I David

L Bodin

D Gianola

A Legarra

E Manfredi

C Robert-Granié

Product versus additive threshold models for analysis of reproduction outcomes in animal genetics 1

Keywords: additive model, Gibbs sampling, product model, reproduction traits

The phenotypic observation of some reproduction traits (e.g., insemination success, interval from lambing to insemination) is the result of environmental and genetic factors acting on 2 individuals: the male and female involved in a mating couple. In animal genetics, the main approach (called additive model) proposed for studying such traits assumes that the phenotype is linked to a purely additive combination, either on the observed scale for continuous traits or on some underlying scale for discrete traits, of environmental and genetic effects affecting the 2 individuals. Statistical models proposed for studying human fecundability generally consider reproduction outcomes as the product of hypothetical unobservable variables. Taking inspiration from these works, we propose a model (product threshold model) for studying a binary reproduction trait that supposes that the observed phenotype is the product of 2 unobserved phenotypes, 1 for each individual. We developed a Gibbs sampling algorithm for fitting a Bayesian product threshold model including additive genetic effects and showed by simulation that it is feasible and that it provides good estimates of the parameters. We showed that fitting an additive threshold model to data that are simulated under a product threshold model provides biased estimates, especially for individuals with high breeding values. A main advantage of the product threshold model is that, in contrast to the additive model, it provides distinct estimates of fixed effects affecting each of the 2 unobserved phenotypes.

INTRODUCTION

The phenotypic observation of some reproduction traits is due to effects contributed by the male and the female. For such traits depending on several individuals, a main approach that has been proposed in animal genetics models the observed phenotype (for continuous traits), or an underlying variable (for binary traits analyzed under the threshold model assumption), as the sum of environmental and genetic effects contributed by the different individuals involved [START_REF] Wilham | The covariance between relatives for characters composed of components contributed by related individuals[END_REF][START_REF] Varona | Variance components of fertility in Spanish Landrace pigs[END_REF][START_REF] Piles | Genetic parameters of fertility in two lines of rabbits with different reproductive potential[END_REF][START_REF] Bijma | Multilevel selection 1: Quantitative genetics of inheritance and response to selection[END_REF]. In some cases, these models give perplexing results (e.g., high negative estimates of the cor-relation between maternal and direct genetic effects; [START_REF] Robinson | Estimation and interpretation of direct and maternal genetic parameters for weights of Australian Angus cattle[END_REF][START_REF] Koerhuis | Models to estimate maternal effects for juvenile body weight in broiler chickens[END_REF]. Some authors have pointed out that the combination of the different sources of variation may not be purely additive (on either the observed or underlying scales). Actually, statistical models proposed for studying human fecundability generally consider the reproduction result as the product of hypothetical unobservable variables. For instance, [START_REF] Speirs | Analysis of the benefits and risks of multiple embryo transfer[END_REF] proposed a model in which the number of observed embryo implantations is the product of the number of viable embryos and a measure of uterus receptivity. For binary traits, [START_REF] Zhou | Modeling conception as an aggregated Bernouilli outcome with latent variables via the EM algorithm[END_REF] assumed that the probability of conception in a menstrual cycle is the product of the probability that the cycle is viable and the probability that conception would occur. This product combination of factors for studying reproduction results has the advantage of being biologically more natural and easier to construe than the purely additive combination. Nevertheless, such models have not been used for studying reproduction traits in animal genetics. In line with human studies, we propose a product threshold model for studying the outcome of an insemination taking into account the action of the male and female and the ge-netic relationships between individuals. The objectives of this study are 1) to present the theory of a product threshold model in a genetic context, and 2) to examine, with illustrations, the feasibility of this model.

MATERIALS AND METHODS

Animal Care and Use Committee approval was not obtained for this study because no animals were used.

Methods

Background: Linear Additive Model for a Continuous Trait Depending on 2 Individuals.

Statistical methodology for studying a quantitative genetic trait dependent on several individuals has already been developed under the assumption of the additive model [START_REF] Wilham | The covariance between relatives for characters composed of components contributed by related individuals[END_REF][START_REF] Bijma | Multilevel selection 1: Quantitative genetics of inheritance and response to selection[END_REF]. To define the notation that will be used in this paper, we recall the corresponding theory as in [START_REF] Bijma | Multilevel selection 1: Quantitative genetics of inheritance and response to selection[END_REF]. The model for a phenotype dependent on 2 individuals {i,j}, consists in expressing the observed phenotypic value, P ij as the sum of 2 unobserved phenotypic effects: a direct effect (P D,i ) of individual i and an associative effect (P S,j ) of the associated individual j:

P P P ij D,i S ,j = + . [1.1]
Phenotypic direct and associative effects can both be decomposed into a heritable component, referred to as the breeding value (A), and a nonheritable environmental component (E). Thus,

P A E A E ij D,i D ,i S,j S ,j = + + +
, where A D,i is the direct breeding value (DBV) and A S,j is the associative breeding value (SBV), which pertain to genetically distinct traits. In matrix notation, the corresponding animal model is as follows:

l Xb Z a Z a D D S S = + + +e, [1.2]
where l l ij = { } is the vector of observed phenotypes; β is a vector of fixed effects, with incidence matrix X; a D and a S are vectors of DBV and SBV, respectively (each having an order equal to the number of animals in the pedigree), with corresponding incidence matrices Z D and Z S . The distributional assumption is Threshold Models for a Binary Trait Depending on 2 Individuals. For dichotomous traits, the observed phenotype P ij * (1 or 0) is modeled using generalized linear mixed model assumptions. The most widely used approach adopts the same linear predictor as for a linear mixed model with a probit link function:

Pr( ) ( ) , * , , , , P A E A E ij D i D i S j S j = = + + + 1 F
where Pr( ) * P ij = 1 is the conditional (given the A and E variables) probability of success for the couple {i,j} and Φ is the standard cumulative distribution function of the normal distribution. This model is called the additive threshold model. This model is equivalent, under the threshold model theory [START_REF] Wright | An analysis of variability in number of digits in an inbred strain of guinea pigs[END_REF][START_REF] Gianola | Theory and analysis of threshold characters[END_REF], to

P l T l T ij ij ij * , = > £ ì í ï ï ï î ï ï ï 1 0 if if
P A E D i D i D i = = + ( ) 1 F and

Pr(

) .

, * , ,

P A E S j S j S j = = + ( ) 1 F
In this case, the relationship between the probability of success for the unobserved phenotypes and the observed phenotype is not obvious with the additive threshold model. A more intuitive way to link observed and unobserved phenotypes in the case of dichotomous traits is to assume that a success is observed only if there is a success for each of the 2 unobserved phenotypes:

P P P ij D i S j
P P P A E A E ij D i S j D i D i S j S j = = = ´= = + ( ) ´+ 1 1 1 F F ( ( ) . [1.3]
According to the classical threshold model theory, this product threshold model is equivalent to , are mutually independent residuals with variances s e D 2 and s e S 2 , respectively.

Contrary to the additive threshold model, the interpretation of unobserved phenotypes is straightforward in the product threshold model. For instance, in the study of AI success, if individual j is the male, Pr( ) , * P S j = 1 is the chance that the male produces a sperm capable of fertilizing the ovum if the latter is viable. Conversely, Pr( ) , * P D i = 1 is the chance that the ovum can be fertilized, provided that the sperm is fecundant.

Product and additive threshold models support different biological assumptions. Figures 1 and2 depict for the additive and product threshold models, respectively, variations of Pr(

) P ij = 1 with re- spect to d D i D i D i A E , ,
, , = + with one curve for each

d S j S j S j A E , , , . = +
In the additive threshold model, the probability of success Pr( ) P ij = 1 can reach very high values as soon as d D i

, is sufficiently large in comparison with d S j

, . In contrast, in the product threshold model, the increase of Pr(

) P ij = 1 with d D i
, is penalized by the value of d S j

, and reaches a maximum value that is generally less than 1. Assuming a product threshold model may be more realistic in some cases. For instance, a sterile male will never have progeny, even if he is mated to highly fertile females. This case corresponds to the change of the lowest lines in Figures 1 and2. For intermediate d D i

, and d S j , , the change of Pr(

) P ij = 1 for differ- ent d S j
, values when d D i , increases are similar and independent of d S j

, values in the additive threshold model. On the other hand, in the product threshold model these changes in probability of success depend on the values of d S j , , and increase faster for greater d S j , . However, for reduced d D i

, and d S j , , the models behave similarly because, in this case, the odds ratio is close to the relative risk.

Heritabilities. In the additive threshold model, the total variance of the underlying variate l is

s s s s s e l A A A D S DS r 2 2 2 2 2 = + + +
, where r denotes the additive genetic relationship between associates in a couple. (  ) Parameter Estimation. Parameter estimation methods in the additive threshold model are well known [START_REF] Gianola | Sire evaluation for ordered categorical data with a threshold model[END_REF][START_REF] Harville | A mixed-model procedure for analyzing ordered categorical data[END_REF][START_REF] Gilmour | The analysis of binomial data by a generalized linear mixed model[END_REF][START_REF] Hoeschele | Estimation of variance components of threshold characters by marginal posterior modes and means via Gibbs sampling[END_REF][START_REF] Moreno | On biased inferences about variance components in the binary threshold model[END_REF] and will not be presented here. Bayesian inference in the product threshold model can be carried out using the Gibbs sampling algorithm with a modification of the data augmentation algorithm described in [START_REF] Sorensen | Bayesian inference in threshold models using Gibbs sampling[END_REF]. In the classical additive threshold model, the idea is to sample the underlying variable from its conditional posterior distribution (a truncated normal distribution, on the left if P = 1 and on the right otherwise). The next step is to sample each parameter from its conditional posterior distribution, with the underlying variable replacing the observed data, so that the Gibbs sampler is as for the linear model [START_REF] Sorensen | Bayesian inference in threshold models using Gibbs sampling[END_REF]. Implementation of the product threshold model can be done using the same approach and a supplementary step, which is the sampling of P D,i and P S,j . Consider the following notation,

The heritability of direct and associative effects on the underlying scale is then

P A E A E ij D i D i S j S j = = + + + ( ) 1 F as a function of the direct value d D i D i D i A E
- = ´= - = ( ) é ë ê ù û ú { 2 2 2 1 1 1 ( ) / Pr( ) Pr * * } } ,
Pr( ) Pr( ) , , ' , ' P w P w D i i D S j j S = = ( ) = = ( ) 1 1 F F q q and
where P D,i and P S,j are the unobserved phenotypes,

q q D S
and are the vectors of parameters (i.e., fixed and random effects) for direct and associative phenotypes, respectively; w

= = = - - 1 0 0 1 1 q q i i n S j n ij D n S n i D n j P P w w = = = = -( ) é ë ê ù û ú - - - 0 1 0 1 1 1 1 , × , ' , , ) q q q F F ' ' , , ) . r(
, , ; r( ,

q S n t D i n S j n ij P P P P - ( ) = = = 1 1 0 0 P , q q q q q D n S n i D n j S n t w w P - - - - = ( ) ´-( ) é ë ê ù û ú 1 1 1 1 1 , ) ; ' ' F F P , r( , , )
, , '

P P P w D i n S j n ij D n S n i D = = = = - - - 0 0 0 1 1 1 q q q F n n j S n t w P - - ( ) é ë ê ù û ú -( ) é ë ê ù û ú 1 1 1 × F ' , q
where P w w

t iD n j S n = -( ) ´( ) - - 1 1 1 F F ' '
. q q Given P D,i and P S,j , parameter sampling is identical to the additive model by regarding P D,i and P S,j as the data. We added this supplementary step to the TM program developed by A. Legarra (Institut National de la Recherche Agronomique-Station d'Amélioration Génétique des Animaux, Castanet-Tolosan, France, personal communication).

Illustrations

A study with 4 different simulated designs (Table 1) was performed to illustrate the feasibility of the product threshold model. The base population consisted of 60 unrelated sires and 200 or 2,000 unrelated dams without records. Sires were randomly mated to dams to generate 600 or 4,200 progeny. Dam (DBV) and sire (SBV) breeding values were generated using bivariate normal distributions with parameters corresponding to the designs shown in Table 1. Genetic values of the progeny were sampled as the mean of sire and dam genetic values plus the Mendelian sampling. Part of the progeny were randomly assigned to be females and have an unobserved direct phenotype (400 or 4000 individuals i), whereas the other part were considered to be males and have an associative unobserved phenotype (200 individuals j). The observed phenotypes, resulting from the association of individuals i and j, were generated according to the product threshold model. The underlying d and s values were generated for each couple using Eq. [1.4] and [1.5]. Two fixed effects were included in the model. The first effect f 1 was a crossclassified effect with 3 levels that affected direct and associative unobserved phenotypes. The second effect f 2 was a cross-classified effect with 2 levels affecting associative unobserved phenotypes only. The first 2 designs had perfectly balanced data: each of the 400 "female" individuals i was associated to each of the 200 "male" individuals j. The first design assumed a large ( variance for associative genetic effect; the second employed a very small (0.05) variance for the direct genetic effects. In the third design, there were unbalanced data (males were randomly mated with females) with a small variance for the direct genetic effect. In the fourth design, few observations per individual i were considered with moderate variances for direct and associative effects.

Each design was analyzed using 3 models: the product threshold model, the additive threshold model, and a multiple-trait threshold model, which considers P D * and P S * as observed phenotypes. Results obtained with the multiple-trait threshold model were a reference considered as the best parameter estimates (called best) that can be obtained. In practice, this third model cannot be applied to real data, because P D * and P S * are unobserved phenotypes.

For all models, the Gibbs sampler analysis was carried out using 1 chain consisting of 300,000 iterations. After discarding the first 30,000 iterations, samples of the parameters of interest were saved every 100 itera- tions. Flat priors were used for all parameters, and beginning values were randomly sampled.

RESULTS

Except for s A D 2 in design 2, genetic parameter estimates obtained with the product threshold model were in accordance with the simulated data (Table 2). Similar posterior means and credibility intervals were obtained with the multiple trait model (results not shown). In nearly all designs, heritability estimates obtained with the additive threshold model understated true values, whereas genetic correlation estimates aligned with those obtained with the product threshold model. Fixed effects were well estimated with the product threshold model but not with the additive one (Table 3). However, fixed effects in product and additive threshold models do not have the same interpretation and cannot be properly compared. Even if posterior means were similar, credibility intervals obtained for fixed effects with the product threshold model were 3 to 4 times larger than those obtained with the multiple trait model (results not shown).

Correlations between "best estimated" and predicted direct or associative breeding values were greater for the product threshold model than for the additive threshold model in all designs (Table 4). A plot between the "best" and estimated breeding values from the product threshold model did not show any trend, whereas the additive model underestimated the largest breeding values (Figure 3). Nevertheless, correlations between breeding values estimated with product and additive threshold models were high.

DISCUSSION

For studying reproduction results, we proposed the product threshold model, which supposes that a success for P * is observed when there is a success for P D * and P S * .

A similar approach has been proposed for modeling embryo implantation after in vitro fertilization in humans: the EU model [START_REF] Speirs | Analysis of the benefits and risks of multiple embryo transfer[END_REF], where E is the number of viable embryos and U is a binary indicator of uterine receptivity. [START_REF] Dukic | A hierarchical Bayesian approach to modeling embryo implantation following in vitro fertilization[END_REF] showed that in the extreme case where the number of embryos transferred is equal to one for all subjects, none of the model parameters is identifiable from observed data.

Our illustrations imply a similar situation where each female event is associated with a unique male event. Nevertheless, our results (with input parameters essentially recovered within high credibility regions) suggest that parameters are identifiable, at least under the conditions considered. In general, identification is very difficult to study in complex hierarchical models such as the one considered here. In any case, if proper priors are adapted for all parameters, this provides unambiguous Bayesian learning [START_REF] Carlin | Bayes and Empirical Bayes Methods for Data Analysis[END_REF]; Sorensen and [START_REF] Sorensen | Likelihood, Bayesian and MCMC Methods in Quantitative Genetics[END_REF]. However, it may be the case that the prior could always be influential, even for very large samples. An argument suggesting why we obtained good estimations of the parameters using flat priors is as follows. In the standard linear animal model, the genetic additive (a) and permanent environmental (p) effects cannot be disentangled from each other at the level of the conditional likelihood because only their sum is identified (an infinite number of values a and p produce the same sum). However, when all random effects are integrated out, the corresponding variance components can be identified in the marginal likelihood, provided their covariance matrices are not diagonal (due to the relationship matrix considered for the additive genetic effect). A similar reasoning holds in the product threshold model: at the level of the conditional likelihood, the probabilities Pr(P S = 1) and or estimated with the additive threshold and product threshold models for the different designs (credibility interval in brackets) Pr(P D = 1) are not identified because an infinite number of values yield the same product, Pr(P S = 1) × Pr(P D = 1). However, the explanatory structure in the probit link functions are distinct for the 2 components, and further, the "male" and "female" genetic effects have different covariance matrices. This led to parameter identification in the cases examined. In short, our illustration results suggest that identification was attained, even though improper priors were adopted for fixed effects and variance components.

The product threshold model was proposed for studying reproduction results under a double assumption: the observed phenotype is the product of 2 unobserved phenotypes and these unobserved events are conditionally independent. When events are not independent, In this case, expressing conditional probabilities as a function of genetic and environmental factors is not trivial and needs further investigations. On the other hand, it may be of interest to include a third unobserved phenotype affecting the reproduction result: the embryo survival effect. Even if, theoretically, the product threshold model can consider more than 2 unobserved phenotypes, including a third one could induce convergence problems. Actually, it is well known that the additive threshold model can produce biased estimates of parameters when the amount of data per level of fixed effect is small, known as the extreme category problem [START_REF] Misztal | Computing aspects of a nonlinear method of sire evaluation for categorical data[END_REF][START_REF] Moreno | On biased inferences about variance components in the binary threshold model[END_REF]. The risk of an extreme category problem is greater in the product threshold model, where the probabilities of success of the unobserved phenotypes are in essence greater than the probability of success of the observed phenotype. This problem increases as the number of unobserved phenotypes increases. Because P D * and P S * are unobservable, it does not seem possible to investigate a priori this kind of problem.

The illustrations aimed to investigate whether or not the product threshold model is feasible and to evaluate the importance of bias from fitting a (wrong) ad-ditive threshold model when observations come from a product threshold model. Even though different designs (balanced vs. unbalanced data; low, medium, or high variances; low vs. medium correlation; scant or considerable information per individual) were considered, these represent only a few of the many possible data scenarios. Due to heavy computing time requirement (2 wk per estimation), there were no replications of each design. Therefore, further investigations are needed to evaluate properties of the product threshold model. Nevertheless, we obtained similar results for simulations with some replications and fewer observations (8,000).

The product threshold model can extract more information from the data than the additive threshold model, provided that it holds. Also, it is able to estimate the effect of an environmental factor on either the direct or associative unobserved phenotypes, whereas the additive threshold model only allows estimating a global effect on the observed phenotype. Our results indicated that the additive threshold model tended to temper the effect of a factor by combining the effects on the direct and associative phenotype. The second level of had a slightly positive effect on the observed phenotype in comparison with its first level in the additive threshold model, whereas it had a positive effect on the direct phenotype and a negative one on the associative phenotype. Therefore, strategies for improving P * may be different in the 2 models. For instance, AI success declines with time in some species [START_REF] Mackey | Associations between genetic merit for milk production and animal parameters and the fertility performance of dairy cows[END_REF]. In species where fresh semen is used, a product model would estimate year effects on male and female fertility separately and then identify which sex is responsible for the decline. Subsequently, fertility research could be focused on this sex.

Discrepancy between best and predicted breeding values with the additive threshold model was especially marked for individuals with increased breeding values. Consequently, fitting an additive threshold model when data are generated under the product threshold model assumption would lead to a less effective evaluation of the best animals in the population. This issue requires additional study.

The objective of the study was to propose an alternative model to the additive threshold model for studying reproduction result in an animal genetics context to evaluate if estimation procedures can work well on this model and to evaluate if results obtained with this model differ from those obtained with the classical approach. Because parameters seem estimable, the next step of the analysis would be to compare the predictive ability of the 2 models on real data to provide validation of the product threshold model.

  , where A is the numerator relationship matrix and Ä represents the Kronecker product. The residuals ε are independent and identically distributed with variance s e 2 .

  to 2 underlying continuous variables, d and s, respectively. and T S are the threshold values for d and s, and distributional assumptions for the genetic effects are the same as in [1.2]. In addition, b D and b S are vectors of fixed effects, with incidence matrices X D and X S linking unobserved direct and associative phenotypes to fixed effects, respectively, and e e D S

  approximate transformation of these heritabilities to the observed scale (pscale) is obtained by multiplying each heritability by z 2 /{Pr(P * = 1)[1 -Pr(P * = 1)]}, where z is the ordinate of a standard normal distribution function correspond-

Figure 1 .

 1 Figure 1. Expected probability of success for a couple (i,j) under the assumption of the threshold additive model Pr( ) , * , , , ,

  to the unobserved phenotypes. P D,i and P S,j are sampled in the nth step of the Gibbs sampling from their joint conditional distribution.

  where the 3 first elements in β S corresponded to the effects of f 1 and the fourth and fifth to the effects of f 2 . Levels of the fixed effects were randomly assigned to each couple with equal probability for each level. We fixed s Values of T D and T S were fixed to 0 in all designs.

)

Figure 2 .

 2 Figure 2. Expected probability of success for a couple (i,j) under the assumption of the threshold product model Pr( ) , * , , , , P A E A E ij D i D i S j S j = = + ( ) ´+ ( ) 1 F F as a function of the direct value d D i

Figure 3 .

 3 Figure 3. Correlation between direct breeding value obtained with product and additive threshold models in design 1 (200 individuals i, 400 individuals j, balanced data, high direct genetic variance).

Table 1 .

 1 Description of simulated designs

	Item	Design 1	Design 2	Design 3	Design 4
	No. of dams	200	200	200	2,000
	No. of individuals i	400	400	400	4,000
	No. of individuals j	200	200	200	200
	No. of records	80,000	80,000	80,000	12,000
	2 s A D s A S 2	1.00 0.25	0.05 0.25	0.05 0.25	0.36 0.25
	r u u D S ( , )	0.30	0	0.30	0.30
	Type of design	Balanced	Balanced	Unbalanced	Unbalanced
	Pr(P D = 1) 1 Pr(P S = 1) 1 Pr(P = 1) 1	0.73 0.47 0.32	0.72 0.46 0.30	0.73 0.47 0.32	0.73 0.45 0.30

1

Probability computed using the simulated data.

Table 2 .

 2 Variance components estimated (posterior mean) with the additive and product threshold models for the different designs (credibility interval in brackets) 1

	Item	s A D 2	s A S 2	r a a D S ( , )	h D p scale ( -	)

Table 3 .

 3 Fixed effects (

	f 1	f 2	)

The authors thank the Ministère de l'Agriculture for supporting this study in the framework of a BELIA action, directed by the Association Nationale Insémination Ovine and Institut National de la Recherche Agronomique. The authors thank Wendy Brand-Williams for editing of the English language. The Midi-Pyrénées region is acknowledged for supporting D. Gianola as Chaire D'Excellence Pierre de

Fermat. 2 Corresponding author: Ingrid.David@toulouse.inra.fr ReceivedOctober 27, 2008. Accepted April 22, 2009.

at INRA Institut National de la Recherche Agronomique on August 2, 2013 www.journalofanimalscience.org Downloaded from

4,000 individuals i, 200 individuals j, unbalanced data.Product threshold model


Marielle Eyraud
email: marielle.eyraud@univ-provence.fr

G Jimenez-Cadena

C Chassigneux
email: carine.chassigneux@univ-provence.fr

F Vacandio

E Comini
email: comini@ing.unibs.it

G Sberveglieri
email: giorgio.sberveglieri@ing.unibs.it

T Djenizian
email: thierry.djenizian@univ-provence.fr

Electrochemical fabrication of oriented ZnO nanorods on TiO 2 nanotubes

Keywords: zinc oxide, titania nanotubes, composite nano-architectured electrode, electrochemical methods

We report the ability to use TiO 2 nanotube as a guide layer to achieve the vertical growth of ZnO nanorods, in additive-free bath. First, we focused on the anodisation conditions (cell voltage and anodisation time) to produce TiO 2 nanotube thin films grown from a 1.5 µm thick Ti layer sputtered onto Si. Highly organised titania nanotubes were obtained in glycerol viscous electrolyte. In a second step, the electrochemical growth of ZnO grains has been investigated from a zinc nitrate bath at 70°C on both Ti foil and TiO 2 nanotubes. ZnO deposition mechanism has been highlighted through the electrochemical experiments in conjunction with XRD technique and scanning electron microscopy (SEM) examinations. On Ti foils, we show that addition of additives is required to obtain a highly oriented nanostructured ZnO deposit. On TiO 2 nanotubes, additives are not necessary to obtain such a deposit: Titania nanotubes can be used to guide the vertical growth of hybrid nano-architectured ZnO/TiO 2 electrode.

Introduction

During the last decades, titanium dioxide (TiO 2 ) has become a very promising material because of multiple applications [START_REF] Diebold | The surface science of titanium dioxide[END_REF][START_REF] Shankar | Fabrication of nanowires of multicomponent oxides: Review of recent advances[END_REF]. Particularly, the different structures of TiO 2 have been successfully used for photocatalysis, gas sensing, Li batteries, electronic devices and solar cells [START_REF] Diebold | The surface science of titanium dioxide[END_REF][START_REF] Armstrong | TiO 2 -B nanowires as negative electrodes for rechargeable lithium batteries[END_REF][START_REF] Berger | High-efficiency conversion of sputtered Ti thin films into TiO 2 nanotubular layers[END_REF][START_REF] Francioso | TiO 2 nanowires array fabrication and gas sensing properties[END_REF][START_REF] Jitputti | Synthesis of TiO 2 nanowires and their photocatalytic activity for hydrogen evolution[END_REF][START_REF] Kitano | Recent developments in titanium oxide-based photocatalysts[END_REF][START_REF] Shiraishi | Selective organic transformations on titanium oxide-based photocatalysts[END_REF][START_REF] Su | Novel low humidity sensor made of TiO 2 nanowires/poly(2-acrylamido-2-methylpropane sulfonate) composite material film combined with quartz crystal microbalance[END_REF]. Although TiO 2 nanoparticles have been used for several applications, the electronic transportation phenomenon limits the efficiency of the material owing to the grain boundaries in the semiconductor. Recently, the use of one-dimensional nanostructures like nanowires and nanotubes has shown a significant improvement of the electronic transport. Moreover, nanotubes offer the option of heterogeneous materials [START_REF] Jiang | Low-temperature hydrothermal synthesis of flower-like ZnO microstructure and nanorod array on nanoporous TiO 2 film[END_REF][START_REF] Wang | Synthesis of ZnO/TiO 2 nanotube composite film by a two-step route[END_REF] opening new perspectives for the development of devices based on photocatalysis and photochemical properties.

With several advantages such as high reproducibility, low temperature operation and the ability to control accurately the size structures on various substrates [START_REF] Bestetti | Structure of nanotubular titanium oxide templates prepared by electrochemical anodization in H 2 SO 4 /HF solutions[END_REF][START_REF] Chen | Fabrication of 10 nm diameter TiO 2 nanotube arrays by titanium anodization[END_REF][START_REF] Choi | Anodization of nanoimprinted titanium: a comparison with formation of porous alumina[END_REF][START_REF] Tang | Preparation of TiO 2 nanotube on glass by anodization of Ti films at room temperature[END_REF][START_REF] Yu | Fabrication of nanostructured TiO 2 by anodization: A comparison between electrolytes and substrates[END_REF], the electrochemical approach is highly appreciated to fabricate 1D nanostructures. The first methods to grow nanostructured TiO 2 and selforganised TiO 2 nanotubes were based on simple anodisation procedures performed in acidic electrolytes containing fluoride ions [START_REF] Gong | Titanium oxide nanotube arrays prepared by anodic oxidation[END_REF][START_REF] Zwilling | Anodic oxidation of titanium and TA6V alloy in chromic media. An electrochemical approach[END_REF]. The nanotubes are formed as a result of a competition between the electrochemical growth and the selective chemical dissolution of the oxide layer [START_REF] Yasuda | Mechanistic aspects of the self-organization process for oxide nanotube formation on valve metals[END_REF]. Further progress was recently achieved on bulk Ti foils by using viscous electrolyte containing fluoride ions for which smoother tubes can be grown compared with viscous electrolyte [START_REF] Macak | Anodic growth of self-organized anodic TiO 2 nanotubes in viscous electrolytes[END_REF]. Very few works about electrochemical oxidation of Ti thin film in viscous electrolyte can be found [START_REF] Leclere | Tracer investigation of pore formation in anodic titania[END_REF].

Because of several remarkable properties [START_REF] Ge | Nanostructured ZnO: from monodisperse nanoparticles to nanorods[END_REF][START_REF] Kao | Low temperature solution-synthesis and photoluminescence properties of ZnO nanowires[END_REF][START_REF] Wang | The influence of orientation on the photoluminescence behavior of ZnO thin films obtained by chemical solution deposition[END_REF], ZnO is a II-VI semiconductor material widely used for many applications and particularly for the fabrication of photovoltaic devices. ZnO can be synthesised not only using template-based processing [START_REF] Wu | Controlled synthesis of ZnO nanowires or nanotubes via sol-gel template process[END_REF][START_REF] Zheng | Fabrication and optical properties of large-scale uniform zinc oxide nanowire arrays by one-step electrochemical deposition technique[END_REF], hydrothermal method [START_REF] Wang | Dye-sensitized solar cells based on oriented ZnO nanowire-covered TiO 2 nanoparticle composite film electrodes[END_REF], wet technique [START_REF] Vayssieres | Growth of arrayed nanorods and nanowires of ZnO from aqueous solutions[END_REF] and metal organic chemical vapour deposition [START_REF] Chen | Electrodeposited nanoporous ZnO films exhibiting enhanced performance in dye-sensitized solar cells[END_REF] but also by electrodeposition process. The one-step electrodeposition of ZnO films was first reported by Izaki and Omi [START_REF] Izaki | Transparent zinc oxide films prepared by electrochemical reaction[END_REF] using nitrate ions as oxygen precursor. More results have been reported by Pauporte and Lincot [START_REF] Pauporte | Heteroepitaxial electrodeposition of zinc oxide films on gallium nitride[END_REF], Peulon and Lincot [START_REF] Peulon | Mechanistic study of cathodic electrodeposition of zinc oxide and zinc hydroxychloride films from oxygenated aqueous zinc chloride solutions[END_REF] and Ramirez et al. [START_REF] Ramirez | Electrochemical growth of ZnO nanowires inside nanoporous alumina templates. A comparison with metallic Zn nanowires growth[END_REF] using dissolved oxygen at 70°C. The synthesis of ZnO nanowires has also been achieved by a template technique [START_REF] Zheng | Fabrication and optical properties of large-scale uniform zinc oxide nanowire arrays by one-step electrochemical deposition technique[END_REF][START_REF] Enculescu | Influence of geometrical properties on light emission of ZnO nanowires[END_REF]. This method consists of filling the pores of a nanoporous insulating membrane (typically anodic alumina or polycarbonate membranes) that can be subsequently removed after the electrodeposition process. Template-free strategies reported also the use of different additives to tailor the size and morphology of the electrodeposited ZnO crystallites [START_REF] Xu | Controllable morphology evolution of electrodeposited ZnO nano/micro-scale structures in aqueous solution[END_REF]. Among them, hexamethylenetetramine (HMT) seems to produce highly oriented ZnO rods. In a recent work of Welling et al. [START_REF] Wellings | Growth and characterisation of electrodepo sited ZnO thin films[END_REF], the influence of deposition potential on the crystallographic structure and transparency of ZnO film deposited on ITO has also been reported.

Both TiO 2 nanotubes and ZnO nanowires have been proposed separately for the fabrication of dye-sensitised solar cell (DSSC) [START_REF] Stergiopoulos | Dye-sensitized solar cells based on thick highly ordered TiO 2 nanotubes produced by controlled anodic oxidation in non-aqueous electrolytic media[END_REF][START_REF] Baxter | Dye-sensitized solar cells based on semiconductor morphologies with ZnO nanowires[END_REF] and photoelectrocatalytic applications. It has also been shown that the combination of TiO 2 and ZnO can improve the efficiency of solar cell [START_REF] Wang | Dye-sensitized solar cells based on oriented ZnO nanowire-covered TiO 2 nanoparticle composite film electrodes[END_REF][START_REF] Lee | TiO 2 nanotubes with a ZnO thin energy barrier for improved current efficiency of CdSe quantumdot-sensitized solar cells[END_REF] or photoelectrocatalytic activity [START_REF] Zhang | Preparation and photoelectrocatalytic activity of ZnO nanorods embedded in highly ordered TiO 2 nanotube arrays electrode for azo dye degradation[END_REF]. In these papers, TiO 2 films were obtained either as slurry spread on glass [START_REF] Wang | Dye-sensitized solar cells based on oriented ZnO nanowire-covered TiO 2 nanoparticle composite film electrodes[END_REF] or by anodisation in acid solutions containing fluoride ions [START_REF] Lee | TiO 2 nanotubes with a ZnO thin energy barrier for improved current efficiency of CdSe quantumdot-sensitized solar cells[END_REF][START_REF] Zhang | Preparation and photoelectrocatalytic activity of ZnO nanorods embedded in highly ordered TiO 2 nanotube arrays electrode for azo dye degradation[END_REF], whereas ZnO layers were deposited using a hydrothermal method with zinc nitrate solution containing HMT at 92°C for 24 h [START_REF] Wang | Dye-sensitized solar cells based on oriented ZnO nanowire-covered TiO 2 nanoparticle composite film electrodes[END_REF] or by successive ionic adsorption and reaction method [START_REF] Lee | TiO 2 nanotubes with a ZnO thin energy barrier for improved current efficiency of CdSe quantumdot-sensitized solar cells[END_REF] or cathodic deposition [START_REF] Zhang | Preparation and photoelectrocatalytic activity of ZnO nanorods embedded in highly ordered TiO 2 nanotube arrays electrode for azo dye degradation[END_REF]. However, the development of low-cost and weak energy consuming approaches has still to be considered to achieve the fabrication of such a tandem material.

In this paper, the fabrication of TiO 2 -ZnO hybrid nanomaterials is achieved by simply using a two-step electrochemical technique. Titania nanotubes were obtained from the anodisation of Ti thin film in a glycerol-containing electrolyte. The effects of applied potential and anodisation time upon the morphology of TiO 2 nanotubes have been analysed. Then, the electrochemical growth of ZnO rods on Ti foils and on TiO 2 nanotubes has been studied. In agreement with previous works recently reported in the case of tin nanowire [START_REF] Ortiz | A novel architectured negative electrode based on titania nanotube and iron oxide nanowire composites for Li-ion microbatteries[END_REF][START_REF] Ortiz | Nanoarchitectured TiO 2 /SnO: a future negative electrode for high power density li-ion microbatteries?[END_REF][START_REF] Ortiz | Nanocomposite electrode for Li-Ion microbatteries based on SnO on nanotubular titania matrix[END_REF][START_REF] Hanzu | Mechanistic study of Sn electrodeposition on TiO 2 nanotube layers: thermodynamics, kinetics, nucleation, and growth modes[END_REF][START_REF] Djenizian | Electrochemical fabrication of tin nanowires: a short review[END_REF], we show that the titania nanotubes could be used as a guide layer to activate the electrochemical growth of vertical ZnO nanomaterials.

Experimental

Titanium thin film on Si

First, Ti thin films were deposited on p-type Si (100) substrates with a resistivity of 1-10 Ω cm (Wafer World, Inc.). Before sputtering, Si samples were sonicated for 20 min alternatively in acetone, isopropanol and methanol, rinsed with deionised water and dried under argon stream. To remove the native oxide layer, the Si substrates were dipped in 1% HF solution during 30 s, then rinsed in deionised water, and dried under argon stream. Ti (99.99% purity) was the sputtering target and the base chamber pressure prior to deposition was kept below 10 -7 Torr. The Si substrates were not heated during the procedure. The high purely argon pressure and the target current during deposition were 6 × 10 -4 Torr and 150 mA, respectively. Under these conditions, the deposition rate was 12.5 nm/min. In this work, Ti layer of approximately 1.5 µm thick with a columnar morphology was obtained after two hours.

Titania nanotubes

Titania nanotubes were obtained from the anodisation of the Ti thin films at room temperature (~25°C) using a two-electrode configuration (Ti thin film as working electrode and a Pt grid as counter electrode). Glycerol (GPR Rectapur 24387.292) +1.3% NH4F (98% Aldrich 12125-01-8) +2% water served as viscous electrolyte. Different potentials were applied during 10 min using a potentiostat Parstat 2273 (EGG). The influence of the anodisation time at a constant applied potential on the growth of titania nanotubes was also checked. After anodisation, the samples were rinsed with deionised water and dried in argon stream.

Zinc oxide deposition

Zinc oxide deposition was first studied using voltammetric experiments in a three-electrode configuration. The equipment consisted in an EGG-PAR model 273 potentiostat-galvanostat. The working electrodes studied were Ti foil. A Pt grid was used as counter electrode and Ag-AgCl KCl saturated as reference electrode. The experiments were done at 70°C in an aqueous solution of Zn(NO 3 ) 2 (98% 10196-18-6 Sigma-Aldrich) 0.005 M with or without additive: HMT (C 6 H 12 N 4 99% 100-97-0 Aldrich) 0.005 M. The pH of the as-prepared solution was almost 5. From voltammetric study, some reduction potentials were chosen to obtain bulk ZnO deposits. The same procedure was carried out on TiO 2 nanotube layers to fabricate ZnO/TiO 2 hybrid nanomaterial.

Characterisations

Atomic Force Microscopy (AFM) measurements in contact mode (CP auto probe provided by Park Scientific Instrument) were performed on Ti thin film and Ti foil to assess the roughness of the surface. SEM images (Philips XL-30 FEG) were used to study the morphology of the titania nanotubes and ZnO deposits. XRD experiments (D5000 diffractometer, with Cu K α radiation) were performed to analyse the ZnO layer electrochemically grown directly onto Ti foil and titania nanotubes.

Results and discussion

Titania nanotubes

The roughness of the Ti layer has a strong influence on the morphology of the titania nanotubes. A decrease in roughness improves the quality of the nanotube arrays. The AFM image of sputtered Ti thin film before anodisation is shown in Figure 1(A). The deposit is homogeneous with a very low roughness (Rms = 2.6 nm) and an average size of Ti grains of around 60 nm. Compared with Ti foil substrate (Figure 1(B)), it is clearly apparent that the roughness is higher (Rms = 41 nm) and the Ti grain size is significantly larger (approximately 160 nm). To understand the influence of the applied potential on the morphology of the nanotubes, Ti thin films were anodised during 10 min in glycerol-containing electrolyte for potential ranging from 40 V to 90 V. From SEM images shown in Figure 2, the diameter of the nanotubes increases with increasing voltage. For an applied potential of 40, 60, 80 and 90 V, the corresponding diameter is around 35, 40, 60-90 and 60-90 nm, respectively. Then, the diameter is more homogeneous at low potential. It can be noted that the layer reveals the presence of cracks when the applied voltage is higher (Figure 2(D)) weakening the mechanical properties of the film. Then, the anodisation voltage has been assessed at 60 V. Cross-sectional SEM images were taken for several anodisation times (Figure 3). The rate of TiO 2 growth and Ti layer consumption was analysed for 0, 10, 20 and 40 min.

From Figure 3(A), the initial Ti layer presents a columnar structure with an initial thickness of 1.5 µm, which is consistent with previous work [START_REF] Premchand | Fabrication of self-organized TiO 2 nanotubes from columnar titanium thin films sputtered on semiconductor surfaces[END_REF]. Figure 3(B)-(D) depicts the cross-sectional views of anodised samples carrying vertical arrays of self-organised TiO 2 nanotubes. In agreement with the literature [START_REF] Macak | Anodic growth of self-organized anodic TiO 2 nanotubes in viscous electrolytes[END_REF], the tubes grown in glycerol-containing electrolyte are smoother with more homogeneous morphological properties than those obtained in very similar conditions by our group in aqueous electrolyte [START_REF] Premchand | Fabrication of self-organized TiO 2 nanotubes from columnar titanium thin films sputtered on semiconductor surfaces[END_REF]. For anodisation time below 10 min, the rate of TiO 2 growth is approximately 150 nm/min. Then, the titania growth rate is found to be 40-50 nm/min after 10 min of anodisation. The rate of Ti consumption was about 40 nm/min and shows also a decrease until 10 nm/min. The dependence of the thickness vs. time (Figure 4) suggests a first-order reaction dependent on the Ti concentration.

ZnO deposition on Ti foil

The electrochemical formation mechanism of ZnO is known to be initiated by the reduction of nitrate ions that produced hydroxide, followed by the precipitation of Zn(OH) 2 . The conversion of Zn(OH) 2 into ZnO occurs in an ultimate step owing to the temperature effect [START_REF] Izaki | Transparent zinc oxide films prepared by electrochemical reaction[END_REF][START_REF] Enculescu | Influence of geometrical properties on light emission of ZnO nanowires[END_REF]. The sequence of the ZnO deposition can be summarised by the following equations:

3 2 2 NO H O + 2e NO 2OH - - - - + → + 2 2
Zn 2OH Zn(OH)

+ - + → 2 2

Zn(OH) ZnO H O → +

To highlight the deposition mechanism involved, voltammograms were performed on Ti electrode from zinc nitrate containing solution with and without additive (Figure 5). The reduction processes obtained are very different. In the additive-free electrolyte, a single increase in current occurs for a cathodic potential lower than -1 V (zone 2 in Figure 5). In the presence of additive, there are two reduction potential zones: the first (zone 1) shows an increase in current followed by a current plateau between -0.8 V and -1 V that indicates a diffusion control process. The second (zone 2) corresponds to that obtained without additive. The examination of the potential values reveals that only the reduction of nitrate to nitrite ions can occur in zone 1 but this reaction is not favourable in an energetic point of view because of the reduction of anion on a cathodic electrode (negative surface). The two other reactions can take place only in zone 2.

Polarisations of Ti electrode were then performed at -0.9 V (zone 1) and -1.1 V (zone 2), during 3 min from both solutions. The SEM images obtained without additive are shown in Figure 6(A) and (B), whereas Figure 6(C) and (D) are obtained from additive-containing solution. In accordance with the voltammetric study, no deposit can be observed in Figure 6(A) confirming that the reduction of nitrate ions and then the precipitation of ZnO can only arise at a more cathodic applied potential. Actually, in Figure 6(B) spherical grains with a quite homogeneous size of about 300 nm in diameter appear at -1.1 V. The Energy Dispersive X-Ray Spectrum given in Figure 7 shows the presence of Ti, Zn and O elements. When HMT is added to the solution, some sticks lying on the Ti surface appear for a potential value of -0.9 V (Figure 6

(C)).

By increasing the cathodic applied potential (Figure 6(D)), a significant deposit is obtained while the shape of the grains is remained unchanged.

XRD analysis performed on deposits carried out at -1.1 V from both solutions is given in Figure 8. The experimental diffractograms were compared with the powder standard JCPDS (vertical line on the figure) of ZnO hexagonal würtzite phase (JCPDS File No: 00-036-1451) and the hexagonally closed packed structure of α-Ti (JCPDS File No: 44-1294) corresponding to the remaining Ti layer. In both cases, three peaks attributed to the ZnO structure are identified. Without additive (Figure 8(A)), no preferential orientation appears, the relative intensity of the peaks is in the same order than the values corresponding to the ZnO JCPDF files: [101] > [100] > [002]. From crystallites grown in the additive-containing solution, the [002] intensity is slightly higher than the [101] showing a preferential orientation in the c axis direction.

Combining the SEM and XRD analysis carried out on the bulk deposits with the voltammograms obtained in Figure 5, we assume that the current obtained in zone 2 is related to nitrate ions and proton reduction responsible for the ZnO formation. No metallic Zn deposit owing to the Zn 2+ reduction could be obtained in this part of the curve, which is not in agreement with results reported in reference [START_REF] Wellings | Growth and characterisation of electrodepo sited ZnO thin films[END_REF]. From additive-containing solution, the current plateau obtained in zone 1 can be related to the reduction of nitrate ions, which is enhanced by the presence of the additive. Otherwise, HMT is also added to chemical bath as precursor at high temperature (higher than 80°C during several hours) [START_REF] Xu | Controllable morphology evolution of electrodeposited ZnO nano/micro-scale structures in aqueous solution[END_REF][START_REF] Yang | Well-aligned ZnO rod arrays grown on glass substrate from aqueous solution[END_REF]. In this case, the chemical decomposition of HMT into ammonia can also lead to the formation of ZnO crystals according to the following reactions [START_REF] Vernardou | The effect of growth time on the morphology of ZnO structures deposited on Si (100) by the aqueous chemical growth technique[END_REF]:

(CH 2 ) 6 N 4 + 6H 2 O → 6HCHO + 4NH 3 NH 3 + H 2 O → NH 4 + + OH Zn 2+ + 2OH -→ Zn(OH) 2 Zn(OH) 2 → ZnO + H 2 O
However, the decomposition of HMT cannot be responsible for the current recorded on the voltammogram (only chemical reactions are involved), nor to the deposit obtained at -0.9 V in Figure 6(C) (temperature and duration are not sufficiently high). The accelerating effect owing to the HMT observed from both voltammetric study and SEM images can be related to an ion pairing mechanism, which has been already described by Franklin et al. [START_REF] Franklin | Ion-pairing as a mechanism of action of additives in electrodeposition[END_REF]. This kind of ion pairing effect occurring for quaternary ammonium salts is expected to lower the energy barrier for adsorption of negatively charged species ( 3NOin our case) onto the surface of the cathode.

ZnO deposition on TiO 2 nanotube arrays

The effect of the TiO 2 nanotube arrays on the ZnO deposition mechanism was firstly checked by voltammetry in a 0.005 M zinc nitrate solution (Figure 9). We can note that on TiO 2 , the reduction of nitrate ions gives rise to larger cathodic currents.

In addition, the onset potential reaction on TiO 2 is found at -0.7 V, which is a lower cathodic potential than that obtained for Ti. This result demonstrates that the reduction reaction of nitrate ions on TiO 2 is thermodynamically enhanced. As a consequence, the precipitation of ZnO is enhanced too. The beneficial effect of TiO 2 may be due to the nature of the substrate as the strong increase in the surface owing to nanostructuring.

ZnO grains were deposited directly on both Ti thin film and titania nanotubes described in Figure 2(B). Potentiostatic experiments were carried out at 70ºC in aqueous solution 0.005 M Zn(NO 3 ) 2 , by applying -1.1 V/SCE during 10 min (Figure 10). Clearly, the morphology of ZnO is strongly influenced by the nature of the substrate. The presence of the nanotubes leads to vertically oriented and densely packed grains showing a wire shape with an average diameter size of 250 nm (Figure 10(C) and (D)). For comparison, ZnO grains exhibit a globular structure without any orientation and an average size of 500 nm when deposition on performed on Ti substrate (Figure 10(A) and (B)). The ZnO surface structuration obtained on TiO 2 nanotubes is significantly higher than that obtained from the additive-containing bath on Ti substrate. As it has been found in the previous work [START_REF] Hanzu | Mechanistic study of Sn electrodeposition on TiO 2 nanotube layers: thermodynamics, kinetics, nucleation, and growth modes[END_REF], the presence of nanotubes can modify the morphology of the electrodeposited layer and enhance the formation of vertical grains owing to a preferred orientation growth mechanism. The influence of deposition time on the ZnO structure has also been studied. Figure 12(A) and (B) shows SEM images of ZnO grains grown onto nanotubes for 5 and 15 min. The corresponding cross-sectional images tilted at 30° are given in Figure 12(C) and (D). Clearly, the length of the ZnO grains increases with the deposition time while the diameter size is not modified (around 250 nm). The length of the particles is ranging from 500 nm to 800 nm after 5 min of deposition and from 1.2 µm to 1.9 µm after 15 min. It can be noted that the number of grains increases with increasing deposition time suggesting that a progressive growth mechanism is involved if nucleation occurs at the top surface of the nanotubes.

Conclusions

The electrochemical formation of ZnO crystallites has been studied using voltammetry. The effect of HMT was determined and the growth potential condition was optimised to obtain ZnO-oriented structure on Ti foil. ZnO rods have been also electrochemically deposited onto TiO 2 nanotubes grown from anodisation of Ti thin films. Besides the fact that titania nanotubes can be fabricated from a Ti thin film in a glycerol-containing electrolyte, we demonstrated that the presence of the nanotubes can promote the wire-like shape of the ZnO grains. The simple procedure described in this work to achieve the fabrication of hybrid ZnO rods/titania nanotubes can be of potential interest for sensors, photovoltaics or photoelectrocatalytic applications.

Figure 1

 1 Figure 1 AFM images of (A) sputtered Ti thin film on Si and (B) Ti foil

Figure 2

 2 Figure 2 SEM images of Ti thin film anodised during 10 min in glycerol-containing electrolyte at applied potential of 40V (A) 60V (B), 80 V (C) and 90V (D)

Figure 3 Figure 4

 34 Figure 3 Cross-sectional SEM images of Ti thin films before anodisation in glycerol-containing electrolyte (A) and after potentiostatic experiments by applying a potential of 60 V during 10 min (B), 20 min (C) and 40 min (D)

Figure 5 2 NO

 52 Figure 5 Voltammograms on Ti foil from zinc nitrate (0.005 M) + 0.005 M HMT electrolyte at 70°C (see online version for colours)

Figure 6 Figure 7 Figure 8

 678 Figure 6 SEM surface images obtained after the polarisation of Ti electrode during 3 min, from a 0.005 M zinc nitrate solution without additive (A) and (B) and with 0.005 M HMT (C) and (D) at different potentials

Figure 9 Figure 10

 910 Figure 9 Voltammograms from zinc nitrate (0.005M) electrolyte at 70°C on Ti substrate and on TiO 2 nanotube arrays

Figure 11 X

 11 Figure 11 X-ray diffraction pattern performed on ZnO deposit on TiO 2 nanotubes corresponding to sample in Figure 10(C), showing the hexagonal ZnO phase and the preferred orientation of ZnO grains (see online version for colours)

Figure 12

 12 Figure 12 ZnO deposited on titania nanotubes by applying -1.1 V/SCE during 5 min (A) and 15 min (B). The corresponding cross sections are shown in (C) and (D), respectively


Florence Vacandio
email: florence.vacandio@univ-provence.fr

Marielle Eyraud

Philippe Knauth

Thierry Djenizian

Tunable electrical properties of self-organized zirconia nanotubes

Keywords:

Structural and electrical properties of self-organized zirconia nanotube layers can be tuned by a simple thermal treatment. The effect of F on the electrical conductivity of the MO x nanotubes grown by anodization in fluoride-containing electrolytes is demonstrated.

Introduction

Zirconia is known to have remarkable properties and to be an electrical insulator which can become a pure ionic conductor if doped (Y 2 O 3 , Gd 2 O 3 …) [1,2]. This leads to technological applications such as industrial catalysts and catalyst supports [3], oxygen sensors [4], solid electrolyte fuel cells (SOFC) [5]. Pure zirconia can be found in three crystallographic structures: monoclinic until 1170 °C, tetragonal between 1170 °C and 2370 °C and cubic above 2370 °C. However, only the tetragonal phase gives ceramics with satisfying mechanical properties. This phase can be stabilized at room temperature by doping with bivalent or trivalent cations, especially by yttrium. During the last decades, the use of porous materials has attracted attention in various domains and particularly in the field of energy. Porous materials have the advantage of large specific surface that can increase the performances of the materials while reducing the size and weigth of the components. A possible way to grow highly-ordered nanostructures is the anodization of valve metals such as Ti [6,7], Hf [8], Zr [9][10][11][12][13][14][15][16] in fluoride-containing electrolytes. Most of these nanostructured oxides are obtained by anodization of metallic foils, which limits their application in functional microdevices. An interesting alternative opening the path towards a wide range of applications is the anodization of thin films. Thus, in previous work, we have reported the synthesis of self-organized TiO 2 nanotubes from sputtered Ti thin layers deposited on Si [17][18][19][20][21][22][23][24].

In this paper, we report the fabrication of ZrO 2 nanotubes (ZrO 2 nt) by anodization of thin layers of Zr deposited by cathodic sputtering on Si substrates. We study the influence of annealing upon the morphological, structural and electrical properties of nanotubes by Scanning Electron Microscopy (SEM), Energy Dispersive Spectrocopy (EDS), X-ray Diffraction (XRD) and Electrochemical Impedance Spectrocopy (EIS) measurements.

Experimental section

Zirconium thin films were deposited by cathodic sputtering using a DC triode system on Si substrates (4 × 4 cm 2 ) prepared from p-type Si (100) wafers with a resistivity of 1-10 Ω.cm (Wafer World, Inc.). In order to remove the native oxide layer, the Si samples were dipped in 1% HF solution for 30 s, then rinsed in deionized (DI) water and dried under a nitrogen stream before being introduced into the chamber. A Zr metal disk (nominal purity 99.9%, diameter 5 cm) was the sputtering target and the base chamber pressure prior to depositions was kept as low as 10 -7 mbar. The high-purity argon pressure and the target current during deposition were maintained at constant values of 7.10 -4 mbar and 150 mA, respectively. Under these conditions, the deposition rate was 16 nm min -1 and a 2.6 μm thick Zr film was obtained after 120 min. Zirconium layers were anodized at room temperature at 40 V during 10 min with a conventional twoelectrode configuration, using an EG&G PARSTAT 2273 potentiostat/ galvanostat. A platinum grid was used as counter electrode. The electrodes were immersed in a 0.35 M NH 4 F, 5% vol. water and glycerol electrolyte.

Impedance measurements were performed in a 1 M (NH 4 ) 2 SO 4 solution with in addition to the previous configuration a reference Calomel Saturated Electrode (ECS), using a Potentiostat-Galvanostat coupled with a Frequency Response Analyser (Solartron 1287 and 1260). Impedance diagrams were recorded at open circuit potential, with a signal amplitude of 20 mV and a frequency range starting from 100 kHz to 10 mHz. Samples were analyzed by X-Ray Diffraction (XRD) with CuKα radiation (λ = 0.15406 nm) using a Siemens D5000 diffractometer; the processing software is BRUKER Diffrac-eva. Scanning Electron Microscopy (SEM) observations were performed using a Philips XL 30 ESEM equipped with an energy-dispersive X-Ray spectrometer (EDS).

Results and discussion

The SEM images (Figs. 1 and2) show the morphology of the selforganized zirconia nanotubes before and after annealing at 450 °C during 3 h in air. The as-formed porous layer exhibits an uniform and ordered nanotube arrangement. The diameters of the ZrO 2 tubes are around 25-30 nm and the wall thickness is estimated to be approximately 5 nm. The examination of the SEM cross-section (not shown) reveals that the thickness of the ZrO 2 nt layer is about 2.1 μm. Additionally, the presence of a remaining zirconium layer of about 0.8 μm indicates a thickness increase of 11.5% as the thickness of the sputtered zirconium layer was 2.6 μm. After the thermal treatment, it can be noticed that the nanoporous matrix does not collapse and is not damaged (no fissure or crack can be seen by SEM). Although a fraction of the tubes are plugged, it is remarkable that the morphology as well as the dimensions of the nanotubes are still preserved.

The corresponding Energy Dispersive X-Ray Spectroscopy (EDS) spectra exhibit two peaks relative to Zr and O. However, as-prepared ZrO 2 nt shows a peak attributed to the presence of F in the oxide matrix. Insertion of F is supposed to take place during the anodization process through the decomposition of the F-containing electrolyte leading to the probable formation of a thin ZrF 4 layer embedding the external surface of the nanotubes. The formation of such a thin layer has been reported in the case of the electrochemical fabrication of titania nanotubes [25]. Another scenario for the incorporation of F could also be substitution of an oxygen atom by a fluorine atom in the oxide bulk near the surface. After annealing, the absence of the peak corresponding to fluorine suggests that it might evaporate as HF during the thermal treatment.

In Fig. 3 are presented the XRD patterns of the as-prepared and annealed ZrO 2 nt layers. The pattern for non-annealed sample shows the presence of a small peak at 2θ = 34.9°relative to the residual layer of hexagonal zirconium (JCPDS file N°005-0665). Four peaks located at 2θ = 28.3; 31.5; 34.5 and 51.1 are attributed to the ZrO 2 monoclinic phase (JCPDS File No 037-1484) and one peak at 2θ = 50.6 to the tetragonal phase (JCPDS File No 050-1089). After annealing, both monoclinic and tetragonal phases are still detected, but two additional intense peaks corresponding to the tetragonal modification appear revealing an increased proportion of tetragonal phase. This result shows that a simple annealing treatment can promote the phase that is known to exhibit good mechanical properties [26].

Electrical properties of ZrO 2 nt before and after annealing were investigated by Electrochemical Impedance Spectroscopy (Fig. 4). The modulus of the impedance at high frequency is a good approximation of the resistance of the layer. The impedance modulus at low frequency is equal to 1.7 10 5 Ω.cm 2 for the as-formed ZrO 2 nt layer and equal to 3.10 8 Ω.cm 2 after annealing. While the insulating behaviour of the annealed ZrO 2 nt layer is comparable to pure zirconia reported in literature, the unexpected semiconductor behaviour observed before annealing can be explained by the presence of fluorine in the structure. Indeed, the insertion of fluorine ions occupying oxygen ion sites is responsible for the generation of excess electrons, as described in Kröger-Vink notation:

O O + F = OO 2 + F ∘ O + e ′ ð1Þ
Thus, fluoride ions incorporated into zirconia nanotubes have a strong effect on the electrical properties, enhancing n-type conductivity. In contrary, the annealing in oxygen-containing atmosphere removes both F and electrons in ZrO 2 nt, as can be immediately concluded by reversing eq. ( 1). Clearly, the electrical conductivity of ZrO 2 nt decreases drastically when fluorine is removed from the structure. This is the first evidence of the direct effect of F -upon the electrical properties of MO x nanotubes prepared by electrochemical techniques. So far, this effect has been hidden by the intrinsic electrical behaviour of the studied materials; this is especially the case for TiO 2 nt that remains semiconducting. More generally, the results presented in this work demonstrate that the electrical properties of MO x nt layers formed by anodization in fluoride-containing electrolytes could be tuned by an appropriate thermal treatment.

O Zr

Conclusion

Electrochemical fabrication of zirconia nanotube thin films is described in fluoride-containing electrolyte. The annealing at 450 °C during 3 h in air does not affect the nanotubular morphology, but changes drastically the structural and electrical properties. Indeed, thermal treatment leads to an increase of the proportion of tetragonal phase, which is the most interesting due to the good mechanical properties. More remarkably, the electrical conductivity of the ZrO 2 nt layer can be also turned from semiconductor to insulator after fluorine removal. This is the first evidence of the effect of F on the electrical properties of MO x nanotubes fabricated by anodization of fluoridecontaining electrolytes.

Fig. 1 .

 1 Fig. 1. SEM observation and EDS analysis of as-formed ZrO 2 nt.

Fig. 2 .Fig. 3 .

 23 Fig. 2. SEM observation and EDS analysis of ZrO 2 nt after annealing.

Fig. 4 .

 4 Fig. 4. Electrochemical impedance spectra of ZrO 2 nt before and after annealing.