A COMPARATIVE STUDY OF ANODIC OXIDE FILMS ON TITANIUM, NIOBIUM AND TANTALUM

A C O M P A R A T I V E STUDY OF A N O D I C OXIDE FILMS ON T I T A N I U M ,

N I O B I U M A N D T A N T A L U M *

F. KOVER AND M. J. MUSSELIN

Centre de Recherches de la Compagnie G~ndrale d'Electricitd, Marcoussis (France)

(Received December 5, 1967; in revised form March 14, 1968)

SUMMARY

Anodic oxide films were formed on titanium, niobium and tantalum, mostly up to about 40 volts, using three electrolytes of quite different composition and a particular electrical program intended to prevent uncontrolled transient pheno- mena. The existence of several different anodic oxides was observed for each metal, depending upon the electrolyte used. The growth of the oxides occurs at the oxide/electrolyte interface by a mechanism of cation migration through a stationary oxygen sub-lattice. At this interface, a transition region similar to an electrochemical double layer appeared to behave as a dielectric layer added to the anodic oxide layer during anodization. Data were compared concerning the differential thickness, the specific capacitance, the dielectric constant and the apparent electronic charge on the anions electrodeposited into the oxides. From the latter it was deduced that water is the main oxidizing agent and that protons are incorporated into the anodic oxides as well as some sulfuric anions when certain electrolytes are used.

Special attention was devoted to data on titanium anodic oxides; fluctuations in thickness were observed from one sample to another, and their effect was eliminated by the use of an interference colour scale to estimate the actual thickness; the dielectric constant was found to remain constant throughout the thickness of the film, and the resistivity was also found constant except in a layer of about 50 A situated next to the growth interface.

From data about crystalline oxides of the same metals the concept of a quasi-compact oxygen sub-lattice with octahedral sites for metallic cations was deduced and applied to the amorphous anodic oxides as well as to the transition layer at the growth interface, the validity of this hypothesis could be tested on one particular titanium anodic oxide, for which interferometric thickness measurements could be checked against oxygen determination by nuclear reaction.

* Work supported by D616gation G6n6rale h la Recherche Scientifique et Technique, Contract No. 62.00.115. The authors have been associated with a cooperative Research Program supported by Centre National de la Recherche Scientifique, RCP No. 69.

Thin Solid Films, 2 (1968) 211-234 - Elsevier, Lausanne - Printed in the Netherlands

212 F. KOVER, M. J. MUSSELIN

1. INTRODUCTION

The formation of highly insulating anodic oxide films is possible only on a small number of elements (A1, Ti, Y, Nb, Ta), on some of their alloys and on silicon. For a better understanding of the properties and of the formation mechanism of these anodic oxides it is particularly interesting to make a comparative study of the anodization of titanium, niobium and tantalum ~, for in the solid state the dimension of the metallic cations Ti 4 +, Nb 5 + and Ta 5 + are very similar, their ionic radii being Ti 4+ = 0.68 •, Nb 5+ = 0.69/~ and Ta 5+ = 0.68/~. These radii

correspond to a 6-fold coordination with oxygen anions, the ionic radii of which are 0 2- = 1.32/k and O H - = 1.33 2~. In all crystalline species of TiO 2, Nb2Os and Ta205 the crystal lattice is built up in such a manner that a metal cation is surrounded by 6 oxygen anions, forming an octahedral pattern with 6 oxygen atoms located at the 6 corners and one metal atom located at the centre. The octahedrons are more or less regular, their symmetry and the interatomic distances vary slightly from one crystalline species to another, but in the first approximation this variation is negligible, and the variety of crystal lattices is mainly due to the various ways of bonding the octahedral patterns together to form a three-dimen- sional lattice. In other words, the differences in the structure of TiO2, NbzO5 and TazO 5 crystals appear mainly in the long-range order. The short-range order (nearest-neighbour arrangement) is very similar from one crystalline species to another. An oxygen sub-lattice thus appears, due to a nearly compact arrangement of oxygen ions, the interatomic distances of which are of the order of 2.4 to

T A B L E I

C A L C U L A T E D VOLUME O C C U P I E D BY 1 A T O M - G R A M OF OXY GEN IN THE CRYSTALLINE SPECIES OF T i O

NbzOs, Ta205 AND IN VARIOUS LOWER OXIDES OF Ti, Nb, Ta

(molecular mass) Volume of 1 at.-g O

(density o f crystal) (number o f O a toms in molecule)

Crystalline Molecular Density Volume (cm ~ ) o f References species mass 1 at.-g oxygen

TiO2 brooki te 79.9 4.17 9.58 2, 3 TiO2 ana tase 79.9 3.84 10.40" 2, 3 TiO2 futi le 79.9 4.26 9.38 2, 3 Nb~O5 265.8 4.47 11.89" 2 TarO5 (mean) 441.9 8.2 10.78" 2, 4 Ta205 a lpha 441.9 9.5 9.30 5 TazO~ beta 441.9 8.9 9.93 5 Ti~O3 143.8 4.60 10.42 2, 3 TiO 63.9 4.93 12.96 2, 3 NbO2 124.9 5.90 10.58 2 N b O 108.9 7.30 14.92 2 TaO2 212.9 10.40 10.24 2

* For the calculat ion o f the thickness o f anodic oxide films, these values have been used.

ANODIC OXIDE FILMS ON TITANIUM~ NIOBIUM AND TANTALUM 213

2.8 A. The metallic cations are inserted into this sub-lattice with a great latitude

in their arrangement; such crystalline species as (Ta, A1)20 4 or (Nb, A1)20 4 are known to exist with a structure identical to the "rutile" species of TiO2, there is a solubility of TiO 2 in the "be ta" form of NbzO5 up to a proport ion of 30 ~ , etc.

The volume of the oxygen sub-lattice is shown in Table I for an oxygen quantity equal to 1 atom-gram. I t is found to be of the same order in the oxides

TiO2, Nb205, Ta2Os, and in the lower oxides Ti203, TiO, NbO2, NbO, TaO 2 (only these ones have had their structures determined). The oxygen volume tends to be larger in the lower oxides, in relation to the larger ionic radii of the metallic cations: Ti 3 + = 0.76 A, Nb 4+ = 0.74 A. At the expense of a certain deformation the oxygen sub-lattice can thus accommodate relatively large cations; besides, it is known that the octahedral coordination between oxygen and metallic cations is generally possible for cation sizes in the range of 0.54 to 0.97 A.

Our basic hypothesis is to extend to the anodic oxides the notion of a nearly compact oxygen sub-lattice, and to adopt for the volume of this sub-lattice the value obtained for the corresponding crystalline species. The order of magnitude obtained by considering the species TiO2, Nb205 and Ta205 will still be acceptable if in the anodic oxides the cation valencies appear to be lower than Ti 4+, Nb s + and Ta 5+, as it is the case in the lower oxides. The general purpose of our work was to verify this hypothesis by a study of the formation mechanism of the oxides and of their various properties.

2. EXPERIMENTATION AND COMMENTS

2.1. Formation of anodic oxide films

The anodization cells are made of chemically inert materials, and designed to prevent the existence of a triple interface metal/electrolyte/atmosphere where the anodization parameters would not be well defined 1. The metal to be anodized is cut into a wafer, one face constituting the bot tom of a cylindrical recipient (Fig. 1); the electrical and thermal contact is provided by the tight screwing of a gold- plated brass stopper. The temperature is controlled to +0.25 ° between - 8 0 °C and + 120 °C. The electrolysis and measurement apparatus includes a programm- able direct current generator, a voltage limiter, a Wien capacitance and loss factor measurement bridge, and the usual devices for measurement of voltage, current and electrical charge.

A three-step anodization process is used. In a first step the connections are established without allowing any irreversible phenomenon to occur, by controlling the current generator for an exactly zero current. In a second step the current is made to increase, generally following a linear increase of 20 mA/h/cm 2 of anode surface. In a third step the voltage limiter takes control and keeps the voltage


Platinum cat h o d e ~ Electrolyte

Titanium a n ode ~iI~___~ .__j.

T ef I o n

~c~lleYalln err

r a s s

Fig. 1, Anodizat ion cell (usual type).

across the terminals of the cell at the desired value, the current flowing through the cell being free to adjust itself to the cell resistance. The formation is considered terminated when the current decrease is less than a few percent per hour; the current density on the anode is then usually of the order of a few #A/cm z. The potential o f the cathode against a reference electrode is then reproducible to a few

150 E U

E g

C

~ 100

b

% 5o- IX

% % %.

o O

o

-~o & +~o Ternperature(°C)

Fig. 2. Resistivity o f the SN electrolyte as a function o f temperature (measured at 1 kHz).

ANODIC OXIDE FILMS ON TITANIUM, NIOBIUM AND TANTALUM 215

hundredths of a volt for a given electrolyte; thus it becomes equivalent to consider that the anodic oxide formation is terminated at constant anodic potential or at constant voltage across the terminals of the anodization cell.

For the anodic oxides of titanium, the differences between the results obtained with various purities of the metal remained small; for most of our experiments a polycrystalline material was used (rolled sheet with disoriented grains of millimeter size), the principal impurities of which were: 3500 ppm Fe, 800 ppm C, 700 ppm O, 100 ppm Mn, traces of AI, Cu, N. For this metal most aqueous solutions are not suitable as electrolytes due to a high current density at the end of the anodization (about 100/~A/cm2). Therefore two non-aqueous electrolytes were used, which gave reproducible results and were insensitive to the addition of 10 volumes percent of water, eliminating the influence of room atmosphere moisture:

SN-- the concentrated sulfo-nitric mixture (20/80 volumes of HNO 3 and H2SO4 of 95 ~o concentration approximately), allowing voltages up to 40 V; the resistivity of this electrolyte is negligible, with a peculiar behaviour (Fig. 2).

BD- -a solution of 100 grams/liter of borax (NazB4Ov,10Hz O) dissolved in 2-2'-oxy-diethanol(HO-C2H4-O-C2H~-OH, also called diethyleneglycol) at q-80°C, allowing voltages up to 200 V; the room temperature resistivity of this electrolyte is rather high (11,700 ohm cm).

Prior to the anodization of the titanium surface, pretreatments are used to obtain a state that is reproducible and favorable to uniformity and dielectric quality of the anodic oxides to be formed, from a physical point of view (constant mean roughness, absence of sharp edges and whiskers, particularly at grain junctions) and from a chemical point of view (nature of the layers formed and of the adsorbed substances, thickness of these layers). These treatments have been published in detail6; they consist mostly of chemical etching, electrochemical polishing and careful rinsing processes. The rugosity becomes then negligible with respect to the overall accuracy of our measurements.

For the anodic oxides of niobium and tantalum, which are better known and simpler to obtain, we did not make any extensive study of the formation and only sought for a satisfying reproducibility with the same electrolytes that were used for the anodization of titanium. The pretreatment of the surface of these metals is only little different of that of titanium. In order to compare our results with those to be found in the literature, we also used dilute HzSO 4 in water (approximately 1.4N) as an electrolyte for niobium and tantalum.

As it was already known 4 for niobium and tantalum, the anodic oxide films on titanium present bright interference colours; no variations of colour could be detected up to a x 600 magnification. The layers are amorphous and homogenous, and no preferential orientation in the direction of the electrical field applied during their formation could be detected (but we feel that this point deserves a more exhaustive study). By heating the films while observing them in an electron microscope, one can observe their complete transformation into anatase around 150 °C


and into rutile above 700 °C: thus their chemical composition appears to be TiO 2. For all three metals, it was observed that the interference colours obtained

in different electrolytes (SN, BD and dilute H 2 8 0 4 ) w e r e different, and could not be matched by any proper adjustment of the formation voltages; for different electrolytes the colours obtained do not fit into a unique "colour scale".

2.2. Thickness of the anodic oxide films

2.2.1. Conventional measurements Titanium anodic oxide films have been isolated by dissolving their metallic

substrate in a bromine/methanol mixture; they could then be transferred on semi- transparent glass slides and their thickness be measured by interferometric methods. The oxides prepared with the BD electrolyte are fairly easy to isolate, to handle and to measure; for a formation temperature of + 2 0 °C, the thickness of the oxides is a linear function of the formation voltage; the corresponding straight line on the thickness/voltage diagram has a slope of 37.9 ___ 5 A/V and an extrapolated intercept of 34 A with the V = 0 axis (zero volts between the titanium anode and the platinum cathode). The oxides prepared with the SN electrolyte are very dif- ficult to isolate mainly because they are extremely thin; some thickness measurements have been made but we think the results too few to be speculated upon ~.

The measurement of the electrical charge passed into the anodization cell cannot be used to calculate the thickness of the anodic films, for the apparent electrochemical yield (cf Section 2.5) is not unity and Faraday's law cannot be used. A direct weighing of the anodic oxides was not feasible on the same layers that were submitted to the electrical measurements.

2.2.2. Oxygen determination by nuclear reaction By means of the nuclear reactions O 16(d, p)O 1 v and O 18(p, ~)N 15 it is possi-

ble to determine the oxygen content of substances such as anodic oxide layers v ; the results can be likened to a weighing of the oxygen quantity when calibration is possible with a known substance*.

For a given surface of ti tanium anodic oxide, the oxygen content is a linear function of the anodization voltage within 3 ~ , but only for voltages lower than 34.5 V with the SN electrolyte and lower than 50 V with the BD electrolyte. For higher voltages the oxygen content is lower than the extrapolated linear behaviour, which is analogous to the behaviour of some other anodic oxides (Ta, A1) 1°.

The thickness of the anodic oxide films can be deduced from the oxygen content if a relation is known between the oxygen quantity and the volume, both density and exact chemical formula being insufficiently determined to base a cal-

* These results have been obtained by a team working on a Cooperative Research Program. The principle and the method have been studied by Amsel 8 and applied by Amsel and Samuel 7,9, Nadai TM and Kover 1.


T A B L E II

DIFFERENTIAL THICKNESS OF ANODIC OXIDES (THICKNESS VARIATION VS. FORMATION VOLTAGE VARIA- TION). FORMATION AT 21-10 °C. STARTING WITH A CURRENT INCREASING FROM ZERO, AND ENDING WITH A CONSTANT VOLTAGE

Calcula t ion based upon the de te rmina t ion of oxygen by nuclear reaction.

Metal Electrolyte Differential thickness (.~/ V)

Ti tan ium 23.8* N i o b i u m SN 23.4 T a n t a l u m 15.7

T i t an ium 35.6** N i o b i u m BD 36.5 T a n t a l u m 23.3

T i t an ium dilute - - N i o b i u m sulfuric 38.7 T a n t a l u m acid 25.6

* Value cor responding to the fo rmat ion condi t ions of the co lour scale. ** At + 2 0 °C the differential thickness is 37.9 A]V, either by this method of ca lcula t ion or by direct interferometr ic measurement . Precision of values es t imated as 10 ~ approximate ly . This is due to an inaccuracy aris ing from the es t imated vo lume of 1 a tom-gram of oxygen in these oxides (ef. Table I). The precision of the oxygen de te rmina t ion is much bet ter and does not interfere with this calculat ion.

culation upon. Therefore we have to introduce this relation by using our basic hypothesis, extending to the anodic oxides the relationship determined for the crystalline oxides (cf. Table I). The resulting calculated value for the thickness of the anodic oxide films is given in Table II, for a formation temperature of + 10 °C. The validity of this calculation could be checked for some titanium anodic oxides prepared with BD electrolyte at +20 °C, the thickness of which was known by interferometric measurements: there is a perfect agreement on a slope of 37.9 A/V. Such a precision is of no significance by itself, the slopes being known with an accuracy of 10~o and 3 ~ respectively, but it reflects a good coincidence of the mean values obtained by a systematic use of the least mean squares method, applied on a sufficient number of samples.

2.2.3. Colour scale To reduce the delays and difficulties inherent in the interferometric or nuclear

thickness measurements, it proved desirable to set up an easy system of thickness comparison which would be standardized later, while helping to anticipate the results of actual thickness measurements. For that purpose a colour scale was set up with titanium anodic oxide samples prepared under rigorously defined conditions, the formation voltages stepping up volt by volt. The samples on the colour scale are indexed with the corresponding formation voltage.

Checked through oxygen determination by nuclear reaction, this colour scale was found linear in oxygen content within 5 ~ . The calculated differential thickness

218 F. K O V E R , M . J . M U S S E L I N

was 23.8 __ 1 .2/k/V with an extrapolated value of 35 /k to the "zero" colour mark. We estimate at about 10 ~ the inaccuracy due to systematic error in the calculation of thickness, in relation to the hypothesis on which is based the estimation of the volume of 1 atom-gram of oxygen. This colour scale can be used between the 6 and 40 colour marks with an incertitude of + ½ mark, and even down to the 3 colour mark with a larger incertitude.

2.2.4. Influence of the formation temperature For a given formation voltage, the colour mark obtained with titanium

anodic oxides prepared in SN electrolyte shows a linear variation with the formation temperature (Fig. 3): the films are "optically" thinner, the lower the forma-

o 2 0 ¸ m

o

8

40] i F o r m o l i o n vo l t age

I • 2 6 . 2 5 V I i ,~ 2 0 . O V

13.7 V

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10

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O DD O D

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o o [] o

D

o - 5b 6 5'o ~-

T e m p e r a t u r e (°C)

Fig. 3. Titanium anodic oxides formed in SN electrolyte. Colour scale mark as a function of formation voltage and temperature.

t ion temperature. The same observation has been made on other anodic oxides, but only in a qualitative way, in the absence o f a systematic colour scale.

2.3. Growth mechanism of titanium anodic oxides

2.3.1. Study by the chemical dissolution rate 6'11'[2 The oxides formed with various aqueous or non-aqueous electrolytes differ

in some of their properties. Such a difference has already been mentioned; it is


the thickness obtained for a given formation voltage. Another difference had been noticed 13 in the rate of chemical dissolution of tantalum anodic oxides. We ex- tended this observation to titanium, niobium and tantalum anodic oxides, using two dissolution reagents: (a) the SN electrolyte itself, but at +60 °C; (b) boiling 6 8 ~ o H N O 3 at + 122 °C. The tantalum anodic oxides do not dissolve in these reagents, but the colours obtained with these oxides show that they fit into the same series as the anodic oxides of titanium and niobium, on which observations could be made. In that way one can set up the following schematic representation for a rate of dissolution increasing from left to right:

metals: Ta ~ Nb ~ Ti

electrolytes: H2SO4 4 ~ ~ BD ~ SN

reagents: SN at 60 °C ~ H N O 3 68 ~ at 122 °C

This set of experiments shows again the existence of various and different anodic oxides of each of these metals, depending upon the electrolyte used for the formation. It also leads to a determination method for the growth mechanism of titanium anodic oxides prepared with SN and BD electrolytes. Indeed titanium anodic oxides formed with BD electrolyte do not dissolve in the SN reagent, whereas the oxides formed with SN electrolyte dissolve in this reagent. Therefore, a sample of titanium was anodized to 15 V in SN electrolyte, and then half of its surface was anodized again to 20 V in BD electrolyte: the colour attained on this second part of the sample became closer but not identical to the colour corresponding to a direct anodization to 20 V in BD electrolyte. After a one-hour treatment in the SN reagent, the SN-only half of the sample was found completely bared of its anodic oxide, the (SN + BD)-half remained unchanged in colour. Conversely, a sample of titanium was anodized to 10 V in BD electrolyte, and then half of its surface was anodized again to 20 V in SN electrolyte; the colour attained on this second part of the sample again became closer to the colour corresponding to a direct anodization to 20 V in SN electrolyte, but did not become identical nor fitting into the same colour scale. After a one-hour treatment in the SN reagent, this new colour had completely disappeared and the whole sample showed uni- formly the colour of the first BD anodization, the boundary between the two halves having become indistinguishable.

Therefore, the titanium anodic oxide situated next to the oxide/electrolyte interface shows some properties of the oxide formed in the second place, while the oxide next to the metal/oxide interface retains properties of the oxide formed in the first place. The lattice of oxygen atoms thus remains stationary during the growth of these anodic oxide films. The growth seems to occur at the oxide/electrolyte interface by means of a cation movement through the oxide. The possibility of a highly correlated movement of the oxygen atoms yet cannot be excluded; it also cannot be determined if the movement of the cations relative to the oxygen


sub-lattice involves or not an inversion of order of the metal atoms. Thus it cannot be decided whether there is a cation vacancy migration or an interstitial cation migration; for this, labelled cations should be used and detected by radioactivity or by nuclear reaction. The validity of the above conclusions should also be verified for different oxide thicknesses.

The influence of the formation electrolyte on the properties of the anodic oxides is compatible only with the above growth mechanism. This influence being observed in preparation and dissolution experiments on niobium and tantalum as well as on titanium, we feel it can be concluded that this mechanism is the same for all three metals.

2.3.2. Study with labelled oxygen atoms (isotope 01 8)

The combination of anodizations in different electrolytes can entail some chemical perturbation of the anodic oxides; in order to avoid this and to confirm the preceding results, the growth mechanism of a single anodic oxide was studied, making use of the 018 isotope of oxygen (cf. footnote on p. 216). There is no noticeable chemical effect as a result of the replacement of 016 by 0 28 in the

anodic oxides, and both isotopes can be detected and determined independently by the specific nuclear reactions O16(d, p)O t7 and O18(p, e)N 15

Samples of titanium have been anodized, first to 7.15 V in OlS-labelled SN electrolyte, then to 34.5 V in unlabelled SN electrolyte. The total quantity of 018 isotope did not change by the second anodization: there was no noticeable exchange of oxygen atoms between the anodic oxide and the electrolyte. The anodic oxides were then partially dissolved in the SN reagent at + 60 °C. As long as the remaining thickness of the anodic oxide is significantly larger than the thickness first obtained by anodization to 7.15 V, the quantity of O 18 remains unchanged. Thus the O 18-labelled layer is situated next to the metal/oxide interface, and this implies that the oxygen sub-lattice remains stationary during the growth of the anodic oxide.

Similar experiments performed on tantalum and aluminium anodic oxides indicated the same growth mechanism 8-10.

2.4. Capacitance of anodic oxides

2.4.1. Specific capacitance The specific capacitance of an anodic oxide film is the capacitance per unit

surface of the film, multiplied by the anodic potential used for the formation of the film. It can be calculated as a function of the surface S and the thickness e of the anodic oxide, and of the anodic potential V. It must be specified how the capacitance C has been measured, particularly at which frequency, and if the auxiliary electrode is constituted by the electrolyte or by a metallic electrode deposited on the anodic oxide film. Calling EM = V/e the Maxwell field in the oxide during


growth, e the dielectric constant of the anodic oxide relative to eo, the vacuum dielectric constant, one can write the following expression for the specific capacitance:

C I/ eoe V specific capacitance - - - goeEM

S e

However, this relation is only valid as long as the thickness e of the film is proportional to the anodic potential V. I f this no longer holds, if for instance the thickness is a linear function of the anodic potential (e = aV+b) , a differential specific capacitance wilt be determined from this linear relation, and a mean specific capacitance will result from neglecting the deviation from proportionality:

1 d(V) differential specific capacitance -

S d(1/C)

C V mean specific capacitance -

S

For "wet" capacitance measurements using an electrolytic contact, it was verified that the usual 0.3 cm 2 size of the platinum wire cathode was sufficient and did not introduce any error in the capacitance measurements on the anode. For "d ry" capacitance measurements, each anodic oxide received 7 vacuum-deposited 1.13 m m 2 gold electrodes. Measurements of capacitance, loss factor and leakage current were made as a function of the applied d.c. voltage, of the measurement signal frequency (30 Hz to 30 kHz) and of the measurement temperature ( - 80 °C to + 120 °C, controlled within +0.25 °) in a dry nitrogen atmosphere.

T A B L E I I I

MEAN SPECIFIC CAPACITANCE W E V / c m 2) FOR ANODIC OXIDES FORMED IN VARIOUS ELECTROLYTES~ USING THE DESCRIBED ELECTRICAL PROGRAM~ AT -]-10 °C AND 27.8 VOLTS

Metal SN electrolyte BD electrolyte 4 % HzSOJHzO

" w e t " (e lec t ro ly t ic ) m e a s u r e m e n t s a t 1 k H z * T i t a n i u m 7.56 - - - - N i o b i u m 9.7 - - 11.0 T a n t a l u m 9.6 - - 10.0

" d r y " (go ld e lec t rode) m e a s u r e m e n t s a t 1 k H z T i t a n i u m 7.89 ** 11 *** - - N i o b i u m 9.3 14.6 14.9 T a n t a l u m 11.9 12.6 10.0

* T h e f o r m a t i o n v o l t a g e r e m a i n s a p p l i e d d u r i n g the m e a s u r e m e n t s . ** T h e d i f fe ren t i a l speci f ic c a p a c i t a n c e is 8.43 # F V/cm~; b o t h va lues h a v e been o b t a i n e d by r e p l a c i n g t he a c t u a l f o r m a t i o n v o l t a g e b y the f ic t i t ious f o r m a t i o n v o l t a g e d e d u c e d f r o m the c o l o u r scale. *** T h i s v a l u e c o r r e s p o n d s to a f o r m a t i o n a t + 2 0 °C. A f o r m a t i o n a t + 1 0 °C as for a l l o t h e r s a m p l e s w o u l d h a v e g iven a v a l u e a b o u t 6 ~ h igher .

222 F. KOVER~ M. J. MUSSELIN

The mean specific capacitances for "wet" measurements on the various metals and electrolytes are presented in Table III. For niobium and tantalum, only anodic oxides formed to 27.8 V were measured; at this voltage there is little difference between the mean and differential specific capacitance values. For titanium anodic oxide formed in SN electrolyte, the mean specific capacitance is 7.56 ___ 0.60 /.iF V/cm 2 for a set of 93 samples prepared at + 10 °C in the voltage range of 20 to 30 V. Capacitance measurements were not possible with the BD electrolyte, because of the high series resistance of this electrolyte.

The "dry" measurements of capacitance on titanium anodic oxides formed in SN electrolyte gave a bad correlation between the values of capacitance and of formation voltage, unlike the "wet" measurements. A set of identically prepared samples shows a dispersion on "dry" capacitance measurements which did not appear on the "wet" measurements of the same set of samples; observing these samples, one can notice a dispersion in their colours. Therefore we sought for a correlation between the "dry" capacitance measurements and the colour marks of the samples; this is equivalent to introducing a fictitious formation voltage deduced from the colour mark. The mean specific capacitance at 1 kHz then becomes 7.89 __ 0.55/~F V/cm 2 for a set of 155 samples of titanium anodic oxide prepared in SN electrolyte at room temperature with formation voltages in the range of 20 to 40 "equivalent volts" deduced from the colour scale. The differential specific capacitance value at 1 kHz is 8.43 +_ 0.42 #F V/cm / for a set of 135 samples prepared at + 10 °C at voltages in the whole range of 0 to 30 "equivalent volts". The difference between the mean and differential values arises from the fact that the inverse of the capacitance becomes extrapolated to a zero value for a colour scale mark of - 2 "equivalent volts". For all these "dry" measurements, the influence of the measurement temperature and of any small applied d.c. voltage seems negligible.

Finally, the apparent dielectric thickness seems well correlated to the formation voltage for "wet" measurements where the formation voltage remains applied while the capacitance measurements are made under electrolyte. For "dry" measurements under a gold electrode, the apparent dielectric thickness is not well correlated to the formation voltage, but it is well correlated to the geometrical thickness evaluated from the colour scale. This leads to an investigation of the influence of the oxide/electrolyte interface on the dispersion of thicknesses with samples prepared under conditions that seem to be identical.

2.4.2. Variation of"wet" capacitance with applied d.c. voltage At the end of the formation of a ti tanium anodic oxide sample in SN elec-

trolyte at - 2 0 °C and 30 V, the voltage was lowered step by step and each time the capacitance and current were quickly measured. Between 30 and about 7 V the inverse capacitance is linear in V 1/2 (Fig. 4); between 7 and 0 V there is little variation in capacitance. The direct current is proportional to V 3/~ between 0 and


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Applied v o l t a g e (V)

Fig. 4. Inverse capacitance as a funct ion o f applied voltage, for t i tanium anodic oxide formed to 30.0 V in S N electrolyte at - -20 °C. "Wet" capacitance measurement in the anodizat ion cell after format ion is terminated.

150.10 -9 -

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8 5 0 , 3 0 . 9 -

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J J

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Applied v o l t a g e ( V )

Fig. 5. Current density as a funct ion o f applied voltage, for t i tanium anodic oxide formed to 30.0 V in S N electrolyte at - -20 °C. "Wet" capacitance measurement in the anodizat ion cell after format ion is terminated.


about 7 V (Fig. 5) and proportional to V '/2 between about 7 and about 20 V (Fig. 6); above 20 V the direct current increases strongly with voltage, the electrical field ap- proaching the value corresponding to the formation of the anodic oxide film (Fig. 7). This behaviour is similar to that of a diode functioning in the space-charge-controlled-current region between 0 and 7 V, and in the saturation region above 7 V. The capacitance measured across the terminals of the anodization cell seems to result from the series connection of the capacitance of this apparent diode and of the capacitance of the anodic oxide film. Extrapolating to zero voltage the V '/2 variation of the cell capacitance, the capacitance of the anodic oxide film can be determined; the difference with the actually measured capacitance at zero voltage is the apparent diode capacitance at zero voltage, which is found to be approximately 4.2 #F/cm z. The presence of this capacitance lowers the total capacitance, it is thus located outside the anodic oxide layer; the order of magnitude found would be acceptable for the capacitance of a double layer at the oxide/electrolyte interface.

A further experiment confirmed that these effects are not due to the cathode or to the bulk electrolyte: two anodization cells were connected by a syphon and the capacitance was measured between the two anodes, whereas the voltage was applied between each anode and its cathode (both polarization circuits being

- 9 150,10 -

c~

8 < 1 0 0 . 1 0 -9.

c o9

,t ~o -9 50.I 0 -

0

1 2 3 4 5

. . . . . . . . . . . . . . . . . . ' ~ ' o " ' " ' " ~ 5 10 0

A p p l i e d v o l t a g e (V ]

Fig. 6. Current density as a function of applied voltage, for t i tanium anodi¢ oxide formed to 30.0 V in SN electrolyte at --20 °C. "Wet" capacitance measurement in the anodization cell after formation is terminated.

A N O D I C O X I D E F I L M S O N T I T A N I U M ~ N I O B I U M A N D T A N T A L U M 225

10-%

7

44

2

J E ..~ 10 -7 <

7

4

t 2

i0 -e

o , • •

• •

2+ 16 zb 3b

Applied voltage(V)

Fig. 7. Current density as a function of applied voltage, for titanium anodic oxide formed to 30.0 V in SN electrolyte at --20 °C. "Wet" capacitance measurement in the anodization cell after formation is terminated.

separated by the insertion of high resistances in the cathode circuits). The capacitance variation followed the same law, showing that the observed effects originate in the vicinity of the oxide/electrolyte interface.

The choice of the - 2 0 °C temperature results from a compromise between the influence of the capacitance external to the oxide, which increases as temperature is lowered and the time required by the experiment, limited by the gradual solidification of the SN electrolyte, which at - 30 °C is in a supercooled state.

A qualitative confirmation of the observed effects was found with the BD electrolyte, the current behaviour being similar but capacitance measurements being impossible.

The possibility of a variation of the dielectric properties of the anodic oxide on account of an influence of the electric field can be discarded, for the "dry" capacitance measurements with a gold electrode do not show any significant variation of the capacitance with the applied voltage, up to 6 0 ~ of the formation voltage of the anodic oxide.

2.4.3. Variation of capacitance with formation temperature The "wet" (electrolytic) mean specific capacitance remains approximately

independent of the formation temperature; its value is of the order of 7.5/~F V/cm 2


10-

E

> LL"

.~ 5-

u

ul

• J ' t • • • Jl • • •

o • AA Q • m A_•

a • a a

Format ion vo l tage

A 7 0 5 V • 2o.ov

• 13.7 V • 2 6 . 2 5 V

~ Y 6 2'~ go 7Y Tempera tu re {°C)

Fig. 8. Mean specific capacitance at 1 kHz as a function of formation voltage and temperature, for t i tanium anodic formed in SN electrolyte. "Wet" capacitance measurement in the anodization cell after formation is terminated, with applied voltage.

1 5 -

E 1o-

>. LL

.o

u

z~

F o r m a t i o n v o l t a g e

• 2 6 . 2 5 V

• 20 .Q V

• 13 .7 V

t~ 7 . 0 5 V

• • ~ . , . I • • | • : • • A • j

~')m " ~ " " - • a aa~ aa •m • • , •

" ) J , I •

• 6

2 " " • a

~' ~ m

z~

-do 8 do Temoenature(°C)

Fig. 9. Mean specific capacitance at 1 kHz as a function of formation voltage and temperature, for t i tanium anodic oxides formed in SN electrolyte. " D r y " capacitance measurement with vacuum-deposited gold electrode.


at 1 kHz (Fig. 8) at the end of the formation, with applied formation voltage and without any change of temperature between formation and measurement.

The "dry" (gold electrode) mean specific capacitance of the same set of samples decreases distinctly when the formation temperature increases (Fig. 9), but the dispersion of results is such that no quantitative interpretation can be deduced from this observation. On the contrary, there is a good correlation between the capacitance measurements and the colour scale marks whatever the formation temperature and voltage are (Fig. 10). Considering only a value offorma-

5 -

T

E u &-4 3

E

.2 3

. . ;

~b 2b 3b 4'0 Colour scale m o r ' k

Fig. 10. Inverse capaci tance at 1 kHz as a funct ion o f the colour scale m a r k and of the format ion voltage, s imul taneous ly for all fo rmat ion temperatures . T i t an ium anodic oxides formed in SN electrolyte. " D r y " capaci tance m e a s u r e m e n t with vacuum-depos i t ed gold electrode.

tion voltage deduced from the colour scale, the differential specific capacitance so calculated has a value of 8.95 _+ 0.54 #F V/cm z at 1 kHz for a set of 113 samples. This correlation a posteriori justifies the use of the colour scale, and the differential specific capacitance so calculated is representative of some properties of the anodic oxide films, it has become independent of the value of the formation temperature and of the attained thickness or colour scale mark.

2 . 4 . 4 . Dielectric constants at 1 k H z

From the mean specific capacitance expression (CV/S ) = Sos(V/e) an approximate value of the 1 kHz dielectric constant can be deduced:

The results of this calculation are given in Table IV for all anodic oxides in-

228 F. K O V E R , M. J . M U S S E L I N

TABLE IV

DIELECTRIC CONSTANTS AT 1 kHz, DEDUCED FROM THICKNESS MEASUREMENTS AND MEAN SPECIFIC

CAPACITANCE MEASUREMENTS~ FOR ANODIC OXIDE FILMS FORMED AT ~ l 0 C V~'ITH THE DESCRIBED

ELECTRICAL PROGRAM

Metal Electrolyte Dielectric constant

Titanium 21.2* Niobium SN 24.6 Tantalum 2 I. I

Titanium 47.1 * * Niobium BD 60.2 Tantalum 33.2

Titanium dilute - - Niobium sulfuric 65.2 Tantalum acid 28.9

* By using the value of the differential specific capacitance, the calculated value of the dielectric constant becomes 22.6. ** Formation at +20 'C. The inaccuracy on these values is estimated at about 10 ~, due on the one hand to the dispersion of the specific capacitance values from one sample to another, on the other hand to the hypothesis included in the calculation of the differential thickness.

vestigated, the value of (e/V)beinggiven in Table I1 and the value of (CV/S) in

Table I l l .

2.4.5. Dielectric constant andresistivity variation across the layers of titanium anodic oxide formed in SN electrolyte Ti tan ium anodic oxide films fo rmed in SN electrolyte can be th inned step

by step by par t i a l d issolut ion in the SN reagent a t + 6 0 °C (cf. Sect ion 3 .3 .1 ) .

Such a d issolut ion does no t involve any change in the chemical na ture of the

reagent in con tac t wi th the anodic oxide ; however , after each dissolut ion step the

samples are r insed in water , dr ied and p la ted with a vacuum-evapora t ed gold elec-

t rode. The remain ing anodic oxide layer shows a homogeneous interference colour

and thickness. Only a synthesis of our results will be presented, the cor responding

figures and discussions having been publ i shed elsewhere 1.

Two invest igat ion processes can be used. On the one hand, several samples

can be subjected to "para l l e l d i sso lu t ions" for var ious dura t ions ; this me thod is

speedy but the results depend upon the d ispers ion o f proper t ies f rom one sample

to another . The mean specific capaci tance at 1 k H z takes the value 7.83 + 0 . 2 4 # F

V/cm 2 for all pa r t i a l ly dissolved samples of thickness greater than 12 "equiv-

a lent vol t s" on the co lour scale. The differential specific capaci tance at 1 k H z is

9.49 _+ 0.57 # F V/cm 2 for the whole set of 101 samples of all thicknesses. On the

o ther hand, a series o f "successive d isso lu t ions" can be pe r fo rmed on a single

sample. Such a sample, o f 650 A s tar t ing thickness, was subjected to 22 successive

dissolut ions o f 1 minute each: the mean specific capac i tance was found to be


8.43 _ 0.25/~F V/cm 2 at 1 kHz and 7.58 +__ 0.23/~F V/cm z at 20 kHz for all steps

of dissolution where the remaining thickness of the sample was greater than 15 "equivalent volts". The differential specific capacitance was 9.07 _ 0.54/~F V/cm 2 at 1 kHz and 9.31 + 0.28 #F V/cm 2 at 20 kHz for the whole set of successive

dissolution steps. The values of the specific capacitance are thus found to be of the same order

when dissolved samples are compared against each other or with undissolved samples. The dielectric constant therefore remains constant throughout the whole thickness of the anodic oxide of titanium formed in SN electrolyte, and is not modified by the dissolution process; moreover the colour scale mark is an acceptable means of evaluation of the dielectric thickness.

The measurements intended to determine the capacitance of the anodic oxides give at the same time a value of the dielectric loss factor. By identification with a R - C parallel circuit the loss factor D at frequency f can be defined as D = l/(2nRCf). The effect of the thickness variation of the samples can be eliminated by multiplying D by the specific capacitance (CV/S). Calling r the mean resistivity across the sample of thickness e to which corresponds a fictitious voltage V deduced from the colour scale, one can write R = re/S and therefore:

It was found 1 that this expression (DCV/S) varies linearly as a function of ( l / f ) ; the extrapolation for infinite f leads to the value of a small loss factor characteristic of anodic oxides, practically independent of frequency and not due to the oxide conductance14. The factor Vie is the inverse of the differential thickness of Table II ; its value is 4.2 MV/cm. One can then calculate the value of r, the mean resistivity across the sample at each step of the dissolution process. The results obtained show a rather large dispersion, but except for the very first steps of dissolution the order of magnitude of the resistivity is 2 x 109 ohm cm; the resistivity is approximately constant across the titanium anodic oxide prepared in SN electrolyte; its rather low value cannot be due to the effect of the dissolution treatment, for this value would then become lower the longer the treatment, which is not the case.

On samples undissolved or dissolved on less than the outer 50 A a much higher resistance was observed, but it could not be determined whether this resistance is due to a very high resistivity near the surface, or to the presence of a semi- conducting junction.

2.5. Comparison of electrochemical and nuclear oxygen determinations

The thickness of the anodic oxide films is a linear function of the electrical charge passed through the anodization cell during the formation of the films. For


a given electrical current program, this electrical charge is a linear function of the formation voltage. In Table V a differential value of the electrical charge is given for an increase of 1 V of formation voltage in the vicinity of 34.6 V, for anodic oxide films formed at + 10 °C and of 1 c m 2 surface. The corresponding oxygen

T A B L E V

D I F F E R E N T I A L C H A R G E S A N D W E I G H T S OF O X Y G E N FO R 1 c m 2 A N O D I C O X I D E F ILMS P R E P A R E D AT

@ l 0 ~'C W I T H THE D E S C R I B E D E L E C T R I C A L P R O G R A M , PE R V O L T I N C R E A S E OF F O R M A T I O N V O L T A G E .

C A L C U L A T E D A P P A R E N T E L E C T R I C A L C H A R G E PER E L E C T R O D E P O S I T E D O X Y G E N ATOM

Metal Electrolyte Charge Weight Apparent charge on (/~C/V/cm~) (l~g/V/cm2) oxygen ion (e)

Ti tan ium 2130 0.367 0.97 Niobium SN 2450 0.362 I. 12 Tan ta lum 1600 0.234 1.14

T i tan ium 4940 0.585 1.41 Ni,~bium BD 4140" 0.491 * 1.40" Tan ta lum 2530 0.346 1.21

T i tan ium dilute - - - - N iob ium sulfuric 4330 0.520 1.38 Tan ta lum acid 2860 0.389 1.22

• Anodic oxides formed at 4-20 C. The indicated values are considered significant within 10 % on account of the usual dispersion of results and propert ies f rom one sample to another. The precision of the involved measurements is much better, in all cases, than 1 ~ .

determinations by nuclear reaction are also given in Table V, expressed as weights of oxygen per cm 2 and per volt increase of formation voltage, and standardized against the weighings of aluminium anodic oxide films by Harris 15 and by Davies, Friesen and McIntyre 16. From these measurements the apparent charge to be at- tributed to one electrodeposited oxygen atom can be deduced and is given in the third column of Table V.

This apparent charge should take the value 2.00 if the ions incorporated from the electrolyte into the anodic oxide were O z- . The values actually found are in the range of 1.2 to 1.4, except in one case where it is lower than 1.00. Therefore, an incorporation of ions of charge lower than 2.00 must be considered; the apparent charge can result from the contribution of several kinds of ions. These anions could be, in our experiments: OH , SO42- and its complexes as S O a H - , borate anions which can be assimilated to B O 2 - , and NO3- . The incorporation of nitrogen can be discarded; negligible amounts of nitrogen were found in these anodic oxides when investigated by nuclear reaction, and moreover the anodization of titanium is unsuccessful in an electrolyte containing very dry KNO3 and diethyleneglycol. Comparing the BD and dilute sulfuric electrolytes, the same apparent charge on anions is found although the first electrolyte should incorporate boron and the second sulphur; moreover, the dimensions of these ions (B 3+ = 0.23 A,


S 6+ = 0.30 A, S 2 - = 1.84/k) are very different from the dimension of cations (about 0.7/k) and of anions (1.32 A) in the oxides considered. The apparent charge on anions is lower with the SN electrolyte. Referring to the composition of the electrolytes, it is observed that the BD electrolyte contains at least 5 ~ water originating from the water of crystallization in borax and from esterification of the diethyleneglycol; on the contrary, it is known that water is strongly bonded to sulfuric acid molecules in concentrated sulfuric and sulfo-nitric solutions.

Finally, the similarities and differences in the apparent charge on anions seem to be correlated to the free water content of the electrolytes, and not to the sulfuric, nitric and boric anions present in these electrolytes. Such a correlation could be due to the incorporation of protons into the anodic oxides. From a crystallographic point of view, these protons should be practically situated inside the 0 2 - anions, converting these into O H - anions of practically the same radius (OH- = 1.33 A). The electrical neutrality of the anodic oxide must however be satisfied in spite of the additional positive charges of these protons; this would be possible if the valency of the metal cations could be lower than Ti 4+, Nb s+ and Ta s +. Now it has been observed in some conditions of electropolishing that the metal cation valency is lower than the usual valency in oxidizing solutions 17'18, and the formation of a dielectric layer adjacent to the anodic oxide layer during the anodization process denotes a certain extent of similarity with the electropolishing process, where a "viscous layer" is known to be formed adjacent to the metal anode.

The chemical formula of an anodic oxide of, say, titanium would then be [Ti (g-x)+, xH +, 202 - ] which can equivalently be written [Ti (4-x)+, ( 2 - x ) O 2-, xOH-] . When such an anodic oxide is induced to crystallize by heating inside the chamber of an electronic microscope, the usual diffraction pattern of TiO2 appears, for the incorporation of protons does not much affect the ionic radii and therefore the lattice short-distance order, and also because the protons could at least partly be expelled by vacuum-heating.

In the case of the SN electrolyte, the very low apparent charge of anions leads to consider that an appreciable amount of SO, 2- or SO4H- anions must also enter the anodic oxides; this could be due to the high strength of the bonding between the S O 4 H 2 and H 2 0 molecules.

The presence of protons incorporated into the anodic oxides would also explain the rather low value of the resistivity measured on these oxides. A similar effect of protons has been observed on silicon anodic oxide 19,20 and is known for crystalline oxides of TiO2, ZrO2, SiO 2 etc. But no direct determination of protons has yet been made in anodic oxide films, for instance by nuclear or radioactive detection of hydrogen, deuterium or tritium, although much work has been intended to relate the proton concentration of the electrolyte either to the electrochemical properties of anodic oxide f i lms 21-23 o r to the electrical properties of these oxides 19,2 0,24--26


3. CONCLUSION

The results of the above experiments and discussions can be summarized in the following comments:

The properties of titanium and niobium anodic oxides are similar, and rather different from the properties of tantalum anodic oxides, except if the SN electrolyte has been used for anodization. In this electrolyte, the bonding between the sulfuric acid and water molecules is strong enough to mask the presence of water, up to 40 m o l e s t , whereas both BD electrolyte and dilute sulfuric acid behave as an aqueous medium. Water is the main oxidizing species. Anomalous values of the apparent valency of anions in the anodic oxides are explained by the incorporation of protons and, in some cases, of anions such as SO42- and SO4H-.

The anodic oxides grow from the oxide/electrolyte interface by a mechanism of cation migration through a stationary oxygen sub-lattice. At this interface an electrochemical "double layer" acts as a dielectric layer external and additional to the anodic oxide layer. A capacitive potential divider is thus formed, causing the specific capacitance to remain of the same value of the order of 10/~F g/cm 2 for all anodic oxides, independently of formation voltage and temperature. The dielectric constant retains the same value throughout all anodic oxides investigated, and the resistivity is also approximately constant and low, except for a layer of the order of 50 A close to the oxide/electrolyte interface.

The influence of the electrolyte on the properties of the anodic oxides, and the constancy of the specific capacitance in spite of the variation of the actual thickness of the anodic oxides, lead to a conception of the oxide/electrolyte interface, following which the structure of the oxygen sub-lattice would extend from the anodic oxide into the electrolyte with a progressive deformation to fit the short- range order of the bulk electrolyte, and with a progressive transition from neutralization by metallic cations to the neutralization by protons. This transition region would correspond to the observed "double layer". Conversely, the short-range order of the bulk electrolyte causes the anodic oxide to become a kind of replica of this order, as it grows from the double layer at the oxide/electrolyte interface. More or less of the transition region should be removed during the rinsing process after the formation of the oxide, and fluctuations of about 20 A are observed indeed and detected with certainty on the colour scale and by capacitance measurements, from one sample to another. The outer layer of about 50 A closest to the growth interface also dissolves at a higher rate than the bulk anodic oxide. The dissolution mechanism itself appears to be similar to a diffusion mechanism for metallic cations and protons through the oxygen sub-lattice of the "double layer" for, even after removal of the outer 50 A, the dissolution of the remaining anodic oxide decreases as a function of dissolution time and increases with temperature, as if a diffusion gradient would assume a constant value after a lapse of time of several minutes ~.


The introduction of a "double layer" or transition region concept may lead to an approach of the "sparking" or "scintillation" problem. Sparking sets a limit to the value of the formation voltage of anodic oxide films. As results from experiment, the relatively constant value of the specific capacitance for all conditions of formation implies the same constancy for the electrical induction vector because these two quantities are simply related by the multiplication factor e o, the vacuum dielectric constant. If the voltage applied to the anodization cell is increased beyond a certain value, the transition layer is seemingly unable to extend sufficiently into the electrolyte to keep a constant value of the induction vector, and avalanche effects occur. This tentative explanation could lead to a better approach on the choice of electrolytes.

The values of the induction and of the specific capacitance are still to be explained, as well as the value of the dielectric constant in the anodic oxides. However, the latter seems to be related to the dielectric constant of cassiterite (SnO~), which displays the most regular short-range octahedral arrangement in the crystalline state, and dielectric constants of 23.4 (_t_) and 24 (II); in the amorphous state of the anodic oxides, regularity of the arrangement would be attained as a statistical mean. There might also be a connection of this problem with the values of the activation energies for conductivity, which are found in many anodic oxides to be lower or equal to 0.7 eV, with multiple values 11. Finally, and among many other problems, it remains to be explained why the highly insulating anodic oxides are obtained easily only with metals, the cations of which present an electronic configuration of the (Ns 2, Np 6, Nd °) type, whereas the present study of anodic oxidation seems to indicate that the metal atoms are only partially ionized and therefore would not present the above configuration.

REFERENCES

1 F. KOVER, ThOse, Paris, 1967, No. A.0 .1088/CNRS. 2 Handbook of Chemistry and Physics, The Chemical Rubbe r Co., 45th edn. 3 G . B . SKINNER, C. BECKETT AND H. L. JOHNSTON, US. Govt. Res. Rept., A TI-81816/NSA-

73108, 1950. 4 YOUNG, Anodic Oxide Films, Academic Press, New York, 1961. 5 F. TERAO, J. Appl. Phys. (Japan), 6 (1) (1967) 21. 6 N. KOVER, Final Report on Contract No. 62.FR.115/DGRST, available f rom Centre de Re-

cherches de la C o m p a g n i e G6n6rale d'Electricit6, 91-Marcouss i s , France. 7 G. AMSEL AND D. SAMUEL, Anal. Chem., 39 (14) (1967) 1689. 8 G. AMSEL, ThOse, Orsay, 1963. 9 G. AMSEL AND D. SAMUEL, J. Phys. Chem. Solids, 23 (12) (1962) 1707.

10 J . P . NADAI, ThOse de 3. Cycle, Ecole N o r m a l e Sup6rieure, Paris, 1967. 11 F. KOVER AND M. J. MUSSELIN, Rev. Gen. Elec., 76 (5) (1967) 793. 12 F. KOVER AND M. J. MUSSELIN, L'Onde Electrique, 47 (480-481) (1967) 375. 13 D . A . VERMILYEA, Acta Met., 2 (5) (1954) 482. 14 C. CHERKI, R. COELHO AND J. L. MARIANI, Solid State Commun., 4 (9) (1966) 411. 15 L. HARRIS, J. Opt. Sac. Am., 45 (1) (1955) 27.


16 J . A . DAVIES, J. I. FRIESEN AND J. D. MCINTvRE, Can. J. Chem., 38 (9) (1960) 1526. 17 M. FROMENT, Th~se, Paris, 1958. 18 GARREAU AND I. EPELBOIN, J. Chim. Phys., 63 (I I--I 2) (1966) 1515. 19 F. KOVER AND R. NANNON1, Rev. Gen. Elec., 75 (6) (1966) 777. 20 R. NANNONI, results presented at N o t t i n g h a m Conference, 1967, to be published. 21 D . A . VERMILYEA, Sblrface Sci., 2 (1964) 444. 22 D . A . VERMILYEA, J. Electrochem. Soc., 112 (12) (1965) 1232. 23 D . A . VERMILYEA, J. Electrochem. Sot . , 113 (10) (1966) 1067. 24 C. VILLEMANT AND F. KOVER, Rev. Phys. Appl., 1 (2) (1966) 90. 25 A . J . BROCK AND G. C. WOOD, Electrochim. Acta, 12 (4) (1967) 395. 26 A . J . BROCK, Manchester Univ. " M U T E C H " Chem. Eng. J., 12 (1966) 17.

A COMPARATIVE STUDY OF ANODIC OXIDE FILMS ON TITANIUM, NIOBIUM AND TANTALUM

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