Study of structural, optical and thermal properties of nanostructured SnSe2 prepared by mechanical alloying

Materials Chemistry and Physics 169 (2016) 47e54

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Study of structural, optical and thermal properties of nanostructured SnSe2 prepared by mechanical alloying ^s d, T.P.O. Nogueira d, Z.V. Borges a, C.M. Poffo b, *, J.C. de Lima c, S.M. de souza d, D.M. Triche L. Manzato e, R.S. de Biasi f a

Faculdade de Tecnologia, Universidade Federal do Amazonas, 3000 Japiim, 69077-000 Manaus, Amazonas, Brazil , 88900-000, Santa Catarina, Brazil Universidade Federal de Santa Catarina, Campus de Ararangua polis, Santa Catarina, Brazil Departamento de Física, Universidade Federal de Santa Catarina, Campus Trindade, C.P. 476, 88040-900 Floriano d Departamento de Física, Universidade Federal do Amazonas, 3000 Japiim, 69077-000 Manaus, Amazonas, Brazil e ~o, Ci^ Instituto Federal de Educaça encia e Tecnologia do Amazonas, 1672, 69075-351 Manaus, Amazonas, Brazil f ~o de Engenharia Meca ^nica e de Materiais, Instituto Militar de Engenharia, 22290-270 Rio de Janeiro, Brazil Seça b c


Nanostructured SnSe2 was produced using Mechanical Alloying technique.
As milled sample has a high fraction of interfacial component (80%).
Thermal diffusivity value for nanostructured SnSe2 was a new report in literature.

g r a p h i c a l a b s t r a c t as milled SnSe Intensity (electron units)

h i g h l i g h t s

2 (degrees)

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 December 2014 Received in revised form 5 November 2015 Accepted 20 November 2015 Available online 27 November 2015

A nanostructured SnSe2 phase was successfully produced by mechanical alloying. The influence of defect centers on the structural, optical and photoacoustic properties of the alloy was investigated by annealing the as-milled SnSe2 powder. From optical absorbance and photoacoustic absorption measurements, the energy band gap, Eg, and the thermal diffusivity, a, values were determined for as-milled and annealed samples. The thermal conductivity values for the as-milled and annealed samples were estimated by using the a values obtained from the photoacoustic measurements, the density values obtained from the Rietveld refinement of the X-ray diffraction patterns and the specific heat value for the bulk SnSe2 phase. These values were used to estimate the dimensionless figure of merit ZT. It was evidenced that the ZT parameter of the as-milled nanostructured SnSe2 sample is almost twice larger than the ZT of the annealed sample. © 2015 Elsevier B.V. All rights reserved.

Keywords: Nanostructures Thermal properties Differential scanning calorimetry (DSC) Optical properties

1. Introduction

* Corresponding author. E-mail address: [email protected] (C.M. Poffo). http://dx.doi.org/10.1016/j.matchemphys.2015.11.026 0254-0584/© 2015 Elsevier B.V. All rights reserved.

Chalcogenide materials have been the subject of many investigations due to good thermoelectric properties [1,2], among others. Tin diselenide, SnSe2, shows potential for application in thermoelectric refrigerator devices [3e5]. Besides the

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thermoelectric field, the unique electrical and optical properties of SnSe2 also present potential for application in film electrodes, photovoltaic and infrared optoelectronic devices, holographic recording systems, and memory switching devices [4,6,7]. In the thermoelectric field, the materials should have a large Seebeck coefficient, S, high electrical conductivity, se, and low thermal conductivity, KT. A high se is necessary to minimize Joule heating, while a low KT is needed to keep a large temperature gradient at the PeN semiconductor junction. Thermoelectric materials are characterized by their dimensionless figure of merit ZT ¼ ðS2 se ÞKT1 T, where T is the absolute temperature. The term PF ¼ S2se is the electrical power factor. For a good performance, thermoelectric materials should have ZT  1 that can be achieved by increasing the PF factor and/or decreasing KT. It has been suggested [8] that thermoelectric materials having fine grains or small crystallite size may have improved thermoelectric conversion efficiency due a decrease in thermal conductivity. However, a strong degradation of the electrical properties should be avoided. Materials having grains or crystallites with nanometer dimensions are being widely investigated due to their potential for new technological applications as well as scientific interest. These materials are known as nanostructured materials [9]. Different techniques have been used to produce nanostructured materials. Koch's book [10] provides a good review of these techniques. From the structural point of view, nanostructured materials are considered to be composed of two components; one crystalline of nanometer dimensions, which preserves the bulk crystal characteristics, and another interfacial, composed of defects (grain boundaries, interphase boundaries, dislocations, etc). From a technological point of view, manipulation of the interfacial component may offer the possibility to design new materials with physical properties well suited for specific applications [11,12]. Mechanical Alloying is an efficient technique to synthesize many unique materials, such as nanostructured crystals, amorphous alloys and metastable solid solutions [13e15]. This technique has many advantages, including processing at low temperatures, easy composition control, inexpensive equipment and the possibility of up scaling. Its main disadvantage is the possibility of contamination by the milling medium and/or the milling atmosphere. Mechanical Alloying has been used to produce commercially important alloys, in particular, those whose components have a high melting point [16], causing difficulties in the use of techniques based on fusion. For some systems, Mechanical Alloying permits an increase in the limit of solubility in solid solutions [13]. It has been applied to mixtures composed of immiscible elements [13,17e19], allowing the formation of unstable solid solutions in equilibrium conditions. However, the physical mechanisms involved are still not well understood. For industrial applications, a better understanding of these mechanisms is required. According to the ICSD Database code 43594 [20], under ambient pressure and temperature, the SnSe2 phase crystallizes with the trigonal/rhombohedral structure (S.G. P 3 m 1, a ¼ b ¼ 3.811(2) Å, c ¼ 6.137(3) Å, a ¼ b ¼ 90 , g ¼ 120 , Z ¼ 1), with Sn atoms at the 1a (0, 0, 0) Wyckoff position and Se atoms at the 2d (0.3333, 0.6667, 0.25) position. This structure is characterized by strongly bonded two dimensional SneSeeSn layers sandwiches, which are weakly coupled by van der Waals forces [21]. Although the SnSe2 phase has aroused the interest of researchers working in the materials science field aiming its applications in thermoelectric devices, there are few studies reported in the literature on its structural, electrical, optical and photoacoustic properties. In order to partially fill this gap, in this paper we report its production in the nanostructured SnSe2 form by Mechanical Alloying and results on its structural, optical, thermal and

photoacoustic properties. 2. Experimental A binary mixture of high-purity elemental powders of tin (Alfa Aesar, purity 99.8%) and selenium (Alfa Aesar, purity 99.999%) with nominal composition of SnSe2 was sealed together with several steel balls 1.5 cm in diameter in a cylindrical steel vial under an argon atmosphere. The ball-to-powder weight ratio was 4:1. A Spex Mixer/Mill model 8000 was used to perform Mechanical Alloying. A ventilation system was used to keep the vial temperature close to room temperature. After 1.5 h (90 min) of milling, the process was stopped and the powder analyzed via X-ray diffraction (XRD). The XRD pattern showed an excellent agreement with the pattern given in the ICSD Code No. 43594 of the SnSe2 phase [20], and the milling process was interrupted. The XRD patterns were recorded on a powder Bruker D2 Phaser diffractometer equipped with a copper target. In order to verify the thermal stability of the as-milled SnSe2 powder, differential scanning calorimetry (DSC) measurements were performed with a heating rate of 10  C/min under argon flux, using a DSC cell model 2010 manufactured by TA Instruments, Inc. Based on DSC results, annealing of the as-milled SnSe2 powder was carried out. For this, a pellet of SnSe2 was inserted into an evacuated quartz tube, which was maintained under low pressure in argon gas. The sample was annealed at 450  C for 5 h, followed by cooling in air. The XRD pattern of the annealed sample was recorded. All XRD patterns were refined using the Rietveld method [22] implemented in the GSAS package [23]. The XRD pattern of a certified elemental silicon sample was used to estimate instrumental broadening for the Rietveld refinements. All refinements were performed using both Cu Ka1 and Ka2 radiation. In order to investigate the influence of the interfacial component (all types of defects) on the energy gap, Eg, absorbance measurements were taken in an energy range of 0.8e4.0 eV, using a Lambda 19 PerkineElmer spectrometer. The PAS measurements were performed using a homemade open photoacoustic cell (OPC) configuration that consists of a 250 W quartz-tungsten halogen QTH lamp stabilized by a Bentham 605 current power supply. The light beam, after being infrared filtered by a water lens, is mechanically chopped by a PerkineElmer light chopper, model 197, and focused onto the sample. The sample is mounted directly on the front sound inlet of an electret microphone [24]. The output voltage of the microphone is applied to a lock-in amplifier, which in turn is connected to a computer in order to record the amplitude and phase of the PAS signal as a function of the modulation frequency. The samples for the PAS measurements were prepared by pressing the powder at the same pressure to form tiny circular pellets of 1.0 cm in diameter. The thicknesses of the asmilled and annealed samples were 290 and 390 mm, respectively. The PAS measurements were recorded in the modulation frequency range of 10e270 Hz in order to achieve the thermally thick regime. 3. Results and discussion 3.1. Some useful physical mechanisms to understand the formation of SnSe2 by mechanical alloying Mechanical alloying can be seen as a process where moderate pressure values are used. The bulk modulus of Sn (B0 ¼ 58 GPa) is larger than that of Se (B0 ¼ 8.3 GPa) [25]. Thus, the energy necessary to achieve plastic deformation of the Sn unit cell is larger than the energy necessary to achieve plastic deformation of the Se unit cell. Besides promoting plastic deformation of the Sn and Se unit cells, Mechanical Alloying promotes the formation of defective chemical

Z.V. Borges et al. / Materials Chemistry and Physics 169 (2016) 47e54

bonds, characterized by angle and length changes, as well as other kinds of defects (vacancies, twins, dislocations, etc.), which constitute the interfacial component. This chemical disorder stores a sizable amount of energy. As the milling time is increased, the chemical disorder in both the Sn and Se particles increases. However, due to the fact that plastic deformation is smaller in the Sn particles, formation of necks in the Sn particles may occur. If these necks are broken, new Sn particles (henceforward called Sn neck particles) arise [26]. Of course, free Sn atoms may also arise. Energy is stored in both Sn particles and Sn neck particles. The elimination of defect centers releases the stored energy, and the sum of these energies to the energy supplied by the balls becomes the driving force to promote diffusion of Sn neck particles and/or Sn atoms into the Se plastic deformed structure. Both Sn neck particles, free Sn and Se atoms are recovered by the Se plastic deformed structure, forming a composite structure, with an interfacial component in which the solid state reaction occurs [27]. Diffusion occurs under moderate pressures and in limited areas (those that are in contact with the balls), restricting the number of degrees of freedom of Sn neck particles, Sn and Se atoms (nonrandom motion). Thus, the local concentration of Sn neck particles, Sn and Se atoms into the Se plastic deformed structure may vary. As the milling time is increased, Se atoms are pushed into the remaining Sn and neck Sn particles, forming a Sn1-xSex solid solution as well as the nanocrystalline and/or amorphous phases. Of course, Sn1-xSex phases with different compositions can be formed as well. In addition, unreacted elemental Sn and Se may remain. 3.2. X-ray diffraction measurements

49

followed by cooling in air, and its XRD pattern (open circles) is shown in Fig. 2. From these figures one can see that annealing promoted grain growth and improving the SnSe2 crystallization. In another study, Achimovi cov a et al. [4] produced the SnSe2 phase by Mechanical Alloying after 100 min of milling using a planetary ball mill, and obtained an XRD pattern similar to those shown in Figs. 1 and 2. The XRD patterns of as-milled and annealed samples, shown in Figs. 1 and 2, were simulated using the Rietveld structural refinement procedure [22] implemented in GSAS package [23], which also calculated the relative amounts of the phases. For this, the structural data given in ICSD codes 43594 and 39174 [20] for SnSe2 and SnO2, respectively, were used and the best fitting of the XRD pattern of the as-milled sample was obtained with the lattice parameters a ¼ b ¼ 3.8110 Å, c ¼ 6.1370 Å for SnSe2 and a ¼ b ¼ 4.7353 Å (4.7391 Å), c ¼ 3.1831 Å (3.1869 Å) for SnO2. The values in parentheses are those provided by the ICSD code. The volume fractions were 93% of SnSe2 and 7% of SnO2. For the annealed sample, the best fitting of the XRD pattern was obtained with the lattice parameters a ¼ b ¼ 3.8104 Å, c ¼ 6.1419 Å for SnSe2 and a ¼ b ¼ 4.7409 Å (4.7391 Å), c ¼ 3.1878 Å (3.1869 Å) for SnO2. The values in parentheses are those provided by the ICSD code. The volume fractions were 94% of SnSe2 and 6% of SnO2. The simulated XRD patterns for as-milled and annealed samples are also shown in Figs. 1 and 2, where one can see an excellent agreement. The broadening of XRD diffraction lines is well described by a Voigt function V(x), which is a convolution of Gaussian and Lorentzian functions. In a single line analysis, the apparent crystallite l size is given by the Scherrer formula D ¼ b 0:91 cosðqÞ [28], and the L

Fig. 1 shows the XRD pattern of the SnSe2 mixture after 1.5 h of milling (open circles). The angular positions and intensities of peaks were compared with those given in the ICSD 43594 and 39174 [20] for the SnSe2 and SnO2 phases, respectively, and an excellent agreement was observed. Although the milling process was performed under argon atmosphere, the SnO2 phase was also nucleated. The XRD patterns of the elemental Sn and Se powders were recorded before milling and no oxide phases were observed. Thus, we believe that the SnO2 phase was formed during the milling process. Based on DSC results, which will be discussed later, a sample of as-milled SnSe2 powder was annealed at 450  C for 5 h,

001

G microstrain is given by the formula εð%Þ ¼ 4100b tanðqÞ [29], where q is

the diffraction angle, l is the X-ray wavelength and bL and bG are the Lorentzian and Gaussian integral breadths of the diffraction line. The latter are related to full width at half maximum (FWHM) of the normalized Lorentzian WL and Gaussian WG components by the pffiffiffiffiffiffiffi expressions bL ¼ p2 WL and bG ¼ W2G lnp2 [30]. The shape of the Voigt function is determined by the relative importance of these two components. The WL and WG values can be obtained directly from the Rietveld simulated pattern by fitting the desirable peak with a Voigt

SnSe refined

SnSe refined

001

SnO refined

SnO refined Experimental

Experimental

Residual

Total refined

Total refined

Intensity (a. u.)

Intensity (a. u.)

Residual

10

20

30

40

50

60

70

80

2θ (degrees) Fig. 1. Experimental and simulated XRD patterns of the as-milled SnSe2 sample. The difference between experimental and simulated XRD patterns (bottom line) is also shown.

10

20

30

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60

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2θ (degrees) Fig. 2. Experimental and simulated XRD patterns of the annealed SnSe2 sample. The difference between experimental and simulated XRD patterns (bottom line) is also shown.

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function. For this, the Origin software [31] can be used. Knowing the WL and WG values, the bL and bG integral breadth values in radians can be calculated and used in the expressions above to calculate the apparent crystallite size D and the microstrain ε of the diffraction line. We used a certified elemental silicon sample to take into account the instrumental broadening for the Rietveld refinements. The (001) peak in simulated XRD patterns of the as-milled and annealed SnSe2 samples shown in Figs. 1 and 2 were used and the estimated values were: D ¼ 73 Å and ε ¼ 0.63% for as-milled SnSe2 and D ¼ 191 Å and ε ¼ 0.17% for annealed SnSe2. These results show that, with annealing, the weighted average of the actual thickness of the crystallites in a direction perpendicular to the (0 0 1) plane increases and the ε value decreases, showing that the variation (distortions) in d-spacing in the [0 0 1] direction decreases, probably due to a reduction of high level of internal stress associated with the presence of dislocations introduced by Mechanical Alloying process, causing an important chemical disorder in the unit cell. These values suggest that the SnSe2 phase present in both as-milled and annealed samples is nanostructured. The contributions of the nanometric SnSe2 crystallites and of the interfacial component to XRD patterns of as-milled and annealed powders were estimated using an approach developed by our research group [32,33]. For this, the measured intensity was corrected for polarization, reabsorption and inelastic scattering and then converted to electron units using the calculated mean square scattering factor for the SnSe2 phase [34]. The contribution of the interfacial component to XRD pattern is diffuse and could not be separated from the background. An evaluation of the background contribution to the normalized XRD pattern and its subtraction yields the contribution of nanometric SnSe2 crystallites. The background was estimated using the Origin software [31]. The contributions of nanometric SnSe2 crystallites (bottom black curve) and of interfacial component (gray curve) are shown in Fig. 3 only for the as-milled sample. The ratio between the integrated intensity from the SnSe2 crystallites and the integrated intensity from the normalized XRD pattern yields the crystalline volume fraction and, consequently, the balance is the interfacial component. The same procedure was performed for the XRD pattern of annealed sample (not shown). For the as-milled sample we estimated 20% of

crystalline component and 80% of interfacial component, while for the annealed sample the estimates were 67% of crystalline component and 33% of interfacial component. The small amount of SnSe2 present in the as-milled sample is probably due to the small time of milling (90 min). These results, associated with the fact that no abrupt changes were observed in the volume fractions of the SnSe2 and SnO2 phases after annealing process, lead to the conclusion that the substantial increasing of the apparent crystallite size of SnSe2 phase can be related with the diffusion of the atoms, from the interfacial component to SnSe2 crystallites.

3.3. Differential scanning calorimetry measurements In order to investigate the thermal stability of the SnSe2 phase in as-milled sample, DSC measurements were performed and the recorded thermogram is shown in Fig. 4. The thermogram of annealed sample was also recorded and is shown in the same figure where insets A and B correspond to the dashed regions. The DSC thermogram of the as-milled SnSe2 sample shows an exothermic broad band located between 100 and 550  C, a weak endothermic peak located at about 383  C (see inset A), and a strong endothermic double peak located at about 612  C and 627  C (see inset B). The DSC thermogram of annealed SnSe2 sample does not show the exothermic broad band observed in as-milled sample. The weak endothermic peak is observed, but shifted to a slightly higher temperature, 402  C (see inset A), as well as the strong endothermic double peak located at about 612  C and 625  C (see inset B). The enthalpy change can be determined calculating the area of the thermogram under the strong endothermic peak. The values for the as-milled and annealed samples are 123.42 J/g and 142.14 J/g, respectively. The presence of an exothermic broad band between 100 and 550  C in the thermogram of as-milled sample and its absence in the thermogram of annealed sample suggests that it is related to structural relaxation and substantial growth of the apparent crystallite size of SnSe2 phase. This seems to be corroborated by the large volume fraction of the interfacial component (80%). The weak endothermic peaks located at about 383  C and 402  C in the thermograms of the as-milled and annealed samples, respectively, are attributed to melting of SeO3, whose melting point is 394  C [35] and that probably is present in too small amounts to be seen in

2500

as-milled annealed

2

2



A

0 1500

Heat flux (mW)

Intensity (electron units)

2000

1000

-2 -4

B A

-6 Temperature ( C)

500

-8 0

-10 20

40

60

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2θ (degrees) Fig. 3. Normalized XRD patterns of an as-milled SnSe2 sample: all contributions (black curve), crystalline contribution (red curve), and mean square scattering factor (blue curve). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

100

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o

Temperature ( C) Fig. 4. DSC thermograms of as-milled and annealed SnSe2 samples with a heating rate of 10  C min1.

Z.V. Borges et al. / Materials Chemistry and Physics 169 (2016) 47e54

the XRD patterns. According to Ref. [35], the melting point of SnSe2 phase is 657  C. The strong endothermic double peaks of as milled and annealed samples are located at temperatures significantly smaller than 657  C. It is well known that the melting point of a solid is related to its microstructure and, particularly, on the strength of the chemical bonds. In the case of nanostructured solids, the melting points may be smaller than those of their bulk counterparts due to the large number of defects. The SneSe phase diagram [35] shows a eutectic point at 628  C at a nominal composition Sn2Se3. Refs. [36e38] reported results of microstructural, XRD and Nuclear Magnetic Resonance (NMR) measurements performed on the SneSe system showing that, under ambient pressure and temperature, there is no Sn2Se3 phase. Thus, the strong endothermic peak is attributed to fusion of the nanostructured SnSe2 phase, which occurs in two steps. Usually, fusion occurring in two steps is related microstructures containing multiphases. As it was mentioned, the Mechanical Alloying process produces a composite powder, which can have several regions with different nominal compositions, and phases with different chemical compositions may nucleate. Thus, one of peaks present in the strong endothermic peak may be due to another metastable phase having stoichiometry close to SnSe2 or to a polytypic phase of SnSe2 [39,40], while the other may be due to fusion of nanostructured SnSe2.

3.4. Optical absorbance spectra of as-milled and annealed SnSe2 samples Fig. 5 shows the optical absorbance spectra as a function of the photon energy for as-milled (blue curve) and annealed (red curve) samples. From this figure one can see that the optical band gap corresponding to the as-milled sample is shifted toward smaller energies probably due to the small crystallite size (D ¼ 73 Å) as well a substantial volume fraction of interfacial component (z80%). On the other hand, the optical band gap corresponding to the annealed sample is shifted toward larger energies probably due to the increase in the crystallite size from 73 Å to 191 Å as well as a substantial reduction in the volume fraction of the interfacial components, from 80% to 33%. The optical band gap can be determined by a McLean analysis of the absorption edge using the equation [41].

51

 1=n bhy ¼ hy  Eg þ Ep

(1)

where b is the absorption coefficient, Eg is the band gap energy, Ep is the phonon energy for indirect transitions, h is the Planck constant and y is the frequency of the incident light. The analysis consists of fitting the absorption edge to Eq. (1) and determining the values of Eg, Ep and n. A value of n ¼ 2 implies a direct allowed transition; n ¼ 2/3 implies a direct forbidden transition; n ¼ 1/2 implies an indirect allowed transition; n ¼ 1/3 implies an indirect forbidden transition. The relationship among the absorbance A, absorption coefficient b and thickness d of a sample is given by [42].

b¼

A d

(2)

For absorbance measurements, the as-milled and annealed SnSe2 powders were dispersed into a powder support KBr and the mixture was pressed in the form of a pellet. In this case, the thickness d and absorption coefficient b of the samples are unknown. Thus, Eq. (1) was changed to

 1=n Ahv ¼ C hv  Eg þ Ep

(3)

where C is related to the sample thickness and is a parameter to be included in the fitting procedure. The best fitting of experimental data of the as-milled and annealed samples to Eq. (3) yielded band gap energies of Eg ¼ 1.02 eV and 1.48 eV, respectively, considering a direct allowed transition, as shown in Fig. 6. In other studies, Achimovicov a et al. [4] reported a direct allowed transition with a value of Eg ¼ 1.25 eV for SnSe2 obtained after 100 min of milling and Martinez-Escobar et al. [43] reported a direct allowed transition with a value of Eg ¼ 1.59 eV for thin film SnSe2 produced by the spray pyrolysis technique. The values obtained in this work are slightly smaller than those reported in Refs. [4,43]. The differences may be related to the techniques used to produce the samples. It is interesting to note, the influence of the apparent crystallite size and volume fraction of interfacial component, on the obtained optical band gap energies for the SnSe2 as-milled and annealed samples. This behavior suggests that it is possible design a SnSe2 nanostructured 8

annealed as-milled fit

as-milled

(Abs X hν) (eV)

2

Absorbance (a. u.)

6

2

annealed

4

2

0

0.75

1.00

1.25

1.50

1.75

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Photon energy (eV) Fig. 5. Absorbance spectra of as-milled and annealed SnSe2 samples.

3.00

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Energy (eV) Fig. 6. Absorbance spectra of as-milled and annealed SnSe2 samples. The solid lines represent the fitting using Eq. (3) of the text.

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Z.V. Borges et al. / Materials Chemistry and Physics 169 (2016) 47e54

sample with specific optical band gap energy. This is particularly interesting in the photovoltaic and infrared optoelectronic devices field [6]. 3.5. Photoacoustic measurements on as-milled and annealed SnSe2 samples The use of photoacoustic absorption spectroscopy to determine the thermal diffusivity parameter and/or the transport properties of semiconducting materials is well documented in the literature [44e46]. A review can be found in some papers [33,47] as well as in references therein and will not be repeated here. Since the thermal diffusivity of SnSe2 was not found in the literature, it was estimated using the expressionKT ¼ r$Cpa, where KT is the thermal conductivity, r is the density, Cp is the specific heat, and a is the thermal diffusivity. The TAPP software [35] gives values of r ¼ 5202 kg m3 and Cp ¼ 258 J kg1 K1 for bulk SnSe2. Busch et al. [5] reported a value of KT ¼ 7.29 W m1 K1 for the thermal conductivity of SnSe2 at room temperature. Using these values in the expression of the thermal conductivity, a thermal diffusivity of a ¼ 0.054 cm2 s1 was calculated. The characteristic frequency corresponding to the transition from the thermally thin regime (f < fc) to the thermally thick regime (f > fc) is given by fc ¼ a=ðpl2s Þ, where ls is the sample thickness. The thicknesses of the as-milled and annealed samples were 290 and 390 mm, giving characteristic frequencies of 20.4 Hz and 11.3 Hz, respectively. In order to perform PAS measurements in the thermally thick regime, the data were acquired between 10 and 270 Hz. On the other hand, it is well documented in the literature that SnSe2 is a n-type semiconductor [48]. Thus, besides the intraband nonradiative thermalization (thermal diffusion) and thermoelastic bending mechanisms, nonradiative bulk recombination and nonradiative surface recombination mechanisms can also contribute to the PAS signal. A brief summary describing the contribution of these heat transfer mechanisms to the PAS signal as well as the procedure to find the contribution of each process to the pressure variation in the photoacoustic cell is given in Ref. [49] and it will not be repeated here. Fig. 7 shows the plots ln(S) vs f½ and Fph(rad) vs f½ for modulation frequencies between 25 and 32 Hz, where the intraband nonradiative thermalization (thermal diffusion) mechanism is the main contribution to the PAS signal amplitude and phase for the as

milled sample. In this frequency range, the slopes of the straight lines were the same: a ¼ 0.2886 for both amplitude and phase. Using the expressiona ¼ p(ls/a)2, the calculated value of the thermal diffusivity was a ¼ 0.031 cm2 s1. For the annealed sample, this heat transfer mechanism was not observed. Fig. 8 shows the plot log(S) vs log(f) for modulation frequencies between 36 and 70 Hz for an as-milled sample and between 26 and 95 Hz for an annealed sample, where the nonradiative surface recombination, thermoelastic bending or thermal dilation [50] heat transfer mechanisms can be the main contribution to the PAS amplitude and phase. For these mechanisms the PAS amplitude changes with modulation frequency as f1. From this figure one can see that the PAS signal amplitudes of the as-milled and annealed samples change with modulation frequency as f0.91 and f0.95, respectively. Thermal dilation produces a signal whose phase is independent of the modulation frequency and equal to 90 . Fig. 9 shows the Fph(rad) vs f plot for the as-milled and annealed samples. From this figure, the heat transfer mechanism can be discarded. Eq. (3) for the phase corresponding to the thermoelastic bending mechanism given in Ref. [49] was successfully fitted to the Fph(rad) vs f plot in the frequency ranges shown in Figs. 8 and 9. From the best fittings, a thermal diffusivity of a ¼ 0.031 cm2 s1 for the asmilled sample and a ¼ 0.056 cm2 s1 for the annealed sample were obtained. The value of the thermal diffusivity obtained for the annealed SnSe2 phase agrees quite well with the value a ¼ 0.054 cm2 s1 calculated using data from the Refs. [5,35]. The smaller value of thermal diffusivity obtained for the as-milled sample is attributed to the presence of a significant volume fraction of interfacial component and strains in the crystalline component. As suggested in the literature [51], the performance of a thermoelectric material can be improved if its thermal conductivity is reduced without strong degradation of the electrical properties. In addition, it has been reported that materials having small crystallite size can have larger thermoelectric conversion efficiency due a decrease in the thermal conductivity of the lattice [8]. As previously mentioned, thermoelectric materials are characterized by their dimensionless figure of merit ZT ¼ ðS2 se ÞKT1 T. The values of density and apparent crystallite size of the as-milled and annealed SnSe2 samples were obtained from the Rietveld refinements of the XRD patterns. These values were 5950 kg/m3 and 73 Å and 5947 kg/

annealed as milled

4

5

6

Square root modulation frequency (Hz)

1/2

7

Fig. 7. PAS amplitude and PAS phase versus modulation frequency of an as-milled SnSe2 sample showing the intraband nonradiative thermalization (thermal diffusion) mechanism.

PAS Signal amplitude (μV)

linear fit

PAS signal phase (a. u.)

PAS signal amplitude (a. u.)

PAS signal PAS signal phase linear fit f

f

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-0.91

-0.95

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Modulation Frequency (Hz) Fig. 8. PAS signal amplitude versus modulation frequency of as-milled and annealed SnSe2 samples showing the thermoelastic bending mechanism.

Z.V. Borges et al. / Materials Chemistry and Physics 169 (2016) 47e54

Acknowledgments

2.5

annealed as-milled fit

1.5

Two of authors, Z.V. Borges and T. P. O. Nogueira, thank the Brazilian agencies CNPq and CAPES for financial support. The authors thank the LABINC-UFSC and C. C. V. Chaves for the optical absorbance measurements.

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PAS Signal Phase (rad)

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270

Modulation Frequency (Hz) Fig. 9. PAS phase versus modulation frequency of as-milled and annealed SnSe2 samples showing the thermoelastic bending mechanism. The solid lines correspond to the best fittings of experimental data to Eq. (3) given in Ref. [49].

m3 and 191 Å for the as-milled and annealed samples, respectively. Thus, it is interesting to estimate the influence of the nanometric apparent crystallite size on the ZT parameter. The thermal conductivity KT (KT ¼ rCpa) was estimated using the values of thermal diffusivity obtained by PAS (0.031  104 m2 s1 and 0.056  104 m2 s1 for the as-milled and annealed samples, respectively), densities obtained by Rietveld procedure and specific heat given in TAPP software [35]. Therefore, the calculated thermal conductivities were 4.759 W/mK and 8.592 W/mK for the as-milled and annealed samples, respectively. Frongillo et al. [52] reported the room-temperature values of electrical resistivity re ¼ 1.5  103 Um (se ¼ 6.667  102 (Um)1) and Seebeck coefficient S ¼ 500 mV K1 of SnSe2 single crystal grown by the Bridgman technique. Using these values in the expression for ZT, values of ZT z 0.0105 and 0.0058 were obtained for the as-milled and annealed samples, respectively. These values show that ZT for asmilled sample is almost twice larger than the calculated for the annealed sample. Of course, for an accurate evaluation of ZT, the parameters re, Cp, and S for the nanostructured SnSe2 sample should be measured. These results seem to corroborate the suggestion found in the literature that thermoelectric material having fine grains or small crystallite size, may have improved thermoelectric conversion efficiency due a decrease in thermal conductivity [8].

4. Conclusions In this work, the mechanical alloying technique successfully produced a nanostructured SnSe2 phase. From the normalized XRD patterns, the volume fractions of crystalline and interfacial components were estimated for both as-milled and annealed samples. From the absorbance measurements, values of energy band gap for both as-milled and annealed samples were obtained. The PAS measurements yielded to thermal diffusivity values a ¼ 0.031 cm2 s1 (0.031  104 m2 s1) and a ¼ 0.056 cm2 s1 (0.056  104 m2 s1) for the as-milled and annealed samples, respectively. Also, it was found that the dimensionless figure of merit, ZT, for the as-milled sample is almost twice larger than that calculated for the annealing sample.

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