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Electronic structure of quasi-crystalline AlMn in comparison with amorphous and crystalline alloys
Materials Science and Engineering, 99 (1988) 361 365
361
Electronic Structure of Quasi-crystalline AIMn in Comparison with Amorphous and Crystalline Alloys* J. M. FRIGERIO and A. MEDDOUR Laboratoire d'Optique des Solides, UA CNRS 781, Universitb Pierre et Marie Curie, 4place Jussieu, 75252 Paris Ckdex 05 (France)
A. PEREZ, M. G. BLANCHIN and J. P. DUPIN Dbpartement de Physique des Mat~riaux, UA CNRS 172, Universitb Claude Bernard, 69622 Villeurbanne (France)
J. RIVORY Laboratoire d'Optique des Solides, UA CNRS 781, Universitk Pierre et Marie Curie, 4 place Jussieu, 75252 Paris C~dex 05, and Dbparternent de Physique des Mat~riaux, UA CNRS 172, Universitb Claude Bernard, 69622 Villeurbanne (France)
Abstract Mixing o f Al/Mn multilayers by xenon ions o f 5 0 0 k e V allows amorphous or single-phase quasicrystalline samples to be obtained for manganese concentrations below 20at. % depending on the substrate temperature during the mixing; at higher manganese concentrations, complex crystalline phases are found. The optical conductivity is determined from reflectance and~or ellipsometric measurements in the energy range from O.5 to 6 e V and is shown to be very sensitive to the atomic structure. All spectra are strongly dominated by the manganese d states. No drastic differences are observed between the amorphous and the icosahedral states in samples with 19at. % Mn. Differences found in samples with the global composition lOat. % Mn are more probably due to the presence o f an aluminium phase and to the changes in the density o f states o f the amorphous phase with manganese concentration.
1. Introduction Several years ago, it was shown that metallic glasses exhibit icosahedral short-range order [1]. Frank-Kasper crystalline phases have been described as a periodic packing of truncated icosahedra [2]. A third phase, in which icosahedral symmetry is observed, is the quasi-crystalline phase, first reported by Shechtman et al. [3] in AI-Mn. This aperiodic phase is characterized by long-range orientational order; it can be produced by the melt-spinning process and by other rapid quenching techniques [4-6]. In this paper, we use sputtering followed by ion beam mixing
*Paper presented at the Sixth International Conference on Rapidly Quenched Metals, Montreal, August 3-7, 1987. 0025-5416/88/$3.50
to produce A1Mn thin films in amorphous, quasicrystalline and crystalline states with good surface quality, suitable for optical measurements. Attempts are made to understand the relationship between the electronic properties of these different structural states.
2. Experimental procedure Alternate layers of aluminium and manganese were deposited by sputtering on amorphous silica, NaCI and carbon substrates using two pairs of layers for a total thickness of about 500/~. The ratio of aluminium to manganese layer thicknesses was adjusted to vary the manganese concentration from 10 to 25 at.%. The layers were ion beam mixed with a 500 keV Xe + beam to a fluence of 1 x 1016 Xe cm -2 at liquid nitrogen temperature or at 150 °C. The composition, the impurity content and the mixing efficiency were checked using Rutherford backscattering analysis (RBS) with 2 MeV ~t particles. Figure 1 shows RBS spectra before and after mixing for an initial stack containing 10 at.% Mn. Before mixing, the two manganese layers are well resolved, while the two aluminium layers, separated by only 25-30/~ of manganese, are not resolved. After mixing, only one wide manganese peak is observed. The Xe ÷ dose is evaluated as well as the manganese concentration, which has decreased by about 1% owing to sputtering effects. In our experimental conditions, most of the Xe ÷ comes to rest in the substrate.
3. Structural studies The atomic structure was examined by transmission electron microscopy (TEM). Our findings are in agreement with the results of Knapp and Follstaedt [5, 7]. © Elsevier Sequoia/Printed in The Netherlands
362
q
A1
bin
Channels" Fig. 1. RBS analysis of a sample containing 10 at.% Mn: spectrum a, before mixing; spectrum b, after mixing with a 500 keV Xe + beam to a fluence of I × 1016 Xe c m - z . Ion beam mixing at 150 °C results in the icosahedral phase for manganese concentrations from 10 to 20 at.%. Figures 2(a) and 2(b) show TEM diffraction patterns (taken at 100 kV) for samples with I0 and 19 at.%. The icosahedral phase was identified by its powder diffraction pattern, all rings of which matched with spacings and relative intensities already reported [8]. At lower manganese contents, f.c.c, aluminium lines were also present. Dark field images indicate that
l I
I
II
I I
II
Fig. 3. Opticaldiffractionpatternofanicosahedralgrainshowing the twofold symmetry (alloy with 19 at.% Mn mixed at 150 °C). the icosahedral grains are 100-300/~ in diameter. Careful examination of the 19 at. % Mn sample with a high resolution microscope (Jeol 200 CX) operated at 200 kV allowed such icosahedral grains to be isolated in a few cases. Figure 3 shows an example of a twofold optical diffraction pattern from such a grain. Mixing at 77 K provided samples in the amorphous state. At high manganese concentrations (1620 at.%), the amorphous phase is the only phase detected (Fig. 2(c)). At about 10 at.%, f.c.c, aluminium lines are also observed (Fig. 2(d)). Mixing of layers with 24 at.% Mn produced a b.c.c, metastable phase previously identified by K n a p p and Follstaedt [7] (called by them the F phase). Its diffraction pattern is shown in Fig. 4.
•
AI V
..-i O er.. O E ¢Q Fig. 2. Electron diffraction patterns observed in samples mixed with 1 x 1016 Xe cm 2 for two manganese concentrations and two temperatures: (a) alloy with 10 at.% Mn mixed at 150 °C showing f.c.c, aluminium and icosahedral rings; (b) alloy with 19 at.% Mn mixed at 150 '~Cconsisting of only the icosahedral phase; (c) alloy with 19 at.% Mn mixed at - 196 °C consisting of an amorphous phase; (d) alloy with 10 at.% Mn mixed at - 196 °C showing amorphous phase halos and f.c.c, aluminium rings.
Fig. 4. Electron diffraction pattern of a 24at.% Mn sample consistingof the b.c.c, metastable crystallineF phase as identified by Knapp and Follstaedt [7].
363
4. Optical properties Optical measurements were performed on samples deposited on silica substrates. Reflectance measurements between 0.5 and 6.2 eV and ellipsometric measurements between 1.5 and 5.4eV were used to calculate the optical conductivity of the A1Mn alloys; the film thickness was determined by X-ray interference fringes at grazing incidence [9]. One advantage of the ion beam mixing method of preparation is the production, for appropriate manganese concentrations, of single-phase material in an amorphous (A) or icosahedral (I) state; therefore it is particularly interesting to investigate the relationship between the two phases in the sample containing 19 at.% M n. Figure 5 displays the reflectivity of the A and the I phases obtained from two AI/Mn stacks containing 19 at.% Mn sputtered together, the first mixed at - 1 9 6 °C and the second at 150°C. The reftectivity is shown to be very sensitive to the atomic structure. Indeed, the curves are close to each other up to 1.8 eV; they diverge at higher energies but no new structure appears in the I phase. The optical conductivity calculated by the Kramers-Kronig transformation from the curves of Fig. 5 is reported on Fig. 6 together with that of pure manganese [ 10]. The spectrum corresponding to the I state presents two well-defined peaks at 0.8 and 2.4 eV. The curve corresponding to the A state shows also two peaks in the same spectral ranges but the oscillator strength of the transition at 2.4 eV is wider than in the I state. The peak at low energy is less pronounced, its small shift is probably not significant and it has to be confirmed with measurements at lower energy. Both spectra are dominated by the manganese d states. Strong similitudes to pure manganese are observed, at energies up to 4 eV, but at higher energies the conductivity of the
--
6
• .. Nn
5
--
(I)
C ~
o
°
(A)
°
4 H o
3
§
2
rJ H
t 0
1
2
3
4
ENERGY
5
6
(e.v.)
Fig. 6. Optical conductivity of the 19 at.% Mn alloy in the A and I states. The pure manganese spectrum [ 10] is shown for comparison. A and the I phases decreases, indicating that the partial manganese d density of states is reduced on the high binding energy side. In samples with a lower manganese concentration, the A or the I phase coexists with aluminium or the A I - M n solid solution. Optical properties are able to throw light on the contribution of each phase. It is necessary, first, to describe again the main features of the optical conductivity of pure aluminium (Fig. 7). It exhibits a monotonic decrease with increasing energy, on which a well-defined peak at 1.6 eV is superimposed. The first contribution is due to intraband transitions of the conduction electrons (Drude term), and the peak is due to interband transitions between s-p parallel bands near the limit of the Brillouin zone at W. This peak is particularly sensitive to the disorder: its intensity decreases as the grain size decreases; it disappears in films deposited at 20 K [ 11]. In Fig. 7, on the curve corresponding to the mixture of alu-
"7, --" A1 0.9
i --=a~ o
0.8 0.7
5
: .. ".
-- A1 + (I) -- A1 + (A) ...-.
4
0.6
3
0.5 0.4 0.3
(A]
0.2
"'-...°
~'-
0.1 0.0
o6 !
2
3 ENERGY
4
5
6
(e.V.)
Fig. 5. Reflectivity v s . energy of the 19 at.% Mn alloy in the A and the I states.
i
~
''~'
~ ENERGY
......
~
(e.V.)
Fig. 7. Optical conductivity of the 10 at.% Mn alloy mixed at 150 °C (A1 + I phase) and at - 196 °C (AI + A phase). The pure aluminium spectrum is shown for comparison.
364
B u
"I' o 4
3
z 2
o 0
1
2
3
ENERGY
4
5
B
(e.V.)
Fig. 8. Optical conductivity of the 24 at.% Mn alloy containing the crystalline metastable F phase.
minium and I phase (10 at.% Mn overall), we recognize the peak at 1.6 eV existing in pure aluminium together with the high energy peak of the I phase as observed in the sample with 19 at.% Mn. The low energy peak of the I phase is probably screened out by the Drude contribution. Significant differences are observed for the mixture of aluminium and A phase. The 1.6 eV peak is no longer observed, and a broad peak emerges around 2 eV from the manganese partial d density of states in the A phase. The presence of the aluminium interband contribution at 1.6 eV proves that the crystalline aluminium phase has a texture in the presence of the I phase; this relation is destroyed by disorder in the presence of the A phase. For manganese concentrations higher than 20 at.% (24 at.% in our example), a new metastable crystalline phase (the F phase) is formed by ion mixing. Its conductivity spectrum exhibits the two-peak shape already observed in the I phase. However, the intensity of the first peak is increased in the F phase and both peaks are shifted towards higher energies by about 0.5 eV with respect to the I phase (Fig. 8). 5. Discussion and conclusion
In crystalline materials, such as pure aluminium and pure manganese, the peaks observed in the optical conductivity spectra are unambiguously attributed to band structure effects, i.e. to interband transitions in extended regions of the Brillouin zone. When the momentum conservation rule is relaxed (this is obviously the case in disordered materials), the optical conductivity can be written as a simple convolution of the initial and final densities of states n(E): E F + hto
tr(co) oc o9 - 1
| el EF
n ( E ) n ( E - hto) d E
Although the optical spectrum of the pure aluminium has been widely investigated and is well understood, this is not so in the case of pure manganese. No attribution of the peaks observed in the conductivity has been carried out; nevertheless, it can be guessed that they are related to transitions between maxima in the density of d states below and above EF or between a maximum and EF. In particular, in transition and noble metals the high binding energy peak (around 5 eV) originates from transitions starting from the bottom of the d band to EF. As underlined above, the spectra of the samples with 19 and 24at.% Mn are dominated by the manganese d states; their behaviours favour an asymmetrical narrowing of the d density of states with respect to pure manganese. Because in the I phase the manganese concentration is thought to remain unchanged, it is not surprising to find in samples at 10 and 19. at.% Mn the same peak position at 2.4 eV. The low energy peak at 0.8 eV clearly seen in the 19 at.% Mn sample is probably masked in the 10 at.% Mn sample (mixture of aluminium and I phase) by the strong contribution of conduction electrons in the aluminium phase. By contrast, one observes a change in the position and the shape of the manganese d states contribution to the optical conductivity of the A phase as a function of the composition. Indeed, as the manganese concentration decreases, the peak initially centred at 2.4 eV moves towards lower energy at about 2 eV as a consequence of the change in the local environment of the manganese atoms. This view is supported by optical measurements performed on fully amorphous sampies obtained by sputtering or co-evaporation. In summary, we have observed comparatively similar optical spectra in I and A phases in single-phase samples with about 19 at.% Mn. Differences found in samples containing two phases with an overall concentration of about 10 at.% Mn are probably due to differences in the manganese concentration in the I and the A phases. In the above discussion, we have neglected an important feature of the electronic structure of metallic alloys: the role played by the hybridization between the aluminium s-p states and the manganese d states. Its role has been emphasized by the calculation of Deutz et al. [ 12] performed for a manganese impurity in aluminium. The manganese impurities turn out to be magnetic and the virtual bound states show strong deviations from a lorentzian form arising from the band structure of aluminium. This calculation could be taken as a starting point for the interpretation of the optical properties of the solid solution A1Mn [ 13] and could also be applied to more concentrated alloys
365 as l o n g as a m a n g a n e s e a t o m h a s n o m a n g a n e s e nearest neighbours. The interpretation of our data a l o n g these lines is in progress.
References 1 Ph. Mangin, Les Amorphes M~talliques, Aussois, 1983, Editions de Physique, Paris, 1984, p. 175. P. J. Steinhardt, D. R. Nelson, M. Ronchetti, Phys. Rev. B, 28 (1983) 784. 2 G. Bergman, J. L. T. Waugh and L. Pauling, Aeta Crystallogr., I0 (1957) 254. P. Guyot and M. Audier, Philos. Mag. B, 52(1985) L15. 3 D. Shechtman, I. Blech, D. Gratias and J. W. Cahn, Phys. Rev. Lett., 53(1984) 1951.
4 K. Urban, N. Moser and M. Kronmiiller, Phys. Status Solidi A, 91 (1985) 411. 5 J. A. Knapp and D. M. Follstaedt, Phys. Rev. Lett., 55 (1985) 1591. 6 D. A. Lilienfeld, M. Nastasi, H. H. Johnson, D. G. Ast and J. W. Mayer, Phys. Rev. Lett., 55(1985) 1587. 7 J. A. Knapp and D. M. Follstaedt, Nucl. lnstrum. Methods Phys. Res. B, 19-20(1987) 611. 8 P. A. Bancel, P. A. Heiney, P. W. Stephens, A. I. Goldman and P. M. Horn, Phys. Rev. Lett., 54 (1985) 2422. 9 L. N6vot and P. Croce, Rev. Phys. Appl., 15 (1980) 761. 10 P. B. Johnson and R. N. Christy, Phys. Rev. B, 9 (1974) 5056. 11 L. G. Bernland, O. Hunderi and H. P. Myers, Phys. Rev. Lett., 31 (1973) 363. 12 J. Deutz, P. H. Dederichs and R. Zeller, J. Phys. F, 11 (1981) 1787. 13 D. Beaglehole and M. Wihl, J. Phys. F, 2(1972) 43.
361
Electronic Structure of Quasi-crystalline AIMn in Comparison with Amorphous and Crystalline Alloys* J. M. FRIGERIO and A. MEDDOUR Laboratoire d'Optique des Solides, UA CNRS 781, Universitb Pierre et Marie Curie, 4place Jussieu, 75252 Paris Ckdex 05 (France)
A. PEREZ, M. G. BLANCHIN and J. P. DUPIN Dbpartement de Physique des Mat~riaux, UA CNRS 172, Universitb Claude Bernard, 69622 Villeurbanne (France)
J. RIVORY Laboratoire d'Optique des Solides, UA CNRS 781, Universitk Pierre et Marie Curie, 4 place Jussieu, 75252 Paris C~dex 05, and Dbparternent de Physique des Mat~riaux, UA CNRS 172, Universitb Claude Bernard, 69622 Villeurbanne (France)
Abstract Mixing o f Al/Mn multilayers by xenon ions o f 5 0 0 k e V allows amorphous or single-phase quasicrystalline samples to be obtained for manganese concentrations below 20at. % depending on the substrate temperature during the mixing; at higher manganese concentrations, complex crystalline phases are found. The optical conductivity is determined from reflectance and~or ellipsometric measurements in the energy range from O.5 to 6 e V and is shown to be very sensitive to the atomic structure. All spectra are strongly dominated by the manganese d states. No drastic differences are observed between the amorphous and the icosahedral states in samples with 19at. % Mn. Differences found in samples with the global composition lOat. % Mn are more probably due to the presence o f an aluminium phase and to the changes in the density o f states o f the amorphous phase with manganese concentration.
1. Introduction Several years ago, it was shown that metallic glasses exhibit icosahedral short-range order [1]. Frank-Kasper crystalline phases have been described as a periodic packing of truncated icosahedra [2]. A third phase, in which icosahedral symmetry is observed, is the quasi-crystalline phase, first reported by Shechtman et al. [3] in AI-Mn. This aperiodic phase is characterized by long-range orientational order; it can be produced by the melt-spinning process and by other rapid quenching techniques [4-6]. In this paper, we use sputtering followed by ion beam mixing
*Paper presented at the Sixth International Conference on Rapidly Quenched Metals, Montreal, August 3-7, 1987. 0025-5416/88/$3.50
to produce A1Mn thin films in amorphous, quasicrystalline and crystalline states with good surface quality, suitable for optical measurements. Attempts are made to understand the relationship between the electronic properties of these different structural states.
2. Experimental procedure Alternate layers of aluminium and manganese were deposited by sputtering on amorphous silica, NaCI and carbon substrates using two pairs of layers for a total thickness of about 500/~. The ratio of aluminium to manganese layer thicknesses was adjusted to vary the manganese concentration from 10 to 25 at.%. The layers were ion beam mixed with a 500 keV Xe + beam to a fluence of 1 x 1016 Xe cm -2 at liquid nitrogen temperature or at 150 °C. The composition, the impurity content and the mixing efficiency were checked using Rutherford backscattering analysis (RBS) with 2 MeV ~t particles. Figure 1 shows RBS spectra before and after mixing for an initial stack containing 10 at.% Mn. Before mixing, the two manganese layers are well resolved, while the two aluminium layers, separated by only 25-30/~ of manganese, are not resolved. After mixing, only one wide manganese peak is observed. The Xe ÷ dose is evaluated as well as the manganese concentration, which has decreased by about 1% owing to sputtering effects. In our experimental conditions, most of the Xe ÷ comes to rest in the substrate.
3. Structural studies The atomic structure was examined by transmission electron microscopy (TEM). Our findings are in agreement with the results of Knapp and Follstaedt [5, 7]. © Elsevier Sequoia/Printed in The Netherlands
362
q
A1
bin
Channels" Fig. 1. RBS analysis of a sample containing 10 at.% Mn: spectrum a, before mixing; spectrum b, after mixing with a 500 keV Xe + beam to a fluence of I × 1016 Xe c m - z . Ion beam mixing at 150 °C results in the icosahedral phase for manganese concentrations from 10 to 20 at.%. Figures 2(a) and 2(b) show TEM diffraction patterns (taken at 100 kV) for samples with I0 and 19 at.%. The icosahedral phase was identified by its powder diffraction pattern, all rings of which matched with spacings and relative intensities already reported [8]. At lower manganese contents, f.c.c, aluminium lines were also present. Dark field images indicate that
l I
I
II
I I
II
Fig. 3. Opticaldiffractionpatternofanicosahedralgrainshowing the twofold symmetry (alloy with 19 at.% Mn mixed at 150 °C). the icosahedral grains are 100-300/~ in diameter. Careful examination of the 19 at. % Mn sample with a high resolution microscope (Jeol 200 CX) operated at 200 kV allowed such icosahedral grains to be isolated in a few cases. Figure 3 shows an example of a twofold optical diffraction pattern from such a grain. Mixing at 77 K provided samples in the amorphous state. At high manganese concentrations (1620 at.%), the amorphous phase is the only phase detected (Fig. 2(c)). At about 10 at.%, f.c.c, aluminium lines are also observed (Fig. 2(d)). Mixing of layers with 24 at.% Mn produced a b.c.c, metastable phase previously identified by K n a p p and Follstaedt [7] (called by them the F phase). Its diffraction pattern is shown in Fig. 4.
•
AI V
..-i O er.. O E ¢Q Fig. 2. Electron diffraction patterns observed in samples mixed with 1 x 1016 Xe cm 2 for two manganese concentrations and two temperatures: (a) alloy with 10 at.% Mn mixed at 150 °C showing f.c.c, aluminium and icosahedral rings; (b) alloy with 19 at.% Mn mixed at 150 '~Cconsisting of only the icosahedral phase; (c) alloy with 19 at.% Mn mixed at - 196 °C consisting of an amorphous phase; (d) alloy with 10 at.% Mn mixed at - 196 °C showing amorphous phase halos and f.c.c, aluminium rings.
Fig. 4. Electron diffraction pattern of a 24at.% Mn sample consistingof the b.c.c, metastable crystallineF phase as identified by Knapp and Follstaedt [7].
363
4. Optical properties Optical measurements were performed on samples deposited on silica substrates. Reflectance measurements between 0.5 and 6.2 eV and ellipsometric measurements between 1.5 and 5.4eV were used to calculate the optical conductivity of the A1Mn alloys; the film thickness was determined by X-ray interference fringes at grazing incidence [9]. One advantage of the ion beam mixing method of preparation is the production, for appropriate manganese concentrations, of single-phase material in an amorphous (A) or icosahedral (I) state; therefore it is particularly interesting to investigate the relationship between the two phases in the sample containing 19 at.% M n. Figure 5 displays the reflectivity of the A and the I phases obtained from two AI/Mn stacks containing 19 at.% Mn sputtered together, the first mixed at - 1 9 6 °C and the second at 150°C. The reftectivity is shown to be very sensitive to the atomic structure. Indeed, the curves are close to each other up to 1.8 eV; they diverge at higher energies but no new structure appears in the I phase. The optical conductivity calculated by the Kramers-Kronig transformation from the curves of Fig. 5 is reported on Fig. 6 together with that of pure manganese [ 10]. The spectrum corresponding to the I state presents two well-defined peaks at 0.8 and 2.4 eV. The curve corresponding to the A state shows also two peaks in the same spectral ranges but the oscillator strength of the transition at 2.4 eV is wider than in the I state. The peak at low energy is less pronounced, its small shift is probably not significant and it has to be confirmed with measurements at lower energy. Both spectra are dominated by the manganese d states. Strong similitudes to pure manganese are observed, at energies up to 4 eV, but at higher energies the conductivity of the
--
6
• .. Nn
5
--
(I)
C ~
o
°
(A)
°
4 H o
3
§
2
rJ H
t 0
1
2
3
4
ENERGY
5
6
(e.v.)
Fig. 6. Optical conductivity of the 19 at.% Mn alloy in the A and I states. The pure manganese spectrum [ 10] is shown for comparison. A and the I phases decreases, indicating that the partial manganese d density of states is reduced on the high binding energy side. In samples with a lower manganese concentration, the A or the I phase coexists with aluminium or the A I - M n solid solution. Optical properties are able to throw light on the contribution of each phase. It is necessary, first, to describe again the main features of the optical conductivity of pure aluminium (Fig. 7). It exhibits a monotonic decrease with increasing energy, on which a well-defined peak at 1.6 eV is superimposed. The first contribution is due to intraband transitions of the conduction electrons (Drude term), and the peak is due to interband transitions between s-p parallel bands near the limit of the Brillouin zone at W. This peak is particularly sensitive to the disorder: its intensity decreases as the grain size decreases; it disappears in films deposited at 20 K [ 11]. In Fig. 7, on the curve corresponding to the mixture of alu-
"7, --" A1 0.9
i --=a~ o
0.8 0.7
5
: .. ".
-- A1 + (I) -- A1 + (A) ...-.
4
0.6
3
0.5 0.4 0.3
(A]
0.2
"'-...°
~'-
0.1 0.0
o6 !
2
3 ENERGY
4
5
6
(e.V.)
Fig. 5. Reflectivity v s . energy of the 19 at.% Mn alloy in the A and the I states.
i
~
''~'
~ ENERGY
......
~
(e.V.)
Fig. 7. Optical conductivity of the 10 at.% Mn alloy mixed at 150 °C (A1 + I phase) and at - 196 °C (AI + A phase). The pure aluminium spectrum is shown for comparison.
364
B u
"I' o 4
3
z 2
o 0
1
2
3
ENERGY
4
5
B
(e.V.)
Fig. 8. Optical conductivity of the 24 at.% Mn alloy containing the crystalline metastable F phase.
minium and I phase (10 at.% Mn overall), we recognize the peak at 1.6 eV existing in pure aluminium together with the high energy peak of the I phase as observed in the sample with 19 at.% Mn. The low energy peak of the I phase is probably screened out by the Drude contribution. Significant differences are observed for the mixture of aluminium and A phase. The 1.6 eV peak is no longer observed, and a broad peak emerges around 2 eV from the manganese partial d density of states in the A phase. The presence of the aluminium interband contribution at 1.6 eV proves that the crystalline aluminium phase has a texture in the presence of the I phase; this relation is destroyed by disorder in the presence of the A phase. For manganese concentrations higher than 20 at.% (24 at.% in our example), a new metastable crystalline phase (the F phase) is formed by ion mixing. Its conductivity spectrum exhibits the two-peak shape already observed in the I phase. However, the intensity of the first peak is increased in the F phase and both peaks are shifted towards higher energies by about 0.5 eV with respect to the I phase (Fig. 8). 5. Discussion and conclusion
In crystalline materials, such as pure aluminium and pure manganese, the peaks observed in the optical conductivity spectra are unambiguously attributed to band structure effects, i.e. to interband transitions in extended regions of the Brillouin zone. When the momentum conservation rule is relaxed (this is obviously the case in disordered materials), the optical conductivity can be written as a simple convolution of the initial and final densities of states n(E): E F + hto
tr(co) oc o9 - 1
| el EF
n ( E ) n ( E - hto) d E
Although the optical spectrum of the pure aluminium has been widely investigated and is well understood, this is not so in the case of pure manganese. No attribution of the peaks observed in the conductivity has been carried out; nevertheless, it can be guessed that they are related to transitions between maxima in the density of d states below and above EF or between a maximum and EF. In particular, in transition and noble metals the high binding energy peak (around 5 eV) originates from transitions starting from the bottom of the d band to EF. As underlined above, the spectra of the samples with 19 and 24at.% Mn are dominated by the manganese d states; their behaviours favour an asymmetrical narrowing of the d density of states with respect to pure manganese. Because in the I phase the manganese concentration is thought to remain unchanged, it is not surprising to find in samples at 10 and 19. at.% Mn the same peak position at 2.4 eV. The low energy peak at 0.8 eV clearly seen in the 19 at.% Mn sample is probably masked in the 10 at.% Mn sample (mixture of aluminium and I phase) by the strong contribution of conduction electrons in the aluminium phase. By contrast, one observes a change in the position and the shape of the manganese d states contribution to the optical conductivity of the A phase as a function of the composition. Indeed, as the manganese concentration decreases, the peak initially centred at 2.4 eV moves towards lower energy at about 2 eV as a consequence of the change in the local environment of the manganese atoms. This view is supported by optical measurements performed on fully amorphous sampies obtained by sputtering or co-evaporation. In summary, we have observed comparatively similar optical spectra in I and A phases in single-phase samples with about 19 at.% Mn. Differences found in samples containing two phases with an overall concentration of about 10 at.% Mn are probably due to differences in the manganese concentration in the I and the A phases. In the above discussion, we have neglected an important feature of the electronic structure of metallic alloys: the role played by the hybridization between the aluminium s-p states and the manganese d states. Its role has been emphasized by the calculation of Deutz et al. [ 12] performed for a manganese impurity in aluminium. The manganese impurities turn out to be magnetic and the virtual bound states show strong deviations from a lorentzian form arising from the band structure of aluminium. This calculation could be taken as a starting point for the interpretation of the optical properties of the solid solution A1Mn [ 13] and could also be applied to more concentrated alloys
365 as l o n g as a m a n g a n e s e a t o m h a s n o m a n g a n e s e nearest neighbours. The interpretation of our data a l o n g these lines is in progress.
References 1 Ph. Mangin, Les Amorphes M~talliques, Aussois, 1983, Editions de Physique, Paris, 1984, p. 175. P. J. Steinhardt, D. R. Nelson, M. Ronchetti, Phys. Rev. B, 28 (1983) 784. 2 G. Bergman, J. L. T. Waugh and L. Pauling, Aeta Crystallogr., I0 (1957) 254. P. Guyot and M. Audier, Philos. Mag. B, 52(1985) L15. 3 D. Shechtman, I. Blech, D. Gratias and J. W. Cahn, Phys. Rev. Lett., 53(1984) 1951.
4 K. Urban, N. Moser and M. Kronmiiller, Phys. Status Solidi A, 91 (1985) 411. 5 J. A. Knapp and D. M. Follstaedt, Phys. Rev. Lett., 55 (1985) 1591. 6 D. A. Lilienfeld, M. Nastasi, H. H. Johnson, D. G. Ast and J. W. Mayer, Phys. Rev. Lett., 55(1985) 1587. 7 J. A. Knapp and D. M. Follstaedt, Nucl. lnstrum. Methods Phys. Res. B, 19-20(1987) 611. 8 P. A. Bancel, P. A. Heiney, P. W. Stephens, A. I. Goldman and P. M. Horn, Phys. Rev. Lett., 54 (1985) 2422. 9 L. N6vot and P. Croce, Rev. Phys. Appl., 15 (1980) 761. 10 P. B. Johnson and R. N. Christy, Phys. Rev. B, 9 (1974) 5056. 11 L. G. Bernland, O. Hunderi and H. P. Myers, Phys. Rev. Lett., 31 (1973) 363. 12 J. Deutz, P. H. Dederichs and R. Zeller, J. Phys. F, 11 (1981) 1787. 13 D. Beaglehole and M. Wihl, J. Phys. F, 2(1972) 43.