size dependence of the local structure and atomic ... · nano-objects exhibit properties that vary...

Published: January 27, 2011

r 2011 American Chemical Society 2931 dx.doi.org/10.1021/jp107475x | J. Phys. Chem. C 2011, 115, 2931–2937

ARTICLE

pubs.acs.org/JPCC

Size Dependence of the Local Structure and Atomic Correlationsin Tellurium NanoparticlesHiroyuki 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 havinga hierarchic structure, contrary to nanoparticles of metals or tetrahedrally bonded semi-conductor materials. Tellurium (Te) is the representative of the elements that have ahierarchic structure, that is, the covalently bonded chains and the interchain interactionsbetween the chains. In this paper, the structure of Te nanoparticles was studied with varyingnanoparticle size. While the covalently bonded 2-fold chain structure is preserved, theintrachain first nearest neighbor (1NN) atomic distance (rintra) shortens, and the interchain1NN coordination number (Ninter) decreases with decreasing nanoparticle size; they havestrong correlation with each other. The correlation suggests not only that piling up of theprimary structure makes the secondary structure but also that the secondary structure affectsthe primary structure. The present results are distinguishing phenomena of the hierarchicelements such as tellurium.

1. INTRODUCTION

The new field of nanoscience has experienced explosivedevelopment over the past decade.1,2 This field extends acrossphysics, chemistry, and engineering and addresses many impor-tant issues, ranging from basic science to various technologicalapplications. The nano-objects studied in this field are inter-mediate in size between systems composed of a handful atoms(atom or molecule) and bulk matter. However, their structuresand properties are often peculiar; that is, they are qualitativelydifferent both from those of simple aggregations of atoms ormolecules 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 physicalproperties have been studied are mostly metals3-5 and tetra-hedrally bonded semiconductor materials (Si, Ge, and CdS).6-8

In a typical semiconductor material such as Ge, the surfacehas different structure from that of the bulk material.9 The size-dependent structural and thermal properties of Ge nanoparticlesembedded in a silica (a-SiO2) matrix were reported.10 As thenanoparticle size decreases, the interatomic distance increasesand approaches the value of the bulk a-Ge. An amorphous layeris formed on the surface of the Ge nanoparticles and separatesthe Ge nanocrystalline core and the silica matrix. The fraction ofthe amorphous layer increases as the nanoparticle diameterdecreases.

Only a few studies have been carried out on materials withan exotic structure, i.e., materials having a hierarchic structure. Incrystalline 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. Ramanscattering studies of Bi nanoparticles exhibit a phase transition

from nanocrystalline to amorphous-like nanoparticles as the sizeof the particles decreases.11 A substantial increase in the fre-quency of the optic-like band as the particle size decreasesindicates strengthening of covalent interactions in the amor-phous phase. The study suggests that the Bi nanoparticles areamorphous semiconductors.

Te is the representative of the elements that have a hierarchicstructure. As in the case of selenium (Se), trigonal tellurium(t-Te) has a highly anisotropic crystal structure, which consists ofhelical chains of covalently bound atoms with three atoms perturn, which are in turn bound together into a hexagonal lattice(a = 4.44693 Å, c = 5.91492 Å).12 In t-Te, the covalently bondedchains form the primary structure, and the interchain interac-tions between the chains produce the secondary structure. Thehybridization between lone-pair (LP) orbitals and antibondingorbitals (σ*) in adjacent chains causes the interchain interactions,and the distance to the interchain nearest neighbor atom issmaller than twice the van derWaals radius. In addition to its rolein the binding between the chains, the hybridization weakens thecovalent bonds. Te exists only in the trigonal form, while Se alsoforms monoclinic variants, where the basic unit is a crown-likeSe8 ring. The chalcogen chains are flexible,

13 so Te nanoparticlesmay have exotic structures, with the chains folded and tangled uplike yarn, or surface effects are negligible in the Te nanoparticles.

First-principles calculations of bulk Te and Te nanowires werecarried out to determine the atomic and electronic structures andvarious properties of these materials.14 A single helix, which isan isolated chain, has a shorter atomic distance and stronger

Received: August 9, 2010Revised: December 15, 2010

2932 dx.doi.org/10.1021/jp107475x |J. Phys. Chem. C 2011, 115, 2931–2937

The Journal of Physical Chemistry C ARTICLE

intrahelical Te-Te bonds than those of t-Te. The structuralchange correlates with the decreasing overlap of electronic wavefunctions of adjacent helices.

We previously reported the local structure of the Te nano-particles.15 The important characteristics of the Te nanoparticlesinclude the existence of the covalently bonded chain structure;shrinkage of the bonds; an increase in the force constant forthe intrachain first nearest neighbor (1NN); and a decrease ininterchain interactions. The primary structure is preserved evenin the Te nanoparticles, whereas the secondary structure, i.e., theinterchain interactions, is easily reduced because the interchaininteractions are weaker than the intrachain interactions. Thedecrease in the overlap between the orbitals in adjacent chains,together with weakening of the interchain interactions, gives riseto covalent bond shrinkage.

Extended X-ray absorption fine structure (EXAFS) analysisis a powerful tool for studying the local coordination anddynamics of selected atomic species in condensed matter.16,17

A prominent feature of EXAFS analysis is that the quality of theobtainable structural parameters is the same for both a crystal-line and a disordered material. As mentioned above, we havealready reported the structural characteristics of the Tenanoparticles.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 structuresplays an important role for nanoparticles of hierarchic elements(Te, Se, Bi, et al.). It is very suggestive to study how thestructural parameters for the Te nanoparticles systematicallyvary with changes in size. In this paper, we study the sizedependence of the structural parameters of the Te nanoparti-cles and discuss the correlation between the primary andsecondary structures.

2. EXPERIMENTAL SECTION

2.1. Sample Preparation. Te of 99.999% purity was slowlydeposited onto the substrates from an effusion cell (Eiko MB-3000). The resulting Te film was discontinuous with isolatedislands formed. Next, NaCl of 99.99% purity was deposited froman alumina crucible to cover the Te islands. By repeating thesedepositions, we obtained a collection of the Te nanoparticlesisolated 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 layersis in the order of micrometers, the peeled-off samples are in apowdered state. The Te nanoparticles were formed in thin films,so in this paper, the samples are referred to by their average Tethin film thickness. The sample of t-Te was made by grinding theingot and mixing with NaCl powders.2.2. X-ray Diffraction. The X-ray diffraction (XRD) mea-

surements were performed at BL1B and BL8B of the PhotonFactory (PF) in the High Energy Accelerator Research Orga-nization (KEK), Tsukuba, Japan. The X-ray wavelength was1.000 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 theglass capillary (Hilgenberg, Lindemann Glass 4007403).2.3. EXAFS Measurements and Analysis. X-ray absorption

measurements were performed using the spectrometer installedat NW10A of the PF-AR in the KEK. The 6.5-GeV storage ring

was operated with 65 mA of the ring current. A Si(311) double-crystal monochromator was used. EXAFS data were obtained forthe Te K-edge (31.8 keV). The intensities of the incident beam(I0) and the transmitted beam (I) were monitored with ioniza-tion chambers; Ar gas was used in the I0 chamber; and Kr gas wasused 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). Thetotal Te layer thickness was optimized as the Te K-edge jumpis about 1.0. The sample was attached to a cryostat forcooling. The measured temperature range was from 25 to300 K.EXAFS analysis was done by a program of miXAFS code that

we created. The EXAFS functions, χ(k), were extracted from theexperimental X-ray absorption spectra. χ(k) is defined as

χðkÞ ¼ μðkÞ-μ0ðkÞ- μbðkÞμ0ðkÞ

ð1Þ

k ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2m

p2ðE- E0Þ

rð2Þ

where k is the photoelectron wavenumber; m is the mass of theelectron; E is the energy of the incident X-ray; and E0 is thethreshold energy, which was tentatively determined to be themidpoint of the edge jump. μ(k) is the experimental absorptioncoefficient; μ0(k) is the absorption for virtual isolated atoms; andμb(k) is the background contribution to μ(k) from the othershells.μb(k) was calculated by a least-squares fitting calculation using

the Victoreen formula.19 In principle, the coefficients could bedetermined by fitting in the pre-edge region. However, extra-polation of the Victoreen formula to the XAFS region leads torolling back of μb(k) in the high k region. To resolve the problem,we determined the Victoreen parameters through fitting in thepre-edge and the postedge regions. In the pre-edge region, theexperimental values μb(k) were fitted with aE

-3þ bE-4þ c, andin the postedge region, they were fitted with aE-3þ bE-4þ cþd{(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 param-eters from the literature,21 where suffixes 1 and 2 denote the pre-and postedges. Another difficult problem in reducing χ(k) isthe extraction of μ0(E). We used a method proposed byMatsubayashi et al.22

kχ(k) was Fourier transformed with a Hamming window inthe k-range from 2.0 to 18.0 Å-1, where the window was usedto reduce the ripples in the Fourier-transformed spectra inr-space. The Fourier peak of interest was filtered by multi-plication with a similar window function and was then inverse-Fourier transformed into the k-space again. The range of theinverse-Fourier transforms was 2.5-4.0 Å including the twomain peaks. The inverse-Fourier transformed kχ(k) was di-vided by the same Hamming window function with the Fouriertransform.EXAFS analysis was used to determine the structural param-

eters, including the coordination numbers and interatomicdistance, the Debye-Waller factor, and the asymmetric thirdcumulant of the interatomic distance distribution. We used acumulant expansion approach to account for possible asym-metric third cumulant deviation from a Gaussian distribution.Such deviations can result from the presence of thermal orstructural disorder.



The EXAFS function was fitted to the following theoreticalfunction by the nonlinear least-squares method

χcalðkÞ ¼Xj

PS20, jðk0ÞNj

k0r2jfjðk0, rjÞexpð- 2σ2

j k20Þ�

exp -2rj

λjðk0Þ

!sin 2k0rj þφjðk0Þ-

43C3, jk

30

� �ð3Þ

k0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffik2 -

2m

p2ΔE0

rð4Þ

P is the scaling factor, and ΔE0 is the energy shift. S0,j2 (k) is the

k-dependent reduction factor resulting from the many-bodyeffect; fj(k,rj) and φj(k) are the backscattering amplitude andthe total phase shift functions; and λj(k) is the electron mean freepath length for an atom in the jth shell, which are calculated byFEFF8.4 code.23 rj is the interatomic distance between X-rayabsorbing and photoelectron scattering atoms, and Nj is thecoordination number in the jth shell. σj

2 is the mean squarerelative displacement, and C3,j is the third cumulant. The freeparameters are rj, Nj, σj

2, and C3,j.15

The index of fit is the residual, R, calculated by

R ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP ðk2χ- k2χcalÞ2P

k4χ2

s� 100 ð5Þ

where χ is the EXAFS signal, and the summation is taken over allthe data points in the k-range used for fitting. In the presentstudy, 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 isfixed for the following EXAFS analyses. The value of P isdetermined 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 micro-

scope (FESEM, JEOL JSM-6700F at the Center for InstrumentalAnalysis, University of Toyama) to measure the size of thenanoparticles. The Te nanoparticles deposited on a NaCl singlecrystal (100) surface were observed.

3. RESULTS

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

An image of the 10 nm thick film is shown in Figure 1. Figure 2shows the size distributions of the particles in the 10 nm thickfilms. For the 5 and 10 nm thick films, the mean particlediameters are D = 44 ( 4 nm and D = 55 ( 5 nm, respectively;these are plotted in Figure 3. The two samples were clearlydifferentiated 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 arenormalized by the integrated intensity of the NaCl (200) peak.All Bragg peaks can be assigned to either t-Te or NaCl, and nopeaks from halides and oxides of Te were observed. The peakintensities are smaller and the peaks are broader for the 0.5 nmthick films than for the 100 nm thick films. Figure 5 shows the

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

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

Figure 3. Diameters of the Te nanoparticles as obtained from the Braggpeaks and SEM analysis. The triangles, circles, crosses, and squaresdenote 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 andblue lines denote the XRD spectrum from the 0.5 and 100 nm thickfilms, respectively. The vertical bars below zero denote the position ofthe Bragg peaks from the PDF cards for t-Te and NaCl.



integrated peak intensities of the Te (102) and (110) peaksversus the Te layer thickness. While the intensities are nearlyconstant above 10 nm, they decrease rapidly below 10 nm. Theintensities reflect the amount of Te crystalline in the nano-particles, so the reduction in the peak intensities indicates anincrease in the amorphous contribution. In fact, the baseline ofthe XRD pattern for the 0.5 nm thick films is higher than thatof the 100 nm thick films. Amorphization has been reportedfor Bi and Ge nanoparticles with nanoparticulation.10,11 In the0.5 nm thick films, the fraction of the amorphous phase is about80-90%.The broadening of the Bragg peak implies a reduction in size

of the Te nanoparticles. Figure 3 shows the diameters of the Tenanoparticles versus the Te layer thickness. The mean diametersare obtained with the Ida method,24 which uses the pseudo Voigtfunction. The size obtained from XRD is in good agreement withthat from SEMmeasurements. The diameter decreases as the Telayer thickness decreases. In Figure 3 the diameters are scattered,but the diameter of the particles in 10 nm thick films can beregarded 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 the0.5 nm thick films as a function of k. Distinct EXAFS oscillationsare observed from 2.0 to 18.0 Å-1. The oscillations for both thesamples 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 aselection of the temperature-dependent spectra of the FT ofkχ(k) as a function of the radial distance for t-Te. There are threeprominent 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 theintrachain 1NN and the interchain 1NN distances, respectively.The third peak corresponds to the second nearest neighbordistances of the intra- and interchain, i.e., 4.4408 and 4.4560 Å,respectively. The shoulder corresponds to the third nearestneighbor distance of the interchain. While every peak dampswith increasing temperature, the damping of the first peak’samplitude is less than those of the other peaks, indicating that thecovalent 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 shellsare evident for these films. The intensity of the first peak of theFT for the 0.5 nm thick films is weak compared with that fort-Te, but the reduction of the higher-order peaks for the 0.5 nmthick films is very large compared with that of the first peak.This indicates that the chain structures are preserved, while theinterchain 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 fromthe intra- and interchain 1NNs, the Fourier peaks were filtered inthe range of 2.5-4.0 Å.3.4. Structural Parameters. Structural parameters were ob-

tained by the least-squares curve-fitting method applied to theFourier-filtered χ(k). The values of the intrachain 1NN atomicdistance (rintra), the intrachain 1NN coordination number (Nintra),and the interchain 1NN coordination number (Ninter) have weaktemperature dependence. The structural parameters for tem-peratures below 100 K were averaged, and the uncertainties wereestimated from the standard deviations. rintra obtained for t-Te is2.834( 0.002 Å, which is in complete agreement with the valuesfrom the literature12 without any constraints for the atomic

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

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

Figure 7. FT of the EXAFS function of t-Te. The red solid, blackbroken, and blue dotted lines denote the temperatures 20, 100, and300 K, respectively.

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



distance at the curve fitting. The absolute values of C3,intra aresmaller than 0.0001 Å3, which are negligibly small for theparameters 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 thicknessesgreater than 10 nm and decreases rapidly once the thicknessdrops below 10 nm. The variation in rintra indicates that nano-particle characteristics appear for samples thinner than 10 nm.This differs from the observation for Ge particles, where adecrease in size is accompanied by an expansion of the meaninteratomic distance.10

In contrast to the size dependence of rintra, the variation inNintra is very small, as shown in Figure 10. For every film thick-ness, the coordination number is close to that for t-Te. The valueof Nintra for 0.5 nm thick films is just 0.1 smaller than that oft-Te. This suggests that the 2-fold coordinated chain structurespecific to t-Te is preserved.

Ninter for t-Te is 4.25( 0.30, which is about 6% larger than thereal coordination number of 4.00. This discrepancy may becaused by the overlap between the intra- and the interchainpeaks and the fact that the intensity of the interchain peak isweaker than that of the intrachain peak in the Fourier transform.Figure 11 shows the trend for Ninter plotted as a function of theTe layer thickness. In contrast to Nintra, there is a clear sizedependence for Ninter. The coordination numbers have strongcorrelation with σ2; for example, the value of N drags down by adecrease of σ2. The values of σinter

2 increase with decreasing filmthickness 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. Thecrystal fraction shows similar variation as those. This suggeststhat they are affected by the amorphization.

4. DISCUSSION

4.1. Force Constant. The most striking results concerningthe 0.5 nm thick films are shrinkage of the covalent bond lengthand preservation of the coordination number of the covalentbonds within the chains. The 2-fold-coordinated chain structurespecific to t-Te is preserved even in the 0.5 nm thick films. Thebond distance is 0.046 Å shorter than that of t-Te, indicating astrengthening 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 Thebond lengths in the 0.5 nm thick films are about 1.5% shorterthan those of t-Te, which is one-fourth of the shortening in thecase of the calculation. The single helix is an extreme case, so thismay imply that the Te chains in the 0.5 nm thick films arepartially isolated or that the interchain interactions are partlybroken. With amorphization, the interchain correlation de-creases, and the Te chains partly act as isolated chains. Thissuggestion is supported by the observed reduction in the valueof Ninter.There is an empirical relation between the covalent bond

length Re and force constant KB

KB ¼ AexpsRe

� �ð6Þ

where Re is the equilibrium bond length, and A and s are con-stants throughout a given period in the periodic system.25 Thevalues of s andA for the fifth period in the periodic system are notprovided in the paper; however, the value of s for the third periodis close to that for the fourth, and the value of A tends to saturateas the number of the period increases. So we adopt the valuess = 14 Å and A = 0.53 (N/m) for the fourth period. Figure 12shows the variation in the force constants (KB) obtained by theempirical relation as a function of the Te-layer thickness, andTable 1 shows values ofKB for t-Te and the 0.5 nm thick films.KB

exhibits a small decrease for thicknesses greater than 10 nm andincreases rapidly once the thickness drops below 10 nm. Theforce constant for the intrachain interactions of the 0.5 nm thickfilm estimated from the bond distances is about 1.1 timesstronger than that of t-Te.Another approach to estimating the force constant is the

harmonic oscillation treatment. The value of σ2 can be expressedby the Einstein model. The Einstein temperature (ΘE) isobtained from a temperature-dependent study of σ2.26 The

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

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

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



values ofΘE for t-Te and the Te nanoparticles have already beenreported.15,27 ΘE of the intrachain interaction increases as thesize of the nanoparticles decreases, while ΘE of the interchaininteractions decreases with decreasing nanoparticle size. Thisindicates that a decrease in the particle size strengthens theintrachain interactions, which is the opposite of the weakening ofthe interchain interactions.In the Einstein model, the relationship between KE andΘE is

given by

KE ¼ μωE2 ¼ μ

kB2

p2ΘE

2 ð7Þ

where μ is the reduced mass. The force constants calculated byeq 7 for t-Te are shown in Table 1. The absolute values ofthe force constants for t-Te do not correspond with those inthe literature.28 The ratio between the intra- and interchainforce constants is 3.5 in the Einstein model, while it is 5.0 inthe literature. Despite this discrepancy between the ratios, it isreasonable to use the Einstein model for a rough estimation ofthe 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 nmthick films are shown inTable 1. If the relation betweenΘE andKE

is accurate, the force constant for the intrachain interactions of the0.5 nm thick films is 1.3 times stronger than that of t-Te. This resultis similar to that obtained from the present empirical equation ofthe covalent bond length, despite the bold assumption.4.2. Correlation between the Intrachain and Interchain

Interactions. In this paper, we have described various structuralparameters for the intrachain and interchain interactions. It isinteresting that most of them show a structural transition aroundthe point where the Te-layer thickness reaches 10 nm, whichcorresponds to a 60 nm diameter, independent of the intrachainand interchain interactions. Below 10 nm, the percentage of thenanoparticles that are amorphous increases, reaching about

80-90% for the 0.5 nm thick films. In the Te nanoparticles,the primary structure (intrachain interaction) is preserved, whilethe secondary structure (interchain interaction) is partly broken.So, the reduction in the interchain correlation may cause theamorphization.The representative parameters for the intra- and interchain

interactions are rintra andNinter, respectively. Figure 13 shows thecorrelation between Ninter and rintra. They have a strong correla-tion with each other; that is, the correlation coefficient is 0.997.As argued above, rintra reflects the covalent bond, especially theforce constant, so the correlation between KB andNinter is shownin Figure 13. The decrease of the interchain correlation inducesthe strengthening of the covalent bond. This implies that thesecondary structure (interchain interaction) affects the primarystructure (intrachain interaction).It is quite suggestive to compare the Te nanoparticles with

those of Ge. As the size of the Ge nanoparticles decreases, the1NN coordination number decreases, and the 1NN interatomicdistance increases. The trends of the coordination numbers andinteratomic distances for the intrachain as a function of particlessize differ significantly between the Te nanoparticles and the Genanoparticles. In both Te andGe, 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 andinterchain interactions. These two types of interactions havedifferent characteristics and strengths. Te atoms are covalentlybonded in chains, and the chains are bound by the hybridizationbetween 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 overlapbetween the σ* and LP orbitals on the adjacent chains. A stableform of Se, a congener of Te, is trigonal, which is similar to Te.Isolated Se chains encapsulated within mordenite, which hasone-dimensional channels of diameter 6.7 Å, have been studiedby others. The confinement reduces the value of rintra to 2.34 Åfrom the 2.37 Å value of t-Se29 and increases the Raman fre-quency assigned to the symmetric bond-stretching mode ofthe chain.30 This can be understood as follows: removing theinterchain interactions induces shrinkage and enhancement ofbonding of the intrachain 1NN because the hybridizationbetween the LP and σ* orbitals on adjacent chains weakens theintrachain covalent bond. A decrease in Ninter implies that theoverlap decreases. This reduction in the overlap causes strength-ening of the covalent bond or, equivalently, shortening of the

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

Table 1. Force Constants of the Intra- and InterchainInteractions for t-Te and the 0.5 nm Thick Filmsa

N/m KB KE K28

t-Te intrachain 74 89 66.4

interchain 25 13.3

0.5 nm intrachain 80 115

interchain 23aThe force constants KB and KE are estimated from the empiricalequation for the covalent bond length and the Einstein model, respec-tively. The values from the literature28 are also shown.

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



covalent bond. The linear correlation in Figure 13 reflects thismechanism.The hybridization between the σ* and LP orbitals on adjacent

chains weakens the covalent bonds. The primary structure oft-Te is a 2-fold chain structure. In the Te system, the trigonalform is a result of piling up of the chains, and in addition thesecondary structure affects the primary structure. In discussionof hierarchic structure, the main topic has been how to build upa higher-order structure; it is interesting that there exists aninfluence in the reverse direction, that is, from the secondary toprimary structures in the case of the Te nanoparticles.

5. CONCLUSION

While nanoparticles larger than 60 nm in diameter are crystal-line, nanoparticles with diameters smaller than 60 nm are a mix-ture of crystalline and amorphous structures. The percentage thatis amorphous increases as the size decreases and reaches about80-90% for 0.5 nm thick films. Nintra has little size dependence,suggesting that the 2-fold chain structure, which is the primarystructure of Te, is preserved. In contrast to Nintra, rintra and Ninter

strongly depend on size. As the size decreases, rintra shortens andNinter decreases; for diameters less than 60 nm in particular, bothchanges are enhanced with the positive correlation. The strongcorrelation is interesting given that rintra and Ninter represent theintra- and interchain interactions, respectively. The correla-tion suggests not only that the piling up of the primary struc-ture creates the secondary structure but also that the secondarystructure affects the primary structure reversely, which is adistinguishing characteristic of hierarchic elements.

Shortening of rintra implies strengthening of the intrachain cova-lent bonds. The force constants were estimated with the empiricalequation for the covalent bond length and the Einsteinmodel. Theforce constant of the intrachain interactions for the Te nanopar-ticles is larger than that for t-Te, but the force constant of theinterchain interactions for the nanoparticles is smaller than that fort-Te. This implies that downsizing of the nanoparticles size leads tostrengthening of the intrachain interaction and weakening of theinterchain interaction. The reduction of the hybridization betweenLP and σ* that accompanies the amorphization of the nanopar-ticles causes the destruction of the interchain interactions whilestrengthening the intrachain interactions.

’AUTHOR INFORMATION

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

’ACKNOWLEDGMENT

The authors thankMr. S. Yoshida, H.Maekawa, Y. Okuda, andDr. K. Nitta for their assistance at various stages. The study waspartly supported by the Kurata Memorial Hitachi Science andTechnology Foundation. The synchrotron radiation experimentswere performed at the Photon Factory in KEK under Proposal No.2005G193, 2006G272, 2007G626, 2009G073, and 2009G119.

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