Acta Biomaterialia 3 (2007) 359–367

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Microstructure and deformation behavior of biocompatibleTiO2 nanotubes on titanium substrate q

G.A. Crawford a, N. Chawla a,*, K. Das b, S. Bose b, A. Bandyopadhyay b

a School of Materials, Arizona State University, Tempe, AZ 85287-8706, USAb School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164, USA

Received 20 April 2006; received in revised form 7 August 2006; accepted 16 August 2006

Abstract

Titanium oxide coatings have been shown to exhibit desirable properties as biocompatible coatings. We report on the quantitativemicrostructure characterization and deformation behavior of TiO2 nanotubes on Ti substrate. Nanotubes were processed using anodicoxidation of Ti in a NaF electrolyte solution. Characterization of the as-processed coatings was conducted using scanning electronmicroscopy and focused ion beam milling. Increases in anodization time had no significant effect on tube diameter or tube wall thickness.Coating thickness, however, increased with time up to 2 h of anodization, at which point an equilibrium thickness was established.Nanoindentation was used to probe the mechanical response in terms of Young’s modulus and hardness. Progressively higher valuesof elastic modulus were obtained for thinner films consistent with increasing effects of the Ti substrate. A possible deformationmechanism of densification of the porous oxide and wear of the dense surface is suggested and discussed.� 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Nanoindentation; Biocompatible; TiO2; Porosity; Coating

1. Introduction

Titanium (Ti) and Ti alloys have been used extensivelyas bone-implant materials due to their high strength-to-weight ratio, good biocompatibility and excellent corrosionresistance [1,2]. Titanium, however, being relatively inert,cannot directly bond to bone, and osseointegration viathe natural oxide (TiO2) is a long process [3,4]. Hence,there is an increased interest in reducing the time neededfor osseointegration. In an effort to enhance the cell-implant material interaction and increase lifetime, bioac-tive ceramic based coatings have been applied to Tiimplants, most notably hydroxyapatite (HA) [5–8].

Recently, TiO2 has been suggested as a potential alter-native to HA coatings. The advantage of using TiO2 is that

1742-7061/$ - see front matter � 2006 Acta Materialia Inc. Published by Else

doi:10.1016/j.actbio.2006.08.004

q Research presented at the TMS 2006 Biological Materials ScienceSymposium.

* Corresponding author.E-mail address: nchawla@asu.edu (N. Chawla).

it can be grown directly on the Ti surface, by cost-effectivetechniques such as anodic oxidation [9–11]. Also, it is wellknown that one problem with HA coatings is poor adhe-sion strength at the HA/Ti interface [5–8]. Using anodicoxidation, TiO2 is formed with a chemical bond betweenthe oxide and Ti substrate that likely results in enhancedadhesion strength. Indeed, a bone-like apatite layer isformed on TiO2 in simulated body fluid (SBF) [9,10]. Fur-thermore, researchers have suggested that TiO2 with a 3-Dmicro/nanoporous structure may enhance apatite form-ability when compared to dense TiO2 [11]. Recently, Gonget al. [12] have shown that TiO2 coatings, consisting of reg-ular self-assembled nanotube arrays, may be formed on thesurface of Ti by anodic oxidation. Treating the TiO2 nano-tubes with NaOH solution induces the growth of nanosizedHA when subjected to SBF [13]. Furthermore, nanophaseceramics such as HA, Al2O3 and TiO2 enhance long-termosteoblast functions relative to typical microstructureforms [14]. Thus, the apatite-forming and bone-bondingability of titanium bone-implant materials may be

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360 G.A. Crawford et al. / Acta Biomaterialia 3 (2007) 359–367

significantly enhanced by anodically oxidized nanotubes onthe surface of Ti.

One of the most important attributes of materials inmedical and dental applications is its mechanical properties[1,2]. This is particularly important in bone-implant mate-rials, where long-term in vivo structural stability is crucial.Here, bone resorption occurs due to the mismatch inmechanical properties (i.e., elastic modulus) between boneand the implant material, causing implant loosening andeventual failure [15]. Thus, it is important to characterizethe mechanical behavior of these implant materials. Fur-thermore, it is important to establish the relationshipbetween microstructure and mechanical behavior, in aneffort to elucidate deformation mechanisms.

Mechanical characterization of thin coatings is challeng-ing because of the small length scales involved. In thisregard, nanoindentation is a very appropriate techniquefor these materials because of its low load (1 lN) and smalldisplacement (1 nm) resolution [16]. Nanoindentation is aneffective technique for probing mechanical properties ofthin (<10 lm) coated systems including soft coatings onhard substrates [17,18], hard coatings on soft substrates[19–21] and multilayered systems [19,22,23]. This techniquehas also been used to investigate the mechanical responseof TiO2 with nanophase microstructure [24,25] and of thinTiO2 coatings on Ti substrates [20,21].

To our knowledge, a systematic investigation of themicrostructure and mechanical behavior of self-assembled,vertically aligned nanotubes has not yet been reported.Thus, in this study we focus on the relationship betweenmicrostructure characterization and deformation behavior,by nanoindentation, of TiO2 nanotubes on Ti substrate.We have studied the effect of changes in anodic oxidationtime on tube diameter, tube wall thickness and coatingthickness. Nanoindentation was conducted to probe themechanical properties, such as Young’s modulus and hard-ness. Post-indentation characterization was employed toprovide insight into deformation mechanisms in thissystem.

2. Materials and experimental procedure

Thin titanium sheets (99.8% purity, Supra Alloys, CA),0.5 mm in thickness, were used for fabrication of TiO2

nanotubes. Disks (12 mm diameter) were ground withSiC paper and ultrasonically cleaned in distilled water.Final polishing of the sample was performed with 1 lmalumina suspension. A two-electrode electrochemicalanodization cell, with a platinum cathode and Ti anode,was used to fabricate the nanotube arrays. Anodizationvoltage was kept constant at 20 V with a DC power supply(Hewlett–Packard 0–60 V/0–50 A, 1000 W). The electro-lyte was made by dissolving sodium fluoride (NaF,Sigma–Aldrich), citric acid (J.T. Baker), 1 M sulfuric acid(Fischer Scientific) in a ratio so that the final electrolytecomponent concentrations were F� 0.1 mol/l, SO2�

4

1.0 mol/l, citric acid 0.2 mol/l. The electrolyte pH was

adjusted to 4.5 using NaOH solution. All experiments wereperformed at room temperature.

Characterization of coating surfaces and cross sectionswas carried out using a field emission scanning electronmicroscope (FESEM, Hitachi S4700). The inner diameterand wall thickness of the tubes were measured by segment-ing SEM micrographs and using image analysis software(ImageJ, Gaithersburg, MD). Micrographs for quantitativeanalysis were taken from at least two different locations oneach sample. This was done to ensure that the measure-ments were representative of the overall microstructureand to gauge the degree of sample variability. About 500measurements of tube diameter were taken per samplelocation. Tube wall thicknesses were measured at randomfrom an average of 50 tubes per sample location.

Characterization of coating/substrate cross sections wascarried out by fracturing the coating by bending, andexamining the detached TiO2 coating. SEM was used toexamine both the bottom of the coating as well as the mat-ing Ti substrate. Coating thickness was measured directlyfrom SEM micrographs. At least six measurements weretaken from different areas of the cross section to ensurethat the measurements reflected the actual coating thick-ness. The coating cross section was also studied by a rela-tively nondestructive means. A focused ion beam (FIB)with high-resolution SEM (FEI Nova 200 SEM/FIB, Hills-boro, OR) was used for ion milling and characterization ofthe TiO2/Ti cross section. Ion milling was conducted at30 keV, with a milling and cleaning cross section currentof 0.4 nA and 10 pA, respectively. In order to minimizeion beam damage, a protective platinum layer (�1 lmthick) was deposited in situ using the electron source, priorto ion milling.

The mechanical properties of the coatings were probedby nanoindentation. A commercial nanoindenter (MTS-Nano Instruments XP-II, Minneapolis, MN) was used witha continuous stiffness measurement (CSM) capability [26].Here, a small-harmonic high-frequency amplitude is super-imposed over indentation loading and the contact stiffnessof the sample is measured from the displacement responseat the excitation frequency. From this contact stiffness, theYoung’s modulus of the material can be derived. Thus, themodulus or hardness can be determined instantaneously asa function of depth. For all experiments, indentation wascarried out using a Berkovich (three-sided pyramid) inden-ter. Calibration for load and hardness was performed on areference sample of fused silica. Indentation experimentswere conducted in displacement control to depths of2000 nm for each sample. At least five indentations wereobtained for each condition.

3. Results and discussion

3.1. Microstructure characterization

We begin with the characterization of the surface andcross section of the TiO2 coatings. Fig. 1 shows a SEM

Fig. 1. FESEM micrograph of TiO2 nanotubes formed by anodicoxidation of Ti in NaF-containing electrolyte (0.1 mol/l F�), at pH 4.5,and constant potential of 20 V for 2 h.

Table 1Dimensions of TiO2 nanotubes fabricated through anodic oxidation of Tiin NaF-containing electrolytes (0.1 mol/l F�), at pH 4.5, and constantpotential of 20 V

Anodization time (h) Tube dimensions (nm)

Inner diameter Wall thickness Tube length

0.25 45 ± 10 12 ± 2 234 ± 60.5 43 ± 8 12 ± 2 245 ± 142 58 ± 12 16 ± 2 650 ± 204 50 ± 9 15 ± 2 625 ± 23

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micrograph of Ti anodized for 2 h in NaF-containing elec-trolyte (0.1 mol/l F�), at a pH of 4.5, and constant poten-tial of 20 V. A uniform structure of thin-walled TiO2

Fig. 2. FESEM micrograph showing (a) fractured cross section, (b) bottomoxidation of Ti in NaF-containing electrolytes (0.1 mol/l F�), at pH 4.5, and

nanotubes was obtained. Table 1 summarizes the quantita-tive measurements of the important dimensions of thetubes. Tube diameter, tube wall thickness and tube lengthwere 35–70, 10–18 and 230–670 nm, respectively. Moreimportantly, tube diameter and wall thickness did notappear to vary with anodization time, for the range oftimes examined here. Our results are consistent with thosefound by other researchers under similar processing condi-tions [29]. A small increase in tube diameter and wall thick-ness with increasing anodization time, from 30 min to 2 h,is observed. Given the standard deviation of the reporteddata, however, this difference is not significant.

Fig. 2 shows a cross section of the fractured TiO2 coat-ing. The mating surfaces of the bottom of the coating andthe top of the substrate are also shown. Slight variations inthe tube wall thickness, or ‘‘ridges,’’ at regular spaced inter-vals are observed. The possible origin of these ridges is dis-cussed below. The bottom surface of the TiO2 nanotubecoating is characterized by a series of regularly spaced‘‘bumps’’ (Fig. 2b). These bumps represent the pore tipof each individual nanotube. The bottom surface clearlyshows the bottom of the barrier layer, which acts as a thinbarrier between the Ti substrate and the tubular structure.The formation of this and other structures are discussedbelow. The mating Ti surface (Fig. 2c) shows correspond-ing concave dimples that match that of the TiO2 coating.This ‘‘cup and cone’’ type structure at the interface mayencourage mechanical interlocking, and may increase theadhesion strength at the metal/ceramic interface.

The cross section of the interface was also observed bymicromilling using a focused ion beam (FIB). The FIBallows one to obtain a smooth surface at the coating/

surface of TiO2 nanotubes, (c) surface of Ti substrate, following anodicconstant potential of 20 V for 4 h.

Fig. 4. Average coating thickness vs. anodization time for Ti samplesanodized in NaF-containing electrolyte (0.1 mol/l F�), at pH 4.5, andconstant potential of 20 V.

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substrate interface. This is particularly important for thematerials studied here, because the substrate and coatinghave large differences in stiffness and hardness. As a result,conventional mechanical polishing would have resulted inpreferential removal of the softer phase. Fig. 3 shows aSEM micrograph of the cross section of TiO2/Ti sampleproduced by the FIB milling technique. The platinum layercan be observed at the top of the micrograph. The interfacebetween TiO2 and Ti is quite uniform. Once again, ridgemarkings can be seen on the walls of the TiO2 nanotubes.

Using the SEM micrographs of the cross sections, quan-titative measurements of the coating thickness wereobtained. Fig. 4 shows a plot of coating thickness (tubelength) vs. anodization time. It appears that there is a sig-nificant increase in coating thickness with time between30 min and 2 h. Between 2 and 4 h, however, the thicknessis relatively unchanged. The origin of this behavior, as wellas other microstructural observations, are now discussed.

TiO2 nanotube formation in F�-containing electrolytesis the result of two competing, electric field-assisted pro-cesses. Hydrolysis of Ti metal to form TiO2 occurs by thefollowing reaction [27–29]:

Ti4þ+ 2H2O!TiO2 + 4Hþ ð1Þ

In addition, chemical dissolution of TiO2 at the oxide/electrolyte interface occurs, resulting in the formation of[TiF6]2� [27–29]:

TiO2 + 6HF! [TiF6]2 + 2H2O + 2Hþ ð2Þ

The growth process of the tubes may be divided into threemain processes: (i) initial barrier layer formation, (ii) for-mation of uniformly distributed pores and (iii) separationof interconnected pores into nanotubes. A detailed under-standing of the exact mechanisms for ordered TiO2 nano-tube formation is still not clear. Several possible

Fig. 3. FESEM micrograph of FIB milled TiO2/Ti cross section preparedby anodization of Ti in NaF-containing electrolytes (0.1 mol/l F�), at pH4.5, and constant potential of 20 V for 4 h. Insert shows surfacemorphology of sample.

mechanisms for formation of these tubes, however, havebeen proposed. During the onset of anodization, a barrieroxide layer begins to form, causing an exponential decreasein the anodic current density. In fluorine-free solutions,both the thickness of the barrier layer and the measuredcurrent density reach steady state [27,29–31]. In fluorine-containing solutions, however, a nanoporous structure be-gins to form due to the chemical dissolution of the barrieroxide layer (Eq. (2)). An increase in current density takesplace during this process. Over time pores become assem-bled in an ordered fashion and become unconnected. Oncean ordered nanotube structure is established, the currentdensity again stabilizes, at a value greater than that in afluorine-free solution [27,30,31]. At this point, further ano-dic oxidation simply increases the length of the tubes butdoes not significantly affect the tube structure or the anodiccurrent density.

The exact mechanism by which nanopores form and areseparated into nanotubes is still the subject of some debate.We address the case of ordered nanopore formation first.Several researchers have suggested that nanopore forma-tion occurs by random local dissolution of the TiO2 surfacewhich drives the formation of pores [30–32]. Here pore for-mation is driven by localized dissolution of TiO2 whichreduces the film thickness locally, increasing the electricfield intensity at the bottom of the pore and inducing theformation of new oxide. Thus, the reactions given above(Eqs. (1) and (2)) take place simultaneously at the bottomof the pore and cause the pore to grow further into the Tisubstrate [29,31]. Beranek et al. [30] suggest that pore for-mation takes place initially at random locations, and self-ordering is merely a product of the competition betweengrowing pores. Raja et al. [27], on the other hand, suggestthat the ordering of pores may be a result of local surfaceperturbations. Here increases in strain energy of the oxidefilm may be caused by variations in dielectric constant andelectrostriction coefficient throughout the film. In this case,

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fluoride ions could migrate to regions of high strain energydensity, causing the migration of hydrogen ions to main-tain electrical neutrality, and leading to the dissolution ofTi4+ ions. As a result, mass flow may occur, such thatlow strain energy locations grow at the expense of the dis-solving high strain energy areas (i.e., pores).

Following pore formation, neighboring nanopores mustbe separated to form individual nanotubes such as thoseseen in Fig. 1. Mor et al. [31] suggested that the unanodizedregions between pores are susceptible to field-assisted oxi-dation/dissolution causing the formation of voids betweennanopore regions. Thus, nanotubes are the result of simul-taneous growth of voids and pores. However, Raja et al.[27] have proposed that void growth in equilibrium withpore growth is an unlikely mechanism for the formationof tubes with well defined circular cross sections. In con-trast, they propose that the separation of pores into indi-vidual nanotubes may be a result of repulsive forcesbetween cation vacancies. Negative cation vacancies areformed when Ti4+ ions dissolve into solution. It is postu-lated that these negatively charged vacancies migrate radi-ally to the center of the interpore region, following thedirection of the electric field. Vacancies arriving at theinterpore region, originating from neighboring pores, willhave the same sign and will repel each other, keeping anequilibrium distance. If the dissolution rate at the Ti/TiO2 interface is higher than the generation of oxygenvacancies (produced to maintain electrical neutrality), thecation vacancies may condense to form voids between theneighboring pores [27].

Let us now address the issue of ‘‘ridge’’ formation in thetubes (Figs. 1 and 3). Macak et al. [32] have suggested thatthese ridges or inconsistencies in wall thickness are a resultof current oscillations during the anodization process. Eachcurrent transient is accompanied by a change in pH at thepore tip and, thus, a temporary increase in the dissolutionrate. In fact, by decreasing the diffusion constant of theelectrolyte, they showed that changes in pH may bedamped and variations in dissolution rate minimized,resulting in nanotubes with smooth tube walls [32].

Finally, the evolution of coating thickness can beexplained as follows. An equilibrium thickness results whenthere is a balance between the rate of porous oxide forma-tion at the pore tip and the chemical dissolution rate of theTiO2 at the pore mouth [27,29–31]. Thus, with anodizationtimes longer than 2 h, new oxide is being formed at themetal/ceramic interface. The thickness of the coating, how-ever, is maintained by chemical dissolution at the ceramic/electrolyte interface. In fact, it has been shown that byadjusting the electrolyte solution and using a voltage sweeptechnique, a pH gradient may be introduced, such thatthere is localized acidification at the pore tip but a basicsolution at the pore walls and mouth [28,32]. The chemicaldissolution rate at the top of the tube is impeded, whileoxide formation at the pore tip is increased. Using thislogic, nanotubes with lengths much longer than thosereported here have been fabricated (i.e. 2.5 lm [28],

7.7 lm [32]). Long (i.e. 4.4 lm [29]) TiO2 nanotubes havealso been formed using constant potential (rather thanvoltage sweeping) anodization.

3.2. Nanoindentation

In this section we describe nanomechanical characteriza-tion of the TiO2 nanotube structures on Ti. Fig. 5a showsrepresentative load vs. displacement curves for the sampleswith varying anodization time. Fig. 5b and c shows theextracted apparent Young’s modulus and hardness, respec-tively, obtained from the continuous stiffness measurement(CSM) system. The term apparent is used because the mea-sured modulus and hardness are not only a function of thecoating, but are also influenced by the substrate. This isimmediately apparent from the modulus vs. displacementcurves for the thinner coatings (15 and 30 min). Here, withincreasing depth, the measured modulus approached thatof the Ti substrate. Average coating thickness for the sam-ples are designated by a dotted vertical line in the plots ofapparent modulus vs. displacement (Fig. 5b). Note,because coating thicknesses are similar for the 2 and 4 hand also the 15 and 30 min, a single line is displayed foreach set. Thus, from inspection of Fig. 5b, total nanoinden-tation depth is much larger than the thickness of thecoating.

In order to gain insight into the underlying deformationmechanisms, SEM of the indentations was conducted.Fig. 6a and b shows a SEM micrograph of typical nanoin-dentations for the 15 min and 2 h samples respectively.Note that the TiO2 coating anodized for 15 min shows evi-dence of delamination. Indeed, delamination was observedin almost all indentations in the 15 and 30 min samples. Webelieve that coating delamination occurred on unloading,due to residual stresses induced from the loading cycle.This conclusion can be made because there were no consis-tent fluctuations in the experimental data that suggest evi-dence of delamination during loading. None of theindentations for 2 or 4 h, however, showed signs of delam-ination. Thus, it is important to note that coating delami-nation occurred only in thin coatings (230–250 nm) anddid not occur in thicker coatings (600–650 nm). This sug-gests that the adhesion strength may be enhanced withincreases in coating thickness. The exact mechanism forthis phenomenon is not well understood. However,increased thickness of the porous layer may retard thebuild-up of stress needed to cause delamination duringthe loading cycle. An additional characteristic of indenta-tions in thicker coatings were wear markings on theindentation surface (Fig. 6b). These markings suggest somedegree of frictional sliding between the indenter and theTiO2 surface. We also observe an increase in density ofthe coating, which decreased radially from tip of the inden-ter. This suggests the densification of nanotubes undernanoindentation. The exact mechanism of densification isnot clear. It is likely, however, that fracture of thenanotubes accompanies densification.

Fig. 6. FESEM micrographs of typical nanoindentations on the surface of Ti anodized for (a) 15 min and (b) 2 h in NaF-containing electrolytes (0.1 mol/lF�), at pH 4.5, and constant potential of 20 V.

Fig. 5. Characteristic (a) load, (b) apparent Young’s modulus and (c) apparent hardness vs. nanoindentation displacement (depth) for Ti samplesanodized in NaF-containing electrolytes (0.1 mol/l F�), at pH 4.5, and constant potential of 20 V for various times.

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From the SEM micrographs and the indentation data,we can construct a proposed model for deformation inthese systems. There appear to be two main deformationprocesses: (i) densification of the porous nanotube struc-ture and (ii) wear of the dense surface. Fig. 7 shows a sche-matic of the proposed deformation process. Regionsimmediately under the indenter tip are subject to densifica-tion, while those at the sides of the indenter are under shear

stresses that induce both densification and wear of the TiO2

nanotubes.The deformation mechanisms can also be correlated to

the measured modulus vs. depth curves. Three distinctregions may be defined and are shown in Fig. 8. Region Iis characterized by a linear increase in modulus withincreasing time. In this region, the increasing modulus isprimarily due to increased densification of the TiO2

Fig. 7. Schematic illustration of the proposed deformation process during nanoindentation of TiO2 nanotubes.

Fig. 8. Typical apparent Young’s modulus vs. displacement plot indicat-ing three characteristic regions of the deformation process. Dotted verticalline represents the average coating thickness.

Fig. 9. Plot of composite modulus vs. coating thickness, from Region III(Fig. 8) of the experimental data.

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nanotubes. Region II is characterized by a parabolicincrease in the indentation modulus. In this region theindentation depth is comparable to the thickness of theTiO2 coating, i.e. the indenter is approaching the substratesurface. Thus, increases in modulus are the result of anincreasing contribution from the substrate. In addition,there are minor contributions of densification of the outerregions of the indentation and wear between the indentersurface and the dense TiO2 surface. Note, as the TiO2 coat-ing under the indenter becomes increasingly dense, themodulus increases. Finally, Region III describes the regionwhere the coating has become nearly fully dense. Thisregion is characterized by a plateau in indentation modu-lus, which we now term the composite modulus, as it is acombination of moduli of the dense coating and the Ti sub-strate. In this region, minor contributions of densificationof the outer indentation regions and wear of the denseTiO2 surface take place.

Since densification plays a major role in the deformationprocess of TiO2 nanotubes, it would be logical for there tobe a strong relationship between coating thickness andmechanical response. Fig. 9 shows a plot of compositemodulus vs. coating thickness for all samples. Here com-posite modulus is the modulus taken from the plateau inRegion III (Fig. 8) of the nanoindentation data. First, itis important to point out that for all cases the compositemodulus is less than the modulus of the underlying sub-strate itself. Thus, the modulus of the coating is most likelylower that that of the Ti substrate. Also, in this plot we canclearly see a decrease in composite modulus with increasingthickness. This can be attributed to a larger contribution ofthe more compliant coating, relative to the Ti substrate.Thus, progressively larger values of composite modulusfor decreases in coating thickness suggest an increasingsubstrate effect in thinner coatings.

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From the above analysis, it is difficult to extract a pre-cise value of the Young’s modulus of the porous coatingitself. In nanoindentation of thin films, it is common todetermine the properties of the film at indentation depthsless than 10% of the film thickness [33]. This is to minimizecontributions from the substrate. In our case, 10% of thefilm thickness is of the order of 60 nm or less. The rough-ness of the coating is higher than this indentation depth.Therefore, it is difficult to determine the Young’s modulusof the porous coating directly from our indentation data. Itis well known, however, that the modulus of ceramic mate-rials decreases with increases in porosity. Several research-ers have proposed theoretical models to predict the effect ofporosity on the elastic properties of ceramic materials[34–36]. One of the simplest models is the ‘‘rule of mix-tures,’’ commonly used for continuous fiber reinforcedcomposites. It assumes an isostrain condition (longitudinalloading, parallel to the fibers) or isostress condition (trans-verse loading, perpendicular to the fibers). In the longitudi-nal orientation, the Young’s modulus of the composite, Ec,is given by:

Ec ¼ Ef V f þ EmV m;

where E and V correspond to Young’s modulus and vol-ume fraction, respectively. The subscripts f and m denotefiber and matrix. Hashin and Rosen [37] derived a relation-ship for a transversely isotropic composite consisting ofcylindrical fibers in various aligned packing arrangements.By assuming the ‘‘fibers’’ to be cylindrical pores (i.e.,Young’s modulus of zero) their equations also reduced toa rule of mixtures type of relationship:

Ec ¼ Emð1� P Þ;where Em is the matrix material and P is the fraction ofporosity. In our system, the nanotubes are aligned, as isthe porosity between the tubes. Thus, we can use the ‘‘ruleof mixtures’’ to determine the Young’s modulus of thisporous system. For our analysis we assume the volumefraction of pores in the coating is approximately 72% (fromimage analysis) and a modulus for dense amorphous TiO2

of 130–150 GPa (for the tubes themselves) [33]. This yieldsa Young’s modulus of TiO2 nanotubes of approximately36–43 GPa. These results seem reasonable, since our nano-indentation results indicate that the modulus of the coatingis significantly lower than that of the Ti substrate.

4. Conclusions

We have reported on the quantitative microstructurecharacterization and deformation behavior of TiO2 nano-tubes on Ti substrate. The following conclusions can bemade:

1. Nanotubes were processed using anodic oxidation, withNaF electrolyte.

2. Increases in anodization time showed no significanteffect on tube diameter or tube wall thickness.

3. Coating thickness increased up to 2 h of anodization, atwhich point an equilibrium thickness was established.Equilibrium thickness is achieved when the rate ofchemical dissolution of TiO2 at the pore mouth matchesthat of new oxide formation at the pore tip.

4. Nanoindentation results yielded progressively highervalues of elastic modulus for thinner films, consistentwith increasing effects of the Ti substrate.

5. A possible deformation mechanism of densification ofthe porous oxide and wear of the dense surface appearsto be taking place.

Acknowledgements

The authors are grateful for financial support from theOffice of Naval Research (Dr. A.K. Vasudevan, programmanager) through a subcontract from Washington StateUniversity. The authors also acknowledge M. Koopman,K. Carlisle and Professor K.K. Chawla, at the Universityof Alabama at Birmingham, for their assistance withnanoindentation.

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