Delicate control of graphite flakes alignment in the copper matrices via powder selections and filling processes

Due to the anisotropy properties of graphite flakes (Gf), the control of their orientation inside copper (Cu) matrice is strictly correlated with the final properties of such metal matrix composite (MMC). In this study, MMCs are fabricated by powder metallurgy process using three types of Cu powder particles (flake, dendritic, and spherical) as well as different powder filling methods. By using Cu flake powder with a relatively lower apparent density as compared to the two other Cu powder types (dendritic and spherical), high aligned Gf could be easily obtained, after uniaxial hot pressing, in a one-step powder filling approach. For the other two types of powders, a comparable orientation degree of Gf could be achieved only via several steps of delicate powder pressing. In-plane thermal conductivities of Cu/Gf composites were enhanced by improving the orientation degree of Gf, agreeing with effective medium approximation predictions (Maximum TC up to 540 W mK−1). A modeling, based on the apparent density of Cu powders, was discussed to show the effect of the alignment process on the final thermal property of such MMCs. This model supplies a basic guideline to obtain highly orientated Gf.


Introduction
With the advent of artificial intelligence (AI) and the boosting need for information processing capability, the trend for the microelectronic chip's development is toward the fabrication of parts with higher integration, high power density, and high frequency.This trend has induced a drastic increase in the heat generation of chips in a confined space.In order to maintain the electronic devices' performances, heat dissipation ability has become a key challenge in the design of electronic devices [1].A solution to this issue is to apply thermal management materials with high thermal conductivity (TC) that could effectively cool down the chips through heat transfer.
Recently, due to their high potential in showing tailored thermal properties, graphite flakes (G f ) reinforced MMCs, have been extensively investigated.These investigations have been mainly focused on G f orientation improvement and interfacial property control [2][3][4][5][6][7].It is noted that G f is a highly anisotropic material as it has different thermal properties between its a axis (high TC close to 1000 W mK −1 ) and c axis (low TC ranging from 10 to 20 W mK −1 ).Considering the initial investigation done on G f reinforced MMCs, the orientation of G f was regarded as a key parameter affecting the in-plane TC of the composites [2].Moreover, G f has poor wettability to copper which is not a favor for heat transfer [8].Increasing the relative density of final composite materials via hot pressing is also necessary for improving the thermal conductivity.
It is thought that due to the flake like geometry of the G f (in-plane 'diameter' ranging from 100 to 600 μm and out of plane thickness in the range of 10 to 30 μm), G f tend to be aligned on top of each other under uniaxial hot pressing.This is linked to the large ratio between diameter and thickness or flaky morphology.Usually, full oriented graphite flakes are achieved by step-by-step powder filling process or stacking-pressing [3,4,9] and so with the control of the thickness of each powder layer.Indeed, misalignments of G f tend to occur when the powder filling process is done via one-step process [10,11].However, it is reported that once flake powder metallurgy is applied, G f with a high orientation degree could be obtained in composite materials processed through a one-step powder pressing procedure [10,12,13].This effect was attributed to the platelet geometry of the used matrix metal powder which tends to get aligned as the added G f [10,12,13].It is mentioned that flake metal powders after the ball milling process have a lower apparent density as compared with the spherical one [14].This can be a key factor for obtaining G f with a high orientation degree.However, no systematic work has yet been done to understand the critical parameters being required to achieve the composites with highly oriented G f .
In this work, various Cu powders, such as flake, spherical, and dendritic, were selected as matrix materials corresponding to different ranges of apparent density.One-step and step-by-step powder filling methods were also implemented to investigate the effect of filling step numbers on the alignment of G f under the application of different Cu powders.The TCs were measured to confirm the relationship between the orientation degree of G f and the TC improvement.Furthermore, a model was proposed that shows the dependence of the G f orientation process on the apparent density of Cu powder when using uniaxial hot pressing as the densification approach.

Experimental
Commercial Cu powders, including spherical (figure 1(a)), dendritic (figure 1(b)), and flaky (figure 1(c)) types, were manually mixed with G f (Yanxin-Granphite Co., Ltd., figure 1(d)), respectively, in which the volume fraction of G f was fixed at 40% for each MMC type.The apparent densities of three types of Cu + G f mixtures were measured by a standard container and scale.
The G f + Cu powder mixtures were filled in a graphite mold under both one-step and step-by-step methods consisting of 9 and 15 steps.In each step, the Cu/G f powder mixture was put into the graphite mold, spread, and then pressed using a punch under 1 MPa.The Cu/G f composite materials were fabricated by the spark plasma sintering (SPS) technique.The heating and pressing curves of the SPS process are illustrated in Figure 2. In brief, under a vacuum environment, the sample was heated to the temperature of 500 °C for 8 min and meanwhile, an axial pressure of 10 MPa was applied within 10 min [15][16][17].The sample was then heated to 800 ℃ and maintained for 30 min.The uniaxial pressure was also increased to 60 MPa.The procedure was then followed by natural cooling to room temperature.These SPS samples had a dimension of 45 mm in diameter and 7 mm in height.Three types of specimens obtained from pure Cu powder particles were also sintered to measure the physical properties of the matrices without G f .
Orientations of G f in the composites were determined by combining both field emission scanning electron microscopy analysis (FE-SEM, Zeiss Gemini 300 system) and image analysis.TCs were calculated by multiplying the thermal diffusivities, the density, and the heat capacity (Cp) of the densified materials.A laser flash method (NETZSCH LFA457) was used to measure the in-plane thermal diffusivity at 70 ℃.The density was measured based on Archimedes' method using a densimeter (AND GHe202).The Cp of the powders (Cu and G f ) were measured using the differential scanning calorimeter method (DSC, PerkinElmer DSC8000) with the sapphire as a reference.The Cp of the Cu/G f composite materials were calculated according to the rule of mixture.

Microstructures of Cu/G f composites and their orientation analysis
The micrographs of Cu/G f composites using different Cu types of powder and powder filling process strategies are presented in Figure 3.In all of the samples, most of the G f were preferentially aligned in a direction perpendicular to the pressing direction, indicating that G f tend to be naturally oriented during the uniaxial pressing.It has to be mentioned that some disorientations were observed in the samples fabricated with both spherical and dendritic Cu powders being treated by the one-step powder filling (figures 3(a) and (d)), As noted, this phenomenon was more evident in the spherical ones (figure 3(a)).Using 9-step method, this phenomenon became less obvious, and got almost disappeared after 15-step process (figures 3(c) and (f)).On the other hand, such disorientation behavior was hardly seen in the composite materials fabricated with Cu flake powder (figures 3(g), (h), and (i)), even if the process was done in a one-step route (figure 3(g)).
According to the effective medium approximation (EMA) [18], <cos 2 θ> is used to represent the alignment degree of reinforcement in the matrix.
ò ò q j q q q q j q q q á ñ= cos cos sin d sin d 6 where ρ(θ) is a distribution function describing the angle distribution of the reinforcement in the matrix.In this work, θ is the angle between the basic graphite plane and the x-y plane of the composite materials.When the value of <cos 2 θ> is equal to 1 the G f reinforcements are exactly oriented in a plane perpendicular to the pressing direction.However, if this value is close to 1/3 the G f reinforcements are randomly distributed inside the Cu matrix.Image analysis was used to statistically calculate the angle θ distribution of G f [19,20].Figure 4 shows the ( ) ( ) where the symbol j(θ) denotes the statistical distribution of the reinforcing graphite phase within the copper matrix, with A1, t1, and y0 serving as fitting variables.
Upon substituting the values obtained from the fitting process, the specific j(θ) functions were presented, and subsequent numerical integration facilitates the computation of the <cos 2 θ> values obtained from the SEM micrographs of each material.<cos 2 θ> values are also shown in the figure 4. Except for the samples processed using spherical and dendritic Cu powders and under one-step powder filling way, the values of <cos 2 θ> in all the other materials were higher than 0.8.Especially, the <cos 2 θ> values were greater than 0.9 for those samples fabricated using the Cu flake powder.This is in accordance with the observation obtained from SEM micrographs (figure 3).
The interface features of all the samples are shown in figure 5.As the copper became soft at 800 ℃, the copper matrix was tightly attached to the graphite flake in a flat interface even in the samples using spherical Cu powder, which is different from the puckered interface using spherical Al powder [10].99% of relative densities can be explained by those interface characterizations.In addition, this void-free interface is also favorable for the thermal transfer between the matrix and reinforcement.

Thermal conductivity of Cu/G f composite materials
Figure 6 shows the values of the calculated TC and their corresponding <cos 2 θ> values within the in-plane direction of Cu/G f composite materials fabricated utilizing both the one-step filling and step-by-step filling approaches.The specimen fabricated using Cu flake powder shows the highest TC as compared to the other two types of materials processed under the one-step processing route and using the other powder types.However, this difference in TC values became smaller when the step-by-step powder filling method was applied.It can be claimed that the increase of <cos 2 θ> values or improved orientation degree leads to the increase of TC values.Moreover, the multiple-step filling process had a much weaker effect on the increase of the TC values of the Cu/G f composites prepared using the Cu flake powder.This is merely because the G f reached a relatively high orientation degree via the one-step route in these parts and there was not much space left for improvement.It should be noted that the <cos 2 θ> values of samples processed using dendritic and spherical powders and treated by the 15-step powder filling process were almost identical.These results fit with previous research findings [22].However, their TC values showed a significant difference.This can be traced back to the noticeable difference observed in the TC values of the sintered pure copper samples (cf table 1).
In this study, given that the size and volume fraction of G f were fixed and by ignoring the little effect caused by the TC properties of different Cu matrices and their interfacial thermal conductance, it could be concluded that, according to the EMA model, the TC value along the in-plane direction has a strong relationship with the orientation degree of G f .Here, we present the in-plane TC formula as follows: where the subscripts L and T are noted as the in-plane and through-plane directions of G f , respectively, f is the volume fraction of G f , and S is the geometrical factor, where D and t are the diameter and thickness of the reinforcement, respectively [10], K m is the TC of the Cu matrix, which was from the measured TC of the assintered Cu samples using different copper powders, K i is intrinsic TC of G f and K L , K T is 1000 W mK −1 [3], and 10 W m −1 K −1 −1 [23], respectively.As shown in figure 7, the theoretical in-plane TC values increase as the <cos 2 θ> value changes from 0.5 to 1 covering the range for the samples processed using three types of powders.As mentioned above, a small deviation between the three curves is mainly caused by the different TC values of the pure Cu powders.The    measured TCs of Cu/G f composites are well consistent with the predictions.It demonstrates that an efficient way to maximize the in-plane TC is to tailor the <cos 2 θ> value or orientation degree.

An interpretation of achieving high in-plane TC of Cu/G f composites
As shown in table 1, the major difference existing among the three Cu powders is the difference in the apparent densities of the powders.The apparent density value of spherical Cu powder is seven times than that for flake Cu one, (cf the inset photos of figure 1).It is worth noting that the G f can get distributed in a larger space after getting mixed with Cu powder particles with a lower apparent density.As illustrated in figure 8, regardless of the type of the used Cu powders, the same mass of G f are distributed in the same mass of Cu powder particles.As Cu powders have different apparent densities, diverse volumes of Cu + G f mixtures can be observed inside the graphite mold for the same quantity of each of these Cu powders.It was assumed that G f are randomly distributed inside the copper powder after the mold filling.During the uniaxial hot densification step, G f can move inside of the Cu + G f mixture and tend to orient in a plane perpendicular to the pressure direction.From the non-dense packing state to the dense state, during the pressing step, G f would travel a greater distance to be aligned in Cu flake + G f mixture, as indicated by the yellow arrows in figure 8.For the step-by-step method, the thickness of the powder layer for each step was determined by the amount of powder mixtures filled in the graphite die.When the thickness of the powder layer was controlled under the average value of the diameter of G f , the G f was constrained in a laying state.Thus, almost all the G f lie flat in a single powder layer.When the Cu/G f composites are stacked by this powder layer, a highly oriented G f can be obtained.However, this process is still unclear, and further investigation via in situ industrial X-ray computed tomography can be a proper approach.

Conclusions
Flake, dendritic, and spherical Cu powders were used to fabricate Cu/G f composite materials.Those three powders show various apparent densities.Flake Cu powder has the lowest apparent density as compared with the others.High orientation of G f was successfully achieved using flake Cu powder and a one-step powder filling method.This could be obtained in parts processed by the others only under multiple-step processes.Under the one-step approach, disordered G f , in which G f were not oriented fully, were easily observed in the samples processed by dendritic or spherical copper powders.Increased orientation degree of G f enhances in-plane TC of Cu/G f composites (Maximum TC up to 540 W mK −1 ).An interpretation based on the apparent density and multiple-step powder filling approach was proposed to explain the mechanism of obtaining highly oriented G f in the copper matrix under powder metallurgy.The lower the apparent densities of the used metal powder, the fewer steps of powder filling are required to obtain G f with high orientation.

Figure 1 .
Figure 1.SEM micrographs showing the morphologies of as-received Cu powders and G f : (a) spherical Cu powder, (b) dendritic Cu powder, (c) flake Cu powder, (d) G f ; Insets showing the transparent bottles with 8 g of Cu powder inside.

Figure 2 .
Figure 2. (a) Temperature and pressure conditions of the SPS operation.(b) Schematic of the SPS specimen showing the dimensions of the specimen and the definition of the in-plane and through-plane directions.

Figure 6 .
Figure 6.Thermal conductivities and orientation degrees along the in-plane direction of Cu/G f composites fabricated using different copper powder and filling processes.

Figure 7 .
Figure 7. Theoretical and experimental thermal conductivity of Cu/G f composites as a function of <cos 2 θ> value.

Table 1 .
Physical properties of sintered Cu samples using as-received pure Cu powders.