Inelastic neutron scattering study of the dynamics of Al74Pd22Mn4 (ξ′)

Journal of Alloys and Compounds 342 (2002) 310–313

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Inelastic neutron scattering study of the dynamics of Al 74 Pd 22 Mn 4 (j9) Max Scheffer*, Jens-Boie Suck ¨ Physik, Materialforschung und Flussigkeiten ¨ , D-01907 Chemnitz, Germany TU-Chemnitz, Institut f ur

Abstract The generalised vibrational density of states (GVDOS) of polycrystalline Al 74 Pd 22 Mn 4 (j9) has been investigated by inelastic neutron scattering at the temperatures 296, 600, 800 and 1000 K. The GVDOS shows two broad main maxima near 14 and 32 meV, which are shifted to lower energies with increasing temperature. The data are compared to the GVDOS of the icosahedral phase [J. Non-Cryst. Solids 156–158 (1993) 872; Mater. Sci. Eng. A 226–228 (1997) 479; J. Non-Cryst. Solids 250–252 (1999) 855] in this system, the structure of which is strongly related to this crystalline phase [Philos. Mag. B 68 (1993) 607; Philos. Mag. A 74 (1996) 939]. At energies below 9 meV, the GVDOS of the j9-phase shows higher densities and a much more harmonic behaviour than that of the icosahedral phase. Thermodynamic quantities like the heat capacity are calculated and compared to measured values.  2002 Published by Elsevier Science B.V. Keywords: Quasicrystals; AlPdMn; Approximant; GVDOS

1. Introduction In the ternary Al–Pd–Mn system, beside the icosahedral (i) and the decagonal phase, several periodic crystalline phases with atomic structures strongly related to the quasicrystals (qc) were found [4]. This coexistence offers the opportunity to figure out the specific properties of quasiperiodicity by a comparison of the physical properties of qc with that of crystalline phases with similar compositions and structures. As an example, the atomic dynamics of icosahedral and tetragonal AlCuFe with similar compositions were compared using inelastic neutron scattering [6]. The results have shown, that in contrast to the quasiperiodic phase, the crystalline phase exhibits sharp structures in the total dynamic structure factor and the generalised density of vibrational states (DOVS). The dynamical structure factor of polycrystalline i-AlPdMn was investigated at several elevated temperatures [1–3]. Since the j9-phase can be regarded as an approximant of the icosahedral structure [4,5] and the dynamical properties of the i-phase were extensively studied, we started a comparative investigation of the j9-phase.

elements Al (99.999%), Pd (99.95%) and Mn (99.99%) in an arc furnace under an inert argon atmosphere (Messer Griessheim 4.8). For the choice of the composition and a suitable heat treatment we used the phase diagrams, given in Ref. [7]. A liquid with the composition Al 74 Pd 22 Mn 4 shows a primary crystallisation of the Pd-rich d-phase (40 at.% Pd) of the binary Al–Pd system. Therefore, for typical cooling rates of an arc furnace, one cannot prevent segregations towards the Al rich region. As a consequence, one expects precipitations of the Pd-rich phase d and pure Al due to an eutectic reaction at 888 K. To resolve the excess of Al and to avoid a remelting of the Al, we first performed a heat treatment at 863 K for 6 days. Afterwards, the sample was annealed at 1098 K for 2 days and cooled down to room temperature with a rate of 5 K min 21 . Light microscopic micrographs show an amount of approx. 0.5% of a second phase. In DSC measurements with heating rates of 5 K min 21 neither endothermic nor exothermic peaks appear, which shows, that there is no phase transition with a detectable latent heat.

3. Neutron scattering experiments and data treatment 2. Sample preparation Ingots of the prealloy were produced from the pure *Corresponding author. Tel.: 149-371-531-3118; fax: 149-371-5318049. E-mail address: [email protected] (M. Scheffer).

The experiments were performed at the cold neutron time focusing time-of-flight spectrometer, IN6, at the High-Flux-Reactor of the Institute Laue-Langevin, Grenoble with an incident energy of 4.75 meV ( l0 50.416 nm) and scattering angles from 13 to 1138. The energy resolution of the energy transfers was DE0 5 170 meV for the

0925-8388 / 02 / $ – see front matter  2002 Published by Elsevier Science B.V. PII: S0925-8388( 02 )00200-1

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elastic line and becomes rapidly worse at higher energies in the neutron energy gain spectra. The samples were measured under a vacuum of 10 25 mbar at temperatures of 296, 600, 800 and 1000 K. The calibration of the efficiency of the 3 He detectors was done by measurements of a vanadium spiral. For a quantitative background subtraction, the empty thin walled Nb container was measured at every temperature. After corrections for absorption and detector efficiency, the data were normalised to the V cross-section. Multiple scattering was subtracted by the use of Monte–Carlo simulations (MSCAT [8]).

4. Results and discussion For a monoatomic material, the vibrational density of states (VDOS) can be evaluated directly from the measured double differential scattering cross-section d 2 s / dV dE. In the case of a sample composed of different elements the coupling of the scattered neutron to each type of element enters the spectra and one determines the generalised vibrational DOS (GVDOS), which is a weighted sum of the partial VDOS, gi (v ), of each element i in the sample. sc i

s Oe c] g v M s d GVDOS(v ) 5 ]]]]]] s Oe c] M 22Wi

i

i

i

i

sc i

22Wi

i

i

i

The weighting factors are the Debye–Waller factors e 22Wi , the atomic concentrations c i , the scattering crosssections s sc i and the mass Mi of the scattering element i. Fig. 1 shows the GVDOS for the temperatures 296, 600, 800 and 1000 K. The GVDOS shows mainly two broad main maxima at about 14 and 32 meV. No sharp and pronounced optical phonon branches can be seen in the

Fig. 1. Generalised vibrational density of states (GVDOS) for the temperatures 296, 600, 800 and 1000 K.

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GVDOS. With increasing temperature a shift towards lower energies occurs, which most likely is due to the expansion of the material with increasing temperature. Beside this shift, a redistribution of the densities takes place from higher energies ( . 30 meV) to the first maximum at approx. 14 meV. The shift as well as the redistribution were already observed for the icosahedral phase [2]. However, the redistribution towards smaller energies is more pronounced in the periodic j9-phase than in the i-phase. At 296 K a smaller maximum at 21.5 meV is present. This maximum is much smaller at 600 K and vanishes with higher temperatures, which possibly indicates a structural change in the sample. In the Al–Pd–Mn system two phases with the same composition were found [9] (j and j9), which are very similar and are built up by the same basic building units. The transformation of these phases is described [9] as very sluggish. Because the measuring time at elevated temperatures was larger than the heat treatments performed in Ref. [9] by one order of magnitude, such a phase transition can occur during the measurement. Additionally, a transformation from j9 to j was observed after plastic deformations of the phase [10]. Fig. 2 shows the GVDOS from the icosahedral phase [2,3] compared with that of the j9-phase. The measurements in Ref. [3] were performed at the same instrument IN6 with comparable parameters. Similarities are the existence of two broad main maxima, located at the same energies. The differences are displayed by a solid line representing the difference GVDOS (j92i). Up to 24.5 meV, the GVDOS of j9 has higher densities, which is reversed at higher energies. As both GVDOS are normalised to 1 with a cut-off energy of 61 meV, this might be caused by the higher content of Pd (3 at.% more) of the j9-phase, whose large atomic mass will influence the GVDOS especially at lower frequencies. The subband in the GVDOS of the i-phase at 13 meV [2] and the maximum at 20 meV of the j9-phase are clearly present in

Fig. 2. Comparison of the GVDOS of the i-phase (n) and the j9-phase (.) at 600 K. The solid phase represents the difference.

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Fig. 3. The double-logarithmic plot indicates a harmonic v 2 Debye dependence of the j9-phase below 8 meV in contrast to the behaviour of the i-phase.

the difference-plot. At energies below 9 meV, the GVDOS of both phases show large differences, which can be seen in Fig. 3. The GVDOS of the j9-phase can be well described by an v 2 dependence up to approximately 9 meV, whereas no quadratic dependence was observed in the data [3] of the i-phase. Measurements of the specific heat in i-AlPdMn [11], which is strongly related to the VDOS, shows an excess T 3 term at temperatures below 15 K, which is explained by non-propagating lattice excitations [11,12] similar to those found in amorphous alloys. The quadratic dependence in v in the case of the j9-phase gives no hint at local modes in this crystalline approximant. Assuming, that the difference between the GVDOS and the DOVS is not too large, the lattice part of the heat capacity Cv can be calculated from the GVDOS by the equation:

Fig. 4. Temperature dependence of the heat capacity of the j9-phase, calculated from the measured GVDOS. Circles indicate measurements of Cp , see Fig. 4.

K, the curve bends off to higher values, which are originated by electronic contributions, extensively investigated for the i-phase in Ref. [11]. This contribution can not be seen by the neutron scattering experiment. First, because the neutrons only see the lattice vibrations and second, because for energies below 2.33 meV, the low energy part of the starting frequency distribution, covered by the foot of the strong peak was bridged by a Debye law (GVDOS(v )~v 2 ). The part of the heat capacity, which originates from the GVDOS below 2.33 meV falls rapidly down from 37% at 6 K to 3.9% at 15 K. This means, that the cubic in T behaviour of the calculated heat capacities are dominated by the quadratic v -dependence of the GVDOS between 2 and 9 meV. If the lattice part of the heat capacity shows a Debye behaviour at low temperatures, it is possible to determine

`

"v E g(v) ]≠T≠ S]]]]] dv exps"v /k Td 2 1 D

Cv (T ) 5

0

B

The results are shown in Fig. 4. As a reference, we performed measurements of Cp in the temperature range from 2 to 80 K using a relaxation-type method. The data between 2 and 32 K are compared with the calculated values from the GVDOS in Fig. 4, assuming that at small temperatures the difference between Cp and Cv is negligible. The shift in the GVDOS to higher energies with decreasing temperature (see Fig. 1) results in a reduction of the heat capacity at lower temperatures. With decreasing temperature, the GVDOS data converges to the measured values of Cp , which shows a nice correspondence between the measured values and the ones calculated using the measured GVDOS. A double-logarithmic plot of the measured Cp data is displayed in Fig. 5. In the intermediate temperature range between 6 and 25 K, the data fits well to the T 3 -Debye behaviour. Below 6

Fig. 5. Temperature dependence of the specific heat Cp of j9, measured with a heat relaxation system. The dashed lines indicate linear and cubic temperature dependences, respectively, which are expected for the electron and the phonon contributions of the Cp at low temperatures.

M. Scheffer, J.-B. Suck / Journal of Alloys and Compounds 342 (2002) 310 – 313

Fig. 6. Calculated velocities of sound c s in dependence of the mass density r. The sound velocity decreases with increasing temperatures.

the averaged velocity of sound c s , which is defined by the equation:

S D

kBT 2p 2 Cp ¯ Cv 5 ]]k B ]] 5 "c s

3

3 2 1 with: ]3 5 ]3 1 ]3 cs ct cl

c t and c l are the velocities of sound for the two transverse and the longitudinal acoustic mode. The weighted average over the velocities is closer to the value of c t , especially if c l is much higher than c t as observed in the i-phase (c t 5 359363 m s 21 , c l 5 6520610 m s 21 , [13]). After fitting the heat capacities by the function Cp 5 a T 1 b T 3 in the temperature range between 6 and 23 K, the coefficients b were converted into averaged sound velocities c s . The obtained values are plotted in Fig. 6 versus the mass density. The density of the j 9 phase is assumed to be slightly smaller than the density of the i-phase (5.08 g cm 23 [13]) due to the higher content of Al together with the similar atomic structure. Therefore, the velocity c s at room temperature becomes about 2.5 km s 21 , which is surprisingly small in comparison to those velocities found in the i-phase [13].

5. Conclusion The GVDOS of the j9-phase shows no pronounced and sharp maxima and a similar structure at energies above 10 meV as the GVDOS of the i-phase. With respect to the close local similarity of the atomic structures of both phases, this result is plausible. With increasing temperature, the small maximum in the GVDOS at 21.5 meV vanishes, which probably is due to a phase transition between very similar phases like j and j9. The transition from j to j9 by a variation of the temperature is an interesting point, which requires further investigation. A softening of the material with increasing temperature was

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observed in the shift of the GVDOS towards lower energies. At smaller energies there are large differences between both phases. In this region, the j9-phase shows a much higher density of states with a harmonic v -dependence. As a consequence, the heat capacity is enlarged at low temperatures, which has been verified by direct measurements of the heat capacity. The harmonic v dependence of the GVDOS is reflected in a T 3 dependence of the heat capacity, which allows the estimation of the averaged velocity of sound. The determined values are in the order of 2.5 km s 21 , which is surprisingly small compared with 3.6 km s 21 of the i-phase. Up to now, no measurements of the velocity of the transverse acoustic modes in the j9-phase were done. The derivation of a v 2 behaviour at small energies in the i-phase due to nonpropagating modes was not found in the j9-phase. The GVDOS of the i-phase shows in addition to the contribution from propagating modes an enlargement in the density due to localised modes. Although those localised modes were not present in the j9-phase, the GVDOS is larger than the GVDOS of the i-phase at small energies. This represents a large difference between both phases beside the similarities at energies above 10 meV.

Acknowledgements It is a pleasure to acknowledge the help obtained from H. Schober at the start up of the experiment and from Mrs. H. Teichmann for her help with the sample preparation.

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