Dmytro Dedovets

Sylvain Deville
email: sylvain.deville@saint-gobain.com

Multiphase imaging of freezing particle suspensions by confocal microscopy

Multiphase imaging of freezing particle suspensions by confocal microscopy

I. INTRODUCTION

Ice-templating is a well-established processing route for porous materials in materials science in general [START_REF] Zou | Ultralight multiwalled carbon nanotube aerogel[END_REF][START_REF] Ahmed | Hierarchically porous silica monoliths with tuneable morphology, porosity, and mechanical stability[END_REF][START_REF] Qiu | Biomimetic superelastic graphene-based cellular monoliths[END_REF][START_REF] Walter | A novel approach for the fabrication of carbon nanofibre/ceramic porous structures[END_REF][START_REF] Pawelec | Ice-templated structures for biomedical tissue repair: From physics to final scaffolds[END_REF][START_REF] Naviroj | Directionally aligned macroporous SiOC via freeze casting of preceramic polymers[END_REF] and in ceramics in particular [START_REF] Tang | Fabrication of lamellar porous alumina with axisymmetric structure by directional solidification with applied electric and magnetic fields[END_REF][START_REF] Ferraro | SiC porous structures obtained with innovative shaping technologies[END_REF][START_REF] Rachadel | A novel route for manufacturing asymmetric BSCF-based perovskite structures by a combined tape and freeze casting method[END_REF]. Hundreds of papers are now published every year on the topic, and the structural or functional properties of ice-templated materials are systematically explored [START_REF] Deville | Properties and Applications of Ice-Templated Materials[END_REF]. Although a considerable number of applications have been proposed, moving ice-templating from the lab towards industrial applications will depend, to a large extent, of our ability to finely understand and control the process to ensure reproducible, reliable architectures.

Ice-templating is based on the segregation of matter by growing crystals, which can then be concentrated between the later. Removal of the ice-whereby "ice" is a generic term for crystals grown from the solvent-provides a macroporous scaffold where the pores are a replica of the ice crystals, and the organization of particles in the scaffold is obtained during freezing. The structure of ice-templated materials, and thus their properties, are therefore largely controlled by the phenomena that takes place during freezing.

A lot of attention has thus been paid to in situ observations of the freezing of particle suspensions. Several techniques have been proposed, each having its advantages and limitations [START_REF] Deville | Investigating the Freezing of Colloids: Experimental Techniques to Probe Solidification Patterns, Crystal Growth, and Particle Movement[END_REF]. Most of what we understand from the interactions of particles with growing crystals have been obtained by optical microscopy [START_REF] Körber | Phenomena at the advancing ice-liquid interface: solutes, particles and biological cells[END_REF][START_REF] Saint-Michel | Interaction of Multiple Particles with a Solidification Front: From Compacted Particle Layer to Particle Trapping[END_REF]. However, it only provides 2D observations, and the spatial resolution is not sufficient when small particles are used. Xray imaging can provide 3D reconstruction of the grown [START_REF] Deville | In Situ X-Ray Radiography and Tomography Observations of the Solidification of Aqueous Alumina Particle Suspensions-Part I: Initial Instants[END_REF][START_REF] Delattre | Unidirectional Freezing of Ceramic Suspensions: In Situ X-ray Investigation of the Effects of Additives[END_REF] or growing [START_REF] Deville | Time-lapse, three-dimensional in situ imaging of ice crystal growth in a colloidal silica suspension[END_REF] crystals. However, its spatial resolution is not sufficient either to image particles. Artifacts induced by the beam are also still problematic [START_REF] Deville | Time-lapse, three-dimensional in situ imaging of ice crystal growth in a colloidal silica suspension[END_REF]. Transmission electron microscopy has also been used [START_REF] Tai | In situ cryogenic transmission electron microscopy for characterizing the evolution of solidifying water ice in colloidal systems[END_REF] but does not provide 3D observations, and is not appropriate for systematic experiments. As the sample is fixed and of small dimensions, only a few interactions events can be imaged.

In absence of appropriate experimental observations, efforts have been put in modelling the redistribution of particles by growing crystals. Discrete elements modelling, in particular, provided numerous insights into the physics of ice-templating. The role of the growth rate of the crystals on the ordering of monodispersed spherical particles [START_REF] Barr | Structural properties of materials created through freeze casting[END_REF] or the alignment of anisotropic (platelets) particles [START_REF] Bouville | Self-assembly of faceted particles triggered by a moving ice front[END_REF], was assessed. These results can be used experimentally to produce a variety of materials with controlled microstructures and functional or structural properties [START_REF] Kim | Honeycomb Monolith-Structured Silica with Highly Ordered, Three-Dimensionally Interconnected Macroporous Walls[END_REF]. Further progress in our understanding now depends on in situ observations of these phenomena.

Ideally, we need thus a technique able to image in situ and without artifacts the growth of ice crystals and the redistribution of particles, as well as the later stages of freezing when ice invades the pores between concentrated particles. We recently demonstrated how confocal microscopy could be used to image in situ in 3D the growth of ice crystals [START_REF] Marcellini | Situ Imaging of Ice Crystal Growth Using Confocal Microscopy[END_REF]. Here we built on this preliminary work and show that particles can also be imaged during freezing.

We developed a cooling stage that provides an independent control of the temperature gradient and the growth rate of the ice crystals, making systematic investigations possible.

In this paper, we demonstrate the benefits of this approach to investigate the physics of ice-templating.

II. METHODS

We used 2 µm diameter PMMA/TEFMA particles, marked in fluorescence with Pyrromethene 546 (emission wavelength: 519 nm). The fluorescent dye (Sulforhodamine B) is dissolved in water at 10 -4 M . The suspensions were then prepared by incorporating 1 vol.% of particles in this aqueous solution. The particle concentration is lower than that typically used in ice-templating (5-40 vol.%) because we cannot properly image a volume if the particle concentration is too high, because of light scattering. Using index-matched particles would be more ideal for imaging, but this means not using pure water as index matching is usually obtained in water/DMSO systems. We prefer to use suspensions which formulation (aqueous) is close to that of ice-templating. The suspensions were sonicated in an ultrasound bath for a few minutes to ensure a good dispersion of the particles. A few suspensions were prepared by dissolving 1 wt.% of PVA (POLYVIOL SOLUTION LL 2830, 25%) in the suspension.

We developed a cooling stage to perform in situ freezing experiments under the confocal microscope. The setup (Fig. 1) is composed of two Peltier modules that provide a constant temperature gradient in the gap d between them. The particle suspension is introduced in a Hele-Shaw cell made of two glass slides, separated by two stripes of double-side sticky tape which act as spacers to ensure a constant sample thickness of 100 µm. The sample is sealed on both sides. This assembly is translated along the x-axis through the temperature gradient at a constant velocity V by a stepper motor (Micos Pollux Drive stepper motor with VT-80 translation stage (PI, USA)). Because the sample is thin (100 µm), thermal equilibrium is achieved in the range of growth rate investigated here (1-50 µm/s); the solidification front is thus at a constant position in the observation frame. We can therefore vary independently the solidification front velocity (adjusted by the stepper motor) and the temperature gradient (established by the Peltier modules).

Confocal imaging is achieved by two different fluorophores: the dye incorporated in the particles, and a second dye (Sulforhodamine B) dissolved in water at 10 -4 M , which fluoresces at 586 nm. Experiments performed with and without Sulforhodamine B revealed that it has no noticeable impact on the freezing behavior of the system [START_REF] Dedovets | Freezing Emulsions[END_REF]. Images are acquired through two photodetectors, operating at the respective emission wavelengths of the dyes.

For image acquisition, we used long working distance non-immersive objectives (Leica HC PL APO 20x/0.70 CS and 10x/0.40 CS2) to minimize the effect of the microscope thermal mass on the freezing process. These objectives have free working distances of 0.59 mm and 2.2 mm respectively.

In a typical experiment, the sample is put in place on top of the Peltier elements, thermal insulation is achieved by covering the sample with a piece of polyurethane foam. A hole in the foam let the objective come in close contact to the sample. The desired temperature gradient ∆T is established by setting the temperatures of Peltier elements and the sample is then put in motion by the stepper motor. The interface velocity stabilizes within a minute after the beginning of the sample translation. The temperature gradient was varied from Depending on the experiments and features investigated, 2D or 3D images were acquired.

Image reconstruction was done with Fiji (ImageJ 1.51h) [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF].

III. RESULTS AND DISCUSSION

The benefits of confocal microscopy to investigate the ice growth and the segregation of particles in a suspension are four-fold:

• we can image individual particles. It is thus possible track the dynamics and organization of particles during and after freezing.

• because the dye is expelled from the growing ice, we can easily discriminate between the water and the ice phases on the images. We can thus image simultaneously the particles, the water, and the ice.

• because of the rapid imaging mode of the microscope, we can image the process in 2D at a rapid time resolution: up to 40 Hz at 512 × 512 pixels. We can thus take snapshots of the solidification microstructures even at fast growth velocities (up to 40 µm/s here.)

• we can use the confocal mode to reconstruct the 3D solidification microstructures. Such combinations provide unprecedented insights into the phenomenon investigated here, as we demonstrate below.

Particle-scale observations

The observation of a partially-frozen structure (Fig. 2) already provides a fresh look at the organization of particles and the late stages of freezing. Elongated regions of concentrated particles, typically encountered in ice-templated materials, can be observed between the crystals. The directionality of growth induced a directional segregation pattern.

If most of the particle reorganization took place here between adjacent ice crystals, some of the particles were also segregated between the crystal and the lower glass slide, resulting in the particle monolayer regions seen for instance in the insets B and C of Fig. 2. Although this is just a boundary limit effect, it provides an ideal configuration to investigate the penetration of ice in the dense packing of particles. Several configurations, highlighted by the different insets can be observed. In inset A, isolated particles were engulfed by the growing crystals.

We could not find evidence of a liquid film around these particles. Although a premelted film is probably still present [START_REF] Dash | The premelting of ice and its environmental consequences[END_REF][START_REF] Wettlaufer | Premelting Dynamics[END_REF], its expected thickness (a few nm) makes it too small to be observable by confocal microscopy. Inset B shows a partially frozen region. Local defects in particle packing can be observed, resulting in pores of different sizes between the particles. The pores between closely packed particles still contain liquid water (as seen by the fluorescence of the dye), while the water in the larger pores is frozen (no fluorescence visible anymore). This observation can be explained by the Gibbs-Thomson depression of the freezing point. The ice entry temperature is lower as the pore size diminishes [START_REF] Wettlaufer | Ice surfaces: macroscopic effects of microscopic structure[END_REF][START_REF] Liu | Measurement of freezing point depression of water in glass capillaries and the associated ice front shape[END_REF]. In inset C, which corresponds to a region at a lower temperature, pore ice can be observed in a densely-packed region. The upper part of the inset is mostly liquid, while the lower part is mostly frozen. The local temperature is therefore probably close to the ice entry temperature for the pore size that corresponds to the close packing of particles. The same behavior can be observed in isolated 3D agglomerates of particles (inset D). A group of particles were concentrated and engulfed by the ice, forming a small agglomerate. The fluorescence signal clearly indicates that liquid water is still present in the agglomerate. However, some particles were also engulfed by the growing crystals without being concentrated. The particles are therefore isolated in the ice in the frozen structure. Such particles would not be observed if subsequent freeze-drying and sintering was performed, as they would just randomly fall into the structure upon removal of the ice. In situ observations of the frozen structures are therefore required to identify them. This means that the segregation of particles by the growing crystals is not 100% efficient. Such behavior was not reported before, and knowing about it is important as this could affect the ice-templated microstructures.

An increase of the growth rate to 40 µm/s (for the same temperature gradient) enhances this behavior (Fig. 3). We can observe that the fraction of isolated, engulfed particles is increased. This can be explained by two phenomena:

• the increase of the growth rate favors the engulfment of particles. The rejection or engulfment of the particles by the freeze front is governed by the force balance on the particles [START_REF] Rempel | Particle trapping at an advancing solidification front with interfacial-curvature effects[END_REF]. In its most simple description, the force balance takes into account the viscous drag on the particle (exerted by the flux of water towards the interface) and the intermolecular interactions between the solidification front and the particle.

When the drag is greater than the intermolecular interactions, the particle is engulfed by the front. There is therefore a critical velocity for engulfment at a given particle size or, conversely, a critical particle size at a given freeze front velocity. However, the particle-particle interactions modify the force balance, and favors the engulfment. In a concentrated system like here, the critical velocity for engulfment is therefore lower than for isolated particles. The most important aspect here is that the concentration of particles at the tip of the crystals will favor their engulfment.

• the increase of the growth rate destabilizes the interface, as illustrated later in the paper (see Fig. 7). Local variations of the ice growth velocity favors the engulfment of isolated particles.

Further work is now required to investigate the dependency of this phenomenon upon the freezing conditions (particle concentration, growth rate, temperature gradient).

Particle organization induced by ice growth

The understanding and control of the organization of particles or more generally objects induced by the growth of crystal is a central question in solidification studies [START_REF] Deville | Freezing Colloids: Natural and Technological Occurrences[END_REF]. In partic- ular, it is necessary to understand how the ordering, packing, and orientation of particles is related to the freezing conditions and morphology of the growing crystals. However, because of the typical space and time scale associated to the ice-templating conditions, these information's were not accessible experimentally so far. Here, confocal microscopy is a suitable tool to investigate these phenomena. An horizontal cross-section taken during freezing is shown in Fig. 4. Parallel ice crystals (in black) repel and concentrate the particles in the inter-crystals space. The regions still liquid appear in magenta. The particles and their organization can clearly be observed in the regions adjacent to the crystals surface. In particular, we can see how the first 2-3 layers of particles, in direct contact with the growing crystals, organize into dense hexagonal packings. When the thickness of the layer of collected particles increases, the ordering is progressively lost. These observations are in good agreement with the output of discrete elements modelling [START_REF] Barr | Structural properties of materials created through freeze casting[END_REF][START_REF] Bouville | Self-assembly of faceted particles triggered by a moving ice front[END_REF], which predicted such segregation patterns. The particle organization was predicted to be strongly dependent on the displacement velocity of the interface in contact with the particles [START_REF] Barr | Structural properties of materials created through freeze casting[END_REF]. If a growth velocity of 2 µm/s was set in this particular case, the lateral growth of the crystals, which is responsible for collecting and concentrating the particles, is much lower than this (less than 2 µm/s in this case). Previous X-ray tomography performed in situ during freezing also reported [START_REF] Deville | Time-lapse, three-dimensional in situ imaging of ice crystal growth in a colloidal silica suspension[END_REF] that the lateral growth velocity of ice crystals in a colloidal suspension is 2 to 3 times lower than the growth velocity along the temperature gradient. The lateral growth velocity is therefore probably less than 1 µm/s here.

Confocal microscopy appears thus as a powerful tool to investigate particle reorganization during freezing. Following this initial assessment, future work will focus on systematic variations of the freezing conditions to investigate its impact on the reorganization of particles.

Effect of crystal tilt on particle segregation

Ice crystals, similar to other solidification systems such as succinotrile [START_REF] Ghmadh | Directional solidification of inclined structures in thin samples[END_REF], do not always grow perfectly aligned with the temperature gradient. Depending on the growth rate, temperature gradient, and the presence of additives, ice crystals can grow titled. The tip of the crystals can, in such case, adopt an asymmetric morphology which may, in turn, impact the particle redistribution. An example is shown in Fig. 5, with a snapshot taken during the growth of ice. The asymmetric morphology can clearly be observed. The tip of the crystals is partly faceted, with a facet facing the incoming particles. The projected area (or length, in 2D) that collects the particles is shown in inset A. The projected length d r of the right-hand side of the crystal is greater than the projected length d l of the left-hand side of the crystal. Because of this tilt and so the different surfaces available to collect the particles, the relative fraction of particles segregated to the right-hand side of the crystals is greater than that segregated to the left-hand side. This can be observed with more details in the inset B, that shows both sides of the same crystal. The thickness of the layer of particles rejected by the lateral growth of the crystal is 2 to 3 times larger on the right-hand side than on the left-hand side. In a given pore channel, such as shown in inset C, the segregation of particles is thus asymmetric. This behavior was not reported before, and may impact the particle segregation pattern.

The particle organization (packing density, orientation in case of anisotropic particles) be- tween the crystals depends, among other parameters, on the thickness of the accumulated layer of particles. Several recent studies have reported that a controlled segregation of particles by ice crystals can be used to induce 2D or 3D structures with structural or functional properties [START_REF] Kim | Honeycomb Monolith-Structured Silica with Highly Ordered, Three-Dimensionally Interconnected Macroporous Walls[END_REF][START_REF] Shen | Assembly of colloidal nanoparticles directed by the microstructures of polycrystalline ice[END_REF][START_REF] Bouville | Strong, tough and stiff bioinspired ceramics from brittle constituents[END_REF][START_REF] Ferraro | Light and Strong SiC Networks[END_REF]. In such cases, the functional response may be optimized by a better control of the particle organization. The effect identified here could thus potentially be used to tune these properties. The temperature gradient, along with the growth velocity, is the parameter with the most dramatic impact on the solidification microstructure. However, in the majority of the ice-templating setups, the temperature gradient is not controlled and evolves as freezing proceeds. The usual approach in ice-templating is to put the suspension in a mold, the base of which is cooled at a constant cooling rate [START_REF] Deville | Ice-Templating and Freeze-Casting: Control of the Processes, Microstructures, and Architectures[END_REF]. In such a configuration, the temperature gradient varies during the experiment. Most studies have thus focused on the impact of the growth rate [START_REF] Waschkies | Control of Lamellae Spacing During Freeze Casting of Ceramics Using Double-Side Cooling as a Novel Processing Route[END_REF][START_REF] Deville | Freezing as a path to build complex composites[END_REF], which is a much easier parameter to control.

Our temperature-controlled setup provides an independent control of the cooling rate and the temperature gradient. We can thus assess separately the impact of the later.

We investigated the impact of the temperature gradient on the solidification microstructure for a constant growth velocity (Fig. 6). The temperature gradient was varied from 5 • C/mm to 15 • C/mm, for a growth rate of 40 µm/s. Two features should be noticed here.

We can observe in Fig. 6 that even at such rapid velocity (40 µm/s), a thin layer of accumulated particles is found at the tip of the crystals. This was not reported before, and could explain some of the previously published results. When the tip of the crystals reach the top of the sample, the layer of concentrated particles will be retained in the frozen sample, and thus in the final ice-templated material. This is usually not a problem as the layer is only a few microns thick, and the top and bottom of the sample are often removed (cut) before being used. However, ice-templated thin films have recently gained traction for a number of applications such as dye-sensitized solar cells or solid oxide fuel cells [START_REF] Rachadel | A novel route for manufacturing asymmetric BSCF-based perovskite structures by a combined tape and freeze casting method[END_REF][START_REF] Ren | Fabrication of Gradient Pore T iO 2 Sheets by a Novel Freeze-Tape-Casting Process[END_REF][START_REF] Sofie | Fabrication of Functionally Graded and Aligned Porosity in Thin Ceramic Substrates With the Novel Freeze-Tape-Casting Process[END_REF][START_REF] Chen | Novel functionally graded acicular electrode for solid oxide cells fabricated by the freeze-tape-casting process[END_REF].

The top layer of an ice-templated film that is only a few microns thick cannot be removed, and may impact the final functional properties. The presence of accumulated particles at the top of the film can be seen for instance in Fig. 2c and 2d of ref. [START_REF] Wang | Ordered porous TiO2 films obtained by freezing and the application in dye sensitized solar cells[END_REF].

The second result is the stabilization of the crystals as the temperature gradient increases.

When the crystals grow at 40 µm/s in a 5 • C/mm temperature gradient, the crystals are not stable. A time-lapse sequence, shown in Fig. 7, reveals how the interface constantly evolves. New crystals appear at the front, while other ones disappear. This behavior has two consequences. The first one is the heterogeneous redistribution of particles. Ice-templating under such conditions would result in discontinuous pore channels, as a crystal that stops growing results in the closing of an ice-templated pore. The second consequence is the engulfment of a large fraction of isolated particles by the front, as shown in Fig. 3 in the frozen structure. Again, from an ice-templating point of view, such behavior is not desirable.

Increasing the temperature gradient from 5 • C/mm to 10 • C/mm and 15 • C/mm, for the same growth velocity, stabilizes the front and should thus result in more homogeneous icetemplated architectures.

These results prove the importance of a proper control of both the growth rate and temperature gradient, because their impact on particle redistribution, but also on the homogeneity of crystals and thus of the ice templated structures. This should be kept in mind when designing ice-templating setups.

Effect of PVA

Several additives are commonly used in suspensions for ice-templating. Additives include surfactants, but also binders, crystal growth modifiers, anti-foaming agents, or plasticizers.

The impact of these additives on the development of ice-templated architectures is difficult to understand, as they typically affect several characteristics of the suspension (viscosity, surface tension, etc. . . ). With our setup, we can investigate the impact of additives on the morphology of ice crystals and the segregation of particles while keeping all other parameters constant. We illustrate here the approach with the impact of polyvinyl alcohol (PVA), which is one of the most used binder in ice-templating studies [START_REF] Zuo | Properties of Microstructure-Controllable Porous Yttria-Stabilized Ziroconia Ceramics Fabricated by Freeze Casting[END_REF][START_REF] Pekor | The Effect of Polyvinyl Alcohol on the Microstructure and Permeability of Freeze-Cast Alumina[END_REF][START_REF] Zuo | Effect of polyvinyl alcohol additive on the pore structure and morphology of the freeze-cast hydroxyapatite ceramics[END_REF][START_REF] Yoon | Macroporous Alumina Ceramics with Aligned Microporous Walls by Unidirectionally Freezing Foamed Aqueous Ceramic Suspensions[END_REF].

The impact of the addition of 1 wt.% of PVA in the particle suspension is shown in Fig. 8. At a growth rate of 20 µm/s, the crystals are titled with respect to the direction of the temperature gradient and solidification front. The tilt here is therefore a consequence of the PVA addition and is not an artifact due to a poorly controlled temperature gradient. A possible explanation is that the increased undercooling of the freeze front, resulting from the rejection of PVA by the growing ice, enhances the growth anisotropy of the ice crystals. This should be taken into account if PVA is added to prepare ice-templated materials, as tilted crystals will result in tilted pores in the final architecture. A tilt might not be desirable in applications that involve fluid or gas transport, for instance [START_REF] Seuba | Gas permeability of ice-templated, unidirectional porous ceramics[END_REF].

Crystals also become thinner with the addition of PVA. The periodicity of the lamellar solidification pattern in a 10 • C/mm is of 38 µm (at 40 µm/s) and just 15 µm (at 20 µm/s) with the addition of PVA (and should thus be even lower if we further increase the growth rate). The thinning of the ice crystals in presence of PVA can be used to align particles in 2D, as shown in Fig. 9. Here, the spacing between adjacent crystals is so thin that it can accommodate only 2 layers of particles. The particles used here sediment in a few minutes and thus rapidly rest at the bottom glass surface, before getting organized by the passing ice front. After freezing, we are thus able to obtain a 2D grid of particles aligned in thin threads. This has been used previously with T iO 2 and V O 2 suspensions [START_REF] Romeo | 2D-ice templated titanium oxide films as advanced conducting platforms for electrical stimulation[END_REF][START_REF] Cao | Nanoporous thermochromic VO 2 (M) thin films: controlled porosity, largely enhanced luminous transmittance and solar modulating ability[END_REF], with applications in conducting platforms for electrical stimulation and thermochromic films. Our approach could thus be used to better understand and control such architectures.

IV. CONCLUSIONS AND PERSPECTIVES

The 3D, multiphase imaging of confocal microscopy, combined with its rapid imaging capacities and submicronic spatial resolution, makes it the almost perfect tool to investigate

Figure 1 .

 1 Figure 1. Experimental setup to perform in situ freezing experiments in the confocal microscope. A constant temperature gradient ∆T = T h -T c is established in the gap d between the Peltier modules. The sample is translated through the temperature gradient at a constant velocity V , which induces a growth of the ice crystals at a velocity V . The interface is thus kept at a constant position in the observation frame. Samples are 100 µm thick. T f is the freezing point of the suspension. c (2017) Sylvain Deville (10.6084/m9.figshare.5722675) CC BY 4.0 license https://creativecommons.org/licenses/by/4.0/

5 •

 5 C/mm to 15 • C/mm in the experiments. The solidification front velocities were varied from 1 µm/s to 40 µm/s.

Figure 2 .

 2 Figure 2. 3D reconstruction of the solidification microstructure. Although most of the structure is frozen, some residual liquid pockets can be observed between particles. Several features of interest are pointed out here: A: isolated engulfed particles. B: Pore ice in larger pores. The ice already invaded the larger inter-particle pores. C: Locally dense packing of particles: pore ice is moving through the packing, into the smaller pores. D: residual liquid pockets in a small agglomerate of particles. Growth rate: 20 µm/s, temperature gradient: 5 • C/mm. c (2017) Sylvain Deville (10.6084/m9.figshare.5722675) CC BY 4.0 license https://creativecommons.org/licenses/by/4.0/

Fig. 2

 2 Fig. 2 also shows that, for these solidification conditions, two fates are possible for the particles. Most of the particles are segregated by the growing crystals in the inter-crystal space. This mechanism is the basis for the development of ice-templated microstructures.

Figure 3 .

 3 Figure 3. 3D reconstruction of the solidification microstructure. The engulfment of isolated particles is enhanced by the increase of growth rate from 20 µm/s to 40 µm/s, compared to fig. 2. Growth rate: 40 µm/s, temperature gradient: 5 • C/mm. c (2017) Sylvain Deville (10.6084/m9.figshare.5722675) CC BY 4.0 license https://creativecommons.org/licenses/by/4.0/

Figure 4 .

 4 Figure 4. 2D cross-section that shows the organization of the particles induced by lateral growth of the crystals. The spatial organization can be compared with the output of discrete elements modelling. The first few layers of particles close to the crystal surface are organized. The particles further show less organization. 1 wt.% of PVA, growth rate: 2 µm/s, temperature gradient: 10 • C/mm. c (2017) Sylvain Deville (10.6084/m9.figshare.5722675) CC BY 4.0 license https://creativecommons.org/licenses/by/4.0/

Figure 5 .

 5 Figure 5. Snapshot of the system during ice growth with titled crystals. A differential lateral segregation of particles is induced by the tilt. The tilted tip of the crystals pushes particles to the right-hand side of the crystals. A: the tip of the crystal is asymmetric, and its relative surfaces (or length, in 2D) that collect the particles on both sides are therefore different. B: Different concentration of particles are found on the right-hand side and left-hand side of the crystals, because of the tilt-induced uneven segregation. C: progressive concentration of particles induced by the lateral growth of the ice crystals. 1 wt.% PVA, growth rate: 1 µm/s, temperature gradient: 10 • C/mm. c (2017) Sylvain Deville (10.6084/m9.figshare.5722675) CC BY 4.0 license https://creativecommons.org/licenses/by/4.0/

Figure 6 .

 6 Figure 6. Effect of the temperature gradient on solidification pattern and particle segregation at the tip of the crystals. Increasing the magnitude of the temperature gradient for a given growth velocity stabilizes the front. Even at such rapid velocity (40 µm/s), a thin layer of particles repelled by the crystal tip is visible. The corresponding temperature gradient is indicated on each picture. c (2017) Sylvain Deville (10.6084/m9.figshare.5722675) CC BY 4.0 license https://creativecommons.org/licenses/by/4.0/

Figure 7 .

 7 Figure 7. Dynamic evolution of the crystal morphology, in an unstable regime. The solidification front in these conditions constantly evolve, with new crystals formed and older ones disappearing. This impacts the homogeneity of the solidification microstructure, but also results in a lot of isolated particles being engulfed. The arrows on the first frame indicate the tip of crystals that stopped growing. The arrows on the other frames indicate the same region in the successive frames; it illustrates how a grain boundary between adjacent ice crystals disappear from the freeze front and is replaced by another crystal tip. Growth rate: 40 µm/s, temperature gradient: 5 • C/mm. c (2017) Sylvain Deville (10.6084/m9.figshare.5722675) CC BY 4.0 license https://creativecommons.org/licenses/by/4.0/

Figure 8 .

 8 Figure 8. Impact of PVA on the solidification microstructure. In presence of PVA, the crystals are tilted. The temperature gradient is vertical, the tilt is thus not an artifact that could be induced by a titled temperature gradient. Such a tilt is typically obtained in solidification system that exhibits a growth anisotropy. The crystals are also thinner, compared to the experiment without PVA. 1 wt.% PVA, growth rate: 20 µm/s, temperature gradient: 10 • C/mm. c (2017) Sylvain Deville (10.6084/m9.figshare.5722675) CC BY 4.0 license https://creativecommons.org/licenses/by/4.0/

Figure 9 .

 9 Figure 9.

ACKNOWLEDGEMENTS

The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement 278004 (project FreeCo). We acknowledge Tom Kodger for providing the particles used in this study.


Jérôme Chevalier

Paola Taddei

Laurent Gremillard

Sylvain Deville

Gilbert Fan- Tozzi

J F Bartolomé

C Pecharroman

J S Moya

L A Diaz

R Torrecillas

Saverio Affatato

Reliability assessment in advanced nanocomposite materials for orthopaedic applications

Keywords: Ceramic nano-composites, Crack resistance, Aging resistance, SEM, AFM, Photoluminescence

Alumina-zirconia nano-composites were recently developed as alternative bearing materials for orthopedics. Previous, preliminary reports show that such aluminazirconia nanocomposites exhibit high crack resistance and low wear rate. In this paper, additional information is given in terms of wear, crack resistance and ageing behaviour: femoral heads are inspected after 7 million cycles of wear testing on a hip simulator, crack resistance is measured and compared to other ceramics used today in orthopedics, slow crack growth is reported under static and cyclic fatigue, and aging resistance is assessed. We also report on the load to failure of femoral heads prototypes during compression tests. This overall reliability assessment ensures a potential future development for these kinds of new nanocomposites in the orthopedic field.

Introduction

Nowadays, the main issue for THR is the generation of wear debris produced mainly by the acetabular component [START_REF] Campbell | Biologic and tribologic consideration of alternative bearing surfaces[END_REF]. Standard artificial hip joints consist of a polymer cup made of Ultrahigh Molecular Weight Polyethylene (UHMWPE), placed in the acetabulum via a metal-back component, and a metal (stainless steel or cobalt chromium alloy) ball fixed to a metal stem introduced in the femur. Any use of the joint results in cyclic stress of the polymer cup against the metal ball. During the reciprocating motion of normal joint use, UHMWPE fibrils are then released, mostly by adhesive wear, to form billions of pieces of sub-micrometer wear debris that shed into the surrounding synovial fluid and tissues with negative biological effects. It is currently believed that the UHMWPE particles generated at the contact surfaces enter the periprosthetic tissues where they trigger a macrophage reaction. Then macrophages release pro-inflammatory cytokines that stimulate osteoclastic bone resorption, leading to osteolysis and eventual loosening of the prosthesis and a need for revision. This has led to the development of alternative surfaces for hip articulation such as ceramic-on-UHMWPE, metal-on-metal and ceramic-on-ceramic couplings. In the former coupling, the amount of ion released can be detrimental to the surrounding tissues; in comparison, the use of bio-ceramic materials reduces wear rate and produces no metal ion release. Due to the low roughness exhibited by ceramic heads (typically lower than a few nanometres) and their good wettability, abrasion is reduced significantly if ceramic femoral heads are used with acetabular cups made of polyethylene and almost completely avoided when using ceramic femoral heads together with ceramic cup inserts.

The clinical success associated to the use of ceramics led to the implantation of more than 3.5 million alumina components and more than 600.000 zirconia femoral heads worldwide since 1990, with a strongly growing market (i.e. more than 25% growth for the alumina-alumina coupling between 2002 and 2004). There are many reports on fracture rates associated with ceramics. Important references have been compiled elsewhere [START_REF] Campbell | Biologic and tribologic consideration of alternative bearing surfaces[END_REF]. If, in the pioneering days, the fracture rate was quite high (up to 13% for some series), the in vivo failure rate reported by the producer of Biolox ® alumina is today below 0.01% [START_REF] Willmann | Ceramic femoral head retrieval data[END_REF]. A comparable failure rate was claimed by the producer of Prozyr ® zirconia heads [START_REF] Cales | Zirconia as a sliding material: histologic, laboratory, and clinical data[END_REF]. Critical events in 2001 are discussed below.

If the clinical follow up with current alumina ceramics is significant, it must be kept in mind that their use has been restricted so far to a limited number of designs of hip components, for which the mechanical loading is less demanding. As an example, 22 mm heads are not currently manufactured using alumina ceramics, for reliability reasons. Alumina-alumina coupling also exhibits a significant increase of failure rates. This is again related to its modest mechanical properties. In the 90's, Yttria-Stabilized Zirconia became a popular alternative to alumina as structural ceramic because of substantially higher fracture toughness and strength. The use of zirconia has opened the way towards new implant designs that were not possible with alumina which was too brittle. Biomedical grade zirconia exhibits the best mechanical properties among single-phase oxide ceramics: this is the consequence of phase conversion toughening, which increases its crack propagation resistance. The stress-induced phase transformation involves the transformation of metastable tetragonal grains to the monoclinic phase at the crack tip. It is accompanied by volume expansion and induces compressive stresses that hinder crack propagation. On the other hand, due to this meta-stability, zirconia is prone to aging in the presence of water [START_REF] Chevalier | What future for zirconia as a biomaterial?[END_REF]. Zirconia manufacturers considered this problem as a minor issue until 2001, when roughly 400 failures of zirconia heads were reported within a very short period. The failure origin is now associated to an accelerated aging in two particular batches. Even if limited in time and number, and clearly identified to be process controlled, these events have had a catastrophic impact for the use of zirconia, some surgeons returning to other solutions. More important, some clinical reports show that zirconia can exhibit a progressive ageing degradation even under 'normal' situations, which limits the long-term stability of zirconia [START_REF]Low temperature degradation of zirconia and implications on biomedical implants[END_REF].

For these different reasons, there is a trend to develop stronger and more reliable ceramics that should expand the field of application of bio-inert ceramics in orthopaedics. Alumina-zirconia micro-composites (with both alumina and zirconia grains in the micrometer range) are today under development in the orthopaedic community and show improvement in mechanical properties and aging resistance [START_REF] Aza | Crack growth resistance of alumina, zirconia and zirconia toughened alumina ceramics for joint prostheses[END_REF][START_REF] Deville | Low-temperature ageing of zirconia-toughened alumina ceramics and its implication in biomedical implants[END_REF][START_REF] Willmann | Ceramics for total hip replacement-what a surgeon should know[END_REF]. In a previous work, new alumina-zirconia composites, with an alumina matrix in the micrometer range and nano-sized zirconia particles have been developed [START_REF]Nanostructured ceramic oxides with a slow crack growth resistance close to covalent materials[END_REF]. In the best cases (1.7 vol.% of intra-granular zirconia nano-particles in alumina), they exhibited fracture resistance properties that were never reached with oxide ceramics before. Wear tests were also run on a hip simulator at 7 million cycles and show that wear rates of these composites were comparable to alumina-alumina couplings, ensuring excellent wear properties as compared to metal-metal or metal-polyethylene coupling [START_REF] Affatato | Advanced nanocomposite materials for orthopaedic applications. I. A long-term in vitro wear study of zirconia-toughened alumina[END_REF]. Following these promising preliminary results, our aim was therefore to give a complete picture of the wear resistance and mechanical properties of these nanocomposites, associated to longterm durability assessment.

Our aim was therefore first to inspect the surface of the components already tested at 7 million cycles on a hip simulator to investigate possible damage after wear.

If wear and potential debris release is one key issue for hip joint replacement, the potential of a new ceramic material must also include its sensitivity to slow crack growth and delayed failure, which is not taken into account in the sole strength and toughness data. As a general trend, the susceptibility of ceramics to Slow Crack Growth (SCG) is discussed on the basis of a V(crack velocity) versus KI (stress intensity factor) diagram (KI representing the stresses at the tip of a crack or any pre-existing defect such as a pore, a scratch, etc., in the ceramic). Recently, the presence of a threshold in the stress intensity factor, under which no crack propagation occurs, has been the subject of important research in the ceramic field [START_REF]Crack velocity functions and thresholds in brittle solids[END_REF]. This threshold corresponds to equilibrium with null crack velocity. For ceramic joint prostheses for example, this threshold, KI0, determines a safety range of use [START_REF] Aza | Crack growth resistance of alumina, zirconia and zirconia toughened alumina ceramics for joint prostheses[END_REF]. Due to the tendency of ceramics to undergo cyclic fatigue degradation (i.e. a decrease of KI0 and an increase of crack rates), Slow Crack Growth (SCG) analysis must include cyclic fatigue experiments, which is rarely done in the bio-ceramics literature [START_REF] Attaoui | Quantitative analysis of crack shielding degradation during cyclic fatigue of alumina[END_REF]Chevalier et al., 1999c;[START_REF] Dauskardt | Cyclic fatigue and fracture in pyrolytic carbon-coated graphite mechanical heart-valve prostheses: role of small cracks in life prediction[END_REF]. Our aim was therefore to characterize deeply the SCG resistance under static and cyclic fatigue of the present nanocomposite material in comparison to biomedical grade alumina, zirconia and to a conventional alumina-zirconia micro-composite.

The addition of alumina to zirconia at least reduces drastically aging kinetics. It is shown that the strength of Biolox delta ® for example does not decrease even when repeatedly steam sterilized. However, 'no decrease in strength' does not necessarily mean 'no aging', since other manifestations of ageing are grain pull out and roughening [START_REF] Chevalier | What future for zirconia as a biomaterial?[END_REF][START_REF]Low temperature degradation of zirconia and implications on biomedical implants[END_REF]. Few studies have been devoted to aging in alumina-zirconia systems, but they show that, even if limited and possibly reduced to zero, some degree of degradation can be observed, depending on microstructural features. As an example, we showed in a previous work [START_REF] Pecharroman | Percolative mechanism of ageing in zirconia containing ceramics for biomedical applications[END_REF] that aging could be significant in a 3Y-TZP-alumina composite above 16 vol.% zirconia. This critical content was related to the percolation threshold above which a continuous path of zirconia grains allowed transformation to proceed. The presence of aggregates in the microstructure may be also detrimental [START_REF] Gutknecht | Key role of processing to avoid low temperature ageing in alumina zirconia composites for orthopaedic application[END_REF]. Any extrapolation to other laboratory scale or industrial composites could be hazardous, but it shows how aging must be checked carefully prior to clinical development of a given alumina-zirconia composite. Accelerated aging tests were therefore conducted on the present material to ensure its perfect aging resistance.

At last, the development of a new material for hip joint applications must include the measurement of mechanical properties on real components. Therefore, we report here on the load to failure of femoral head prototypes during compression tests for a specific design where commercial alumina fail to follow ISO specifications.

Materials and methods

Materials preparation

The processing route to obtain the nano-composites specimens was described in detail elsewhere [START_REF]Extending the lifetime of ceramic orthopedic implants[END_REF][START_REF] Schehl | Alumina nanocomposites from powder-alkoxide mixtures[END_REF]. It consists in doping a stable suspension of a high purity alumina powder (Condea HPA 0.5, with an average particle size of 0.45 μm and a surface area of 10 m 2 /g) in ethanol absolute (99.97%) by drop wise addition of a diluted (2/3 vol.% Zr alkoxide, 1/3 vol.% ethanol absolute) zirconium alkoxide (Aldrich Zirconium-IV-propoxide 70 wt% solution in 1-propanol). In the present work, a low amount of zirconia precursor was added, in order to obtain composites with only 1.7 vol.% (2.5 wt%) zirconia nano-particles. After drying under magnetic stirring at 70°C, the powders were thermally treated at 850°C for 2 h to remove organic residues and were subsequently attrition milled with alumina balls for 1 h. Green compacts were then obtained by a pressure-casting method. The optimum sintering to obtain the desired nano-structural distribution of zirconia particles consisted of a thermal treatment of 1600 °C/2 h. Fig. 1 shows the microstructure of the material, consisting in zirconia nano-particles (D50≈150nm) evenly distributed in the alumina matrix (D50≈5μm). Those zirconia particles were found to be mainly (>70%) intragranular, with almost perfect spherical shape. These particles are well below the critical size for phase transformation [START_REF] Schehl | Alumina nanocomposites from powder-alkoxide mixtures[END_REF]. All ceramics were fully dense.

Inspection of worn ceramic components after 7 million cycles

Twelve 28 mm×44 mm ceramic femoral heads, processed under the conditions mentioned above, were articulated with twelve ceramic acetabular cups of the same composition. The following configurations were tested on a hip simulator under bovine calf serum as a lubricant:

• four commercially available alumina heads and acetabular cups (Biolox forte ® in the following referred to as AL); • four experimental pure alumina heads and acetabular cups (in the following referred to as BK); • four experimental nanocomposite heads and acetabular cups (in the following referred to as NK). Major details about this experimental in-vitro test are available in literature [START_REF] Affatato | Advanced nanocomposite materials for orthopaedic applications. I. A long-term in vitro wear study of zirconia-toughened alumina[END_REF].

Scanning Electron and Atomic Force Microscopy observations

Scanning Electron Microscopy (SEM, XL-20, FEI, Netherlands) observations were conducted at the surface of a commercial alumina head (AL), an experimental alumina head (BK) and a NK head after 7 million cycles. The heads were coated with a gold layer of 10 nm prior to observations. Atomic Force Microscopy (AFM, D3100, Digital Instruments) measurements were conducted at the surface of the same heads. The Atomic Force Microscope (AFM) was used in contact mode, with an oxide-sharpened silicon nitride probe exhibiting a tip radius of curvature of 20 nm. The scans were performed at the surface with an average scanning speed of 10 μm/s. The scans were all conducted on the same day (i.e. with the same probe, with the same state) to lower the scatter of the data and to obtain comparative results. Different zones of the same head were observed in order to get statistical data. A computer-assisted treatment was conducted to suppress the roundness of the heads and to obtain Ra (roughness) values. These values were compared to those measured on the as-processed heads, i.e. before the wear tests.

Photoluminescence measurements

The surface residual stress state in the acetabular cups was measured via a piezospectroscopic technique, widely applied to the study of alumina and alumina-zirconia composites [START_REF] Garcia | Relationship between mechanical grinding and photoluminescence of zirconia-toughened-alumina ceramics[END_REF][START_REF] Garcia | Relationship between mechanical grinding and photoluminescence of zirconia-toughened-alumina ceramics[END_REF]Clarke, 1994, 1993;[START_REF] Merlani | Residual stresses in alumina/zirconia composites: effect of cooling rate and grain size[END_REF][START_REF] Sergo | Grain size inflence on residual stresses in alumina/zirconia composites[END_REF]. The piezospectroscopic effect may be defined as the shift, induced by strain, in the frequency of a spectral band. The bands here considered to evaluate the residual stress state were the R1 and R2 fluorescence bands (at about 14 400 cm -1 and 14 430 cm -1 , respectively), which have a long known and well-defined stress dependence [START_REF] Garcia | Relationship between mechanical grinding and photoluminescence of zirconia-toughened-alumina ceramics[END_REF][START_REF] Garcia | Relationship between mechanical grinding and photoluminescence of zirconia-toughened-alumina ceramics[END_REF]Clarke, 1994, 1993;[START_REF] Merlani | Residual stresses in alumina/zirconia composites: effect of cooling rate and grain size[END_REF][START_REF] Sergo | Grain size inflence on residual stresses in alumina/zirconia composites[END_REF]. Photoluminescence is due to the radiative electronic transitions of the Cr 3+ ions, naturally present in alumina ceramics as trace impurities which substitute the Al 3+ ions in the Al2O3 lattice [START_REF] He | Determination of the piezospectroscopic coefficients for chromium-doped sapphire[END_REF][START_REF] Selcuk | Analysis of the Cr3+ luminescence spectra from thermally grown oxide in thermal barrier coatings[END_REF]. The origin of the piezospectroscopic effect is that when the lattice of ions surrounding the Cr 3+ is distorted, for instance by an applied stress, the crystal field potential at the site of the Cr 3+ ion is altered, which, in turn, alters the energies of the electronic transitions. Thus, the analysis of the fluorescence spectrum of Cr 3+ -doped alumina can give information on the residual stress state of the sample. Moreover, the intensity of the above mentioned bands was used to non-destructively investigate the surface finishing of the acetabular cups, according to other authors [START_REF] Garcia | Relationship between mechanical grinding and photoluminescence of zirconia-toughened-alumina ceramics[END_REF].

The fluorescence spectra were obtained using an argon-krypton laser (Innova Coherent 70) operating at 488 nm to excite the fluorescence and a Jasco NRS-2000C micro-Raman spectrometer equipped with a 160 K frozen digital CCD detector (Spec-10: 100B, Roper Scientific Inc.) to collect the excited fluorescence. To ensure that no laser heating occurred and contributed to the observed frequency shifts, all measurements were performed at a low laser power (i.e. 1 mW). Instrumental fluctuations represent another source of possible variation in the measured frequency. In order to correct for this, a characteristic neon line at 14 431 cm -1 was used as a frequency calibration standard.

The spectra were recorded in back-scattering conditions with 1 cm -1 spectral resolution using an objective lens of 10× magnification; the laser spot size was larger than the grain size of the ceramics, assuring that the fluorescence was being averaged over a large number of grains. Moreover, to obtain a good representation of the stress distribution, ten spectra were collected in ten different points of each sample.

Ten spectra were recorded, on each sample, in the inner surface near the centre (in a spatial range of about 1.5 mm from the centre). A soaked unworn cup of each set of specimens was analyzed as control.

The bands monitored were at about 14 396 cm -1 (R1) and 14 424 cm -1 (R2). Their width (expressed as full width at half maximum, FWHM), intensity and frequency were determined by fitting the experimental spectra with mixtures of Lorentzian and Gaussian functions. The fitting was done using a commercial software (OPUS 5.0, Bruker Optik GmbH, Germany).

Crack resistance measurements

Short-crack resistance curves (R-curve behaviour) were measured and analyzed by the indentation-strength in the bending (ISB) method [START_REF] Braun | Objetive evaluation of short-crack toughness curve using indentation flaws: case study on alumina-based ceramics[END_REF] using prismatic bars in which the centres of the tensile faces, polished down to 1 μm, were indented with a Vickers diamond at contact loads, P, between 10 and 500 N. The specimens were tested at room temperature using a three-point support with a span of 40 mm in an universal testing machine (Instron Model 4411). The specimens were loaded to failure with a cross-head speed of 0.05 mm/min. The mechanical test was performed immediately after indentation to avoid any subcritical crack growth due to stress corrosion effects. Special effort was made to examine all specimens after testing using reflected light optical microscopy (Leica, DMR model), to verify that the indentation contact site acted as the origin of failure. R-curves were measured considering a radial crack c produced by the indentation at a load P and subjected to the action of a tensile stress σa due to the applied stress load during three-point bending. During post-indentation bending, the crack is subjected to a total stress intensity, Kt, which is the sum of contributions from the residual stress intensity factor acting on the indentation crack resulting from the elastic-plastic mismatch associated with the indentation, Kr, and the stress intensity factor resulting from the applied stress, Ka:

K t (c)=K a (c)+K r (c)=ψ⋅σa⋅c 1/2 +ξ⋅(E/H) 1/2 ⋅P/c 3/2 =K R (c) (eq. 1)
where ψ is a crack geometry factor, ξ is the dimensionless geometrical constant, E is Young's modulus, H hardness, and KR is the crack resistance of the material. For a given indentation load, P, failure is assumed to occur at the stress where the applied stress σa is equal to the fracture stress, σf, which satisfies the following balance and tangency conditions:

Kt(c)=KR(c) (eq. 2)
dKt(c)/dc=dKR(c)/dc (eq. 3)

The R-curve is determined by solving Eqs. ( 2) and (3) for each beam simultaneously.

Crack velocity functions and threshold determination

Crack velocities from 10 -12 m s -1 (necessary for threshold determination) to 10 -2 m s -1 (fast fracture) were measured by the double torsion technique, in order to get insight on the crack velocity versus stress intensity factor functions. The double torsion specimens (40 mm * 20 mm * 2 mm plates) and the loading configuration are shown in Fig. 2. The tensile surface is polished down to 1 mm in order to observe the crack with a precision of ±2 mm. A notch of dimension ao=10mm and root ρ=0.1mm is machined with a diamond saw and an indentation performed at low load (5 kg) in order to initiate a small crack. Subsequent pre-cracking is performed by loading the specimens at low rate in order to induce a 'real' sharp crack of initial length ai=12mm. The double torsion configuration has for a long time been known to give rise to a stress intensity factor which is independent of crack length, given by [START_REF] Shyam | The double-torsion testing technique for determination of fracture toughness and slow crack growth behavior of materials: a review[END_REF]:

𝐾 = 2 3(1+ ) 1/2
(eq. 4)

P is the load, Wm the span, U and W the width and the thickness of the specimen, ν the Poisson's ratio (taken here as equal to 0.3), and ψ a calibration factor.

Fig. 2. Double Torsion specimen and loading configuration.

However, it has been demonstrated recently, both experimentally and by numerical simulation [START_REF]Double torsion testing a 3Y-TZP ceramic[END_REF][START_REF] Ciccotti | Realistic finite-element model for the double-torsion loading configuration[END_REF] that KI is slightly dependent on the crack length. To obtain accurate V-KI diagrams a correction factor should be introduced in the conventional expression of KI, as expressed with the following empirical equation:

𝐾 = 𝐻𝑃 0 (eq.5)
a0 is the notch length and a is the total crack length. γ depends on the geometry of the test sample. For the dimensions used for the present study γ=0.19 [START_REF]Double torsion testing a 3Y-TZP ceramic[END_REF].

Crack velocity functions were determined via two methods: relaxation tests and constant-loading tests. The load-relaxation method, which was first reported by Williams and [START_REF] Williams | A simple method to study slow crack growth[END_REF], was used to obtain the slow crack growth V-KI diagrams in the velocity range 10 -2 -10 -7 m/s. This method does not allow measurements at very low velocity but it does present the advantage of being quick to obtain measurements at high velocities. Pre-cracked specimens are loaded at a constant rate of 0.2 mm/min, followed by subsequent stopping of the cross-head at constant displacement, when the crack starts to propagate. The obtained load-relaxation versus time (P versus t) plot allows the determination of the V-KI curve by a compliance calibration [START_REF]Double torsion testing a 3Y-TZP ceramic[END_REF][START_REF] Ciccotti | Realistic finite-element model for the double-torsion loading configuration[END_REF][START_REF] Shyam | The double-torsion testing technique for determination of fracture toughness and slow crack growth behavior of materials: a review[END_REF][START_REF] Williams | A simple method to study slow crack growth[END_REF].

Measurement of the crack velocities V under constant load presents the advantage of allowing the measurement of very low velocities, down to 10 -12 m/s. Thus, the specimens are subjected to different static loads under a prescribed duration Δt. The crack length is measured via optical microscopy, with a precision of ±2 μm, and V is defined as the ratio of crack increment Δa to the duration Δt:

𝑉 = ∆ ∆ (eq. 6)
Crack velocities were also measured under cyclic loading, at a frequency of 1 Hz on the same testing machine than for static fatigue measurements, which presents the advantage of allowing a direct crack velocity comparison with static tests. The specimens were loaded at an imposed sine shape load between Pmin and Pmax, for a given duration Δt. The R=KImin/KImax=Pmin/Pmax ratio was selected to 0.1. The crack length increment Δa was again measured by optical microscopy with a precision of ±2 mm and the crack velocity V by Eq. (3).

Aging resistance

The transformation being both thermally activated and accelerated by the presence of water, samples were put in an autoclave in steam during controlled duration at 134 °C, under 2 bars pressure, in order to induce the phase transformation at the surface with time. Knowing the thermal activation (-106 kJ/mol) of the aging process (Chevalier et al., 1999a), it is possible to calculate that 1 h of such a treatment would correspond roughly to three years in vivo. The transformation was followed by measuring the monoclinic phase fraction evolution by X-ray diffraction (XRD). XRD data were collected with a 𝜃-2𝜃 diffractometer using the Cu-K α radiation. Diffractograms were obtained from 27° to 33°, at a scan speed of 0.2 °/min and a step size of 0.02°. The monoclinic phase fraction Xm was calculated using the Garvie and Nicholson method [START_REF] Garvie | Phase analysis in zirconia systems[END_REF], modified by [START_REF] Toraya | Calibration curve for quantitative analysis of the monoclinic-tetragonal ZrO2 systems by X-ray diffraction[END_REF]:

𝑋 = -111 + (111) -111 + 111 + (101)
(eq. 7)

It and Im represent the integrated intensity (area under the peaks) of the tetragonal (101) and monoclinic ( 111) and (-111) peaks. The monoclinic volume fraction, Vm, is then given by: 𝑉 = 1.311 1+1.311

(eq. 8)

Fracture resistance of femoral heads prototypes

Compressive loads to failure of NK heads were performed according to ISO-DIS 7206-10 protocol. In order to evaluate the potential of the nano-composite for critical designs, 28 mm long neck femoral heads were coupled with CrCo conical tapers. 7 heads were loaded in compression (crosshead speed: 0.5 mm/min) according to the configuration of Fig. 3, on a universal INSTRON hydraulic testing machine. 7 AL femoral heads were tested with the same testing configuration.

Fig. 3. Testing configuration for the measurement of the fracture resistance of aluminazirconia nanocomposite prototype femoral heads.

Results and discussion

Inspection of worn ceramic components after 7 million cycles

Strain can induce a shift of the characteristic frequencies of spectral bands, i.e. Raman, infrared or luminescence bands. However, in this work we concentrated on the R1 and R2 fluorescence bands as a function of stress. The reason for this is that the fluorescence signal is several orders of magnitude greater in intensity than the Raman bands (Fig. 4) and hence more precise measurements can be conducted. All the samples contained an adequate Cr 3+ impurity level for the R1 and R2 bands to be recorded with a high signal-to-noise ratio, so that precise measurements of band frequency, intensity and FWHM were assured. As an example, Fig. 4(a) reports the fluorescence spectrum of a control unworn commercial alumina acetabular cup fitted into the two R1 and R2 components.

The data obtained from the fitting of the photoluminescence spectra are reported in Table 1. By comparing the three sets of control unworn specimens, the most significant observable change involved the intensity of both R1 and R2 bands; less significant changes were observed for their frequencies and FWHM. As regards the latter, its value has been reported to be correlated with grain size and microcracking. Actually, microcracks are more easily formed in materials with large grain size (Rice and [START_REF] Rice | Grain size dependence of spontaneous cracking in ceramics[END_REF] and are known to reduce the width of the Gaussian residual stress distribution and thus the FWHM of the fluorescence bands [START_REF] Ortiz | Statistical properties of residual stresses and intergranular fracture in ceramic materials[END_REF]. As can be easily seen from Table 1, the intensity of the fluorescence bands for the unworn control samples increased along the series: BK<NK<AL.

Recent studies have indicated the dependence of photoluminescence on surface quality [START_REF] Garcia | Relationship between mechanical grinding and photoluminescence of zirconia-toughened-alumina ceramics[END_REF]. It can be affirmed that the higher the roughness of the sample, the lower the photoluminescence intensity. In fact, pores or scratches act as scattering centers of the incident laser beam and reduce the transmission and hence excitation depth. In this light, it can be affirmed that commercial alumina showed the best surface finishing. Going from this set of samples to NK the surface quality worsened and the worsening was even more pronounced for experimental alumina. However, it should be remembered that the analyzed NK and experimental alumina specimens were only prototypes and therefore their surface finishing can be worse than for a production type, as previously observed for ceramic couplings [START_REF] Affatato | Mixed oxides prosthetic ceramic ball heads. Part 3: effect of the ZrO2 fraction on the wear of ceramic on ceramic hip joint prostheses. A long-term in vitro study[END_REF]. Hip joint wear simulator tests did not significantly alter the surface finishing and residual stress state of the three sets of acetabular cups; no significant changes in frequency and FWHM of the R1 and R2 bands were observed upon wear testing (Table 1). However, it must be recalled that from a statistical point of view, the three sets of specimens did not show significant differences in wear behaviour in hip joint wear simulator tests [START_REF] Affatato | Advanced nanocomposite materials for orthopaedic applications. I. A long-term in vitro wear study of zirconia-toughened alumina[END_REF]. Interestingly, gravimetric measurements showed the same trend as photoluminescence intensities: the highest and lowest weight losses were observed for AL and BK samples, respectively, while the NK specimens were characterized by intermediate weight losses [START_REF] Affatato | Advanced nanocomposite materials for orthopaedic applications. I. A long-term in vitro wear study of zirconia-toughened alumina[END_REF].

These findings suggest that the better the sample finishing, the better the wear behaviour. Therefore, full density should be reached to limit wear in ceramics. This is particularly true for the cups, where it is hard to obtain excellent forming conditions and surface finishing (concave surface).

Scanning Electron Microscopy (Fig. 5) and Atomic Force Microscopy (Table 2) observations confirm the fact the commercial alumina exhibits the best initial surface finish, followed by NZTA and experimental alumina prototypes. This leads then to less surface damage after 7 million cycles. Even if the damage is low for all ceramics of the study, it can be argued that the experimental alumina exhibits the most important amount of grain pull out and third body wear. We must remind however, the amount of wear debris generated by such ceramic-ceramic configurations is exceptionally low when compared to standard metal-polyethylene or even ceramic-polyethylene.

Crack resistance measurements

The fracture behaviour of short cracks has been studied in flexure using the indentation method to produce controlled surface cracks. The advantage of this technique is that it is able to provide an assessment of the mechanical properties at the correct microstructural length scale. The R-curve behaviour is caused by the increase of fracture toughness with increasing crack length due to crack-tip process zone phenomena and/or crack bridging due to interlocking grains. For example, in a coarse grained alumina (∼16 μm grain size) the fracture toughness saturates at ∼6 MPa m 1/2 , which is about double its short crack value [START_REF] Reichl | Determination of crack-bridging forces in alumina[END_REF]. Whilst this is an impressive increase in fracture toughness in a material, it should be realised that the critical flaws in these experiments were much larger (>1 mm) than would be encountered in real components. On the other hand, for short cracks in the range of 50-200 μm, the effect of these toughening mechanisms can be significantly reduced. Therefore, in applications where small cracks are of interest, i.e., in biomedical implants, R-curves measured on long cracks are not relevant. On the contrary, the increase in the initial fracture toughness and the crack growth resistance in the short crack region (<100 μm) is necessary. Moreover, the fracture toughness operative at small crack-size scales is a relevant material property which controls deformation response during wear [START_REF] Scattergood | R-curve effects for machining and wear of ceramics[END_REF]. The resulting short-crack resistance curves obtained for alumina, zirconia, zirconia toughened alumina "micro"-composite and nanostructured alumina-zirconia composite have been plotted in Fig. 6. The result for the alumina shows no such rising R-curve.

For monolithic alumina, the main toughening mechanism was grain bridging by large elongated Al2O3 grains behind the crack tip. Due to the small grain size of the biomedical grade alumina, no bridging effect would be expected.

Fig. 6. Short-crack resistance curves obtained for biomedical grade alumina, yttria stabilized zirconia, conventional zirconia toughened alumina 'micro'-composite and currently developed nano-structured alumina-zirconia composite.

The alumina-zirconia nanocomposite specimens show a flat R-curve with the highest toughness value. In these nanocomposites, the toughening mechanisms operate on a scale smaller than that of the matrix microstructure, enhancing the "intrinsic" fracture properties of the material.

On the other hand, zirconia and alumina-zirconia "micro"-composites show a slight rising crack growth resistance with crack extension due to a transformation toughening mechanism that promote a process zone in the neighbourhood of the crack tip. Consistent with the very fine microstructure and the relatively narrow transformation zone of these ceramics, the R-curve rises steeply during the first 100 μm extension of the crack. Over this crack length, fracture resistance reaches a plateau toughness, meaning that toughness no longer increases with crack extension.

Crack velocity functions and threshold determination

Fig. 7 shows crack velocity diagrams under static loading, for the nanostructured alumina-zirconia composite, standard biomedical grade alumina and zirconia ceramics, and for a zirconia toughened alumina 'micro'-composite developed previously. The results for the four ceramics show the typical three stages of Slow Crack Growth (SCG) and a threshold, below which no crack propagation occurs. The threshold (KI0), was determined from the points on the V-KI diagram, below which there is an abrupt drop of the crack velocity, V<10-12ms -1 . On the other hand, the toughness (KIC) was determined by extrapolation of the V-KI curve to high crack velocities (10 -2 m s -1 ). Their values are represented in Table 3 for the different ceramics. Fig. 7. Crack velocity diagrams under static loading, for biomedical grade alumina, yttria stabilized zirconia, conventional zirconia toughened alumina 'micro'-composite and currently developed nano-structured alumina-zirconia composite.

Table 3. Toughness (KIC), static fatigue threshold (KI0s) and cyclic fatigue threshold (KI0c) of the currently developed alumina-zirconia nanocomposite (NK), alumina-zirconia micro-composite (ZTA), biomedical grade alumina (AL) and yttria-stabilized zirconia (3Y-TZP).

Alumina-zirconia nano-composite (NK)

Alumina-zirconia micro-composite (ZTA) Biomedical grade alumina (AL) Biomedical grade alumina (3Y-TZP) KIC (MPa√m) 6.2 ± 0.2 6.0 ± 0.2 4.2 ± 0.2 5.5 ± 0.2 KI0S (MPa√m) 5.0 ± 0.2 4.0 ± 0.2 2.5 ± 0.2 3.2 ± 0.2 KI0C (MPa√m) 5.0 ± 0.2 Not measured 2.5 ± 0.2 2.8 ± 0.2
Contrasting results are first underlined for alumina and zirconia monolithic ceramics. Zirconia exhibits a higher toughness than alumina but their thresholds are close, meaning that the necessary crack tip stress to initiate slow crack growth is roughly the same in both materials. The high toughness of zirconia for a monolithic ceramic is attributed to the stress induced phase transformation of metastable tetragonal grains towards the monoclinic symmetry ahead of a propagating crack, leading to an increase of the work of fracture [START_REF] Evans | Review-transformation toughening in ceramics: Martensitic transformations in crack-tip stress fields[END_REF]. This phenomenon is referred to as 'transformation toughening'. Alumina has lower susceptibility to water and thus to stress assisted corrosion. As a consequence, the V-KI curve of alumina presents a higher slope than the curve corresponding to zirconia. Even if alumina is intrinsically more brittle than zirconia (lower toughness), it exhibits a threshold of the same order. From an atomistic point of view, this means that the fracture energy of zirconia is lower in the presence of water or body fluid, because the zirconia bonds are prone to chemisorption of the polar water molecules (like silica glass for example). In practical terms, the benefit of using zirconia instead of alumina is limited if we consider long-term behaviour.

The zirconia-toughened alumina 'micro'-composite possesses both a larger toughness and threshold than the two monolithic ceramics. First, alumina rich composites present crack propagation through the alumina matrix. Thus, these composites possess a lower susceptibility to stress assisted corrosion by water or body fluid. Second, these materials are reinforced by the presence of transformable zirconia particles, shifting the V-KI diagram of alumina towards higher KI values. The authors have shown [START_REF] Aza | Crack growth resistance of alumina, zirconia and zirconia toughened alumina ceramics for joint prostheses[END_REF] in a previous work that the presence of small amounts of transformable zirconia particles in a given matrix leads to a shift of the V-KI diagram towards higher KI values, preserving the slope of the curve. Therefore, the large slope of the V-KI diagram of alumina is preserved, but the diagram is shifted to large KI values due to transformation toughening, which means in turn a large toughness and threshold. It is worth noting that 10 vol.% of transformable zirconia particles, with a size ranging between 100 and 600 nm, corresponds to the maximum amount of transformation toughening [START_REF] Aza | Slow-crack-growth behavior of zirconia-toughened alumina ceramics processed by different methods[END_REF].

Including a smaller amount of zirconia particles, with a size lower than 100 nm totally hinders the possibility of transformation toughening, since the particles become too small to transform even at the crack tip. This was verified by X-ray Diffraction, which revealed no transformation from the tetragonal to the monoclinic symmetry at the surface of fractured nanostructured alumina-zirconia composites. However, both the toughness and threshold of the alumina-zirconia composite are significantly larger than that of the 'micro'-composite, and much larger than alumina. This means that only 1.7 vol.% of zirconia nano-particles in the alumina matrix dramatically improve its crack resistance. This dramatic increase of SCG resistance can be attributed neither to transformation toughening, nor crack bridging, since the R-Curve was proven to be flat (Fig. 6). Moreover, the mode of failure was predominantly transgranular. On some occasions, some crack bridging ligaments were observed on the crack path but their number was clearly too low to account for a significant toughening effect. Including transgranular nano-particles of a second phase with a different thermal expansion coefficient, however, induces large residual stresses in the composite, which may have a strong impact on the SCG behaviour. In order to determine the presence of a residual stress field in the alumina matrix, high angular precision diffraction patterns (monocromatized incident beam Philips Xpert diffractometer) were recorded between 27° and 45° for pure sintered alumina and for the nano-composite. Small angular displacements were found in the α-alumina peaks of nanocomposite corresponding to the following planes: (104), ( 110), ( 006), ( 113). According to these data, a compressive strain of 3×10 -4 and 2×10 -4 was found for the a and c axes of the α-alumina matrix. These strains correspond to a compressive average stress of 150 ± 50 MPa. These compressive stresses superimpose on the stresses applied by the external stress field. In other words, the stress intensity factor at the crack tip is lowered in the presence of the residual compressive stresses. For a semi-elliptical flaw of dimension a subjected to a uniform tensile stress, the actual stress intensity factor at the crack tip is given by: 𝐾 = (𝜎 -𝜎 ) 𝜋𝑎 (eq. 9)

where σa is the applied stress, and σres the residual compressive stress. The ratio between KI tip (stress intensity factor at the crack tip) and KI (the applied stress intensity factor) is therefore given simply by:

𝐾 𝐼 𝑡𝑖𝑝 𝐾 𝐼 = (𝜎 𝑎 -𝜎 𝑟𝑒𝑠 )
𝜎 𝑎 (eq. 10)

The relative influence of the residual stress field is therefore higher for low applied stress intensity factor (i.e. around KI0) than for high applied KI (i.e. at KIC), which is in agreement with a higher slope of the apparent V-KI diagram. In other words, transformation toughening in micro-composites leads to a shift of the V-KI curve, preserving the slope of the alumina matrix, while residual stresses in nanostructured, intra-type zirconia particles, composites lead to an increase of the V-KI slope.

The comparative sensitivity of ceramics to SCG can be plotted in a normalised V-KI/KIC diagram, where KIC is the toughness. The higher the slope of the diagram, i.e. the higher the KI0/KIC ratio, the lower the sensitivity to SCG by stress assisted corrosion. Fig. 8 represents a schematic summary of results obtained in the different materials of the study and compared to covalent ceramics (SiC and Si3N4). The results illustrate the commonly accepted idea that the higher the covalent to ionic bonding ratio, the lower the susceptibility to SCG. This is directly related to the atomic structure of the material. The nano-composite exhibits a peculiar behaviour, with a slope of the V-KI/KIC diagram and a KI0/KIC ratio close to covalent ceramics (the Al2O3-nZrO2 lying between Si3N4 and SiC). In order to evaluate the cyclic fatigue behaviour of the alumina-zirconia nano-composite, crack velocities were also measured under cyclic loading. The tests were conducted at a frequency of 1 Hz on the same testing machine as for static fatigue measurements, which presents the advantage of allowing a direct crack velocity comparison with static tests. The specimens were loaded at an imposed sine shape load between Pmin and Pmax, for a given duration Δt. The R=KImin/KImax=Pmin/Pmax ratio was selected to be 0.1. The crack velocity function under cyclic fatigue is compared to that obtained under static fatigue in Fig. 9. The comparison of the thresholds for the different materials, under cyclic and static fatigue, is given in Table 3. A slight increase of crack velocity and a tendency to a lower threshold under cyclic loading is noticed. However, the cyclic fatigue degradation is low, in particular in comparison to monolithic zirconia or aluminazirconia micro-composites, where transformation toughening acts to resist crack propagation but is degraded under cyclic loading (Chevalier et al., 1999b,c). Pure alumina is not affected by cyclic loading since the amount of crack bridging is negligible for that grain size [START_REF] Attaoui | Quantitative analysis of crack shielding degradation during cyclic fatigue of alumina[END_REF]. Since residual stresses are elastic by nature, the only source of cyclic degradation in the alumina-zirconia nanocomposite is the small amount of crack bridging observed under static fatigue. However, the threshold below which no crack propagation occurs, still stands well above that of the other ceramic materials, providing a large crack resistance for long-term applications.

Aging resistance

Fig. 10 represents the aging kinetics of the 3Y-TZP, alumina-zirconia micro-composite and nano-composite, in terms of monoclinic fraction increase versus time. As expected, the 3Y-TZP ceramic undergoes rapid surface transformation, since the monoclinic fraction reaches saturation after less than 10 h in the autoclave (i.e. roughly 30 years in vivo). On the contrary, the two alumina-zirconia composites do not exhibit any phase transformation during aging, even for long (un-realistic) duration. Previous papers published recently on the aging behaviour of alumina-zirconia composites have shown that alumina-zirconia could be considered as safe against aging, provided that the zirconia content in the composite is kept lower than 10% in the case of un-stabilized zirconia and that no aggregates are present in the composite. The present results stand on this line. This ensures perfect stability of the alumina-zirconia composite, which is a clear advantage versus 3Y-TZP zirconia.

Fracture resistance of femoral heads

The load to failure of 7 prototypes processed from the alumina-zirconia nanocomposite is given in Table 4. The results show that, even for the critical design chosen for the load to failure test (28 mm heads, long neck, against CoCr taper), the prototypes satisfy the ISO 7206-10 standard:

• The mean load to failure (49.2 kN) is higher than 46 kN, • The lowest load to failure reported is higher than 20 kN. For the same design and the same testing configuration, the commercial alumina failed to satisfy the ISO requirements. Indeed, the main load to failure (39 kN) was below the required value.

Conclusions

Due to the modest failure resistance of alumina and the problem of yttria stabilized zirconia in terms of long term reliability, there is a trend today to develop new alternatives, especially for critical and/or new designs for which alumina does not satisfy mechanical requirements. The aim of the present paper was to present a global picture of the mechanical performance and the durability of newly developed alumina-zirconia nanocomposites. We have shown that such nanocomposites exhibit a very limited surface damage after 7 million cycles in a hip simulator. They also exhibit a crack resistance under static and cyclic fatigue well beyond that of all existing biomedical grade ceramics, opening the possibility to develop critical designs that are not possible with monolithic alumina. Associated to an expected full stability in vivo, the overall set of results ensures a potential future development for these kinds of new nanocomposites in the orthopedic field.

Fig. 1 .

 1 Fig. 1. Microstructure of monolithic alumina (a), yttria stabilized zirconia (b), conventional alumina-zirconia composite (c) and of the advanced nano-composite material (d).

Fig. 4 .

 4 Fig. 4. Photoluminescence (a) and Raman (b) spectra of a control unworn commercial alumina acetabular cup. The R1 and R2 fluorescence bands (a) are several orders of magnitude greater in intensity than the Raman spectrum. The fluorescence spectrum was fitted into the two R1 and R2 components to more precisely evaluate band frequencies, intensities and FWHM.

Fig. 5 .

 5 Fig. 5. Scanning Electron Microscopy images of ceramic heads after 7 millions cycles hip simulator study. (a) Commercial alumina (AL), (b) experimental alumina (BK), (c) experimental alumina-zirconia nano-composite (NK).

Fig. 8 .

 8 Fig. 8. V-KI/KIC laws of biomedical grade alumina, yttria stabilized zirconia, conventional zirconia toughened alumina 'micro'-composite and currently developed nanostructured alumina-zirconia composite. Schematic V-KI/KIC laws of covalent ceramics (SiC and Si3N4) are given for comparison.

Fig. 9 .

 9 Fig. 9. Crack velocity function of the nano-structured alumina-zirconia composite under cyclic fatigue, compared to that obtained under static fatigue.

Fig. 10 .

 10 Fig. 10. Aging kinetics (monoclinic fraction increase versus time at 134°C, 2 bars) of biomedical grade zirconia (3Y-TZP), alumina-zirconia micro-composite and nano-composite.

Table 1 .

 1 Frequency, intensity and full width at half maximum (FWHM) of the R1 and R2 bands (mean values ± standard deviations) as obtained by fitting the experimental.

	Sample		Frequency	R1 band	FWHM	Frequency	R2 band	FWHM
			(± standard	intensity	(± standard	(± standard	intensity	(± stan-
			deviation)	(± stand-	deviation)	deviation)	(± stand-	dard devia-
				ard devia-			ard devia-	tion)
				tion)			tion)
	Commer-	Control	14 396.2 ± 0.1	45 ± 2	11.63 ± 0.05 14 424.2 ± 0.1 30 ± 1	9.59 ± 0.02
	cial
	alumina	Worn a	14 396.1 ± 0.1 45 ± 2	11.57 ± 0.08 14 424.1 ± 0.1 30 ± 1	9.52 ± 0.04
	Experi-	Control	14 396.0 ± 0.1 18 ± 2	11.52 ± 0.02 14 424.0 ± 0.1 12± 1	9.31 ± 0.01
	mental
	alumina	Worn a	14 396.1 ± 0.2 17 ± 2	11.50 ± 0.04 14 424.2 ± 0.1 12 ± 1	9.31 ± 0.09
	experi-	Control	14 395.8 ± 0.1 25 ± 2	11.39 ± 0.01 14 423.7 ± 0.1 16 ± 1	9.35 ± 0.01
	mental
	NZTA	Worn a	14 395.8 ± 0.1 25 ± 2	11.38 ± 0.06 14 423.8 ± 0.1 16 ± 1	9.31 ± 0.06

a Mean values obtained on three worn cups.

Table 2 .

 2 Ra (roughness) values measured at the top of a commercial alumina head (AL), an experimental alumina head (BK) and a NK head, before and after 7 million cycles.

		Commercial	Experimental	Experimental
		alumina (AL)	alumina (BK)	nano-composite (NK)
	Ra (0 Mc)	2.3 (nm)	7.1 (nm)	5.1 (nm)
	Ra (7 Mc)	3.0 (nm)	18 (nm)	11 (nm)

Table 4 .

 4 Load to failure measured on 7 femoral heads prototypes processed from alumina-zirconia nano-composites.

	Femoral head n° Load to failure (kN)
	1	50.96
	2	34.50
	3	54.06
	4	44.96
	5	58.82
	6	45.75
	7	55.56
	Mean value	49.23

Acknowledgement

The work was funded by the EU under contract n°G5RD- CT-2001-00483 (BIOKER).

Disclosure statement

All authors disclose any actual or potential conflict of interest including any financial, personal or other relationships with other people or organizations within three (3) years of beginning the work submitted that could inappropriately influence (bias) their work.