Abstract
A nanostructured SnTe phase was produced by mechanical alloying after 2 h of milling. Part of the as-milled powder was annealed and its X-ray diffraction (XRD) pattern was recorded. The XRD patterns of the as-milled and annealed samples were refined using the Rietveld method. After annealing, partial decomposition of the SnTe phase was observed and corroborated by estimating the mean crystallite size using a Willianson-Hall plot. The Cowley-Warren parameter for the first coordination shell was calculated, showing a preference for homopolar pairs. This preference is consistent with the partial decomposition observed. According to the optical absorbance spectra, the band gap energy is inversely proportional to crystallite size, following a decaying exponential function. From the photoacoustic absorption spectroscopy measurements, the thermal diffusivity parameter and the transport properties of as-milled and annealed SnTe powder were determined.
Key-words:
Semiconductors; Nanocrystals; Mechanical alloying; Thermoelectric materials; X-ray diffraction; Photoacoustic absorption spectroscopy
1. Introduction
Chalcogenide semiconductor compounds are of considerable interest due to their optical11 Schaller RD, Petruska M, Klimov VI. Tunable Near-Infrared Optical Gain and Amplified Spontaneous Emission Using PbSe Nanocrystals. The Journal of Physical Chemistry B. 2003;107(50):13765-13768., electronic22 Talapin DV, Murray C. PbSe nanocrystal solids for n- and p-channel thin film field-effect transistors. Science. 2005;310(5745):86-89., and optoelectronic33 Cao WY, Banin U. Growth and Properties of Semiconductor Core/Shell Nanocrystals with InAs Cores. Journal of the American Chemistry Society. 2000;122(40):9692-9702. applications. In particular, the tin telluride (SnTe) compound has potential applications in mid-infrared (3-14 µm) detection and thermoelectric conversion44 Lovett D. Semi-Metals and Narrow-Bandgap Semiconductors. London: Pion Limited; 1977.
5 Das VD, Bahulayan C. Variation of electrical transport properties and thermoelectric figure of merit with thickness in 1% excess Te-doped Pb0.2Sn0.8Te thin films. Semiconductor Science and Technology. 1995;10(12):1638-1644.
6 Berger LI. Semiconductor Materials. Boca Raton: CRC Press; 1996.-77 Fürst J, Pascher H, Schwarz T, Böberl M, Heiss W, Springholz G, et al. Midinfrared IV-VI vertical-cavity surface-emitting lasers with zero-, two-, and three-dimensional systems in the active regions. Applied Physics Letters. 2002;81(2):208-210..
According to the Inorganic Crystal Structure Database (ICSD)88 FIZ. Inorganic Crystal Structure Database (ICSD). Kalrsruhe: Gmelin-Institute fur Anorganische Chemie and Fachinformationszentrum (FIZ); 1995., code 188457, at room temperature and atmospheric pressure, the SnTe compound crystallizes in a cubic structure (S.G. Fm3-m, Z = 4), with the Sn atoms occupying the Wyckoff site 4a (0, 0, 0) and the Te atoms occupying the site 4b (0.5, 0.5, 0.5). This compound can be synthesized using the techniques of molecular beam epitaxy99 Mengui UA, Abramof E, Rappl PHO, Ueta AY. Characterization of SnTe films grown by molecular beam epitaxy. Brazilian Journal of Physics. 2006;36(2A):324-327., electrodeposition1010 Sisman I, Öz H. Preparation of SnTe thin films on Au(111) by electrodeposition route. Electrochimica Acta. 2011;56(13):4889-4894., solution-phase synthesis1111 An C, Tang K, Hai B, Shen G, Wang C, Qian I. Solution-phase synthesis of monodispersed SnTe nanocrystallites at room temperature. Inorganic Chemistry Communications. 2003; 6(2):181-184. and mechanical alloying (MA)1212 Saini R, Pallavi, Singh M, Kumar R, Jain G. Structural and electrical characterization of sintered SnTe films. Chalcogenide Letters. 2010;7(3):197-202.,1313 Saini R, Singh M, Kumar R, Jain G. Electrical properties of SnTexSe1-x sintered films. Optoelectronics and Advanced Materials - Rapid Communications. 2009;3(1):49-52.. MA has been used for synthesizing crystalline compounds, amorphous materials and solid solutions1414 de Lima JC, Borba EC, Paduani C, dos Santos VHF, Grandi TA, Rechenberg HR, et al. Mechanical alloying of Fe and Zn: phase analysis and Mössbauer studies. Journal of Alloys and Compounds. 1996;234(1):43-47.
15 Weeber AW, Bakker H. Amorphization by ball milling. A review. Physica B: Condensed Matter. 1988;153(1-3):93-135.
16 Mukhopadhyay DK, Suryanarayana C, Froes HH. Extended solid solutions in Cd-Zn powders by mechanical alloying. Scripta Metallurgica et Materialia. 1994;30(1):133-137.-1717 Yavari AR, Desré PJ, Benameur T. Mechanically driven alloying of immiscible elements. Physical Review Letters. 1992;68(14):2235-2238.. It has also been used to produce nanostructured materials as well as alloys whose components have large differences in their melting points, making difficult their production through techniques based on fusion1818 Che J, Yao X, Jian H, Wang M. Application and preparation of ZnSe nanometer powder by reduction process. Ceramics International. 2004;30(7):1935-1938..
Nanostructured materials are metastable and can be described by two structural components, one containing crystallites with nanometer dimensions (2-100 nm), that have the same structure as the bulk crystalline counterpart, and an interfacial component formed by different kinds of defects (grain boundaries, interphase boundaries, dislocations, etc.)1919 Gleiter H. Materials with ultrafine microstructures: Retrospectives and perspectives. Nanostructured Materials. 1992;1(1):1-19.. Commonly, the volume fractions of the two components are of the same order, leading a strong dependence of the material properties on the atomic arrangements of the interfacial phase1919 Gleiter H. Materials with ultrafine microstructures: Retrospectives and perspectives. Nanostructured Materials. 1992;1(1):1-19.. Manipulation of these atomic arrangements leads to the possibility of designing new materials with the properties required for specific technological applications2020 Stern EA, Siegel RW, Newville M, Sanders PG, Haskel D. Are Nanophase Grain Boundaries Anomalous? Physical Review Letters. 1995;75(21):3874-3877..
Since MA yields materials containing a high concentration of defect centers, it is interesting to investigate the influence of concentration of defect centers on the structural, optical, thermal, and photoacoustic properties of SnTe. For this, the X-ray diffraction (XRD), differential scanning calorimetry (DSC), optical absorbance (UV-VIS-NIR), and photoacoustic absorption spectroscopy (PAS) techniques were used. This paper reports the results obtained for as-milled and annealed nanostructured SnTe.
2. Determination of mean crystallite size and strain using the Williamson-Hall plot and a pseudo-Voigt function to describe the diffraction line profiles
The diffraction line broadening is well described by a Voigt function, which is described by a convolution of Gaussian and Lorentzian (also called as Cauchy) functions. In a single line analysis, the apparent crystallite size is calculated using the Scherrer formula2121 Cullity BD. Elements of X-Ray Diffraction. 2nd ed. Reading: Addison-Wesley; 1978. and the strain is calculated using the formula2222 Young RA, ed. The Rietveld Method. IUCr Monographs on Crystallography - 5. Oxford: International Union of Crystallography/Oxford University Press; 1993. where θ is the diffraction angle, λ is the X-ray wavelength and βL and βG are the Lorentzian and Gaussian integral breadths of the diffraction line. The βL and βG integral breadths are related to full widths at half maximum (FWHM) of the normalized Lorentzian ΓL and Gaussian ΓG components by the expressions and . The shape of the Voigt function is determined by the relative intensities of the two components. The pseudo-Voigt function, pV(x), is an approximation of the Voigt function that substitutes the shape parameters ΓL and ΓG by two other parameters, Γ and η. The function is a linear combination of Lorentzian and Gaussian functions with the same FWHM, Γ, and a parameter 0.3282323 Dasgupta P. On the intrinsic hook effect associated with pseudo-Voigt profiles. Journal of Applied Crystallography. 2002;35(Pt 2):267-269. ≤ η ≤ 1 used to specify the relative intensity of the Lorentzian component.
The relations between the ΓG and Gaussian ΓL of the Voigt function and the Γ and η of pV(x) are given by the expressions,
and
Using the relations and , where and , we have
βL + βG = (c1c3 + c2c4) Γ
or
Expression (4) is the standard equation for a straight line (y = a + bx). By plotting Γ cos θ versus sin θ we obtain the mean microstrain component from the slope and the mean crystallite size from the interception with the Γ cos θ axis. Such plot is known as the Williamson-Hall plot. The Γ and η values are obtained directly from the Rietveld refinement of the XRD pattern.
A relationship between the crystallite size D and the microstrain σp can be obtained due to the fact that pV(x) is a linear combination of Lorentzian and Gaussian functions with the same FWHM (Γ), and
Eq. (5) should be used in a single line analysis only, i.e., after determining the apparent crystallite size.
3. Experimental Procedure
High-purity elemental powders of tin (Alfa Aesar 99.8 %) and tellurium (Alfa Aesar 99.999 %) were blended with SnTe nominal composition was sealed together with several steel balls of 1.5 cm in diameter into a cylindrical steel vial under argon atmosphere. The ball-to-powder weight ratio was 5:1. MA was performed using an 8000 Spex Mixer/Mill at room temperature, and a ventilation system was used to keep the vial temperature close to room temperature. The milling process was stopped after 2 h when the XRD pattern of the as-milled powder showed an excellent agreement with the pattern given in the ICSD code 188457 for the SnTe phase88 FIZ. Inorganic Crystal Structure Database (ICSD). Kalrsruhe: Gmelin-Institute fur Anorganische Chemie and Fachinformationszentrum (FIZ); 1995.. The XRD patterns were recorded using a Philips X-Pert powder diffractometer, using the Cu K⍺ radiation (λ = 1.5406 Å). The XRD patterns were refined using the Rietveld method2424 Rietveld HM. A Profile Refinement Method for Nuclear and Magnetic Structures. Journal of Applied Crystallography. 1969;2:65-71., implemented in the GSAS package2525 Larson AC, von Dreele RB. General Structure Analysis System (GSAS). Report LAUR 86-748. Los Alamos: Los Alamos National Laboratory; 2004.. The XRD pattern of a certified elemental silicon sample was recorded in the same experimental conditions and used to take into account the instrumental broadening for the Rietveld refinements. A pV(x) function was used to describe the diffraction lines profiles. Thermal parameter (Uiso) was assumed to be isotropic.
The thermal stability of the SnTe phase was investigated using DSC measurements from room temperature up to 500 ºC, with a heating rate of 10 ºC min-1, under nitrogen flow, using Al pans in a TA Instruments 2010 DSC cell. Based on the thermograms, annealing was carried out on a portion of the as-milled SnTe powder in order to study the influence of concentration of the defect centers on the properties previously mentioned. For this, a pellet of SnTe was inserted into an evacuated quartz tube, which was maintained under low pressure (≈ 10-3 Torr) in argon gas. The sample was annealed at 320 ºC for 2.5 h, followed by air cooling.
The optical properties of the as-milled and annealed nanostructured SnTe samples were studied using UV-VIS-NIR measurements. The optical transmittance measurements were taken in an energy range of 0.06-0.50 eV, using a Perkin-Elmer FT-IR Spectrometer, Spectrum 100. For measurements, as-milled and annealed powders were dispersed into KBr powder and pressed using the same pressure to form pellets.
The PAS measurements were carried out in an open photoacoustic cell (OPC) setup built at home. Details about the OPC setup can be found in Refs. 26 and 27. The samples for the OPC measurements were prepared by compressing at the same pressure (6 tons) the as-milled and annealed SnTe powders to form tiny circular pellets, 10 mm in diameter, with thickness of 440 µm and 450 µm, respectively. The samples were mounted directly onto the front sound inlet of an electret microphone, and periodically illuminated to generate the photoacoustic effects, as described by the thermal diffusion model.
4. Results and Discussion
4.1 XRD and DSC measurements
Figure 1 shows the XRD pattern (black open circles) recorded for 2 h of milling. It was compared with those given in the ICSD Database88 FIZ. Inorganic Crystal Structure Database (ICSD). Kalrsruhe: Gmelin-Institute fur Anorganische Chemie and Fachinformationszentrum (FIZ); 1995. for the Sn-Te system, and an excellent agreement was observed with that for cubic SnTe (ICSD code No. 188457). Besides the diffraction peaks of SnTe, two low intensity diffraction peaks at about 2θ = 27º and 34º were observed, and indexed to SnO2 (ICSD code 9163). The SnO2 peaks did not appear in the XRD patterns of the Sn and Te powders used to prepare the samples. Then, its nucleation probably occurred during manipulation of the powder to perform the XRD measurements and is probably restricted to the region close to the particle surface. The enthalpies for formation of the SnO2, TeO2, and SnTe phases are -596.429 kJ/mol, -345.503 kJ/mol, and -91.737 kJ/mol2828 Microwave Inc. TAPP Software, Version 2.2. E.S. Wade Court: Microwave Inc.; 1998., respectively.
(color online): Experimental and simulated XRD patterns of an as-milled SnTe sample after 2 h of milling. The simulated SnTe and SnO2 phases as well as the difference between experimental and simulated patterns (bottom line) are also shown
For the Rietveld refinement of the XRD pattern of the as-milled sample, shown in Fig. 1, the structural models in the ICSD codes for SnTe and SnO2 given above were used. The best fit was reached for the lattice parameters a = 6.3183 Å (6.3183 Å), η = 0.328 for SnTe and a = b = 4.7333 Å (4.7380 Å), c = 3.1971 Å (3.1865 Å), η = 0.328 for SnO2. The values within parentheses are those given in the ICSD codes above. The thermal parameter (Uiso) was assumed to be isotropic. The simulated XRD patterns for the as-milled sample as well as the individual patterns for SnTe and SnO2 and the difference between experimental and simulated patterns (bottom line) are shown in Fig. 1, from where one can see an excellent agreement.
The Rietveld refinement does not take into account the contribution of the background to calculate the relative volume fractions of phases composing the experimental XRD pattern. The relative volume fractions were 96 % for SnTe and 4 % for SnO2. The goodness-of-fit indicators Rp and Rwp are shown in this figure.
The XRD pattern of as-milled samples shows broad peaks, suggesting that the mean crystallite size D of the SnTe phase is of nanometer dimension. The values of D and of the microstrain σp were estimated through the Williamson-Hall plot, using a pseudo-Voigt function to describe the profiles of peaks in the Rietveld refinement, as shown in Section 2. The values of Γ and θ were obtained from the Rietveld refinement. Figure 2 shows the Γ cos θ vs sin θ data for the SnTe phase. By fitting the data to a straight line, values of D = 75.2 nm and of σp = 0.45 % were obtained.
As described in the Section 3, part of the as-milled SnTe powder was annealed in order to study the influence of concentration of the defect centers on the properties previously mentioned. Figure 3 shows the XRD pattern of the annealed sample. The pattern shows, besides the peaks of SnTe and SnO2, low intensity peaks at about 2θ = 27.6º and 38.3º that were indexed to elemental Te (ICSD code 65692)88 FIZ. Inorganic Crystal Structure Database (ICSD). Kalrsruhe: Gmelin-Institute fur Anorganische Chemie and Fachinformationszentrum (FIZ); 1995.. The best Rietveld refinement of this XRD pattern was reached considering the values of lattice parameter a = 6.3155 Å, η = 0.328 for SnTe; a = b = 4.7390 Å, c = 3.1907 Å, η = 0.328 for SnO2; and a = b = 4.4718 Å (4.456 Å), c = 5.9167 Å (5.921 Å), η = 0.328 for elemental Te. The values within parentheses are those given in the ICSD code 65692. The simulated XRD patterns for the annealed sample and individual patterns for SnTe, SnO2, elemental Te, and the difference between experimental and simulated patterns (bottom line) are shown in Fig. 3, from where one can see an excellent agreement. The relative volume fractions were 77 % for SnTe, 13 % for SnO2, and 10 % for elemental Te. It is interesting to note that after annealing, the volume fraction of SnTe decreased 19 % and the volume fraction of SnO2 increased 9 %. The goodness-of-fit indicators Rp and Rwp are shown in this figure.
(color online): Experimental and simulated XRD patterns of an annealed SnTe sample. The simulated SnTe, SnO2 and elemental Te phases as well as the difference between experimental and simulated patterns (bottom line) are also shown
As for as-milled SnTe, the values of D and σp for annealed SnTe were estimated using the Williamson-Hall plot, which is shown in the inset of Fig. 2. By fitting to a straight line, values of D = 59.3 nm andσp = 0.075 % were obtained. It is interesting to note that, after annealing, a variation of ≈ 21% in the mean crystallite size is observed, and this value is close to the variation in the volume fraction of SnTe (19 %).
Chemical disorder is among the physical mechanisms responsible for phase transformation, amorphization and decomposition of alloys with increasing pressure and/or temperature, but it has not received the attention it deserves. Trying to explain the partial decomposition of nanostructured SnTe under annealing, the influence of chemical disorder was investigated. The Cowley-Warren chemical short-range order (CSRO) parameter αCW, used to study the statistical distribution of atoms in solids, is given by2929 Maret M, Chieux P, Hicter P, Atzmon M, Johnson WL. Partial structure factors and chemical short-range order in Ni33Y67 and Cu33Y67 metallic glasses. Journal of Physics F: Metal Physics. 1987;17(2):315-333.
where Nii, Nij and Njj are the coordination numbers and ci and cj are the concentrations of atoms of the elements i and j. The αCW parameter is zero for a random distribution, negative if there is a preference for forming unlike pairs and positive if homopolar pairs (clusters or local order) are preferred. Although the αCW parameter is usually applied to amorphous phases, it can also be used to determine the relative preference for forming different atomic pairs and thus to investigate the crystallization behavior of a binary alloy. The coordination numbers NSnSn, NSnTe , NTeSn and NTeTe were obtained using the structural data given in ICSD 188457 for SnTe in the Crystal Office 98 software3030 Atomic Softek. Crystal Office 98 software. Hamilton: Atomic Softek. to build the 3D structure, and using the tool "shell structure" the RSnSn, RSnTe, and RTeTe interatomic distances were calculated up to 10 Å. By putting the origin at Sn atoms (site 4a), the coordination numbers for the first neighbors are NSnSn = 12 at 4.4670 Å and NSnTe = 6 at 3.1590 Å. By putting the origin at Te atoms (site 4b), the coordination numbers for the first neighbors are N TeSn = 6 at 3.1590 Å and N TeTe = 12 at 4.4675 Å. Using the values in Eq. (6), a value of = 0.333 is obtained, indicating a preference for forming homopolar pairs in the first coordination shell. This value suggests that the repulsive part of the crystalline field plays an important role in the structural stability of this phase. During annealing, the thermal movements of the Sn and Te atoms may be responsible for introducing structural instability, promoting the partial decomposition of SnTe.
In order to understand the partial decomposition of the SnTe phase under annealing, part of as-milled powder was studied using DSC measurements. Figure 4 shows two sequentially recorded DSC thermograms for the same as-milled sample, and one run for the annealed sample, with a heating rate of 10 ºC min-1 under nitrogen flow. In the first run (blue top line), one can see an exothermic peak at about 278 ºC and a low intensity exothermic broad band between 384 ºC and 417 ºC. In the second run (black middle line) one can see the previous exothermic peak slightly shifted toward lower temperatures (≈ 265 ºC), and an endothermic peak at about 392 ºC. In the thermogram for the annealed sample (red bottom line), one can see the previous exothermic peak shifted toward higher temperatures (≈ 291 ºC) and the endothermic peak at about 395 ºC, now well-defined and seeming to be formed by two endothermic peaks (see inset).
In order to analyze the DSC thermograms shown in Fig. 4, the following values of the melting points (Tm) are useful: 232.08 ºC for Sn, 449.6 ºC for Te, 806 ºC for SnTe, 1080 ºC for SnO, 1727 ºC for SnO2, 733 ºC for TeO2, and 430 ºC for TeO3. Based on these values, one can see that the endothermic peak at about 395 ºC cannot be associated with the fusion of any of the phases above. Youngku Sohn3131 Sohn Y. Structural/Optical Properties and CO Oxidation Activities of SnO2 Nanostructures. Journal of the American Ceramic Society. 2014;97(4):1303-1310. investigated the formation of SnO2 starting from the decomposition a Sn-polymer complex. The TG/DSC thermogram shown in Fig. 4 (right) of Ref. 31 displays an endothermic peak at about 395 ºC, similar in shape and temperature to the endothermic peak observed in this study, that was attributed to formation of SnO2. Only in the DSC thermograms of the as-milled (second run) and annealed samples this endothermic peak is observed. On the other hand, the XRD pattern of the annealed sample showed a decrease in the relative volume fraction of SnTe. Thus, we attribute the endothermic peak located between 390 ºC and 400 ºC to the formation of SnO2 from Sn atoms originated from the partial decomposition of SnTe under annealing. With respect to the exothermic peak observed between 260 ºC and 295 ºC in the three thermograms, it can be associated with crystallization from an amorphous phase and/or with a phase transformation. No amorphous phase was observed in the XRD patterns of as-milled and annealed samples; if it exists, its intensity is too low to be separated from the background or from the contribution of the interfacial component (diffuse scattering) to the XRD pattern. Manzato et al.3232 Manzato L, Trichês DM, Souza SM, Oliveira MF. Synthesis of nanostructured SnO and SnO2 by high-energy milling of Sn powder with stearic acid. Journal of Materials Research. 2014;29(1):84-89. synthesized SnO and SnO2 by high-energy milling. In the thermogram shown in Fig. 5 of Ref. 32, two exothermic peaks located at about 195 ºC and 287 ºC were attributed to the formation of SnO and SnO2, respectively. Thus, we attribute the exothermic peak located between 260 ºC and 295 ºC to formation of the SnO2 phase starting from the relaxation of Sn atoms located in the interfacial component of SnTe. Formation of pure Te can be due to the diffusion of Te atoms located at the interfacial component and/or from the partial decomposition of SnTe.
(color online): McLean plot for the as-milled SnTe sample (bottom inset), the annealed SnTe sample, and absorbance spectra for the as-milled and annealed SnTe samples (top inset)
4.2 Optical absorbance measurements
Commonly, the value of the optical band gap energy of a thin film is obtained by McLean analysis of the absorption edge3333 McLean TP. The Absorption Edge Spectrum of Semiconductors. In: Gibson AF, ed. Progress in Semiconductors. Vol 5. New York: John Wiley & Sons; 1960.. Another way to obtain the optical band gap energy is presented in Ref. 34. The expression given in Ref. 33 was modified to be applied to a powder; the details are presented in Refs. 35,36 and will not be repeated here. The modified McLean equation is written in the form3535 Souza SM, Campos CEM, de Lima JC, Grandi TA, Pizani PS. Structural, thermal and optical studies of mechanical alloyed Ga40Se60 mixture. Solid State Communications. 2006;139(2):70-75.,3636 Baltazar-Rodrigues J, de Lima JC, Campos CEM, Grandi TA. Effects of photoacoustic measurements on a nanostructured ZnSe mechanically alloyed. Journal of Physics: Condensed Matter. 2008;20(46):465205-465213.
where A is the absorbance, h is the Planck constant, ν is the frequency of the incident beam, ls is an adjustable parameter and n is an index representing the transition order. A value of n = 2 corresponds to a direct allowed transition, n = 2/3 to a direct forbidden transition, n = 1/2 to an indirect allowed transition and n = 1/3 to an indirect forbidden transition.
In this study, the transmittance data were converted to absorbance data using the expression A = 2 - log10T. Figure 5 shows the (hν ˟ A)2 vs photon energy plot for the annealed sample and the inset (top) shows the absorbance vs photon energy plots for as-milled (red curve) and annealed (blue curve) samples. In the inset one can see that the optical absorption edge of the as-milled sample (red curve) is very broad due to the mean crystallite size of D = 75.2 nm and the microstrain of σp = 0.45%, as well as the substantial interfacial component. These features hinder the precise determination of the optical band gap energy. On the other hand, the absorbance spectrum for the annealed SnTe sample (blue curve) shows a narrow optical absorption edge, despite decomposition of SnTe promoted by annealing, led to a reduction of the mean crystallite size (D = 59.3 nm). According to the Refs. 37 and 38, SnTe has a direct optical band gap (n = 2). Fitting of experimental data to the McLean equation (red straight line) yields a band gap energy of Eg = 0.187 eV.
It is interesting to compare the band gap energy for the annealed SnTe sample obtained in this study with other values reported in the literature. Ref. 38 reported a value of Eg = 0.54 eV for nanocrystals SnTe with dimension of 6.5 nm; Ref. 37 reported values of Eg
= 0.54 eV and 0.39 eV for nanocrystals SnTe with dimensions of 7.2 nm and 14 nm, respectively; Refs. 38 and 39 reported a value of Eg
= 0.18 eV for bulk SnTe (D ≥ 100 nm) at room temperature. Figure 6 shows Eg vs D data above fitted to an exponential function Eg = y
0+A*e(-D/B). This figure suggests that the band gap energy is inversely proportional to the crystallite size and follows an exponential law. Assuming that this behavior is true, the mean crystallite size D = 75.2 nm of as-milled sample leads to a value of Eg ≈ 0.182 eV. By fixing this value, a fitting of experimental data to the McLean equation (red straight line) is shown in the inset (bottom) of Fig. 5. A brief theoretical explanation for the behavior observed above is the following: for any isolated X atom, for instance, semimetals (X = Si, Ge) or nonmetals (X = Se), the band gap is equal to the distance between the ground state and the first excited state. Due to the Pauli exclusion principle, both levels are broadened in a solid. This broadening leads to narrowing of the bandgap and, therefore, it is expected that the band gap in a solid be less than in an isolated atom4040 Aleksandrovsky A, Deshmukh VM, Fthenakis ZG. Why do optical band gaps increase with decreasing size of nanomaterials? Available from: https://www.researchgate.net/post/Why_do_optical_band_gaps_increase_with_decreasing_size_of_nanomaterials
https://www.researchgate.net/post/Why_do...
. In nanomaterials, the small number of atoms leads to a smaller interaction between atoms than in a bulk material. Thus, the energy levels are similar to those of isolated atoms. As the number of atoms decreases (i.e., as the volume of the nanomaterial decreases) the energy levels become more similar to those of isolated atoms4040 Aleksandrovsky A, Deshmukh VM, Fthenakis ZG. Why do optical band gaps increase with decreasing size of nanomaterials? Available from: https://www.researchgate.net/post/Why_do_optical_band_gaps_increase_with_decreasing_size_of_nanomaterials
https://www.researchgate.net/post/Why_do...
. A brief quantitative analysis is given by Z.G. Fthenakis4040 Aleksandrovsky A, Deshmukh VM, Fthenakis ZG. Why do optical band gaps increase with decreasing size of nanomaterials? Available from: https://www.researchgate.net/post/Why_do_optical_band_gaps_increase_with_decreasing_size_of_nanomaterials
https://www.researchgate.net/post/Why_do...
.
4.3 PAS measurements
The determination of the thermal diffusivity parameter and/or the transport properties of semiconducting materials using PAS is widely documented in the literature. A theoretical summary of the PAS principles and applications are given in Refs. 41-47 and references therein and will not be repeated here.
The thermal diffusivity for bulk SnTe can be calculated using the expression for the thermal conductivity k = ρCpα, where ρ is the density, Cp is the specific heat and α is the thermal diffusivity. The TAPP software (version 2.2)2828 Microwave Inc. TAPP Software, Version 2.2. E.S. Wade Court: Microwave Inc.; 1998. gives values of ρ = 6509 kg﹒m-3 and C p = 211 J kg-1K-1 for SnTe. Gelbestein4848 Gelbstein Y. Thermoelectric power and structural properties in two-phase Sn/SnTe alloys. Journal of Applied Physics. 2009;105(2):023713. reported a value of K = 7.9 Wm--1K-1 for bulk SnTe. Using these values in the expression above, a value of αcalc = 0.0575 x10-4 m2 s-1 (0.0575 cm2 s-1) is obtained. Zhang et al.4949 Zhang Q, Liao B, Lan Y, Lukas K, Esfarjani W, Opeil C, et al. High thermoelectric performance by resonant dopant indium in nanostructured SnTe. Proceedings of the National Academy of the United States of America (PNAS). 2013;110(33):13261-13266. produced an undoped SnTe phase and reported a value of αSnTe = 0.056 cm2 s-1 for the thermal diffusivity at room temperature. The characteristic frequency , where ls is the sample thickness, is the modulation frequency corresponding to the transition from the thermally thin regime (f < fc) to the thermally thick regime (f > fc), where f is the modulation frequency. The thicknesses of the as-milled and annealed samples were 440 and 450 µm, yielding characteristic frequencies of 11.1 Hz and 10.6 Hz, respectively. The PAS data were acquired between 10 and 270 Hz to remain in the thermally thick regime.
Figure 7 shows the PAS signal amplitudes for as-milled and annealed SnTe and Fig. 8 shows the corresponding signal phases. According to Fig. 7, both signal amplitudes decrease with increasing modulation frequency. A similar behavior is observed in Fig. 8 for the signal phases. We used the procedure described in Ref. 44 to find the contribution of each heat transfer mechanism to the pressure variation in the photoacoustic cell and thus to take into account the contribution of intraband nonradiative thermalization (thermal diffusion). Figure 7 also shows that between 40 and 110 Hz and between 50 and 70 Hz, the PAS signal amplitudes for as-milled and annealed samples are proportional to f --0.9807 and f--0.9959, respectively, a behavior that may be attributed to nonradiative surface recombination, thermoelastic bending or thermal dilation4343 Pinto Neto A, Vargas H, Leite NF, Miranda LCM. Photoacoustic characterization of semiconductors: Transport properties and thermal diffusivity in GaAs and Si. Physical Review B: Condensed Matter. 1990;41(14):9971-9979.,4444 de Lima JC, Schmitt M, de Souza SM, Almeida TO, Jerônimo AR, Trichês DM, et al. Structural and thermal study of nanostructured GaSb alloy prepared by mechanical alloying. Journal of Alloys and Compounds. 2007;436(1-2):13-18.,5050 Rousset G, Lepoutre F, Bertrand L. Influence of thermoelastic bending on photoacoustic experiments related to measurements of thermal diffusivity of metals. Journal of Applied Physics. 1983;54(5):2383-2391.. Thermal dilation heat transfer mechanisms produce a signal whose phase is independent of the modulation frequency and equal to 90°. Since, according to Fig. 8, the signal phase decreases as the modulation frequency increases, this mechanism can be disregarded. The contribution of nonradiative bulk recombination heat transfer is proportional to f--1.5. Usually, the phase of the photoacoustic signal corresponding to nonradiative bulk recombination exhibits a minimum that corresponds roughly to the point at which the phase dependence changes from f --1.5 to f--1.0, that is, it marks the transition from bulk to the surface recombination as the dominant mechanism responsible for the photoacoustic signal. This fact is discussed in Ref. 43. On the other hand, as reported by Dramicanin et al.5151 Dramicanin MD, Nikolic PM, Ristovski ZD, Vasiljevic DG, Todorovic DM. Photoacoustic investigation of transport in semiconductors: Theoretical and experimental study of a Ge single crystal. Physical Review B: Condensed Matter. 1995;51(20):14226-14233., as the sample thickness decreases the minima in both amplitude and phase are shifted to higher frequencies and their intensities around this minimum decrease. It is interesting to note that the positions of these minima depend on the material investigated. By considering the results reported in Ref. 51 and the sample thicknesses used in this work, it is expected that these minima cannot be observed in the amplitude and phase PAS signals.
(color online): PAS signal amplitude vs modulation frequency for the as-milled (open circles) and annealed (open stars) samples. The solid lines are the best fits of the experimental data to straight lines
(color online): PAS signal phase vs modulation frequency for the as-milled (circles) and annealed (stars) samples. The solid lines are the best fits of the data for as-milled samples to Eq. (8) and of the data for annealed samples to Eq. (9).
In as-milled SnTe, the absence of the contribution of nonradiative bulk and surface recombination heat transfer mechanisms were verified by not being possible to fit the phase data to the phase expression given by Pinto Neto et al.4343 Pinto Neto A, Vargas H, Leite NF, Miranda LCM. Photoacoustic characterization of semiconductors: Transport properties and thermal diffusivity in GaAs and Si. Physical Review B: Condensed Matter. 1990;41(14):9971-9979. for these mechanisms, taking the thermal diffusivity value of αcalc = 0.0575 cm2 s-1 as the initial value. On the other hand, the expression for the phase corresponding to the thermoelastic bending heat transfer mechanism4343 Pinto Neto A, Vargas H, Leite NF, Miranda LCM. Photoacoustic characterization of semiconductors: Transport properties and thermal diffusivity in GaAs and Si. Physical Review B: Condensed Matter. 1990;41(14):9971-9979.
44 de Lima JC, Schmitt M, de Souza SM, Almeida TO, Jerônimo AR, Trichês DM, et al. Structural and thermal study of nanostructured GaSb alloy prepared by mechanical alloying. Journal of Alloys and Compounds. 2007;436(1-2):13-18.-4545 Trichês DM, Souza SM, de Lima JC, Grandi TA, Campos CEM. Structural and photoacoustic studies of Zn4Sb3 and ZnSb phases prepared by mechanical alloying. Journal of Applied Physics. 2009;105(6):063518. written as
where , f is the modulation frequency, ls
is the sample thickness, and αs its thermal diffusivity, was successfully fitted to the Φph versus f plot in the modulation frequency range of 44-100 Hz. From the best fit, a value of αeff = 0.0825 cm2 s-1 was obtained for the thermal diffusivity. Similarly, in the annealed sample, the absence of the contribution of nonradiative bulk recombination and thermoelastic bending heat transfer mechanisms was verified by not being possible to fit the phase data to the phase expressions given in Refs. 43-45 for these mechanisms, taking the thermal diffusivity value of αcalc
= 0.0575 cm2 s-1 or0.0825 cm2s-1 as the initial value. On the other hand, the expression for the phase corresponding to nonradiative surface recombination heat transfer mechanism4343 Pinto Neto A, Vargas H, Leite NF, Miranda LCM. Photoacoustic characterization of semiconductors: Transport properties and thermal diffusivity in GaAs and Si. Physical Review B: Condensed Matter. 1990;41(14):9971-9979.
44 de Lima JC, Schmitt M, de Souza SM, Almeida TO, Jerônimo AR, Trichês DM, et al. Structural and thermal study of nanostructured GaSb alloy prepared by mechanical alloying. Journal of Alloys and Compounds. 2007;436(1-2):13-18.-4545 Trichês DM, Souza SM, de Lima JC, Grandi TA, Campos CEM. Structural and photoacoustic studies of Zn4Sb3 and ZnSb phases prepared by mechanical alloying. Journal of Applied Physics. 2009;105(6):063518., written as
where τeff = τ(D/a - 1), b = (πf/α)1/2, ω = 2πf, α is the termal diffusivity, D is the carrier diffusion coefficient, v is the surface recombination velocity and τ is the recombination time, was successfully fitted to the Φph versus f plot in the modulation frequency range of 52-70 Hz. From the best fit, values of αeff = 0.07305 cm2s-1, D = 29.82 cm2s-1, ν = 149.94 cm s-1 and τ = 343.8 ns were obtained for the thermal diffusivity, carrier diffusion coefficient, surface recombination velocity and recombination time, respectively. The slight reduction in the thermal diffusivity for the annealed sample can be associated with decreasing the crystallite size and volume fraction of SnTe, accompanied by an increase in the volume fraction of SnO2 and the emergence of a significant volume fraction of elemental Te. The last two phases can behave as phonon scattering centers, thus reducing the phonon free path.
It will be assumed that the measured effective thermal diffusivity α for as-milled and annealed samples can be described by the Lichtenecker's logarithmic mixture law5252 Lichtenecker K. Die Dielektrizitätskonstante künstlicher und natürlicher Mischkörper. Physikalische Zeitschrift. 1926;27:115-158.,5353 Simpkin R. Derivation of Lichtenecker's; logarithmic mixture formula from Maxwell's equations. IEEE Transactions on Microwave Theory and Techniques. 2010;58(3):545-550.
where n is the number of phases and αn
and xi are the thermal diffusivity and volume fraction of each phase, respectively. According to the Rietveld analysis, the relative volume fractions for the as-milled sample were 96% SnTe and 4% SnO2, while for the annealed sample were 77% SnTe, 13 % SnO2, and 10% elemental Te. The thermal diffusivity values of elemental Te5454 ChemGlobe. Periodic Table of the Elements. Available from: <http://pol.spurious.biz/projects/chemglobe/ptoe/>. Access in: 26/4/2018.
<http://pol.spurious.biz/projects/chemgl...
and SnO22828 Microwave Inc. TAPP Software, Version 2.2. E.S. Wade Court: Microwave Inc.; 1998.,5555 Turkes P, Pluntket C, Helbig R. Thermal conductivity of SnO2 single crystals. Journal of Physics C: Solid State Physics. 1980;13(26):4941-4951. are αTe
= 0.0188 cm2s-1 and αSnO2
= 0.3767 cm2s-1, respectively. Using the effective thermal diffusivity value of αeff
= 0.0825 cm2s-1 for the as-milled sample and the relative volume fraction values above, a value of αSnTe
= 0.0774 cm2s-1 is obtained for the as-milled SnTe phase, while a value of αSnTe = 0.0660 cm2s-1 is obtained for the annealed SnTe phase. These values are similar, but slightly larger than the value calculated using the TAPP data 2828 Microwave Inc. TAPP Software, Version 2.2. E.S. Wade Court: Microwave Inc.; 1998.(αcalc
= 0.0575 cm2 s-1). Using the high-energy ball milling and hot-pressing techniques, Zhang et al.4949 Zhang Q, Liao B, Lan Y, Lukas K, Esfarjani W, Opeil C, et al. High thermoelectric performance by resonant dopant indium in nanostructured SnTe. Proceedings of the National Academy of the United States of America (PNAS). 2013;110(33):13261-13266. produced an undoped SnTe phase and reported a value of αSnTe = 0.056 cm2 s-1 for the thermal diffusivity at room temperature. This value agrees quite well with those obtained in this study.
The performance of a thermoelectric material can be improved if its thermal conductivity is reduced without strong degradation of the electrical properties. 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 lattice5656 Rowe DM, Shukla VS. The effect of phonon-grain boundary scattering on the lattice thermal conductivity and thermoelectric conversion efficiency of heavily doped fine-grained, hot-pressed silicon germanium alloy. Journal of Applied Physics. 1981;52(12):7421-7426., 5757 Ur SC, Nash P, Kim IH. Mechanical alloying and thermoelectric properties of Zn4Sb3. Journal of Materials Science. 2003;38(17):3553-3558.. In this study, both as-milled and annealed samples have mean crystallite sizes of nanometric dimensions (75.2 nm and 59.3 nm).
According to Tripathi and Bhandari5858 Tripathi MN, Bhandari CM. Material parameters for thermoelectric performance. Pramana. 2005;65(3):469-479., the ratio, where Eg is the energy gap in eV and K the thermal conductivity in W/mK, can be used as an initial guide to evaluate the good thermoelectric materials and gives a reasonably good agreement with the maximum value of ZT for these materials. Tof energy gap Eg = 0.182 eV for the as-milled and Eg = 0.187 eV for the annealed samples were obtained from the UV-VIS-NIR measurements; the values of density ρ = 6486 kg m-3 for as-milled and ρ = 6463 kg m-3 for annealed samples were obtained from the Rietveld refinements of the XRD patterns; the values of thermal diffusivity α = 0.0774 𝘅 10-4 m2s-1 for the as-milled and 0.0660 𝘅 10-4 m2s-1 for annealed samples were obtained from the PAS measurements. Considering the value of specific heat given in TAPP software 2828 Microwave Inc. TAPP Software, Version 2.2. E.S. Wade Court: Microwave Inc.; 1998. for the bulk SnTe phase (Cp = 211 J kg-1 K-1), the thermal conductivity k (k = ρCpα) was estimated and the calculated values were 10.59 Wm-1K-1 for the as-milled and 9.00 Wm-1K-1 for annealed samples. These values are slightly larger than that reported by Gelbestein4848 Gelbstein Y. Thermoelectric power and structural properties in two-phase Sn/SnTe alloys. Journal of Applied Physics. 2009;105(2):023713. of k = 7.9 Wm --1K-1 for bulk SnTe. Values of = 0.0403 for the as-milled and 0.0480 for annealed samples were obtained. Zhang et al.4949 Zhang Q, Liao B, Lan Y, Lukas K, Esfarjani W, Opeil C, et al. High thermoelectric performance by resonant dopant indium in nanostructured SnTe. Proceedings of the National Academy of the United States of America (PNAS). 2013;110(33):13261-13266. reported values of ZT ≈ 0.01 for the nanostructured undoped SnTe phase for temperatures smaller than 600 K and ZT ≈ 1.1 for the nanostructured Sn1-xInxTe phase, with x = 0.25 at.%, for temperatures around 873 K. These values show that for applications of the SnTe phase as thermoelectric material, in addition to using crystallites of nanometric dimensions, it is also necessary to perform doping with pure elements and/or other phases to act as phonon spreading centers to reduce the thermal conductivity without promoting a strong degradation of the electrical properties. In this work, the presence of the SnO2 and elemental Te phases in the as-milled and annealed SnTe samples did not reduce the thermal conductivity. The values of thermal conductivity of the SnO25959 Shi L, Hao Q, Yu C, Mingo N, Kong X, Wang ZL. Thermal conductivities of individual tin dioxide nanobelts. Applied Physics Letters. 2004;84(14):2638-2640. and elemental Te phases are k ≈ 11 Wm-1K-1 and k ≈ 3 Wm-1K-1, respectively.
A final comment: Poffo et al.6060 Poffo CM, de Lima JC, Souza SM, Trichês DM, Nogueira TPO, Borges ZV, et al. Structural, optical and photoacoustic study of milled and melted Bi2Se3. Journal of Molecular Structure. 2014;1076:737-742. produced rhombohedral Bi2Se3 [space group R-3m (166)] using melting and mechanical alloying. They investigated the structural, optical and photoacoustic properties of the materials produced using the two methods and observed no significant differences.
5. Conclusions
A nanostructured SnTe phase was produced by MA. Using the Rietveld structural refinement procedure, the XRD patterns of as-milled and annealed samples were simulated. The parameter showed that in the first coordination shell of SnTe there is a preference among the first neighbors for forming homopolar pairs. Probably due to this preference, the annealing process promoted a partial decomposition. This partial decomposition was corroborated by estimating the mean crystallite size using the Willianson-Hall plot corrected for a pV (x) function used to represent the diffraction lines profiles, and relative volume fractions obtained from the Rietveld refinement procedure. The optical absorption measurements show that the band gap energy is inversely proportional to the crystallite size and follows an exponential law. Although the PAS analysis and the dimensionless figure of merit ZT for nanostructured SnTe showed that no significant advances relative to the results already reported in the literature were reached, the transport properties for the annealed nanostructured SnTe sample were determined.
6. Acknowledgments
One of authors (Z.V. Borges) thanks the Brazilian agency CNPq for financial support. We are indebted to the LABINC-UFSC for the optical transmittance measurements.
7. References
-
1Schaller RD, Petruska M, Klimov VI. Tunable Near-Infrared Optical Gain and Amplified Spontaneous Emission Using PbSe Nanocrystals. The Journal of Physical Chemistry B 2003;107(50):13765-13768.
-
2Talapin DV, Murray C. PbSe nanocrystal solids for n- and p-channel thin film field-effect transistors. Science 2005;310(5745):86-89.
-
3Cao WY, Banin U. Growth and Properties of Semiconductor Core/Shell Nanocrystals with InAs Cores. Journal of the American Chemistry Society 2000;122(40):9692-9702.
-
4Lovett D. Semi-Metals and Narrow-Bandgap Semiconductors London: Pion Limited; 1977.
-
5Das VD, Bahulayan C. Variation of electrical transport properties and thermoelectric figure of merit with thickness in 1% excess Te-doped Pb0.2Sn0.8Te thin films. Semiconductor Science and Technology 1995;10(12):1638-1644.
-
6Berger LI. Semiconductor Materials Boca Raton: CRC Press; 1996.
-
7Fürst J, Pascher H, Schwarz T, Böberl M, Heiss W, Springholz G, et al. Midinfrared IV-VI vertical-cavity surface-emitting lasers with zero-, two-, and three-dimensional systems in the active regions. Applied Physics Letters 2002;81(2):208-210.
-
8FIZ. Inorganic Crystal Structure Database (ICSD) Kalrsruhe: Gmelin-Institute fur Anorganische Chemie and Fachinformationszentrum (FIZ); 1995.
-
9Mengui UA, Abramof E, Rappl PHO, Ueta AY. Characterization of SnTe films grown by molecular beam epitaxy. Brazilian Journal of Physics 2006;36(2A):324-327.
-
10Sisman I, Öz H. Preparation of SnTe thin films on Au(111) by electrodeposition route. Electrochimica Acta 2011;56(13):4889-4894.
-
11An C, Tang K, Hai B, Shen G, Wang C, Qian I. Solution-phase synthesis of monodispersed SnTe nanocrystallites at room temperature. Inorganic Chemistry Communications 2003; 6(2):181-184.
-
12Saini R, Pallavi, Singh M, Kumar R, Jain G. Structural and electrical characterization of sintered SnTe films. Chalcogenide Letters 2010;7(3):197-202.
-
13Saini R, Singh M, Kumar R, Jain G. Electrical properties of SnTexSe1-x sintered films. Optoelectronics and Advanced Materials - Rapid Communications 2009;3(1):49-52.
-
14de Lima JC, Borba EC, Paduani C, dos Santos VHF, Grandi TA, Rechenberg HR, et al. Mechanical alloying of Fe and Zn: phase analysis and Mössbauer studies. Journal of Alloys and Compounds 1996;234(1):43-47.
-
15Weeber AW, Bakker H. Amorphization by ball milling. A review. Physica B: Condensed Matter 1988;153(1-3):93-135.
-
16Mukhopadhyay DK, Suryanarayana C, Froes HH. Extended solid solutions in Cd-Zn powders by mechanical alloying. Scripta Metallurgica et Materialia 1994;30(1):133-137.
-
17Yavari AR, Desré PJ, Benameur T. Mechanically driven alloying of immiscible elements. Physical Review Letters 1992;68(14):2235-2238.
-
18Che J, Yao X, Jian H, Wang M. Application and preparation of ZnSe nanometer powder by reduction process. Ceramics International 2004;30(7):1935-1938.
-
19Gleiter H. Materials with ultrafine microstructures: Retrospectives and perspectives. Nanostructured Materials 1992;1(1):1-19.
-
20Stern EA, Siegel RW, Newville M, Sanders PG, Haskel D. Are Nanophase Grain Boundaries Anomalous? Physical Review Letters 1995;75(21):3874-3877.
-
21Cullity BD. Elements of X-Ray Diffraction 2nd ed. Reading: Addison-Wesley; 1978.
-
22Young RA, ed. The Rietveld Method. IUCr Monographs on Crystallography - 5 Oxford: International Union of Crystallography/Oxford University Press; 1993.
-
23Dasgupta P. On the intrinsic hook effect associated with pseudo-Voigt profiles. Journal of Applied Crystallography 2002;35(Pt 2):267-269.
-
24Rietveld HM. A Profile Refinement Method for Nuclear and Magnetic Structures. Journal of Applied Crystallography 1969;2:65-71.
-
25Larson AC, von Dreele RB. General Structure Analysis System (GSAS) Report LAUR 86-748. Los Alamos: Los Alamos National Laboratory; 2004.
-
26de Lima JC, Cella NL, Miranda LCM, An Chying C, Franzan AH, Leite NF. Photoacoustic characterization of chalcogenide glasses: Thermal diffusivity of GexTe1-x Physical Review B: Condensed Matter 1992;46(21):14186-14189.
-
27Trichês DM, de Lima JC, Souza SM, Poffo CM, Grandi TA, de Biasi RS. Mechanical alloying of Co and Sb: Structural, thermal, optical, and photoacoustic studies. Journal of Applied Physics 2011;110(8):083528.
-
28Microwave Inc. TAPP Software, Version 2.2. E.S Wade Court: Microwave Inc.; 1998.
-
29Maret M, Chieux P, Hicter P, Atzmon M, Johnson WL. Partial structure factors and chemical short-range order in Ni33Y67 and Cu33Y67 metallic glasses. Journal of Physics F: Metal Physics 1987;17(2):315-333.
-
30Atomic Softek. Crystal Office 98 software Hamilton: Atomic Softek.
-
31Sohn Y. Structural/Optical Properties and CO Oxidation Activities of SnO2 Nanostructures. Journal of the American Ceramic Society 2014;97(4):1303-1310.
-
32Manzato L, Trichês DM, Souza SM, Oliveira MF. Synthesis of nanostructured SnO and SnO2 by high-energy milling of Sn powder with stearic acid. Journal of Materials Research 2014;29(1):84-89.
-
33McLean TP. The Absorption Edge Spectrum of Semiconductors. In: Gibson AF, ed. Progress in Semiconductors Vol 5. New York: John Wiley & Sons; 1960.
-
34Boldish SI, White WB. Optical band gaps of selected ternary sulfide minerals. American Mineralogist 1998;83:865-871.
-
35Souza SM, Campos CEM, de Lima JC, Grandi TA, Pizani PS. Structural, thermal and optical studies of mechanical alloyed Ga40Se60 mixture. Solid State Communications 2006;139(2):70-75.
-
36Baltazar-Rodrigues J, de Lima JC, Campos CEM, Grandi TA. Effects of photoacoustic measurements on a nanostructured ZnSe mechanically alloyed. Journal of Physics: Condensed Matter 2008;20(46):465205-465213.
-
37Kovalenko MV, Heiss W, Shevchenko EV, Lee JS, Schwinghammer H, Alivisatos AP, et al. SnTe nanocrystals: A new example of narrow-gap semiconductor quantum dots. Journal of the American Chemical Society 2007;129(37):11354-11355.
-
38Xu Y, Al-Salim N, Hodgkiss JM, Tilley RD. Solution Synthesis and Optical Properties of SnTe Nanocrystals. Crystal Growth & Design 2011;11(7):2721-2723.
-
39Wang YY, Cai KF, Yao X. Facile synthesis and characterization of SnTe films. Applied Surface Science 2011;258(2):919-922.
-
40Aleksandrovsky A, Deshmukh VM, Fthenakis ZG. Why do optical band gaps increase with decreasing size of nanomaterials? Available from: https://www.researchgate.net/post/Why_do_optical_band_gaps_increase_with_decreasing_size_of_nanomaterials
» https://www.researchgate.net/post/Why_do_optical_band_gaps_increase_with_decreasing_size_of_nanomaterials -
41Rosencwaig A, Gersho A. Theory of the photoacoustic effect with solids. Journal of Applied Physics 1976;47(1):64-69.
-
42Vargas H, Miranda LCM. Photoacoustic and related photothermal techniques. Physics Reports 1988;161(2):43-101.
-
43Pinto Neto A, Vargas H, Leite NF, Miranda LCM. Photoacoustic characterization of semiconductors: Transport properties and thermal diffusivity in GaAs and Si. Physical Review B: Condensed Matter 1990;41(14):9971-9979.
-
44de Lima JC, Schmitt M, de Souza SM, Almeida TO, Jerônimo AR, Trichês DM, et al. Structural and thermal study of nanostructured GaSb alloy prepared by mechanical alloying. Journal of Alloys and Compounds 2007;436(1-2):13-18.
-
45Trichês DM, Souza SM, de Lima JC, Grandi TA, Campos CEM. Structural and photoacoustic studies of Zn4Sb3 and ZnSb phases prepared by mechanical alloying. Journal of Applied Physics 2009;105(6):063518.
-
46Poffo CM, de Lima JC, Souza SM, Trichês DM, Grandi TA, de Biasi RS. Photoacoustic study of nanocrystalline silicon produced by mechanical grinding. Physica B: Condensed Matter 2011;406(8):1627-1632.
-
47Schmitt M, Poffo CM, de Lima JC, Fernandes CP, Santos VSS. Application of photoacoustic spectroscopy to characterize thermal diffusivity and porosity of caprocks. Engineering Geology 2017;220:183-195.
-
48Gelbstein Y. Thermoelectric power and structural properties in two-phase Sn/SnTe alloys. Journal of Applied Physics 2009;105(2):023713.
-
49Zhang Q, Liao B, Lan Y, Lukas K, Esfarjani W, Opeil C, et al. High thermoelectric performance by resonant dopant indium in nanostructured SnTe. Proceedings of the National Academy of the United States of America (PNAS) 2013;110(33):13261-13266.
-
50Rousset G, Lepoutre F, Bertrand L. Influence of thermoelastic bending on photoacoustic experiments related to measurements of thermal diffusivity of metals. Journal of Applied Physics 1983;54(5):2383-2391.
-
51Dramicanin MD, Nikolic PM, Ristovski ZD, Vasiljevic DG, Todorovic DM. Photoacoustic investigation of transport in semiconductors: Theoretical and experimental study of a Ge single crystal. Physical Review B: Condensed Matter 1995;51(20):14226-14233.
-
52Lichtenecker K. Die Dielektrizitätskonstante künstlicher und natürlicher Mischkörper. Physikalische Zeitschrift 1926;27:115-158.
-
53Simpkin R. Derivation of Lichtenecker's; logarithmic mixture formula from Maxwell's equations. IEEE Transactions on Microwave Theory and Techniques 2010;58(3):545-550.
-
54ChemGlobe. Periodic Table of the Elements Available from: <http://pol.spurious.biz/projects/chemglobe/ptoe/> Access in: 26/4/2018.
» <http://pol.spurious.biz/projects/chemglobe/ptoe/> -
55Turkes P, Pluntket C, Helbig R. Thermal conductivity of SnO2 single crystals. Journal of Physics C: Solid State Physics 1980;13(26):4941-4951.
-
56Rowe DM, Shukla VS. The effect of phonon-grain boundary scattering on the lattice thermal conductivity and thermoelectric conversion efficiency of heavily doped fine-grained, hot-pressed silicon germanium alloy. Journal of Applied Physics 1981;52(12):7421-7426.
-
57Ur SC, Nash P, Kim IH. Mechanical alloying and thermoelectric properties of Zn4Sb3 Journal of Materials Science 2003;38(17):3553-3558.
-
58Tripathi MN, Bhandari CM. Material parameters for thermoelectric performance. Pramana 2005;65(3):469-479.
-
59Shi L, Hao Q, Yu C, Mingo N, Kong X, Wang ZL. Thermal conductivities of individual tin dioxide nanobelts. Applied Physics Letters 2004;84(14):2638-2640.
-
60Poffo CM, de Lima JC, Souza SM, Trichês DM, Nogueira TPO, Borges ZV, et al. Structural, optical and photoacoustic study of milled and melted Bi2Se3 Journal of Molecular Structure 2014;1076:737-742.
Publication Dates
-
Publication in this collection
2018
History
-
Received
08 Dec 2017 -
Reviewed
03 Apr 2018 -
Accepted
15 Apr 2018