E Neubauer

M Kitzmantel

M Hulman

P Angerer

Potential and challenges of metal-matrix-composites reinforced with carbon nanofibers and carbon nanotubes

With a continuous improvement of the production techniques for carbon nanofibers and carbon nanotubes along with an improvement of the available qualities of the materials, these reinforcements have been introduced into polymers, ceramics and metals. While in the field of polymers first success stories have been published on carbon nanofiller reinforcements, up to now metals containing these types of nanofillers are still a topic of intensive research. Basically a similar situation were found in those days, when micron sized carbon fibers came on the market. Today many applications of carbon fiber reinforced composites are existing, while metals reinforced with conventional carbon fibers are still only found in niche applications.

Several reasons can be identified, why the introduction of carbon based nanofillers (nanofibers/nanotubes) into metallic matrices is a difficult task. Nevertheless it is worthwhile to carry out systematic studies in this field due to the excellent and promising thermal, electrical, mechanical or tribological properties of the nanofillers. This paper gives an overview and summarises the activities related to carbon nanotubes and nanofibers used as a reinforcement in metallic matrix materials. The main challenges and the potential with respect to material properties will be discussed.

1) Introduction

Within the past years there was a significant increase on publications related to carbon nanofiber (CNF) and carbon nanotube (CNT) reinforced composites. Most of these publications are related to polymer based composites. Up to now there has been a limited number of publications and especially of success stories, where CNTs or CNFs have been successfully introduced in metallic or ceramic matrix materials resulting in significant improvements of the properties of the matrix material. This situation is similar to those several decades ago, when micron sized carbon fibers were already used in commercial applications in polymers while the successful introduction of carbon fibers in metal matrix composites took several additional years before showing first success. The reason why polymer based matrix composites resulted in a faster success compared to metal based ones, is of course related to the fact that a polymer matrix is in general characterised by a rather poor thermal, mechanical, electrical or tribological performance. By introduction of a filler material, which is characterised by several orders of magnitude better/higher properties than the one of the matrix, it is much easier to generate benefits through the reinforcement. The situation is quite different when speaking about reinforcing a metallic or ceramic matrix. Here the matrix material itself exhibits good material properties already, which hampers significant improvement through the reinforcement. To take advantage of the promising properties of the filler many aspects related to the processing of materials have to be considered. Especially when using nanosized fillers with high thermal, high electrical conduc-tivity and high mechanical strength, the compatibility of matrix and filler as well as the interface are crucial bottlenecks.

Carbon nanotubes with their -theoretically -high properties are of special interest to be introduced in metallic matrix materials. The mechanical properties of CNTs are usually reported to have an average modulus of elasticity of about 1-2 TPa. The average bending strength for MWNTs was measured at 14.2+/-8 GPa and the tensile strength is on the order of 11 to 63 GPa. Because SWNTs tend to assemble in "ropes" of nanotubes, their mechanical properties vary with the rope characteristics. In this case the modulus varies in the range of 32-1470 GPa and the tensile strength is 13-52 GPa [1].

Thermal conductivity of CNTs can be estimated using the values of the thermal conductivity of graphite. It can be expected that the axial thermal conductivity of CNTs could exceed that of II-a diamonds, with a thermal conductivity 1800-6000 W/mK. On the other hand, the radial thermal conductivity of MWNTs can be expected to be on the same order as the c-axis thermal conductivity of graphite or even lower. Home et al. [2] have measured the thermal conductivity of a loosely packed tangled mat of SWNTs in the temperature range from 8 K to 350 K. They have found that the thermal conductivity of this mat is 0.7 W/mK at room temperature. They have estimated the value of the thermal conductivity of the bulk material to be 36 W/mK. It must be noted that the mat possesses a disordered structure, when SWNTs could be aligned longitudinally, the thermal conductivity could possibly reach 6000 W/mK. Furthermore new types of carbon fibers have been brought to the market in the past years. These so called vapor grown carbon fibers (VGCF) or carbon nanofibers are characterised by a diameter of approx. 100-200 nm. Their thermal conductivity reaches values up to 2000 W/mK, which makes these fibers attractive as reinforcement for metal matrix composites. With the availability of these fibers in kg batches and at an affordable price, they are promising candidates to achieve a metal-CNF-material combining high thermal conductivity and improved mechanical properties with a reduced coefficient of thermal expansion (CTE).

Summarising the previous considerations the introduction of nanosized carbon based fillers into a metallic matrix would have the potential to improve the mechanical properties to reduce the coefficient of thermal expansion to improve the thermal conductivity to reduce the coefficient of friction to improve the electrical conductivity of the primary matrix material significantly. These are of course results based on theoretical considerations. The following section of the paper will summarise and give examples of the main technological challenges, which have to be fulfilled at the same time and represents important aspects for being successful in taking advantage of the excellent properties of the carbon nanofillers. To demonstrate the importance of addressing all the individual challenges, examples from experimental work on copper-CNF/CNT composites will be shown.

2) Challenges in Copper-CNF composites

As described in the introduction there is a potential for the application of copper reinforced with carbon nanofibers, although several problems have to be solved. These problems are basically known already from the work with carbon fibers, but some of them turn out to represent key problems when working with CNFs/CNTs (e.g. dispersion or interface). Key problems in the metal-CNX system are listed in Table 1 and compared to those in the metalcarbon fiber system. The abbreviation CNX stands for CNF/CNT throughout the following paper.

Challenge No.1: Selection of raw materials and their characterisation

Due to the fact that there is a huge number of CNX suppliers on the market ranging from small and medium enterprises to multinational companies, it is rather difficult to select the appropriate supplier and the corresponding raw materials. In addition the production capabilities range in from some grams/hour to several hundreds of kilograms/hour. Due to the size of the CNX with typical diameters ranging from some nanometers (e.g. in single walled nanotubes) to some hundreds of nanometers in carbon nanofibers it is rather difficult to get precise datasheets of the raw materials from the producer. The direct access to the properties of the CNXs is rather difficult. While in conventional micron sized carbon fibers single fiber testing is an appropriate tool for the determination of mechanical, electrical or thermal properties, these methods cannot be applied to CNXs. Therefore today´s analytic tools have not yet reached a status, where they could not successfully carry out quality control of thermal, mechanical, tribological or electrical properties. Beside different production techniques (CVD, Laser ablation,…) for the production of these nanomaterials, the appearance of the raw material can have a broad range depending on their structure as well as dimensions.

• SWCNT (single walled), DBWCNT (double walled), MWCNT (multiwalled),..

• Nanofibers, Herringbone type (HB), Platelet CNFs (PL), Screwtype (SC)

In addition all these materials are available in different modifications such as as-received, purified, functionalised (e.g. COOH, OH), coated (e.g. with Cu, Ni), heat treated (2000°C/3000°C). These raw materials can either be directly used as a "powder" or also in form of skeleton materials (e.g. paper or felt). Figure shows the SEM image of a CNT paper (Figure 1a) and carbon nanofibers in a felt (Figure 1b).

In order to assess the quality of the raw materials, different aspects have to be checked. Scanning electron microscopy combined with statistic analysis can be used to evaluate the average aspect ratio and average diameter of the CNX materials. The purity level (remaining elements from the used catalysts from the synthesis of the CNX materials) can be determined by chemical analysis. Amorphous carbon phases can be determined by XRD or Raman Spectroscopy. The problems start when coming to mechanical, electrical or thermal properties. As already mentioned to get a direct measurement of the properties of individual nanofillers is rather difficult. Therefore attempts to correlate the thermal/electrical/mechanical properties to the structure of the CNX materials have been made.

It is indicated by Ivanov et al. [3] that a high temperature treatment (2.800°C) significantly increases the thermal properties of a carbon nanotube array. In a similar way there are indications from literature that a heat treatment in CNTs has a positive effect on their thermal properties. Up to now it requires a huge effort to characterise the thermal properties of single CNTs. Therefore other characteristics (degree of graphitisation) are expected to be related to the intrinsic properties of the CNTs [4]. Up to now only indirect methods (via the crystallinity or the measurement of a CNX pre-form such as CNT paper or CNF felt) allow an assessment of the quality to some degree (at high statistic numbers), or even to some extent a quality control of different lots of CNXs. As an example the impact of a thermal treatment of CNT raw material on its thermal properties (thermal diffusivity) is shown in Figure 2. With the increasing temperature of the heat treatment of a CNT material a shift of the peak intensities (ratio of D/G peak is observed) is also observed as shown in Figure 3. Therefore both techniques offer a possible method for the indirect analysis of the thermal properties of CNT materials. Of course these measurements still not allow deriving the intrinsic thermal properties of the individual CNTs

Challenge No.2: Dispersion of CNX in the matrix material

Dispersion of CNXs is challenging since there are acting strong forces between them. CNXs tend to agglomerate due to their electrostatic and van der Waals forces. Therefore dispersion plays an important role to reach the theoretically predicted properties for various composites, which haven't been experimentally confirmed up to now. Several strategies were followed in literature to disperse the fillers, which can be roughly divided into the following categories:

Mechanical dispersion

Of course a common way to disperse and distribute fillers in a matrix material is based on mixing and milling operations. Nevertheless the success of dispersion by dry mixing of metal powders with CNXs is rather poor. As an example Figure 4 shows the result of dry mixing of dendritically copper powders with CNFs. Here the big agglomerates, initially present in the raw materials, were not separated. By applying high energetic mixing processes such as ball milling, better dispersions can be achieved. Of course these procedures must be handled with care and optimised very carefully in order to keep the properties of the CNXs since in some cases a damage/modification of the CNX materials due to the mixing/milling procedure was reported [5].

Dispersion in solvents and surfactant/ultrasonic support

Some of the solvents, which are used for dispersion of CNTs, especially for SWCNTs, are based on amides such as N,N-dimethylformamide (DMF) and N-methylpyrrolidone (NMP) [6]. Chen et al. reported on the dispersion of SWCNTs dissolved in organic solutions with thioylcloride and octadecylamine [7]. Another possibility is to disperse CNTs in water by using surfactants. CNTs are covered by the surfactants and help to form a stable colloidal dispersion [8]. The surfactant acts as a coupling agent and may introduce repulsive forces between individual CNTs. These repulsive forces are larger than the van der Waals attractive forces between the surfaces of the CNTs. A promising method is to disperse high weight-fraction carbon nanotubes in water using a surfactant for this purpose. Sodium dodecylbenzene sulfonate (NaDDBS), having a benzene ring moiety, a charged head group, and an alkyl chain, dramatically enhances the stability of carbon nanotubes in aqueous dispersions compared to commonly used surfactants such as sodium dodecyl sulphate (SDS) or Triton X-100 (TX). Dispersion concentrations were improved by approximately a factor of one hundred compared to the commonly used surfactants by using a single step process which includes mixing CNTs with the surfactant in a low power, high frequency sonicator. The resulting dispersions prepared with NaDDBS remained dispersed for at least three month [START_REF] Yodh | Carbon nanotubes: high solids dispersions and nematic gels thereof[END_REF]. The positive effect of surfactants on breaking up of the agglomerations in a Cu-CNF powder mixture is shown in Figure 5.

Nevertheless it must be mentioned that for the manufacturing of metal matrix nanocomposites the previously dispersed CNX have to stay homogeneously dispersed when admixed with the metal. In many cases surfactants are used in combination with ultrasonic support and ball milling to provide a good dispersion. Beside the selection of a suitable surfactant, the appropriate concentration and the parameters for ultrasonic mixing, a huge influence is also observed depending on the quality/purity level of the CNX raw material. As an example Figure 6 shows the results of a copper-CNFs composite using nanofibers from one supplier but with different quality/purity. The conditions of the CNFs are a) cleaned, b) after graphitisation and c) after iron free graphitisation. All the CNF raw materials where mixed by using ultrasonic support and dispersants, and the consolidation took place under identical conditions. As it can be seen from the figures, there is a difference in the achieved dispersion within the composites.

Dispersion in acids

In the untreated state nanotubes may be dispersed using ultrasound, but the effect of causing defects is not always clear. Chemical oxidation of their surfaces with acids can introduce oxygen containing functional groups onto the surface. During this process, open ends are formed in the oxidizing environment, which result in a well dispersed, electrostatically stabilised colloid in water and ethanol. Using HNO 3 for short period already results in a good dispersion of CNTs. Homogeneous dispersion of VGCFs (Vapor Grown Carbon Fibers) was achieved by the addition of polyacrylic acid [10]. Typically the latter procedure is also one of the first steps used for a subsequent chemical coating of CNFs.

Coating of CNF/CNTs

Besides conventional powder metallurgic methods of blending the powder and the CNX filler, an advanced process is based on coated reinforcements resulting in a good distribution of the CNXs in the matrix. Additionally this advanced process avoids severe mixing and milling operations. A promising coating process involves the following steps: surface modification of the reinforcement, increase of active surface sites to improve the bonding between the matrix and the reinforcement, but also to maintain the superior performance and excellent intrinsic properties of reinforcement. The deposition of various metallic coatings (such as Cu, Ni, Co) onto short fibers or particles by electrochemical methods is emerging as a state of the art technology [11,12,[START_REF] Wan | [END_REF].

1) Electroless methods/Molecular Level Mixing Process have also been used to deposit various elements such as Cu [14] Au [15], Ag [16], Co-B [17], Ni [18] [19] or Co [20] onto CNXs. To obtain a metallisation of a CNX several steps are necessary such as pre-treatment comprising of acid pre-clean (e.g. with nitric acid), sensitisation and activation. 2) CVD methods, which are used to coat short fibers or particles, are based on fluidised bed reactors [21,22,23] and have been optimised during the past years [24,25]. In order to achieve uniform coatings it is necessary to have suitable precursor gases. Depending on the use of different powders -particles or short fibers -the fluidised bed conditions must be optimised for each system. The process is suitable to deposit nanometer layers of different metals, carbides, nitrides, etc., e.g. WC, TaC, Co und Ni nano-layers as well as the treatment and coating of nanofibers [26]. CVD processes (fluidised beds) are promising methods since uniform deposition of thin layers, even intermediate layers, is possible. Al, Cu or Mg have already been deposited onto CNFs and CNTs [START_REF] Edtmaier | Proceedings of PM 2004[END_REF].

3) PVD coating of various metals on suspended single-walled carbon nanotubes (SWNT) was carried out by electron-beam evaporation [START_REF] Dag | [END_REF]. TEM studies reveal that Ti, Ni and Pd coatings on the suspended tubes are continuous and quasi-continuous, resulting in nanotube-supported metal nanowire structures. In strong contrast thereto Au, Al, and Fe coatings on the suspended SWNTs only form isolated discrete particles on the nanotubes. These results shed light into the nature of metal-tube interaction, an important topic to many fundamental and practical aspects of nanotubes [29]. Of course PVD processes would offer an attractive alternative with a number of advantages such as the possibility to modify the carbon/metal interface by a plasma pre-treatment, the easy realization of interlayers or even multilayers and the broad variety of elements or alloys, which can be deposited [30]. Plasma pre-treatment and coating of carbon nanofibers (VGCFs) was already successfully demonstrated by Brüser et al. [31,32] and Seo et al., who used an atmospheric plasma for pre-treatment of nanofibers [33].

As a general remark to all dispersion and coating processes it must be mentioned that all these processes introduce additional impurities to the final compact material (e.g. coming from chemicals used in the coating process), as well all of these method are possible sources for additional carry-over of oxygen/oxides to a final product.

Challenge No.3: Processing of composite materials -Densification

The literature describes several ways for the preparation of metal matrix composites (MMCs), especially of copper based MMCs. These methods can be divided into two groups according to the state of the matrix or matrix alloy during the fabrication, namely, liquid state or solid state fabrication methods. In the following section the most important advantage and disadvantage are described.

Solid State Fabrication Methods:

This includes fabrication methods utilising powder metallurgical techniques. Basically reinforcement and matrix material (metal powder) are mixed together and subsequently pressed to consolidate at elevated temperatures. In many cases additional pressure is applied to achieve a composite material without or with low porosity.

For preparation of copper-carbon based composites by powder metallurgical methods in general mechanical blending of the components, cold pressing and hot consolidation such as sintering, hot pressing, hot isostatic pressing, forging or extrusion are used. When working with nano-reinforcements the final composite properties are extremely sensitive on the preparation steps before the consolidation and have to be optimised for each materials system. In the following section, several methods for consolidation of metal-CNX-composites and their advantage/disadvantage are summarised. Pressing followed by sintering is only a feasibly processing technique, if a low concentration of CNXs is used in the composite, otherwise densification during sintering will be a problem.

The main advantage of pressing and sintering is the possibility to obtain a net shaped or near net shaped part without the need for expensive post machining processes. In addition, if a metal-CNX composite material can be successfully sintered, it would be possible to process such a composite via powder injection moulding and therefore allowing very complex shapes and structures.

For material applications where the CNX loading is larger than 5-10 vol% and full densification is the target, external pressure assisted techniques have to be employed.

Hot pressing is a commonly used process to consolidate materials either with high melting points or to achieve a fully dense part in the case of highly loaded metal matrix composites. In addition this process can be used if a material system generally has a tendency for de-wetting (as in the case of copper and carbon).

Generally the latter method uses uni-axial pressurisation. The powder mixture is filled into a graphite die and loaded with an external hydraulic system by two punches. The advanced process for the manufacturing of CNX reinforced MMCs is based on the use of pre-coated CNXs. The heating up of the filled graphite die can be achieved by different techniques such as: Direct heated hot pressing Inductively heated hot pressing Conventional hot pressing (indirect heated) Advanced hot pressing concepts, e.g. spark plasma sintering, plasma pressure compaction etc.

Figures 10 and11 show the microstructure and the distribution of CNFs in a copper matrix for a) a simple powder mixture and b) the corresponding copper coated CNF using the same type of CNF. A clear advantage in terms of distribution as well as in terms of densification is found.

The advantage of the fiber coating process can be summarised as follows:

• Higher density compared to powder mixtures • Continuous matrix network • Better CNX distribution • no reinforcement to reinforcement contact • better interfacial contact between CNX and matrix.

Liquid Phase fabrication methods (infiltration processes)

The method of choice to realise high CNX volume percentages and at the same time a material with high densification is liquid phase fabrication. Here the pre-form (a CNX felt or paper) is inserted into a die and the metal or alloy is placed on top, followed by heating the setup above the metal melting point. Depending on the wetting behaviour, spontaneous wetting and infiltration can take place. Most of the time -due to the rather poor or even non-wetting metal-carbon-system -additional pressure (either mechanical or via a gas) has to be applied to overcome the threshold pressure of the system and infiltrate the pre-form. Methods typically used are gas pressure infiltration or squeeze casting. In addition to the non-wetting system characteristics this threshold pressure becomes extremely high with a decreasing pore size (which is definitely the case for CNX pre-forms). This challenge can be solved by modifying the surface of the reinforcement to promote the wetting on the metal-carbon interface. A simple explanation for this is given by the wetting angle (solid/liquid) of the two components, which should at least be below 90°. In the case of carbon based reinforcements and copper this promotion of the wettability can be achieved by introducing alloying elements. The CNXmetal system is extremely sensitive on the amount of alloying elements added and usually has to be optimised together with the consolidation parameters to avoid degradation of the mechanical, thermal or electrical properties of the matrix on the one hand, and to avoid too severe reactions between the alloying elements and the CNXs on the other hand. The interlayer formed by carbide formation of the alloying elements also guarantees a good internal thermal interface and reduced thermal resistance between the composite components. A careful control and optimisation of the amount of alloying elements is crucial for a successful improvement of the macroscopic composite properties.

Figure 12 shows the cross section of an infiltrated conventional carbon fiber woven with a Cu-Cr alloy. The carbon fiber woven is completely infiltrated, this means good wetting was observed. At the same time the alloying elements resulted in a significant formation of an interface zone in the range of 1 µm. By using a similar infiltration process for a CNF pre-form the infiltration was also possible, but here a gradient structure was observed (Figure 13). At the beginning of the infiltration front, due to a higher concentration of the alloying element and a longer contact time between the melt and the pre-form, already reaction -in some areas complete consumption of the CNF -was observed, while at the area of the end of the infiltration front the CNF are still present without any indication of a severe reaction with the alloying additives.

Challenge No.4: Alignment/Anisotropy of material properties

Due to a high aspect ratio of 1:10 to 1:100 of CNX during solid or liquid state processing, a certain alignment/orientation is observed. By using e.g. unidirectional pressure in hot pressing the CNT/CNF show a certain preferred alignment in x-y direction (perpendicular to the pressing direction). This is of course directly related to anisotropic material properties. The fiber alignment is not only visible from SEM micrographs but is also mirrored in the anisotropic behaviour of the thermal properties of the composite. While hot pressing results in a preferred 2D random in-plane alignment, the usage of an extrusion process can result in a longitudinal alignment of the CNX in the matrix [34]. The alignment of course is for specific application of advantage, but in most applications isotropic material behaviour is required. Figures 14 show the cross section of a Cu-CNF composite prepared by hot pressing. While Figure 14 (upper image) represents the view along the pressing direction, Figure 14 (lower image) represents the radial view (perpendicular to the hot pressing direction). It has to mentioned, that in a composite with well dispersed and randomly oriented fiber reinforcements, the exploitation of the potential increase of the composite properties is only one third compared to a composite with a 1D fiber orientation. In thermal applications this is very important, because metals themselves exhibit for example very good thermal conductivity.

Challenge No.5: Interface Design

One of the most critical challenges, when coming from micron sized fillers to nanosized fillers, is the appropriate design of the interface between the matrix and the filler. Due to the significantly increased surface/volume ratio when going to nanosized fillers, the overall interfacial area also increases significantly and therefore plays an essential role. Especially for those composite materials, where the thermal or mechanical properties of the carbon nanomaterials are of interest, a good mechanical bond as well as a low thermal contact resistance between the metal and the reinforcement must be guaranteed. The concepts to improve the mechanical and thermal interface are basically related to surface modifications like roughening of the surface of the reinforcement, the deposition of intermediate layers or the addition of alloying elements to ensure a certain reaction (i.e. carbide formation) at the interface. For specific matrix materials (e.g. Al) possible direct reactions with carbon filler material must be considered and controlled. Figure 15 shows the influence of various additions of carbide forming elements on the thermal conductivity in a CNF-copper MMC. As it can be seen, the addition of Ti or Cr (different amounts) increases the thermal conductivity significantly in comparison to the composite with a not-modified interface. In a similar way alloying elements have a strong impact on the thermal stability of the coefficient of thermal expansion of a metal-CNF composite during thermal cycling.

Challenge No.6: Applications

As already mentioned in the introduction, it took several years, almost decades, before products of carbon fiber reinforced metal matrix composites became available. R&D work related to metal matrix nanocomposites using CNFs/CNTs is still at the beginning and the most promising areas of applications are not yet identified. For some specific compositions a more clear picture is given, if they will succeed in specific applications or not. As an example from today´s knowledge the hurdles to realise a high thermal conductive (better conductivity than copper) combined with low CTE (approximately half of that of pure copper) for applications as heat sinks are very big. On the other hand such a material is probably of interest to be used in tribologically loaded applications. In a similar way these questions have to be addressed for other metal matrices such as Al, Mg, Ag or Ni. Probably in some of these materials the carbon nanofibers or carbon nanotubes can be used in applications with the focus on the electrical properties, in other applications to improve the mechanical material properties.

Conclusions and Remarks

Some general statements as conclusions and remarks to the field of metal-matrix nanocomposites: Within the next years there will be a "consolidation" of the many suppliers of CNF/CNT (=CNX) materials. On the one hand major producers of CNX materials are meanwhile able to produce from several tons to hundreds of tons per year such as Showa Denko, Sun or Bayer, which will significantly bring the price of nanomaterials down.

On the other hand the quality of these high volume products is questionable. For sure it will be sufficient for polymer reinforcement, but high quality products will be needed for reinforcing metals. The assessment of the quality/properties of the CNX materials is an open question, which has to be addressed in the future. Meanwhile various methods for the dispersion of CNX have been established, which work quite well already. Coating of the reinforcement with the matrix materials is one of the most promising, but of course additional costs for the coating process have to be considered.

The comparison of CNX reinforced metals with the unreinforced metals processed (e.g. ball milling of the pure Cu or Al powder) under the same conditions is important.

Otherwise in some cases a wrong interpretation of the achieved experimental results might be the case. Some metals -if processed e.g. by ball milling -will exhibit different properties compared to those when the metal powder is consolidated without previous milling [35].

Due to a high surface area of the CNX material this is directly related to additional oxygen, which will be brought into the composite. As a result of this e.g. fine dispersed oxides could be formed, which could possibly have a positive impact on the mechanical properties ("dispersion strengthening effect").

In some cases (e.g. titanium) the addition of CNX results in a refinement of the matrix grain size. So in such a case CNX indirectly effect the material properties. Probably such a grain refining effect could be also observed by the addition of other types of nanomaterials [START_REF] Montealegre | Influence of Nano-Reinforcements on the Mechanical Properties & Microstructure of Titanium Matrix Composites[END_REF].

Finally the formation of carbides from the reaction between the matrix and the CNX must be considered. In a CNX reinforced composite it has to be ensured that there are still CNXs present in the final composite.

When bringing CNXs together with a matrix metal under high temperatures/pressures, this might also result in a modification, amorphisation or complete degradation of the CNX material [START_REF] Lloyd | Effect of Titanium on Copper-Titanium / Carbon Nanofibre Composite Materials[END_REF], especially when additives are involved in a surface modification process. Table 2: Influence of alloying elements in copper on the wetting behavior (contact angle) of copper and carbon substrates (VC: Vitreous Carbon)

  These steps are essential to clean and purify the CNXs and increase the catalytic sites on the CNXs for the following deposition process. During deposition the tendency of CNXs to agglomerate may hinder a continuous formation of a layer. Depending on the selection of deposition parameters it is possible a) To implant the CNT/CNF in metal particles ("composite powder") b) To deposit metallic particles on CNT/CNFs ("decorated CNT/CNFs") c) To completely coat the individual CNT/CNFs Examples of the different possibilities obtained by the controlling of the deposition parameters are shown in the Figures 7 -9.

Figure 1 :Figure 2 :

 12 Figure 1: SEM image of a CNT paper (a); carbon nanofibers in a felt (b)

Figure 3 :Figure 4 Figure 4 :

 344 Figure 3: RAMAN shifts of CNT felts. With increasing heat treatment temperature of the felt the D/G peak ratio changes from 1.74 (as produced) to 1.62 (heat treated at 1.000°C) and finally to 1.34 (heat treated at 2.000°C)

Figure 5 : 6 Figure 6 :

 566 Figure 5: SEM image of dentritic copper powder and CNF after mixing using dispersion aids (a); magnification shown in (b)

Figure 7 :Figure 8 Figure 8 :

 788 Figure 7: SEM image of "composite powder" consisting of copper particles with embedded CNFs

Figure 9 :µm 1 µm 17 Figure 10 :Figure 10 :

 9171010 Figure 9: SEM of fully copper coated CNFs

Figure 11 :Figure 11 :Figure 12 :

 111112 Figure 11:

Figure 13 :µm 19 Figure 14 Figure 14 :Figure 15 :

 1319141415 Figure 13: Light microscope image of carbon nanofiber felt infiltrated with a copper alloy

TABLE 1

 1

	Challenges	Carbon fibers	Carbon Nanofibers/Nanotubes (CNX)
	Selection of suitable raw mate-	Data sheet of different carbon fibers	Lack of data from suppliers,
	rials (different suppliers &	are available	characterisation of CNX properties is not
	qualities)		easy, there are many suppliers,
			Reproducibility of data/quality?
	Dispersion of reinforcement in	Optimisation of conventional blend-	To coat the CNTs seems to be the most
	the matrix material	ing techniques is sufficient, coating of	appropriate way to get a homogenous dis-
		fibers provides an advanced solution,	tribution
		fiber breakage has to be taken into ac-
		count
	Densification of the composite	Optimisation of processing conditions	Remaining porosities are higher, maxi-
	Processing/	with regard to densification and inter-	mum CNX loading is lower, liquid phase
	Reactivity with Matrix	facial reactions,	processing is difficult
		Liquid phase processing allows high	Reactivity of the matrix with CNX has to
		loading of carbon fibers/flakes	be considered
	Alignment/ Orientation/	Aspect ratio of 1:10 to 1:100 results	Alignment of CNXs takes place depend-
	Anisotropy	in an orientation of the fibers/flakes	ing on the processing due to the high as-
		during processing => anisotropy of	pect ratio
		properties
	Interface	Interface plays an important role for	Interface plays an essential role to exploit
		mechanical and thermophysical prop-	the properties of the reinforcement
		erties
	Applications	Applications as heat sinks reported,	Up to now only a few products are re-
		companies on the market selling	ported -volume of sellings are not
		products	known

Table 1 :

 1 Overview and summary of challenges in carbon fiber and carbon nanofiber/nanotube reinforced metal matrix composites

Table 2

 2

	Matrix	Substrate	Temperature	Contact Angle	Reference
	Cu (1at% Cr)	Vitreous Carbon	1100°C	41±4	[38]
	Cu (<0.2at% Cr)	Vitreous Carbon	1050°C	~130	[39]
	Cu (>0.2at% Cr	Vitreous Carbon	1050°C	~45
	Cu (<0.2at% Ti	Vitreous Carbon	850°C	~150
	Cu (>10at% Ti	Vitreous Carbon	850°C	Close to 0
	Cu (10at% Ti)	VC/Pyro-C	1180°C/1150°C	Close to 0	[40]
	Cu/Cu+1at%V	Vitreous Carbon	1150°C	45/62	[41][42]
	Cu (1at% Cr)	VC/graphite	1150°C /60 min	50/45
	Cu	VC/Pyro-C	1150°C	136±2, 133±3
	Cu	Vitreous Carbon	1100°C	139±2, 122±2

Acknowledgements

This work was supported by the FP6 EU project STRP 031712 INTERFACE and the FFG Research Studio under contract 818649.


D Marcos-Gómez

J Ching-Lloyd

M R Elizalde

W J Clegg

J M Molina- Aldareguia

Predicting the thermal conductivity of composite materials with imperfect interfaces

Keywords: C. FEA, B. Interface, A. Short-fibre composites, A. Carbon nanotubes

This paper compares the predicted values of the thermal conductivity of a composite made using the equivalent inclusion method (EIM) and the finite element method (FEM) using representative volume elements. The effects of inclusion anisotropy, inclusion orientation distribution, thermal interface conductance, h, and inclusion dimensions have been considered. Both methods predict similar overall behaviour, whereby at high h values, the effective thermal conductivity of the composite is limited by the inclusion anisotropy, while at lower h values, the effect of anisotropy is greatly diminished due to the more dominant effect of limited heat flow across the inclusion/matrix interface. The simulation results are then used to understand why in those cases where it has been possible to produce CNF reinforced Cu matrix composites with a large volume fraction of well dispersed CNFs, the measured thermal properties of the composite have failed to meet the expectations in terms of thermal conductivity, with measured conductivities in the range 200-300 W/m•K. The simulation results show that, although degradation of the thermal properties of the CNFs and a poor interfacial ACCEPTED MANUSCRIPT 2 thermal conductance are very likely the reasons behind the low conductivities reported, great care should be taken when measuring the thermal conductivity of this new class of materials, to avoid misleading results due to anisotropic effects.

Introduction

With the increase in computing capacity of modern computers, brute force characterization of heterogeneous materials is becoming more and more accessible.

What could only be done with simple or highly symmetrical models, especially in 2D, only a couple of decades ago, is now feasible even for home computers. The key concept of this progress is the representative volume element (RVE) [START_REF] Drugan | A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites[END_REF][START_REF] Trias | Determination of the critical size of a statistical representative volume element (SRVE) for carbon reinforced polymers[END_REF][START_REF] Kanit | Determination of the size of the representative volume element for random composites: statistical and numerical approach[END_REF], which defines how large a representative cell must be to give properties of a composite material under a given error. This is the case of the finite element method (FEM), which is based on dividing the geometry under study in a large number of discrete elements.

Both, the number of elements and the size of the model, which depends on the number of inclusions and the volume fraction, are the main factors affecting the computational power required to run the simulations. With the currently available computer power, it is now possible to simulate sufficiently large RVEs to study the properties of new metal matrix composites reinforced with carbon nanofibres (CNF). These are a new class of engineering materials that offer opportunities to tailor properties and meet specific requirements, e.g. in heat sinks. For instance, CNF reinforced copper composites constitute an ideal candidate to work as an electrical contact material and/or substrate for semiconductor devices due to their potentially high electrical and thermal conductivity, small coefficient of thermal expansion, good machinability and low price.

Processing these materials is challenging due to the poor wetting between copper and carbon, which makes very difficult the fabrication of dense composites with homogeneously distributed fibres. However, even in those cases where the experimental difficulties have been overcome and a large volume fraction of well dispersed CNFs has been obtained, the measured thermal properties of the composite have failed to meet the expectations in terms of thermal conductivity [START_REF] Neubauer | Potential and challenges of metalmatrix-composites reinforced with carbon nanofibers and carbon nanotubes[END_REF][START_REF] Ullbrand | Thermomechanical Properties of Copper-Carbon Nanofibres Composites Prepared by Spark Plasma Sintering and Hot Pressing[END_REF]. There are two possible reasons for this: (1) the highly anisotropic properties of CNFs combined with a preferred orientation of the fibres during processing and (2) the interfacial contact resistance of the Cu-C interface limiting the potential benefit of incorporating these inclusions into the matrix.

In this context, the objective of this study has been to use a range of modelling methods to evaluate the effect of fibre anisotropy and interfacial thermal contact resistance into the global thermal properties of a CNF reinforced Cu matrix composite. The modelling method employed has been the FEM of a RVE. Despite the considerable computer power required, the advantage of this approach is that it allows the study of the local fields, which cannot be accomplished by homogenization methods, and that the generated RVE can also be used to study other thermomechanical properties, such as the thermal expansion coefficient or the plastic deformation of the composite. The FEM results, when possible, have been contrasted with results obtained through different homogenization methods such as two different equivalent inclusion methods (EIM), the mean field approach (MFA) and, to some extent, the differential effective medium (DEM) approach. Comparisons have been made for cylindrical and spherical inclusions, while various parameters, such as volume fraction or inclusion conductivity, have been varied in order to understand the origin of the discrepancies observed between all the methods.

The paper is organized as follows. First, spherical inclusions are analyzed and values of the three methods are compared in two parametric studies, one varying the volume fraction and the other one varying the interfacial conductance. A further comparison is made between FEM and MFA for different inclusion sizes and thermal conductivity differences between phases. This is followed by two other studies for the case of cylindrical inclusions. FEM and MFA are compared for long and short fibres with low and intermediate volume fractions and different values for the interfacial conductance.

Finally, FEM is used to carry out a more complete parametric study for short fibre composites as a function of the anisotropy of the inclusion and the interface conductance.

Model description

All RVE considered were cubes of periodic geometry. That is, it was assumed that the composite microstructure was given by an infinite translation of this RVE along three axes to eliminate boundary effects and, thus, the fibre positions within the RVE kept this periodicity condition. This means that inclusions cut by a face of the cube reappear in the opposite face with the rest of its volume (see fig. 1). The numerical analyses of the RVE were carried out using the finite element method (Abaqus® [6]). To this end, the prismatic RVE (matrix and inclusions) were meshed using tetrahedral elements.

Finally, periodic boundary conditions, which have been demonstrated to improve the accuracy of results [START_REF] Kanit | Determination of the size of the representative volume element for random composites: statistical and numerical approach[END_REF], were applied to the RVE surfaces to ensure continuity between neighbouring RVEs.

The modelling strategy to calculate the thermal conductivity of the composite in a given direction is depicted in fig. 2. The boundary condition applied is a temperature difference of 100 K in that direction. This is implemented by tying together in temperature the nodes of opposite faces defined by the same coordinates, while node couples of faces parallel to this axis have imposed a temperature difference of 0 K, as heat flux in that direction is to be avoided. Heat going through each face is measured at reference nodes (to which all the nodes of that face are tied), and the thermal conductivity is calculated using Fourier's law. Thermal resistance at the interface was implemented through a standard interaction tool in Abaqus® [6] that, by defining a value for the thermal conductance, slows the heat transfer at the interface between phases.

As for EIM, in both the MFA and DEM techniques, the thermal interface conductance is implemented by replacing the inclusion with a non-ideal interface by an "effective" inclusion with the thermal conductivity, K i eff , given by:

ha K K K i i eff i + = 1 (1)
where K i is the inclusion thermal conductivity, a is the inclusion radius and h the interfacial thermal conductance.

The composite thermal conductivity, K c , given by MFA for a spherical inclusion is the same as that derived by Hasselman and Johnson [START_REF] Hasselman | Effective Thermal-Conductivity Of Composites With Interfacial Thermal Barrier Resistance[END_REF]:

( ) ( ) ( ) ( ) f f eff f f eff m c V V V V K K + + - - + + = 2 1 2 2 2 1 ϕ ϕ (2)
where K m is the matrix thermal conductivity, V f is the inclusion volume fraction and eff is the ratio of the effective inclusion thermal conductivity and the matrix thermal conductivity (K i eff /K m ). The DEM counterpart is given by: ( )

3 1 1 1 - × - - = - m c eff m c eff f K K K K V ϕ ϕ (3)
The composite thermal conductivity can be obtained by expanding out the equation, which is cubic and is solved analytically. (1.8 times the inclusion length). Although the size of such a RVE is slightly under the recommendable RVE size according to [START_REF] Trias | Determination of the critical size of a statistical representative volume element (SRVE) for carbon reinforced polymers[END_REF], simulations obtained with different fibre distributions led to very similar results and hence the size of the RVE was considered to be representative. The results presented here are the average value of three independent realizations with the same volume fraction and different fibre distributions.

Model Comparison

Spherical inclusions. Comparison between FEM, MFA and DEM

Figure 4 shows the predicted thermal conductivity of a composite with spherical inclusions (K i =3850 W/m•K) and a perfect interface (h= ) as a function of inclusion volume fraction using MFA, DEM and FEM techniques. In this case the size of the inclusion is not relevant since the thermal contact at the interface is perfect. The predictions of the different models match perfectly at low volume fractions and begin to deviate at an inclusion volume fraction of 0.3. The DEM consistently predicts higher values than the MFA, where the greatest relative difference between the two (~18%) is observed at a volume fraction of 0.7. Note that the MFA technique assumes that there is a continuous coating surrounding the inclusion. This condition is unlikely to be met at volume fractions greater than the optimum packing fraction in cubic close packed spheres, which is 0.74. Making predictions using the MFA for composites with volume fractions of 0.5 may be reaching the limit of the model as the inclusion particles begin to form a percolating network. This effect combined with meshing problems when the spacing between neighbouring inclusions is very small effectively limits the volume fraction in FEM simulations to 0.4. Up to this volume fraction it can be observed that FEM predictions are between DEM and MFA values. The values predicted by MFA will also tend to be lower than other prediction schemes as it gives a lower bound estimate [10].

The effect of the interface thermal conductance on the composite thermal conductivity can be observed in figure 5 for volume fractions of 0.2 (fig. 5a) and 0.4 (fig. 5b), again considering a K i of 3850 W/m•K. It has been discovered that this effect is always the same with the conductivity showing an asymptotic behaviour both for low and high conductances with an inflection point in the middle, that is, behaving as a sigmoid curve. Therefore, three regions can be identified: two plateaus for high and low values of h and a transition zone. For low h the composite behaves as a porous material whereas for high h the composite conductivity corresponds to a material with a perfect interface and hence it depends on the inclusion properties. In all the figures from now on, figure 5 included, values of the thermal conductance have been chosen to show these three regions. The model studied includes spheres with a diameter of 10 m and interface thermal conductances ranging from 1 to 10 15 W/m 2 •K. In the transition zone with the three methods the behaviour of the composite is dominated by the interface thermal conductance. In both instances, the DEM, MFA and FEM schemes exhibits discrepancies for the extreme values whereas very close predictions are obtained in the transition zone. For low h the upper bound is predicted by FEM and the lower bound by DEM whilst for a perfect interface the upper bound is given by DEM and the lower bound by MFA, as discussed previously. The greatest difference occurs for high conductances and is more significant in the case of an inclusion volume fraction of 0.4 with a difference of 11%. Note that the transition occurs at the same range of h for both volume fractions.

A more thorough comparison is made between the FEM and MFA techniques in Figure 6, where variations in the phase contrast and particle size are made. The differences in predicted values between these techniques for all cases are not significant, always below 6%. The overall trends are very similar and consistent, where an inclusion with higher thermal conductivity increases the composite thermal conductivity and the increase in the inclusion size has improved composite thermal conductivity at lower interface thermal conductance values. As previously stated, the predictions of the different schemes are almost equal in the transition zone, however, it is observed that as the phase contrast increases the maximum composite thermal conductivity is reached for higher values of h, that is, the extension of the transition zone increases with the phase contrast. Nevertheless, FEM and MFA predict the same extension of the transition zone for different values of the inclusion size. It is important to note that the method used to introduce the thermal interface conductance in both techniques is valid since no differences are observed in the transition zone and the discrepancies in the extreme values do not depend on the size of the reinforcement, i.e., on the surface area of interface.

Cylindrical inclusions. Comparison between FEM and MFA

Table 1 compares the predicted thermal conductivities by FEM and MFA for the three possible architectures (3DRandom, Planar Random and Uniaxial) of a fibre reinforced composite for a fibre volume fraction of 0.3. It should be pointed out that while the fibres simulated by FEM had an aspect ratio l/d=5, the MFA simulation results correspond to a long fibre reinforced composite. Contrary to the case of spherical inclusions that was used to compare the different simulation strategies, in this case the anisotropy of the fibres was taken into account, assuming a longitudinal thermal conductivity of 3000 W/m•K and a transversal thermal conductivity of 6 W/ m•K, which are typical values for carbon nanotubes found in the literature [11]. The matrix thermal conductivity was chosen to be that of Cu, 385 W/m•K, as before. In all cases, the interfacial thermal conductance was set at a relatively high value of 10 12 W/m 2 •K, to ensure that the behaviour lays on the inclusion dominated plateau and not on the interface dominated transition zone. The predictions of MFA and FEM match within 1-3%, except in the directions where there is a substantial fraction of fibres in the direction of the heat flow, in which case the FEM predicts lower values (12% lower in the planar case and 14% lower in the uniaxial case) than MFA. This seems to be in contradiction with the spherical inclusion results in which MFA represented a lower bound. However, this trend is related more to the length of the fibres, that were long in the case of the MFA computations and short, with an aspect ratio of l/d=5, for FEM and the size of the RVE simulated by FEM.

To confirm this, some MFA results were computed again for the case of a uniaxial orientation of fibres with a volume fraction of 0.15 (within the range of low volume fractions where MFA and FEM gave identical results for spherical inclusions) and considering spheroidal inclusions, instead of long fibres. In this case, the interfacial conductance was varied from 500 W/m 2 •K to 10 13 W/m 2 •K and the results are compared in figure 7. The differences between both methods are kept always below an acceptable 6%, indicating that the size of the RVE considered in FEM is large enough to capture the thermal behaviour of the composite with good precision.

Thermal conductivity of the composite

The results presented above show that, given enough precautions are taken to define the RVE, FEM is a reliable method to compute the thermal conductivity of metal matrix composites and is specially well suited for intermediate reinforcement volume fractions (~0.3), with the advantage on top of homogenization methods that the local fields can be studied in detail at the scale of the reinforcement. As explained in the introduction, the main objective of this work has been to use simulation tools to understand why in those cases where it has been possible to produce CNF reinforced Cu matrix composites with a large volume fraction of well dispersed CNFs, the measured thermal properties of the composite have failed to meet the expectations in terms of thermal conductivity, with measured conductivities in the range 100-300 W/m•K [START_REF] Neubauer | Potential and challenges of metalmatrix-composites reinforced with carbon nanofibers and carbon nanotubes[END_REF][START_REF] Ullbrand | Thermomechanical Properties of Copper-Carbon Nanofibres Composites Prepared by Spark Plasma Sintering and Hot Pressing[END_REF]. To do this, the FEM tools described above were used to carry out a complete parametric study as a function of the thermal anisotropy of the inclusion and the interface conductance to identify the most important factors limiting the real thermal conductivity of this new class of materials. Fig. 8 represents the simulated thermal conductivity of a CNF reinforced Cu composite as a function of interface thermal conductance, assuming three different preferred orientations of the CNFs: 3DRandom (8.a), Planar Random (8.b) and UA (8.c). The conductivities of matrix and fibres are the same as those assumed in section 3.2. The results show that in those cases where a preferred orientation of the CNFs is assumed (Planar Random and Uniaxial), the thermal conductivity can boost in these directions even at values higher than that of the Cu matrix, provided the thermal conductivity of the interface is above a threshold value of around 10 9 -10 10 W/m 2 •K. However, in these cases, the directions perpendicular to the preferred directions of the fibres show a reduced thermal conductivity due to the thermal anisotropy of the CNFs, as the transversal conductivity of the fibres (6 W/m•K) is much lower than that of the matrix.

The results also show that if the fibres are randomly oriented in all directions, it is only possible to obtain an enhancement in thermal conductivity with respect to Cu if the interface thermal conductance reaches values as high as 10 10 W/m 2 •K, and even in those cases the predicted values are very close to the thermal conductivity of Cu.

The experimentally measured thermal conductivities found elsewhere [START_REF] Neubauer | Potential and challenges of metalmatrix-composites reinforced with carbon nanofibers and carbon nanotubes[END_REF][START_REF] Ullbrand | Thermomechanical Properties of Copper-Carbon Nanofibres Composites Prepared by Spark Plasma Sintering and Hot Pressing[END_REF] correspond to CNF-Cu composite plates processed by hot-press. During processing, the CNFs tend to align perpendicular to the applied load, and hence, the CNFs display a random planar preferred orientation. Hence, there are three possible explanations for the low thermal conductivities obtained: (1) degradation of the thermal properties of the CNFs, as has been shown to occur in some cases [12], (2) a poor interfacial thermal conductance, very likely in Cu-CNF composites and (3) that the measurements are taken in transversal directions in which the CNFs display a very poor thermal conductivity.

Although the most plausible explanations are (1) and ( 2), (3) cannot be discarded, as most of the time the composites display a random planar configuration and the measurements are taken in the transversal direction by a laser flash method. Therefore, it should be emphasized that, when measuring the thermal conductivity of these composites, special care should be taken in order to evaluate their thermal anisotropy and avoid misleading results due to anisotropic effects. Techniques such as modulated photothermal radiometry constitute a good choice to carry out such studies [13].

Conclusions

A thorough comparison of different simulation strategies to model the thermal conductivity of CNF reinforced Cu matrix composites has been carried out. The different strategies were based on the FEM of a RVE and on homogenization methods, such as MFA and DEM. In order to separate the influence of the different parameters involved (size of reinforcement, volume fraction, phase contrast, interface thermal conductance, anisotropy of the reinforcements), the comparison has been made first with spherical inclusions and then with short fibres represented by cylinders. The predictions show three regions: two plateaus at high and low thermal conductances and a transition zone between them.

First, in order to study the influence of the volume fraction, size of the reinforcement, phase contrast (difference in thermal conductivities between matrix and reinforcement) and interface thermal conductance, a composite with spherical isotropic inclusions was considered. The position of the transition zone depends strongly on the inclusion size, with smaller inclusions showing a more interface dominated behaviour, as expected.

The results show a perfect match between MFA, DEM and FEM in the interface dominated transition zone, while some difference in the predictions were observed in the plateau. The differences are larger the larger the volume fraction and the phase contrast between matrix and inclusions. It has to be noted too, that larger inclusion radius and, therefore, less interface area per unit volume, results into the transition zone starting at lower thermal conductances, i.e., the interface thermal conductance is less critical.

Secondly, the case of a short fibre reinforced composite was considered. In this case, the most important parameters controlling the thermal conductivity are the interface thermal conductance and the preferred orientation of the fibres. For largely anisotropic inclusions, the thermal conductivity is limited by the transversal thermal conductivity if the fibres are randomly oriented. In this case, a substantial enhancement in thermal conductivity is only possible if the fibres are randomly oriented in the plane or if they are all aligned in one direction, but at the expense of displaying very poor thermal conductivities in the transversal directions. To benefit from these effects, a minimum interfacial thermal conductance of 10 9 -10 10 W/m 2 •K would be needed. Finally, the simulation results show that, although degradation of the thermal properties of the CNFs and a poor interfacial thermal conductance are very likely the reasons behind the low conductivities reported, great care should be taken when measuring the thermal conductivity of this new class of materials, to avoid misleading results due to anisotropic effects. FEM is limited to a maximum volume fraction of 0.4 Fig. 5: Variation in composite thermal conductivity with interface thermal conductance for a composite containing spherical inclusions with 10 µm in diameter and with a phase contrast of 10 (K i =3850Wm -1 K -1 ), using the MFA, FEM and DEM schemes.

Volume fractions are a) 0.2 and b) 0.4 (0.387 for FEM predictions).

For

  the case of spherical inclusions, diameters of 0.1, 1 and 10 m and volume fractions of 0.2 and 0.4 have been studied. In all the cases, the conductivity of the matrix was considered to be that of copper, 385 W/m•K [8]. In the case of the inclusions, different studies range the thermal conductivity of CNFs between 10 to 3000 W/m•K but these numbers are based on theoretical predictions rather than on actual experimental measurements. To understand the role of the interfacial thermal resistance as a function of inclusion properties, isotropic spherical inclusions with different thermal conductivities have been considered as a function of the thermal conductivity of the Cu matrix. Thus, three different phase contrasts (c=K i /K m ) of 0.1, 1 and 10 have been studied, corresponding to K i values of 38.5, 385 and 3850 W/ m•K respectively. The length of RVEs considered was ten times the inclusion diameter which is enough to obtain representative results [9]. For the case of fibre reinforced composites, the inclusions were represented by cylinders with an aspect ratio l/d of 5, where l stands for the length of the cylinder and d stands for the diameter. Three different architectures were studied: 3DRandom (fig. 3.a), Planar Random (fig. 3.b) and Uniaxial (UA) (fig. 3.c). The volume fraction studied was 0.28 in all cases, except for the UA architecture in which an extra simulation with a volume fraction of 0.15 was also performed. The fibre length was fixed at l = 500 nm and the diameter at d = 100 nm. The RVEs considered were cubes of side L = 900 nm

  /www.matweb.com/search/DataSheet.aspx?MatGUID=9aebe83845c04c1db5126fa da6f76f7e&ckck=1 9. Gusev AA. Representative volume element size for elastic composites: A numerical study. Journal of the Mechanics and Physics of Solids, 1997. 45(9): 1449-1459. 10. Mori T, Tanaka K. Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions. Acta Metallurgica, 1973. 21(5): 571-574. 11. Dresselhaus MS. Science of Fullerenes and Carbon Nanotubes. San Diego: Academic Press, 1995. 12. Lloyd JC, Neubauer E, Barcena J, Clegg WJ. Effect of Titanium on Copper-Titanium / Carbon Nanofibre Composite Materials. Composite Science and Technology, this issue (2010). 13. Gibkes J, Bein BK, Krüger D, Pelzl J. Thermophysical Characterization of Fine-Grain Graphites Based on Thermal Waves. Carbon, 1993. 31: 801-807.

Fig. 1 :

 1 Fig.1: A simple 2D model of a periodic short-fibre unit cell. When a fibre is cut, the rest of its volume reappears periodically through the opposite face.

Fig. 2 :

 2 Fig. 2:Example of periodic boundary conditions. A difference of 100 K is imposed in X axis. Each node in surface X = L is 100 K hotter than the node couple in the same

Fig. 3 :Fig. 4 :

 34 Fig. 3: Reinforcement architectures studied. a) 3DRandom: All the fibres are randomly positioned and oriented. b) Planar: Same as 3DRandom, but all the fibres are

Fig. 6 :

 6 Fig. 6: Variation in composite conductivity with interface thermal conductance for a composite with V f =0.4, three different inclusion diameters (0.1, 1 and 10 m) and three different phase contrasts (K i =38.5, 385, 3850 Wm -1 K -1 ).

Fig. 7 :Fig. 8 :

 78 Fig. 7: Comparison of MFA and FEM results for Uniaxial architecture and V f = 0.15

Table 1 :

 1 MFA and FEM results with %95 CI for the three architectures with averaged values over equivalent directions. In the case of FEM, values are averaged over three realizations. MFA simulates long fibre and V f = 0.3, while FEM simulates short fibre with l/d = 5 and V f = 0.28.

Fig. 1 :

 1 Fig. 1: A simple 2D model of a periodic short-fibre unit cell. When a fibre is cut, the rest of its volume reappears periodically through the opposite face.

Fig. 2 :

 2 Fig. 2: Example of periodic boundary conditions. A gradient of 100 K is imposed in X axis. Each node in surface X = L is 100 K hotter than the node couple in the same

Fig. 3 :Fig. 4 : 4 Fig. 5 :

 3445 Fig. 3: Reinforcement architecture studied. a) 3DRandom: All of the fibres are randomly positioned and oriented. b) Planar: Same as 3DRandom, but all of the fibres

InterfacialFig. 6 :

 6 Fig. 6: Variation in composite conductivity with interface thermal conductance for a composite with V f =0.4, three different inclusion diameters (0.1, 1 and 10 m) and three different phase contrasts (K i =38.5, 385, 3850 Wm -1 K -1 ).

Fig. 7 :Fig. 8 :

 78 Fig. 7: Comparison of MFA and FEM results for UA architecture and V f = 0.15

Table 1 :

 1 MFA and FEM results with %95 CI for the three architectures with averaged values over equivalent directions. In the case of FEM, values are averaged over three realizations. MFA simulates long fibre and V f = 0.3, while FEM simulates short fibre and V f = 0.28.

					Model
	(W/m•K)	K 11	K 22	K 33	Used
		424.42		MFA
	3DRandom	430±30		FEM
		538.57		212.88	MFA
	Planar	500±100		240±20	FEM
		225.52		960.18	MFA
	UA	233±2		840±20	FEM

Acknowledgements

The financial contribution of the European Commission to INTERFACE project (EU FP6 031712 ) is gratefully acknowledged. The Basque Government (project PI-07/17) is also acknowledged for the funds received.


Jorge Barcena
email: jorge.barcena@inasmet.es

M Garcia De Cortazar

R Seddon

J C Lloyd

A Torregaray

J Coleto

Effect of the incorporation of interfacial elements on the thermophysical properties of Cu/VGCNFs composites

Keywords: Vapour grown carbon nanofibres, A. Metal-matrix composites (MMCs), A. Nano composites, B. Interface, B. Thermal properties

Vapour grown carbon nanofibres exhibit high mechanical properties and thermal conductivities. Therefore they are potential reinforcements in composites materials for high strength and high thermal conductivity applications. A problem not yet solved is the promotion of an improved copper/carbon interface. Several strategies have been envisaged for the incorporation of alloying elements (Ni, Co, B and Ti) at the interface. These techniques are based on duplex electroless plating coatings (combination of Cu and Ni or Cu and Co), electroless plating of alloys (Cu-B) and addition of metal nanoparticles (Ti) to Cu matrix deposited by electroless plating. The effect of the incorporation of these metallic elements on the microstructure and thermophysical properties is discussed. B and Ti lead to higher interaction at the Cu/C interface over Ni and Co.

This allows the reduction of the coefficient of thermal expansion but regarding the thermal conductivity it was not possible to obtain a value higher than that of copper.

Introduction

Vapour Grown Carbon Nanofibres (VGCNFs) exhibit excellent mechanical and thermophysical properties. Therefore they are very promising reinforcing materials for metal matrix composites (MMCs) in multiple applications [START_REF] Arai | Nickel-coated carbon nanofibers prepared by electroless deposition[END_REF][START_REF] Kang | Introduction to carbon nanotube and nanofiber smart materials[END_REF]. The large volume production of VGCNFs enables an immediate availability and excellent performance-to-cost ratio for the mass production of industrial components [START_REF] Kang | Introduction to carbon nanotube and nanofiber smart materials[END_REF], better than other candidates such as carbon fibers or nanotubes (CNTs). However, the manufacturing of components containing such kind of material is not trivial, especially at high volume fraction of VGCNFs. Three key issues must be fulfilled in order to obtain high quality MMCs: dispersion of the reinforcement, high degree of densification and promotion of a suitable matrix/reinforcement interface. Regarding interface there is a lack of interaction between copper and carbon [START_REF] Mortimer | The wetting of Carbon by Copper and Copper Alloys[END_REF]. This is a problem that is urgent to solve in order to get advantage of the performance of VGCNFs in MMCs, especially for thermal management applications, where low coefficient of thermal expansion (CTE) and high thermal conductivity are required [START_REF] Córdoba | Growth and characterization of electroless deposited Cu films on carbon nanofibers[END_REF].

Experimental Work

Manufacture of composites

The carbon nanofibres used in the present study were purchased from Showa Denko KK (VGCF grade, 150 nm diameter, 100-200 µm length). One of the main problems of the incorporation of CNTs and VGCNFs is the lack of wetting, diffusion and interaction between carbon and inert metals such as silver and copper [START_REF] Mortimer | The wetting of Carbon by Copper and Copper Alloys[END_REF][START_REF] Lopez | The solubility of C in Solid Cu[END_REF][START_REF] Berner | Microstructure of Cu-C interface in Cu-based metal matrix composite (1)[END_REF] (i.e the wetting angle between carbon and copper is 120 º and no physical bond is formed at the interface [START_REF] Mortimer | The wetting of Carbon by Copper and Copper Alloys[END_REF]). The fibre reinforcements must maintain their graphitic structure and be strongly bonded to the matrix, in order to achieve improved thermophysical properties. Therefore it is necessary to study in detail this interface in order to achieve composites with the required properties. One interesting solution is the addition of elements able to interact at interfacial level. The electroless plating technique has been earlier discussed for the manufacture of plain Cu/VGCNFs composites by the present authors in a previous work [START_REF] Barcena | Microstructural study of vapour grown carbon nanofibre/copper composites[END_REF]. This process allows obtaining composite powders with the desired amount of reinforcement by controlling the deposited copper. Controlling these conditions, samples containing 20 vol. % of nanofibres were manufactured. Different methods, derived from this copper electroless plating technique, have been envisaged for the incorporation of the interfacial elements (Ni, Co, B and Ti) at the copper/carbon interface. The first method consists of duplex coatings through the electroless plating methods. In this method a thin layer of nickel [START_REF] Wang | Metallization of multi-walled carbon nanotubes with copper by an electroless deposition process[END_REF] or cobalt [START_REF] Chen | Carbon-nanotube metal-matrix composites prepared by electroless plating[END_REF] has been placed on the surface of the nanofibres, followed by a second layer of copper [START_REF] Barcena | Microstructural study of vapour grown carbon nanofibre/copper composites[END_REF], which will be the matrix after the consolidation. By this duplex method an interfacial element below 10 wt. % is typically added. The second method consisted of the coating of the nanofibres by an electroless copper alloy, in this case copper plus few ppm of boron [10]. The last method is based on the mixture of copper coated nanofibres with metallic nanopowders, in this case, Ti nanoparticles (Argonide Corp, USA). The Ti nanoparticles were sonicated under ethanol for 30 min. and then mixed with the coated nanofibres in an ethanol solution with Argon bubbling to prevent oxidation. Two different amounts of Ti (0.3 and 5 wt %) were studied. Once the composite powders were vacuum dried they were consolidated by hot-pressing at 900 ºC and 35 MPa for 2 h.

Characterization (Materials and methods)

Chemical, microstructural and thermophysical characterisation has been carried-out on composite powders and consolidated composites. The chemical characterisation was performed by the EDS (Energy Dispersive Spectrometry) microprobe attached to the Scanning Electron Microscope (SEM) in order to assess the presence of possible contamination during the coating process, the oxygen amount and interfacial elements. Furthermore a more accurate value for these elements was given by the ICP-OES (Inductively coupled plasma -Optical Emission Spectrometer) technique. The extent of densification was calculated by comparing the real density with the theoretical one, taking into account a density of 2.0 g/cm3 for the pristine nanofibres. The microstructure of the consolidated composites was inspected by optical, scanning electron microscopy (SEM) and transmission electron microscopy (TEM) . The samples were cut and embedded into epoxy resin holders. Once cured, the samples were progressively polished using a silicon carbide grid, and finally polished with diamond paste to a mirror finish. These samples were etched with a FeCl3:HCl:H2O (1:1:1) solution for 7 seconds.

The presence of an interfacial layer and the distribution of the alloying element was observed by TEM (Transmission electron microscopy) where a focused ion beam (FIB) mills away material to obtain a proper surface to be further observed. The coefficient of thermal expansion (CTE) and the thermal conductivity were measured in the x-y direction (assuming that the z axis is the pressing direction). The CTE was measured by dilatometry in the RT-100 ºC range (two cycles).

The room temperature CTE was calculated from the second cycle to prevent the effect of residual stressed during the consolidation of the material.

The room temperature thermal conductivity was calculated by the indirect method (measurement of the thermal diffusivity). The thermal conductivity can be derived through the expression (1).

) ( ) ( ) ( ) ( T T c T a T P ρ λ ⋅ ⋅ = (1)
specific heat (J/kgK) and ρ is the density (kg/m 3 ). The thermal diffusivity was measured through the laser flash technique, while the specific heat was measured through Differential Scanning Calorimetry (DSC). The density was measured by the Archimedes method under absolute ethanol.

Results and discussion

Microstructure

The inspection and the microstructure of the pristine nanofibres was analyzed in a previous work [START_REF] Barcena | Microstructural study of vapour grown carbon nanofibre/copper composites[END_REF]. It was concluded there that this type of nanofibres present a more graphitic structure than the ones from other manufacturers. Moreover the nanofibres were clean of the metallic seeds employed for their synthesis. The copper coating description and characterization was also reported there, as well as the microstructural characterisation after hot-pressing. A rearrangement of the nanofibres to form a random planar configuration was observed.

Figure 1 shows the microstructure of the composites modified with Ni. The nickel coating is successfully deposited on the surface of the nanofibres forming a continuous coverage (see Figure 1a). The copper coating on the nickel coated VGCNFs is shown on Figure 1b. The copper coating on the nanofibres was seen to be granular and homogeneous. As shown in Figure 1c the consolidated composite shows a fine distribution of the nanofibres in the matrix with a low presence of nanofibre agglomerates. The distribution of the composite elements was checked by EDS mapping (see Figure 1d for Ni). This confirmed a uniform distribution of the nickel along the microstructure composite. The amount of nickel was 7 wt % (ICP-OES). In addition, the oxygen content was shown to be very low (< 0.1 wt %). It would be probably completely removed if the consolidation were carried out under reductive gases (such as H 2 ) instead of vacuum. The TEM inspection revealed that a low amount of nickel was present in the proximity of the interface, but the amount of nickel in the copper matrix was high. This measurement suggested that the amount of nickel, formerly present on the interface, diffused into the copper rather than reacting with the nanofibres, while the consolidation was carried out.

This could be explained by the low solubility between nickel and carbon, like in the case of copper.

Figure 2 shows the microstructure of the Cu/VGCNFs modified with Cobalt, following a similar procedure as for the Cu/Ni/VGCNFs composites. The microstructure of the cobalt coated nanofibres is shown in Figure 2a. Cobalt deposits were found not only on the nanofibres, but also as tiny particle precipitates between the nanofibres. The microstructure of the consolidated composite is shown Figure 2b. After the consolidation the nanofibres were well distributed in the matrix, although some small agglomerates (< 5 µm) are present. The final amount of cobalt was around 9 wt %. The distribution of the different constituents of the composite was inspected by SEM inspection and EDS mapping, showing that interfacial element (cobalt) was present in terms of isolated deposits. This suggested that the interfacial element was not located on the copper/carbon interface. A similar explanation of this phenomenon than the above explained for Ni can be given. The presence of oxygen in the composite was quite low.

The microstructure of the composites containing Boron is shown in Figure 3. The Boron was incorporated during the deposition of copper, coming as impurity from the reducing agent employed in the electroless plating process (from the Sodium Borohydride). The Boron content in the samples was very low (0.001 wt % by ICP-OES). The microstructure was inspected by SEM and TEM. Firstly the coating resulted to be smooth and homogeneous with small amounts of VGCNFs bundles. From the inspection by SEM an excellent distribution of the nanofibres and a homogeneous microstructure were observed. Moreover, the detailed observation by TEM (Figure 3b), shows that the carbon-copper interface is continuous, leading to a good physical contact between these two phases.

Figure 4 shows the composites samples after the Ti nanoparticles addition. The mixture with copper coated nanofibres was intensively inspected by SEM. As shown in Figure 4a no evidence of the presence of Ti particle agglomeration was seen during the SEM inspection even at 5 w % of Ti. This suggested that the nanoparticles were finely distributed through the coated nanoparticles. The consolidated samples are shown in Figure 4b and c for the 0.3 and 5 w % of Ti (optical images, in order to give a representative macroscopic view). The microstructure of the sample with 0.3 wt % of Ti resulted to be more homogeneous as compared with the one containing 5 wt %. In this case the lower amount of Ti prevented the formation of carbon nanofibre agglomerates. The mechanism of the formation of these carbon nanofibre agglomerates is still unknown and more work is required to elucidate this effect. The presence of TiC was detected by XRD and EFTEM mapping. As shown in Figure 4d, in the case of the composite with 5 wt % of Ti an interfacial layer of TiC of about 100nm is formed after the diffusion of Ti through the copper. The TEM inspection has not shown evidences of the presence of TiC at the interface of the 0.3 wt % Ti composite. Furthermore, the random planar configuration was observed in both the samples with 0.3 and 5 wt. % of Ti, showing that the nanofibres are rearranged on planes perpendicular to the pressing direction. This configuration has been observed on the samples containing Ni and B as interfacial material as well as on the plain composite [START_REF] Barcena | Microstructural study of vapour grown carbon nanofibre/copper composites[END_REF].

Thermophysical properties

The thermophysical properties are shown in Table 1. The properties of pure copper and a Cu/VGCNFs plain material with no additives [START_REF] Barcena | Proceedings of X Congreso Nacional de materiales[END_REF] are shown as a comparison of properties. These properties have been measured "in plane", i.e. the most favourable direction due to the random planar configuration. The composite with Co additions was discarded due to the inhomogeneous microstructure. The values of the densification are also shown. In all the cases was above 95 %, although the composite with 5 wt. % of Ti has the lowest value. This should be connected with the high presence of carbon nanofibre agglomerates (see Figure 4) in the composites with higher amount of Ti. Extra Ti would also alloy with the Cu and reduce the thermal conductivity of the matrix.

Regarding the CTE, only slight reduction as compared with copper was achieved (see the last column of Table 1). The composite with nickel expanded even more than the copper. Moreover the composites containing Boron and the Ti were more effective over those including Nickel.

The composite with the lowest amount of Ti showed the lowest value of CTE. This can be attributed to a better distribution of the nanofibres (less agglomerates) that allows the transmission of stressed more homogeneously.

Concerning the thermal conductivity a similar trend as for the CTE was observed. On the one hand the composite containing Nickel showed the lowest value of thermal diffusivity and conductivity. This can be explained through the observed microstructure. The Nickel, instead of being placed at the interface, was solubilised through the copper matrix. This was detrimental for the thermal conductivity of the matrix. On the other hand the composites containing B and Ti showed better results. This would be attributed to the formation of carbides, which are beneficial for the thermal transport at the metal/carbon interface [START_REF] Schubert | Interfacial design of Cu-based composites prepared by powder metallurgy for heat sink applications[END_REF].

In any case the values of the thermal conductivity were lower than the pure copper. Several possibilities are arisen that would explain these low values of thermal conductivity:

1) The presence of small defects in the composite, such as low amount of impurities (oxides, carbides and other elements), porosity, poor quality of the interface and so on.

2) The thermal conductivity of the carbon nanofibres was claimed to be 1200 W/mK [13].

This should be considered as an ideal upper value, since it does not take into account defects, structure disorders and fully straightness. On the other hand, Yu et al. reported an experimental value close to 10 W/mK [START_REF] Yu | Thermal contact resistance and thermal conductivity of a carbon nanofiber[END_REF], but they also concluded that the defect density and thermal resistance at the contact of the VGCNFs with the transmission line device would have a significant effect on the measured values.

3) Poor metal/carbon. The thermal transport in metals (like copper) is based on electrons, while the thermal transport of nanofibres is based on phonon [START_REF] Yu | Thermal contact resistance and thermal conductivity of a carbon nanofiber[END_REF]. Therefore scattering at the interface will take place [START_REF] Schubert | Interfacial design of Cu-based composites prepared by powder metallurgy for heat sink applications[END_REF].

As shown in Table 1 the thermal diffusivity is the factor than in accordance with the expression (1) mainly dominates the final value of the thermal conductivity therefore the efforts should be addressed to the increase of the thermal diffusivity especially through the interface. The results of the thermal diffusivity on Table 1 showed an improvement of the composites containing B and Ti (0.3 w %) over the plain composite (no interface), but this enhancement was not enough.

Further efforts must be addressed to the optimization of the Ti and B amount of the composites or the inclusion of alternative elements at the interface able to react with carbon to promote the formation of carbides such as Mo, Ta, Cr or W.

Conclusions

The present study contains a preliminary work for the modification of the interface of copper/carbon nanofibre composites with alloying elements such as nickel, cobalt, boron and titanium. A comparison of the effect of these elements on the microstructure and thermophysical properties (coefficient of thermal expansion and thermal diffusivity) is given.

The incorporation of nickel and cobalt is less effective than boron and titanium. On the one hand nickel and cobalt led to heterogeneous distribution of these elements in the final composites, which prevent to obtain the required properties. On the other hand, the incorporation of boron and titanium have given better results in terms of microstructure and therefore in thermophysical properties, presumably due to the formation of interfacial carbides.

There was a significant reduction in the CTE in the end but regarding the thermal conductivity it has not been possible to obtain a value higher than the value of copper. Two likely explanations are arisen. The first one assumes to take into account a low thermal conductivity of the carbon nanofibres. The second one concerns a loss in thermal conduction at the metal/carbon interface.

Figure Captions

Fig. 1 .

 1 Fig. 1. Microstructures of the Cu/Ni/VGCNFs composites: a) Nickel plating, b) Duplex coating after copper deposition, c) Consolidated composite and d) EDS Ni mapping.

Fig. 2 .

 2 Fig. 2. Microstructures of the Cu/Co/VGCNFs composites: a) Cobalt plating and b) Consolidated composite.

Fig. 3 .

 3 Fig. 3. Microstructures of the Cu/B/VGCNFs composites: a) Cu-B electroless plating and b) TEM images of the Cu/C interface.

Fig. 4 .

 4 Fig. 4. Microstructures of the Cu/Ti/VGCNFs composites: a) Coated VGCNFs + Ti nanopowders (5 wt %), b) Consolidated sample (0.3 w % Ti), c) Consolidated sample (5

Figures Figure 1

 1 Figures

Figure

  Figure 2

2

 2 Figure 2

  Figure 3

Table 1

 1 Thermophysical properties of Cu/VGCNFs composites

	Tables
	Sample Ref.	Thermal Diffusivity* (cm 2 /s)	Specific Heat (J/KgK)	Density (g/cm 3 )	Degree of densification (%)	Thermal conductivity* (W/mK)	CTE* (room T)
	Pure Copper	1.12	384	8.93	100	395	16.5
	Cu/CNFs	0.74	503	7.51	99.67	280	16.4
	Cu/Ni/CNFs	0.17	505	7.47	98.30	64	17.0
	Cu/B/CNFs	0.78	514	7.56	98.51	306	15.6
	Cu/0.3Ti/CNFs	0.80	517	7.52	99.16	311	13.6
	Cu/5Ti/CNFs	0.56	493	7.27	97.47	200	15.7

*Measured in the x-y direction

Acknowledgements

This study was funded by the European Commission grant project "New Materials for Extreme Environments -ExtreMat", contract ref. NMP3-CT-2004-500253" and by the Spanish ministry of science and education (MEC) through the grant project: "Nuevos materiales para encapsulado de dispositivos de SiC de muy alta potencia, temperatura y frecuencia", ref. TEC2005-07937-C02-02/MIC. The help of Dr. Neubauer (Austrian Institute of Technology) in the measurement of the thermal expansion and conductivity is also appreciated.