Cooling of electronic devices is very important to avoid temperature rising of its components during passing the current through it and slowing down its efficiency and destroying it. Cooling of electronic equipment using heat sink metallic materials is better than cooling by air due to the higher thermal conductivity of metals than air. Heat sink should be a passive component that cools a device by dissipating heat into surrounding air. Traditional heat sink and heat spreader is made of aluminum and copper with low Thermal Expansion Coefficient (TEC). New composite materials of suitable electrical and thermal conductivity for heat sink materials applications are required to prevent the failure of electronic equipment and high thermal stresses in electronic components resulting from temperature variations. The thermo-mechanical fractures may be formed during semiconductor chip production especially with temperature fluctuations from 323 K (50˚C) to 473 K (200˚C) and during cooling  . A design of a heat sink of Aluminum base for cooling of Printed Circuit Board (PCB) was used to dissipate about 19.5 watts of heat energy  . Al/SiC composite was used with acceptable properties. The graphite/metal composites represent a clear alternative to Al/SiC materials. The graphite-based composites are cheap and machinable, keeping at the same time very high thermal properties  ,  . Copper is indeed characterized by a high thermal conductivity but at the same time its high density (8.9 g/cm3) increases weight of the final product, which in most of the cases does not meet specific application requirements  .
Powder metallurgy is one of the techniques used to fabricate sintered metallic heat sink materials from its powder. The sintered materials made from coated powders have better structure homogeneity and electrical resistivity than those made from mixed powders. Coated diamond particles have a uniform distribution in copper composite and the interface between diamond particles and Cu matrix  . Because diamond has TEC value of 2.3 × 10−6/K higher 6 times than Cu. Cu/diamond composites with matched TEC are used to eliminate the high heat produced during semiconductor component operation. Also a mixture of graphite (Gr) and other materials may be used  ,  .
It was founded from previous research work that the materials used in heat transfer such as aluminum/silicon carbide compared to copper are insufficient in cooling electronic devices  ,  . A new generation of heat sink materials was developed to enhance the thermal properties such as diamonds reinforced copper composites. However diamond in general is expensive and the consolidation of the materials needs high pressure and high temperature  . Researchers suggested using alternative materials such as graphite, short carbon fibers instead of diamond as reinforced materials  ,  . On the other hand some researchers improved the properties of the copper composites by powder coating with silver and copper before sintering  ,  and to increase the bonding between the copper matrix and the reinforcement particles by decreasing the air gap between the constituents.
The main aim of this research is to produce a material characterized by high thermal conductivity, low coefficient of thermal expansion, good mechanical properties, low density and good electrical conductivity. In this study copper matrix composites reinforced with diamond (Di) particles, graphite (Gr) particles, silver coated graphite particles, short carbon fiber (CF) and copper coated short carbon fiber are tested. The investigated reinforcement powders were mixed separately with copper powder and underwent cold compaction and sintering at 1123 K (850˚C) to prepare sintered copper matrix composites. The morphology of the powder as well as the microstructure of the sintered composites was investigated the test specimens were tested by optical, scanning electron microscopes and XRD. The physical, electrical and thermal properties were measured to evaluate the produced sintered composites.
2. Materials and Methods
2.1. Starting Materials
High purity electrolytic copper powder (99.9) with an average particle size of 44 µm was purchased from OXFORD laboratory reagent; India. Graphite and carbon short fiber were purchased from Austria institute of technology. Diamond, with particle size less than ~1 µm was provided from Iljin Co. LTD, South Korea. Figure 1 shows SEM images with different magnifications of the starting copper powder, the diamond, graphite particles and the short carbon fibers. Silver nitrate, copper sulphate, potassium sodium tartarate, nitric acid, sodium hydroxide, formaldehyde and Ammonia solution were provided from El-Nasser Chemical Co. LTD. Egypt.
2.2.1. Fabrication of Copper Base Composite Powder
Graphite, diamond and short carbon fiber powders were treated by soaking and stirring in nitric acid for 5 min with stirring rat of 250 rpm. To clean and etching the surface of the particles. The treated particles and short fibers were cleaned by 50% sodium hydroxide solution to neutralize the excess of the nitric acid followed by acetone to dissolve any organic foreign matter. The obtained graphite particles underwent metallization and coating by electroless silver deposition in ammoniacal silver nitrate solution using formaldehyde as a reducing agent. On the other hand the treated carbon short fiber was metallized and coated by electroless copper deposition process using bath composition in Table 1. Five compositions were prepared by simple mixing in porcelain
Figure 1. SEM images with different magnifications of the investigated powders. (a), (b) Cu powder, (c), (d) graphite, (e), (f) diamond powder and (g), (h) carbon short fiber.
Table 1. The chemical composition of the electroless nickel baths which used to prepare sample coated with copper powder.
mortar with 1 wt% paraffin wax of diamond, graphite, short carbon fiber, graphite coated silver and carbon fiber copper coated with copper powder. A reference copper sample was prepared under same conditions  .
2.2.2. Consolidation of Copper Base Composite Powder
The obtained mixtures as well as the pure copper powder samples underwent cold compaction at 600 MPa in a uniaxial die of dimension (50 mm diameter and 150 mm length). The green compacts were sintered under mixture of hydrogen/nitrogen gas at 1173 K (900˚C) for 2 h (see the sintering cycle in Figure 2  ).
2.2.3. Microstructure and Density Measurements
The produces powders as well as the sintered compacts underwent microstructure investigations and chemical analysis by using SEM model QUANTA FE250-EDAX Genesis and XRD model Bruker advanced X-ray diffract meter model D8 Kristalloflex.
The properties of the sintered samples were evaluated by measuring the density according to MPIF Standards 42, 1998, using Archimedes rule. The density (ρ) of the samples was calculated according to Equation (1)  ,  .
where the of densities Cu (8.94 g/cm3), Gr (2.17 g/cm3), CF (2.15 g/cm3), Di (3.48 - 52 g/cm3), and Wa and Ww are the weights of the samples in air and water respectively  ,  .
2.2.4. Thermal Properties of Copper Base Composites
The thermal conductivity of the prepared sintered samples was measured by the conduction method. The thermal heating test was done by an electrical heater. It consists of an electrical isolated plate heater 1000 W, 220 V, 50 Hz. It was insulated with one inch insulator at all directions. One hole from the top of the heater is drilled to force the heat transfer in only one direction. Two groves were made at the outside surface and two thermocouples are put inside groves to measure the temperature of heater surface.
The heat transfer conduction is determined by measuring the temperature difference
Figure 2. Heating cycle for sintering process in hydrogen atmosphere.
between the upper and the lower surface of the prepared samples as a function of time by means of five K type thermocouples distributed on the specimen surface and was fixed above one inch isolated hot plate. The thermocouples were connected with a multipoint swatch. The output from the multipoint swatch was connected with digital thermometer type K to record the temperature. The volt and current pass through the specimen were measured by electric meter. Figure 3 shows the experimental setup circuit of measuring the temperature gradient under controlled temperature range from 293 K (20˚C) to 473 K (200˚C).
The thermal conductivity was calculated by substituting the values of current, volt, temperature, area and thickness of the samples in the Fourier formula  as the average temperature and calculated from the Equation (2).
where (A), the cross section area in (m2), (K) the thermal conductivity in W/m∙K, (q), the power (W), (Δt) temperature difference in (K), and (Δx) thickness for heat sink, (m). The experimental test rig is designed to measure the thermal conductivity.
The heat transfer convection was calculated by natural convection and forced convection from the Equation (3)  -  .
where hc = convective heat transfer coefficient of the process W/(m2∙K). The average Nusselt number for horizontal surfaces can be determined from the simple power-law relations. The hydraulic characteristic length for horizontal surfaces is calculated.
In natural convection:
The dimensionless parameter represents the natural convection effects, and is called the Grashof number GrL.  -  .
Figure 3. The experimental setup circuit of measuring the thermal conductivity.
where Ra is the Rayleigh number, which is the product of the Grashof and Prandtl numbers  -  :
In forced convection, the experimental data for heat transfer is often represented conveniently with reasonable accuracy by a simple power-law relation of the form  -  .
g = gravitational acceleration, m/s2
β = coefficient of volume expansion, 1/K (β = 1/T for ideal gases)
Ts = temperature of the surface, ˚C
T∞ = temperature of the fluid sufficiently far from the surface, ˚C
Lc = characteristic length of the geometry, m
v = kinematic viscosity of the fluid, m2/s.
m and n are constant exponents and the value of the constant (C) depends on geometry and flow.
where Re ranged 40 : 4000.
2.2.5. Electrical Properties of Copper Base Composites
The electrical resistivity of the sintered materials was measured using the four probe method by using Omega CL 8400 micrometer device. The rectangular sintered specimen was placed in a specially designed for making the electrical connection. The resistivity (Ro) was calculated according to Equation (8)
where Ro the resistance in µΩ・m and R the resistance in µΩ.
3. Results and Discussion
3.1. Powder Fabrication and Characterization
A pretreatment process was employed to remove organic and nonorganic impurities and improve the surface properties of the reinforcement particles (diamond, graphite particles and short carbon fiber) by using fairly aggressive chemicals. Sodium hydroxide (50% conc.) and nitric acid (67% conc.) was used to dissolve any inorganic impurities such as metals but acetone was used to remove the other organic impurities, such as greases or oils. The pretreated reinforcement was activated by silver deposition method. The silver deposition system takes place using a solution of silver nitrate and ammonium hydroxide to form silver layer on the graphite particles using formaldehyde as a reducing agent. Figure 4(a) and Figure 4(b) shows SEM images with different magnifications of the coated graphite particles with silver. It was observed that the graphite particles is completely coated and encapsulated by silver metal layer. On the other hand the pretreated short carbon fibers were encapsulated by copper layer using the autocatalytic electroless deposition of copper metal on its surface shows the morphology of the coated short carbon fibers with copper and its composition (see Figure 4(c) and Figure 4(d)). The copper is uniformly deposited on the short carbon fiber. Figure 4(e) shows an EDAX analysis of the copper coated short carbon fibers and provides a complete chemical composition of the coated short fibers which is composed of copper and carbon.
Figure 5(a) and Figure 5(b) shows the X-ray diffraction patterns of the investigated powders and the corresponding sintered composites to assess the formation of phase’s transformation. It was observed from the results that the X-ray diffraction patterns of
Figure 4. SEM images with different magnifications and EDAX analysis of the prepared coated powders; where (a), (b) silver coated graphite particles, (c), (d) copper coated carbon short fiber and (e) the EDAX compositional analysis of the copper coated carbon short fiber.
Figure 5. X-ray diffraction patterns of the investigated powder, the coated powders and the copper base sintered composites.
the powder as well as the sintered copper matrix composites shows peaks of only copper metal and the reinforcement particles and there are not any foreign peaks of any contaminates or new phase. It is due to the non interaction between the copper metal and the reinforcements during the sintering process. The crystal size of Cu and different reinforcements materials were calculated from the X-ray line broadening using Scherer’s formula (D = 0.9λ/Bcosθ)  , where; D is the crystallite size, λ is the wavelength of the radiation, θ is the Bragg’s angle and B is the full width at half maximum. The average size of Cu (88 nm), Gr (60 nm), Gr coated silver (56.4 nm), Di (57.1 nm), CF (8.1 nm) and CF coated Cu (25.3 nm). Showed that all of the fee equal values because cu ratio equal to 99 wt% of all values and other materials 1 wt% in all other.
Consolidation of the metallic powders is mainly carried out using compaction followed by sintering. Sintering is a thermal process which increases the strength of a powder mass by bonding adjacent particles via diffusion or related atomic level events. As a result of this process, the material acquires the required physical and mechanical properties. Most of the properties of a powder compact are improved with sintering  .
The microstructure of the prepared copper matrix composites were investigated by SEM after grinding and polishing of the sample cross section. Figure 6 shows Back Scattered Electron (BSE) images for the produced copper base composites containing different reinforcements of Di, Gr, Gr coated silver, CF, CF coated Cu. During scanning using the backscattered electron detector, the higher the average atomic number of the area being analyzed, the greater the probability is that a (BSE) will be generated. As a result, BSE images display atomic number contrast with brighter regions being generated from areas of higher average atomic number. In other words, the BSD images easily
Figure 6. SEM micrographs of the produced copper base sintered composites; where (a) Cu pure, (b) Cu/Gr one wt%, (c) Gr coated silver one wt%, (d) Cu/one wt% Di, (e) Cu/one wt% CF, (f) Cu/one wt% CF coated Cu.
show the difference between the different phases (areas of different atomic number) through the difference in contrast. The result observed that the reinforced materials (diamond, graphite or carbon fiber) were homogeneously distributed in the copper matrix. In addition the coated reinforcement materials (graphite coated by silver and carbon fiber coated by copper) were strongly bonded by the copper matrix due to the improvement in the wet ability between the coated reinforcement particles and the copper matrix. Also the porosity of the treated reinforcements by coating has lower values than the composites prepared by mixing of its constituents. Since the uncoated reinforcements are easy to be stripped off during mechanical polishing, small pits are left on the surface of samples. While, the composite made from the coated reinforcements have lower porosity content due to the good contact between the particles and the matrix during sintering, and the metallic binders decrease all the existing cavities between Cu particles.
Figure 6(a) and Figure 6(b) shows SEM micrographs for the sintered pure Cu and the corresponding 1 wt% diamond particles/Cu coated composites. The microstructures show good sinterability and a homogeneous distribution of the diamond particles in the copper matrix. Figure 6(c) and Figure 6(d) illustrates SEM micrographs for the sintered 1 wt% uncoated graphite/Cu and 1 wt% graphite/Cu silver coated composites. On the other hand Figure 6(e) and Figure 6(f) illustrates SEM micrographs for the sintered 1 wt% uncoated short carbon fiber/Cu and 1 wt% short carbon fiber/Cu coated composites. The micrographs show that, the sintered materials prepared by electroless coating method have higher bonding between the graphite particles as well as the short carbon fibers and the Cu matrix with low-porosity contents. The reason behind increasing the bonding and density of Cu-coated composites is mainly due to the good sinterability as a result of the encapsulation of short carbon fibres with Cu, the particle/particle contacts are mainly Cu/Cu contacts and sintering behaves like Cu compacts sintering. In order to determine the distribution of the elements in the sample a compositional analysis was performed by EDAX. Figure 7(a) and Figure 7(b) shows
Figure 7. SEM images with EDAX compositional analysis of the produced copper base sintered composites; where (a) 1 wt% Diamond/Cu, (b) 1 wt% Graphite/Cu.
reprehensive images and EDAX compositional analysis of 1 wt% Graphite/Cu and 1 wt% Diamond/Cu sintered composites. The reinforcement particles were appeared to have a dark color and this was being confirmed by the EDAX analysis.
3.2. Density of Sintered Copper Base Composites
The density of the powder metallurgy products is one of the most important properties which reflect the sinterability and the effect on the other properties. It is very sensitive to composition and porosity in the sample.
Figure 8 shows the density values of the green compacts as well as the sintered density and its relation with the porosity of the produced copper base composites. It was observed from the results that the relative green densities as well as the relative sintered density of the coated particles have higher values than the uncoated one. It was due to the good distribution and homogeneity of the coated particles inside the copper matrix which decrease the reinforcement’s particle-particle interaction and decrease the grain growth. In addition the low-porosity contents of the coated particles due to the strong adhesion between the Cu matrix and reinforced particles. The reason behind decreasing the porosity and increasing in the density is the encapsulation of the reinforced particles with Cu and the particle-particle contact are mainly Cu-Cu which improve the adhesion between the particle and the copper matrix and improving the consolidation of the compacts during the sintering process.
3.3. Thermal Conductivity
Table 2 listed the obtained thermal conductivity values of the produced copper base sintered materials. As seen, the thermal conductivity of the uncoated Cu composites is significantly lower than the thermal conductivities of the coated composites. However the thermal conductivity of the pure copper metal is higher than the composites. This feature indicates low interfacial bonding of the uncoated reinforcement particles (diamond, graphite and short carbon fiber), owing to the non-wetting of Cu and the reinforcement particles. With particle coating process the interfacial bonding gets better. It can be concluded that the interfacial thermal conductance of coated type Cu base
Figure 8. The relative green density, relative sintering density and porosity values of the produced copper base sintered composites.
Table 2. The thermal conductivity value of the produced copper base sintered composites.
composites is much higher than that of uncoated one. It is due to the interface in the uncoated Cu base composites is filled in with a layer of air because Cu is non-wetted to diamond, graphite and short carbon fiber (see Figure 6). The low thermal conductivity of air, 0.026 W/m∙K, offsets the high thermal conductivity of the reinforcement particles. The formed silver as well as Cu coated particles reduces the air gap improves the thermal conductivity of the coated composites. However, most of the interface is still filled in with air due to the small amount of the deposited silver as well as the copper metal. Most of the graphite and short carbon fiber surface were encapsulated with silver or copper, even though there are still few air gaps at the interface. As a result of too much amount of deposited silver or copper encapsulate the reinforcement particles, an undesirable thick Ag or Cu layers are coate the graphite particles or short carbon fibers surface, as seen in Figure 4. Certainly, the Ag or Cu layer could be tailored to a thinner one to reduce the undesirable interfacial thermal resistance. This can be regarded as an optimized interface in this study  ,  -  .
Table 2 also shows the variation of the thermal conductivity of the produced sintered copper and its composites at temperature rang 323 - 393 K (50˚C - 120˚C). The thermal conductivity of 398 W/m∙K was obtained for sintered Cu. This result is reasonably consistent with the thermal conductivity value of sintered Cu reported by Davis  as well as by Kim et al.  .
It is clear from Table 2 that the thermal conductivity increased in case of Cu/diamond composite to be 405 W/m∙K. Figure 9(a) and Figure 9(b) shows the influence of temperature on the thermal conductivity of the prepared samples. It is observed that as the temperature increases; the thermal conductivity decreases in case of pure copper as well as Cu/diamond composite. It is also observed that the thermal conductivity of Cu/Dia- mond is higher than the thermal conductivity of pure copper by 3.5%. From the above results it can observed that the diamond improved the thermal conductivity of the Cu/diamond composite. The additions of diamond particles to Cu matrix increase the thermal conductivity of pure Cu. The low thermal conductivity of this composite was indicating a high thermal barrier resistance. This result due to separation between copper and diamond particles are which lead to low chemical affinity between copper and surrounded by cavities, diamond. Therefore, it is difficult to produce a bond of low thermal resistance and high mechanical strength between the matrix and the reinforcement.
Figure 9. The influence of temperature on thermal conductivity of (a) copper, (b) copper and Cu/Diamond, (c) Cu/Graphite and (d) Cu/Carbon fiber at a temperature range 232 - 393 K (50˚C - 120˚C).
In case of graphite silver coated, the thermal conductivity has the mean value of 394 W/m∙K as shown in Figure 9(c). The results also show that the densification of the materials has a significant influence in the thermal conductivity. This reduction could also be due to the orientation of the measured thermal transport which could be different to the orientation of carbon fiber in the Cu matrix after consolidation. The random distribution of carbon fiber orientation could disturb the unidirectional heat transfer which could result in the reduction of the effective heat conduction of carbon fibers  . It is clear that a considerable increase of thermal conductivity is observed due to the coating of the graphite particles with copper improve the bonding between the graphite particles and the copper matrix which decrease the voids located in the interface between the graphite particles and the copper matrix and enhance the electron transfer through the sintered material. This increase is about 0.5% at 323 K (50˚C) and 1% at 393 K (120˚C). This means that the effect of silver coating of Cu/graphite is increase the total thermal conductivity by increasing the temperature. In case of carbon fiber coated by Cu the mean thermal conductivity is 393 W/m∙K as shown in Figure 9(d). It was observed that the coating process of Cu/carbon fiber by Cu increases the thermal conductivity by about 1.25% at 232 K (50˚C) and by 1.75% at 393 K (120˚C). While the reinforced particles lead to increase the thermal conductivity of the composites and coated material, which demonstrated the effectiveness of the coated layer to obtain a good thermal contact between the matrix and powder particles  .
3.4. Electrical Resistivity and Conductivity
The electrical resistivity values of the fabricated composites are shown in Figure 10. It can be noticed that the electrical resistivity for investigated coated composites is lower than the uncoated one. It is evident that the electrical conductivities of the composites depend on the electrical conductivity of each component, volume fraction of the reinforcement, distribution and size of the reinforcement, density, and bonding between matrix and reinforcement as well as the synthesis method. It is known that the adhesion between diamond, graphite and carbon fiber and Cu matrix is very weak, because some nanosized interfacial gaps are often observed (see Figure 7). According to the C/Cu phase diagram, the C solubility in Cu is negligible. In addition, copper is known to be chemically inert with respect to carbon. The chemical incompatibility of carbon and copper can result in a weak mechanical interfacial bonding between diamond and graphite particles as well as short fiber and Cu matrix, therefore to severely reduce the electrical conductivity of the uncoated composite. An improved interfacial adhesion, by contrast, was obtained due to the formation of a continuous silver or copper interlayer of metalized graphite or carbon fibers, and in turn facilitated the enhancement of the composite electrical conductivity. Under the premise of ensuring the ability to form a good combination between diamond and graphite particles as well as short fiber with the Cu matrix  .
3.5. Heat Transfer Convection Test
There are six specimens with deferent materials this (Cu, Cu/Diamond. Cu/Gr, Cu/Gr coated silver, Cu/CF, Cu/CF coated Cu). The convection test was done in to cases of natural, forced convection.
Figure 11 shows the results relation between (Ra) and (Nu) of the specimen. It is
Figure 10. The electrical resistivity values of the produced copper base sintered composites.
Figure 11. (Ra) versus (Nu) cases of natural convection for the prepared sintered samples.
clear that the values of Nu are decrease with increase of Ra due to the increase of the air temperature which is the density of a decrease the phenomena lead to decreasing the Ra number.
In forced convection Figure 12 explains the relation between the Reynolds and Nusselt number in cases of the forced convection tested. It is clear that the values of Re constant with difference spacemen because the constant velocity. The value Re number ranged 40 - 4000. The Nu are difference with other spacemen The relation between local Nusselt number and local (Re) number which obtained from experimental results.
It possible to obtain a general equation for all the test specimens. The general equation is Nu = 0.25Re + 34.5. Figure 13 shows the relation between Re and Nu for general equation in the present work.
A method to fabricate cohesive diamond, graphite or short carbon fiber uniform dispersed copper matrix composites by powder mixing as well as powder coating followed by cold compaction and sintering was developed in this article. The influence of type of reinforcement and their surface treatment is investigated. The coated and uncoated diamond, graphite particles or short carbon fibers were well embedded and uniformly dispersed in the obtained copper matrix composites. The experimental results show that the increase in the electrical resistivity and decrease in the thermal conductivity of
Figure 12. The relation between the (Re) and Nusselt number in cases of the forced convection.
Figure 13. (Re) versus (Nu) number for the prepared specimens.
copper are due to the incorporation of the reinforcement particles as well as fibers in the copper matrix. However, the coating process of the reinforcements leads to the increase in effective thermal conductivity of composites and decreasing in the electrical resistivity. The signification increasing in the density, electrical and thermal conductivity of the copper based composites prepared from the coated particles could be due to the good interfacial bonding between the reinforcement particles and the Cu matrix. Due to the higher densification of the coated graphite particles and the coated short carbon fibers, the composites have showed higher electrical and thermal conductivities as compared to those having uncoated particles and short fibers. Compared to the composites with uncoated particles or fibers, the particle intermediate coating greatly improved the interface bonding and decreased the interfacial electrical and thermal resistance of the copper base composites. These results indicated that the particle coating played a crucial role in the electrical and thermal properties of the copper base composites. This enhancement can be explained by the increase of electrical and thermal conductivity of the samples as due to the formation of conductive network by through the particles or short fibers. The new pretreatment coating method not only solves the interface problem with a lower price by a simple sintering furnace but also ensures the electrical and thermal conductivity of the copper matrix. The tested specimens were tested thermally by calculating natural and forced heat transfer. A general equation of heat transfer was conducted.
The authors thank the XRD and SEM technician staff at the central metallurgical research and development institute in Helwan for their cooperation.