have a metallic bond character and electrons form ... annihilation is realized at the d electron shells and valence electrons of the crystalline phase nuclei.
ISSN 10274510, Journal of Surface Investigation. Xray, Synchrotron and Neutron Techniques, 2010, Vol. 4, No. 4, pp. 609–613. © Pleiades Publishing, Ltd., 2010. Original Russian Text © Yu.V. Funtikov, O.V. Prokopjev, N.O. Khmelevsky, O.V. Ilyukhina, V.S. Khmelevskaya, K.A. Gorchakov, V.I. Grafutin, 2010, published in Poverkhnost’. Rentgenovskie, Sinkhrotronnye i Neitronnye Issledovaniya, No. 7, pp. 80–84.
Electron Transport Properties of IronBased Amorphous Alloys under Crystallization Yu. V. Funtikova, O. V. Prokopjeva, N. O. Khmelevskya, O. V. Ilyukhinaa, V. S. Khmelevskayab, K. A. Gorchakovb, and V. I. Grafutina aInstitute
of Theoretical and Experimental Physics, Moscow, Russia Obninsk State Technical University of Nuclear Power Engineering, Obninsk, Russia
b
Received June 15, 2009
Abstract—The changes in the electron properties of amorphous alloys of the iron–boron system under crys tallization have been studied by the angular distribution of annihilation photons, the temperature dependence of thermal emf, and Mössbauer spectroscopy. The obtained qualitative estimates allow us to draw conclusions about some features of metallic bond in the amorphous crystalline state, in particular, to propose that positron annihilation is realized at the d electron shells and valence electrons of the crystalline phase nuclei. DOI: 10.1134/S1027451010040129
INTRODUCTION Amorphous alloys are of apparent practical interest and have quickly become part of technological prac tice. At the same time, our knowledge of their nature, including the electron structure, is currently obviously poor. Although most investigations suggests that they have a metallic bond character and electrons form degenerated Fermi gas, the natures of the bond and transport processes in them have substantial features as compared to the crystalline analogs. As is known, the structure of amorphous materials (AMs) in contrast to crystals has only a shortrange order and, as a result of disordering, the electrical resistivity is large and has a small temperature coeffi cient that can have positive, negative, or close to zero values [1–3]. In addition, the mean free path of electrons in these systems is of the order of the interatomic dis tance (0.3–0.5 nm) because of a high degree of disor dering, which also introduces corrections into the electron transport processes—namely, electron anni hilation is probable. In the present work, alloys of the Fe–Cr–B system, which is most used in engineering, were taken as the object of investigation. The changes in the electron subsystem under crystallization of amorphous alloys were estimated by three different methods of metallo physical experiment: thermal emf measurements, M[umlaut]ossbauer spectroscopy (nuclear gamma resonance), and electron–positron annihilation. EXPERIMENTAL The amorphous alloy FeCr18B15 was prepared by the standard spinning method in the form of ribbon samples 20 µm thick and 20 mm in width. The samples
were investigated using a DRON2.0 diffractometer with computer recording and processing of the results. As is seen in Fig. 1, the initial samples were amorphous (halo in the diffraction patterns). Then the samples were annealed at different temperatures for 1 h in vac uum 10–4 Pa. In this case the diffraction peaks appeared against the halo background; the width of peaks decreased with an increase in the annealing temperature, which testifies to an increase in the coherentscattering region (CSR) and the size of the nuclei of the crystalline phase integrated into the amorphous matrix. The samples were investigated by the thermal emf method. It is known that this method is quite sensible to conduction electron scattering and these measure ments can give real information about transport phe nomena. However, every so often it is difficult to eval uate completely the nature of concrete changes in the electron subsystem because of the complexity of the laws of interaction of electrons with phonons and impurity atoms and because of difficulties in the sepa ration of diffusion thermal emf and the phonon drag effect [4–7]. There are two methods of thermal emf measure ment, differential and integral. In the given experi ment, the integral method of measurement was used. The unit was installed on the basis of a microhardness tester, and an indenter was replaced by a tungsten nee dle inserted inside a microfurnace. A needle was touched with the investigated sample surface (hot junction). It is considered [6] that the absolute thermal emf coefficient S = –dE/dT, which can be determined by the slope of the temperature dependence of thermal emf (Е(T)) for the given temperature of measurement, correlates with the density of states on the Fermi sur
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50
55
60
65
70
75
80
85
90 2θ, deg
Fig. 1. Diffraction pattern of the initial amorphous alloy.
face and can be used for estimation of changes in the electron subsystem of the material. In addition, the materials were investigated by gammaray absorption and conversion electron M[umlaut]ossbauer spectroscopy [8–10]. A gamma resonance spectrum is the dependence of the intensity of gammaray quanta emitted by a source and transmitted through an absorber or scattered by it on an arbitrary velocity of a source or an absorber. The isomer shift of the line (δ) is determined from the NGR (M[umlaut]ossbauer) spectrum as the posi tion of the center of absorption line (in velocity units) relative to the line of the standard absorber. The appearance of the isomer shift is associated with the difference in the local chemical environment of the emitting and absorbing nuclei. The s electron density at both nuclei (i.e., at the points where both nuclei are placed) proves to be different, and the different Cou lomb interaction of a nucleus with electrons leads to shift of the resonance energy. An increase in the positive value of isomer shift (δ) for iron ions means a decrease in the s electron density at the absorber nucleus. To implement the selection over the alloy depth, the M[umlaut]ossbauer spectra were measured in the backscattering geometry with the recording of conver sion electrons or К characteristic Xrays. When the resonance conversion electrons are recorded, infor mation on the depth of an order of 0.3 µm from the surface is obtained and, in the case of recording sec ondary resonance Xrays, on the depth of ~15 µm. Since a rigorous theory of metallic bonds is absent, the consideration of electron structures and discussion of the bond character based on M[umlaut]ossbauer spectra are mainly qualitative. The spectra of angular distribution of annihilation photons (ADAP)were also measured. Since a positron coming into a solid is thermalized for a time of the
order of 10–12 s, whereas the annihilation characteris tic time is two orders of magnitude larger, this spec trum gives an indication of the momentum distribu tion of electrons surrounding a positron. Since the atomic cores in metal have a positive charge, then positrons annihilate mainly by two channels, on valence electrons and core electrons, i.e. on electrons of upper shells of the atomic cores. In this case, several components are observed in the ADAP spectra, giving an indication of annihilation channels. A detailed description of a unit and the theory of the method are given in [11, 12]. The interpretation of the ADAP spectra, except for simple metals, is ambiguous, requires theoretical prerequisites, and becomes com plicated by the fact that a positron polarizes a medium and takes electrons, which complicates the determina tion of the electron concentration but, however, does not change the momentum distribution. RESULTS AND DISCUSSION Samples of amorphous alloys were annealed at dif ferent temperatures (400–700°С) for 1 h, and their diffraction pattern substantially changes (Fig. 1). Dis crete diffraction maxima appeared after annealing at 500°С against the background of a halo obtained for the initial sample. Identification of the peaks showed that they belong to the nuclei of the metallic solid solution (probably to Fe–Cr); in addition to these lines, there are peaks of metastable boride Fe3B. These lines appeared after annealing at temperatures of 400– 550°С. However, the peaks of metastable boride disap pear at 600°С and only lines of a solid solution are present in the diffraction pattern. It is clearly observed that the line width of a solid solution notably decreases with an increase in the annealing temperature, which testifies to growth of nucleus size. The line width of boride (and, consequently, the size of precipitates) varies slightly. Thus, one can state that the metastable
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ELECTRON TRANSPORT PROPERTIES OF IRONBASED AMORPHOUS ALLOYS I, arb. units
FeCr FeCr FeB FeB
(FeCr)
Fe3B Fe3B
400°С
FeCr FeB FeCr FeB
FeCr
Fe3B
Fe3B
450°С FeCr FeB FeCr FeB FeCr
Fe3B Fe3B
500°С FeCr FeB FeCr FeCr FeB FeB
FeCr
Fe3B Fe3B
550°С
600°С FeCr FeB
FeCr
650°С
FeCr FeB FeCr
700°С 55
60
65
70
75 80
400 450 500 550 Tann 600 650 700 inn 0
50
100
150
200 250 tmeas, °C
Fig. 3. Thermal emf in the initial amorphous alloy and after annealing at different temperatures.
FeCr
50
E, mV 0.4 0.2 0 –0.2 –0.4 –0.6 –0.8 –1.0 –1.2 –1.4 –1.6 –1.8 –2.0 –2.2 –2.4
611
85 90 2θ, deg
Fig. 2. Xray diffraction after annealing of the amorphous alloy at different temperatures.
atom groups participate in crystallization at the first stage with the participation of boron. The temperature dependence of thermal emf was measured in parallel. The results of primary measure ments of E(T) are shown in Fig. 3; the absolute thermal emf coefficient (S) can be determined by the slope of curves. It is seen that notable changes in the electron subsystem occur with the onset of crystallization; the points for the initial sample are in a negative range of values and have a linear dependence on the measure ment temperature for a certain approximation, as is usually observed for metallic materials. The slope sharply changes with the onset of crystallization (it is close to zero), and the difference between the samples after annealing at different temperatures is insignificant. The investigations of M[umlaut]ossbauer spectra have shown [13, 14] that irreversible changes take place still in the region of the amorphous state in the alloy. As a result of these changes, regions of precipi tates similar to the crystalline phases of this alloy, according to the M[umlaut]ossbauer spectra, are formed, but with a much greater value of isomer shift. This testifies to a decrease in the electron density at the nucleus of iron atoms under crystallization. The ADAP measurements were carried out using a unit at the Institute of Theoretical and Experimental Physics. The spectra were processed by a computer to separate their components. In spite of the fact that the correlation factor taking into account the polarization effect of electron gas is larger for valence electrons by more than twofold, it proved to be impossible to isolate the spectrum component representing free electron gas in the amorphous sample. This allows us to assume that electrons with a metallic bond forming degener ated gas are not observed in the samples of amorphous
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FUNTIKOV et al. Count 20000 Fe–Cr–B
0.16 18000
0.12
Fe–Cr–B700n
R/S
0.08
16000 Fe–Cr–B600n
0.04 14000
Fe–Cr–B500n
0 Fe Fe Fe Fe Fe Fe CrB Cr Cr Cr Cr B B B B 450 500 600 700
12000 Fe–Cr–B450n 10000
Feн
8000
Crн
6000 4000 2000 –30
–25
–20
–15
–10
–5
0
5
10
15
20 25 Angle, mrad
Fig. 4. ADAP measurements of the initial amorphous alloy and after annealing at different temperatures.
alloy of the Fe–Cr–B system. It appears that annihi lation mainly occurs at electrons of the d shell. In the samples annealed at temperatures of 500°С and higher, an inverted parabola is observed that conforms to the presence of free electron gas with the Fermi dis tribution the parameters of which comply with the parameters of an Fe–Cr metallic alloy known in [15]. The ADAP spectra of the samples annealed at a tem perature of 500°С or higher have no cardinal differ ences. Thermal emf does not differ qualitatively, which allows us to assume that there are thermally active hops between nuclei of the metallic phase as a conduc tion mechanism for amorphous samples and a sharp change in conduction as a result of a decrease in the distance between nuclei down to the scale at which the energy necessary for tunneling between particles is comparable to the Fermi energy [16]. A narrow component with an intensity of several percent is observed in the annealed samples and is not observed in the samples of pure iron, chromium, and amorphous alloy. This can be explained by the pres ence of free space and by positronium formation— namely, quasistable formation consisting of an elec tron and positron in a pore with a characteristic size of the order of 4–5 Å. The spectra normalized to the area are shown in Fig. 4. The change in the R/S parameter (the ration of the area under the central part of the spectrum to the tails) is shown in the right corner of the diagram. Since the strongly localized electrons of the d shells have
high momentum and valence electrons have low, the large value of this parameter means a low annihilation probability at s electrons both localized and in the form of gas. CONCLUSIONS The features of the changes in the electron struc ture under thermally activated crystallization have been studied by the angular distribution of annihila tion photons, the temperature dependence of thermal emf, and nuclear gamma resonance (M[umlaut]oss bauer spectroscopy). The results of experiments allow us to assume that degenerated electron gas is not formed in amorphous Fe–Cr–B alloys. Fe–Cr nuclei with a metallic bond are formed under fractional crys tallization. ACKNOWLEDGMENTS The work was supported by the Rusatom state cor poration. REFERENCES 1. J. L. Black, Metallic Glasses 1, Ed. by H. J. Guntherodt and H. Beck (Springer, New York, 1980), pp. 167–189. 2. J. H. Mooij, Phys. Stat. Solidi A 17, 521 (1973). 3. N. F. Mott, MetalInsulator Transitions (Nauka, Mos cow, 1979; Taylor Francis, London, 1974).
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ELECTRON TRANSPORT PROPERTIES OF IRONBASED AMORPHOUS ALLOYS 4. P. J. Cote and L. V. Meisel, Phys. Rev. B 20, 3030–3035 (1979). 5. M. N. Baibich, W. B. Muir, G. Belanger, et al., Phys. Lett. A 73, 328–330 (1979). 6. J. Ziman, Electrons and Photons (Clarendon, Oxford, 1960; Inostr. Liter., Moscow, 1962). 7. F. J. Blatt, P. A. Schroeder, C. L. Foiles, D. Greig, Thermoelectric Power of Metals (Plenum, New York, London, 1976; Metallurgiya, Moscow, 1980). 8. G. Principi, C. Tosello, E. Kuzmann, et al., Mat. Sci. Forum 87–99, 393 (1992). 9. E. Kuzmann, M. LakatosVarsanyi, et al., Electro chem. Commun. 2, 130 (2000). 10. A. A. Kiselev, R. N. Kuz’min, and A. A. Novakova, Pis’ma Zh. Tekh. Fiz. 12 (1), 32 (1986)[Sov. Tech. Phys. Lett. 12, 14 (1986)].
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11. A. A. Novakova, D. S. Golubok, V. S. Khmelevskaya, et al., in Proc. of the 9th Conf. on Structure Principles of Material Modification by Original Technology Methods (IATE, Obninsk, 2005), p. 89. 12. A. A. Novakova, G. A. Syrotynina, V. I. Kyrko, et al., Hyperfine Interact. 69, 663 (1991). 13. V. I. Grafutin and E. P. Prokop’ev, Usp. Fiz. Nauk 172, 67–83 (2002) [Phys. Usp. 45, 59 (2002)]. 14. S. Berko and J. Mader, Appl. Phys. 5, 287–306 (1975). 15. J. Chojcan and M. Szuszkiewicz, Phys. Scr. 36, 820– 823 (1987). 16. N. Mott and E. Davis, Electronic Processes in Non Crystalline Materials (Clarendon, Oxford, 1971; Mir, Moscow, 1982).
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