X-RAY DIFFRACTION DATA

2.5. X-RAY DIFFRACTION DATA

As explained above, it is difficult to sinter silicon carbide under normal conditions. However, the nano particles of SiC preparared by attrition milling could be sintered under suitable conditions for a

87 variety of novel applications. The silicon carbide is known to develop different polytypes during and

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after proper sintering. This is developed through a dislocation mechanism, which is discussed here along with the quantitative aspects of determining the contents of different polytypes by X-ray diffrac- tion analysis.

Different polytypes are formed during and after sintering (4H, 6H, etc.), through the nucleation of stacking faults by a dislocation mechanism in these different polytypes [48]. In order to throw light on the formation of these polytypes, it is importat to make quantitative determination of these polytypes in the sintered masses, which has been attempted here by following the standard techniques [49].

The identification and quantitative analysis of different polytypes present in the sintered silicon carbides, doped with different additives and fired at different temperatures and time, were done by the X-ray diffraction. The X-ray diffraction pattern was taken by using a X-ray Diffractometer (Model : PW 1840 of M/s Philips NV, Holland). All X-ray diffractograms were taken by using Cu-K α radiation (wavelength, λ = 1.54178 Å) at a scanning speed of 0.10 per second in 2θ. A tube voltage of 40 KV, a tube current of 20 mA, and a time constant of 10 seconds were used. The lines were drawn by one line recorder (Model : PW 1879 of M/s Philips NV, Holland) with a speed of 10 mm per degree 2 θ. The diffraction patterns are standard patterns with the intensity ( I ) vs. 2 θ curves, and are not shown here.

2.5.1. X-ray Data Analysis

The quantitative analysis by X-ray diffraction is based on the fact that the intensity of the diffrac- tion pattern of a particular mixture depends on the concentration as :

⎛ IA 3 2 4 2 − 0 2M λ ⎞ ⎡ ⎛ µ 0 ⎞ e ⎤ ⎛ 1 ⎞ ⎡ 2 ⎛ + 1 cos 2 θ ⎞ ⎤ ⎛ e ⎞ I= ⎜ ⎜

⎝ π 32 r ⎟ ⎜

⎥ ⎢ |F|P

⎝ sin θ cos θ ⎠ ⎥ ⎦ ⎝ 2 µ ⎠ where, I = Integrated intensity per unit length of diffraction line, I 0 = Intensity of incident beam (Joules

Sec –1 m –2 ), A = Cross sectional area of incident beam (m 2 ), λ = Wavelength of incident beam (m), r = Radius of diffractometer circle (m), V = Volume of the unit cell (m 3 ), F = Structure Factor, P = Multi- plicity Factor, θ = Bragg Angle, m = Linear Absorption Coefficient (which enters ½, i.e. the absorption factor).

Let us write different important parameters as :

2 ⎛ + 1 cos 2 θ ⎞ ⎤ R= ⎜ 2 ⎟ ⎢ |F|P ⎜

which is a constant for a fixed incident beam and particular diffractometer, and is represented by K. The temperature factor is not important and thus, it can be neglected.

Then, the expression for the intensity can be represented by :

KR

I=

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It applies only to a pure substance for a particular phase in a mixture. Thus, the intensity of a particular line of the phase becomes the intensity of the amount of the phase present in the mixture. Moreover, there are several kinds of polytypes of silicon carbide, which contain mainly 6H, 4H, 3C (Cubic) and 15R peaks. Therefore, the equations have been developed to calculate different peaks at the same ‘d’ value, although their intensities are different for different polytypes at different ‘d’ values. Different phases of polytypes present in the sintered silicon carbides are calculated from these equa- tions.

Table 2.2 : X-ray Data for various Polytypes of SiC.

3C Polytype : hkl

d -Spacing (nm)

4H Polytype : hkl

d -Spacing (nm)

6H Polytype : hkl

d -Spacing (nm)

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89 15R Polytype :

hkl

d -Spacing (nm)

As stated above, the X-ray intensities are proportional to the volume fraction of a phase in a mixture of phases. The calculated intensities, as shown in Table - 2.2, were normalized setting 1 (111) of 3C polytype to 100, and were then used to derive the equation system given in this table for the volume fraction of different polytypes A, B, C and D, which are the volume fractions of polytypes, such as 15R, 6H, 4H and 3C respectively.

Thus, the following equations were derived :

Peak at d (nm) K(3.2a + 9.9c) =

Peak

A 0.266 K(11.2a + 19.4b) =

B 0.263 K(26a + 38.9c) =

C 0.257 K(31.1a + 59.2b + 25.1c + 100d) =

D 0.251 K(18.1b + 34.1c) =

E 0.235 K(2.4a + 6.5b + 13.1d) =

F 0.217 By solving these equations, different polytypes present in the sintered silicon carbide were deter-

mined from the observed X-ray diffraction intensities. The above results can be summatized as follows :

A. For α-SiC doped with boron carbide, the X-ray diffraction analysis shows 6H to 4H polytype transformation with about 72% 4H polytype.

B. For β-SiC doped with boron carbide, it is 72% 6H transformed from 3C polytype.

C. For α-SiC doped with AlN, it is 72% 4H transformed from 6H.

D. For β-SiC doped with AlN, it shows a polytype transformation to 4H, through 15R polytype route, from the 3C-cubic polytype, with 50% 4H and 50% 6H.

This is the result from the analysis of the X-ray diffraction patterns through the above standard formalism. From the dislocation behaviour of SiC crystals, this transformation seems to result from a suitable layer displacement mechanism, which is caused by the nucleation and expansion of the stacking faults within the silicon carbide crystal structure, as detailed below.

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2.5.2. The Dislocation Mechanism

As shown later in this section, both TEM and SEM micrographs show that both boron and alu- minium have entered within the structure of silicon carbide, but did not show the presence of any dopant- related phases or any liquid/glassy phase in the grain-boundaries. The presence of boron or aluminum within the structure was further confirmed by the electron diffraction patterns, wherein double spots were observed. It can be said that the sintering mechanism of silicon carbides doped with boron carbide and aluminium nitride is a solid state sintering process through the creation of vacancies and solid state diffusion through the increase of the diffusion coefficients by many orders of magnitude [2, 3]. It should

be pointed out that the fracture mehanical behaviour of these materials also confirm the absence of any liquid/glassy phase, where both the flexural strength and the fracture toughness, i.e. the critical stress intensity factor or K IC , remain constant over a wide temperature range upto 1400°C showing no degra- dation of strength [19, 20].

2.5.2.1. Dislocation Behaviour

At this point, some discussion is necessary on the dislocation behaviour of the polytype forma- tion in α-silicon carbide. The formation of SiB 4 increases the cell dimension of 6H α-silicon carbide, whereas the formation of B 4 C decreases the cell dimension. During sintering, the structure of SiB 4 and

B 4 C may begin to coalesce in different cells in layer displacement mechanism. The cells are likely to become disordered and strained.

The cells containing SiB 4 structure begin to recrystallize as 4H polytype, whereas the cells con- taining B 4 C begin to precipitate from the cells having B 4 C structure. Thus, it may be the reason for obtaining 72% 4H polytype from the grains containing mainly 6H polytype, which was determined by X-ray diffraction analysis. The quantitative measurement of silicon carbide polytypes from X-ray dif- fraction peak intensities developed by Ruska et al. [49] has been utilized for this calculation.

() a () b

() d () c

Figure 2.14: Dislocation behaviour of different polytypes of SiC [50].

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91 Figure 2.14 shows the dislocation of various atomic sites in silicon carbide crystals. The polytype

transformation from 6H to 4H might result from suitable layer displacements, which is caused by the nucleation and expansion of the stacking faults in individual close-packed double-layers of Si and C. This process is governed by the thermal diffusion, such as the grain boundary diffusion, since the nucleation of a stacking fault would require the migration of atoms inside the crystal.

This layer displacement is likely to occur in such a manner so as to minimize the free energy, and take the structure towards the stable state. If the stable state happens to be the one with a different order, such an order will tend to result. Such a mechanism was also suggested by Jagadzinski, as mentioned in reference [50].

During sintering by the addition of boron and carbon, and the increase of temperature, the vacan- cies would be created, and the atoms would become free to migrate within the crystal and to the surface by diffusion. If the number of vacancies come closer together, it will become possible for the neighbour- ing atoms to move into “B” sites thereby nucleating a fault. Within the region, the atoms are in “B” sites, while the rest of the atoms are in ‘A’ sites causing a partial dislocation to bind the fault.

This partial dislocation glides, which causes the fault to expand, until the entire layer of atoms is displaced into ‘B’ sites, and the partial dislocation moves out of the crystal. The entire layer is then displaced from ‘A’ to ‘B’ orientation, as shown in Figure - 2.14. By the same mechanism, the displacements occur for other layers throughout the structure in such a manner so as to result in a new structure.

Moreover, by this mechanism, the transformation would proceed through one-dimensional disor- der caused by the nucleation of stacking faults and it is expected to exhibit a considerable one-dimen- sional disorder, as observed by the needle-like crystals of 4H polytype. The growth of these needle-like crystals in the later stage of sintering may also be governed by the screw dislocation, which might be generated from the strains in the crystal structure due to the incorporation of boron atom in the α-silicon carbide crystal.

During recrystallization of β-silicon carbide during sintering with 2 wt% aluminium nitride and

1 wt% carbon, the crystals containing Al 4 C 3 presumably recrystallize as 4H polytype, whereas the crys- tals containing Si 3 N 4 recrystallize as 6H polytype. From the quantitative analysis of polytypes, it is found that 50% of β-silicon carbide (3C) recrystallizes as 6H polytype, whereas the rest as 4H polytype. As the formation of Al 4 C 3 in silicon carbide creates ‘strain’ in the structure, this leads to the recrystallization as 4H polytype. It is found that the recrystallization of 4H polytype occurred through 15R transformation from β-silicon carbide with the change of sintering time, as shown in Figure 2.14.

Again, in the case of AlN doping in silicon carbide, similar discussion may be made about the dislocation behaviour of different polytype formation. The formation of Al 4 C 3 increases the cell dimen- sion. During sintering, the cells containing the structure of Al 4 C 3 begin to coalesce by layer displace- ment mechanism, not by screw dislocation, as it would require clockwise as well as anti-clockwise movement in the transformation that is possible. The cells become disordered and strained, and thus the structure begins to recrystallize as 4H polytype leading to an increase of the entropy, i.e. a higher degree of disorder prevails in the structure.

As in the case of boron carbide doping, as described above, here the transformation from 6H to 4H might result from a suitable layer displacement, which is caused by the nucleation and expansion of the stacking faults in individual close-packed double layers of Si and C. This process is similar to that mentioned by Jagadzinski, as in reference [50].

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