Effect of Carbon

2.7.3.3. Effect of Carbon

The doping level, temperature and other parameters being constant, the role of carbon seems to

be important from the thermodynamic point of view and for generating vacancies, eventually to drive a bulk diffusion mechanism for both silicon and carbon to better densification of silicon carbides. The effect of carbon has been studied as a function of carbon content to ascertain the role of carbon in the sintering process in both the silicon carbides.

Figures 2.19 and 2.20 show the sintering curve as a function of temperature of α-silicon carbide doped with both boron carbide and aluminium nitride. It is seen that in both cases, 99% of TD is achieved at 2050°C and 2100°C for boron carbide and aluminium nitride respectively for a sintering time of 15 minutes under vacuum (3 mbar). A study of varying the concentration of the dopants showed that the optimum densification occurs at 0.5 wt% boron carbide and 2 wt% aluminium nitride with 1 wt% carbon, as already shown above. In order to see the effect of carbon on sintering, the carbon content was varied up to 5 wt%, and the results are shown in Figures 2.21 and 2.22 for α-silicon carbide. Figures

2.23 and 2.24 show the microstructure with optimum carbon content for β-silicon carbide, for both these dopants, keeping the doping level constant as above.

SILICON CARBIDE

c /c

g ( 2.6 Y

IT

2.4 NS DE TEMPERATURE (°C)

Figure 2.19: Densification curve of α-SiC doped with B 4 C against temperature.

c /c

g ( 2.6 Y

IT

2.4 NS DE TEMPERATURE (°C)

Figure 2.20: Densification curve of α-SiC doped with AlN against temperature.

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DE 2.4 2000°C 2050°C 2100°C

2.2 4 B C = 0.5 wt%

CARBON (wt%)

Figure 2.21: Densification curve of α-SiC doped with B 4 C against carbon content.

2050°C 2000°C

65 AlN = 2 wt%

CARBON (WT%)

Figure 2.22: Densification curve of α-SiC doped with AlN against carbon content. It is seen that in both the cases, the maximum density was obtained at 1 wt% carbon for both the

dopants at each temperature from 2050° – 2100°C. These curves also demonstrate that the addition of

101 carbon is quite effective for enhancing the sintered density. For instance, at zero % carbon, the sintered

SILICON CARBIDE

density is 2.15 g/cm 3 , which is only an increase of 7.5% from the green density of 2.0 gm/cm 3 .

Figure 2.23: Microstructure of sintered β-SiC doped with B 4 C and carbon.

Figure 2.24: Microstructure of sintered β-SiC doped with AlN and carbon. Now, a detailed analysis is necessary on the role of carbon during sintering of silicon carbide,

which is important primarily due to the following reasons :

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A. De-oxidation of SiO 2 films originally developed on the silicon carbide grains,

B. Coating of the surface of silicon carbide to lower the free energy of the surface and conse- quently lowering the surface vapour energy, and

C. Decreasing the diffusivity of C atoms to match with the diffusivity of Si atoms, which is essential for the effective sintering.

One of the roles of carbon during sintering of SiC was examined by the measurement of the grain size of the sintered body. It was found that the grain size decreases with increasing content of carbon. This means that carbon decreases the surface vapour energy, and thus prevents the surface vapour trans- port responsible for the grain growth.

In Figure 2.25, the microstructure of a sintered α-SiC specimen is shown with a starting compo- sition of 97 wt% α-SiC, 2 wt% AlN and 1 wt% C. The grain size is in the range of 5-10 µm. The grain size is smaller compared to the sample doped with boron as a sintering aid. In order to study the sintering mechanism, the grain boundary regions have been thoroughly studied by using transmission electron microscope, as shown in Figure 2.26. No liquid phase is found to be present in the micrographs. From the “electron diffraction” patterns, as shown in Figure 2.27, it is also found that aluminium has entered into the structure of silicon carbide. Thus, it may be concluded that the sintering of silicon carbide is a solid state process involving 6H to 4H polytype transformation for which some evidences have been presented in the section 2.5.1 on the quantitative analysis of the X-ray data.. The results are very similar for boron carbide doping.

Figure 2.25: TEM photo of α-SiC doped with 2 wt% AlN

SILICON CARBIDE

Figure 2.26: TEM photo of α-SiC doped with AlN showing no liquid phase present in the grain boundary region.

The sintered density increases almost linearly with increasing carbon content up to 1 wt%, and above 1wt%, it becomes almost constant. The role of carbon during sintering of silicon carbide has several effects. The silicon carbide always contains a very small percentage of oxygen, which is present as a very thin layer of silica, which is usually present on the surface of silicon carbide powder particles [23, 30]. A detrimental side reaction can take place in which the silica layer is reduced by the silicon carbide itself by the reaction as :

(2.1) for which ΔG = 0 at 1870°C. This volatile SiO is further reduced at higher temperature through the

2SiO 2 + SiC → 3SiO + CO

reaction as :

(2.2) This reaction with ΔG = 0 at 1950°C is very efficient at usual sintering temperatures (2050° -

SiC + SiO → 2Si + CO

2150°C). Thus, the silicon vapour is usually present at sintering temperatures, when carbon is not added.

It is known that the equilibrium concentration of point imperfections, i.e. the vacancies or Schottky defects for the minimum free energy at a particular temperature is given by [51] :

(2.3) where N is the number of sites, and n the number of vacancies.

n = N exp(– ΔH f /kT)

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Figure 2.27: Electron diffraction pattern α-SiC doped with AlN. The silicon carbide is a covalent compound. Thus, the carbon vacancies and silicon vacancies

can be written as :

n C = N exp(– ΔH C /kT)

n Si = N exp(– ΔH Si /kT)

(2.6) This product of n C .n Si is constant for a particular temperature and for a particular atmosphere

n C .n Si =N 2 exp [– (ΔH C + ΔH Si )/kT]

for silicon carbide. Thus, the increase of carbon vacancies must be followed by a decrease of silicon vacancies and vice-verse. The diffusion coefficient is simply the product of vacancy concentration, the jump frequency and one sixth of the jump distance squared. As there are 12 possible adjacent carbon and silicon sites, the diffusion coefficient of carbon and silicon can be represented by :

SILICON CARBIDE

D Si = 12 [V Si ]ω 0 (2.7)

D C = 12 [V C ]ω 0 (2.8)

where ω 0 is the jump frequency, and α is the jump distance [52]. Thus, the increase of diffusion coefficient of carbon will increase the carbon vacancies, which

will be followed by a decrease of the diffusion coefficient of silicon due to the decrease of silicon vacancies, and vice-verse. The chemical analyses of both pure 6H α- and β-silicon carbide single crys- tals have shown that the crystals are silicon rich. The ratio of silicon to carbon of 6H α-SiC and β-SiC were reported to be 1.032 and 1.049 respectively. Thus, the excess of silicon must result in the carbon vacancies.

From the equation (2.6), it can be concluded that the higher carbon vacancies with respect to silicon would result in the higher diffusion coefficient of carbon. This was exactly found by Hong et al [53-55] that the carbon diffusion coefficient is two orders of magnitude larger than that of silicon in argon atmosphere, as shown in Figure 2.28.

Carbon

1 ) 2– s

P ure

c –12

D(

Silicon

1/T (×10 K) –5 Figure 2.28: Carbon and silicon self-diffusion rates in SiC single crystals. [53]

Also carbon and silicon vacancies are related to partial pressure of carbon and silicon. The higher carbon partial pressure would result in a decrease in the carbon vacancies, but would promote an in- crease in the silicon vacancies, according to the equation (2.6), as already explained.

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An atmosphere rich in silicon would result in the higher carbon vacancies, thereby showing an increase in the carbon diffusion coefficient, which is followed by a very high decrease in the silicon diffusion coefficient. This was also found by Hong et al. [53]. that the carbon diffusion co-efficient is three orders of magnitude larger than that of silicon and the diffusion coefficient of silicon is also low, as shown in Figure 2.29.

2227°C

1727°C

–5 Grain Boundary

Diffusion –6

C (in Si atm.)

c –9 Si (in C atm.)

D(

G – 10 LO

C (in C atm.) – 12

Si (in Si atm.)

4 10 / T(K)

Figure 2.29: SiC self-diffusion in various atmospheres. [53]

This large discrepancy between the diffusion coefficients of carbon and silicon in silicon rich atmosphere, and generally the very low value of diffusion coefficient of both silicon and carbon, pre- vent the sintering of silicon carbide in silicon rich atmosphere, which is generally present in the sintering range of 2050° - 2150°C. This role of the diffusion coefficients was found to be effective in the case of doping with boron carbide in α-silicon carbide [3].

SILICON CARBIDE

107 It is found that the self-diffusion rate of each element is enhanced by the presence of the other

element, due to the creation of the vacancies. Thus, the carbon atmosphere would equalize the ratio of Si to C to unity or less than unity in silicon carbide, thereby creating silicon vacancies, and thus increasing the bulk diffusion of silicon, which is further activated by the addition of boron carbide [3]. For the densification to occur, the mass transport of silicon and carbon should be more or less equal.

Without the addition of boron and carbon, the mass transport of silicon and carbon is not equal, and it is also low, and the densification does not occur. The addition of boron carbide increases the diffusion coefficient and the carbon creates a partial carbon atmosphere, which make the diffusion coefficients equal. Thus, it makes the mass transport of silicon and carbon equal in order to make the densification to occur. This sums up the effect of carbon along with boron in the sintering of silicon carbides in part. The other part obviously deals with the removal of surface silica, which is discussed below.

The addition of carbon in a well-distributed manner reduces the layer of silica film on the sur- faces of the silicon carbide powder particles by the overall reaction :

(2.9) for which the change in the Gibbs free energy ΔG = 0 at 1520°C.

SiO 2 + 3C → SiC + 2CO

Moreover, the excess partial pressure of carbon decreases the carbon vacancies, thereby promot- ing the silicon vacancies, according to the equation (2.6) by increasing the diffusion coefficient of silicon, whereas decreasing that of carbon. It was also found by Ghostagore and Coble [45] that the silicon diffusion coefficient is higher than the carbon diffusion coefficient in a sintering temperature range of 2050°-2150°C in carbon atmosphere for silicon carbide. Therefore, the sintering behaviour of silicon carbide is different depending on silicon rich or carbon rich atmosphere, due to the respective role of the diffusion coefficients, as described above in the entire discussion.

In this work, it has been found that the highest sintered densities have been obtained when the percentage of carbon has been 1 wt%. The oxygen content of the processed powder is 0.33 wt%. This oxygen has remained as silica on the surface of the processed powder. The most of carbon has been utilized to remove the surface silica according to the equation (2.9), and the rest of carbon creates a low partial pressure of carbon, which is suitable enough to increase the diffusion coefficient of silicon. It was found by Hojo et. al. [40] that the highest sintered density was achieved when the amount of carbon was just enough to completely remove the surface silica.

Therefore, it can be concluded that the addition of 1 wt% of carbon is required for not allowing the formation of silicon atmosphere, which is normally present when carbon is not added, according to the reactions (2.1) and (2.2), and which hinders the densification process, as stated earlier. Moreover, it forms an atmosphere of neutral to very low partial pressure of carbon, and hence enhances the densification by increasing the diffusion coefficient of silicon, which is very low at silicon rich atmosphere.

As shown in Figures 2.21 to 2.22 that the sintered density actually tends to decrease as the carbon content increases beyond 1 wt%. The addition of excess carbon increases the partial pressure of carbon. As carbon vacancies are inversely related to the partial pressure of carbon, the number of carbon vacancies would, therefore, decrease thereby decreasing the diffusion coefficient of carbon resulting in

a decrease of the sintering rate, as observed. It was found by Suzuki and Hase [35] that the grain growth also becomes very prominent above

1900°C. The observed ‘structure development’ could be described as :

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(a) The larger grains dissolve the surrounding smaller grains, and (b) The mass of dissolving grains engulf the pores, which are located at the surface of the grains. Thus, when the sintering rate decreases due to the decrease in the diffusion coefficient of carbon

in the presence of excess carbon partial pressure, two possibilities are as follows :

1. The exaggerated grain growth which is very prominent at this sintering temperature be- comes operative at a very fast rate over the sintering rate, engulfing the pores and causing entrapment of these pores, thereby making a decrease in the sintered density.

2. To coat the surface of silicon carbide to lower the free energy of the surface and consequently lowering the surface vapour energy and thus prevent vapour surface transport of materials, thereby preventing the exaggerated grain growth.

For a study on the effect of atmosphere on the sintering of silicon carbides, it is important to reconcile with the concept of vacancy formation. As already mentioned above, the product of the number of Schottky defects (n C .n Si ) is constant for a particular temperature and for a particular atmos- phere. Therefore, the effect of atmosphere needs to be discussed later in the light of the above diffusion model as a confirmation of the model [16, 18].

In summary, it can be stated that even for nano particles of SiC, it is important to study the sintering behaviour of SiC with different “dopants mixed with 1 wt% carbon”, which is an optimum quantity for a maximum densification. The effect of carbon is to remove the surface silica from the ‘nano particles’ of silicon carbide to help these particles to sinter better. The effect of addition of carbon up to 1 wt% also helps in the formation of vacancy of both silicon and carbon, and thereby increasing the bulk diffusion coefficients in silicon carbide, which increase the densification of silicon carbides to nearly theoretical density. The diffusion model shows that the relation between number of vacancies and the diffusion coefficients of both silicon and carbon explains the densification behaviour of both α- and β-silicon carbides.