Size Dependence of the Local Structure and Atomic Correlations in

Jan 27, 2011 - Department of Advanced Physics, Hirosaki University, Hirosaki 036-8561, Japan. ABSTRACT: Only a few studies have been carried out on ...
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Size Dependence of the Local Structure and Atomic Correlations in Tellurium Nanoparticles Hiroyuki Ikemoto,*,† Akimichi Goyo,† and Takafumi Miyanaga‡ † ‡

Department of Physics, University of Toyama, Toyama 930-8555, Japan Department of Advanced Physics, Hirosaki University, Hirosaki 036-8561, Japan ABSTRACT: Only a few studies have been carried out on nanoparticles of materials having a hierarchic structure, contrary to nanoparticles of metals or tetrahedrally bonded semiconductor materials. Tellurium (Te) is the representative of the elements that have a hierarchic structure, that is, the covalently bonded chains and the interchain interactions between the chains. In this paper, the structure of Te nanoparticles was studied with varying nanoparticle size. While the covalently bonded 2-fold chain structure is preserved, the intrachain first nearest neighbor (1NN) atomic distance (rintra) shortens, and the interchain 1NN coordination number (Ninter) decreases with decreasing nanoparticle size; they have strong correlation with each other. The correlation suggests not only that piling up of the primary structure makes the secondary structure but also that the secondary structure affects the primary structure. The present results are distinguishing phenomena of the hierarchic elements such as tellurium.

1. INTRODUCTION The new field of nanoscience has experienced explosive development over the past decade.1,2 This field extends across physics, chemistry, and engineering and addresses many important issues, ranging from basic science to various technological applications. The nano-objects studied in this field are intermediate in size between systems composed of a handful atoms (atom or molecule) and bulk matter. However, their structures and properties are often peculiar; that is, they are qualitatively different both from those of simple aggregations of atoms or molecules and from those of fragments of matter. In particular, nano-objects exhibit properties that vary dramatically with size. To date, the small particles whose structure and physical properties have been studied are mostly metals3-5 and tetrahedrally bonded semiconductor materials (Si, Ge, and CdS).6-8 In a typical semiconductor material such as Ge, the surface has different structure from that of the bulk material.9 The sizedependent structural and thermal properties of Ge nanoparticles embedded in a silica (a-SiO2) matrix were reported.10 As the nanoparticle size decreases, the interatomic distance increases and approaches the value of the bulk a-Ge. An amorphous layer is formed on the surface of the Ge nanoparticles and separates the Ge nanocrystalline core and the silica matrix. The fraction of the amorphous layer increases as the nanoparticle diameter decreases. Only a few studies have been carried out on materials with an exotic structure, i.e., materials having a hierarchic structure. In crystalline Bi, the atoms are bonded with 3-fold covalent bonds, which implies that the primary structure is a layered structure. These layers stack, which forms the secondary structure. Raman scattering studies of Bi nanoparticles exhibit a phase transition r 2011 American Chemical Society

from nanocrystalline to amorphous-like nanoparticles as the size of the particles decreases.11 A substantial increase in the frequency of the optic-like band as the particle size decreases indicates strengthening of covalent interactions in the amorphous phase. The study suggests that the Bi nanoparticles are amorphous semiconductors. Te is the representative of the elements that have a hierarchic structure. As in the case of selenium (Se), trigonal tellurium (t-Te) has a highly anisotropic crystal structure, which consists of helical chains of covalently bound atoms with three atoms per turn, which are in turn bound together into a hexagonal lattice (a = 4.44693 Å, c = 5.91492 Å).12 In t-Te, the covalently bonded chains form the primary structure, and the interchain interactions between the chains produce the secondary structure. The hybridization between lone-pair (LP) orbitals and antibonding orbitals (σ*) in adjacent chains causes the interchain interactions, and the distance to the interchain nearest neighbor atom is smaller than twice the van der Waals radius. In addition to its role in the binding between the chains, the hybridization weakens the covalent bonds. Te exists only in the trigonal form, while Se also forms monoclinic variants, where the basic unit is a crown-like Se8 ring. The chalcogen chains are flexible,13 so Te nanoparticles may have exotic structures, with the chains folded and tangled up like yarn, or surface effects are negligible in the Te nanoparticles. First-principles calculations of bulk Te and Te nanowires were carried out to determine the atomic and electronic structures and various properties of these materials.14 A single helix, which is an isolated chain, has a shorter atomic distance and stronger Received: August 9, 2010 Revised: December 15, 2010 Published: January 27, 2011 2931

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The Journal of Physical Chemistry C intrahelical Te-Te bonds than those of t-Te. The structural change correlates with the decreasing overlap of electronic wave functions of adjacent helices. We previously reported the local structure of the Te nanoparticles.15 The important characteristics of the Te nanoparticles include the existence of the covalently bonded chain structure; shrinkage of the bonds; an increase in the force constant for the intrachain first nearest neighbor (1NN); and a decrease in interchain interactions. The primary structure is preserved even in the Te nanoparticles, whereas the secondary structure, i.e., the interchain interactions, is easily reduced because the interchain interactions are weaker than the intrachain interactions. The decrease in the overlap between the orbitals in adjacent chains, together with weakening of the interchain interactions, gives rise to covalent bond shrinkage. Extended X-ray absorption fine structure (EXAFS) analysis is a powerful tool for studying the local coordination and dynamics of selected atomic species in condensed matter.16,17 A prominent feature of EXAFS analysis is that the quality of the obtainable structural parameters is the same for both a crystalline and a disordered material. As mentioned above, we have already reported the structural characteristics of the Te nanoparticles.15 In contrast with the well-studied nanoparticles, i.e., metal nanoparticles and 4-fold semiconductors (Ge and Si), the correlation between the primary and secondary structures plays an important role for nanoparticles of hierarchic elements (Te, Se, Bi, et al.). It is very suggestive to study how the structural parameters for the Te nanoparticles systematically vary with changes in size. In this paper, we study the size dependence of the structural parameters of the Te nanoparticles and discuss the correlation between the primary and secondary structures.

2. EXPERIMENTAL SECTION 2.1. Sample Preparation. Te of 99.999% purity was slowly deposited onto the substrates from an effusion cell (Eiko MB3000). The resulting Te film was discontinuous with isolated islands formed. Next, NaCl of 99.99% purity was deposited from an alumina crucible to cover the Te islands. By repeating these depositions, we obtained a collection of the Te nanoparticles isolated in a NaCl matrix.18 The substrate was cooled with water. The thickness was monitored with a quartz oscillator system (ULVAC, CRTM6000, and CRTS-4). The multilayers were peeled off with a razor blade from the substrate in an inert gas. Because the total thickness of the layers is in the order of micrometers, the peeled-off samples are in a powdered state. The Te nanoparticles were formed in thin films, so in this paper, the samples are referred to by their average Te thin film thickness. The sample of t-Te was made by grinding the ingot and mixing with NaCl powders. 2.2. X-ray Diffraction. The X-ray diffraction (XRD) measurements were performed at BL1B and BL8B of the Photon Factory (PF) in the High Energy Accelerator Research Organization (KEK), Tsukuba, Japan. The X-ray wavelength was 1.000 Å. The ratio of the total thickness of Te to that of NaCl was 1:22 for all XRD samples. The peeled-off powders were filled in the glass capillary (Hilgenberg, Lindemann Glass 4007403). 2.3. EXAFS Measurements and Analysis. X-ray absorption measurements were performed using the spectrometer installed at NW10A of the PF-AR in the KEK. The 6.5-GeV storage ring

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was operated with 65 mA of the ring current. A Si(311) doublecrystal monochromator was used. EXAFS data were obtained for the Te K-edge (31.8 keV). The intensities of the incident beam (I0) and the transmitted beam (I) were monitored with ionization chambers; Ar gas was used in the I0 chamber; and Kr gas was used in the I chamber. The peeled-off samples were pressed on to a disk with a press (Jasco MP-1) and a forming tool (Jasco MT-1E). The total Te layer thickness was optimized as the Te K-edge jump is about 1.0. The sample was attached to a cryostat for cooling. The measured temperature range was from 25 to 300 K. EXAFS analysis was done by a program of miXAFS code that we created. The EXAFS functions, χ(k), were extracted from the experimental X-ray absorption spectra. χ(k) is defined as χðkÞ ¼

μðkÞ - μ0 ðkÞ - μb ðkÞ μ0 ðkÞ

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2m k ¼ ðE - E0 Þ p2

ð1Þ ð2Þ

where k is the photoelectron wavenumber; m is the mass of the electron; E is the energy of the incident X-ray; and E0 is the threshold energy, which was tentatively determined to be the midpoint of the edge jump. μ(k) is the experimental absorption coefficient; μ0(k) is the absorption for virtual isolated atoms; and μb(k) is the background contribution to μ(k) from the other shells. μb(k) was calculated by a least-squares fitting calculation using the Victoreen formula.19 In principle, the coefficients could be determined by fitting in the pre-edge region. However, extrapolation of the Victoreen formula to the XAFS region leads to rolling back of μb(k) in the high k region. To resolve the problem, we determined the Victoreen parameters through fitting in the pre-edge and the postedge regions. In the pre-edge region, the experimental values μb(k) were fitted with aE-3 þ bE-4 þ c, and in the postedge region, they were fitted with aE-3 þ bE-4 þ c þ d{(C2-C1)E-3 þ (D2-D1)E-4}.20 d is the total Te layer thickness, and C1, C2, D1, and D2 are the Victoreen parameters from the literature,21 where suffixes 1 and 2 denote the preand postedges. Another difficult problem in reducing χ(k) is the extraction of μ0(E). We used a method proposed by Matsubayashi et al.22 kχ(k) was Fourier transformed with a Hamming window in the k-range from 2.0 to 18.0 Å-1, where the window was used to reduce the ripples in the Fourier-transformed spectra in r-space. The Fourier peak of interest was filtered by multiplication with a similar window function and was then inverseFourier transformed into the k-space again. The range of the inverse-Fourier transforms was 2.5-4.0 Å including the two main peaks. The inverse-Fourier transformed kχ(k) was divided by the same Hamming window function with the Fourier transform. EXAFS analysis was used to determine the structural parameters, including the coordination numbers and interatomic distance, the Debye-Waller factor, and the asymmetric third cumulant of the interatomic distance distribution. We used a cumulant expansion approach to account for possible asymmetric third cumulant deviation from a Gaussian distribution. Such deviations can result from the presence of thermal or structural disorder. 2932

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Figure 2. Diameter distribution of the 10 nm thick films, as obtained from SEM analysis.

Figure 1. SEM image of the 10 nm thick films.

The EXAFS function was fitted to the following theoretical function by the nonlinear least-squares method X PS20, j ðk0 ÞNj fj ðk0 , rj Þexpð - 2σ2j k20 Þ χcal ðkÞ ¼ 2 k r 0 j j !   2rj 4 exp ð3Þ sin 2k0 rj þ φj ðk0 Þ - C3, j k30 3 λj ðk0 Þ k0 ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2m k2 - 2 ΔE0 p

ð4Þ

P is the scaling factor, and ΔE0 is the energy shift. S20,j(k) is the k-dependent reduction factor resulting from the many-body effect; fj(k,rj) and φj(k) are the backscattering amplitude and the total phase shift functions; and λj(k) is the electron mean free path length for an atom in the jth shell, which are calculated by FEFF8.4 code.23 rj is the interatomic distance between X-ray absorbing and photoelectron scattering atoms, and Nj is the coordination number in the jth shell. σ2j is the mean square relative displacement, and C3,j is the third cumulant. The free parameters are rj, Nj, σ2j , and C3,j.15 The index of fit is the residual, R, calculated by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 ðk χ - k2 χcal Þ2 P 4 2  100 ð5Þ R ¼ kχ where χ is the EXAFS signal, and the summation is taken over all the data points in the k-range used for fitting. In the present study, R is in a range from approximately 5 to 20%. The value of ΔE0 is determined to minimize the R-factor for t-Te at 25 K, which gives the most reliable EXAFS data. ΔE0 is fixed for the following EXAFS analyses. The value of P is determined from the intrachain 1NN coordination number (Nintra) of t-Te data for four temperatures between 25 and 100 K. 2.4. SEM. We used a field emission scanning electron microscope (FESEM, JEOL JSM-6700F at the Center for Instrumental Analysis, University of Toyama) to measure the size of the nanoparticles. The Te nanoparticles deposited on a NaCl single crystal (100) surface were observed.

3. RESULTS 3.1. SEM. We obtained SEM images for the 5 and 10 nm thick films but could not obtain those for films thinner than 5 nm.

Figure 3. Diameters of the Te nanoparticles as obtained from the Bragg peaks and SEM analysis. The triangles, circles, crosses, and squares denote the diameters obtained from the (102), (110), and (111) surfaces, and SEM, respectively.

Figure 4. XRD patterns for the 0.5 and 100 nm thick films. The red and blue lines denote the XRD spectrum from the 0.5 and 100 nm thick films, respectively. The vertical bars below zero denote the position of the Bragg peaks from the PDF cards for t-Te and NaCl.

An image of the 10 nm thick film is shown in Figure 1. Figure 2 shows the size distributions of the particles in the 10 nm thick films. For the 5 and 10 nm thick films, the mean particle diameters are D = 44 ( 4 nm and D = 55 ( 5 nm, respectively; these are plotted in Figure 3. The two samples were clearly differentiated by their different, well-defined size distributions. 3.2. X-ray Diffraction. Figure 4 shows the X-ray diffraction patterns from the 100 and 0.5 nm thick films. The intensities are normalized by the integrated intensity of the NaCl (200) peak. All Bragg peaks can be assigned to either t-Te or NaCl, and no peaks from halides and oxides of Te were observed. The peak intensities are smaller and the peaks are broader for the 0.5 nm thick films than for the 100 nm thick films. Figure 5 shows the 2933

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Figure 5. Variations of the integrated Bragg peak intensity as a function of the Te layer thickness. The circles and triangles denote the integrated intensity of the Bragg peaks for the Te (102) and (110) surfaces, respectively.

Figure 7. FT of the EXAFS function of t-Te. The red solid, black broken, and blue dotted lines denote the temperatures 20, 100, and 300 K, respectively.

Figure 6. EXAFS spectra χ(k) measured at 25 K, weighted by k2, for t-Te (black dotted line) and the 0.5 nm thick films (red solid line).

Figure 8. FT of the EXAFS function of the 0.5 nm thick films. The red solid, black broken, and blue dotted lines denote the temperatures 20, 100, and 300 K, respectively.

integrated peak intensities of the Te (102) and (110) peaks versus the Te layer thickness. While the intensities are nearly constant above 10 nm, they decrease rapidly below 10 nm. The intensities reflect the amount of Te crystalline in the nanoparticles, so the reduction in the peak intensities indicates an increase in the amorphous contribution. In fact, the baseline of the XRD pattern for the 0.5 nm thick films is higher than that of the 100 nm thick films. Amorphization has been reported for Bi and Ge nanoparticles with nanoparticulation.10,11 In the 0.5 nm thick films, the fraction of the amorphous phase is about 80-90%. The broadening of the Bragg peak implies a reduction in size of the Te nanoparticles. Figure 3 shows the diameters of the Te nanoparticles versus the Te layer thickness. The mean diameters are obtained with the Ida method,24 which uses the pseudo Voigt function. The size obtained from XRD is in good agreement with that from SEM measurements. The diameter decreases as the Te layer thickness decreases. In Figure 3 the diameters are scattered, but the diameter of the particles in 10 nm thick films can be regarded as about 60 nm. 3.3. EXAFS Functions and the Fourier Transform. Figure 6 displays the K-edge EXAFS oscillations k2χ(k) for t-Te and the 0.5 nm thick films as a function of k. Distinct EXAFS oscillations are observed from 2.0 to 18.0 Å-1. The oscillations for both the samples are significantly damped with increasing temperature. The Fourier transform (FT) of the kχ(k) data provides useful information for identifying atomic correlations. Figure 7 shows a selection of the temperature-dependent spectra of the FT of kχ(k) as a function of the radial distance for t-Te. There are three prominent peaks at 2.88, 3.54, and 4.53 Å and a shoulder at 5.1 Å. By comparing these with the XRDs in the literature,12 we can

assign the first and second peaks to contributions from the intrachain 1NN and the interchain 1NN distances, respectively. The third peak corresponds to the second nearest neighbor distances of the intra- and interchain, i.e., 4.4408 and 4.4560 Å, respectively. The shoulder corresponds to the third nearest neighbor distance of the interchain. While every peak damps with increasing temperature, the damping of the first peak’s amplitude is less than those of the other peaks, indicating that the covalent bond is strong compared to the other interactions. Figure 8 shows the FT of the EXAFS function for the 0.5 nm thick films. The scattering contributions from the two 1NN shells are evident for these films. The intensity of the first peak of the FT for the 0.5 nm thick films is weak compared with that for t-Te, but the reduction of the higher-order peaks for the 0.5 nm thick films is very large compared with that of the first peak. This indicates that the chain structures are preserved, while the interchain interactions are weakened in the nanoparticles. The first and second peaks overlap each other and are well separated from other peaks. To extract the peaks originating from the intra- and interchain 1NNs, the Fourier peaks were filtered in the range of 2.5-4.0 Å. 3.4. Structural Parameters. Structural parameters were obtained by the least-squares curve-fitting method applied to the Fourier-filtered χ(k). The values of the intrachain 1NN atomic distance (rintra), the intrachain 1NN coordination number (Nintra), and the interchain 1NN coordination number (Ninter) have weak temperature dependence. The structural parameters for temperatures below 100 K were averaged, and the uncertainties were estimated from the standard deviations. rintra obtained for t-Te is 2.834 ( 0.002 Å, which is in complete agreement with the values from the literature12 without any constraints for the atomic 2934

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Figure 9. Variation in rintra for the intrachain 1NN with the Te layer thickness.

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Ninter for t-Te is 4.25 ( 0.30, which is about 6% larger than the real coordination number of 4.00. This discrepancy may be caused by the overlap between the intra- and the interchain peaks and the fact that the intensity of the interchain peak is weaker than that of the intrachain peak in the Fourier transform. Figure 11 shows the trend for Ninter plotted as a function of the Te layer thickness. In contrast to Nintra, there is a clear size dependence for Ninter. The coordination numbers have strong correlation with σ2; for example, the value of N drags down by a decrease of σ2. The values of σ2inter increase with decreasing film thickness for all temperatures. This implies the trend of Ninter is not artificial. In the region below 10 nm, the value of Ninter decreases abruptly, much like that of rintra. While rintra and Ninter are nearly constant above 10 nm, they change below 10 nm. The crystal fraction shows similar variation as those. This suggests that they are affected by the amorphization.

4. DISCUSSION

Figure 10. Variation in Nintra for the intrachain 1NN with the Te layer thickness.

Figure 11. Variation in Ninter for the interchain 1NN with the Te layer thickness.

distance at the curve fitting. The absolute values of C3,intra are smaller than 0.0001 Å3, which are negligibly small for the parameters obtained by EXAFS analysis. Figure 9 shows the variation in rintra as a function of the Te-layer thickness. rintra exhibits a small decrease for thicknesses greater than 10 nm and decreases rapidly once the thickness drops below 10 nm. The variation in rintra indicates that nanoparticle characteristics appear for samples thinner than 10 nm. This differs from the observation for Ge particles, where a decrease in size is accompanied by an expansion of the mean interatomic distance.10 In contrast to the size dependence of rintra, the variation in Nintra is very small, as shown in Figure 10. For every film thickness, the coordination number is close to that for t-Te. The value of Nintra for 0.5 nm thick films is just 0.1 smaller than that of t-Te. This suggests that the 2-fold coordinated chain structure specific to t-Te is preserved.

4.1. Force Constant. The most striking results concerning the 0.5 nm thick films are shrinkage of the covalent bond length and preservation of the coordination number of the covalent bonds within the chains. The 2-fold-coordinated chain structure specific to t-Te is preserved even in the 0.5 nm thick films. The bond distance is 0.046 Å shorter than that of t-Te, indicating a strengthening of the covalent bonds. First-principles calculations show that the covalent bond length in the single helix is about 6% shorter than that of t-Te.14 The bond lengths in the 0.5 nm thick films are about 1.5% shorter than those of t-Te, which is one-fourth of the shortening in the case of the calculation. The single helix is an extreme case, so this may imply that the Te chains in the 0.5 nm thick films are partially isolated or that the interchain interactions are partly broken. With amorphization, the interchain correlation decreases, and the Te chains partly act as isolated chains. This suggestion is supported by the observed reduction in the value of Ninter. There is an empirical relation between the covalent bond length Re and force constant KB   s KB ¼ A exp ð6Þ Re

where Re is the equilibrium bond length, and A and s are constants throughout a given period in the periodic system.25 The values of s and A for the fifth period in the periodic system are not provided in the paper; however, the value of s for the third period is close to that for the fourth, and the value of A tends to saturate as the number of the period increases. So we adopt the values s = 14 Å and A = 0.53 (N/m) for the fourth period. Figure 12 shows the variation in the force constants (KB) obtained by the empirical relation as a function of the Te-layer thickness, and Table 1 shows values of KB for t-Te and the 0.5 nm thick films. KB exhibits a small decrease for thicknesses greater than 10 nm and increases rapidly once the thickness drops below 10 nm. The force constant for the intrachain interactions of the 0.5 nm thick film estimated from the bond distances is about 1.1 times stronger than that of t-Te. Another approach to estimating the force constant is the harmonic oscillation treatment. The value of σ2 can be expressed by the Einstein model. The Einstein temperature (ΘE) is obtained from a temperature-dependent study of σ2.26 The 2935

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Figure 12. Variation in KB for the intrachain 1NN with the Te layer thickness.

Table 1. Force Constants of the Intra- and Interchain Interactions for t-Te and the 0.5 nm Thick Filmsa N/m t-Te

intrachain

KB

KE

K28

74

89

66.4

25

13.3

80

115 23

interchain 0.5 nm

intrachain interchain

a The force constants KB and KE are estimated from the empirical equation for the covalent bond length and the Einstein model, respectively. The values from the literature28 are also shown.

values of ΘE for t-Te and the Te nanoparticles have already been reported.15,27 ΘE of the intrachain interaction increases as the size of the nanoparticles decreases, while ΘE of the interchain interactions decreases with decreasing nanoparticle size. This indicates that a decrease in the particle size strengthens the intrachain interactions, which is the opposite of the weakening of the interchain interactions. In the Einstein model, the relationship between KE and ΘE is given by kB 2 ð7Þ KE ¼ μωE 2 ¼ μ 2 ΘE 2 p where μ is the reduced mass. The force constants calculated by eq 7 for t-Te are shown in Table 1. The absolute values of the force constants for t-Te do not correspond with those in the literature.28 The ratio between the intra- and interchain force constants is 3.5 in the Einstein model, while it is 5.0 in the literature. Despite this discrepancy between the ratios, it is reasonable to use the Einstein model for a rough estimation of the force constants even if this model is very simple. So, we apply the above relation to the system of the Te nanoparticles, and the resulting force constants for the 0.5 nm thick films are shown in Table 1. If the relation between ΘE and KE is accurate, the force constant for the intrachain interactions of the 0.5 nm thick films is 1.3 times stronger than that of t-Te. This result is similar to that obtained from the present empirical equation of the covalent bond length, despite the bold assumption. 4.2. Correlation between the Intrachain and Interchain Interactions. In this paper, we have described various structural parameters for the intrachain and interchain interactions. It is interesting that most of them show a structural transition around the point where the Te-layer thickness reaches 10 nm, which corresponds to a 60 nm diameter, independent of the intrachain and interchain interactions. Below 10 nm, the percentage of the nanoparticles that are amorphous increases, reaching about

Figure 13. Correlations of the intrachain 1NN atomic distance (rintra) with the interchain 1NN coordination number (Ninter) and the force constant (KB) with Ninter. Black closed circles, rintra; red open triangles, KB.

80-90% for the 0.5 nm thick films. In the Te nanoparticles, the primary structure (intrachain interaction) is preserved, while the secondary structure (interchain interaction) is partly broken. So, the reduction in the interchain correlation may cause the amorphization. The representative parameters for the intra- and interchain interactions are rintra and Ninter, respectively. Figure 13 shows the correlation between Ninter and rintra. They have a strong correlation with each other; that is, the correlation coefficient is 0.997. As argued above, rintra reflects the covalent bond, especially the force constant, so the correlation between KB and Ninter is shown in Figure 13. The decrease of the interchain correlation induces the strengthening of the covalent bond. This implies that the secondary structure (interchain interaction) affects the primary structure (intrachain interaction). It is quite suggestive to compare the Te nanoparticles with those of Ge. As the size of the Ge nanoparticles decreases, the 1NN coordination number decreases, and the 1NN interatomic distance increases. The trends of the coordination numbers and interatomic distances for the intrachain as a function of particles size differ significantly between the Te nanoparticles and the Ge nanoparticles. In both Te and Ge, the covalent bonds bind atoms, but while there is only one type of interaction between Ge atoms, there are two types in the case of Te, i.e., the intrachain and interchain interactions. These two types of interactions have different characteristics and strengths. Te atoms are covalently bonded in chains, and the chains are bound by the hybridization between LP and σ* orbitals on an adjacent chain. In contrast to the isotropic bonding of Ge, Te has a hierarchic structure. The interchain interactions are due to an overlap between the σ* and LP orbitals on the adjacent chains. A stable form of Se, a congener of Te, is trigonal, which is similar to Te. Isolated Se chains encapsulated within mordenite, which has one-dimensional channels of diameter 6.7 Å, have been studied by others. The confinement reduces the value of rintra to 2.34 Å from the 2.37 Å value of t-Se29 and increases the Raman frequency assigned to the symmetric bond-stretching mode of the chain.30 This can be understood as follows: removing the interchain interactions induces shrinkage and enhancement of bonding of the intrachain 1NN because the hybridization between the LP and σ* orbitals on adjacent chains weakens the intrachain covalent bond. A decrease in Ninter implies that the overlap decreases. This reduction in the overlap causes strengthening of the covalent bond or, equivalently, shortening of the 2936

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The Journal of Physical Chemistry C covalent bond. The linear correlation in Figure 13 reflects this mechanism. The hybridization between the σ* and LP orbitals on adjacent chains weakens the covalent bonds. The primary structure of t-Te is a 2-fold chain structure. In the Te system, the trigonal form is a result of piling up of the chains, and in addition the secondary structure affects the primary structure. In discussion of hierarchic structure, the main topic has been how to build up a higher-order structure; it is interesting that there exists an influence in the reverse direction, that is, from the secondary to primary structures in the case of the Te nanoparticles.

5. CONCLUSION While nanoparticles larger than 60 nm in diameter are crystalline, nanoparticles with diameters smaller than 60 nm are a mixture of crystalline and amorphous structures. The percentage that is amorphous increases as the size decreases and reaches about 80-90% for 0.5 nm thick films. Nintra has little size dependence, suggesting that the 2-fold chain structure, which is the primary structure of Te, is preserved. In contrast to Nintra, rintra and Ninter strongly depend on size. As the size decreases, rintra shortens and Ninter decreases; for diameters less than 60 nm in particular, both changes are enhanced with the positive correlation. The strong correlation is interesting given that rintra and Ninter represent the intra- and interchain interactions, respectively. The correlation suggests not only that the piling up of the primary structure creates the secondary structure but also that the secondary structure affects the primary structure reversely, which is a distinguishing characteristic of hierarchic elements. Shortening of rintra implies strengthening of the intrachain covalent bonds. The force constants were estimated with the empirical equation for the covalent bond length and the Einstein model. The force constant of the intrachain interactions for the Te nanoparticles is larger than that for t-Te, but the force constant of the interchain interactions for the nanoparticles is smaller than that for t-Te. This implies that downsizing of the nanoparticles size leads to strengthening of the intrachain interaction and weakening of the interchain interaction. The reduction of the hybridization between LP and σ* that accompanies the amorphization of the nanoparticles causes the destruction of the interchain interactions while strengthening the intrachain interactions. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] Phone: þ81-76-445-6587. Fax: þ81-76-445-6549.

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’ ACKNOWLEDGMENT The authors thank Mr. S. Yoshida, H. Maekawa, Y. Okuda, and Dr. K. Nitta for their assistance at various stages. The study was partly supported by the Kurata Memorial Hitachi Science and Technology Foundation. The synchrotron radiation experiments were performed at the Photon Factory in KEK under Proposal No. 2005G193, 2006G272, 2007G626, 2009G073, and 2009G119. ’ REFERENCES (1) Encyclopedia of Nanoscience and Nanotechnology; Nalwa, H. S., Ed.; American Scientific: New York, 2004. (2) Burda, C.; Chen, X.; Narayanan, R.; El-Sayed, M. A. Chem. Rev. 2005, 105, 1025–1102. 2937

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