HAL Id: jpa-00215497
https://hal.archives-ouvertes.fr/jpa-00215497
Submitted on 1 Jan 1974
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
rf-MÖSSBAUER DOUBLE RESONANCE
L. Pfeiffer
To cite this version:
L. Pfeiffer. rf-MÖSSBAUER DOUBLE RESONANCE. Journal de Physique Colloques, 1974, 35 (C1), pp.C1-67-C1-72. �10.1051/jphyscol:1974122�. �jpa-00215497�
JOURNAL DE PHYSIQUE Colloque C1, s~ipplktnenr au no 1, Torne 35, Janvier 1974, page Cl-67
rf-MO s SBAUER DOUBLE RESONANCE
L. PFEIFFER
Bell Telephone Laboratories, Murray Hill, NJ, USA
RksumC. - Des experiences dans lesquelles des noyaux Mossbauer sont perturbes par les champs magnetiques de frequence radio sont passees en revue. De ce point de vue sont interessants I'effet de double resonance, I'effet acoustique des bandes laterales et l'effet de relaxation, induite par la rf, du champ hyperfin. D'autres effets sf-Mossbauer possibles qui, jusqu'a present, n'ont pas etC observes, sont aussi brievenient discutes.
Abstract. - Experiments are reviewed in which Mossbauer nuclei are perturbed by radio fre- quency magnetic fields. Of interest in tliis connection is the double resonance effect, the sf acoustic sideband effect, and the effect of sf induced relaxation of the hyperfine field. Briefly discussed also are other possible rf-Mossbauer effects which so far have not been observed.
The use of time varying magnetic fields to perturb Mossbauer nuclei lias opened up rick possibilities for new physics. In some cases qualitatively new phe- nomena have been observed with these techniques.
I11 others, deeper insights have been gained into known plienoniena. T o date all experiments have involved use of the isotope Fe" in a magnetically ordered host.
This choice, although by no means necessary, lias been convenient i n tlie initial exploratory work because of the large FeJ7 Mossbauer effect and also because of tlie possibility afforded for sf magnetic enhancement of the comp:lratively s ~ n a l l time varying fields wliicli are easily obtained at the frequencies of interest.
Three distinct physical effects liave t l i ~ ~ s far been observed when radio frequency magnetic fields are applied to F e j 7 Mossbauer nuclei in a magnetically ordered material. They are : radio frequency acoustic excitation of the Mossbauer nuclei, radio frequency induced electronic relaxation of tlie nuclear lipperfine field, and radio frequency induced transitions between the ~iuclear magnetic sublevels.
Before beginning our discussion of these effects we will mention otlier sf-Mossbauer effects which have been predicted but s o far have not been observed.
One such effect is tlie plienoriienon of gamma magne- tic resonance wliicli was proposed by A. V. Mitin [I].
[2]. Tlie effect is a two quantum process : the Moss- bauer nucleus would emit a gamma quantum and simultaneously emit o r absorb one or more radio frequency photons. Another possible effect is tlie proposal of Poole and Faracli for electron spin Miiss- bauer double I-esonunce [3]. T o obser\,e [4] tliis elicct one would expect to see in the Mossbn~rer spectsu~n a perturbation of a paramagnetic sample by :In c l ~ e r - nal microwave field.
A tliird effect is tlie suggestion of broadening and splitting of the Mossbauer gamma ray line sliape due to tlie applied I-f-field. These effects were predicted in 1960 by Hack and Hammermesh [5]. Refinements of tlie calculations have subsequently appeared by Gabriel [6] in 1968 and by Krislianmurtliy and Sinha [7]
in 1973. Tlie calculations indicate that the distortion of tlie line sliape will become observable when the rf-field applied to the nucleus is made sulliciently large so that it is comparable \vith tlie or-iginal static liyperfine field. The best way to obtain a physical understanding of the effect is to consider a coordi- nate system which is rotating with one of the tircul:~r components of the applied sf-field. In this frame at the nuclear magnetic resonance frequency, the original hyperfine field is zero, a n d H,, is a static licld. Thc nuclear tiionlent begins to precess about this field with tlie result that tlie Mossbauer nuclear levels are Zeeman split by tlie sf-field. With this picture one can see why the broadening and splitting calculated by Hack and Hanimerniesh was found to be propor- tional to tlie amplitude of tlie sf-field.
Before reviewing tlie experimental work i t is well to remind ourselves of tlie FeJ7 ~ ~ ~ r c l e n r energy levels (see Fig. I ) . TIie ground state of ~ e " is spin
i
and lias a Larli~or precession frequency of 45.5 M H z i n iron metal. The excited state is spin-2
a n d has a Larmor precession frequency of 26.0 MHz in iron nietal. I 1 will bc useful to keep this energy level d i ~ ~ g r a r n in mind for all of the cxperiments to be rcvie\ved in this paper. In pill-tic~rlar the reader should be aware thal 26 MHz is tlie excited state nuclear magnetic reso- nancc 1'1-cq~rency and 16 M I-lz is also thc distancc het\vccn adjacent absorption lines, for esample (a n d ,/ in the Mossb:~ucr spectrum.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974122
MAGNETIC DIPOLE SPLITTING OF ~e~~
I I
-'
26.0 MHza b c d e f
+- (q.++$ 45.4 MHz 7 v-
--
I 2FIG. 1. - Nuclear energy level diagram for Fej7 in iron metal.
Let us now turn to some of the early sf-Mossbauer experiments. The first rf-Mossbauer experiments were done by Gilbert Perlow and were reported at the Allerton Conference [8] in 1960. I n 1967 at the Asilo- inar hyperfine conference E. Matthias [9] reported 011 a more extensive series of experilnents similar in con- cept t o those of Perlow. I n both sets of experinlents a split source and absorber ( ~ e " in iron) were used and the measurements were carried out at zero velo- city. The source and absorber were rigidly attached t o each other and placed within a shielded rf-helix so that sf-fields could be applied to either the source o r the absorber or both. Provision was also made for applying a d c magnetic field. Both the sf and the dc magnetic fields were applied in the plane of the foils, that is perpendicular to the gamma ray propagation direction. A gamma detector counted the 14.4 k e y gamma rays in transmission. The experiment consist- ed of varying the frequency of the sf-field and observ- ing the transmission through the absorber as a func- tion of this frequency. It was hoped that one would see a resonance effect at 26 M H z o r at 45.5 M H z either because of Hack-Ha~iimern~esh effects o r because of NMR-transitions. Resonances at 26 M H z were indeed seen in both experiments.
In figure 2 we have reproduced data of E. Matthias published in the proceedings of the 1967 Asilomar conference. In discussing this data at the time D r . Mat- thias emphasized that these were preliminary results.
H e did not claim that the resonance of figure 2 were surely due t o NMR-transitions. The reason for his caution was because of the large and unexpected nonresonant background. Observe in figure 2 that the rf off rate was 61 thousand counts, whereas when the rf was turned on at 20 M H z the count rate increas- ed to 82 thousand counts. It was not clear a t the time why the gamma transmission increased as the non- resonant rf was turned on or \vhy this nonresonant
Source and absorber sandwlched H, = 1 0 0 G ti, = I G
Expected 14.4 heV
$tote resononce
1
F r e q u e n c y ( M H z )
FIG. 2. - (From ref. [9].) Frequency spectrun~ observed in transmission a t zero velocity.
rate appeared to be a strong function of the rf-fre- quency.
T11 the following year Neil Heiman, J. C. Walker and niyself reported
[lo]
experiments which suggested that the data in figure 2 might be interpreted in a diffe- rent way. Using a single line Co5' source moving at constant acceleration and a stationary iron foil absor- ber it was found that additional absorption lines could be made to appear in the Mossbauer spectrum by the application of an rf-field of a few cersteds to the is011 foil absorber. Figure 3 which is taken from that report is an example of the effect of a 13 MI-lz I-f-field on an iron foil absorber. Recalling from figure 1 that the spacing of the original six lines is 26 M H z it is seenVELOCITY (crn/secl
FIG. 3. - (From ref. [lo].) The rf-Mossbauer sideband clTect observed in Fe metal at 13 MHz.
rf-MOSSBAUER DOUBLE RESONANCE CI-69
that the extra lines appear to be displaced at precisely 13 M H z on either side o f each of these lines. These extra satellite lines were called sf-Mossbauer sidebands.
Notice in figure 3 that the generation of sideband lines reduces tlie Mossbauer absorption in tlie original six hyperfine lines. If we assulne that sf-sidebands were generated in eitlier the sources or absorbers of the transmission experiments of Perlow or Mat- thias we can account for the increased transmission count rate when nonresonant sf was turned on. The generation of sidebands spreads recoilless gamma ray absorption among many more lines and this reduces the effective Mossbnuer absorption a t tlie original six lines. At tlie resonant frequency of 26 M H z however some of the sidebands overlap the normal Mossbauer lines. This overlap results in a partial resonant restoration o f the Mossbauer absorption at 26 M H z . TI~LIs, one can account for the resonance in figure 2 without invoking NMR-transitions. Tlie unexpected sf-Mossbaue~- sideband effect masked any possible nuclear magnetic resonance efyects.
Sincc 1968 as tlie result of worlc by groups in Italy [ I I]-[14], tlie Soviet Union [I 51-[I71 and the United States [18]-1271 thc physics of the sf-sideband elrect has become well ilnderstood : Tlie ferromagnetic absorber responds magnetostrictively t o the applied sf-field. This sf magnetostl-ictive response generates acoustic vibrations at the applied rf-frequency in the M o s s b a ~ ~ e r absorber. Thus the Fe" absorber nuclei are caused to vibrate at the sf-frequency. From the point of view of these moving absorber nuclei, the incoming g a m m a rays appear to be Doppler modu- lated. This Doppler modulation of the gamma rays results in the absorption sidebands. The proof of these statements may be found in tlie references cited. For our purposes it is enongli to establish that rf sidebands are caused by induced ;!caustic vibration in the absorber.
The ]nost direct evidence that rf-sidebands are an acoustic effect is the quenching of low frequency sidebands obscrved in small crystals of F e z 0 3 . Tlie acoustic explanation for this quenching is as follows : as the rf-frequency is decreased the acoustic wave- length is increased. I f tlie acoustic half wavelengtlis becomes larger than the crystal diameter, then tlie acoustic vibration will no longer fit within the crystals of a given size and will bc suppressed. These considera- tions suggest that for eacli crystal size some cutom frequency exists below which sidebands are sup- pressed. Tlie cutoff frequency is given simply b!i the equation
where v is tlie velocity of sound in the crystal and tl is the diameter of the crystal. The espcri~ncntal results from reference [23] are given in figurc 4. For cucli of four crystal sizes the figure shows the s ~ d e b a n d etrect in terms of the modulation effec~ versu, the frequency
FIG. 4. - (From ref. [23].) Observation of low frequency acous- tic cutoff effect.
of the sf. Observe that the data show a pronounced quenching of the sideband effect for low frequencies.
The arrows associated with each curve are tlie predict- ed low frequency cutoffs using tlie equation given above. There are two arrows for eacli curve corres- ponding to use of either tlie sheer velocity o r the corii- pressional velocity of sound in the F e z 0 3 crystals.
The asreenlent between tlie experimental and the predicted cutoff is excellent, showing directly t!:at rf- sidebands result from an acoustic excitation of' the Mossbauer absorber by the applied sf-field. As a n acoustic effect sf-sidebands arc tlit~s largely indepen- dent both of the properties of the nucleus and of the hyperfine field. This point is neatly made in tlie lia1,- leigli scattering expcrimcnts [74]. [27] ol' Iiobert Heile. Heile was able to dcrnonstr:~tc thc gcncration of sf acoustic sidebands in a foil of' pure Ni metal which contained no Fe" (see Fis. 5).
C1-70 L. PFEIFFER
FIG. 5. -(From ref. [27].) Acoustic sidebands in Ni metal observed by recoilless Rayleigh scattering.
Let us turn now to another rf-Mossbauer effect : rf induced relaxation of the nuclear hyperfine field.
This effect was first observed in 1970 by the author [28]
at Bell Laboratories. Since then experimental work on the effect has been reported by the group at Panna, Italy [29] and theoretical work by a group in the Soviet Union [30].
To observe the effect it is necessary to control the direction of the hyperfine field at the ~ enuclei by ' ~ an externally applied sf-field. It is possible to do this in certain magnetically soft alloys of the permalloy group. Magnetic fields of only a few cersteds are suffi- cient to magnetically saturate annealed permalloy foils. The hyperfine field at the fe" nuclei in these materials will, because of the core polarization of the Fe s electrons, always point in the direction opposite to the magnetization M. Thus, applied fields of only a few cersteds are sufficient to control the direction of the much larger hyperfine fieId. Now, if the sense of the applied field changes in time at a high frequency then the sense of the much larger hyperfine field of the iron nuclei will be forced by this mechanism to follow in similar reversals of direction.
To be specific, we wlll consider the permalloy alloy 58
%
Fe- 42P,,
NI. I n this material the hyperfine field at the Fe5' nuclei is 270 kG, and the Larrnor precession frequency of these nuclei about this field is at approximately 21 x 106 revolutions per second.This means when our sf-equipment is operating at for example 106 MHz, that the entire hyperfine field of the 270 kG will reverse itself nearly five times during the time it takes the Fej7 nuclear moment to make one precession about the hyperfine field. As a result the time average hyperfine field experienced by the Fej7 nuclei during such sf-reversals will be very nearly zero. The experimental signature that this rf induced zero field condition has occurred would be quite dramatic. The entire S I X lines Mossbauer absorption spectrum characteristic of iron In a magnetic environ- ment should collapse into a single central line.
The experimental results (ref. [28]) with such a permalloy absorber fotl confirm these tdeas (see
Fig. 6). At the bottom of the figure is a Mossbauer spectrum of the permalloy foil without an applied rf-field. The six line absorption pattern indicates that the hyperfine field seen by the Fe" nuclei is of the order of 270 kG. In the upper spectra the same per- malloy absorber foil is subjected to an rf-field of 15 cersteds peak amplitude at a frequency of 106 MHz.
This 106 MHz data shows the collapse of the hyper- fine field very clearly. The resolved six line permalloy hyperfine pattern has disappeared and has been replaced by a single dominant absorption line at zero velocity. Besides the collapse line at zero velocity there are in addition first order rf-sidebands in the spectrum displaced at
+
106 MHz from the central line. The sidebands also show the collapsed single line structure. The permalloy alloy in these experi- ments is magnetostrictive. Thus the appearance of sidebands in this experiment was to be expected and is entirely consistent with our understanding of the origin of sf-sidebands in terms of the acoustic-magneto- striction model.I I I 1 I I I
I
-18 -12 -6 0 6 12 18 VELOCITY (rtVt?/s)
I I I I I I I I I I I
2 0 0 100 0 100 2 0 0 FREQUENCY (MHz)
FIG. 6. - (Adapted from ref. [ZS].) 1.f induced collallsc of the 270 kG hypelfine field at Fe37 in a per~iialloy alloy.
These rf induced reversals of the nuclear hyperfine field may be thought of as a simulation of the random reversals characteristic of paramagnetism. The simula- tion is of interest because the rf allows a well defined reversal frequency and the reversal rate is under thc control of the experimenter. I n a recent Soviet paper by Yu. V. Baldokhin and others [30], consideration is given to the case where the rf reversal rate of the hyperfine field is comparable to the Larmor frequency.
rf-MOSSBAUER D O U B L E R E S O N A N C E CI-71
Their paper attempts t o describe theoretically the onset of the rf collapse at low frequencies. S o far, it has not been possible to test this theory because of the difficulty of adequately suppressing the large rf acoustic sideband effect found a t low frequencies. If metliods are found for suppressing acoustic sidebands there will be many interesting experiments of this kind to do.
Let us turn now to the third class of rf-Mossbauer experiment : Mossbauer nuclear magnetic double reso- nance. Using the isotope Fes7 there are two general types of NMR-experiments to consider. Cain has repor- ted 1311 N M R on the parent Co" state as detected by the Mossbauer effect in Fes7. The C o s 7 nuclei were polarized by reducing their temperature to millidegrees K, and depolarizing nuclear magnetic resonance transitions were induced with the rf-field.
The effect of these transitions was observed in the Mossbauer pattern of the daughter Fes7 state.
The other possibility is to induce and detect N M R - transitions between the excited state levels of F e s 7 itself. T o d o this one needs polarized excited state
~ e " nuclei. Note atomic alignment is not enough.
There must actually exist some population difference among the four excited sublevels (see Fig. 1). If this is not the case, then any nuclear magnetic resonance
NMR transitton between nuclear hyperhne levels
transition in one direction will always be exactly ofisel by transitions the opposite way.
We can, however, use the Mossbauer effect itself to create a true population difference it1 the Fes7 sublevels. Consider again the energy level diagram given in figure I . Suppose a single line gamma ray source with exactly the energyj'existed. If such gamma rays are incident on an iron metal foil, then only the transition f ' would be energetically allowed. Only the - $ sublevel could absorb the radiation. Thus any Fes7 nucleus in the excited state would necessarily be in the illj = -
-2
sublevel. We \+,auld thus have 100 ';;: polarization of the excited nuclei in the foil.Experimentally [32]-[35] one can produce gamma rays at exactly the energy of transition j' by adding to a single line source sufficient Doppler energy using 3 constant velocity Mossbauer drive. Allo\ving these gamma rays to be incident on a n iron metal scatterer creates a new polarized Mossbauer source, and this source can be analyzed using a second Moss- bauer drive with a single line absorber.
The NMR-Mossbauet- double resonnllce experi- ment in ~ e " is summarized by the diagram at the top of figure 7. A single line source at constant velocity is used to populate the state labeled c!. NMR-transitions are induced using an rf-field from the state labeled a t o the state labeled b, a n d the deexcitation gamma rays are observed from the state b using a second Mossbauer drive. The Mossbauer spectrum on tlie lower portion of this figure is taken from reference [34]
where NMR-Mossbauer double resonance was first demonstrated.
Gammas are re-emitted at two new energies
- 2 0 t 2 t 4 + 6 + A I
Veloclty (rnrn / s ) FIG. 8. - ( F r o m ref. [21].) NMR-M6ssb;111cr double rcsonancc Emltted ~ a m m a . r a y s p e c t r u m in Fc metal ;IS a function of applicd frccli~ency. The points marked by circles o r crosses arc thc 14.4 kcV Fc-'i ;.-rays. The FIG. 7. -(Adapted [ram ref. [34].) Observation o f N M R - points at the bottom marked by square\ reprcscnt a control
Mossbauer double resonance. experiment using tllc 0.4 kcV Fc-X rays.
T o actually display the N M R resonance between states a and b one can monitor one of the deexcitation gamma rays from stare b with a second constant velo- city drive. If one does this, one obtains the results shown in figure 8. This figure taken from reference [2 1 ] shows the deexcitation gamma rays from state b as a function of the frequency of the applied sf-field induc- ing the transitions between states a and b. The figure shows that the frequency of the nuclear magnetic resonance transition occurs at 26.0 M H z as expected for these states in iron metal. The natural linewidth of the resonance is expected to be 2.2 MHz. The observed resonant linewidth appears to be more like 3 t o 4 MHz. This line broadening is probably an indi- cation that the rf-field is siifficiently large that the
el'fects considered by Hack a n d Hamtnerniesh are becoming important in these experiments.
I11 these N M R-Mossbauer double resonance expe- riments [36] as in the sf hyperfine relaxation experi- ment, a major problem is the suppression of the rf acoustic sideband effects. Acoustic sidebands were suppressed in the experiments represented by figures 7 and 8 by using samples of powdered iron metal.
Unfortunately inconveniently large sf-fields are requir- ed for powdered san~ples because of the large dema- gnetizing fields associated with the tiny spherical powder particles. If more sophisticated methods are developed for suppressing the acoustic sidebands the potential for new and useful NMR-Mossbauer double resonance experiments appears t o be great.
References MITIN, A. V., Sol.. P11j.s. JETP 25 (1967) 1062.
MITIN, A. V., Suv. Pllys. Uokl. 15 (1971) 827.
POOLE, C . P. and FAIIACH, H. A,, J. 1\4q,,r?e/ic Rc~sonnrrce 1 (1969) 551.
LOCK, J. A. and REICHERT, J. F., J. A4ri~~rreiic Resor~mrce 7 (1972) 74. The authors of this paper claim to have observed electron spin-Mossbauer double resonance.
The statistical quality of their experimental data leaves some doubt on this point, however.
HACK, M. N. and HAMMEIIMESH, M., NIIOI.O Citrlet~to 19 (1961) 546.
GABRIEL, H., P I ~ L . ~ . RPIJ. 184 (1969) 359.
KRISHNAMURTHY, B., SINHA, K. P., PIIJ~S. S t ~ t . Sol. ( 0 ) 55 (1973) 427.
PERLOW, G . J., (( Mossbauer Effect D, Allerton House Conference ( H . Frauenfelder and H. Lustig, ed.) Univer- sity of Illinois Report (1960) (unpublished).
MATTHIAS, E., (( Angular Correlations and NMR-Moss- bauer >>, in I-/!perfire Strrictrirc, arid N ! I C / C N ~ Rn(liatioirs, E . Matthias, ed. (North Holland Press, Amsterdam) 1968.
HEIMAN, N. D., PFEIFFER, L. and WALKER, J. C., PIrys. Rev.
Lett. 21 (1968) 93.
ASTI, G., ALBANESE, G . and Buccr, C., N~iovo Cirrlo~to 57 (1968) 531.
ASTI, G., ALBANESE, G . and Buccr, C., Plrj~s. Rev. 184 (1969) 260.
ALBANESE, G., ASTI, G . and RINALDI, S., Rev. Sci. I ~ I S I ~ I I I N . 42 (1971) 1887.
ALBANESE, G., ASTI, G. and RINALDI, S., Lett. Nlrovo Cir~zento 4 (1972) 220.
POKOZAN'EV, V. G . and GRIGOR'EV, M. L., SOIJ. P/IJ?Y.
JETP 33 (1971) 771 ; Zlr. Eksp. & TL'o~. Fiz. 60(,1971) 1423.
[I81 PERLOW, G. J., P11j.s. Rev. 172 (1968) 319.
[I91 H E M A N , N. D., I'FEIFFEII, L., WALKER, J. C., J. AppI. Phys.
40 (1969) 1410.
[2O] HI'IMAN, N. D., Dissertation (The Johns Hopkins Univer- sity, 1969) (unpublished).
[21] HEIMAN, N. D., WALKER, J. C . and PFEIFFER, L., in Moss- Drrrter E1fic.t Metl~mrlolc~g,~~, Vol. VI, edited by 1. Gru- verman (Plenum Press, New York) 1971.
[??I PFEIFFEII, L., in MiiSSDnrr~~r Effcjcr A4c~t/1odolog)~, Vol. VII, edited by 1. Gruverman ( P l e n ~ ~ n l Press, New York)
1972.
[23] PFE[FFF.II, L., in Procec.clirrg.s ( I / ' tile 17/11 Cottf~~rcrrcc, or1
~ ~ f t ~ ~ i l e ~ i s t t r N I I ~ MCI~;JII(>~I'C Mfll~rinls, C/ti(.(rgo, 1 97 1 (AIP Conf. Proceedings Series, New York, 1972).
[24] HI.ILE, R. F. and WALKER, J. C., Brill. A I ~ . Phj9s. Sot. 17 (1972) 546.
[25] PI.EIFFER, L., H E I M A N , N . D. and WALKER, J. C., PIIJ.s.
Rev. B 6 ( 1 972) 74.
[26] HEILE, R. F. and WALKER, J. C., BIIII. A I I I . P11j.s. SOL.. I8 (1973) 85.
[27] HEILE, R. F., Dissertation (The Johns Hopkiris University, 1973) (~~npublished).
[28] PFEIFFFR. L., J. //pp1. PIIJJS. 42 (1971) 1725.
[29] ALBANESE, G., ASTI, G . and R I N A L D I , S., N I I O I ~ O C i t t ~ ~ ~ t l t u 6B (1971) 153.
[30] BALDOKIHIN, Yu. V., BORSHCI-I, S. A., KLINGER, L. M. and POVITSKY, V. A., ZII. EIisp. Trnr. Fi:. 63 (1972) 708.
[31] CAIN, G., P11ys. Lrtr. 38A (1972) 279.
[32] HEIMAN, N. D., ECK, J . S., PFEIFFER, L., WALKER, J. C., Brtll. A I I I . P11ys. Suc. 13 (1968) 716.
[33] ARTEM'EV, A. N., SMIROV, G . V., STEPHANOV, E. P., Sov.
P1rj.s. JETP 27 (1968) 547.
[16] DUBOVTSEV, I. A. and STEPANOV, A. P., p / l y ~ . Met. & [341 HEIMAN, N., WALKER, J. and P F E I ~ F E R , L., ~ 1 1 ~ 1 s . Rev. 184 Metallogr. 33 (1972) 200 ; Fiz. Met. Metnlloved. 33 (1969) 281.
(1972) 1108. [35] MEISEL, W., Mber. Dt. Akad. Wiss. 11 (1969) 355.
[17] BALDOKHIN, Yu. V., GOLDANSKII, V. I., MAKAROV, E. F., [36] MEISEL, W., in Mossbniterspektro~~~etric~, Proc. of 4th Inl'l MITIN, A. V. and Povl~SKlr, V. A,, J. Physiqrte 33 (1972) Conf. of Socialist Countries, H. Schnorr, ed. (Akademic-
C6 145. Vcrlag GmbH, Berlin) 1972.
