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Keywords:

  • antimonides;
  • density of phonon states;
  • nanoparticles;
  • nuclear inelastic scattering

Abstract

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Experimental
  5. 3 Results and discussion
  6. 4 Conclusions
  7. Acknowledgments
  8. References

The121 Sb partial density of phonon states (DPS) in nanopowder antimonides were obtained with nuclear inelastic scattering on inline image, inline image, and NiSb prepared by a wet chemistry route. The DPS is compared with the bulk counterpart. An increase of the Debye level indicative of a decrease of the isothermal speed of sound is systematically observed. This observation reveals that the decrease in speed of sound observed in nanostructured thermoelectric materials is not restricted to sintered nanocomposites.

1 Introduction

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Experimental
  5. 3 Results and discussion
  6. 4 Conclusions
  7. Acknowledgments
  8. References

Nanostructured materials have been the focus of several studies, since they possess significantly different properties when compared to the equivalent bulk material. Of particular interest is the effects of nanostructuration on the lattice dynamics of these materials, because it can change its thermal and electrical properties and has been intensely investigated by means of theoretical calculations [1-9] and observed with methods such as inelastic neutron scattering [10-15], Raman spectroscopy [16, 17], nuclear inelastic scattering (NIS) [14, 18], and measurements of the specific heat [19, 20].

An enhancement in the density of phonon states (DPS) at low energies for nanocrystalline materials, as well as a broadening of the bands on the DPS, was previously observed [10, 11, 13, 14, 18] and calculated [1, 2, 4, 5, 8, 9, 21]. In these studies, it was suggested that these additional modes can be attributed to the vibrations of atoms located in the grain boundaries, where the atomic structure is more open than in the crystalline part of the material, resulting in a change of the force field and softening of the force constants.

Although most of the theoretical and experimental studies reported so far focus on nanocrystalline bulk materials and the role of grain boundaries and changes in the interatomic distances, investigations on nanopowders also yield information about acoustic vibrational modes confined in nanoparticles in the powder form [15-17].

Transition metal antimonides such as inline image1, inline image, and NiSb exhibit several interesting properties for diverse applications. Whereas inline image is a well known thermoelectric material [23, 24], both inline image and NiSb are potential anode materials in rechargeable lithium-ion batteries [25, 26] and provided that a reduction of the the thermal conductivity is achieved, they could also be valuable thermoelectric materials [27, 28].

Thermoelectric materials are a perfect example of the use of nanostructuration to improve functional properties. They are used for waste heat recovery by converting a heat flow into electricity and vice versa and its conversion efficiency is dependent on the Seebeck coefficient, electrical conductivity, and inversely proportional to the thermal conductivity of the material. Therefore, it was previously suggested ([29]) and observed [30-32] that one way of improving the thermoelectric properties of a material is through nanostructuring, where the thermal conductivity is decreased due to the creation of scattering centres for phonons. Furthermore, reduced speed of sound and larger unit-cell volume are also known mechanisms to decrease thermal transport.

Herein, we report for the first time measurements on the lattice dynamics of nanopowder antimonides done with NIS on121 Sb on inline image, inline image, and NiSb prepared by a wet chemistry route, comparing it with their bulk counterpart.

2 Experimental

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Experimental
  5. 3 Results and discussion
  6. 4 Conclusions
  7. Acknowledgments
  8. References

The nanopowders were prepared by a wet chemistry route based on the reaction of Sb nanoparticles with the appropriate metal precursor. In a first step, antimony nanoparticles were produced by reduction of inline image with lithium triethylborohydride inline image. In the case of NiSb and inline image, Ni, and Zn nanoparticles were prepared from the corresponding chlorides and then mixed with the antimony nanoparticles. For inline image, a dispersion of the metal precursor, cyclopentadienyl iron(II) dicarbonyl dimer was added to the suspension of Sb nanoparticles. The details of the individual reactions, i.e., reaction temperatures, heating rates, holding times, the crystal structures are reported elsewhere [33-35]. The particles exhibit a broad size distribution with diameters as determined from TEM of 30 nm –ranging from 5 to 70 nm –for inline image ([35]), between 20 and 60 nm both for inline image ([34]) and NiSb, with however an X-ray diffraction correlation length of only 13 nm ([33]) for the latter. The inline image particles were washed with HCl in order to remove iron oxide.

121Sb NIS [36, 37] was carried out on bulk and nano inline image and NiSb, and on nano inline image in 16-bunch mode at the nuclear resonance station ([38]) ID22N of the European Synchrotron Radiation Facility in Grenoble, France. Energy scans were performed with a temperature-controlled high-resolution backscattering monochromator ([39]). The sample was cooled with a closed cycle cryostat to inline image20 K inside a vacuum chamber with Kapton windows for the incoming and scattered beams and the fluorescence products. The temperature of the sample was monitored by a temperature sensor in the vicinity of the sample. The precise temperature was better determined through the Bose–Einstein statistics, comparing the signal on the Stokes and anti-Stokes sides.

The corresponding partial DPS for121 Sb, inline image, were derived from the NIS spectra using a modification of the program DOS ([40]) by taking into account and deconvoluting by the instrumental resolution and then by convoluting with a Gaussian function with the same FWHM, inline image1.5 meV, a slightly higher value than the measured instrumental function, 1.2 meV, in order to avoid unphysical termination ripples in the DPS and to reduce the effect of our slightly asymmetric resolution function.

3 Results and discussion

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Experimental
  5. 3 Results and discussion
  6. 4 Conclusions
  7. Acknowledgments
  8. References

A comparison of the NIS spectra of bulk and nano inline image, NiSb, and inline image is given in Fig. 1, where the instrumental function given by the elastic scattering, i.e., nuclear forward scattering (NFS), is plotted as dotted lines. The reduced partial densities of phonon states for121 Sb, inline image, are plotted in Fig. 2 and the121 Sb specific density of vibrational states are plotted on the insets.

image

Figure 1. NIS spectra of nano inline image, NiSb, and inline image (blue circles) compared to the spectra of the bulk counterpart (red triangles). The elastic scattering is shown as gray line with y scale on the right side of the plots.

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image

Figure 2. Reduced density of121 Sb phonon states of nano inline image, NiSb, and inline image compared to the bulk counterpart: a decrease on the speed of sound is observed upon nanostructuration.

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The vibrational spectra of bulk and nano inline image are in good agreement with each other and also with previously calculated and obtained with NIS ([41]) and with Raman spectroscopy ([42]), while the vibrational spectra of nano inline image slightly differs from the bulk inline image ([43]) above 12 meV probably due to its different symmetry and stoichiometry. When trying to synthesize nanoparticles of inline image with a wet chemistry approach, Birkel et. al. ([35]) obtained a new phase “inline image” according to electron diffraction tomography results, with a crystal structure belonging to the space group inline image, whereas bulk inline image belongs to the space group inline image ([22]). The vibrational spectra of bulk and nano NiSb also presents minor differences above 20 meV. Both bulk and nano NiSb were confirmed to have the same crystal structure [33, 44], inline image, but with small discrepancy on the c lattice parameter, which is 0.5% larger for nano when compared to the bulk ([33]). Comparing between materials, the shape of the DPS for the three compounds is very different, mostly due to the different space groups and local metal-antimony coordinations. Note that in inline image, the softest among these materials, Sb–Sb bonds are a prominent structural feature.

The DPS of inline image nanoparticles exhibits a peak at around 5 meV corresponding to acoustic phonons and is better observed in the reduced DPS, inline image (Fig 2). Such a peak was previously observed by Saviot et al. ([15]) in the inelastic neutron scattering spectra by inline image nanopowder and was attributed to acoustic modes confined in the nanoparticles and compared to a Boson peak observed from glasses ([14]). In a similar study carried out on nanocrystalline Si ([45]), such peak was also observed and attributed to a Boson peak due to amorphous inline image impurities on the sample. In the present study, we have considered to attribute the low energy peak observed in nano inline image to a small percentage of inline image contribution, since the DPS of inline image ([46]) also has a peak on this energy. Modeling the data with 85 or 90% of inline image bulk and 15 or 10% of inline image would however lead not only to the presence of the peak at 5 meV, but also to a shift of the peaks at 9.5, 13.3, and 21 meV toward higher energies, which is not seen when comparing the vibrational spectra of bulk and nano inline image. The peak at 5 meV can thus not be attributed to inline image. We could not attribute this peak to any other impurity and its precise origin is still an open issue. Note also that even though the particles have been washed by HCl, traces of iron oxide might still be present. These would not directly affect the antimony specific DPS but might have a minor effect on possible particle surface modes below or resolution limit.

An increase of the Debye level in the low energy region (below inline image 8 meV) was observed for all three nano compounds with respect to bulk in the reduced DPS, Fig. 2, leading to a decrease of the speed of sound upon nanostructuration. The average speed of sound (inline image) can be extracted from the Debye level, i.e., the limit of inline image for small energies according to the relation ([47]):

  • display math(1)

where inline image is the mass of the resonant121 Sb atom, inline image is the mean atomic mass and V is the volume per Sb atom and can be obtained by taking into account the density of the materials obtained from the lattice parameters published previously [33-35]. Note that because our resolution is 1.2 meV, possible low energy nanoparticle breathing modes are not accessible, and inline image corresponds to the average group velocity for acoustic phonons in the inline image1 to inline image5 meV energy range.

The high energy optical phonons remain unaffected from nanostructuration, i.e., no phonon broadening or phonon stiffening is observed. This lack of broadening or shift is most likely due to the rather large size of the nanoparticles under study.

In a simple Debye model, the thermal conductivity is expressed as the product of the specific heat, the average phonon relaxation times, and the square of the speed of sound ([48]). The observed increase in the Debye level corresponding to a reduction in the speed of sound by inline image18% for the case of inline image is thus expected to significantly reduce the thermal transport, by inline image40%, even under the assumption that there is no change in the average phonon relaxation time. The same applies to inline image and NiSb with reductions on the speed of sound of inline image9% and inline image8%, respectively. Thus an enhancement of the thermoelectric figure of merit is expected, provided that the nanoparticles can be sintered while preserving their nanostructure.

The reduction in the average phonon group velocity might be responsible for obtaining lower thermal transport in nanostructured materials –in addition to interface scattering processes –and this effect should be systematically investigated in future research on thermal transport in nanomaterials. The origin of the reduced speed of sound itself needs to be clarified, as it could be related either to the presence of grain boundaries, surface effects, or strain. A further effect from phonon lifetime modification was not observed herein, either because of our limited 1.2 meV resolution or because it is not significant in these range of nanoparticles sizes (inline image30 nm).

4 Conclusions

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Experimental
  5. 3 Results and discussion
  6. 4 Conclusions
  7. Acknowledgments
  8. References

An excess of low energy phonon modes upon nanosctructuration was previously predicted [1, 2, 4, 5, 8, 9, 21] and observed [10, 11, 13, 14, 18] for the case of bulk materials due to a large amount of grain boundaries. Such an excess is observed in the present study of121 Sb NIS in nanoparticles of inline image, inline image, and NiSb prepared by a wet chemistry route although the broadening of the bands on the DPS was not observed. This excess is related to an increase of the Debye level and consequently to a decrease in speed of sound or, more precisely, in the average acoustic phonon group velocity in the 1–5 meV range, a decrease which is suggested to also lead to a decrease of the thermal conductivity. Our study reveals a rather important enhancement in the Debye level –although the nanoparticles are quite large –and that the associated reduction in the speed of sound can not be neglected when discussing thermal transport in nanoparticle systems.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Experimental
  5. 3 Results and discussion
  6. 4 Conclusions
  7. Acknowledgments
  8. References

The European Synchrotron Radiation Facility (ESRF ’ Grenoble, France) is acknowledged for beam time at ID-18. The Helmholtz Association of German Research Centers is acknowledged for grant NG-407 “Lattices Dynamics in Emerging Functional Materials”. WT and RPH acknowledges support from the DFG priority program SPP1386 “Nanostructured Thermoelectrics”.

References

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Experimental
  5. 3 Results and discussion
  6. 4 Conclusions
  7. Acknowledgments
  8. References
  1. 1

    The precise stoichiometry is actually inline image ([22]).