Effect of thermal conductivity of alumina-nanodiamond

The thermal diffusivity and heat capacity are determined with the flash technique. Fig.5-23(a) compares the thermal diffusivity of all samples as a function of temperature. Fig.5-23(b) shows the specific heat capacity of the different alumina-nanodiamond composites as a function of temperature. By knowing the values of density, heat capacity, and thermal diffusivity, the thermal conductivity can be calculated by Eq(1) (K= ρ Cp α). Fig.5-24 shows the effect of nanodiamond addition on the thermal conductivity of alumina-nanodiamond composite at different temperatures [52-53].

Thermal diffusivity / mm2 /s

(a)

(b)

Specific heat capacity / J/gK

Fig.5-24 Calculated thermal conductivity of alumina-nanodiamond composites as a function of temperature.

5.4 Comprehensive comparison and discussion

5.4.1 Comparison of thermal conductivity of alumina-CNT composites with different production methods

The comparison of the thermal conductivity of alumina composites with carbon nanotubes has been carried out quite experimentally in the past, but only in this experiment, the method of tape casting was carried out, and the results of several previous experiments were compared. The thermal conductivity of different specimen preparation methods is compared as follows:

Amount of CNT

/ vol% Densification process Thermal conductivity

/ W/mK Note

Table.5-1 Previously reported values for the thermal conductivity of alumina-CNT composites

These composites were all prepared using spark plasma sintering

alumina by 30 % [8]. However, the thermal conductivity of alumina–CNT composites could reach 90 W/mK using a higher sintering temperature. A recent study confirmed that the addition of CNT reduced the thermal conductivity of alumina [9]. Ahmad suggested that low thermal conductivity could be related to the high thermal resistance at the alumina/CNT interface. The reported data from Kumari et al. [7] suggested that the microstructure might play an important role in the thermal conductivity. Nevertheless, previous studies paid little attention to the influence of microstructure.

5.4.2 Comparison of thermal diffusivity of alumina-graphene/CNT composites

Consider adding 0.88 %, 1.8 %, 3.5% and 8.5% graphene and carbon nanotubes respectively. The thermal diffusivity obtained for the measurement is shown in Figure 5-25-5-28.

Fig.5-25 Experimental data for thermal diffusivity of alumina-0.88 vol% CNT/graphene composites as a function of measurement temperature.

Thermal diffusivity / mm2 /sThermal diffusivity / mm2 /s

Fig.5-27 Experimental data for thermal diffusivity of alumina-3.5 vol% CNT/graphene composites as a function of measurement temperature.

Fig.5-28 Experimental data for thermal diffusivity of alumina-8.5 vol% CNT/graphene

composites as a function of measurement temperature.

Thermal diffusivity / mm2 /sThermal diffusivity / mm2 /sThermal diffusivity / mm2 /s

5.4.3 Comparison of the specific heat capacity of alumina-graphene/CNT composites

Consider adding 0.88 %, 1.8 %, 3.5% and 8.5% graphene and carbon nanotubes respectively. The specific heat capacity obtained for the measurement is shown in Figure 5-29 - 5-32.

Fig.5-29 Experimental data for specific heat capacity of alumina-0.88 vol%

CNT/graphene composites as a function of measurement temperature.

Specific heat capacity / J/gK

Fig.5-30 Experimental data for specific heat capacity of alumina-1.8 vol%

CNT/graphene composites as a function of measurement temperature.

Fig.5-31 Experimental data for specific heat capacity of alumina-3.5 vol%

CNT/graphene composites as a function of measurement temperature Specific heat capacity / J/gKSpecific heat capacity / J/gK

Fig.5-32 Experimental data for specific heat capacity of alumina-8.5 vol%

CNT/graphene composites as a function of measurement temperature

5.4.4 Comparison of thermal conductivity of alumina-graphene/CNT composites

Consider adding 0.88 %, 1.8 %, 3.5% and 8.5% graphene and carbon nanotubes respectively. The thermal conductivity obtained for the measurement is shown in Figure 5-33-5-36.

Specific heat capacity / J/gK

Fig.5-33 Calculated thermal conductivity of alumina-0.88 vol% CNT/graphene composites as a function of temperature

Fig.5-34 Calculated thermal conductivity of alumina-1.8 vol% CNT/graphene composites as a function of temperature

Fig.5-35 Calculated thermal conductivity of alumina-3.5 vol% CNT/graphene composites as a function of temperature

Fig.5-37 Previous reported values for the thermal conductivity of alumina-CNT composites

According to the related literature [7-9], even if different specimen preparation methods, the thermal conductivity has a linear relationship with the added CNT vol%, and the thermal conductivity decreases as the amount of addition increases (see Fig.5-37). It quite appears linear within 10 vol%. It can be inferred that the addition of CNT does not help to improve the thermal conductivity of alumina. Although the thermal conductivity of CNT can reach 2800 W/mK and the thermal conductivity of pure alumina is only about 28 W/mK. It is expected to add CNTs for increasing the thermal conductivity of alumina and exert a multiplier effect.

In practice, the thermal conductivity of alumina depends on the grain size and relative density of the specimen after sintering. Adding CNT in alumina, although the excellent thermal conductivity of CNT can increase the thermal conductivity of the composite, the voids in the sintered alumina are regarded as heat transfer insulators. So the more voids, the lower the grain boundaries, the more adiabatic voids is created. Although the CNTs form a local network structure with each other, they can slightly assist the conduction of heat at the grain boundaries. However, the formed heat conduction network can only be formed in a local area due to the insufficient amount of addition. Due to the whole process of heat conduction, it will find the area where the thermal resistance is low, but the local heat conduction network is not enough to connect the whole specimen. Therefore, as the amount of added CNTs increases, the thermal conductivity also decreases.

Until the amount of CNT added reaches 10 vol% or more, the

vol% causes divergence. There is a specimen that produces a CNT thermal network, and the thermal conductivity can be higher than the trend line.

5.4.5 Calculation of mean free path of alumina-graphene/CNT composites

The mean free path is the average traveling distance between two consecutive collisions of particles with other particles in the medium. This mode of transmission is limited by elastically scattered by the phonon at the lattice defect. The mean free path of phonon is directly related to the effective relaxation length in the process, while the mean free path varies with the number of impurities or grain boundaries in the material.

The thermal conduction behavior in dielectric solid is primarily discussed in terms of the phonon-scattering theory [54-57]. The thermal conductivity can be determined by direct measurement of the density (ρ) and thermal diffusivity (α) of the solid:

K = ρ C

p

α

……… (1)

The thermal conductivity (K), as well as the diffusivity (α), is inversely proportional to the temperature.

In addition, considering thermal conduction to be a result of the transportation of thermal elastic waves, thermal conductivity (K) of solid materials is a relation to the mean free path by [55,58]

K =

¹

3

ρ L Cp ν

………..……… (2) Where L is the phonon mean free path, Cp is the specific heat per unit, and ν is elastic wave velocity. Combining equations (1) and (2), the following relationship is obtained,

L = 3 α / ν

……….. (3)

Where ν is roughly constant with respect to temperature [22]. The primary elastic wave velocity in dense fine-grained polycrystalline Al2O3

was measured to be 10.92 km/s [59].

In our experiments, the mean free path of the pure alumina sintered specimen is around 15 – 7 Å at room temperature to 300°C. The mean free path of Al₂O₃ + 0.5 wt% CNT sintered specimen is 19 – 8 Å at room temperature to 300°C. The mean free path of Al2O3 + 0.5 wt% graphene sintered specimen is 21 – 9 Å at room temperature to 300°C. In addition, the mean free path of a phonon decreases gradually with increasing temperature because as the number of exciting phonons increases with increasing temperature, so does the number of collisions between them, on account of the anharmonic forces between atoms [58]. The densification and intrinsic thermal property of the material are a predominant factor to affect the mean free path of phonons diffusing through the solid.

5.4.6 Comparison of porosity effect on thermal conductivity

 porosity effect of Alumina-graphene Nanocomposites

The thermal conductivity of alumina depends on the amount of

Through the help of the above equation, the influence of porosity can then be removed.

The defect acts as a source for scattering phonons [58]. The concentration of defects near the grain boundary is the highest. The thermal conductivity is thus affected by the amount of grain boundary area.

Total grain boundary area (A) within one unit cell can be expressed in the following equation

---(5)

In the above equation, n is the number of grains with a size of G. In each unit cell, the number of grain, n, can be estimated with the following equation

……….……….(6)

Therefore, the grain boundary area within one unit cell is proportional to (1/G). Assuming that the thermal conductivity depends on the amount of grain boundary area, the effect of grain size can thus be estimated as

K =K_g(1

G)………(7)

The Kg is the thermal conductivity with certain grain size (G). The above equation demonstrates that a larger grain size results in higher thermal conductivity. It is certainly the case, as shown in Fig. 5-19. The values for two alumina specimens with different grain size can be treated as bounding values; the thermal conductivity for the alumina–graphene composites with the grain size of 〜1 μm can then be estimated. After correcting the effect of porosity (Eq. 4) and grain size (Eq. 7), the values for composites are shown in Fig. 5-38.

Fig.5-38 Experimental data and calculated values for the thermal conductivity of alumina-graphene composite as a function of volume content. The value corrected by removing the effect of porosity (Eq. 4) and grain size (Eq. 7) is also shown. The straight line indicates the lower bound (Eq. 9) for a layered structure.

The estimated values for graphene-containing alumina are slightly higher than that of alumina as the volume fraction of graphene is lower than 2 %. However, the addition of 8.5 % graphene reduces the thermal conductivity by 25 %. Therefore, the addition of graphene imposes negative effect on the thermal conduction of alumina as the graphene content is higher than the critical value. An amount of 8.5 vol% graphene

is high enough to form the interconnecting network, as shown in Fig. 4b. In the present study, our experimental data illustrate that the thermal conductivity drops as the graphene form an interconnecting network.

The thermal conductivity of two-phase composites has attracted much attention in the last several decades [61]. Although many theoretical models are available, none of the model predictions can describe all the experimental data. Instead of predicting the values for two-phase composites precisely, an envelope composing of upper bound (in-series model) and lower bound (in-parallel model) are favorable [62]. The lower bound for a two-phase composite (K_C) is as following

1

graphene is low, the above equation can be simplified as follows:

The thermal conductivity for alumina–graphene composite (K_C) can thus be estimated from the thermal conductivity of alumina (Kalumina) directly. The values shown in Eq. 9 are also shown in Fig. 5-20.

thermal conductivity of graphite exhibits unique anisotropic characteristics.

The thermal conductivity along the plane of graphite layer can reach 2000 W/mK, and only 〜7 W/mK in the direction perpendicular to the graphite layer [58]. It implies that the graphene sheets may act as a thermal barrier if they are lying on the plane perpendicular to the heat conduction.

Therefore, the addition of graphene sheets is blocking the movement of phonons when they are interconnected. As the amount of graphene is low, the phonons can transport through the alumina matrix.

The processing condition may also affect thermal conductivity.

Phonon transportation is sensitive to the presence of lattice defects. The external heat and load used during PECS may introduce many defects into the graphene, reducing its thermal conductivity. It should be noted that the above analyses assume no thermal barrier at the alumina/graphene interface.

5.4.7 Comparison of nano-carbon adding effect on thermal conductivity

Fig.5-39 shows the thermal conductivity at 25°C for Al₂O₃-graphene/CNT/nanodiamond composites as a function of second phase content. The figure demonstrates that the thermal conductivity decreases with the increase of nano-carbon content.

Fig.5-39 Calculated thermal conductivity of alumina- graphene/CNT/nanodiamond composites as a function of volume content.

vol %

relative density is indeed an important factor affecting the thermal conductivity. However, at the same relative density, adding nanodiamond is the best, adding graphene second, and adding CNT is the worst. The relative density is positively related to thermal conductivity. Regardless of the composition, the higher the relative density, the greater the thermal conductivity.

Fig.5-40 Calculated thermal conductivity of alumina- graphene/CNT/nanodiamond composites as a function of relative density.

Nano-carbons such as nanodiamond, carbon nanotube, and graphene have high thermal conductivity. Dispersing the above carbon allotropes and

their derivatives into an alumina matrix must consider the thermal and mechanical properties of the composite. It is necessary to maintain the insulation and strength of the alumina, and it is desirable to increase the thermal conductivity of the alumina. It is well known that the thermal transfer mechanism of Al₂O₃ depends on phonon delivery.

Diamonds are a particularly good crystal with very few defects. The carbon atom has a small mass and a very strong carbon-carbon bond, allowing it to propagate very high-energy phonons so that fewer phonons can transmit the same energy. In contrast, graphite conducts heat very well in phonons (and free electrons) along with the layer, but the layers are out of tolerance, so there is a heavy anisotropy.

The heat transfer of Alumina composites is different in the addition of nano-carbons, mainly due to the tightness of crystal structure. Adding excess carbon derivatives (greater than 1%), whether it is 0D-nanodiamond, 2D-graphene, and 1D -CNT results in lower heat transfer. Due to below 1400 °C, Carbon & alumina does not bond together, so excessive carbon accumulates in the grain boundary during the densification process, hindering grain growth and densification. The densification and grain growth of alumina is prohibited. The thermal conductivity has to consider these microstructure features.

heat transfer direction of 2D-graphene is planar. It happens to be perpendicular to the heat transfer direction of the target. The best heat transfer direction of 1D-CNT is along the axis direction. Because of the CNT winding effect, the direction of heat transfer results are random, and the heat transfer benefit may also offset each other, failed to play the excellent heat transfer of CNT.

The only good application is 0D-diamond. Since the heat transfer has no specific directionality and the specific surface area is small relative to graphene and CNT. The effect of the prohibiting alumina grain growth in the PECS process is relatively small. A small amount of nanodiamond (less than 1 vol%) will have better heat transfer than pure alumina.

Finally, it is considered that the effect of adding various nano-carbon on the heat transfer of alumina, in which the amount of CNT and graphene added, is insufficient to become a network, and it is not allowed to be completely connected to lose insulation. The added carbon allotropes and their derivatives all have good thermal conductivity. However, the best heat transfer direction of 2D-graphene is planar, and the CNTs are easy to wind.

Hence, the nanodiamond becomes the regional fast channel center, as shown in Figure 5-41. On the other hand, nanodiamond has more particles when it is added in the same proportion, that is, it has a better effect when the dispersion is better. Nanodiamond has a regional heat-transfer acceleration effect in alumina to achieve the best heat-transfer effect. The results show that the above method is much better than the previous method.

Fig.5-41 Schematic representation of fast channel for alumina-nanodiamond composites.

Chapter 6 Conclusions

 In this study, the alumina composite with carbon nanotubes/graphene was prepared by tape casting. The alumina powder was directly added to the CNT/graphene suspension solution to form a slurry. The green compact was made from the slurry and then sintered with PECS. This study conducts the manufacturing process that is different from other journal papers did.

 By removing the influence of porosity and grain boundary area, the thermal conductivity begins to drop at graphene contents of 2–3 vol%. As the graphene content is higher than this value, the thermal conductivity will drop accordingly due to low density, poor interface, and inadequate grain size.

 The addition of a small amount of nanodiamond can significantly increase the thermal conductivity, and both the thermal conductivity of 0.57 and 1.1 vol%

nanodiamonds are higher at 25 ° C than pure alumina. That nanodiamond forms a fast channel that provides a shortcut for heat transfer, but as the number of additive increases, the density decreases. Therefore, it reduces the benefits of nanodiamond.

 The effect of adding a small amount (<1 vol %) nano-carbon in the composite depends on the structural characteristics of the nano-carbons. Since the directionality of 1D-CNT and 2D-graphene heat transfer is inconsistent with the direction required by the actual application, the benefit of addition is limited.

0D-diamond is currently the best addition because it has no specific heat transfer direction and its structure does not cause hindrance at the grain boundary, which affects densification.

Chapter 7 Future works

 This thesis seeks to examine the effect on the thermal conductivity of alumina composites with the addition of nano-carbons such as carbon nanotubes, graphene, and nanodiamond. However, does alumina react with carbon at high-temperature sintering with plasma? The TEM observation will be used to explain the microstructure and heat transfer mechanism of the nanocomposite.

 Raman spectra indicate that the graphene becomes crystal defective in the nanocomposite after PECS sintering. That means the crystallinity is affected by the sintering process. However, we cannot rule out that these characteristic peaks are affected by carbon infiltration from the graphite die. More relevant experiments should be carried out to verify.

 The thermal conductivity of two-phase composites many theoretical models. In this thesis, we use an envelope composing of upper bound and lower bound models. However, the thermal resistance concept maybe imports to describe all the experimental data.

 The unexpected results of this work show that the use of nanodiamonds as second phases in alumina-based composites presents fascinating possible applications, such as wear-resistant and high temperature resistant structural components, etc.

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