APPLICATIONS OF MÖSSBAUER SCATTERING TECHNIQUES

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APPLICATIONS OF MÖSSBAUER SCATTERING

TECHNIQUES

F. Wagner

To cite this version:

F. Wagner. APPLICATIONS OF MÖSSBAUER SCATTERING TECHNIQUES. Journal de

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JOURNAL DE PHYSIQUE CoIloque C6, supple'ment au no 12, Tome 37, De'cembre 1976, page C6-673

F. E. WAGNER

Physik Department, Technische Universitat Munchen, D-8046 Garching, Germany

R6sum6.

-

Les expkriences Mossbauer en geomktrie de diffusion fournissent souvent des informa- tions que I'on ne peut pas obtenir par la mkthode habituelle de transmission rnais leur technique expkrimentale et leur conception sont plus complexes et il faut qu'elles soient adaptkes soigneuse- ment B I'ktude correspondante. Dans cet article de synthkse on discute des techniques permettant, ou qui permettront des applications plus ktendues, notamment la diffraction de monocristaux, la diffusion Rayleigh de rayons gamma Mossbauer, la spectroscopie Mossbauer B. excitation sklective double, les mesures par rayons gamma de haute knergie, l'analyse non destructive, et I'ktude de couches minces en surface par spectroscopie Mossbauer utilisant les 6lectrons de conversion ou la rkflexion totale des rayons gamma.

Abstract.

-

Mossbauer scattering experiments often yield information that cannot be obtained in the standard transmission arrangement, but they are also more complex both experimentally and conceptually, and they must be carefully adapted to the specific problems to be studied. In the present survey some of the techniques that have found, or promise to find, wider application will be discussed briefly, notably Mossbauer diffraction from single crystals, Rayleigh scattering of Mossbauer gammarays, selective excitation double Mossbauer spectroscopy, experiments with high-energy gammarays, non-destructive testing, and the investigation of thin surface layers using conversion electrons or total reflection of gammarays.

1. Introduction. -The basic experimental procedure

in Mossbauer spectroscopy is the detection of the resonant excitation of nuclear states by gammarays of the right energy that are, in nearly all cases, emitted by a radioactive source. Ever since the early days of Mossbauer spectroscopy, the vast majority of experiments has been performed in a transmission geometry, where the resonant excitation is detected by the fact that it removes photons from the direct beam of radiation falling from the source through the resonant absorber into the detector. This absorption of photons can easily be observed by comparing the countrates with the Massbauer resonance switched on and off by means of the Doppler effect. Reasons for the nearly universal use of the transmission geometry are its experimental simplicity, the fact that it yields all the information wanted in most applications of Mossbauer spectroscopy, and the fact that the evaluation of the data is relatively simple. The simplicity of transmission Mossbauer spectra is largely due to the fact that, according to the optical theorem, the resonant absorption cross-section is simply proportional to the imaginary part of the coherent nuclear forward scattering amplitude. In cases of static hyperfine interactions the absorption cross-section can therefore be expressed as a simple sum of Lorentzian terms with relative intensities that can be calculated in a rather straight- forward way (see, e. g. [I]). Deviations from the simple Lorentzian form exist [2-41 but are negligibly small in most cases of major interest [41.

The interpretation of scattering experiments is generally more complex. It must take into account a number of additional experimental conditions like the nature of the outgoing radiation or particles, the scattering angle, and the angles between both the incident and the scattered radiation and the axis of quantiza- tion defined by the hyperfine interaction. Moreover one has to consider interference effects between different scattering processes, e. g. between Rayleigh and Moss- bauer scattering or between waves scattered from different atoms in regular array. On the other hand, and for just these reasons, scattering experiments can yield information that could not be obtained in Moss- bauer absorption experiments.

The different applications of scattering techniques entrail a variety of experimental methods, including for instance diffraction from single crystals or Rayleigh scattering from materials that do not even contain the respective Mossbauer isotope. A considerable amount of diversification in scattering experiments also stems from the possibility to use a variety of events (other than the removal of a photon from the transmitted beam) to testify of the resonant excitation of a nucleus. In view of this diversity no attempt will be made here to throroughly review all applications of Moss- bauer scattering techniques, which comprise virtually all experiments that do not employ the standard transmission method. Rather, after a brief review of some typical features of Mossbauer scattering, some techniques that have found - or promise to find

-

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'AGNER

relatively widespread use will be discussed. Also, no attempt is made of a complete coverage of the lite- rature on these subjects, and the quoted papers will often be relied upon to generate further references to earlier work.

2. Radiation or particles detected in scattering

experiments.

-

The most obvious way of performing a Mossbauer scattering experiment is to look for scattered gammarays of the same energy as the incident ones in an arrangement according to figure la.

- ' " .' SCATTERER

A/y,,

VELOCITY DRIVE ,' ,A,

SHIELDING 'ECTOR CITY DRIVE VELOCITY DRIVE " SHIELDING

FIG. 1.

-

Mijssbauer scattering arrangements : (a) Simple setup consisting of source, scatterer, and detector. (b) Setup in which the scattered radiation is analyzed by a Mossbauer

resonant absorber.

When the excited Mossbauer level also decays via a y-y cascade, these gammarays can also be observed. Probably the only case where it is promising to look for such gammarays is the 136 keV second excited state of 57Fe, which decays with an 89

%

probability via the 122 keV-14 keV cascade. Indeed efforts have been made to observe this Mossbauer resonance by looking for the reemitted 14.4 keV or 122 keV gammarays (see section 6 and ref. [ 5 ] ) .

For nuclear excited states with energies accessible to Mossbauer spectroscopy a considerable fraction of the decays goes via internal conversion. Detection of the conversion electrons is an alternative way of performing a Mossbauer scattering experiment. In the course of the filling of the electron hole in an inner shell created by a conversion process, X-ray photons, Auger electrons, or both, will be emitted. Conversion and Auger electrons as well as X-rays from Mossbauer atoms have been used in scattering experiments, particularly in non-destrictive testing and studies of surfaces (see section 7). Photons in the ultraviolet or visible light range, as would for instance result from

5d

to 4f transitions in rare earths in the aftermath of

internal conversion processes, sofar have not been detected. A recent experiment [6] in which optical fluorescence of Eu in CaF, was observed after Moss- bauer excitation of the 21 keV level in 15'Eu came close to it, but in this case the fluorescent light actually was emitted by Eu2+ centers excited by conversion and Auger electrons passing through the lattice.

3. Coherence and interference effects.

-

The occurence of a variety of interference phenomena constitutes one of the major differences between scattering and transmission experiments. Soon after the discovery of the Mossbauer effect, the coherent nature of nuclear resonant scattering was confirmed in experiments demonstrating its interference with Ray- leigh scattering 17, 81. This results in typical asymme- tric lineshapes. Interference between Mossbauer and Rayleigh scattering from the same atom is not limited to cases where the gammaray is re-emitted without emission or absorption of phonons, although the excitation of the nucleus obviously has to occur in a recoilfree process. For interference with Rayleigh scattering from the same atom it is only important that both processes lead from a given initial state to the same final state of the total system comprising the lattice in addition to the Mossbauer nucleus [9].

Figure 2 illustrates the possible transitions between hyperfine levels in a Mossbauer scattering experiment.

EXCITED STATE l e >

1

+ 312 I N I T I A L FINAL STATE STATE l i > I f >

FIG. 2.

-

Illustration of nuclear hyperfine transitions in a scattering experiment. The possible transitions starting from the mi =

+

sublevel are shown for the case of a MI transition and pure m states. The solid vertical lines indicate coherent

scattering processes, the dashed ones spin-flip incoherent scattering.

A nucleus that is initially in the substate

I

i

>

can be excited to any substate

I

e

>

that is compatible with the selection rules for the multipolarity of the nuclear transition. The re-emission of the gammaray can occur again to any substate

If

>

compatible with the selection rules. Only transitions for which

I

i

>

and

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interfere with electronic (Rayleigh) scattering. Moss- bauer scattering processes that change the nuclear spin orientation

(I

i

>

#

If

>)

have no electronic counterpart since Rayleigh scattering always leaves the nuclear spin unchanged. Therefore they cannot interfere with electronic scattering processes. Obviously for this spin-flip incoherence no actual hyperfine splitting is necessary. Spin-flip incoherence is absent only when the nuclear groundstate has zero spin, as is in practice the case for the 1, = 2+

+

I, = 0' transitions in even-even nuclei.

However, scattering transitions that connect any two groundstate sublevels

I

i

>

and

If

>

but proceed via different sublevels of the excited state interfere with each other since one cannot decide which intermediate state was actually excited. This type of interference gives rise to non-Lorentzian terms in the purely nuclear resonant scattering cross section [lo-151. These terms vanish when the hyperfine splittings of the excited state are large compared with its natural width, and reduce to a Lorentzian shape for zero hyperfine splitting.

The general rule for deriving the cross section for a specific scattering problem is to add the scattering amplitudes for processes that are mutually coherent before the intensities are calculated by taking the square of the moduli of the total scattering amplitudes.

Finally, these intensities must be averaged over all initial states and summed over all final states and types of observed processes. The resulting expressions [lo- 141 are usually rather lengthy and become even less amenable after the convolution with the source emission spectrum. Additional problems arise for thick scatterers, where the attenuation of the incident and scattered beam and multiple scattering processes become important. Therefore the evaluation of Mossbauer scattering experiments has often been based on approximations (e. g. [16-221) neglecting either the interference between Rayleigh and Moss- bauer scattering or between scattering on different nuclear sublevels, or thickness effects. Such approximations are indeed often justified. For instance, the interference with Rayleigh scattering vanishes for nuclear M1 transitions at scattering angles of 8 = 900 [21,22] and in purely nuclear Bragg peaks [15], or it may be negligible in experiments with high- energy gammarays [16-201.

The explicit expression for the total gammaray intensity of pure Mossbauer scattering from a single nucleus for the case of unpolarized radiation from a single-line source and a powder scatterer with a static hyperfine interaction producing pure m substates

is relatively simple [lo, 111. In this case the intensity scattered at a Doppler velocity v takes the form

if both the source and the scatterer are assumed to have lines of the natural width

T.

The coefficients Bk(mi ; me, m:) depend on the nuclear spin quantum numbers I, and I,, and the multipolarities L and L' (e. g. MI and E2) of the Mossbauer transition. The Legendre polynomials Pk(cos 9) describe the dependence of the individual components on the scattering angle. The subscript k takes all even integer values between 0 and Min (2 L' ; 2 I,), where

L'

is the highest multipolarity involved in the Mossbauer transition. The quantities V(m,, me) are the Doppler velocities

for which transitions between ground and excited state sublevels are at resonance. The second sum in the curly brackets in eq. (1) gives the non-Lorentzian contribution airsing from interference between scattering on different nuclear sublevels. Even when these terms become negligible for large hyperfine splittings, the relative intensities of the individual hyperfine lines are generally different - although often very little - from those expected in an absorption spectrum, and they depend on the scattering angle because of

the different angular dependence of the intensity of scattering from the individual hyperfine levels.

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AGNER

which actually constitute y-e- resonance scattering experiments in which the conversion electrons (and photoelectrons) are accepted at a large solid angle.

4. Diffraction of gammarays on single crystals. -

The discussion of coherence effects given sofar was restricted to radiation scattered from a single atom. This situation is rather difficult to observe with crystalline materials, in which radiation scattered coherently from different atoms is concentrated into Bragg reflections, whereas radiation scattered incoherently is found in the diffuse continuum between the Bragg peaks. Cases in which it is justified to consider only single atoms are mainly experiments with high- energy gammarays at large scattering angles (see section 6), and experiments with amorphous scatterers, although even in these diffraction effects will arise owing to short-range order.

With crystalline scatterers and the geometry shown in figure la, the large solid angles of the incident and scattered radiation will usually admit both Bragg reflections and the incoherent background between these. To obtain well-defined experimental conditions one has to use single crystals and a diffractometer similar to the instruments used in X-ray diffraction work (see figure 3 and ref. [32]). One can then study

SOURCE

r i CRYSTAL FO? MOSSBAUER DIFFRACTION

FIG. 3. - Schematic drawing of a diffractometer for Moss- bauer work. The single-crystal collimator (e. g. graphite, Si or Ge) reduces the angular width of the incident beam to a value determined by its mosaic spread and may be omitted when this is not important. An X-ray tube may be used for calibration purposes. The Mossbauer diffraction crystal can be positioned in either a Bragg or a Laue (dashed)

geometry.

individual Bragg (or Laue) reflections with angular resolutions down to a few seconds of arc depending on the quality of the instrument and the type of collimator crystal used. With the availability of strong single- line 57Co sources on small areas, diffraction experiments with the 14.4 keV gammarays of 57Fe have become a major field of interest, but some work has :!so been done with the 23 keV resonance in '19Sn (e. g. [33-351). The Mossbauer diffraction work has recently been reviewed by Belyakov 1361. Here only a brief description of the capabilities and possible applications of this technique will be given.

In principle the diffraction of Mossbauer gammarays follows the same principles as the diffraction of X-rays and thermal neutrons, but there are important differences that are not merely of theoretical interest, but

also foster the hope that Mossbauer diffraction will become a tool for the investigation of solids that is complementary to X-ray and neutron diffraction. An outstanding property of Mossbauer gammarays as compared to X-rays and neutrons is their extremely well-defined energy, which enables one to change the phase and modulus of the nuclear scattering amplitude by merely scanning through the resonance with a Doppler velocity drive, and to single out diffraction from individual nuclear sublevels in cases where a hyperfine splitting is present.

A

major difficulty in diffraction experiments with both 57Fe and '19Sn arises from isotopic incoherence of the nuclear scattering. This is analogous to isotopic incoherence in neutron scattering and arises from the fact that, for instance, not all iron sites in a crystal of natural isotopic composition are occupied by the Mossbauer isotope. The average coherent nuclear scattering amplitude per iron site then becomes [36,37]

where f h: is the mean amplitude for coherent scattering from a single nucleus and h the relative abundance of the Mossbauer isotope. Since the intensity of a _- purely nuclear reflection is proportional to if h:

'

1

and thus to h2, it is often important to use single crystals of enriched 57Fe or '19Sn in Mossbauer diffraction work.

Another source of incoherence arises from thermal motion, which reduces the coherent nuclear scattering amplitude by the Mossbauer-Lamb factor exp(- k2

<

x2

>) [37].

For 57Fe this is close to unity for most inorganic crystals even at room temperature, but in organic materials, or in experiments with 'l9Sn, diffractometers for work at liquid nitrogen temperature or even below may be required.

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scattering amplitude of 57Fe corresponds to the scattering power of about 500 electrons 1411 is a particular asset with such large molecules. The main difficulty is to measure the phases of a large number of structure factors in a tolerable length of time despite the fact that even the strongest Mossbauer sources are still much inferior to the intensity of an X-ray tube [38, 411. Sofar Mossbauer diffraction has not yet been used to unravel unknown protein structures, but the first measurement of a phase for a myoglobin with a known structure has just been reported at this confe- rence [381.

A perhaps less difficult field of future application of Mossbauer diffractometry will be the determination of magnetic structures (see, e. g. [42]). This application is closely similar to magnetic neutron diffraction. It is based on the dependence of the Mossbauer scattering amplitude on the hyperfine interaction, and consequently on the direction of the magnetic hyperfine field at the Mossbauer nucleus. Experiments 115, 431 with a single crystal of a-Fe20, grown from enriched 57Fe show that such experiments are indeed feasible. In a-Fe203 the odd orders of (n, n, n) Bragg reflections are extinguished for purely electronic diffraction, i. e. they are not observed with X-rays. The antiferromagnetic order of hematite is such, however, that they appear in Mossbauer diffraction [15]. Examples of velocity scan spectra for odd-order and even-order (n, n, n) reflections of a-Fe,03 are given in figure 4. A striking difference between the even-order

and odd-order spectra is that the former show no interference between nuclear and electronic scattering, because there is no electronic contribution to the scattering length of the unit cell. The even-order reflections, on the other hand, are strongly asymmetrical owing to the interference between electronic and nuclear scattering, except at scattering anglx close to 900 where this interference vanishes du:: to the different multipolarities of electronic (El) and nuclear (MI) scattering. Figure 4 also shows that the spectra change markedly when the iron spins, which lie in the (n, n, n)

planes above the Morin transition of r-Fe,O,, are aligned perpendicular or parallel to the scattering plane of the gammarays by an external magnetic field. Obviously this can also be helpful in magnetic structure determination. The existence of purely nuclear Bragg reflections may also find future use in filtering a narrow band of Mossbauer photons out of a broad continuum of synchrotron radiation.

It has been pointed out [42, 44-46] that Mossbauer diffraction is also sensitive to the orientation of the electric field gradient. This may also make reflections appear in Mossbauer diffraction that are absent for X-rays because of cancellation effects. Diffraction experiments with sodium nitroprusside [44], and with metallic Te and the 35 keV gammarays of lZ5Te [45], have demonstrated the existence of this effect. It is not quite clear whether it can give any information that could not, at least in principle, also be obtained from

I I 1

-15 -10 -5 0 5 10 15

VELOCITY ( r n r n l s )

Fig. 4.

-

Mossbauer spectra taken [15, 431 in the (666)

and the (555) Bragg positions of a-FezO3. The (555) reflection is purely nuclear and therefore shows no interference between Mossbauer and electronic diffraction. The two spectra of the (666) reflection are for the hyperfine fields aligned perpendicular and parallel to the scattering plane. The curves

drawn to the data points are discussed in refs. [15, 431.

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C6-678 F. E. WAGNER

that has nodes at the positions of the nuclei and therefore does not induce nuclear excitation. Sofar all experiments with perfect single crystals were performed with the intention to study the basic physical phenomena of the diffraction of gammarays and to test the predictions of the dynamical theory. The sensitivity of these effects to crystal imperfections, however, nourishes the hope that the dynamical diffraction of gammarays can eventually be developed into a sensitive method to study crystal properties. It seems, however, that a considerable amount of work will be necessary before such applications can be considered seriously.

5. Investigation of lattice dynamics using the

Rayleigh scattering of Miissbauer gammarays.

-

Sofar only scattering or diffraction experiments with scatterers containing Mossbauer resonant nuclei have been discussed. The presence of Mossbauer nuclei is not necessary, however, when the scattered radiation is analyzed by a Mossbauer absorber inserted between the scatterer and the detector as shown in figure lb. When the scatterer does not contain Mossbauer nuclei, it is sufficient to vibrate either the absorber or the source in order to scan the Mossbauer resonance, the latter being usually easier from the experimental point of view. The gist of such experiments is that the Mossbauer analysis of the scattered radiation permits one to detect changes in energy with a resolution given by the natural line width of the Mossbauer resonance. For the 14.4 keV gammarays of 57Fe, which are best suited for such experiments for many reasons, the linewidth is about 5 x l o p 9 eV. With this accuracy one can distinguish between truly elastic scattering and inelastic scattering with a small energy transfer arising, for instance, from inelastic processes involving low-energy phonons. In principle such experiments are very similar to neutron scattering experiments for the determination of the scattering function S(Q, w), where Q and o are the momentum and energy trans- ferred in the scattering process (see, e. g. [53]). The usefulness of X-rays for such experiments is limited by the insufficient energy resolution, which permits only the measurements of the quantity

The traditional way to obtain information on the o-dependence of S(Q, o ) is to use thermal neutrons. For these one obtains an energy resolution of about eV with triple axis spectrometers. With a backscattering neutron spectrometer the energy resolution can be improved to somewhat better than l o u 6 eV [54], but the energy resolution of 5 7 ~ e Mossbauer spectroscopy is still superior by a factor of 100. This means that scattering experiments with Mossbauer gammarays can be complementary to neutron diffraction. Actually, an energy transfer at the resolving limit of

neutron spectrometers (6 x lo-' eV [54]) would just correspond to a Doppler shift of 13 mmls for 57Fe, which is the magnitude of magnetic hyperfine splitting observed with this resonance. It therefore seems quite possible to measure energy transfers in inelastic scattering that are just below the resolving power of neutron scattering.

From the Mossbauer point of view, Rayleigh scattering experiments can be performed in the on-off mode or in the velocity-scan mode. In the former, the countrate of 14.4 keV gammarays is measured with the absorber at rest (No) and vibrated at a high velo- city for which the resonance absorption is destroyed (Nv). For normalization one performs the same measurements with the absorber between the source and the scatterer (NL, Ni). The ratio.

then is just the fraction

f,

of gammarays that has been scattered with an energy loss smaller than the energy interval ti Aw absorbed by the absorber at rest. Depend- ing on whether one uses a narrow single-line absorber (e. g. Na,Fe(CN), . I 0 H,O) or a broad black absorber (e. g. lithium ammonium fluoferrate), one obtains energy windows ti Ao between 1 x lo-' eV and 5 x lo-' eV. The quantity that can be obtained from eq. (4) is thus

which can in most applications be considered as the truly elastic fraction

There are cases, however, where the Rayleigh scattering process modifies the energy of the gammarays by amounts that are comparable to the energy resolution of Mossbauer spectroscopy, for instance when diffusion takes place in the scatterer or, perhaps, close to structural phase transitions when soft or central phonon modes become important. Then it may be of interest to measure the scattered energy distribution in a velocity-scan Mossbauer experiment rather than in the off-on mode.

An important point to be considered is the angular resolution required for a specific purpose. When amorphous materials are studied, a rather wide solid angle will usually be acceptable since the scattering function varies smoothly with the momentum transfer, and thus with the scattering angle. A normal scattering

setup according to figure 1 can then be used [55,56]. To increase the solid angle, and hence the countrates, a ring geometry 1571 can also be used. For crystalline materials most of the elastically scattered radiation is peaked into Bragg reflections. It is then best to use a gammaray diffractometer (Fig. 3) and a single-crystal

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with sufficient accuracy in order to select special ed radiation in velocity-scan experiments [55, 561. points in reciprocal space for investigation. This type These measurements show that the linewidth of the of experiments has recently been reviewed by O'Con- scattered radiation increases substantially in the nor [58]. One of the main applications has been the temperature region where the elastic fraction falls off. determination of the thermal diffuse (inelastic) scatter- The glasses and supercooled liquids studied sofar ing contribution under the Bragg peaks in various were easy to prepare from the experimental point of materials, e. g. Si and KC1 [59-621. By virtue of its view. For materials like amorphous semiconductors, high energy resolution Mossbauer spectroscopy can which are a wide field for future studies, it will often distinguish between elastic coherent scattering and be necessary to produce the scatterer at low tempera- thermal diffuse scattering, which also peaks a t reci- tures, e. g. by evaporation or sputtering onto cold procal lattice points and gives a considerable contri- substrates. For such studies it is a particular advantage bution particularly for high momentum transfers that the Rayleigh scattering technique can be applied to and at elevated temperatures. any material without the usual restriction to substances Another application is the investigation of the which naturally contain a Mossbauer isotope, or into dynamics of structural phase transitions and other which a Mossbauer isotope can be incorporated as a ordering phenomena. Here the Mossbauer technique probe.

can be useful in cases where soft or central phonon

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C6-680 F. E. WAGNER

admitting both Bragg and diffuse scattering [21, 721. be achieved and the scattered spectrum is no longer In the diffuse continuum between the Bragg directions sensitive to changes in z,. When the relaxation is too of a single crystal made of enriched 57Fe, on the other slow (7, % z), no substantial redistribution among the hand, one expects to see very little of the elastic cohe- sublevels will occur during the nuclear lifetime and the rent component, and a strong relative enhancement of additional lines in the scattered spectrum will be too the incoherent inelastic scattering. For applications of weak to be observed.

A

further desirable condition is selective excitation Mossbauer spectroscopy this is a that energy separations AE between the individual serious complication, because the relative intensities hyperfine levels should be well resolved, i. e. z % RIAE. of the elastic and inelastic peaks will depend on the This is actually the case in most magnetic iron systems. ratio of Bragg-reflected to diffuse intensity that is In such cases relaxation with z, z z will produce present in the solid angle admitted by the scattering mainly a line broadening in the transmission spectrum, apparatus, a quantity that is difficult to control in and this may be difficult to distinguish from other practice. These problems will, however, be alleviated broadening effects. Selective excitation double Moss- somewhat owing to the averaging effect occuring for bauer spectroscopy, however, allows one to study the powder samples and large solid angles. redistribution in a very direct way. This makes such Approximate expressions for the scattered intensity studies worth while to do despite the fact that the dl(us, v,)/dS2 have been given by Balko and Hoy [22], inclusion of relaxation into the formulae for the who include the influence of scatterer thickness but scattered intensity [78, 791 leads to much greater neglect all interference effects. For interference bet- computational complexity than it does in the case of ween Rayleigh and Mossbauer scattering this is justi- transmission experiments.

fied only for a scattering angle of 9O0. This geometry Until now the selective excitation technique has but was chosen in all experiments performed sofar with rarely been used in relaxation studies. Balko and polycrystalline scatterers 121, 71, 72, 75-77]. The Hoy [21, 751 have studied antiferromagnetic a-Fe,O, interference between scattering on different hyperfine near the Morin transition, where the iron spins change levels of the excited state, which gives rise to the non- from an alignment parallel to the rombohedral (1 11) Lorentzian terms in the expression for the scattering direction to an orientation perpendicular to this axis. cross-section (eq. (I)), is also of minor importance The question to be studied is whether relaxation bet- when the hyperfine spIittings are large and the excita- ween these two spin directions takes place near the tion is close to a resonance. General formulae for the Morin transition. Although only a narrow region of energy distribution of the scattered radiation have been the scattered spectrum near the incident energy was given by Afanasev and Gorobchenko 1781 and by analyzed, and although the relaxation formalism Hartmann-Boutron [14, 791, who also take relaxation used to interpret the data is not quite adequate for the effects into account but do not consider interference situation of a 900 flip of the electronic spin, these with Rayleigh scattering and diffraction effects. experiments indicate that relaxation processes do The selective excitation technique has recently been indeed occur with relaxation times of the order of suggested [76] for the measurement of Rayleigh lo-' s. More recently, the same authors have used scattering cross-sections. This application basically the SEDM technique to study the charge hopping makes use of the fact that Rayleigh scattering contri- relaxation in Fe,O, above, near and below the Verwey butes only to the elastic but not to the spin flip in- transition [77]. Redistribution among the excited elastic peak in the scattered spectrum. When the state sublevels can also be induced by an applied Mossbauer scattering cross-section is known, the radiofrequency field. The selective excitation technique Rayleigh cross-section can therefore in principle be can therefore be used to detect the nuclear magnetic determined from the intensity ratio of the elastic and resonance of the excited Mossbauer level [72].

inelastic lines in the scattered spectrum. In practice, Recently [80], Mossbauer scattering has been used difficulties will arise, however, because this intensity in a different way to study a relaxation phenomenon, ratio also depends on the relative amounts of Bragg namely the critical fluctuations in FeF, and Fe,C near and diffuse scattering observed in the geometry of the the magnetic ordering temperature, by observing the experiment, which is difficult to obtain quantitatively. critical small-angle scattering of Mossbauer gamma- The main interest in SEDM spectroscopy lies in the rays. The small-angle scattering of Mossbauer gamma- fact that it is a very direct way of observing relaxations rays by fluctuations of the short-range magnetic order between the hyperfine sublevels of the nuclear excited is largely analogous to small-angle scattering of neu- state. To this end one selectively excites a single trons, except that the sensitivity to the electronic sublevel of the excited state. The energy spectrum of spin directions and their correlations arises from the the reemitted radiation will then tell how the excita- dependence of the Mossbauer scattering amplitude on tion has migrated to other sublevels during the lifetime the hyperfine interaction. In FeF, critical small-

z of the excited nuclear state. The typical range of angle scattering of the 14.4 keV gammarays of 57Fe relaxation times ZR accessible to a meaningful investi- was found at angles of a few degrees in the vicinity gation by this method is z, x 2. When the relaxation is of the NCel temperature. Such measurements of the

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information on the spatial extension of short-range spin correlations. The Mossbauer scattering data indicate that these are of the order of 20

A

in the case of FeFj.

7. Scattering experiments with high-energy gammarays.

-

In the experiments described sofar the scattering process as such has been the essential point of interest. Scattering experiments with gammarays having energies E, around or above 100 keV have often [16, 17, 19, 20, 85-87] although not always [81- 841, been performed to obtain information on hyperfine interactions that could, in principle, also have been obtained from transmission measurements. In these cases the motive for using scattering techniques has been that in favourable cases these yield much larger resonance effects than transmission experiments. For the latter, and assuming that source and absorber have single lines of natural width and that there is no background in the single channel analyzer window, the resonance effect E is at best equal to the recoilfree

fraction of the source, i. e.

In a scattering experiment with a thin scatterer containing only the resonant isotope one has (see, for instance, [86] for a detailed discussion)

where dc,/dQ is the differential nuclear cross-section for scattering of a gamma quantum having the exact resonance energy and doR/dQ the cross-section for Rayleigh scattering. The factor

3

stems from the averaging over the incident Lorentzian energy distribution, and f,, is the recoilfree fraction of the scatterer. Rayleigh scattering of gammarays in the 100 keV range is very strongly peaked in the forward direction, whereas Mossbauer scattering has only a weak angular dependence (see eq. (1) and refs. [lo, 11, 141). In a backscattering geometry, the ratio (do,/dQ)/(do,/dQ) may therefore be as large as lo4 or even lo5. Conse- quently, rather large values of e can be obtained even for the small recoilfree fractions usually encountered with high-energy gammarays. This is illustrated in table I, which gives the relevant cross-sections for several Mossbauer transitions that are suitable for scattering experiments. The Rayleigh cross-sections given there were calculated from the formula

which is a reasonably good approximation for gammaray energies of the order of 100 keV and large scattering angles [89]. The Mossbauer scattering cross-sections given in table I are averaged values disregarding

Mossbauer and Rayleigh scattering cross-sections for several high-energy transitions that are suitable for scattering experiments. The Mossbauer cross- sections d</dQ are mean values that do not take the rather weak angular dependence into account ; the Rayleigh cross-sections doR/dO are for a scattering angle of 8 = 1350. The values for 57Fe given in paran- theses are for resonance excitation of the 136 keV level and subsequent emission of a 122 keV quantum (see text). Isotope

-

57Fe 141Pr 1 5 3 E ~ lSS0s lgllr lg5Pt lg7Au lg9Hg

the angular dependence, i. e. they are just the absorption cross-section multiplied by the probability of subsequent decay via emission of a Mossbauer gammaray,

with

The ratio T,,/T of the radiation width for the ground- state gamma decay and the total width of the Moss- bauer level is

r,,/r

= pl(l

+

a3

9 (13)

(11)

C6-682 F. E. WAGNER

Rayleigh scattering of the 122 keV gammarays emitted by the source into account.

The scattered gammarays must be observed in the presence of Compton scattering which is between 10 and 100 times stronger than Rayleigh scattering. With Ge(Li) detectors one can discriminate the Comp- ton backscattering peak from the Mijssbauer gammarays (see Fig. 5), but Compton scattering of gammarays of higher energy would produce a disastrous background. Scattering experiments are therefore promising only when the nuclear decay scheme is so simple that no substantial amounts of high-energy gammarays are emitted. Radioactivity of the scatterer, on the other hand does not necessarily preclude scattering experiments, as has been shown for the case of 237Np [go]. COMPTON PEAK FROM 103 keV y - R A Y S 0 l 1 I 1 I I I 50 100 ENERGY (keV)

FIG. 5.

-

Pulse height spectrum of the gammarays of a 153Sm source scattered through an angle of 9 = 135". The source of 153Sm203 and the scatterer of enriched 153Eu203 were cooled to liquid He temperature in the cryostat shown in figure 6. The solid curve is for the source at rest, i. e. with the 97 keV and 103 keV transitions a t resonance. The dashed curve is for source motion with a high velocity that destroys the Mossbauer resonance and leaves only the Rayleigh scattering. Owing to its relatively large Mossbauer cross-section, the 97 keV resonance can easily be observed in scattering, although the 97 keV level is very weakly populated in

the l53Sm decay.

To obtain tolerable recoilfree fractions with high- energy gammarays, sources and scatterer usually must be kept at cryogenic temperatures. Figure 6 shows a liquid helium cryostat used for this purpose in the author's laboratory. In this apparatus the gammarays are backscattered through an angle of 1350 in a geometry that avoids the velocity smearing occuking in other geometries sometimes used in backscattering experiments [16,18,19]. The scatterer is vibrated with a sinusoidal velocity waveform. The scattered gammarays are counted by six Ge(Li) detectors in separate

dipstick cryostats.

FIG. 6. - Mossbauer scattering apparatus used in the author's Munich laboratory for scattering experiments with gamma-rays

having energies around or above 100 keV.

(12)

APPLICATIONS OF MOSSBAUER SCATTEKING TECHNIQUES C6-683 activities of several Curies can be made, like in the resonant excitation process, the nucleus spends on the case of 14'Pr [16, 17, 19, 201 or lg9Hg [86]. In average more time in the excited state than in a y-y

such cases scattering experiments offer an advan- coincidence experiment. The resulting increased rota- tage over transmission experiments in which the tion of the angular distribution pattern has been pre- source activity is limited because, at least with Si(Li) dicted by theory [94, 951 and confirmed by experi- or NaI(T1) detectors and standard pulse handling ment [84].

electronics, the total countrate can hardly exceed a The observation of conversion electrons instead of few times lo5 s-I. However, in cases that are suited for scattered gammarays has also been used to obtain scattering, i. e. when there are little or no gammarays large effects with resonances of relatively high energies of higher energy than that of the Mossbauer transition, like those in "OW (103.6 keV) or lS2W (100.1 keV) [31].

energy resolution is usually not needed. particularly In these experiments an electron spectrometer of the since low-energy X-rays and gammarays can usually orange type has been used, but less complicated elec- be attenuated by absorbing materials. In transmission tron detectors, e. g. Si surface barrier detectors, might experiments with such resonances one can therefore also be used for such experiments when good energy forego energy resolution and use tin or lead loaded resolution for the electrons is not needed.

plastic scintillators together with a fast level discrimi-

nators. This allows countrates of the order of lo7 s-I _{7. Non-destructive testing and surface studies.}

_-

(see e. g. [911). When no energy resolution is needed, _{Mossbauer backscattering experiments can be used to} one can even abandon pulse counting altogether _{probe the surfaces of solids at different depths, depend-} and measure the integrated detector current (see e. g. _{ing on the conditions of the experiment. Depth selec-} [92]). Recent experiments with the 158 keV transition _{tivity can be obtained mainly by looking for different} in Ig9Hg [86~ _{931 show that the scattering technique types of scattered radiation, the choice being between} and the current integration method give comparable _{re-emitted gammarays, X-rays and conversion or} results when sources eciual strength are used. _{Auger electrons. With electrons different depth regions} However, in the scattering experiments the Source can, within certain limits, be sampled by selecting strength is limited to about 1 Ci by the high countrate _{emerging from the}_surface_with

from Compton scattering into the Ge(Li) detectors, energies. par the most promising isotopes, 57Fe and whereas there is virtually no limitation On Source _{119Sn, the main types}_{of scattered photons or electrons,} strength with the current integration technique. their intensities, and their approximate ranges are Scattering still has an advantage, however, in cases _{given in table}_11._{Since both Mossbauer transitions are} where energy discrimination is necessary because there highly converted (a, = 8.7 for 57Fe and a, = 5.2 for are two Mossbauer transitions, like in experiments 119sn), the probabilities for conversion and Auger with the 97 k e ~ and 103 keV resonances in 153 EU [871- _{electron emission are considerably higher than those}

he evaluation of hyperfine spectra taken in a _{for reemission of gammarays. The same is true for} scattering geometry is somewhat complicated by the _K _{emission with}_{5 7 ~ ~ .}

_rn

_the1 x 9 ~ ~ case, K-

lengthy expression for the scattering cross-section _{conversion is energetically forbidden.}_L_{X-rays are} (eq. (1) and refs. [lo, 11, 141) the deviations from the _{weak in both cases because the L-shell fluorescence}

transmission lineshape may be negligibly small in _{yields are lowe}

some cases. Diffraction effects and interference with _~ _~ _~_{of backscattering techniques with}_l _i _~ _~ _~ ₅ ₇_i _~ _~_~ _~ _~ Rayleigh scattering can usually be neglected, the _{and "YSn comprise roughly three depth ranges}_:

former because the backscattering of high-energy

gammarays is virtually all inelastic and the latter (i) Depth of several vm, in which one usually because the Rayleigh scattering amplitude is very encounters bulk properties and expects to see the much smaller than the nuclear scattering amplitude in hyperfine interactions that would also be observed in a most cases that are suitable for such scattering experi- solid. Table I1 shows that such studies are best done ments (Table I and ref. [9]). with backscattered gammarays or X-rays. In this Mossbauer scattering experiments with high-energy depth range the advantage of scattering over trans- gammarays have also been performed to measure the mission is essentially that it is non-destructive. This angular distribution of the scattered radiation. From method has, for instance, been used in studies of such experiments the multipole mixing ratio of the works of art and archeological artefacts 1101-1041, in 129 keV transition in lglIr has been obtained [81, 821. metallurgy [105-1071, or in prospecting for minerals Moreover, the rotation of the angular distribution of containing tin [108].

(13)

C6-684 F. E. WAGNER

Energies, intensities, and ranges of photons and electrons emitted after resonant excitation of the 14.4 keV state of 57Fe and the 23.8 keV state of 9Sn. The intensities are given per decay of the excited nuclear state. The photon ranges are the mean penetration depths for electronic attenuation in metallic Fe and Sn, respectively. The upper and lower limits given for the electron ranges_ are the maximum range, after which all electrons have been stopped and the mean free path for penetration without energy loss. The former have been calculated from the empirical formula of Feldman [96], the latter have been estimated from the data given in refs. [97-1001.

57Fe '19Sn

E Inten- Range R in E Inten- Range R in Type of emitted radiation keV sity Fe metal keV sity Sn metal

-

X-rays 14.4 0.10 R w 20 ym 23.8 0.16 R w 100ym

K X-rays 6.4 0.28 R w 2 0 y m

- -

-

L X-rays 0.7 0.002 3.6 0.05

K-shell conversion electrons 7.3 0.79 100

A

5 R

5 4 000

A

- +

L-shell conversion electrons 13.6 0.08 200

A

5 R

5 1.3 ym

19.6 0.83 300

A

6 R

5 5 ym

M-shell conversion electrons 14.3 0.01 200

A

6

R

5

1.5 ym 23.0 0.13 300

A

6 R

6 7 ym

K-LL Auger electrons 5.5 0.63 70

A

5 R

5 2 000

A

- -

-

L-MM Auger electrons 0.53 0.6 1 0 A 5 ~ 6 2 0 A 2.8 0.74 50

A

8, R

5 500

A

the scattering angle, on the composition of the material and on the importance of attenuation by reso- nance absorption. The 14.4 keV gammarays and the KX-rays of 5 7 ~ e will usually have somewhat different mean ranges, the virtually equal ranges for photo- absorption in pure iron (Table 11) being merely acci- dental. For X-ray detection with 57Fe, a particularly simple arrangement [I101 is to mount the sample behind the exit window of a commercial Ar/Me proportional counter and to pass the 14.4 keV gamma- rays from the source through the counter before scattering. This is possible because the efficiency of a counter having the proper diameter is much higher for the 6.4 keV X-rays than for the 14.4 keV gammarays. For this reason the flow counters often used in conversion electron Mossbauer spectroscopy (see below) can also be used to detect the iron K X-rays if one merely replaces the helium-methane flowgas commonly used for electron counting by an argon- methane mixture [I 1 I ] . In practice this is a very simple way of changing the depth region probed by the Mossbauer experiment, although some amount of crosstalk between X-ray and conversion electron detection may exist in such systems, e. g. when the argon-methane counter is not completely insensitive to conversion electrons, or when X-rays can produce secondary electrons in the walls of a helium-methane counter.

Gammaray backscattering spectra in principle will show the interference effects discussed in the preceed- ing sections. Interference between Rayleigh and Moss- bauer scattering, however, becomes small for scattering angles close to 900 owing to the different multipolari- ties of Rayleigh ( E l ) and Mossbauer (MI for 5 7 ~ e and l19Sn) scattering, but for other geometries it should be considered in the interpretation of the data, even

though it may often be negligible in backscattering geometries because coherent Rayleigh scattering is peaked in the forward direction. For spectra taken with backscattered X-rays, interference effects should be negligible except for El Mossbauer transitions, because such spectra will have the same shape as conversion electron spectra averaged over all directions of outgoing electrons. This averaging will lead to a cancella- tion of the interference term [27-301 for M1 and E2 Mossbauer resonances.

(ii) Depths of the order of lo2-lo4

A

can conve- niently be probed by Mossbauer spectroscopy with backscattered conversion and Auger electrons (Table 11). The most convenient and therefore the most frequently used device to detect the backscattered electrons are the gas-filled flow counters just men- tioned (see, e. g. [ I 1 1 - 1 161) or parallel-plate avalanche detectors 129, 301. When operated with a helium- methane mixture, such detectors are insensitive to gammarays, and the sample surface may be simply put against an opening in the back of the detector. The incident gammarays from the source can pass through the counter gas virtually unattenuated.

(14)

APPLICATIONS OF MOSSBAUER SCATTERING TECHNIQUES C6-685

peculiar consequences : They can give rise to lines that at a Doppler velocity v in the Mossbauer spectrum are narrower than natural when they are used with a taken with the electron spectrometer set at an energy stationary source and a moving absorber [121], and E, is therefore, somewhat simplified, an average they may give rise to small line asymmetries arising -A

from the interference between conversion and photoelectrons 127-301. The latter effect is reduced, however, for M1 transitions by the directional averaging

effect of multiple scattering of the electrons before they where N,(v, z) dz is the number of primary Mossbauer enter the detector gas volume. This averaging over all events in a layer of thickness dz at a depth z in the directions of outgoing electrons is perfect for reso- scatterer and P1(ES, z) is P(E, z) as introduced above nance detectors in which the resonant material is modified by the spectrometer function p(E, Es) that embedded in the detecting medium, like l19Sn0, or describes the energy resolution of the electron spectro- Ca119Sn0, in plastic scintillator materials [121-1221, meter, i. e.

or lSIEu in a europium-doped CaF, scintillator [6]. For conversion electron Mossbauer spectroscopy the gas-filled backscattering detector has two disadvan- tages : Unless windows are introduced, the sample cannot be cooled to cryogenic temperatures because of the organic component in the filling gas, and it has virtually no energy resolution. It has been suggested to overcome the former difficulty by the use of a pure He gas filling [124]. Alternative ways to overcome this problem would be to detect the electrons with an open electron multiplier, a channel electron multiplier [125], a plastic scintillator, or a Si surface barrier detector, the latter if necessary with an acceleration voltage applied to overcome the insensitive surface layer.

However, none of these devices has the energy resolution required if one wants to get a grip on depth selectivity of conversion electron Mossbauer spectroscopy. The spectra taken with them are actually rather ill-defined averages over depths roughly up to the maximum range of the electrons of highest primary energy. In order to improve the depth selectivity of the technique substantially, one must analyse the energy of the electrons leaving the surface of the sample with an accuracy of the order of a few percent. This can only be achieved with magnetic or electrostatic electron spectrometers. To obtain reasonable intensities, spectrometers designed for high transmission and, even more important, high luminosity have been built [31, 1261, but most of this type of work has sofar been done with solenoid or n

,/Z

type spectrometers [127- 1301 designed originally for work in low-energy nuclear physics. These instruments were operated at energy resolutions between 2

%

and 5

%,

which seems to be quite sufficient, particularly if one takes into account that further improvements in the resolution would necessarily reduce the countrate in the energy window. The measurements of Mossbauer spectra with the electron spectrometer set at different energies Es solves only part of the depth selectivity problem anyway, however good the energy resolution of the spectrometer may be. This is so because for an electron emerging from the scatterer surface with an energy E, one can at best give a probability distribution P(E, z) that the primary Mossbauer absorption process giving rise to this electron has taken place in a depth z below the surface of the sample. The countrate N(E,, v)

It has been pointed out [128, 1311 that, at least in principle, one can obtain N,(v, z) by deconvolution of eq. (14) if a sufficient number of spectra N(Es, v) for different energy settings E, have been measured.

In practice, the main problem is that P(E, z) is a rather ill-known function for a variety of reasons. Most seriously, the passage of low-energy electrons through matter is in itself not very well understood. The proba- bility P(E, E,, z) that an electron set free in a depth z with an energy Eo emerges from the surface with an

energy E therefore cannot be given reliably even when the composition of the surface layers is known, which often will not be the case. Also, one has to take into account that electrons with different primary energies Eo 2 E may contribute to the observed intensity of electrons of energy E. When looking for K conversion electrons of 57Fe (Eo = 7.3 key) that have lost virtually no energy, for instance, one expects to sample a surface film of the order of 100

A

thickness. However, one will also count some L conversion electrons (Eo = 13.6 keV) that have lost 6.3 keV, and therefore have, on the average, travelled about

3 000

A

through the material. Even worse, scattered gammarays may eject photoelectrons close to the surface, and these will also be counted. For appro- priate spectrometer settings, scattered X-rays will act in a similar way, also giving rise to electrons whose Mossbauer spectra are representative for regions as deep as tens of microns below the surface. A11 this means that P(E, z) has tails reaching rather deep into the material. These may sometimes be negligible, but they certainly become important when N,(v, z ) is small near the surface, as would be the case, for instance, when a surface film of a few hundred

A

of non-resonant material covers a backing containing the Mossbauer atoms. The importance of the tails of P(E, z) in such cases has recently also been demonstrated experimentally (T. Cranshaw, private communica- tion).

(15)

AGNER

scatterer material. Theoretical and semiempirical efforts in this direction have been made by various authors [128, 131-1341, but it seems that more work will be necessary before the depth selectivity problem can be solved quantitatively. Eventually, the measurement of a rather large number of Mossbauer spectra at different settings of the electron spectrometer will be time consuming unless one builds a spectrograph that can analyze electrons of different energies simulta- neously.

(iii) The depth regions considered in the previous section were of the order of a few thousand A, and the depth resolution aimed at would be of the order of 100

A,

depending somewhat on the depth in the sample. When one is interested in Mossbauer atoms less than a few tens of

A

below the surface, or even in or on the surface atomic layer, the mean free path of the electrons [97-1001 sets an unsurmontable limit to any efforts to improve the selectivity for regions close to the surface. For the electron energies one mainly has to deal with, the free path - i. e. the mean distance an electron travels before it looses energy by an inelastic process

-

is of the order of 100

A.

This means that, however good the resolution of the electron spectrometer may be, one cannot reduce the mean sampling depth below that value. Notably, the same is true for the sampling depth of XPS and Auger electron spectroscopy (AES), except that these techniques commonly use electrons with energies around or below 1 keV, for which the mean free path is only 10-30

A

198-1001. If electrons in this energy range, e. g. the L-MM Auger line of Fe (Table 11), were used in Mossbauer spectroscopy, the depth probed would indeed be the same as in XPS and AES.

For practical purposes, the limited surface sensitivity of Mossbauer conversion electron spectroscopy means that atoms in or on the surface atomic layer can only be studied without a large background from regions deeper in the sample if one carefully prepares a surface that contains a monolayer of resonant (e. g. 5 7 ~ e ) atoms on a nonresonant (e. g. 56Fe) substrate. If this is done, e. g. by evaporation or sputtering techniques, the sensitivity of conversion electron spectroscopy should be sufficient for the detection of such monolayers, at least for 57Fe [135]. This method would, however, be in direct competition with source experiments in which 5 7 ~ o is deposited on the surface, or with absorption experiments with evaporated multi- layer stacks in which monolayers of 57Fe are interca- lated between films of nonresonant materials [136]. A Mossbauer technique that should, at least under ideal conditions, yield better surface sensitivity than conversion electron spectroscopy, is the total reflection of gammarays [137-1391. Total reflection occurs for gammarays incident on a sufficiently smooth surface under a grazing angle 8 that is smaller than the critical angle

8, =

JD

,

(16)

where 1-6 is the real part of the complex index of refraction

of the mirror material. For 8 ,< 8, the reflectivity R of the mirror, i. e. the ratio of reflected to incident intensity, would become unity for

P

= 0. Due to the non- zero imaginary part of the index of reflection, however,

R

always remains somewhat smaller than unity. Nevertheless the term total reflection is commonly used for the phenomenon that R rises steeply when 8 falls below 8,. The index of refraction depends on the complex coherent forward scattering amplitude f,,,(O) of the individual atoms in the mirror, i. e.

where N is the number of scattering centers per unit volume and 1 the wavelength of the gammarays. For Mossbauer garnmarays,f,,,(O) is the sum of an electronic and a nuclear contribution. The latter changes when one scans through the Mossbauer resonance, and the reflectivity R becomes a function of the Dopp- ler velocity [137-1391. An experimental arrangement for total reflection Mossbauer spectroscopy is shown in figure 7. For the 14.4 keV gammarays of 57Fe and

ANALYZI ENTRANCE COLLIMATOR SLIT S3URCE S L ~ T

FIG. 7.

-

Schematic drawing of an apparatus for the observation of total reflection of Mossbauer gamrnarays. The mirror is curved in order to focus the entrance slit on the analyzing slit and to eliminate first order variations of the angle of inci-

dence [139].

a mirror of metallic iron, the electronic scattering yields a critical angle of 8, = 3.8 x rad. Moss- bauer experiments with totally reflected gammarays have sofar only been performed with 57Fe (14.4 keV) [I371 and 1 6 ' ~ m (8.4 keV) [139].

The penetration depth d of the radiation field, i. e. the depth after which the intensity of the electroma- gnetic field in the reflecting medium has fallen to lle, falls abruptly when 8 becomes smaller than 8, and rapidly approaches the asymptotic value (see e. g. [140])

for 8 Q 8, and

p

= 0. For j3 # 0 the penetration depth becomes even smaller. Considering only electronic scattering ,one finds d = 13

A

for the 57Fe gammarays and a mirror of Fe metal. This then would roughly be the depth probed by a total reflection experiment. It is considerably less than the mean free path of, for instance, the K conversion electrons of 57Fe (Table 11).