G EN E R A L R EM A R K S A BOU T M OSSB A U ER SPEC TR O SC O PY
R.M.Mirzababavev
Gaziantep University, Gaziantep 21310, Turkey e-mail: mirza®,şantep. edn. tr
More than forty years have passed since the discovery of Mossbauer effect - one of the most brilliant findings in modem physics. This effect proved itself to be the powerful tool in almost all disciplines of the natural sciences and technology. Its unique feature is that it gives the possibility to get the results which cannot be obtained by any other physical methods. Mossbauer effect has been used as a key to unlock some basic physical, chemical and biological phenomena, as a guide for finding the new ways of solving applied scientific and technical problems of electronics, metallurgy, civil engineering, and even fine arts and archaeology. Very few scientific techniques can claim entry into as many countries as Mossbauer spectroscopy. Due to its wide application in an education and research processes the community of Mossbauer spectroscopists extends to almost 100 different countries. Laboratory equipment necessary for conducting gamma resonance spectroscopy, do not require large investments, premises, personnel. The spectrometer is rather small in size and could be installed on the ordinary laboratory table. That is why Mossbauer effect is widely used at numerous Universities all over the world as an universal instrument for tuition and research.
There are no alternatives in future to the nuclear energy as an energy source. Almost all countries surrounding Turkey came to such a conclusion long ago. They already use or design new nuclear stations. Turkey which lacks hydrocarbon energy resources inevitably will come to similar decisions. From this point of view one of the big advantages of Mossbauer effect is that to some extent it can familiarize scientists with a nuclear technology without spending much efforts.
Several attempts have been made to set Mossbauer investigations in Turkey. First laboratory (Prof. Dr.Adil Gediklioğlu)started to operate at Ankara University in 1976. Another one was established in 1978 at METU (Prof.Dr. Necmi Bilir, Prof.Dr.Mehmet Aydin, and Prof.Dr. Esen Ercan Alp). Later Prof. Dr. Mehmet Aydin continued his activity at Ege University. It is a pity that I did not find recent publication related to this topic in Turkey. This situation does not conform to the potential of the fast developing country as Turkey is. This deficiency can be eliminated if the necessary steps will be undertaken.
The Mossbauer effect for 57Fe is a useful technique for determining the magnetic field at the iron nucleus. The transitions between the first excited state and the ground state can be directly observed and used to determine the hyperfme splitting of these levels and correspondingly the magnetization of a sample.
It is assumed that the magnetic hyperfine field as measured using the Mossbauer effect should have a unique value independent of whether the experiment is performed in transmission or in scattering geometries. In examining the possibilities for using scattering techniques to investigate the critical behaviour near the magnetic ordering temperature in Pd-Fe alloys, anomalous differences in the measured values of Curie point Tc were observed between Mossbauer spectra taken in scattering and in transmission geometries. For the first time these differences were observed and published in [1]. It was just a short letter which did not include the details of experiment and explanation of results. Similar results were obtained later by other experimental groups with the differences defying any simple or apparent explanation, for example [2,3]. So, in spite of the long time passed since the first observation of the Tc differences, the problem is still remained open. This report is an attempt to present the qualitative explanation to the Tc differences observed in various geometries.
The Mossbauer effect in 57Fe can be detected by several different methods. All involve the resonant absorption of a 14.4 keV y-ray. The resulting excited nucleus can decay by emitting a 14.4 keV y-ray (10% probability) or by the internal conversion of an inner shell electron (90% probability). The internal conversion process produces a 7.3 keV electron, 6.3 keV x-ray and, with lower probability, a variety of lower energy Auger electrons and x-rays.
The traditional Mossbauer experiment is performed in a transmission geometry so that the decrease in the forward scattered 14.4 keV y-rays is observed. For this technique the effect size is always less than 40% and decreases linearly with thickness for thin samples (~1 ^m or less). As an alternative, the scattered 6.3 keV x-rays can be detected. The count rate is much lower but the effect size can be as large as 150%. (This entails minimizing the background by using a thin aluminum, teflon or lucite sample in the incident beam to filter out 6.3 keV x-rays from the source, and keeping other scattering surfaces in the experimental system to a minimum.) The scattered 14.4 keV y-rays can also be observed. However, the effect size is decreased due to the large internal conversion coefficient and scattering of nonresonant y-rays off the sample.
The scattered conversion and Auger electrons provide an additional method. It is possible to minimize the background so that as large as 600% can be observed. Since electrons with energies of a few keV are readily absorbed in matter, it is necessary to place the sample inside the detector so that only a surface layer of the of the sample (~300 nm) is observed.
While the effect size in the transmission geometry decreases rapidly with thickness, the effect size in the scattering geometry is relatively constant since the background and signal both decrease. In the electron case, where only the surface layer is observed in any case, the count rate does not vary much with thickness.
The Mossbauer effect in 57Fe involves recoilless absorption or emission of a 14.4 keV y-ray. This is a nuclear magnetic dipole transition between a - 3 / 2 excited state and the - 1 / 2 ground state with a lifetime of T = 1.1 * 10-7 s. The cross section has a Lorentzian shape
O(E) = Go ( 1 ) ( r / 2)2 + (E - Eo)2
where E0 is the transition energy and r is the linewidth. (Practically, the observed linewidth is at least twice the natural linewidth since it involves the convolution of the source and absorber lineshapes.)
In a magnetic material, the outer electrons of the iron atom are polarized, leading to a polarization of the s-electrons. This in turn produces an effective magnetic field Hz at the iron nucleus and a hyperfine Zeeman splitting with energy
E (mi) = - g P mi Hz, ( 2 )
where mI is the nuclear spin projection quantum number,and P is the nuclear magneton.
With the selection rules Am = 0 and ± 1, there are six allowed transitions for a given constant field Hz in iron. Ideally, the Mossbauer spectra of a ferromagnet should involve six lines, each corresponding to a transition, with the spacing proportional to the magnetization. This is usually the case if several conditions are commonly met. It is expected that ro^t > 1, where m = I g İP Hz is the Larmor frequency, so that the splitting is greater than the linewidth. In addition, it is necessary that the spin flip frequency M = 1 / Ts for the system be greater than wl and ros T > 1. As the temperature of a ferromagnet is increased, its order is decreased by the activation of spin wave and spin flip modes characterized by Ms. If the time for a spin change is longer than the precession time for the nuclear moment (m < m ) the value of Hz is not established. The field is chasing the spin orientation but does not catch it, so a single line results. This is known variously as superparamagnetism and motional line narrowing. For Mi ~ wl the spectra will have two components with one split out and the other narrowed to a single line. '
If MST < 1 the spin is quasi-stationary over the lifetime of the Mossbauer transition so that the field at the nucleus H has effectively constant orientation and magnitude. The orientation of H affects the amplitude but not the energy of the transitions. Under these conditions the spectra should have six lines but with a splitting which is temperature independent.
Figure 1.Simultaneous registration of Mossbauer effect in transmission-A, and scattering-B geometries. 1-pulse generator, 2-vibrator, 3-gamma source, 4- sample, 5-detectors, 6- preamplifier, 7-amplifier, 8-energy window, 9-analiser, 10-controller.
The splitting is temperature dependent for > 1 because the rapid spin flipping results in the transition averaging of the hyperfine field over time to produce an effective field at the nucleus. The splitting is proportional to the magnetization because time averaging of one nucleus and space averaging of the group of nuclei yield the same result
The experimental setup allowed spectra to be acquired simultaneously in transmission and scattering geometries (Fig. 1). By having the ability to collect data in both geometries without disturbing the sample, it was able to dismiss the possibility that any differences observed are the result of systematic errors in determining the absolute temperature.
Two Pd-Fe alloy foils, of thickness l0 pm and 25 pm, have been observed. They were annealed after rolling to remove strains. Each was fabricated with iron isotopically enriched to 50 % 57Fe and had a 14.4 at.% iron concentration. Pd-Fe alloys of this composition have a convenient magnetic ordering temperature just above room temperature. Heating was provided by a heat lamp directed at the sample. The thermistor and a copper-constantan thermocouple used as temperature sensors were attached to the sample by conductive solder and were situated so that they were not directly illuminated by the lamp.
Figure 2. The first setup for scattering-transmission anomaly experiment
Two experimental configurations were used. In setup 1. (Fig.2) a Pd-Fe foil was mounted at 45° to the incident 14.4 keV y-rays. Two proportional counters were arranged so that spectra can be simultaneously obtained in scattering and transmission geometries. The scattering detector was situated at 90° to the incident y-rays and was adjusted for 6.3 keV x-rays. The transmission detector was set up for a conventional 14.4 keV y-ray experiment . The heat lamp was set to illuminate the side of the sample away from the scattering detector.
Figure 3. The second setup for scattering-transmission anomaly experiment
In setup 2 ( Fig.3), the foil is mounted inside a flow proportional counter. By using either a mixture of 90% argon - 10% methane or 90% helium - 10% methane for the counter gas, one can detect respectively, either the 6.3 keV conversion x-rays or the conversion electrons. The counter was situated so that it detected the x-rays or electrons scattered backwards through 2n solid angle. The counter was optically thin for 14.4 keV y-rays so that a detector situated behind it can simultaneously be used in the transmission geometry. The whole flow counter was maintained at the desired temperature by the temperature control system.
A series of runs on the 25 pm thick foil were made using setup 1 to compare scattering and transmission spectra at various temperatures (Fig.4). Below 309 K the scattering and transmission spectra, each of which show magnetic splitting, had similar behaviour. However, between 309 K and 313 K, where the hyperfine splitting collapses and the individual spectral lines are not resolved, the character of the scattering and transmission spectra differ significantly. The scattering spectra show narrower linewidths than the corresponding transmission spectra. Inferring the hyperfine field from the overall linewidths, the transmission data indicates an ordering temperature of 313 K (Fig.5). The more rapid collapse of the scattering spectra with increasing temperature suggests a lower critical temperature of 310.5 K. Above 313 K the spectra for both geometries are a single lines with comparable linewidths.
Figure 4. Mossbauer spectra for Pd-Fe alloy sample with 14.4 at.% iron obtained in transmission geometry for 14.4 keV y-rays and scattering geometry for 6.3 keV x- rays. First experimental setup.
Figure 5. Effective hyperfine field versus temperature for Pd-Fe alloy sample in the first experimental setup
The lü^m foil was also observed in this configuration in transmission and in scattering with both the 6.3 keV x-ray and the 14.4 keV y-ray. Again near the critical temperature 6.3 keV scattering spectra have significantly narrower linewidths than the transmission spectra. The 14.4 keV scattering spectra have a lineshape comparable to, but slightly broader than, the 6.3 keV scattering spectra.
Figure 6. Mossbauer spectra obtained 1 K below Tc using: 1-conversion electron scattering, 2 6.3 keV x-ray scattering, 3-transmission geometry. Above Tc the linewidths in all three geometries are found to be 0.58 mm/s. (Second experimental setup)
The l0|im Pd-Fe foil was again observed in setup 2. Near the ordering tempera-ture, the spectra from the scattered conversion electrons show a slightly narrower linewidth than the corresponding transmission spectra (Fig. 6). The linewidths for the scattered 6.3 keV x-rays observed in this configuration are much narrower than the corresponding spectra from the conversion electrons. Away from the critical temperature region, the corresponding transmission and scattering spectra had identical behaviour.
The significant features of the anomaly can be summarized as follows:
a) . Differences have been observed between transmission and scattering lineshapes, with the transmission data acting in the conventional manner of a collapsing six-line hyperfine splitting.
b) . The difference in lineshapes is only observed near the critical temperature - in our case, the anomaly is seen only been 0.9 Tc and Tc.
c) . The scattering spectra show smaller effective hyperfine fields than those in transmission, due apparently to the presence of an unsplit component which increases in relative size close to the critical temperature.
d) . The anomaly is observed in scattering data for the 14.4 keV y-ray, the 6.3 keV x-ray and the internal conversion electrons. It is more prominent in 6.3 keV x-rays observed at 90° to the incident y-rays than in those which are backscattered. It is also more prominent in the 6.3 keV x-ray data than in that of the conversion electrons.
Trivial explanations such as thermal gradients can be ruled out. The apparatus in setup 1 was arranged so that the scattering and transmission detectors observed the same portion of the sample. Further, with the heat lamp illuminating the opposite side of the sample from the scattering detector, any thermal gradient should cause the scattering data to appear "colder" than the corresponding transmission data. But this would cause the scattering data to collapse more slowly, which is the opposite of what is observed. The simultaneous nature of the observations in the two geometries precludes systematic variations in temperature with time.
The fact that the anomaly is more prominent in the 6.3 keV scattering data than in the conversion electron data rules out the possibility that it is due to a surface phenomena. For Pd- Fe alloy foils of the thickness used, the 6.3 keV x-rays detected in scattering can come from anywhere within the thickness of the sample. However, because of their high cross-section, only conversion electrons produced within a 300 nm of the surface have a good probability of escaping and being detected. A surface phenomenon thus should be more prominent in the spectra for the conversion electrons and this is not observed.
The anomalous behaviour might be the result of interference, particularly between transitions with energies that overlap near the critical temperature. This would explain why the anomaly occurs only in the critical region as this is the only place where significant overlap occurs. An interference explanation would also predict that the scattering spectra should have an angular dependence. This is consistent with the anomaly being more prominent for the 6 keV x-rays detected at 90° than for those detected in backscattering since the latter technique integrates over a large solid angle. Also, the conversion electron data, as observed, should be closer to the transmission data than the 6.3 keV x-rays since effectively all directional information is lost by the electrons getting out of the sample. However, this explanation should be also ruled out For interference to successfully explain the anomaly, it is necessary to justify why the 6.3 keV x-rays should be coherent, which is not the case. It would be clear if the experiment involve the 14.4 keV y-rays only, in both scattering and transmission, but, as noted before, these are more difficult to observe in scattering.
Lineshapes, such as those observed in the scattering spectra for the 6.3 keV x-rays, are similar to those resulting from relaxation phenomena or superparamagnetism. For this to be the cause of the anomaly, the electron spin-flip frequency ms would have to be comparable to 1/Tsc, where Tsc is the mean lifetime of the scattering process. Since the transmission lineshapes have no unsplit
component below Tc, it is true that > 1 where Ta is the lifetime of the absorption process. This would imply Ta > Tsc.
An explanation based on a relaxation mechanism would have to explain why msT > 1 ~ ffltTsc near the critical temperature while mSTa > 1 and msTsc > 1 for temperatures below 0.9 Tc. Theory predicts that m increases to a singularity at Tc for a ferromagnet so this could only result if a mechanism can be found by which the lifetime for the scattering process increases near the critical temperature [4]. Such a mechanism would have to differentiate between the scattering and transmission lifetimes.
According to the Uncertainty principle the linewidth of the Lorentzian distribution is related to the lifetime as T = h/2nr. The wider the linewidth, the shorter the lifetime of the excited state. Beam with the Lorentzian distribution in energy consists of quanta whose energy have values symmetrically distributed around the resonant energy E0. When the resonant beam falls on an absorber, quanta with the various energies are absorbed there differently. Quanta with the energy equal to E0 are absorbed with a higher probability than those on the wings of the distribution. As a result, most of them are absorbed at the layers close to the very front surface of a sample.
As the beam propagates deeper in an absorber, amount of quanta with the energy E0 decreases. Most of quanta in more deep layers have now the energy not exactly resonant, but close to it E0 ± AE. Correspondingly, most of the absorbed quanta here are related to the wings of the distribution. The further away from the front surface, the more is the value of AE. Due to the different cross section of an absorption, the spectral distribution of the beam begin to broaden and cease to be the Lorentzian at the rear side of an absorber.
Figure 7.Spectral distribution of the resonant quanta at the rear side of an absorber versus its thickness
The spectral distribution of the beam is a function of the thickness of an absorber. The calculations show that if p.t > 2, then the Lorentzian distribution of an initial beam coming from the source transforms into the complicated curve with the deep on the E0, instead of peak [5]. The deeper is the layer in an absorber, the more is the role of the wings (Fig.7). And the more the AE, the shorter the lifetime. Thus, certain lifetime of the excitation corresponds to each layer. Since the initial resonant distribution is always Lorentzian, one should talk only in terms of an effective lifetimes of the excited nuclear levels.
Mean free path of each kind of radiation, that is 14.4 keV y-rays, 6.3 keV x-rays and conversion electrons are different. Hence, they come out of an absorber from different depths [6]. Thus, to each method of detection should correspond certain range of energies of the absorbed quanta, effective lifetimes and, consequently the measured values of the Curie temperatures.
The relations between the Ts and T, should be valid only in the critical region, where the role of the spin fluctuations is decisive. Below the critical region the spin-wave time average ceased to be itself time dependent. The role of the spin fluctuations falls down. The static collective viewpoint becomes valid and, hence, the differences in the Curie temperatures could not be observed any more. The critical regions of the ordered magnets are usually very narrow, about the fractions of degree. Maximum difference in the Curie temperatures could not exceed the temperature interval of the critical range. That is why it is impossible to observe the big differences in the measured values of Curie temperatures in the ordered magnets, even if they are measured by various physical methods, with their much more differing time scales. In Pd-Fe alloy the differences are ~ 2,5 K. This relatively big difference is the result of the disordered magnetic structure of the Pd-Fe alloy, which has the noticeable spin-glass properties, causing relatively wide critical region of the bulk specimen.
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