M A T E R I A L S C H A R A C T E R I Z A T I O N 8 7 ( 2 0 1 4 ) 1 6 6 – 1 7 1

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Study of titanate nanotubes by X-ray and electron

diffraction and electron microscopy

Tereza Brunatovaa, Daniela Popelkovab, Wei Wanc,d, Peter Oleynikovd, Stanislav Danisa,Xiaodong Zouc,d, Radomir Kuzela,⁎aCharles University, Faculty of Mathematics and Physics, Dept. of Condensed Matter Physics, Prague, Czech RepublicbInstitute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, Prague, Czech RepubliccBerzelii Center EXSELENT on Porous Materials, Stockholm University, SE-106 91 Stockholm, SwedendDept. of Materials and Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden

A R T I C L E D A T A

⁎ Corresponding author. Tel.: +420 221911394E-mail address: kuzel@karlov.mff.cuni.cz

1044-5803/$ – see front matter © 2013 Elseviehttp://dx.doi.org/10.1016/j.matchar.2013.11.01

A B S T R A C T

Article history:Received 21 May 2013Received in revised form14 October 2013Accepted 26 November 2013

The structure of titanate nanotubes (Ti-NTs) was studied by a combination of powder X-raydiffraction (PXRD), electron diffraction and high resolution transmission electron micros-copy (HRTEM). Ti-NTs are prepared by hydrothermal treatment of TiO2 powder. Thestructure is identified by powder X-ray diffraction as the one based on the structure ofH2Ti2O5·H2O phase. The same structure is obtained by projected potential from HRTEMthrough-focus image series. The structure is verified by simulated PXRD pattern with theaid of the Debye formula. The validity of the model is tested by computing Fouriertransformation of a single nanotube which is proportional to measured electron diffractionintensities. A good agreement of this calculation with measured precession electrondiffraction data is achieved.

© 2013 Elsevier Inc. All rights reserved.

Keywords:Computer simulationsTransmission electron microscopyElectron diffractionTitanate nanotubesX-ray powder diffractionDebye formula

1. Introduction

Recently, high interest has been given to titanate (titania)nanotubes (Ti-TNs) in particular, due to their potential use indifferent applications. Ti-NTs can be used inmany applicationswhere TiO2 powders are utilized nowadays. However, theadvantage of utilizing Ti-NTs is mainly due to their elongatedstructure assisting the electron transport. Bavykin and Walsh[1] discussed their possible uses in dye sensitive solar cells,lithiumbatteries, photocatalysis, magneticmaterials, hydrogenstorage or covering orthopedic or dental implants.

Unfortunately, the structure of Ti-NTs has not been clearlyunderstood yet. An inexpensive method of preparation of

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Ti-NTs was described by Kasuga [2]. The preparation is basedon a hydrothermal treatment of TiO2 powder with NaOH. Thatpublication initiated quite a huge interest on Ti-NTs and alsothe discussion about their structure. Kasuga [2] reported thestructure of Ti-NTs as the one of anatase. Other structuresbased on TiO2 phases were reported by Deng [3] as brookitestructure and by Armstrong [4] as beta TiO2 phase. On theother hand, Chen [5] showed that the structure of Ti-NTscould possibly be assigned as H2Ti3O7. The tubular structurecould not be obtained by just replacing NaOH by LiOH or KOHin the synthesis. The authors [5] removed Na ions from thestructure by washing it in H2O. Another reported structure ofTi-NTs was H2Ti2O5·H2O, by Chen [6]. The authors studied thenecessary time for obtaining Ti-NTs. The final tubularstructure was obtained after 20 h of reaction time and theresulting Ti-NTs had a multiwall structure with four walls. ThestructureofTi-NTswas related to theone ofNa2Ti2O5·H2Oand it

167M A T E R I A L S C H A R A C T E R I Z A T I O N 8 7 ( 2 0 1 4 ) 1 6 6 – 1 7 1

was possible to remove Na ions [7]. Nakahira [8] suggested thatthe possible structure of Ti-NTs was H2Ti4O9·H2O. The authorsstudied the influence of the structure of TiO2 initial powder onthe structure of Ti-NTs. They used different initial powders:anatase TiO2 powder, a mixture of anatase and rutile TiO2

powder (3:1) and rutile TiO2 powder. Surprisingly, they foundthat all powders gave the same final structure of Ti-NTs. Byreplacing NaOH by KOH the H2Ti4O9·H2O structure of Ti-NTswas formed. The nanotube had a diameter of about 10 nm. Thesodium salt (for example Na2Ti2O5·H2O) of these structurescould be found as well if the sample was not well washed andsome sodium ions are still presented.

Our aimwas to find the structure of Ti-NTs prepared by thehydrothermal method. In order to accomplish this task, acombination of three complementary methods: powder X-raydiffraction (PXRD), high resolution transmission electronmicroscopy (HRTEM) and electron diffraction (ED) was used.A computer simulation of PXRD pattern utilizing the Debyeformula was used for the structure verification. The intensitydistribution in the calculated Fourier transformation of thesingle nanotube based on model is comparable to that ofprecession electron diffraction.

Fig. 1 – SEM image of nanotubes.

2. Methods

The investigated Ti-NT samples were prepared by hydro-thermal treatment of nanocrystalline TiO2 anatase powder.The powder was dispersed in 10 M NaOH aqueous solution.This suspension was put into a closed vessel and heated at120 °C for 48 h. After the synthesis, the sample was washedand neutralized by HCl. In order to obtain powder samples ofTi-NTs, the sample was freeze-dried.

The structure investigations were performed by threecomplementary methods: X-ray diffraction (XRD), HRTEMand ED.

The XRD is a widely used method for structure determi-nation. The X-ray measurements on the Ti-NT samples wereperformed on a PANanalytical MPD diffractometer with theCuKα radiation. The sample was mixed with a solvent andspread on a glass or the so-called non-diffracting Si substrateholder. The sample was measured in the Bragg–Brentanogeometry with variable slits and the PIXcel detector, in the 2θrange from5° to 80°. Powder diffractionpatternsweremeasuredwith the step size of 0.0263° 2θ; total integrating time for onestep was 180 s. Incident beam was conditioned by Soller slit(divergence 0.04 rad) and a beam mask of width 5 mm wasused. Automatic divergence slits were used both in primary anddiffracted beam in order to achieve constant irradiated areaduring measurement (5 × 8 mm2.) In front of the PiXCeldetector (in scanning mode), Soller slits (0.04 rad divergence)and a beta-filter (Ni) were placed.

PXRD gives information on the crystalline structureaveraged over irradiated volume. On the other hand, HRTEMcan be used to visualize the structure of a single nanotube.One of the challenges of this study was to find the requiredsingle nanotube because nanotubes prefer to stick togetheras shown in Fig. 1.

Ti-NTs were ultrasonically dispersed in ethanol and then adrop of the sample was spread on a holey carbon-coated

microscope copper grid. Individual nanotubes were studied byHRTEM imaging, performed on JEOL JEM 2100 F FEG (fieldemission gun) operated at 200 kV accelerating voltage.

A through-focus series of HRTEM images consisting 20images at different defocus values were taken. These imageswere corrected for distortions by contrast transfer function(CTF) and the individual CTF-corrected images were combinedinto a reconstructed image of structure using the structureprojection reconstruction method [9].

ED patterns were collected on the single nanotube as well.As the interaction of electrons with matter is ~104 timesstronger than that for X-rays, dynamical effects should betaken into account and the interpretation of ED patterns ismore complicated than that of XRD patterns. In order toovercome this problem, digital precession electron diffrac-tion (PED) [10] was used to collect ED data. In this method theelectronmicroscope is controlled by dedicated software only.The electron beam is rotated along a circle at a certain angle(so-called precession angle; 2° in this work) around theoptical axis of the microscope. The beam rotation along thecircle is sampled with a fixed azimuthal step (3° in this work)which results in 120 individually beam-tilted EDpatterns. Thesepatterns are combined into the final PED pattern by (1) aligningall patterns against each other using cross-correlation and(2) summingup thealignedpatterns. The set of structure factorsextracted from the final PED pattern is closer to kinematicalintensities.

PED patterns were recorded on JEOL JEM 2100 LaB6 operatedat 200 kV accelerating voltage. The sample preparation was thesame as in for HRTEM imaging.

EDS was used for investigation of chemical compositionsof the sample. EDS studies were performed on a Tescan Mira1microscope. This microscope had auto emission electron gunoperated at 15 keV. Scanning electron microscopy (SEM)studies were performed also on this microscope at 30 keV in

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168 M A T E R I A L S C H A R A C T E R I Z A T I O N 8 7 ( 2 0 1 4 ) 1 6 6 – 1 7 1

order to study the morphology of Ti-NTs. Commercialscanning electron microscope Mira I (Tescan) was used forSEM and EDS investigations. The microscope use EDS BrukerQuantax 800 analyzer equippedwith detector XFlash 6|10 withenergy resolution 129 eV. Samples were placed on carbon tapein the case of EDS. For SEM measurement the samples wereput directly on the aluminum sample holder without coating.No charging effect was observed during measurements.

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Fig. 2 – a—Comparison of measured XRD powder patternand theoretical positions of diffraction peaks of H2Ti2O5·H2O

3. Results and Discussion

Energy dispersive X-ray spectroscopy (EDS) was first per-formed in order to find whether the samples may have thestructure of TiO2 or one of the titanium salts. EDS analysisrevealed certain contents of sodium ions and thus thestructure was assumed to be one of the titanium salts. Theresult of EDS is shown in Table 1. where only Ti K-edge andNaK-edge were given.

The following titanium acids H2Ti4O9·H2O, H2Ti3O7 andH2Ti2O5·H2O are selected from database and the theoreticalpositions of diffraction lines for each of them were comparedwith measured PXRD pattern. This comparison is shown inFig. 2.

The best match was achieved for the H2Ti2O5·H2O phasewith an orthorhombic structure and the unit cell parameters:

a ¼ 18:03 ); b ¼ 3:78 ); c ¼ 2:998 ):

The predicted structure from PXRD analysis should be thatof NaxH2 − xTi2O5·H2O where the content of sodium ions × isdetermined from EDS to be 0.4.

XRD gave information on the average crystalline structureof nanotubes. However we were also interested in thestructure of a single nanotube. A through-focus series ofHRTEM images was taken at different defocus values. Theobtained picture is shown in Fig. 3. in which the black dotsrepresent Ti–O octahedron.

Characteristic features of the nanotube are the following:a zig–zag shape on the edge of the nanotube and smallsquares in the middle of the tube. The distances between theatomic columns in themiddle and on the edge could be foundfrom the reconstructed structure image. To obtain thedistances more accurately, 10 dots in the edge and in themiddle of the tube were measured. Both measured distancesare illustrated in Fig. 3. The distance of 38 Åwasmeasured onthe edge of the nanotube and so one lattice parameter shouldbe 3.8 Å. In the middle of the tube, the obtained distance was30 Å—the other lattice parameter should be 3 Å. These

Table 1 – EDS analysis of Ti-NTs. The abbreviation ‘atom.C [%]’ means atomic concentration of given element, ‘nor.C [%]’ denotes weight concentration. Reported errors arethe total errors according to the statistical treatment of thedata.

Element Nor. C [%] Atom. C [%] Error [%]

Titanium K-series 91.2 83.3 2.1Sodium K-series 8.8 16.7 0.5

phase. b—Comparison of measured XRD powder patternand theoretical positions of diffraction peaks of H2Ti3O7

phase. c—Comparison of measured XRD powder patternand theoretical positions of diffraction peaks of H2Ti4O9·H2Ophase.

distances are compared with the structure suggested fromPXRD—H2Ti2O5·H2O. The distance in the ‘zig–zag’ edge corre-sponds to cell parameter b of this structure. The secondmeasured distance corresponds to the lattice parameter c of

Fig. 3 – The structure image reconstructed from thethrough-focus series.

Fig. 4 – Side view of the model of nanotube—only Ti atomsshown (displayed by [12]).

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this structure. Therefore, we assume that Ti–NT has thestructure of H2Ti2O5·H2O and it is possible to orient the unitcellwith respect to thenanotube as follows: the c axis is directedaround the nanotube circumference, the b axis is along thedirection of the nanotube axis and a axis is directed perpendic-ular to the center of the tube.

In order to verify the orientation of Ti-NTs it was necessaryto create a model, simulate the PXRD and ED patterns andcompare them with the experimental data. The atom posi-tions in the unit cell of H2Ti2O5·H2O have been published [7],but unfortunately the positions of water molecules were notcorrect in this model. Thus for our computer simulation amodel based on the structure of (H3O)0.11Cs0.24Ti0.91O2(H2O)0.12presented [11] was used. It is also orthorhombic just likeH2Ti2O5·H2O and the lattice parameters are very similar. OnlyTi–O octahedron from the structure [11] was used for ourcalculations because they create the main building blocks intitanates. In order to have correct numbers of titanium atomsin the calculations, because used structure (H3O)0.11Cs0.24-Ti0.91O2(H2O)0.12 has only one Ti atom unlike our predictedstructure H2Ti2O5·H2O having two Ti atoms, the z positions oftitanium and oxygen atoms were replaced. The nanotube hasa spiral base as can be seen in Fig. 3. There are two walls onthe left side and three on the right—the nanotube ismade by arolling 2D sheet. The first step in our computer simulationwas to build a model. The radius of nanotube is one necessaryparameter of the model and it could be estimated from theHRTEM image. The inner diameter of the nanotube is 53.8 Å.The second important parameter of the model is the distancebetween walls. This distance could not be obtained fromHRTEM images because the high vacuum could decrease thedistance. Thus the distance from the HRTEM image was takenas the first approximation and then the PXRD pattern wascalculated with the aid of the Debye formula and comparedwith the experimental one. This was repeated for severalvalues of the parameter until a reasonable match wasachieved. The distance between walls was changed in themodel in order to obtain a good match of the first diffractionpeak position. This peak corresponds to the direction ofstacking walls as can be seen in Fig. 2. The final value ofdistance between the walls of Ti-NT obtained by calculations—approximately 8.3 Å—is in good agreement with the valuereported by Nakahira [8] which is 9 Å or less.

A side view of the Ti-NT with only Ti atoms is presented inFig. 4.

The 2D Fourier transformation of this view was calculatedand compared with the diffraction pattern measured byprecession ED. The squared amplitudes of the Fourier transfor-mation are proportional to the intensities in diffraction pattern.Relatively good correspondence of the Fourier transformationand the experimental ED pattern is shown in Fig. 5.

XRDpattern of a nanotube can be computed bymeans of theDebye formula [13]. In this formula the sumover all atomic pairsmust be calculated:

Ieu ¼X

i

X

j

f i f jsinqrijqrij

; ð1Þ

where rij is distancebetween twoatoms, fi, fj theatomic scatteringfactor of atom i, j respectively and q is the diffraction vectormagnitude, q ¼ 4π

λ sinθ . Formula (1) describes the intensitydistribution of randomly oriented (nano)particles. The sum runsover all the pair distances rij of the atoms i, j. Unfortunately, thesummation is very timeconsumingandonehave toapply certainapproximations. One of widely used numerical methods is basedon using histograms of distances between the atoms. In the caseof Ti-NT three histogramsmust be calculated—the first one fromthe positions of only Ti atoms, the second one from Ti and Oatoms and the last one from oxygen atoms. Then, the Debyeformula changes to the following:

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where Ni,j,k is the frequency of positions in each histogram.Formula (2) speeds up the calculation more than a thousand-times.

The best agreement between the calculated and experi-mental PXRD patterns is shown in Fig. 6.

As it can be seen, the computer simulation of PXRD patternhas the same basic characteristic peaks as the experimental

Fig. 5 – Fourier transformation of nanotube (left) and recorded ED pattern (right).

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PXRD pattern. The main disagreement can be seen on thepeak at about 2θ = 40°. This could be caused by neglectingpossible preferred orientations of nanotubes in the calcula-tions. Our specimens for PXRD in reflection mode wereprepared on glass substrate. It is very probable that thenanotubes were lying on the holder so that in symmetricalBragg–Brentano diffraction they can be hardly seen alongthe b axis. Preliminary studies of preferred orientation withthe aid of the Eulerian cradle showed significant changesof the diffraction pattern with the specimen inclination andthe narrow diffraction peak 020 increased with the sample

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inclination. Therefore, in the next investigation we willinclude preferred orientation in the calculation with theDebye formula.

4. Conclusions

The structure of titanate nanotubes prepared by the hydro-thermal method was identified to be related to the structureof NaxH2 − xTi2O5·H2O. This was approved by the comparisonof powder X-ray diffraction pattern calculated via the Debyeformula with the experimental data, the comparison of theFourier transformation of the model with the experimentalprecession electron diffraction pattern and also from thestructure image reconstructed from a series of HRTEM images.For improving the agreement of the simulated and experi-mental X-ray diffraction patterns, it is suggested that theeffect of preferred orientation of nanotubes on the substrateholder should be considered and accurate atomic positions inthe nanotubes should be determined as well.

Acknowledgments

We kindly acknowledge A. Mantliková for making SEMpictures. The work is supported by the Grant Agency of theCzech Republic no. P108/11/1539 and by the Grant Agency ofCharles University under the Grant no. 470413, the SwedishResearch Council (VR), the Swedish Governmental Agency forInnovation Systems (VINNOVA) and Göran Gustafsson Foun-dation for Natural Sciences and Medical Research. Wei Wanwas supported by a post doctoral grant from the Carl-Trygger

171M A T E R I A L S C H A R A C T E R I Z A T I O N 8 7 ( 2 0 1 4 ) 1 6 6 – 1 7 1

Foundation. The EM facility was supported by a grant fromKnut and Alice Wallenberg Foundation. EDS experimentswere performed in MLTL (http://mltl.eu/), which is supportedwithin the program of the Czech Research Infrastructures(project no. LM2011025).

R E F E R E N C E S

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[2] Kasuga T, Hiramatsu M, Hoson A, Sekino T, Niihara K.Formation of titanium oxide nanotube. Langmuir1998;14:3160–3.

[3] Deng Q, Wei M, Ding X, Jiang L, Ye B, Wei K. Brookite-typeTiO2 nanotubes. Chem Commun 2008;31:3657–9.

[4] Armstrong G, Armstrong AR, Canales J, Broce PG. Nanotubeswith the TiO2-beta structure. Chem Commun2005;19:2454–6.

[5] Chen Q, Zhou W, Du G, Peng LM. Trititanate nanotubes madevia single alkali treatment. Adv Mater 2002;14:1208–11.

[6] Chen W, Gou X, Zhang S, Jin Z. TEM study on the formationmechanism of sodium titanate nanotubes. J Nanopart Res2007;9:1173–80.

[7] Tsai ChCh, Teng H. Structural features of nanotubessynthetized from NaOH treatment on TiO2 with differentpost-treatments. Chem Mater 2006;18:367–73.

[8] Nakahira A, Kato W, Tamai M, Isshiki T, Nishio K. Synthesisof nanotube from a layered H2Ti4O9·H2O in a hydrothermaltreatment using various titania sources. J Mater Sci2004;39:4239–45.

[9] WanW,Hovmoller S, ZouXD. Structure projection reconstructionfrom through-focus series of high-resolution transmissionelectron microscopy images. Ultramicroscopy 2012;115:50–60.

[10] Zhang DL, Grüner D, Oleynikov P, Wan W, Hovmöller S, ZouXD. Precession electron diffraction using a digital samplingmethod. Ultramicroscopy 2010;111:47–55.

[11] PDF4 ICCD database, n. 04-011-1868.[12] Jmol. www.jmol.org.[13] Warren BE. X-ray Diffraction. Dover Publication; 1990 116–7.