High pressure monoclinic phases of Sb2Te3

Physica B 407 (2012) 3781–3789

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High pressure monoclinic phases of Sb2Te3 S.M. Souza a,1, C.M. Poffo a, D.M. Trichˆes a,1, J.C. de Lima b,n, T.A. Grandi b, A. Polian c, M. Gauthier c a b c

´rio Trindade, S/N, C.P. 476, 88040-900 Floriano ´polis, Santa Catarina, Brazil Departamento de Engenharia Mecˆ anica, Universidade Federal de Santa Catarina, Campus Universita ´rio Trindade, S/N, C.P. 476, 88040-900 Floriano ´polis, Santa Catarina, Brazil Departamento de Fı´sica, Universidade Federal de Santa Catarina, Campus Universita Physique des Milieux Denses, IMPMC, CNRS-UMR 7590, Universite´ Pierre et Marie Curie-Paris 6, 4 Place Jussieu, 75252 Paris Cedex 05, France

a r t i c l e i n f o

abstract

Article history: Received 17 February 2012 Received in revised form 3 May 2012 Accepted 8 May 2012 Available online 19 June 2012

The effect of pressure on nanostructured rhombohedral a-Sb2Te3 (phase I) was investigated using X-ray diffraction (XRD) and Raman spectroscopy (RS) up to 19.2 and 25.5 GPa, respectively. XRD patterns showed two new high pressure phases (named phases II and III). From a Rietveld refinement of XRD patterns of a-Sb2Te3, the unit cell volume as a function of pressure was obtained and the values were fitted to a Birch–Murnaghan equation of state (BM-EOS). The best fit was obtained for bulk modulus B0 ¼36.1 70.9 GPa and its derivative B00 ¼ 6:2 7 0:4 (not fixed). Using the refined structural data for a-Sb2Te3, for pressures up to 9.8 GPa, changes in the angle of succession [Te–Sb–Te–Sb–Te], in the interaromic distances of Sb and Te atoms belonging to this angle of succession and in the interatomic distances of atoms located on the c axis were examined. This analysis revealed an electronic topological transition (ETT) along the a and c axes at close to 3.7 GPa. From the RS spectra, the full widths at half maximum (FWHM) of the Raman active modes of a-Sb2Te3 were plotted as functions of pressure and showed an ETT along the a and c axes at close to 3.2 GPa. The XRD patterns of phases II and III were well reproduced assuming b-Bi2Te3 and g-Bi2Te3 structures similar to those reported in the literature for a-Bi2Te3. & 2012 Elsevier B.V. All rights reserved.

Keywords: Nanocrystals Thermoelectric materials Mechanical alloying X-ray diffraction Raman spectroscopy High pressure

1. Introduction Isostructural layered Bi2Te3, Sb2Te3, Bi2Se3 compounds and their alloys are the best known materials for thermoelectric applications at room temperature or below [1–4]. Their figure of merit ZT has a maximum close to room temperature. At room temperature and atmospheric pressure, they crystallize in a rhombohedral structure, the a-phase (S.G. R3¯m, Z ¼3) [5]. Fig. 1 shows the conventional unit cell for a-Sb2Te3. One layer (L) consists of five alternating sheets (S) of Te and Sb. The angle of succession is [Te(S1)–Sb(S2)–Te(S3)–Sb(S4)–Te(S5)] and is represented in Fig. 1 by atoms joined by thick black lines. For this angle of succession, the interatomic distances Te(S1)–Sb(S2) are equal to Sb(S4)–Te(S5) and the interatomic distances Sb(S2)– Te(S3) are equal to Te(S3)–Sb(S4). The Te(S1), Sb(S2) and Sb(S4) atoms occupy the 6c Wyckoff sites (in the hexagonal setting) and the Te(S3) atoms occupy the 3a sites [6]. The c hexagonal axis is perpendicular to the plane of the layers. Within each sheet the chemical bonds are of the ionocovalent type, while those between the sheets (intersheets) and between the layers (interlayers) are

n

Corresponding author. Tel.: þ55 48 37212847; fax: þ 55 48 37219946. E-mail address: fsc1jcd@fisica.ufsc.br (J.C. de Lima). 1 Present address of the authors S. M. Souza and D. M. Trichˆes: Departamento de Fı´sica, Universidade Federal do Amazonas, 3000 Japiim, 69077-000 Manaus, Amazonas, Brazil. 0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.05.061

of the van der Waals type [6]. The building block of this structure is a SbTe6 octahedron centered on an Sb atom. From this point of view, the layers are formed by two planes of adjacent edgesharing SbTe6 octahedra with common Te(S3) atoms. The effect of pressure on these isostructural compounds has been studied by several researchers using different techniques, and new high pressure phases were observed [7–9]. We studied the effect of pressure on nanostructured a-Bi2Te3 (phase I) using X-ray diffraction (XRD) and Raman spectroscopy (RS) measurements up to 31.7 and 15.6 GPa, respectively. From the XRD patterns, three new high pressure phases (named phases II–IV) were observed, but their structures were not determined. For pressures up to 9.8 GPa, the XRD patterns are characteristic of a-Bi2Te3 and they were refined using the Rietveld method [10]. Using the refined lattice parameters as functions of pressure and the Birch–Murnaghan equation of state (BM EOS) [11], reduced pressure versus Eulerian strain plots for the a and c lattice parameters were obtained. They showed an electronic topological transition (ETT) or Lifschitz transition [12] only along the a axis, at close to 3.7 GPa [13]. An ETT takes place when some external agent, such as pressure, changes the topology of the Fermi surface of an electronic system. Einaga et al. [14] investigated the effect of pressure on bulk aBi2Te3 for pressures up to 29.8 GPa. The XRD patterns showed the three high pressure phases (named phases II–IV) previously observed. The XRD pattern of phase IV was well reproduced

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S.M. Souza et al. / Physica B 407 (2012) 3781–3789

S1 L1

S2 S3 S1 S2

L2

S3 S4 S5 S5 S4

L3

S3 S2 S1

c

S3 L4

S2 b

S1 a

Fig. 1. Conventional unit cell of a-Sb2Te3. One layer (L) consists of five alternating sheets (S) of Te and Sb. The angle of succession is [Te(S1)–Sb(S2)–Te(S3)–Sb(S4)– Te(S5)] formed by the atoms joined by thick black lines in L2.

assuming a disordered cubic structure (S.G. Im3m), with the Bi and Te atoms sharing the 2a Wickoff site. More recently, Zhu et al. [15] investigated the effect of pressure on bulk a-Bi2Te3 for values up to 52.1 GPa. Again, the XRD patterns showed the high pressure phases II, III and IV. The XRD patterns of phases II and III were well reproduced assuming ordered monoclinic b-Bi2Te3 (S.G. C2/m, Z¼4) and g-Bi2Te3 (S.G. C2/c, Z ¼4) structures, respectively. From ab initio calculations, they proposed an ordered monoclinic d-Bi2Te3 structure (C2/m, Z ¼4) for phase IV. However, the XRD pattern was well reproduced only assuming a disordered monoclinic d-Bi2Te3 structure, with the Bi and Te atoms sharing the same sites. Using the mechanical alloying (MA) technique, we previously produced a nanostructured a-Sb2Te3 powder with an average crystallite size of E22 nm. The structural, optical, thermal, and photoacoustic properties of this powder were studied under room conditions and the results reported in Ref. [16]. For the present study, the same as-milled powder was used. The effect of pressure on nanostructured a-Sb2Te3 (phase I) was investigated using XRD and RS measurements up to 19.2 and 25.5 GPa, respectively. From the XRD patterns, two new high pressure phases (named phases II and III) were observed. In another unpublished paper [17], we reproduced the XRD pattern of phase II assuming a similar b-Bi2Te3 structure (C2/m, Z ¼4) [15], but the structure of phase III remained undetermined. The RS spectrum of phase II is typical of an ordered structure, corroborating the ordered monoclinic b-Sb2Te3 structure assumed. The RS spectrum of phase III measured at 25.5 GPa is also typical of an ordered structure.

Zhao et al. [18] investigated the effect of pressure on bulk aSb2Te3 for values up to 38.6 GPa. Besides the phases II and III observed in our studies, a third high pressure phase (named phase IV) was noted. The XRD pattern of phase II was well reproduced assuming a b-Bi2Te3 structure similar to that proposed in Ref. [17]. However, the XRD pattern of phase III was partially reproduced assuming a disordered monoclinic structure (S.G. C2/m), with the Sb and Te atoms sharing 2a and 4i Wickoff sites. On the other hand, the XRD pattern of phase IV was well reproduced assuming a disordered cubic Bi2Te3 structure (S.G. Im 3 m) [14], with the Sb and Te atoms sharing the 2a Wickoff site. Since Bi2Te3 and Sb2Te3 are isostructural compounds, there is a divergence in the structures of phases III and IV. Recently, RS spectra for Bi2Te3 [19], Sb2Te3 [20] and Bi2Se3 [21] were measured for pressures up to 23, 26 and 30 GPa, respectively. Ab initio calculations of the Raman active modes for these isostructural compounds as functions of pressure were performed assuming the b-Bi2Te3 and g-Bi2Te3 structures, respectively, for phases II and III. For phase IV, the bcc-like monoclinic d-Bi2Te3 structure [15] was assumed given that the calculations for a disordered bcc phase (S.G. Im3m) [14] cannot be performed using the VASP code. An excellent agreement between the theoretical results and experimental data was obtained. From the experimental RS spectra for a-Bi2Te3, a-Sb2Te3 and a-Bi2Se3, the full widths at half maximum (FWHM) of the Raman active modes were obtained and plotted as functions of pressure. An ETT along the a and c axes was observed at close to 4, 3.5 and 5 GPa, respectively. For the Bi2Se3 compound, besides RS measurements, Vilaplana et al. [21] measured XRD patterns up to 20 GPa. Along with the a-Bi2Se3 phase, a new high pressure phase (named phase II) was observed. Its XRD pattern was well reproduced assuming a similar b-Bi2Te3 structure. From the refined XRD patterns of a-Bi2Se3, reduced pressure versus Eulerian strain plots for the a and c lattice parameters were obtained. An ETT was observed along the a axis at close to 5 GPa, as in the case of a-Bi2Te3 [13]. On the other hand, the FWHM of the Raman active modes versus pressure plots showed an ETT along the a and c axes, as observed for a-Bi2Te3 and a-Sb2Te3 [19,20]. These results show that it is necessary to understand the reasons why RS shows ETT along a and c axes, while XRD shows ETT along the a axis only. This paper has two main purposes: (1) to understand why the RS data for a-Sb2Te3 shows an ETT along the a and c axes and XRD data displays an ETT along the a axis only, and (2) to determine the structure of phase III observed in nanostructured Sb2Te3 in order to select the most appropriate structural model from those proposed in the literature [15,18].

2. Experimental procedure A binary Sb2Te3 mixture of high-purity elemental powders of Sb (Aldrich 99.999%) and Te (Alfa Aesar 99.999%) was sealed, together with several steel balls 11.0 mm in diameter, in a cylindrical steel vial under argon atmosphere. The ball-to-powder weight ratio was 7:1. The vial was mounted on a SPEX mixer/mill, model 8000. The temperature was kept close to room temperature by a ventilation system. After 3 h of milling, the XRD pattern was indexed to a-Sb2Te3 [5] and the milling process was interrupted. A membrane diamond anvil cell (DAC) [22] with an opening that allowed probing up to 281 (2y) was used. A small amount of a-Sb2Te3 was compacted between diamonds to a final thickness of approximately 15 mm. A small chip of this preparation, around 80 mm in diameter, was loaded into a stainless-steel gasket hole of 150 mm diameter. Neon gas was used as a pressure-transmitting medium. The pressure was determined by the fluorescence

S.M. Souza et al. / Physica B 407 (2012) 3781–3789

shift of a ruby sphere [23] loaded in the sample chamber. Quasi-hydrostatic conditions were maintained throughout the experiments by monitoring the separation and widths of R1 and R2 lines. In situ XRD patterns as functions of pressure were recorded at the XRD1 station of the ELETTRA synchrotron radiation facility. This diffraction beamline is designed to provide a monochromatic, high-flux, tunable X-ray source in the spectral range 4–25 keV [24]. The study was performed using a wave˚ The detector was a 345-mm imaging plate length of 0.68881 A. from MarResearch. The sample-to-detector distance was calibrated by diffraction data from Si powder loaded in the diamond anvil cell. The data were recorded with a 10 min exposure time. The two-dimensional diffraction patterns were converted to intensity versus 2y using the fit2D software [25] and analyzed by the Rietveld method [10] using the GSAS package [26]. For the Raman measurements as a function of pressure, one particle of approximately 50  60  20 mm3 was loaded in the DAC. The Raman spectra and ruby luminescence were recorded in the backscattering geometry by means of a Jobin-Yvon T64000 Raman triple spectrometer and a liquid-nitrogen-cooled charge coupled-device multichannel detector. An excitation line of l ¼514.5 nm of an Ar laser was used for excitation and focused down to 5 mm with a power of around 20 mW at the entrance of the DAC. The acquisition time was 1800 s.

3. Results and discussion 3.1. X-ray diffraction measurements 3.1.1. Structural phase transitions in a-Sb2Te3 under pressure In situ XRD measurements on as-milled nanostructured a-Sb2Te3 were performed for pressures up to 19.2 GPa. No XRD patterns were recorded during decompression. Fig. 2 shows some selected XRD patterns for several pressures. With increasing pressure, the following structural changes were observed: (1) from room pressure up to 9.8 GPa the XRD patterns are characteristic of a-Sb2Te3. With increasing pressure, the peaks are shifted toward higher 2y values and their intensity remains almost unchanged, except for the peak located at around 2y ¼18.51, associated with the plane (1 1 0), which decreased. This indicates that the planes parallel to the c axis are the m ost affected by pressure; (2) At 9.8 GPa, the XRD pattern shows a shoulder emerging at around 2y ¼13.81, showing that a-Sb2Te3 Ne Ne Intensity (arb. unit)

19.2 GPa

13.2 GPa

9.8 GPa

0.5 GPa

10

12

14

16

18 20 2θ (degrees)

22

24

26

28

Fig. 2. (color online): XRD patterns measured with increasing pressure for the nanostructured rhombohedral Sb2Te3 alloy. The maximum pressure was 19.2 GPa.

3783

starts a transformation into a first high pressure phase (phase II), which is completed at 13.2 GPa, (3) Between 15.2 and 19.2 GPa, phase II starts a transformation into a second high pressure phase (phase III), which is almost complete at 19.2 GPa, as shown in Ref. [17]. At 19.2 GPa, the peak located at 2y ¼13.81, associated with plane (312) of phase II, is still observed.

3.1.2. Analysis of the XRD pattern of a-Sb2Te3 under pressure The XRD patterns of a-Sb2Te3 measured up to 9.8 GPa were refined using the Rietveld method [10] and the results are listed in Table 1. Fig. 3(a), (b) and (c) shows the lattice parameters a, c, and volume and c/a ratio versus pressure, respectively. These figures also show data from Refs. [7,8]. The inset in Fig. 3(c) shows that the c/a ratio decreases up to 2.6 GPa, reaching a minimum at 3.7 GPa and increasing thereafter. A similar behavior of the c/a ratio was observed for a-Bi2Te3 [7,13] and a-Bi2Se3 [21]. The increase in the c/a ratio indicates that the repulsive part of the van der Waals bonds begins to play an important role. The volume as a function of pressure obtained from the Rietveld refinement was fitted to a Birch–Murnaghan equation of state (BM EOS) [11]:   3 3 p ¼ B0 X 5 ðX 2 1Þ 1 þ ðB0 4ÞðX 2 1Þ ð1Þ 2 4 where X¼(V0/V)1/3. From this fitting [see Fig. 3(b)], the values for the bulk modulus B0 ¼36.170.9 GPa and its derivative B00 ¼ 6:2 70:4 (not fixed) were obtained. These values agree quite well with those reported in Ref. [20]. Previously, plots of XRD data versus pressure for a-Bi2Te3 and a-Bi2Se3 showed an ETT along the a axis [13,21], while plots of the FWHM of Raman active modes versus pressure for these phases and for a-Sb2Te3 [20] showed an ETT along the a and c axes. In order to relate the ETT to the changes in a-Sb2Te3 promoted by pressure, we monitored the changes in the angle of succession [Te(S1)–Sb(S2)–Te(S3)–Sb(S4)–Te(S5)], in the intrasheet distances, in the intersheet distances within one layer, and in the interlayer distances. For this, the refined structural parameters listed in Table 1 were used together with the Crystal Office 98 software [27] to build the 3D structure. Fig. 4 shows the changes in the angle of succession [Te(S1)–Sb(S2)–Te(S3)–Sb(S4)– Te(S5)] versus pressure, where an initial decrease up to 0.5 GPa, a minimum at around 3.7 GPa, a smooth decrease up to 7.6 GPa and a fast increase thereafter can be observed. Between 7.8 and 9.8 GPa, the values increase steeply, reaching values similar to those obtained at close to room pressure. However, in this pressure range, a-Sb2Te3 is unstable energetically, due to the high level of defective chemical bonds and strains, and finally transforms into a new structure (phase II). Fig. 5 shows the calculated intrasheet Te(S1)–Te(S1) distances versus pressure (full pentagons curve) for layer L2 (see Fig. 1). A similar behavior was observed for the intrasheet distances considering the sheets S2–S5. Here a smooth decrease with increasing pressure can be noted. Under room conditions, at the angle of succession, the interatomic distances Te(S1)–Sb(S2) and ˚ respectively. Fig. 5 also Sb(S2)–Te(S3) are 2.9823 and 3.1711 A, shows the calculated interatomic distances Te(S1)–Sb(S2) (full squares curve) and Sb(S2)–Te(S3) (full circles curve) versus pressure for layer L2 (see Fig. 1), and minima at close to 3.7 and 5 GPa are observed, respectively. Since the Te and Sb atoms participating in these chemical bonds belong to different sheets within layer L2, these minima indicate that the balance of the attractive and repulsive terms of the van der Waals bond favors the cohesion energy of the structure, leaving it more stable at these pressures. Clearly, with increasing pressure, a-Sb2Te3 becomes energetically unstable due to the high level of defective chemical bonds and strains.

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S.M. Souza et al. / Physica B 407 (2012) 3781–3789

Table 1 Refined structural parameters obtained from the Rietveld refinement for a-Sb2Te3 up to 9.8 GPa. P (GPa)

0.0

˚ a (A) ˚ c (A)

4.2714

4.2582

4.2028

4.1726

4.1421

4.1130

4.0868

4.0470

30.4513

30.1274

29.6823

29.4506

29.2661

29.1015

28.9639

28.7938

0.3988 0.7872

0.3984 0.7853

0.4011 0.7864

0.4014 0.7840

0.3991 0.7846

0.4030 0.7848

0.4044 0.7849

0.3963 0.7864

Sb 1 (Z) Te 1 (Z)

0.5

2.6

3.7

5.0

31.0

6.3

7.6

9.8

7.6 7.12 c/a 7.08

Intra- and intersheets distances (Å)

c (Å)

30.5 30.0

7.04

29.5

0

2

4

6

8

10

a (Å)

29.0 Sakai et al. Present work

4.2 4.1 4.0

Volume (Å3)

460

7.2 7.0

3.2

3.0

2.8

Jacobsen et al. Present work BM fit

480

Te(S1)-Sb(S2) at L2 Te(S1)-Te(S1) at L2 Sb(S2)-Te(S3) at L2

7.4

0

2

B0= 36.1 ± 0.9 GPa B0'= 6.2 ± 0.4

420

10

0

2

4 6 Pressure (GPa)

8

10

Fig. 3. Pressure variation of the structural parameters of Sb2Te3 deduced from the Rietveld adjustments. (a) Lattice parameters; (b) volume; (c) c/a ratio.

92.0 91.8 91.6 ETT

91.4

Intersheet and interlayer distances (Å)

Sb(S4)L2-Sb(S2)L3 (c-axis)

400

Angle Te(S1)-Sb(S2)-Te(S3) (degrees)

8

Fig. 5. Pressure dependence of the intrasheet distance Te(S1)–Te(S1), and intersheet distances Te(S1)–Sb(S2) and Sb(S2)–Te(S3) present in layer L2.

V0=481.1 ± 0.8 Å3

440

4 6 Pressure (GPa)

Te(S1)L2-Sb(S4)L2 (c-axis)

6.5

Te(S3)L1-Te(S1)L2 (c-axis)

6.0

5.5

5.0

91.2

0 91.0 90.8

2

4 6 Pressure (GPa)

8

10

Fig. 6. Pressure dependence of the intersheet distance Te(S1)L2–Sb(S4)L2, and interlayer distances Sb(S4)L2–Sb(S2)L3 and Te(S3)L1–Te(S1)L2. Te and Sb atoms are located on the c axis and belong to layers L1, L2 and L3.

90.6 90.4 90.2 90.0 89.8 0

2

4 6 Pressure (GPa)

8

10

Fig. 4. Pressure dependence of the angle of succession is [Te(S1)–Sb(S2)–Te(S3)– Sb(S4)–Te(S5)].

We also considered only the Sb and Te atoms located on the c axis. Fig. 6 shows the intersheet distance Te(S1)–Sb(S4) versus pressure within the layer L2 (full stars curve), which displays a minimum at close to 5 GPa. This figure also shows the interlayer distances Te(S3)L1–Te(S1)L2 (full circles curve) and Sb(S4)L2– Sb(S2)L3 (full squares curve), which display maximum and minimum values at close to 3.7 GPa, respectively. The physical meaning of a minimum value at around 5 GPa has been

S.M. Souza et al. / Physica B 407 (2012) 3781–3789

3.1.3. Analysis of XRD patterns of b-Sb2Te3 and g-Sb2Te3 As reported in Ref. [17], the XRD pattern of phase II recorded at 13.2 GPa is well reproduced assuming a structure similar to that of b-Bi2Te3 (S.G. C2/m, Z¼4). The best simulation was achieved for the structural parameters listed in Table 2. Fig. 7 shows the experimental and simulated patterns and an excellent agreement can be noted. The peaks located at 2y ¼17.91 and 20.71 belong to the cubic neon structure (S.G. Fm3¯m, Z ¼4) [28]. Due to the low intensity of the latter peak, it is not clearly seen in the experimental XRD pattern. Zhao et al. [18] also reproduced the XRD pattern of phase II assuming a structure similar to that of b-Bi2Te3. As mentioned earlier, there is a divergence regarding the high pressure structures of phases III and IV observed in the isostructural Bi2Te3 and Sb2Te3 compounds. The highest pressure used in this study permitted the XRD pattern of phase III to be recorded. Thus, both ordered and disordered monoclinic structural models proposed in Refs. 15,18 for this phase were used to simulate the XRD pattern measured at 19.2 GPa, and the results are shown in Figs. 8 and 9, respectively. The small amount of phase II was also

taken into account in the simulation. The peaks located at 2y ¼20.11 and 23.31 belong to the cubic neon structure (S.G. Fm3¯m, Z ¼4) [28]. The best simulations were achieved using the structural parameters listed in Table 2. The insets in Fig. 8 show that the ordered monoclinic g-Bi2Te3 structure (S.G. C2/c, Z ¼4) reproduced all details present in the experimental XRD pattern of phase III. In contrast, the insets in Fig. 9 show that the disordered monoclinic Bi2Te3 structure (S.G. C2/m, Z ¼4) was not able to reproduce the shoulder at around 2y ¼13.51 or the peaks located at around 2y ¼18.31 and 26.71. There are constraints that the ordered monoclinic structures proposed for phases II and III must satisfy: (i) the density of the new phase must be larger than that of the previous one, while the volume per number of chemical formulas (V/Z) must be smaller; (ii) the smallest Sb–Te interatomic distance must not be less than roughly the sum of the covalent radii of Sb and Te atoms. At room pressure and 9.8 GPa, the volume and density of a-Sb2Te3 obtained from the Rietveld refinement were V¼478.90 A˚ 3 (V/Z¼159.63 A˚ 3), r ¼7.639 g cm  3 [16] and 408.41 A˚ 3 (V/Z¼136.14 A˚ 3), 8.224 g cm  3, respectively. For b-Sb2Te3, at 13.2 and 19.2 GPa, these values were V¼505.83 A˚ 3 (V/Z¼ 126.46 A˚ 3), 8.224 g cm  3 and 471.46 A˚ 3

Intensity (arb. unit)

previously discussed. On the other hand, the maximum and minimum values being close to 3.7 GPa in the interlayer distances Te(S3)L1–Te(S1)L2 and Sb(S4)L2–Sb(S2)L3 indicate that the balance of the attractive and repulsive terms of the van der Waals bond favors the repulsion and cohesion energies, respectively. Despite the values for the intersheet and interlayer distances being high, giving weak contributions to the ETT observed at close to 3.7 GPa [20], they are sufficient to increase the c/a ratio at pressures above 3.7 GPa [see Fig. 3(c)]. From the results shown in Figs. 4–6, it is clear that the ETT is associated with van der Waals bonds. From the XRD data analysis, no ETT was observed along the c axis for a-Bi2Te3 [13] and a-Bi2Se3 [21]. On the other hand, analysis of the RS data showed an ETT along the a and c axes [19,21]. This apparent contradiction can be explained by the following argument: the XRD technique gives average structural information. Thus, detection of ETT along the a axis in Refs. [13,19] was observed because the attractive part of the van der Waals bonds of Te(S1)–Sb(S2) within the layers (see Fig. 5) is stronger due to the shorter interatomic distance. In contrast, ETT along the c axis was not observed because the van der Waals bonds are weaker due to larger interatomic distances (see Fig. 6). Its detection requires more sensitive techniques, such as RS, as shown in Refs. [19–21]. In this study, RS data for a-Sb2Te3 showed an ETT along the a and c axes, as described later.

3785

10

Neon

Phase II

12

14

16

18 20 2θ (degrees)

22

24

26

28

Fig. 7. XRD pattern of high pressure b-Sb2Te3 (phase II) at 13.2 GPa (open circles) and Rietveld simulation (solid line) for the structural data listed in Table 2. Residual intensities (bottom line) are also shown.

Table 2 Refined structural parameters for b-Sb2Te3 and g-Sb2Te3. For Rietveld simulation of g-Sb2Te3, the ordered monoclinic g-Bi2Te3 (S.G. C2/c) [15] and disordered monoclinic g-Sb2Te3 (S.G. C2/m) [18] structures were considered as initial data. Atom

Site

x

y

z

˚ b¼ 4.0138 A, ˚ c¼ 17.0901 A, ˚ b ¼149.121; Phase II (P¼ 13.2 GPa): space group: C2/m; a ¼ 14.3717 A, Sb1 4i 0.1971 Sb2 4i 0.4599 Te1 4i 0.2321 Te2 4i 0.0451 Te3 4i 0.3470

Rp¼ 1.62%, Rwp¼ 2.07%; r ¼ 8.224 g cm  3 0 0.2079 0 0.2340 0 0.3965 0 0.6106 0 0.9853 ˚ b ¼6.8028 A, ˚ c ¼10.0356 A, ˚ b ¼134.891; Rp ¼3.27%, Phase III (P ¼ 19.2 GPa), simulation considering the model proposed by Zhu et al. Space group: C2/c; a ¼9.7082 A, Rwp¼ 4.27%; r ¼8.860 gcm  3; V ¼469.58 A˚ 3.

Sb1 Te1 Te2

8f 8f 4e

0.2772 0.5843 0

0.1201 0.3585 0.5819

0.8393 0.9391 0.25

˚ b ¼4.6256 A, ˚ c ¼ 3.7174 A, ˚ b ¼88.861; Rp ¼3.15%, Phase III (P ¼19.2 GPa), simulation considering the model proposed by Zhao et al. Space group: C2/m; a ¼8.1899 A, Rwp¼ 4.27%; Occ. (Sb)¼ 0.4, Occ. (Te)¼ 0.6; r ¼8.863 gcm  3; V ¼ 140.83 A˚ 3. Sb/Te1 Sb/Te2

2a 4i

0 0.6780

0 0

0 0.3310

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S.M. Souza et al. / Physica B 407 (2012) 3781–3789

I

160

*

*

Intensity (arb. unit)

13.0

13.5

14.0

16

17

18

19

Phase ΙΙ Neon

V / Z ratio (Å3)

150

140

I

130

II

Phase ΙΙΙ II + III

120

12

*

*

* 14

16

0

18 20 22 2θ (degrees)

24

26

28

5

10 Pressure (GPa)

15

20

Fig. 10. Pressure dependence of the unit cell volume per number of chemical formulas (V/Z) of Sb2Te3 up to 19.2 GPa.

Fig. 8. XRD pattern of high pressure g-Sb2Te3 (phase III) at 19.2 GPa (open circles) and Rietveld simulation (solid line) for the ordered monoclinic structure (S.G. C2/ c) given in Ref. [15]. The refined structural parameters are listed in Table 2. Residual intensities (bottom line) are also shown.

25.5 GPa 19.1 GPa 16.1 GPa

* 13.5

14.0

16

17

Intensity (arb. unit)

13.0

* 18

19

Phase ΙΙ

Intensity (arb. unit)

13.8 GPa 10.6 GPa 8.1 GPa 6.5 GPa 4.8 GPa 3.2 GPa 2.4 GPa

A

Neon 60

12

14

16

18 20 22 2θ (degrees)

24

26

80

0 GPa

100 120 140 160 180 200 220 240 260 280 Wave number (cm-1)

Fig. 11. Raman spectra for nanometric a-Sb2Te3 as a function of pressure. Raman active modes of unreacted elemental tellurium and those of a-Sb2Te3 are assigned. The excitation wavelength was l ¼ 514.5 nm.

*

*

Te Te

Phase ΙΙΙ

*

E

A

28

Fig. 9. XRD pattern of high pressure g-Sb2Te3 (phase III) at 19.2 GPa (open circles) and Rietveld simulation (solid line) for the disordered monoclinic structure (S.G. C2/m) given in Ref. [18]. The refined structural parameters are listed in Table 2. Residual intensities (bottom line) are also shown.

(V/Z¼117.86 A˚ 3), 8.823 g cm  3, respectively. For g-Sb2Te3, at 19.2 GPa, these values were V¼ 469.55 A˚ 3 (V/Z¼117.39 A˚ 3) and 8.860 g cm  3, respectively. At 19.2 GPa, the volume and density of phases II and III are similar, suggesting that perhaps phase III is a structural distortion of phase II. Fig. 10 shows the V/Z value versus pressure, and one can see different behaviors for phases I and II, as for ˚ bulk Bi2Se3 [21]. The covalent radii of Sb and Te are 1.41 A˚ and 1.37 A, respectively [29]. Using the structural data listed in Table 2 in the Crystal Office 98 software [27], the smallest calculated average Sb–Te distances were 2.99 A˚ for phase II at 13.2 GPa and 3.04 A˚ for phase III at 19.2 GPa. From the Rietveld refinement for phase III using the disordered monoclinic structure model proposed by Zhao et al. [18], volume and density values of V¼142.14 A˚ 3 and r ¼8.78 g cm  3 were obtained. The number of chemical formulas Z was calculated

P using the expressionr ¼ 1:66042Z A=V, where r is the density 3 P in g cm , Ais the sum of the atomic weights of 2Sb and 3Te, and V is the volume of the unit cell in A˚ 3 [30]. The value obtained was Z ¼1.2, leading to V/Z ¼118.45 A˚ 3. This value is of the same order as that for g-Bi2Te3. Thus, we disregarded the disordered monoclinic model for phase III since it was not able to reproduce the shoulder and the peaks listed above. As will be shown later, the RS spectra measured for b-Sb2Te3 at 13.8 GPa and for g-Sb2Te3 at 19.2 GPa are very similar, suggesting that the structure of phase III is ordered. 3.2. Raman measurements 3.2.1. Analysis of Raman spectra for a-Sb2Te3 under pressure Fig. 11 shows the RS spectra as a function of pressure for nanostructured a-Sb2Te3. The Raman active modes of elemental trigonal Te A1 E125 cm  1 (119.7 cm  1) and Eupper E143 cm  1 (139.5 cm  1) were observed and are indicated in the figure. The numbers between parentheses are those given in Ref. [31]. The presence of these modes is due to a small fraction of unreacted Te, as shown in Ref. [16]. The fact that they were not detected in the in situ XRD measurements may be due to the small size of the sample. Richter et al. [32] studied the effect of pressure on

S.M. Souza et al. / Physica B 407 (2012) 3781–3789

11 2

A1g 10

1

A1g 2

Eg

9 FWHM (cm-1)

the Raman active modes of Te. With increasing pressure, the wave numbers shift to smaller values. This behavior is observed in Fig. 11, and the Raman active modes are not observed for pressures higher than 4.8 GPa. At room pressure, the RS spectra for a-Sb2Te3 collected inside and outside the DAC are similar [16]. For pressures up to 10.6 GPa, the Raman active modes of a-Sb2Te3 shift to higher wave numbers, and broaden, and the intensities decrease. They disappear at 13.8 GPa, indicating a gradual transformation of a-Sb2Te3 into b-Sb2Te3. Under room conditions, the normal modes of a-Sb2Te3 at the G point of the Brillouin zone are classified according to the irreducible representations of this point group [33],

3787

8 7 6

G ¼ 2ðA1g þEg Þ þ 3ðA2u þ Eu Þ

ð2Þ 5 0

2

4 Pressure (GPa)

6

8

Fig. 13. Experimental pressure dependence of FWHM of the Raman modes for aSb2Te3. Solid lines are visual guides only.

4.5 2

A1g

4.0 dω /dP (cm-1 / GPa)

The u and g letters denote infrared and Raman active modes, respectively. Recently, Sosso et al. [34], using the density functional perturbation theory, computed the infrared and Raman spectra for a-Sb2Te3 under ambient conditions. The wave numbers of the Raman active modes are E1g —46 cm  1 (49 cm  1), A11g – 62 cm  1 (67 cm  1), E2g –113 cm  1 (117 cm  1) and A21g –166 cm  1 (169 cm  1). The numbers between parentheses are experimental values listed in Ref. [34]. These workers also correlated each Raman irreducible representation with a set of displacement patterns: the Eg modes correspond to atomic vibrations in the plane of layers (shear vibrations), while the A1g modes correspond to vibrations along the c axis perpendicular to the layers. Fig. 12 shows the pressure dependence of the wave number of Raman active E2g , A11g and A21g modes up to 10.6 GPa. The wave numbers of the Raman active modes o were obtained through a fitting procedure using Lorentzian profiles. They exhibit a hardening with increasing pressure. A kink at around 4 GPa can be observed, indicating the occurrence of an ETT. Fig. 13 shows the pressure dependence of FWHM for the Raman active modes. One can observe a minimum at close to 3.3 GPa for theE2g , A11g and A21g modes, corroborating the ETT along the a and c axes observed in the XRD analysis. These results are in agreement with those reported for single crystal a-Bi2Te3, a-Sb2Te3 and a-Bi2Se3 [19–21]. As pointed out in Ref. [20], the sharp anomaly observed for the Raman A21g mode indicates a strong electron–phonon coupling leading to hardening of this mode, while the broad anomalies observed for the Raman A11g and E2g modes indicate an

Eg2 A1g1

3.5 3.0 2.5 2.0 1.5

0

5 Pressure (GPa)

10

Fig. 14. Derivative of analytical expressions (4) for fitting the experimental pressure dependence of Raman modes frequencies for a-Sb2Te3. The symbols represent calculated derivative for the pressure used and the solid lines are visual guides only.

200

160

important phonon–phonon coupling, leading to softening of these modes. The pressure dependence of the wave number shown in Fig. 12 was approximated to a standard second-order polynomial:

140

oðPÞ ¼ o0 þAP þ BP2 ,

Wave number (cm-1)

180

2

A1g

where o0 is the wave number in cm  1 at zero pressure and P is in GPa. The fits are not shown in the figure. The polynomials are:

2

120

Eg

oðP,ÞA11g ¼ 70:58 þ 4:42P0:13P2

100

oðP,ÞA21g ¼ 166:35 þ 2:75P0:04P2

1

80

ð3Þ

A1g

oðP,ÞE2g ¼ 114:20 þ2:86P0:88P2

60 0

2

4 6 Pressure (GPa)

8

10

Fig. 12. Experimental pressure dependence of Raman mode frequencies for aSb2Te3. The dashed lines represent different behavior of the experimental Raman modes with pressure.

ð4Þ

The effect of high pressure on the Raman active modes can be better understood by considering the derivative of Eq. (4): do/ dP¼ Aþ2BP. Fig. 14 shows the derivative of the analytical expressions (4) obtained from fitting to Raman active E2g , A11g and A21g modes. It can be observed that theA21g mode is the least affected, followed by E2g and A11g modes.

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S.M. Souza et al. / Physica B 407 (2012) 3781–3789

there is a broad peak between 100 and 200 cm  1 and two broad bands between 225 and 650 cm  1, whose intensities decrease with increasing pressure. These bands are not reported in Ref. [20]. We have no explanation for these two bands. Ref. [20] shows, at 14.5 GPa, a broad band between 100 and 200 cm  1 which is in quite good agreement with the broad peak shown in Fig. 15. According to Ref. [20] and references therein, group theoretical considerations predict for the monoclinic g-Sb2Te3 structure (s.g. C2/c, Z ¼4) 30 vibrational modes with the representation

25.5 GPa

Intensity (arb. units)

19.1 GPa

G ¼ ð7Ag þ 7Au Þ þð8Bg þ8Bu Þ

:ð7Þ

We are thus led to expect 15 zone-center Raman active (7 Ag þ8Bg)modes. Their assignment as well as the corresponding calculated and measured wave numbers at room temperature and 15.2 GPa are listed in Table IV of Ref. [20]. They are concentrated in the frequency range 50–200 cm  1. However, due to mode overlapping, only two broad peaks centered at around 75 and 140 cm  1 are observed up to 24.3 GPa, and their intensity decreases with increasing pressure. In Fig. 15, at 25.5 GPa, only the broad peak and the two broad bands described previously are observed. All intensities are smaller than those at 13.8 GPa values. These results agree with those reported in Ref. [20] for g-Sb2Te3, corroborating an ordered structure for phase III.

16.1 GPa

13.8 GPa

4. Conclusions

100 150 200 250 300 350 400 450 500 550 600 650 Wave number (cm-1) Fig. 15. Raman spectra for b-Sb2Te3 (up to 16.1 GPa) and g-Sb2Te3 (up to 25.5 GPa). The excitation wavelength was l ¼ 514.5 nm.

¨ The Gruneisen parameter g0 describes the effect of high pressure on the volume of the structural lattice of the material, and consequently, on the phonons vibrations. The zero-pressure ¨ mode Gruneisen parameters g0 are determined using the equation [35,36]   B @o g0 ¼ 0 ð5Þ o0 @P P ¼ 0 where B0 and o0 are the bulk modulus in GPa and the wave number in cm  1 at zero pressure, respectively. From the XRD analysis, a bulk modulus B0 ¼36.1 70.9 GPa was obtained. Using the B0 and o0 values in Eq. (5), the g0 values for the A11g , E2g and A21g modes were 2.27, 0.90, and 0.60, respectively. Again, it is observed that the A11g mode is the most affected by pressure. 3.2.2. Analysis of Raman spectra for b-Sb2Te3 and g-Sb2Te3 According to Ref. [20] and references therein, group theoretical considerations predict for the b-Sb2Te3 structure (S.G. C2/m, Z ¼4) 30 vibrational modes with the representation

G ¼ ð10Ag þ10Bu Þ þ ð5Bg þ5Au Þ

ð6Þ

where u and g denote infrared and Raman active modes, respectively. We are thus led to expect 15 zone-center Raman active (10Ag þ 5Bg) modes. Their assignment and corresponding calculated and measured wave numbers at room temperature and 8.6 GPa are listed in Table III of Ref. [20]. They are concentrated in the frequency range of 50–200 cm  1. Fig. 15 shows the Raman spectra measured for pressures between 13.8 and 25.5 GPa. Here

Nanostructured a-Sb2Te3 was produced by mechanical alloying. Its structural and vibrational properties were investigated using in situ high pressure XRD and RS measurements. Two new high pressure phases were observed and their XRD patterns were well reproduced assuming structures similar to those of b-Bi2Te3 and g-Bi2Te3. Fitting the volume versus pressure obtained from the Rietveld refinement to a BM EOS, the bulk modulus B0 ¼36.1 70.9 GPa and its derivative B00 ¼6.270.4 were obtained. The influence of pressure on the angle of succession [Te(S1)– Sb(S2)–Te(S3)–Sb(S4)–Te(S5)] and on the intrasheet, intersheet and interlayer distances was studied and showed an ETT along the a and c axes, which was corroborated by the RS measurements. It was also observed that the effect of pressure is strongest on the A11g mode, followed by the E2g and A21g modes. The XRD pattern of phase III was well reproduced assuming a structure similar to that of g-Bi2Te3. This ordered structure is corroborated by the similarity between the Raman spectra for the b-Sb2Te3 and g-Bi2Te3 phases.

Acknowledgments This research was financially supported by the Brazilian– French CAPES/COFECUB Program (Project No. 559/7). We thank ELETTRA synchrotron (Italy) for the XRD measurements as a function of pressure. We are indebted to Jean-Claude Chervin, Pascal Munch and Gilles Le Marchand for technical support. We are also indebted to Dr. R.S. de Biasi for suggestions and careful reading of the manuscript. References [1] O. Yamashita, S. Tomiyoshi, K. Makita, J. Appl. Phys. 93 (2003) 368. [2] X.F. Tang, W.J. Xie, H. Li, W.Y. Zhao, Q.J. Zhang, M. Niino, Appl. Phys. Lett. 90 (2007) 012102. [3] Y.Q. Cao, X.B. Zhao, T.J. Zhu, X.B. Zhang, J.P. Tu, Appl. Phys. Lett. 92 (2008) 143106. [4] Y. Ma, Q. Hao, B. Poudel, Y. Lan, B. Yu, D. Wang, G. Chen, Z.F. Ren, Nano Lett. 8 (2008) 2580. [5] ICSD—Inorganic Crystal Structure Database, Gmelin-Institut fur Anorganische Chemie and Fachinformationszentrum FIZ Karlsruhe, 1995.

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