” absorber pattern. Solid line shows the theoretical prediction given by Eq. (6).
Fig. 10. Comparison of the ¹"0.5 s (f"2 Hz) velocity scans for the “Full” and “Hole” absorber patterns with theoretical predictions.
Numerical integrations were performed to determine the theoretical shape of the resulting data for the two samples for ¹"0.5 s and are shown in Fig. 10 along with the experimental results. Only two free parameters, the baseline and the total area, were varied to fit the data. Good agreement is seen to be obtained, illustrating the proper functioning of the prototype device.
pixels N : IJ N (h)"N(0, h). (7) Other rows in N can be obtained by modulating IJ the source in a constant velocity mode. This type of measurement indicates angular variations in the ME absorption on the sample. Proof-of-principle experiments using test patterns as in Fig. 5b were performed, for the case ¹"0.5 s. Fig. 11 shows the results for the “quadrant” and “octant” patterns, along with the theoretical curve. Note that the folding operation has not been performed so that the phase angle h runs from 0 to 2p. Folding the data improves the signal-to-noise ratio as well as the agreement with the theoretical curves. Again, only two free parameters have been varied to fit the experimental results. In both cases good agreement is obtained between experimental and theoretical curves. Note that these data involve 630 data points, which could be reduced considerably (e.g. by binning into a smaller number of channels) in actual imaging data, resulting in better statistics.
3.3.2. Type 2 experiments with zero source velocity As discussed above, the type 1 experiments result in data which indicates the radial dependence of the sample absorption, averaged over angle. The type two experiments involve leaving the source at rest, and triggering the multichannel scaler on the sample rotation sync as obtained with the notched wheel. This measurement is important as it represents the essential data-acquisition technique to be used in the full imaging device. For v "0, one obtains the central row in the matrix of
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Fig. 11. Results of the type 2 angular scans at ¹"0.5 s ( f"2 Hz) with the “Quadrant” and “Octant” absorbers showing N (h) as a function of h. Solid curves indicate the theoretical predictions. Note that h runs from 0 to 2p, indicating these data have not been reduced by superposing the data from 0 to p with those from p to 2p.
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halves of the raw data, an n by n matrix of data would result, ready for image reconstruction. In addition to imaging the total absorption, one can vary the angular frequency of the sample drive and obtain data as a function of of the three variables v , h, and X. In a manner similar to chemical shift imaging in NMR, in which the magnetic field gradient is varied in magnitude as well as direction, one can image in spectroscopy mode. This would allow, in principle, the extraction of the ME spectrum as a function of the position on the sample surface. Note that one may not need a large number of such two-dimensional sets of data to obtain interesting results: for example, with only a few channels one could determine the presence of austenite (narrow line) and martensite (broad magnetic spectrum) in a steel surface. Finally, we note that the imaging technique could also be performed in a “near-source” geometry, as described in Ref. [8]. In this geometry, the source is quite close to the sample, resulting in greater count rates, although the analysis is somewhat more complicated. This geometry is rather interesting as the absorption profile is no longer a strip, as in Fig. 1b, but is now sharply peaked near x"0, giving a “blurred” image of the sample directly in N(v , h) even before image reconstruc tion.
5. Conclusions 4. Proposed imaging system We propose incorporating the present prototype device into a state-of-the-art ME system which can be run in a constant velocity mode. The constant velocity mode involves moving the source uniformly for a period, followed by a brief flyback period. Data would be obtained as in the type 2 (angular) proof-of-principle experiments, with the MCS in the ME system triggered with the sample motor sync obtained from the notched wheel. Each angular set of data would be binned into an appropriate number of channels: if, e.g. a square N matrix is IJ desired (as in the simulations of Section 3.2), then the angular data would consist of 2n data points and n such data sets at various v would be ob tained. After “flipping” and superposing the two
The proof-of-principle experiments performed with the prototype CESI device indicate that this device can be used with a constant velocity ME spectrometer to obtain all of the data necessary for two-dimensional imaging of the ME absorption over sample surfaces. The primary limitation to resolution is signal-to-noise. In the proof-of-principle experiments a relatively weak source of 1 mCi was used. The data in Fig. 11 were obtained with 630 data points, which could be reduced several fold in actual imaging experiments, improving the signal-to-noise and reducing the counting time necessary. Experiments with stainless steel samples with natural abundance of Fe have been performed with similar results but much poorer statistics, but improvement would result from the
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use of a much stronger source, as well as the use of a near-source geometry. The technique could also be extended to count conversion X-rays, which would have greater penetration in the sample. Counting both conversion electron and conversion X-rays would give some depth information. Eventually the technique will be developed into a surface imaging system with a wide range of application in material science.
Acknowledgements This work was funded in part by the Faculty Research Committee and University Research Committee at Idaho State University, and the NASA Idaho Space Grant Consortium.
References [1] G.J. Long (Ed.), Mo¨ssbauer Spectroscopy Applied to Magnetism and Magnetic Materials Science, vol. 1, Plenum Press, New York, 1993. [2] J.J. Spjikermann, American Laboratory (Nov. 1971) 29. [3] C.A. McCammon et al., Meas. Sci. Technol. 2 (1991) 657. [4] L. Gra bæk, et. al., Metal. Trans. A 20 (Nov. 1989) 2259. [5] J.J. Spjikermann, American Laboratory (Nov. 1971) 35. [6] D.S. Goldman, D.E. Bewley, J. Am. Ceram. Soc. 68 (12) (1985) 691. [7] D. Jiles, Introduction to Magnetism and Magnetic Materials, Chapmann and Hall, New York, 1991, p. 114. [8] S. J. Norton, Nature 330 (12 November 1987). [9] T.R. Brown et al., Proc. Natl. Acad. Sci. USA 79 (1982) 3523. [10] Ranger Scientific, Inc. model SD-300. [11] A. Wehner, M.S. Thesis, Idaho State University, 1994.
Conversion electron surface imaging G.M. Irwin *, J. Green, A. Wehner Department of Physics, Lamar University, P.O. Box 10046, Beaumont, TX 77710, USA Idaho State University, Pocatello, ID 83209, USA Utah State University, Logan, UT 84322, USA Received 30 June 1997
Abstract A method of imaging the Mo¨ssbauer absorption over the surface of a sample based on counting conversion electrons emitted from the surface following resonant absorption of gamma radiation is described. This Conversion Electron Surface Imaging (CESI) method is somewhat analogous to Magnetic Resonance Imaging (MRI), particularly chemical shift imaging, and similar tomographic reconstruction techniques are involved in extracting the image. The theory behind the technique and a prototype device is described, as well as the results of proof-of-principle experiments which demonstrate the function of the device. Eventually this same prototype device will be part of a system to determine the spatial variation of the Mo¨ssbauer spectrum over the surface of a sample. Applications include imaging of variations of surface properties of steels and other iron containing alloys, as well as other surfaces over which Fe has been deposited. 1999 Elsevier Science B.V. All rights reserved.
1. Introduction The Mo¨ssbauer Effect (ME) [1] has found many applications in the study of materials, particularly those containing iron. The gamma-ray absorption spectrum one obtains is uniquely sensitive to the local environment of the iron nucleus (specifically Fe, the active isotope). The hyperfine effects on the spectrum are due essentially to three effects: (1) the electric monopole interaction, due to the local charge density at the nucleus, (2) the electric quadrupole interaction, due to the interaction of the quadrupole moment of the nucleus with the local
* Corresponding author. Tel.: #1 409 880 8243; e-mail: [email protected].
electric field gradient, and (3) the magnetic dipole interaction, due to the possible presence of a magnetic field on the nucleus. All of these hyperfine effects are sensitive to the crystal structure and magnetic properties of a given material. We propose a technique for analysing surfaces of materials based on the detection of conversion electrons emitted from nuclei in the surface of the sample following ME absorption, which we call Conversion Electron Surface Imaging (CESI). The technique is based on the Conversion Electron Mo¨ssbauer Spectroscopy (CEMS) method, in which the conversion electrons following resonant absorption of gamma radiation are counted. The conversion electrons emitted have a range of only 200—300 nm, making the technique truly surface sensitive. Even a monolayer of Fe can be
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detected using the CEMS method [2]. The CESI technique utilizes a specialized detector in which the sample is mounted on a rotating platform (the device is described in more detail below). Using the specialized detector and a conventional ME spectrometer system, one may obtain the ME spectrum as a function of position on the surface of the sample. The technique makes use of the same type of tomographic reconstruction methods used in MRI and X-ray CT, although one is not looking in the interior of a sample, rather on its surface. Nonetheless, one may consider the proposed technique to be a tomographic form of ME spectroscopy. The need for spatially resolved ME spectra has been identified by researchers studying properties of quenched metallurgical slags [3]. They used a “brute force” method, using a small (0.5 mm) collimator and a very intense, point-like gammaray source. By moving a prepared cross-sectional specimen across the collimator, they were able to obtain the ME spectrum as a function of depth from the surface in a sample. The variation in the spectrum as a function of depth indicated effects of the rapid quenching. However, the spatial resolution of the technique is limited by the size of the collimator. Such data is of great interest in the study of rapidly solidified “splats” and ribbons in which the details of the rapid quenching process are poorly understood. It is known, for example, that variations in the relative amounts of austenite and martensite in surface and bulk occur when steels are formed into rapidly solidified ribbons [4]. The proposed technique would allow one to image the variation of properties of the surface and of cross sections internal to samples, giving important information concerning the formation of the material. For example, the percentage of retained austenite in a rapidly solidified sample of stainless steel could be imaged, giving information regarding cooling rate over the surface of the sample. Also variations in the direction of surface magnetism due to surface stresses are known to affect the ME spectrum [5], and these properties could similarly be imaged, e.g. in welds. However, unlike the technique described in Ref. [2], the spatial resolution of the proposed technique is not limited by any sort of collimation.
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Besides the aforementioned studies of rapidly solidified materials, the proposed technique has a variety of other potential applications. One may group these applications in a few broad categories: 1. materials containing natural iron (about 2% Fe), 2. materials enriched with Fe, 3. surfaces over which a thin film of Fe has been deposited, 4. generalization to other Mo¨ssbauer effect isotopes, such as Sn and rare earths. Other specific applications might include analysis of geological specimens such as meteorites, including both surfaces and cross sections of samples. The sensitivity of the ME technique to the oxidation state of the iron (e.g. Fe>, Fe>) would allow one to image such variations of a sample or cross section of a sample. Such data is of interest, e.g. in the study of vitrification of radioactive waste [6], in which the oxidation state of the glass is important in maintaining the integrity of the material for such uses. ME spectroscopy has provided an alternative to wet chemical analysis, and the spatial resolution of such effects could not be obtained using wet-chemical techniques. The sensitivity of the Mo¨ssbauer absorption spectrum to the magnetic properties of a surface suggest several applications. Both the magnitude and direction of the surface magnetization affects the ME spectrum. The proposed technique could be used to image magnetic domains in ferromagnets, perhaps providing an alternative to the Bitter method [7], and imaging the magnetization in magnetic recording media and thin films. In addition, the penetration of the conversion electrons emitted by the nuclei following resonant absorption will also affect the observed count rate at different positions, providing unique possibilities for contrasting different regions of a sample. Mo¨ssbauer Imaging has been suggested in transmission geometry, and simple one-dimensional demonstration experiments have been performed, but with little apparent application [8]. The conversion electron surface imaging system proposed here is centered around a specialized conversion
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electron counter, described in detail below, in which the sample is mounted on a rotating platform. As described below, the device has been tested utilizing a conventional ME spectrometer system in a constant acceleration mode, and it has been shown to function as predicted. The principle of operation is similar to MRI: in Nuclear Magnetic Resonance (NMR) one obtains resonant absorption as a function of magnetic field strength. Thus by imposing a magnetic field gradient across a sample spectral information is converted to spatial information. In Mo¨ssbauer Effect Spectroscopy one obtains resonant absorption as a function of relative source-to-absorber velocity. Thus by imposing a velocity gradient across a sample (e.g. by rotating), spectral information is converted to spatial information. In either MRI or the proposed technique, conventional tomographic reconstruction techniques are used to obtain an image of the sample. The technique proposed here is the direct analog of chemical shift imaging in NMR [9], in which the NMR spectrum is obtained as a function of position in the sample. The specialized detector is based on a commercially available conversion electron counter for ME spectroscopy [10]. The sample rotates within the conversion electron counter chamber at an angular frequency X. The source makes an angle a with respect to the axis of rotation. The conversion electrons are counted as a function of source velocity v and the rotational phase h of the sample (a rotating notched wheel and LED-detector pair provide a synchronization signal). Using standard tomographic reconstruction techniques, the ME spectrum is obtained as a function of the position on the sample. For a narrow line spectrum such as austenite (FWHM C+0.5 mm/s), the spatial resolution of the technique is d+C/X sin a (a is the angle between the gamma-ray direction and the normal to the sample surface), which can be as small as 1 lm for angular velocities of 100 revolutions per second. Note that no arrangement of collimating slits is used to obtain this fine resolution. We begin with a discussion of the theory of CESI. We then describe the prototype device and the system used for proof-of-principle experiments, which involve “test patterns” of Fe-enriched foil.
These initial experiments do not allow for tomographic image reconstruction, primarily due to limitations of the available ME spectrometer system, but illustrate the function of the device. Finally, we describe a proposed system incorporating the prototype device into a state-of-the-art ME spectrometer which will allow for the full tomographic surface imaging, including the extraction of the ME spectrum as a function of position on a sample surface.
2. Principle of conversion electron surface imaging As described in the introduction, the principle behind CESI is essentially the same as Magnetic Resonance Imaging (MRI). In CESI, a velocity gradient is obtained on the sample by rotating the sample, analogous to the magnetic field gradient in MRI. The essential geometry of the concept is illustrated in Fig. 1a. The circular sample is mounted on a rotating platform, which is inside the conversion electron counter (not indicated in Fig. 1). The normal to the sample surface makes an angle a with the direction of the gamma-ray beam. The gammaray source (e.g. Co) is mounted on a standard Mo¨ssbauer velocity transducer, which we will assume for the moment is run in a constant velocity mode, with source velocity v . Let us suppose for the moment that the sample material consists of a narrow-line material (linewidth C) which is present on the surface of the sample in some pattern. As the sample rotates at a given angular velocity X, absorption can occur over a narrow strip of width d"C/X sin a at a position y"!v /X sin a as in dicated in Fig. 1b, due to the doppler effect on different portions of the rotating sample (note that it is necessary to have the sample oriented at the angle a: for a"0 the width of the strip diverges, giving no spatial information. Of course a"90° gives the best resolution, but the source does not illuminate the sample). This strip of absorption is essentially analogous to the plane of absorption one obtains in MRI for a given orientation and field strength. Thus by varying the velocity of the source, the sample is “scanned” along the y-axis. By counting the conversion electrons resulting from the resonant absorption of the gamma radiation as
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a three-dimensional set of data which will give the Mo¨ssbauer spectrum at the point (or pixel) at (x,y). This three-dimensional imaging scheme is analogous to chemical shift imaging in MRI in which the NMR spectrum is obtained as a function of position in the sample, as described in Ref. [9]. A unique quality of this technique is that the resolution of the method, as given by d, is not related to some arrangement of collimating slits. The entire sample is “bathed” in the gamma radiation at any given time. It is the doppler effect resulting from the relative velocity of the source and a given point on the rotating sample which determines the resolution. As the angular velocity X of the sample is increased, the resolution improves. Of course, the practical resolution obtainable in an actual device is signal-to-noise limited. Let N(v , h) be the number of counts obtained with source velocity v and sample phase h. This can be represented as a kind of integral transform of the absorption M(x,y) on the sample surface:
N(v ,h)"
Fig. 1. Geometry of CESI. (a) indicates the rotating sample and the source moving with velocity v at an angle a with respect to the sample normal indicated by vector X. (b) Absorption profile over the sample surface with the source moving with velocity v . Here a narrow-line absorbing material is assumed, resulting in the Lorenztian absorption profile.
a function of the angular phase h of the sample rotation and the source velocity v , one can use standard tomographic reconstruction algorithms to obtain the Mo¨ssbauer absorption as a function of position (x,y) on the sample. This two-dimensional imaging scheme gives the integrated absorption at the point (or pixel) at (x,y), which depends on the pattern of Mo¨ssbauer-active material on the sample. By obtaining data also as a function of the angular velocity X of the sample, one can obtain
M(x,y)n(v ,h;x,y) dx dy,
(1)
where the integration extends over the dimensions of the sample surface. The function n(v , h; x, y) ex presses the overlap between the absorption profile and the density of absorbing material on the sample. Consider, for example, a single small spot of absorbing material, with a narrow-line spectrum, on an otherwise non-active substrate. In the v , h plane this spot traces out a sine-wave (sometimes called a “sinogram” in conventional tomography), with a velocity profile given by a Lorentzian of width C at each angle h for a narrow-line material. The equation of the resulting sine-wave, indicating the position of the peak of the Lorentzian is v (h)"!oX sin a sin(h! )
(2)
for a spot at polar coordinates o, (x" o cos , y"o sin ) on the sample. Thus we can write the function n(v ,h; x, y) as n(v , h; x, y)"P (v, v , C), *
(3)
where P (v, v , C) is a Lorentzian distribution with * mean v and full-width C. Fig. 2 shows a plot of the
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surface n(v , h; x, y) for a spot at x"R/2, y"0. Here v "RX sin a is the maximum speed needed
to scan the complete circular sample, and the linewidth of the Lorentizan is taken as v /10. For
differential area elements at other positions x, y, the sine wave Eq. (2) would be shifted by angle and would have an amplitude o X sin a. Fig. 2 illustrates a symmetry in N(v , h): the second half from p to 2p is a mirror image of the first half from 0 to p, or N(v , h#p)"N(!v , h).
(4)
Thus the data can be reduced by “flipping” the second half about v "0 and adding it to the first half. This process is similar to “folding” conventional velocity spectra obtained with a trianglewave modulated source to eliminate parabolic baseline distortion. Extraction of the image M(x, y) from the data essentially involves inverting Eq. (1), for which many tomographic reconstruction algorithms have been developed for X-ray CT, MRI, etc. For a more complex spectrum, e.g. iron metal, several lines would occur as a function of velocity at each value of h. As the angular velocity of the sample drive is increased, however, the six-line spectrum is “squeezed” into a smaller spatial width, giving the same result as the single line material for
Fig. 2. The function n(v , h; x, y) indicating the count rate of conversion electrons as a function of v and h for a differential element of a narrow-line Mo¨ssbauer-active material at x"R/2, y"0, as indicated in the inset.
a large enough X. The lower angular velocities are of interest for imaging in spectroscopy mode, in which the spatial variation of the ME spectrum is extracted from the data.
3. Prototype device We describe here the prototype device which has been constructed and the proof-of-principle experiments which indicate the proper functioning of the device. 3.1. Device description The prototype CESI device was built around two commercially available devices: (1) A Ranger Scientific, Inc. model SD-300 conversion electron detector designed for ME spectroscopy, and (2) an Oriel Corporation model 75154 variable frequency open chopper motor which was altered to provide the sample rotation. The conversion electron detector is a gas-flow proportional counter with a gas mixture of helium with 4% methane, with a flow rate of 1 cc/min. A pre-amp for the detector is contained in the same housing, resulting in a compact device. A LED/Detector pair on the chopper was used with a notched wheel to provide a synchronization signal. The Co source was mounted on a Technical Measurements Corporation model 305 ME transducer with a model 306 drive unit. This transducer was capable of modulating the source with either triangle or ramp waveforms. The transducer could not be driven reliably for speeds greater than 30 mm/s, nor could it be driven in a constant velocity mode. This significantly limited the scope of proof-of-principle experiments to test the function of the device. Also the low activity of the available source (&1 mCi) limited signal-to-noise in the present measurements. The samples are mounted on a 5.0 mm radius aluminum peg which mounts with set screws to the motorized platform and notched synchronization wheel. The whole CESI device is mounted on an optical bench oriented to make an angle a"16.0° with respect to the gamma-ray beam direction. The sample is set inside the gas counter chamber which
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Fig. 3. Diagram of the prototype CESI system. The two sync signals are used to trigger the MultiChannel Scaler (MCS) for the two types of proof-of-principle experiments.
contains two anode wires, and the gas simply flows past the sample and out a small annular gap between the rotating peg and a hole in the counter. Fig. 3 shows a diagram of the prototype CESI system. Here the two synchronization signals are used to trigger the mutichannel scaler in the two types of proof-of-principle experiments to be described in Section 3.3 below. Not indicated in the diagram are the high voltage and low voltage power supplies for the conversion electron detector. 3.2. Numerical simulation of the cesi prototype Numerical simulations were performed to illustrate the theoretical performance of the CESI prototype. In these simulations it was assumed that a sample having a single narrow absorption line (e.g stainless steel) was present on the sample surface in a particular pattern. The simulation then calculated assuming a particular number n;n of pixels in the matrix N(v , h)"N . Fig. 4 shows IJ various absorber patterns (a) expressed as a discrete matrix M . The theoretical matrices N for these GH IJ patterns are shown in (b). Darker shades indicate
higher values of M and N . The vertical velocity GH IJ scale for N runs from !v to #v , where IJ
v "R X sin a is the maximum velocity needed to
completely scan the absorber. The horizontal angular scale runs from 0 to p, indicating that the folding operation has been performed. Numerical simulations were also performed to extract the matrix M from N using tomographic GH IJ reconstruction algorithms developed by the authors [11]. The algorithms used to extract the image are based on minimizing chi-squared between the given N data and the transform of the IJ extracted image, as calculated with a discrete form of Eq. (1). These algorithms were performed by assuming a particular noise level on top of the theoretical N , to simulate real data. Fig. 5 shows IJ the results for a “quadrant” absorber pattern. Fig. 5a indicates the absorber pattern, and Fig. 5b indicates the theoretical N matrix. The scales of IJ the axes are the same as in Fig. 4. Fig. 5c shows the results of the tomographic reconstruction algorithms assuming random noise of 5% of the peak signal added to the N in 5b, and Fig. 5d shows the IJ results with 8% noise. The algorithms used are not
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Fig. 4. Simulated CESI data. (a) Assumed sample patterns, where dark areas indicate the presence of Mo¨ssbauer-active material; (b) indicates the resulting N matrices, where darker shades indicate higher conversion electron count rate. The velocity scale (vertical) runs IJ from !v to v , and the horizontal (angular) scale runs from 0 to p.
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Fig. 5. Example of tomographic reconstruction algorithms. (a) Assumed M absorber pattern. (b) Simulated N matrix. (c) ReconstrucGH IJ ted image with 5% noise added to N . (d) Reconstructed image with 8% noise added to N . IJ IJ
necessarily the best, but they indicate the process by which the sample image can be obtained from experimental data. 3.3. Proof-of-principle experiments Two types of proof-of-principle experiments were performed to test the operation of the prototype detector and compare with theoretical predictions. These experiments involve: 1. triggering the multichannel scaler (MCS) with the source velocity sync signal (with source in
a triangle, or constant acceleration mode) and ignoring the sample drive sync, and 2. triggering the MCS with the sample drive sync with the source at rest. The second measurement amounts to obtaining the central row in N(v ,h), while the first involves sum ming the rows in N(v ,h) giving a kind of integral result. These preliminary experiments were limited by the available source strength (+1 mCi), and the rather old ME spectrometer system used (a 30 year old Technical Measurements Corp. model 305 transducer and model 306 Mo¨ssbauer Drive Unit).
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These experiments with the current system are not able to reconstruct the image of the sample surface, but indicate that the device, in conjunction with a modern MES system, can be used to obtain all data necessary for 2-dimensional image reconstruction. Samples used to test the prototype device consisted of Fe-enriched iron foils. The enriched foils allowed data acquisition in reasonable times with the rather weak Co source which was available. The use of Fe foil complicated the analysis of the data due to the six-line spectrum. The use of Feenriched stainless steel foil would have been more suitable for the proof-of-principle studies, but the Fe-foil was available. Samples were made by placing masks of plastic tape over a uniform sample of Fe-enriched foil, thus blocking the conversion electron emission from those regions of the sample. This allowed a number of patterns to be studied with a relatively small amount of the expensive enriched foil. The sample patterns used in the proof-of-principle patterns are shown in Fig. 6. Black areas indicates the mask, and light areas indicate the Fe foil. For the experiments of type 1 described above, samples with no angular dependence were used, including a “full” absorber (no mask) and a “hole” absorber (small circular mask in the center), as indicated in Fig. 6a. For the experiments of type 2 (zero source velocity), samples with no radial dependence to the pattern were used, as indicated in Fig. 6b. It should be noted that the results obtained are not unique to the patterns shown in Fig. 6: any patterns in addition to those in Fig. 6a having the same average radial dependence will give the same results in type 1 measurements. Similarly, any patterns in addition to those in Fig. 6b which have the same average angular dependence will give the same results in type 2 measurements. Obviously, more than just two measurements are necessary to obtain enough information to extract the image of an arbitrary absorber pattern. 3.3.1. Type 1 experiments with triangle-wave source velocity The first type of proof-of-principle experiment involves counting conversion electrons as a function of source velocity v with the source transducer
Fig. 6. Sample patterns used in the proof-of-principle experiments. (a) “Full” and “Hole” absorber patterns for the type 1 velocity scan experiments. (b) “Quadrant” and “Octant” absorber patterns for the type 2 angular experiments. All of these absorbers were made by placing plastic adhesive tape masks (indicated by dark areas) over the “Full” absorber to block conversion electron emission.
run in a constant acceleration mode with a triangle waveform. By using a triangle waveform the solid angle effect which results from the varying distance between source and sample can be eliminated by folding the data, as in a typical Mo¨ssbauer experiment. The multichannel scaler (MCS) is triggered on the motion of the source, and the sample rotational phase is ignored. This essentially gives an integral measurement, which can be expressed as
p
N(v , h) dh (5) Q which amounts to a sum for discrete data, as is obtained from the multichannel analyser. For zero angular velocity, one simply obtains a conventional Mo¨ssbauer spectrum. As the angular velocity of the sample X is increased, the spectral lines broaden in a way that is dependent on the spatial distribution of the absorbing material on the sample (that is, the pattern of the sample). This type 1 experiment thus gives information related to the radial dependence of the sample, as averaged over the sample rotation. Fig. 7 shows the results obtained from the prototype device with the “full” absorber, a uniform circular sample of Fe-enriched iron foil. Indicated
N (v )"
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Fig. 7. Results of the type 1 velocity scan experiments with the “Full” absorber, showing N (v ) as a function of v . The rotational period ¹"1/f"2p/X are indicated for the various scans.
in Fig. 6 is the period of sample rotation ¹"2p/X for each spectrum. At a given ¹, the resulting data can be represented by a convolution of the six-line pattern (e.g. ¹"R, X"0) with an elliptical function. This elliptical function would be the result from a similar circular sample of material with a single very narrow line. Fig. 8 shows the results obtained with the “hole” absorber, consisting of a 4 mm diameter circular mask placed over the center of the 10 mm diameter “full” absorber. In this case the six-line spectrum is convoluted with an elliptical function with a smaller elliptical “notch” removed in the center. Clearly the effects due to the different spatial distribution of iron foil on the two samples is evident. Similar results were obtained using stainless steel absorbers with natural abundance of Fe, but with poorer statistics.
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Fig. 8. Results of the type 1 velocity scan experiments for the “Hole” absorber, showing N (v ) as a function of v . The rota tional period ¹"1/f"2p/X are indicated for the various scans.
The total width of the velocity scans in Figs. 7 and 8 can be written ¼"¼ #2R X sin a, (6) where ¼ is the width from the six-line iron spec trum alone (X"0). The spacing of the outer peaks is 10.65 mm/s (this value was used to calibrate the velocity scale). The width of the X"0 spectrum was taken to be 10.65 mm/s plus two linewidths (C+0.4 mm/s here) for a value ¼ "11.45 mm/s. The experimental widths of the scans at various values of X were compared with Eq. (6) with the values R"5.0 mm and a"16.0°. Fig. 9 shows the results. Filled circles indicate the widths for the “full” absorber, and open circles indicate the widths for the “hole” absorber. The experimental widths are seen to be in reasonable agreement with the theoretical predictions.
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Fig. 9. Comparison of the widths of the velocity scans in Figs. 7 and 8 with theoretical prediction. Filled circles correspond to the “Full” absorber pattern and open circles correspond to the “Hole” absorber pattern. Solid line shows the theoretical prediction given by Eq. (6).
Fig. 10. Comparison of the ¹"0.5 s (f"2 Hz) velocity scans for the “Full” and “Hole” absorber patterns with theoretical predictions.
Numerical integrations were performed to determine the theoretical shape of the resulting data for the two samples for ¹"0.5 s and are shown in Fig. 10 along with the experimental results. Only two free parameters, the baseline and the total area, were varied to fit the data. Good agreement is seen to be obtained, illustrating the proper functioning of the prototype device.
pixels N : IJ N (h)"N(0, h). (7) Other rows in N can be obtained by modulating IJ the source in a constant velocity mode. This type of measurement indicates angular variations in the ME absorption on the sample. Proof-of-principle experiments using test patterns as in Fig. 5b were performed, for the case ¹"0.5 s. Fig. 11 shows the results for the “quadrant” and “octant” patterns, along with the theoretical curve. Note that the folding operation has not been performed so that the phase angle h runs from 0 to 2p. Folding the data improves the signal-to-noise ratio as well as the agreement with the theoretical curves. Again, only two free parameters have been varied to fit the experimental results. In both cases good agreement is obtained between experimental and theoretical curves. Note that these data involve 630 data points, which could be reduced considerably (e.g. by binning into a smaller number of channels) in actual imaging data, resulting in better statistics.
3.3.2. Type 2 experiments with zero source velocity As discussed above, the type 1 experiments result in data which indicates the radial dependence of the sample absorption, averaged over angle. The type two experiments involve leaving the source at rest, and triggering the multichannel scaler on the sample rotation sync as obtained with the notched wheel. This measurement is important as it represents the essential data-acquisition technique to be used in the full imaging device. For v "0, one obtains the central row in the matrix of
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Fig. 11. Results of the type 2 angular scans at ¹"0.5 s ( f"2 Hz) with the “Quadrant” and “Octant” absorbers showing N (h) as a function of h. Solid curves indicate the theoretical predictions. Note that h runs from 0 to 2p, indicating these data have not been reduced by superposing the data from 0 to p with those from p to 2p.
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halves of the raw data, an n by n matrix of data would result, ready for image reconstruction. In addition to imaging the total absorption, one can vary the angular frequency of the sample drive and obtain data as a function of of the three variables v , h, and X. In a manner similar to chemical shift imaging in NMR, in which the magnetic field gradient is varied in magnitude as well as direction, one can image in spectroscopy mode. This would allow, in principle, the extraction of the ME spectrum as a function of the position on the sample surface. Note that one may not need a large number of such two-dimensional sets of data to obtain interesting results: for example, with only a few channels one could determine the presence of austenite (narrow line) and martensite (broad magnetic spectrum) in a steel surface. Finally, we note that the imaging technique could also be performed in a “near-source” geometry, as described in Ref. [8]. In this geometry, the source is quite close to the sample, resulting in greater count rates, although the analysis is somewhat more complicated. This geometry is rather interesting as the absorption profile is no longer a strip, as in Fig. 1b, but is now sharply peaked near x"0, giving a “blurred” image of the sample directly in N(v , h) even before image reconstruc tion.
5. Conclusions 4. Proposed imaging system We propose incorporating the present prototype device into a state-of-the-art ME system which can be run in a constant velocity mode. The constant velocity mode involves moving the source uniformly for a period, followed by a brief flyback period. Data would be obtained as in the type 2 (angular) proof-of-principle experiments, with the MCS in the ME system triggered with the sample motor sync obtained from the notched wheel. Each angular set of data would be binned into an appropriate number of channels: if, e.g. a square N matrix is IJ desired (as in the simulations of Section 3.2), then the angular data would consist of 2n data points and n such data sets at various v would be ob tained. After “flipping” and superposing the two
The proof-of-principle experiments performed with the prototype CESI device indicate that this device can be used with a constant velocity ME spectrometer to obtain all of the data necessary for two-dimensional imaging of the ME absorption over sample surfaces. The primary limitation to resolution is signal-to-noise. In the proof-of-principle experiments a relatively weak source of 1 mCi was used. The data in Fig. 11 were obtained with 630 data points, which could be reduced several fold in actual imaging experiments, improving the signal-to-noise and reducing the counting time necessary. Experiments with stainless steel samples with natural abundance of Fe have been performed with similar results but much poorer statistics, but improvement would result from the
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use of a much stronger source, as well as the use of a near-source geometry. The technique could also be extended to count conversion X-rays, which would have greater penetration in the sample. Counting both conversion electron and conversion X-rays would give some depth information. Eventually the technique will be developed into a surface imaging system with a wide range of application in material science.
Acknowledgements This work was funded in part by the Faculty Research Committee and University Research Committee at Idaho State University, and the NASA Idaho Space Grant Consortium.
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