IR Reflectivity Studies of Mechanically Alloyed PbTe Nanocrystals Thomas Ch. Hasapis1, Chrysi Papageorgiou2, Euripides Hatzikraniotis1, Theodora Kyratsi2 and Konstantinos M Paraskevopoulos1

1Department of Physics, Aristotle University of Thessaloniki, 54123 Thessaloniki, Greece. 2Department of Mechanical and Manufacturing Engineering, University of Cyprus, 1678 Nicosia, Cyprus ABSTRACT

Nano-crystalline lead telluride powder was synthesized by mechanical alloying using a high-energy planetary ball mill. The broadening of the X-ray diffraction peaks vs ball milling time, indicates small crystalline size of the order of 30nm. IR spectroscopy results are discussed and compared to the material prepared from melt. INTRODUCTION

Nanostructuring is one of the effective approaches to increase the figure-of- merit of thermoelectric materials. Recent work has shown that small, dimensionally-confined systems can exhibit figures of merit well in excess of one [1]. A major trend in recent research involves the incorporation of nanoscale constituents within bulk materials to form nanocomposites [2]. Additionally, application of low cost techniques on the preparation of nano-materials is of great interest. Research has shown the importance of nano-structured materials and the effect of the nanofeatures on the enhancement of the thermoelectric performance. However, due to the difficulty in applying expensive fabrication techniques in commercial systems, a high-ZT-low-cost approach on nanomaterials is of great interest. Therefore, techniques such as ball milling and sintering are being investigated because of their advantages, which include, beyond the cost, easy shaping and mass production.

In this work, nano-crystalline lead telluride powder was synthesized by mechanical alloying using a high energy planetary ball milling system. Phase transformation and crystallite size evolution during ball milling was followed by powder X-ray diffraction (PXRD) and the morphology was studied by scanning electron microscopy (SEM). IR spectroscopy results are discussed and compared to the material prepared from melt.

EXPERIMENTAL

PbTe was synthesized by mechanical alloying in a Fritsch planetary ball mill, using pure 99.999% Pb and Te elements, as starting materials, taking the processing route described in ref [3]. The speed was 400 rpm and the initial ball-to-material ratio 10:1. Ball milling was interrupted several times (at 1h, 3h, 6h, 12h and 31h) and powder was taken from the batch to be examined by PXRD (Shimadzu), SEM (TESCAN) and TEM (JEOL) system. After the end of ball milling at 31h, the powder was sintered at 700oC for 48 hours, and this sample was taken as a reference for PXRD analysis. Infrared spectra (113V Bruker spectrophotometer) were carried out on cold pressed pellets using about 0.7 GPa pressure. The reflection coefficient was determined by typical sample-in, sample-out method with a gold mirror as the reference. Infrared

Mater. Res. Soc. Symp. Proc. Vol. 1166 © 2009 Materials Research Society 1166-N03-12

measurements were taken at near normal incidence, with a resolution of 2cm-1. IR spectroscopy results are compared to those from the material prepared from melt; poly-crystalline material was first grounded using mortar and pestle and then cold pressed at the same pressure. RESULTS and DISCUSSION Structural and morphology studies

The XRD patterns for different ball milling times are shown in Fig. 1a. As shown, the produced phase is pure PbTe, at least after 6h of ball milling, which is in agreement with the findings in ref. 3. As is evident, there is a broadening of the peaks compared to the reference (annealed) sample. From the broadening of the peaks, using the well-known Scherrer method [4], the average observed crystallite size is calculated to be of the order of 30nm.

20 30 40 50 602Θ(Ο)

Intensity

31h

6h

annealed

PbT

e(20

0)

PbT

e(22

0)

PbT

e(31

1)

PbT

e(22

2)

PbT

e(40

0)

PbT

e(11

1)

(a) (b) Figure 1: (a) XRD pattern evolution for different ball-milling times (b) SEM micrograph

for material after 31hrs ball milling.

In order to further study the structural changes, SEM images were taken as shown in Fig. 1b. Based on these images, the typical size of the particles in ball-milled samples is found to be <2μm. TEM diffraction images for the annealed samples present a crystalline cubic phase, while bright field images show large crystallites in different orientations. In ball-milled samples diffractions present, mainly, rings with spots and bright field images show clusters of nano-crystalline areas against a background of a different relief, while further studies are in progress.

IR Reflectivity studies

The IR spectrum (shown in Fig.2) for PbTe is well known for years. PbTe belongs to a class of semiconductor materials that exhibit significant dispersion of optical phonon modes. Pure PbTe is characterized by a TO phonon at ~32cm-1 and the corresponding LO at ~104cm-1 [5]. In Fig. 2a are presented the spectra of PbTe samples synthesized by ball milling at different times of activation. These spectra are analyzed in order the spectroscopic parameters to be received.

50 100 150 200 250 300 350 400 4500,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Ref

lect

ivity

Wavenumbers [cm-1]

31h 12h 6h 3h 1h

50 100 150 200 250 300 350 400 450

Im(-

1/ε)

Wavenumbers [cm-1]

31h 12h 6h 3h 1h

Figure 2: (a) IR reflectivity spectra and (b) the corresponding Im[-1/ε] for different ball milled PbTe samples. Spectra are shifted vertically for clarity

The IR reflectivity (R) is given by the expression:

2

1)(1)(

)(+

−=

ωεωε

ωR (1)

where, ε(ω) is the complex dielectric function (ε=ε1+i⋅ε2), which, in the case of PbTe, is expressed in terms of the TO and LO frequencies (ωΤ and ωL) and the plasma frequency (ωP) as:

ωγω

ωεωγωωωγωω

εωεP

P

j jTjT

jLjL

iii

⋅+−

⋅+−

⋅+−= ∞

∞∏ 2

2

,22

,

,22

,)( (2)

where γT, γL and γP are the damping constants for the phonons and the plasmon, and ε∞ is the high frequency value for the dielectric function. Analysis results are summarized in Table I. Table I: IR analysis results for sample taken from melt and sintered sample From melt Sintered Plasmon

j=1 j=2 j=1 j=2 from melt SinteredωL (cm-1) 101.4 82.9 100.3 81.0 ωP (cm-1) 56.0 61.8 γL (cm-1) 23.6 30.6 16.8 30.8 γP (cm-1) 26.9 36.4 ωT (cm-1) 32.0 79.7 32.0 80.6 N (cm-3) 171076.0 ⋅ 171097.0 ⋅ γT(cm-1) 10.0 17.5 10.0 15.8 ε∞ 21.8 22.7

As can be seen in Table I, two phonons are required to fit reflectivity spectra for samples taken from melt as well as for the sintered samples. The 1st phonon (ωΤ=32cm-1, ωL~100cm-1) is the typical phonon for PbTe, while the 2nd one (ωΤ=80cm-1), results from the edge of the Brillouin zone [6]. Plasma frequency is related to the free carrier concentration (N) by the expression:

∞

⋅=

εεω

0

22

*meN

P (3)

where m*=0.1me is the free carrier effective mass [7], ε0 the permittivity of vacuum and e the free electron charge. Typically, in PbTe, plasmon is coupled with the ωΤ=32cm-1, ωL~100cm-1 phonon, and the two coupled modes appear in the Im(-1/ε) curve (Fig. 2b), at frequencies [8]:

( ) 22222222 4)(2 TPPLPL ωωωωωωω +−±+=⋅ ± (4)

The graph of eq. 4 is presented in Fig. 3b. As can be seen, due to the low value of plasma frequency, the ω+ mode is phonon like, and appears as a strong peak in the Im(-1/ε), while the ω- mode, is not shown, as our data begin from 70cm-1.

0 50 100 150 200 250 300 350 400 4500,2

0,3

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1,0

Ref

lect

ivity

Wavenumbers [cm-1]

PbTe melt PbTe sintered

0 50 100 150 2000

50

100

150

200

ωT

ωL

ω-

melt sintered

Cou

pled

mod

es ω

+ , ω- [c

m-1

]

plasmon frequency ωP [cm-1]

ω+

Figure 3: (a) IR reflectivity spectra for PbTe from melt and sintered, along with the

calculated spectra by dispersion analysis. Spectra are shifted vertically for clarity. (b) The dependence of ω+ and ω- optical coupled modes as a function of plasma

frequency (ωP).

Application of the Effective medium theory in the analysis of IR Reflectivity

Since ball milled samples are grounded and then cold pressed, a significant surface roughness is expected, and this manifests itself by a lowering trend in the reflectivity at high frequencies. Assuming a Gaussian distribution of surface roughness, the reflectivity of the rough surface (RSR) is related to the reflectivity of a smooth one (R0) by [9]

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅⋅−⋅≈

2

0

00

4exp

λσπ n

RRSR (5)

where λ0 is the vacuum wavelength and σ is the RMS value of the surface roughness. The effect of surface roughness, corrected, is presented in Fig.4a.

In Table II the values of density of the cold pressed pellets, as a function of the ball milling time are given. Density was calculated by the mass/volume ratio. As can be seen, there is a decrease of the observed density from 7.6 to 6.6 g/cm3. We performed an effective medium analysis, taking the Bruggerman approximation [10], and three phases, namely, the micro-

crystalline phase, with the characteristics taken from sintered sample, a B phase (nano-crystalline clusters) and the air inclusions. The 3-phase Bruggerman approximation for the dielectric function (εBR) is given as:

02

=+

−∑

j BRj

BRjjf

εεεε

(6)

where εj is the dielectric function of each of the three phases considered, and fj their volume fraction. The volume fraction f3 (the air inclusions) was taken constant (f3= 0.066) for all samples, as estimated from the sample prepared from melt and since pellet fabrication conditions were the same. The other two (f1 and f2) were calculated from density and the condition Σfj=1. Calculated values for fj are presented, also, in Table II.

50 100 150 200 250 300 350 400 4500,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

Ref

lect

ivity

Wavenumbers [cm-1]

31h 12h 6h 3h 1h

50 100 150 200 250 300 350 400 4500,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Ref

lect

ivity

Wavenumbers [cm-1]

1h 3h 6h 12h 31h

Figure 4: (a) IR reflectivity spectra for ball milled PbTe of Fig. 2(a), after the surface roughness correction. Spectra are shifted vertically for clarity.

(b) Reconstructed IR reflectivity spectra for the phase “B”.

In Figure 4b, the reconstructed IR spectra for the phase “B” are shown. As can be seen, apart from the 1h ball milled sample, which clearly deviates from the rest, presumably due to incomplete reaction, all the rest follow the same pattern. This is a clear indication for the co-existence of phase “B” which is present even from the 3h ball milling time, and its volume fraction tends to increase, as ball milling time progresses.

Table II: Volume fractions of different phases and IR results for various ball-milled samples

Sample d (g/cm3)

Relative d (%) f1 f2

ωP (cm-1)

γP (cm-1) ε∞ N

(cm-3) from melt 7.61 92.6% 0.934 - 56.0 26.9 21.8 171076.0 ⋅ 1h 6.92 84.1% 0.692 0.242 52.5 77.4 21.2 0.65·1017 3h 7.03 85.5% 0.582 0.352 49.9 78.2 22.9 0.64·1017 6h 6.57 79.9% 0.513 0.421 52.3 77.7 22.9 0.7·1017 12h 6.78 82.5% 0.446 0.488 52.7 78.4 22.8 0.7·1017 31h 6.61 80.4% 0.356 0.578 52.0 74.2 22.8 0.69·1017

CONCLUSIONS

In this work, nano-crystalline lead telluride powder was synthesized by mechanical alloying using a planetary ball mill. Phase transformation and crystallite size evolution during ball milling was followed by powder X-ray diffraction (PXRD) and the morphology was studied by scanning electron microscopy (SEM). From the broadening of the PXRD peaks in ball milled samples an average crystalline size in the order of 30nm was obtained. TEM shows clusters of nano-crystalline areas against a background of a different relief. IR spectroscopy results indicate the presence of this nano-crystalline phase and analysis shows that the volume fraction tends to increase, as ball milling time progresses. From the values of optical parameters (ωP and γP) it is evident that ball milling of Pb and Te powders produces samples with low free carrier concentration (ωP~52cm-1 that corresponds to the order of 1017cm-3) which is typical for undopped PbTe [11] and with relatively large damping factor (γP~78cm-1). These values are slightly improved in sintered samples (ωP~62cm-1 and γP~36cm-1).

ACKNOWLEDGMENTS The Greek authors would like to acknowledge financial support from European Community and the General Secretariat for Research and Technology-Hellas in the framework of the program PENED 2003 (03EΔ887) and the Hellenic Telecommunications Organization (OTE S.A.). The UCY authors acknowledge financial support from INTERREG IIIA Greece-Cyprus and Cyprus Promotion Foundation (PENEK/ENISX/ 0308/43). REFERENCES 1. Thermoelectrics Handbook: Macro to Nano, (2006) Ed: D. M. Rowe, CRC Press 2. M.S. Dresselhaus, G. Chen, M.Y. Tang, R. Yang, H. Lee, D.Z. Wang, Z.F. Ren, J.P.

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