Biomaterials
Volume 24, Issue 11 , May 2003, Pages 1837-1852

In situ imaging and impedance measurements of titanium surfaces using AFM and SPIS

Jane P. Bearinger^{a, b, 1}, Christine A. Orme^c and Jeremy L. Gilbert<sup>, , d

a</sup> Department of Biomedical Engineering, Northwestern University, Evanston, IL, USA
^b Lawrence Livermore National Laboratory, Medical Technology Program, 7000 East Ave, Livermore, CA, USA
^c Lawrence Livermore National Laboratory, Chemistry and Material Science, 7000 East Ave, Livermore, CA, USA
^d Department of Bioengineering and Neuroscience, Syracuse University, Syracuse, NY 13244-5290, USA

Received 11 April 2002;  accepted 17 October 2002. ; Available online 5 February 2003.

1. Abstract

Surfaces of commercially pure titanium and titanium, 6-aluminum, 4-vanadium were subjected to simultaneous polarization/impedance testing and in situ electrochemical atomic force microscopy imaging to evaluate how the structure and properties of the passive oxide film is affected by varying potential and hydration. Current transients were acquired via a step polarization impedance spectroscopy technique: the voltage was stepped between −1 and 1 V in 50 mV increments, while current transients and surface morphology were digitally recorded. Numerical Laplace transformation applied to the current transient data provided frequency-dependent admittance (impedance⁻¹). Simultaneous AFM imaging of dry surfaces, initially hydrated surfaces, and surfaces immersed and changing with potential revealed that all sample surfaces were covered with protective titanium oxide domes that grew in area and coalesced due to hydration and as a function of increasing applied voltage and time. Reversal of dome growth did not occur upon voltage reduction, while impedance behavior was quasi-reversible, suggesting independence between structural and electrical properties. Oxide growth appeared to occur in part by lateral spreading and overgrowth of domes at the oxide-solution interface. Interfacial impedance data reflect oxide passivity and n-type semiconductor behavior. Non-linear Mott-Schottky fits specified multi-layer donor concentrations between 10¹⁸ and 10¹⁹ cm⁻³, depending on the surface.

Author Keywords: Titanium; Titanium oxide; Atomic force microscopy; Electrochemical methods; Corrosion; Surface structure; Interfaces

2. Article Outline

1. Introduction

2. Materials and methods

3. Results

4. Discussion

5. Conclusion

Acknowledgements

References

3. 1. Introduction

A unified theory of titanium and its protective oxide, accounting for both its steady state composition and transient behavior, remains elusive. Most previous studies have collected electrochemical data through in situ techniques, while accompanying structural data typically has been collected through ex situ, high vacuum techniques, in which the oxide is no longer in its native environment. Thus, titanium's response—be it morphologically, structurally, electrically, or corrosion resistivity—to transient electric fields and potential shifts in solution is not well understood. A more complete understanding of this response is critical in a variety of applications, including biomedical applications, which are the focus of this study.

By weight or volume, orthopedic implants far exceed any other biomaterial application. These implants often contain titanium and may be used as fracture fixation devices or as joint replacement devices or prostheses. At present, average life span of an artificial hip is approximately 10 years. Total hip replacement procedures are becoming more common in younger patients; patients are therefore exposed to greater mechanical stress over a longer period of time. Increasing the life span of artificial joints is clearly a challenging focus of biomaterial research. Specifically, identifying how to achieve fast, strong, permanent bone-implant fixation is a goal of the orthopedic community. Our focus is on examining nanometer scale implant material characteristics and performance in physiological electrochemical environments related to fixation.

It is the metallic oxide, as opposed to substrate metal, that comes into direct contact with biological milieu, and chemical properties of the oxide may influence interactions with biomolecules. Biocompatibility considerations make characterization of metallic biomaterial surface oxides of utmost importance. This study sought to concurrently obtain data on titanium's electrical properties and surface morphology to understand the relationship between oxide structure and properties and to assess the role of solution exposure and potential variations. Titanium samples were immersed in solution and subjected to step polarization impedance spectroscopy (SPIS) [1] experimentation along with concurrent electrochemical atomic force microscopy (EC AFM) imaging, to more fully characterize titanium's response to transient electric fields and potential shifts.

Oxide structure of commercially pure titanium (CPTi) and titanium, 6-aluminum, 4-vanadium (Ti-6Al-4V) differ [2, 3, 4, 5 and 6]. Previous studies have shown that immersion time, chemical pre-treatment, and potential may affect oxide film structure [7, 8, 9 and 10]. Crystallization may occur on oxides thickened over time, and ion incorporation, including calcium and phosphate influx [7] may take place [7, 11 and 12]. Additionally, hydration causes documentable shifts in binding energies, which may be measured with XPS or Auger [11 and 13]. Changing environmental conditions may also result in open circuit potential (OCP) drops approaching 1 V, with subsequent oxide fracture [14 and 15].

A drawback of all these studies is that they collected surface structure information using high vacuum techniques, thus presenting a very different environment to surfaces than observed in solution. Only electrochemical information was obtained in situ. The differences between hydrated oxide and an oxide in vacuum remain unexamined.

The paucity of surface structure probes operable in solution has impeded characterization of titanium's native surface structure. Although photo-electrochemical microscopy has been used to map grain structure and oxide heterogeneities at a Ti/TiO₂ interface, as well as to determine properties of electrochemically grown films [16 and 17], illumination with energy above Ti's bandgap is necessary, and surface physics therefore are altered. Conversely, AFM provides near-atomic level imaging of topographical changes in wet surfaces without such interference. While promising, only basic AFM characterization of Ti/TiO₂ has been published to date. Browne et al. [13] used AFM to investigate titanium under various surface treatments and with biolayer coverage, as well as to examine growth of oxide domes and dissolution of titanium metal electrodes immersed in oxalic acid [10].

Turning now to electrochemical characterization, such characterization provides invaluable insight into chemical reactions, potential activity ranges, kinetics, and oxide film parameters (e.g., resistance, thickness). For titanium, relevant electrochemical characterization probes are typically separated into DC polarization-type and AC impedance-type. DC polarization probes provide a first-order determinant of corrosion resistance, while AC electrical impedance spectroscopy (EIS) probes characterize electrochemical interfaces. Pan et al. [18] studied TiO₂ with both probe types. They separately performed EIS and polarization tests in phosphate buffered saline (PBS) on titanium and stainless steel substrates. Starting topography of one substrate was characterized with an AFM image, but the morphological changes in the surface were not tracked over the course of the study.

Recent work by the authors of the present study examined the effects of voltage on titanium hydration [19], which prompted inquiry into the relationship between structural and electrical properties of hydrated titanium surfaces. Thus, experimentation was conducted on titanium oxide from CPTi and Ti-6Al-4V. The samples were immersed in PBS and imaged with in situ EC AFM during simultaneous impedance testing. Impedance measurements, collected using SPIS, provided concurrent, inexpensive determination of polarization and electrochemical impedance behavior at an electrochemical interface as a function of potential.

4. 2. Materials and methods

An experimental method based on slowly stepping potential and concurrently imaging the sample surface while collecting polarization and impedance data was employed to simultaneously characterize the morphology and electrical characteristics of titanium and its oxide film.

Sample preparation, as well as the experimental testing configuration, have been described in a previous publication [19]. Briefly, in situ testing was performed on an electropolished and Kroll's solution etched titanium substrate of CPTi and Ti-6Al-4V. The experimental setup included a glass fluid cell (Digital Instruments), which removably held the silicon nitride cantilever tip (Nanoprobe SPM tip, Digital Instruments). The fluid cell was clamped on top of a titanium test substrate and sealed with an O-ring ( Fig. 1 and Fig. 2). The setup included a three-electrode electrochemical testing configuration, in which the titanium sample acted as a working electrode (WE), a silver wire (99.99% purity, 0.25 mm diameter) provided a quasi-reference electrode (RE), and a platinum wire (99.99% purity, 0.25 mm diameter) served as a counter electrode (CE). The silver wire was inserted through the top of the cell, and the platinum wire was contained in immersed outport tubing. The sample chamber held 50 
l of solution and was maintained at 25°C.

(7K)

Fig. 1. Schematic illustration of underside of electrochemical fluid cell (top view).

(12K)

Fig. 2. Side view of EC AFM system design.

Using Digital Instruments software (v4.42 r4), surfaces were first imaged dry in contact mode, on the electrochemically etched titanium surface. The images were centered on a distinct surface feature, such as a triple point of grain boundaries. Both height and deflection (the error signal) images were obtained. After disengaging and retracting the tip, PBS was injected into the fluid cell input port via a syringe coupled by luer lock to the port, immersing 0.5 cm² of titanium, the imaging tip, the reference electrode, and the CE in solution. A potentiostat (Model 362, EG&G Princeton Applied Research, Princeton, NJ) applied −1 V to the titanium surface from the instant of fluid injection. The syringe was left in place during experimentation, and exit port tubing was clamped off to provide backpressure.

The AFM tip was then re-engaged on the surface, and the exact location of dry imaging was reacquired. Si₃N₄ tips with 200 
m cantilevers (nominal stiffness of 0.06 N/m), exhibiting an approximate change of 1 V between undeflected and contacted cantilever positions (a positional change of approximately 70 nm/V), exerted a nominal force in the range of 4 nN. This is an approximation; however, higher forces did not influence surface morphology, but lower forces resulted in poor contact and "double-layer" effects. Because the direction of the reflection AFM beam changes slightly when switching from an air to liquid environment, scanning initially resumed over a 50×50 
m² area, thus allowing easy identification of the previously analyzed triple point of grain boundaries. Once this area was re-identified, the scanning area was reduced to the original area of interest (typically 5×5 
m²). Surfaces were held at −1 V for approximately 1 h before SPIS testing commenced [1].

Small steps in potential (50 mV) were then applied to the electrochemical interface with concurrent AFM imaging, and the resulting current transient response was logarithmically collected by a computer from 50 
s to 10 s, using A-D methods (National Instruments A/D Board, AT-MIO16; and Lab Windows Software, Austin, TX) (Fig. 3 and Fig. 4). The impedance of the interface was determined using a transfer function analysis (the Laplace transform of the current output divided by the Laplace transform of the voltage input) using a previously developed numerical Laplace transform algorithm [1] to determine the frequency-dependent admittance (inverse impedance). By comparing the admittance to a model Randle's circuit ( Fig. 5), minimum and maximum currents per step, high frequency (or early time) resistance (R_e), polarization resistance (R_p), capacitance (C), and admittance (A′ and A″) were determined. Current-voltage relationships yielded polarization behavior, charge transfer, and interfacial capacitance.

(6K)

Fig. 3. Schematic of experimental EC AFM/SPIS setup where the voltage is stepped in 50 mV increments over the course of approximately 60 min. Current transients as well as an image of the surface are collected at each step.

(6K)

Fig. 4. Exemplary current transient collected logarithmically over 10 s resulting from a 50 mV step in voltage from −1 V to—950 mV versus Ag wire on CPTi surface.

(2K)

Fig. 5. Schematic of Randle's circuit, where R_e represents an oxide resistance, R_p represents polarization resistance, and C_MS represents Mott-Schottky capacitance.

Capacitance determined from current transient data was used for Mott-Schottky plots of C⁻² versus potential to obtain flat band potentials and donor density concentrations. The slope of six or seven initial anodic points on each plot was calculated and used to determine an initial donor density value, N(V), for the non-linear Mott-Schottky fits. Initial N(V) and associated applied voltage and capacitance values were then used to determine N(V) versus voltage for the approximate range of 0-1 V for the CPTi and Ti-6Al-4V.

Though researchers have reported uniform donor concentrations based on linear Mott-Schottky plots [18 and 20], these concentrations only apply to single crystal materials. It is expected that polycrystalline and amorphous TiO₂ Mott-Schottky plots will deviate from a linear relationship because of the multiple donor levels which result from lattice defects, grain boundaries, dislocations, etc. in oxide films [21 and 22]. Dean and Stimming [23], Pyun and Kim [22], and Lee and Pyun [24] therefore non-linearly modeled Mott-Schottky by assuming consecutive ionization of donor levels and by utilizing the Euler method [25].

All statistical calculations were performed using Statistica (Statsoft, Tulsa, OK) unless otherwise noted.

5. 3. Results

Fig. 6 presents two AFM deflection images (10 
m×10 
m) of titanium surfaces taken in air after electropolishing and etching. Fig. 6(a) depicts CPTi, while Fig. 6(b) is of Ti-6Al-4V. The CPTi surface of Fig. 6(a) has a hexagonal close packed (HCP) microstructure and is available in four grades of increasing oxygen content. The CPTi surface has three oxide-dome-covered
phase grains separated by grain boundaries. Note that the domes appear qualitatively different on the different metal grains. The bottom grain is likely a different crystal plane.

(33K)

Fig. 6. AFM deflection images (10 
m×10 
m) of titanium surfaces; (a) CPTi and (b) Ti-6Al-4V. Both are electropolished and Kroll etched. The CPTi (a) shows a triple point of grain boundaries and 3 oxide-dome-covered
grains. The Ti-6Al-4V (b) contains
grains covered with oxide domes and is occasionally interrupted by
grains sitting higher on the surface. The oxide morphology appears to be grain dependent (affected by substrate crystallographic orientation).

Referring now to Fig. 6(b), Ti-6Al-4V is a bi-modal alloy consisting of globular
phase grains surrounding transformed
phase. The transformed
is comprised of retained
(body centered cubic, BCC) and acicular
. On the Ti-6Al-4V surface, thermo-mechanical processing disrupts acicular
, which results in a high fatigue strength, bi-modal microstructure. Distinct transformed
grains interrupt the
phase across the Ti-6Al-4V. Needle-like acicular
grains in the vicinity of the
grains are also apparent. Here too, the morphology of the oxide domes appears to be
grain specific (compare lower left to lower right grains), where the height and density of domes varies from grain to grain. Also, the blocky
grains do not have oxide domes, but appear more uniform.

The 5 
m×5 
m images of Figs. 7(a)-(f) depict transient oxide dome evolution on CPTi as a function of hydration and voltage. Oxide dome broadening, nucleation, and roughening may be imaged, but rising or lowering of the whole surface with respect to a lower plane may not. Therefore, the height of a prominent oxide dome with respect to background height has been tracked as potential was changed (see Table 1). A triple point of grain boundaries on the CPTi surface provides a common reference throughout the voltage sequence. The black arrow points to the specific oxide dome tracked, the height of which is recorded at each voltage condition and listed in Table 1. Image roughness values are also listed. Fig. 7(a) shows the dry surface, where oxide domes on the far left grain are more dispersed than on the other two grains. Fig. 7(b) shows the surface just after immersion in PBS at −1 V, and Fig. 7(c) illustrates the surface after nearly an hour at −1 V. Domes on the far left grain nucleate to shield the entire substrate. Figs. 7(b) and (c) show a progressive swelling of oxide domes with time. Although a cathodic voltage reduces oxide dome growth kinetics as will be shown below, thermodynamics still force the surface to oxidize via hydration, as evidenced by oxide dome growth, even at −1 V. Oxidation via hydration, under both freely corroding and potentiostatically held conditions, is described in a previous paper [19].

(28K)

Fig. 7. Sequential AFM deflection images (5 
m×5 
m) of electropolished and Kroll etched CP titanium. All images include the same triple point of grain boundaries; (a) dry, (b) after initial hydration in PBS at −1 V, (c) held at −1 V for ~1 h showing nominal oxide dome growth, (d) after at 0 V, (e) titanium at +1 V, and (f) titanium returned to −1 V. Note that increasing in potential leads to drastic oxide dome growth and coalescence. Cathodic ramping of voltage back to −1 V does not cause oxide domes to shrink. The arrow indicates oxide dome used for specific height measurement (Table 1).

Table 1. Relative oxide dome height of CPTi feature (see arrow in Fig. 5) recorded as a function of potential in PBS, and entire image roughness as a function of applied potential (5 
m×5 
m)

Subsequent slow, linear ramping of potential to 1 V results in observable, increased lateral oxide dome growth, as well as coarsening, across the grains and grain boundaries, as seen in Figs. 7(d) and (e). The oxide dome area of the initially immersed surface at −1 V is 1.4×10⁴ nm²±1.1×10⁴ nm²; the −1 V oxide dome area at 1 h is 1.8×10⁴ nm²±1.2×10⁴ nm², and the +1 V area is 1.8×10⁵ nm²±7.5×10⁴ nm² 
m² (n=30 domes). Dome area increased approximately 1.47 times at −1 V (~1 h), and approximately 5.31 times between the −1 and +1 V.

The −1 V area data is statistically different than the +1 V data (p=0.0001 Anova, post hoc Newman-Keuls). The two −1 V data sets, meanwhile, are more similar (p=0.76 Anova, post hoc Newman-Keuls). Clearly, dome broadening cannot be eliminated through application of potential within the described regime, but initial hydration conditions influence it. The word initial is stressed, because reversion to an applied potential of −1 V over approximately 30 min, as seen in Fig. 7(f), did not cause dome area to decrease. Films are thought to thin under cathodic bias, but AFM is unable to yield absolute height data in these experiments. Irreversible expansion of dome area may seem surprising and is a focal point of the discussion section.

As mentioned above, Table 1 includes relative height changes of a specified oxide dome with respect to background (see arrow series in Fig. 7 for identification of dome tracked with potential). The dome was on a grain boundary and was chosen because it was the easiest dome to follow through the entire series of images. Vertical distance between dome peak height and background floor first increased upon immersion in solution, presumably due to the oxide dome growing as the floor remained constant. As oxidation via hydration increased, however, the relative height of the dome decreased with time and increasing potential. It appears that as oxide domes nucleate to cover the entire surface, then impinge and coalesce, the relative oxide floor rises, the boundaries between oxide domes decrease in number and in height, and relative heights therefore decrease. Reversion of the potential to −1 V did not significantly alter height in the particular dome tracked.

Roughness first decreased upon immersion in solution, probably due to dome impingement and initial coalescence, which served to lessen the height variation between all domes. Maintaining a cathodic potential on the surface of the sample for an extended period of time slightly increased roughness, and raising the potential slightly decreased roughness, but the absolute changes are so small (subnanometer) that they are not thought to be significant.

Oxide dome areas as a function of potential and time were quadratically fitted (Figs. 8(a) and (b)). The R² value for area versus potential is 0. 89 and the R²value for area versus time is 0.90. The quadratic relationships are assumed based on the fact that potential was increased during the experiments (increasing growth rate with increasing potential). Had potential been held constant, a linear relationship would have been expected.

(16K)

Fig. 8. (a) Average oxide dome area as a function of potential (R²=0.90); (b) average oxide dome area as a function of time (R²=0.89). (Quadratic fit according to Y=Y₀+aX+bX²; for (a) Y₀=7.529×10⁴, a=−1.727×10³, b=1.486×10¹; for (b) Y₀=4.94×10⁴, a=6.108×10⁴, b=4.026×10⁴.)

Referring back to the Ti-6Al-4V sample, as seen in the sequential images of Fig. 9, the Ti-6Al-4V surface responded to hydration and applied voltage in a manner similar to CPTi. The sequence begins with the dry 5 
m×5 
m AFM image of Fig. 9(a) and then shows the same region immersed in PBS at −1 V in Fig. 9(b). Oxide domes on the
and acicular
phases nucleate and impinge on the surface upon hydration. Hydration does not initially lead to a notable increase in dome area. However, by the time the voltage was increased to -0.5 V (Fig. 9(c)), the flat substrate was no longer visible, and all areas were protected with domes.

(31K)

Fig. 9. AFM deflection images (5 
m×5 
m) of electropolished and Kroll-etched Ti-6Al-4V. All images include identical central region of needle-like acicular
phase extending from a
grain on a predominant
phase background. Downward drift in images is noted; (a) dry titanium, (b) titanium initially hydrated in PBS at −1 V, (c) titanium at -0.5 V, (d) titanium at 0 V, (e) titanium at +1 V, and (f) titanium returned to −1 V. Again, increase in potential leads to drastic oxide dome growth and coalescence. Oxide dome growth is prevalent on
phase; growth of
features is also seen. Cathodic ramping of voltage back to −1 V decreases height but not lateral dimensions on
features. See text for arrow explanation.

phase change was also visible. Area of
grains increased, but oxide domes were not apparent. Rather, the surface oxide was smooth on the top and ridged on the sides (Fig. 9). When potential was anodically ramped, the oxide domes expanded on the
and acicular
phases.
grain oxides grew upon anodic ramping as well, and oxide covering these grains appeared to grow out over the adjacent
phase. However, it is unknown whether
oxide predominantly covers
oxide, or if the two phases are miscible. Fig. 9 illustrates the progression as voltage was ramped to -0.5 V (Fig. 9(c)), 0 V (Fig. 9(d)), 1 V (Fig. 9(e)), and finally back to −1 V (Fig. 9(f)). As with the CPTi surface, reducing the voltage to −1 V did not result in surface structure reversion (Fig. 9(f)). Although downward drift is apparent in the image sequence, at least three
grains may be followed. A large expansion in
grain area is clearly visible.

Similarly to Fig. 7, Fig. 9 contains arrows pointing to both an
phase oxide dome and a
grain in each image of the potential-dependent series presented in Fig. 9. Relative heights of these features, as well as image roughness values, are listed in Table 2. Some tip convolution is apparent on the anodized images, but post-experimental analysis confirmed that the AFM remained calibrated and that the tip maintained sufficient resolving power. It should also be noted that as domes spread and flatten, convolution should decrease. Thus, more convolution would be expected at low applied voltages than at higher applied voltages and later times.

Table 2. Relative heights of
phase oxide dome and
phase grain of Ti-6Al-4V features (see arrows in Fig. 9) recorded as a function of potential in PBS, and entire image roughness as a function of applied potential (5 
m×5 
m)

Due to the inclusion of the
phase, these results differ from the CPTi results. The isolated
phase oxide dome examined had a comparable relative height to the one measured in Fig. 7, but anodic ramping caused such drastic coalescence that it became difficult to decipher oxide dome boundaries by +1 V. Accordingly, the height of the
phase oxide dome on the Ti-6Al-4V surface at 1 V, as listed in Table 2, reduced to 2.3 nm. In contrast, the
phase oxide dome examined on the CPTi surface at 1 V was still 18.4 nm tall. However, examined grains were chosen according to which ones could be tracked across the entire voltage series with confidence. The
phase oxide is thought to behave similarly on the two substrates and Table 1 and Table 2 both indicate a trend of coalescing oxide leading to a decrease in relative height between domes.

The
phase grain selected grew considerably in its lateral dimensions, from 478.5 to 830.1 nm (173.5%) along the top edge, and increased ~17 nm (117.4%) in the z-direction. Height increased slowly upon substrate immersion and anodic ramping of potential. The largest height change was seen when potential increased from 0 to +1 V. Notably, cathodic ramping back down to −1 V decreased the
phase grain height by 9 nm. This suggests increased reactivity of the
phase, as compared to the
phase, within the sample. Roughness of the Ti-6Al-4V sample is dominated by the tall
phase grains and is therefore greater than that of CPTi. Roughness first decreased upon immersion in solution, but then kept increasing with anodic ramping. This suggests a trend of roughness changing directly with
grain height during anodic ramping.

With reference now to Fig. 10, Fig. 11, Fig. 12, Fig. 13, Fig. 14, Fig. 15 and Fig. 16, electrical data is presented. Fig. 10 and Fig. 11 show the in-phase admittance, A′, of the CPTi and Ti-6Al-4V samples, respectively, as a function of frequency and voltage, while Fig. 10 and Fig. 11 illustrate out-of-phase admittance, A″, of the CPTi and Ti-6Al-4V samples, respectively, as a function of frequency and voltage within the EC AFM fluid cell. For both surfaces, in-phase admittance peaks at highest frequency before decaying with decreasing frequency and increasing voltage. Peak values are: 8064 
S/cm² for CPTi (4136 rad/s), and 14196 
S/cm² for Ti-6Al-4V (6990 rad/s). With respect to voltage, CPTi rolls off gradually, and Ti-6Al-4V drops to approximately 7000 
S/cm² and then rolls off. These results are similar to those obtained for CPTi in a previous study, but slightly lower in amplitude, suggesting a thicker oxide film [1].

(31K)

Fig. 10. Three-dimensional plot of (a) in-phase (A′) and (b) out-of-phase (A″) admittance of CPTi in PBS versus frequency (rad/s) and potential (V).

(30K)

Fig. 11. Three-dimensional plot of (a) in-phase (A′)and (b) out-of-phase (A″) admittance of Ti-6Al-4V in PBS versus frequency (rad/s) and potential (V).

(20K)

Fig. 12. Polarization plot and impedance characteristics for CPTi in PBS. Polarization plot (a) indicates maximum currents (50 
s after potential steps) and minimum currents (10 s after potential steps) versus voltage. Interfacial capacitance, C, is plotted in (b) versus voltage. Resistance in (c) is plotted as early (R_e), calculated from polarization data, or high frequency (R_s), calculated from admittance data, versus voltage; resistance in (d) is plotted as late (R_L), calculated from polarization data, or polarization (R_p), calculated from admittance data, versus voltage. Capacitance was calculated as, C=(R_s+R_p)/R_sR_p
A, where
_A is the frequency (rad/s), where the peak of the loss admittance, A″ occurs. Early (R_e) and solution (R_s) resistance were calculated as, R_e=ΔV/(I_max−I_initial), and
. Late (R_L) and polarization (R_p) resistances were calculated as: R_L=ΔV/(I_min−I_initial),
.

(20K)

Fig. 13. Polarization plot and impedance characteristics for Ti-6Al-4V in PBS. Polarization plot (a) depicts maximum currents (50 
s after potential steps) and minimum currents (10 s after potential steps) versus voltage. Interfacial capacitance, C, is plotted in (b) versus voltage. Resistance in (c) is plotted as early R_e and R_s versus voltage; resistance in (d) is plotted as R_L and R_p versus voltage.

(8K)

Fig. 14. Calculated and experimental charge versus voltage step number. Each step was 50 mV; potential was ramped linearly from −1 to +1 V (step 40) and back down to −1 V (step 80). Calculated charge calculated according to: Q=ΔX
ZFA/MW, where ΔX=
(V−V_i),
is the anodization rate for titanium (2 nm/V), and V−V_i is 50 mV;
is density of the oxide (4.4 g/cm³); Z is the valence state of the oxide (+4); F is Faraday's constant (96,480 c/mol); A is electrode area (0.5 cm²); and MW is molecular weight of TiO₂ (79.9 g/mol). The area under the current transient curves equals experimental charge and was determined by trapezoidal Reimann sum approximation.

(5K)

Fig. 15. Mott-Schottky plot of C⁻² versus voltage for CPTi anodically ramped from −1 to +1 V over 40 steps. Note the curve on the right where the applied potential is positive. This is due to multiple donor levels in a polycrystalline sample.

(5K)

Fig. 16. Donor concentration (cm⁻³) as a function of voltage for the CPTi and Ti-6Al-4V surfaces, as calculated by the non-linear Mott-Schottky fit.

Out-of-phase admittance curves of Figs. 10-11(b) are bell shaped. On both surfaces, peak values occur at characteristic frequencies and decrease with increasing frequency and voltage (see discussion). Peak A″ values have associated characteristic frequencies of relaxation of 390 rad/s at -0.95 V, 507 rad/s at -0.5 V, 857 rad/s at 0 V, and 2447 rad/s at 1 V for CPTi; and 177 rad/s at -0.95 V, 390 rad/s at -0.5 V, and 659 rad/s at 0 V, and 845 rad/s at 1 V for Ti-6Al-4V.

Fig. 12 and Fig. 13 plot polarization data for maximum currents (50 
s) and minimum currents (10 s), after each step in potential for the CPTi and Ti-6Al-4V surfaces. These minimum current results are similar to those measured in standard potentiodynamic polarization tests. Minimum current polarization plots all contain a potential where current approaches zero, referred to as zero current potential, as well as a passivity region where current stays constant with increasing voltage (approximately -0.5 and +1 V for CPTi and Ti-6Al-4V). This passivity region is characteristic of valve metals like titanium. Maximum current polarization plots are similar for both surfaces, although more hysteresis is present in the CPTi curve than in the Ti-6Al-4V curve. Maximum currents also allude to the passivity region, but bowing of the curves at roughly -0.5 V is not nearly as defined as the demarcation of Corrosion potential, E_corr, from minimum current readings.

Early/solution resistances also reflect oxide film passivity, as seen in Figs. 12-13(c). Thus, early resistance (R_e) appears to be a more appropriate label than the traditional solution resistance label (R_s). Anodic voltage ramping yielded the lower curves of Figs. 12-13(c), and cathodic ramping yielded the top curves. R_e clearly varies with potential, even though resistances continued to increase when potential ramping was first reversed from +1 V toward −1 V, and hysteresis is present on all surfaces. Nevertheless, starting and ending resistance values are the same. Late (R_L) and polarization (R_p) resistances are noisy, but also similar (see Fig. 12 and Fig. 13).

Capacitance values started high at approximately 100 
F/cm² and decreased with increasing voltage to approximately 1 
F/cm². The top curves of Fig. 12 and Fig. 13 correspond to increasing voltage from −1 to +1 V; the bottom curves correspond to voltage ramping back down to −1 V. When voltage was first reversed, capacitance temporarily continued to decrease, and hysteresis is present in all three curves in a similar, yet opposite, trend to the early (solution) resistance plots. In contrast to oxide dome expansion, which is irreversible while surfaces are maintained in a hydrated state, electrical properties are reversible.

Fig. 14 provides calculated and experimental charge for all voltage steps on the Ti-6Al-4V sample. Current transients require charge transfer through the oxide film. Hysteresis present in the current-voltage relationships of Fig. 12 and Fig. 13 initially suggested that current transients were not taken over a sufficient time interval. However, if 10 s had not been long enough, currents transients should not have indicated such drastic decay (as in Fig. 9).

Fig. 14 shows that, on average, the measured charge was one-fifth of the calculated charge needed for oxide growth. Early and late steps, roughly corresponding to steps between −1 and -0.5 V and then between -0.5 and −1 V, indicate higher charge transfer. The time constant,
, was calculated as the inverse of
_A, the peak of admittance, A″, by plotting A″ versus log 
. Four times
describes a time process that is 98.2% complete and five times
describes a nearly completed process [26]. Five
corresponds to 16 ms in the above experiment. Therefore, current acquisition time was sufficient, even though experimental values were less than calculated.

Finally, Fig. 15 presents an exemplary non-linear Mott-Schottky plot of initial C⁻² versus voltage for CPTi, while Fig. 16 plots N(V) versus V for both surfaces. Dielectric constant for TiO₂ was held at 50. Equations used are valid for all potentials positive of the flatband potentials. Thus, values between 0 and 1 V are plotted, as the flatband potentials were -0.01 V for CPTi, and 0.073 V for Ti-6Al-4V. A range of flatband potentials for TiO₂ have been reported in the literature; typically, values between −0.3 V [20 and 27] and −0.5 V [18] are reported. The non-linearity of polycrystalline samples makes it difficult to accurately assign flatband potentials to Mott-Schottky plot data. It is thought that the consistent strategy of taking the first six anodic points from the C⁻² versus potential plots for initial N(V) values, may have slightly increased flatband potential calculations. However, using fewer data points would have introduced more error into initial N(V) values. CPTi donor values were on the order of 10¹⁸, and Ti-6Al-4V values were on the order of 10¹⁹.

6. 4. Discussion

Simultaneously probing structural and electrical characteristics of titanium oxide films allowed direct observation of lateral dome spreading, the voltage and time dependence of oxide processes, as well as notable surface roughness changes. Specifically, the oxide growth rates discussed previously reveal a quadratic relationship between dome area and increasing, positive applied potential.

Our previous examination of Ti/TiO₂ hydration under various electrochemical conditions [19] revealed that applying a static cathodic potential results in an oxide area growth rate that is slower than the corresponding rate at quasi-static potential, near 0 V OCP. In this study, ramping of applied potential in the anodic direction results in a constantly changing growth rate. However, assuming a linear relationship in the region of applied potential around ~0 V, a rate of 1070 nm²/min is obtained (R²=0.77); this value closely approximates the OCP rate obtained previously (1098 nm²/min) [19].

Data also reveal reversible electrical responses with respect to voltage, but irreversible structural response. Structurally, dome area continually increases with time and voltage for all surfaces, but does not decrease over time with decreased voltage. This independence of structure and electrical properties after hydration was initially unexpected. However, as qualitatively modeled in previous TiO₂ hydration experiments [19], TiO₂ is classified as an n-type semiconductor, and its oxide primarily grows and changes at the metal/oxide interface, not the oxide/solution interface, where image acquisition occurred. While new oxide is forming, existing oxide domes at the metal/oxide interface expand laterally, and material is pushed up from below. What was once a surface with many small domes, changes into a surface exhibiting only a few broad domes. Upon ramping potential cathodically, the broad oxide domes at the oxide/solution interface, located nanometers above the metal/oxide interface, do not transform back to the multiple small domes. Rather, the oxide domes just appear to flatten slightly. Much more significant remodeling is anticipated at the metal/oxide interface. However, since EC AFM probes morphology at the oxide/solution interface, electrical changes are more apparent than structural changes during cathodic ramping. Future work X-ray experiments are required to probe morphological changes at the metal/oxide interface.

The one noted exception to the surface achieving steady state morphology independent of applied, or more specifically reduced, potential is the
phase of Ti-6Al-4V surfaces.
phase grain heights and applied potential are proportional, as provided in Table 2. This should be considered with respect to vanadium dissolution observed and reported in physiological systems [28]; high vanadium concentrations in persons with Ti-6Al-4V orthopedic implants may result from rapid growth and dissolution of
grain oxide. Comparing changes in
phase grain heights to the negligible height changes noted in
phase oxides during ramping of applied potential from anodic to cathodic conditions (where Al is more soluble) supports this.

The decoupled nature of surface morphology and electrical properties may be useful in biological systems, due to the presence of a more stable interface for an adsorbed biolayer. TiO₂ is modeled as initiating growth or recession/reduction at the metal/oxide interface. However, the solution/oxide interface initially presents growing oxide domes to the physiological environment. It is therefore hypothesized that osseointegration begins during lateral oxide dome growth, incorporating selected material into the oxide.

As Zitter and Plenk described [29], electron flow in orthopedic implant metal systems must equal ion flow through tissue and biological fluids. As an electric field arises assisting oxide growth at the expense of the substrate metal and transported electrons ionize oxygen atoms, adsorption of H₂O, OH⁻, HPO₄²⁻, and H₂PO⁴⁻ may occur at the oxide/solution interface [19 and 30]. Additionally, the protein albumin is known to bind to titanium in significant amounts [31, 32 and 33], and is the major calcium binding protein in the blood [31]. The Ca²⁺ ions bridge the negatively charged albumin and the TiO₂ surface [31]. Such calcium and phosphate ion incorporation has already been suggested to contribute to oxide growth [34] and provide a gradual transition from metal to living cells [35]. However, this has not been documented on a nanometer scale, in which titanium oxide domes and biological moieties such as proteins interact. As well, ion, protein, and oxide integration may be relatively impervious to mild load related cathodic conditions placed on titanium implants. Even if cathodic potentials are applied to the oxide, interlocking bonds incorporating the material are expected to maintain integrity; instead, bonds at the metal/oxide interface would be expected to restructure. Obviously, integrity might be compromised under conditions of wear, which could result in direct removal of oxide, and thus interlocked regions, starting from the surface and moving inward.

Electrical properties follow expected trends for oxide growth, although hysteresis is present and charge transfer is less than calculated. Early resistance, thought to correspond to a combination of oxide resistance, which increases with potential, and solution resistance, which is constant, is directly proportional to potential, which means that oxide film resistance should increase and decrease with voltage, due to oxide growth and dissolution. Early resistance steadily increases upon anodic ramping (suggesting that oxide dome lateral growth is directly proportional to early resistance), but exhibits a kink upon cathodic ramping, where two different slopes may comprise the voltage reduction curve (Fig. 12).

Due to aspects of the reductive dissolution process that are not fully understood, film growth apparently is not fully reversible, as evidenced by hysteresis. Some oxide growth may occur via the reaction

Ti+O2→TiO2.

(1)

No electrons are transferred in this reaction, but a thermodynamic drive to spontaneously form oxide exists (associated free energy: ΔG=−82.92 kcal/mol). The change in slope upon cathodic ramping and charge increase between -0.5 and −1 V can be attributed to reduction of titanium in a Ti⁴⁺ valence state to a Ti³⁺ valence state. Lower experimental charge at potentials above -0.5 V suggests that non-Faradaic events (e.g., double-layer charging) play an important role, and that oxide thickening between 0 and +1 V acts to block charge transfer. According to Kelly [36], applied anodic potential may oxidize titanium to Ti³⁺ ions, in addition to Ti⁴⁺ions, and cathodic potential may cause reduction of Ti⁴⁺ ions to Ti³⁺ ions. Furthermore, Ti³⁺ ions are not present at voltages greater than 0 V and become increasingly soluble with application of cathodic potential. Thus, TiO₂ films may thin during cathodic potential ramping as reductive dissolution of Ti⁴⁺ to Ti³⁺ takes place. Some researchers have reported this transition as being responsible for an observed blue coloration [37, 38 and 39]. Since experiments were conducted in neutral pH solutions, onset potentials for reduction reactions were greatly reduced. However, even at cathodic potentials, substrate metal never contacts the solution directly because lower order films, including TiH₂ and Ti₂O₃, are present even at active potentials [29]:

2TiO2,hydr+2H^++2e^− Ti2O3,hydr+2H2O,E^o=−0.091 V,

(2)

TiO2+6H^++6e^− TiH2+2H2O,E^o=−0.47 V.

(3)

Considering all samples were subjected to a cathodic overpotential for close to an hour before SPIS experiments commenced, it is likely that these hydride and lower order oxide films coexist with TiO₂.

Dolata et al. [40] studied rutile and anatase TiO₂ film impedance. They noted the high electron mobility of anatase films, and that conduction in doped anatase films undergoes metallic transition. Donor concentrations in anatase films were on the order of 5×10¹⁸ cm⁻³. Their theoretical model anatase data coincides with the experimental donor concentration data of Fig. 16. When examined in conjunction with the data of Blackwood [27] suggesting an intermediate layer, as well as conclusions from the previously mentioned Pan article [18], this information further supports that CPTi's oxide is multi-layered, with an anatase-like uppermost TiO₂ layer. We believe that the intermediate layer is Ti₂O₃. This Ti/Ti₂O₃/TiO₂ physical model assumes that Ti₂O₃ has a lower resistance than TiO₂.

SPIS also provided admittance and capacitance data, which may be related to oxide film growth. A′ values consistently decrease with applied potential, consistent with oxide growth. Peak A″ values have associated
_A values, their characteristic frequencies of relaxation. A″ data is inversely proportional to
_A. Large
_A values imply nominal current passage through an oxide film, which in turn implies a thick oxide film; conversely, as film thickness increases, film resistance increases, and less current is passed. The SPIS method, and associated Laplace transforms, assumed a Randle's circuit consisting of an oxide resistor, R_e, in series with a parallel connection of a double-layer capacitor and a polarization resistor, R_p (Fig. 4). Capacitance can thus be modeled as

(4)

Clearly, as
_A increases, capacitance decreases, again associated with thickening of the oxide film. We note that capacitance data was used to determine donor density data. For the sake of simplicity,
, dielectric constant, was held at 50 for these calculations. However, we hypothesize that
is actually a function of applied potential in the solution-oxide-metal construct.

The reported early resistance and current data is reminiscent of magnetic or ferroelectric hysteresis plots of polarization versus electric field. A model analogous to piezoelectricity is therefore postulated for oxide electrical response. Oxidation at cathodic potentials yields some Ti³⁺ ions, in addition to the more abundant Ti⁴⁺. Most likely, as experiments proceed from −1 to 1 V, Ti³⁺ manifests itself as the Ti₂O₃ intermediate layer, while Ti⁴⁺ manifests as TiO₂. Subsequent cathodic ramping from 1 V does not physically or electrically change the oxide until cathodic potentials sufficient to reduce Ti⁴⁺ to Ti³⁺ are reached. Then, some of the TiO₂ is reduced to Ti₂O₃, and oxide resistance decreases. In a piezoelectric, electrical potential controls dimension and strain; in an oxide, electrical potential may control interfacial oxide state. In fact, strain may also be controlled via electrical potential in the oxide, as growth of the interfacial oxide Ti₂O₃ layer is also expected to reduce strain. Blackwood [27] purported an intermediate thin film that formed irreversibly. Such irreversible growth could potentially act as a micromechanical lock. As mentioned previously, future work X-ray experiments are necessary to analyze oxide film layer composition as a function of depth, although required sensitivity of a few atomic layers may prove challenging.

7. 5. Conclusion

For the first time, polarization, impedance, and surface structure behavior are concomitantly reported after simultaneously monitoring pure and alloy titanium electrode samples. Lateral oxide dome spreading was directly observed, and changes in surface roughness were noted. Early resistance and interfacial capacitance data show interesting hysteresis and reflect passive oxide characteristics, as well as trends toward growth and dissolution. Initial oxide growth processes depend on time and voltage. Although initial hydration events may be controlled with applied potential, subsequent hydrated titanium surface structure acts independently of electrical properties. This phenomenon may be due to titanium oxide's n-type semiconductor classification; growth and dissolution apparently occur at the metal/oxide interface, as opposed to the oxide/solution interface.

8. Acknowledgements

This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory (LLNL) under contract W-7405-Eng.48. The Medical Technology Program and the Materials Research Institute at LLNL provided funding. We graciously thank Robert Haskins at DePuy for the commercially pure titanium and the titanium, 6-aluminum, 4-vanadium.

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Corresponding author. Tel.: [phone]; fax: [phone]

¹ Presently at ETH Zurich, Institut für Biomedizinische Technik und Departement Werkstoffe, Moussonstrasse 18, CH-8044 Zürich, Switzerland.

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