# XRD Peak Profile Analysis of SiC Reinforced Al2O3 Ceramic Composite Synthesized by Electrical Resistance Heating and Microwave Sintering: A Comparison

Authors: Madhan Mohankumar; S. Praveen Kumar; B. Guruprasad; Sreekanth Manavalla; Joshua Stephen Chellakumar Isaac JoshuaRamesh Lalvani; P. L. Somasundaram; P. Tamilarasu; Prakash Singh Tanwar
Journal: Advances in Materials Science and Engineering
 (2021)

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## Abstract

Al2O3 with 10 wt.% of SiC ceramic composite is synthesized at 1500°C by electrical resistance heating sintering with a holding time of 5 hours and microwave sintering methods with a holding time of 15 minutes. The samples generated by the two methods are characterized using powder X-ray diffraction and field emission scanning electron microscopy (FESEM). Experiments with both samples showed that the existence of the α-Al2O3 and β-SiC phases in both samples was verified by the findings of XRD pattern on both samples. Microstructure study illustrates that the Al2O3 matrix particles have spherical-like shape and their average matrix particle size is 67 ± 5 nm for electrical resistance heating sintered sample and 38 ± 5 nm for microwave sintered sample. The lattice strain and crystallite size of Al2O3 matrix were measured using Williamson–Hall (W-H) methods, which were achieved via the use of XRD peak broadening, based on a diffraction pattern. Three modified W-H models were used to compute other parameters, including strain (ε) and stress (σ), as well as energy density (u). These models were the uniform deformation model (UDM), the uniform deformation energy density model (UDEDM), and the uniform deformation stress model (UDSM). The average crystallite sizes of α-Al2O3 attained from these three models of Williamson–Hall (W–H) methods and FESEM analysis are correlated and found very close to each other. In all three models of the W-H technique, X-ray diffraction peak profile examination of electrical resistance heating-sintered and microwave-sintered Al2O3/10 wt. % SiC ceramic composite reveals that the microwave-sintered sample has finer crystallite size with less strain.


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## Body

## 1. Introduction

Among all the ceramics, alumina (Al2O3) are extensively used in engineering applications owing to its thermal and chemical inertness, comparably high strength, and electrical and thermal insulators together with the availability and bounteousness [1–8]. In spite of the abovementioned advantages, brittleness and low fracture toughness of Al2O3 create restrictions of its applications. One of the methods to overcome this limitation is the synthesis of fibre or particulate reinforced Al2O3 ceramic composites. In this, reinforcement can be a polymer, metal, or ceramics. A ceramic material, silicon carbide (SiC), perchance, is one of the options for the secondary phase which bring about the enhancement of Al2O3 matrix [9–14]. Nihara stated that inclusion of SiC particles in little amount to the Al2O3 matrix can enhance the mechanical properties of Al2O3/SiC structural ceramic composite substantially in comparison with monolithic Al2O3 [15–19]. They found that the addition of 5 wt.% SiC as a secondary phase improved the strength and fracture toughness of the material from 350 to 1520 MPa and 3.5 to 4.8 MPam1/2, respectively, by increasing the amount of SiC in the material [15]. There are various ways to sinter this structural ceramic composite such as standard pressureless sintering, hot isostatic pressing, spark plasma sintering, and microwave sintering. Among these, microwave sintering is one of the effective and energy-saving methods which also enhances the mechanical and microstructure of Al2O3/SiC ceramic composites [16, 17].Crystallite size and morphology play vital parts in several applications of the ceramic composites, which have induced the researchers to concentrate on the fabrication methods, type of composites, and sintering methods. XRD peaks’ profile investigation has become a very compelling tool for microstructural characterization of ceramics either in bulk or in powder form. It was widely accepted that the Debye–Scherrer technique and the Williamson–Hall method were both appropriate for calculating the lattice strain (ε) and the crystallite size (D) from the broadening of XRD peaks, respectively [18–24]. No material has a perfect crystal structure because of their finite size which leads to an anomaly from ideal crystallinity which produces the X-ray diffraction peak broadening [24, 25]. The information from the pattern obtained from diffractometer apparently gives about the expansion of X-ray diffraction peaks and can be directly quantified. However, it is essential to become aware of that broadening of diffraction peaks arises primarily as a result of the following two factors, namely, crystallite size and lattice strain [26]. It is a common practice to use peak profile analysis of diffraction pattern to estimate microstructural characteristics such as lattice strain and crystallite size, and the findings are compared with the observable attributes of the material [27]. Both the microstructural quantities mentioned above influence the intensity and width of the Bragg peak and produce a 2θ peak position shift.Al2O3/10 wt.% SiC ceramic composite is developed in this study using both electrical resistance heating sintering and microwave sintering techniques. To estimate the following microstructural properties, the authors perform an XRD peak profile analysis utilising the Debye–Scherrer and modified Williamson–Hall (W-H) techniques. There are three properties of α-Al2O3 that have been determined: crystallite size (D), lattice stress (σ), and lattice stiffness (S). In order to compute the above properties, modified W-H plots were utilised. According to the literature review, a thorough and comparative study of X-ray diffraction peak profile analysis using these modified W–H models on electrical resistance heating sintered and microwave sintered Al2O3/10 wt.% SiC ceramic composite has not been published.


## 2. Experimental Procedure

The ceramic composite Al2O3/10 wt.% SiC was synthesized at 1500°C using electrical resistance heating sintering and microwave sintering techniques. The appropriate weight percentage of Al2O3 (Sigma Aldrich Chemicals Pvt Ltd, 99.5%) and SiC (Sigma Aldrich Chemicals Pvt Ltd, 99%) was milled at a speed of 350 rpm for 6 hours with isopropyl alcohol in a planetary ball mill (VB Ceramics, Chennai, India) using tungsten carbide (WC) lined vial and tungsten carbide (WC) ball. After milling, the homogeneous mixture was dried and sieved. With a dwell period of 30 seconds and a pressure of 60 MPa, the homogeneous mixture was compacted into pellets of circular cross section with 5 mm radius and 3 mm thickness using a cold uniaxial press. An initial batch of pellets was sintered at 1500°C for 5 hours in an electrical resistance heating furnace with molybdenum disilicide (MoSi2) as the heating element, and an additional batch of pellets was sintered at the same temperature with a minimum holding time of 15 minutes in a microwave furnace equipped with a magnetron that produces microwaves at 2.45 GHz and a susceptor that served as the axillary heating element. In both the sintering methods, 10°C per minute heating was used. In both the electrical resistance heating furnace and the microwave furnace, the specimens were furnace cooled after they had been sintering. X-ray diffractogram of the synthesized specimens were reported using XRD-Smart Lab (9 kW), Japan, diffractometer with CuKα radiation (λ = 1.54060 Å) utilising 45 kV and 30 mA as operating conditions. 4° per minute, 0.02° per step, and a scan range of 10° to 90° were the scan speeds, steps angles, and scan ranges, respectively. An FESEM (Supra 55-Carl Zeiss, Germany) was used to examine the morphology of the powders in the sintered sample and estimate their composition. Using ImageJ software, the particle size was calculated using the line interpolation technique.


## 3. Results and Discussion

### 3.1. X-Ray Diffraction Analysis

Figure1 exemplifies the diffractogram of microwave-sintered and electrical resistance heating-sintered Al2O3/10 wt.% SiC ceramic composite sample, recorded between 10° and 90° of Bragg angle (2θ). All the observed peaks of X-ray diffraction pattern can be indexed with the rhombohedral system of α-Al2O3 and β-SiC, referenced in the JCPD’s file no. 71–1123 with space group R3c and 89–4793 with space group R3m, respectively. The R3c space group has both hexagonal and rhombohedral unit cells. The fundamental structure is made up of hexagonal oxygen planes interspersed with aluminium planes. The R3m space group of β-SiC indicates the rhombohedral polymorphs, which have zigzag atomic position of Si and C.Figure 1
XRD pattern of Al2O3/10 wt.% SiC: (a) microwave sintered and (b) electrical resistance heating sintered.
(a)(b)The lattice parameter ofα-Al2O3 matrix phase determined from the X-ray diffraction pattern of electrical resistance heating sintered sample were a = b = 4.758 Å and c = 12.998 Å and microwave sintered samples were a = b = 4.759 Å and c = 12.995 Å and those relatively close when equated with the lattice parameter of α-Al2O3 unit cell were a = b = 4.761 Å and c = 12.99 Å from the JCPD’s file no. 71–1123. In both microwave-sintered and electrical resistance heating-sintered sample, strong and sharp peaks of stable α-Al2O3 phase were present and indicate that the samples have crystalline phase, and no other phases of Al2O3 were found because the starting powder used was stable α-Al2O3. In the X-ray diffraction analysis, it was found that the microwave-sintered sample peaks were more intense than those of the electrical resistance heating-sintered sample, indicating that the microwave-sintered sample exhibits higher levels of crystallinity than the electrical resistance heating sample.


### 3.2. Crystallite Size and Strain Determination

#### 3.2.1. Debye–Scherrer Method

In general, the increase in peak width in the X-ray diffractogram and in the peak profile analysis as a result of dislocation growth is by reason of an increase in lattice strain, crystallite size, and instrumental magnification as a result of dislocation growth [28]. The peak broadening caused by instrumental magnification must be taken into consideration while conducting a systematic examination for lattice strain and crystallite size effects. The X-ray diffractogram of a standard Al2O3 was obtained in order to isolate the instrumental peak widening from the sample. The corrected peak broadening corresponding to the various peaks of α-Al2O3 was calculated using the following equation [29]:(1)βhkl=βhklmeasured2−βhklinstrumental21/2.Equation (2) shows how to determine the size of a crystallite using the Scherrer formula, which is given below:(2)D=kλβhklcosθ⇒βhkl=kλDcosθ,where k is the shape factor (0.9), D is the crystallite size in nm, λ is the wavelength of X-ray (Cu Kα = 0.15406 nm), and βhkl is the full width at half maxima (FWHM) of an individual peak at 2θ. Table 1 shows the α-Al2O3 average crystallite size of electrical resistance heating-sintered and microwave-sintered Al2O3/10 wt.% SiC composite.Table 1
Results of Debye–Scherrer, WH plots and SEM image
MethodDebye–SchererW-H methodsSEMUDMUDSMUDEDMD in nmD in nmStrainD in nmStrainStressσ in MPaD in nmStrainStressσ in MPau in kJm−3D in nmElectrical resistance heating sintering67.1561.414.1E-0.570.674.3E-0.5389.8174.954.5E-0.5394.65183.3467 ± 5Microwave sintering37.7137.054.7E-0.639.634.6E-0.6388.7740.364.6E-0.6392.43189.6738 ± 5


#### 3.2.2. Williamson–Hall Method

(1) Uniform Deformation Model (UDM). In addition to the strain, the crystallite size and defects in the crystallite lattice may cause X-ray diffraction peaks to be generated in a variety of other situations. By examining the full width half maximum of the peak as a function of Bragg’s angle (2θ), Williamson–Hall analysis clearly separates the peak deformation caused by the crystallite size and the lattice strain [30]. Equation (3) was used to calculate the amount of crystal defect and distortion that produces strain in the powders which results in peak broadening:(3)ε=βhkl4tanθ.It has been shown that the crystallite size-induced peak width changes as1/cosθ and that the lattice strain varies as tanθ using equations (2) and (3), respectively. The total peak widening, which is the sum of the peak broadening caused by both lattice strain and crystallite size, is given by [31](4)βhkl=βD+βε,where βD is the peak broadening on account of crystallite size, βε is the peak broadening as a result of lattice strain, and βhkl is the instrumental adjusted full width half-maximum intensity of the peak broadening. The value of the instrumentally adjusted full width half-maximum intensity of each peak is calculated using equation (1). Given the assumption of self-reliant contributions of lattice strain and crystallite size to peak broadening, the broadening of the peak is equal to the sum of equations (2) and (3), which is denoted by [32](5)βhkl=kλDcosθ+4εtanθ.We may get by rearranging equation (5) the following:(6)βhklcosθ=kλD+4εsinθ.Based on the assumption that strain is even in all crystallographic directions, as shown in equation (6), the Williamson–Hall equation, also known as the uniform deformation model (UDM), may be used to predict crystallographic direction in a variety of situations. UDM models assume that crystal nature is isotropic, with the assumption that the material’s characteristics are not affected by the direction of measurement in the crystallographic direction, as the case with conventional models. With βhklcosθ on the y-axis and 4εsinθ on the x-axis, a graph was created and a linear fit was performed. The y-intercepts of the graph represent the crystallite size (D) of the matrix and the slope represents the amount of strain (ε) in the α-Al2O3 matrix. While the UDM plots for electrical resistance heating-sintered sample and microwave-sintered sample are shown in Figures 2(a) and 2(b), respectively, and the average crystallite size and lattice strain are shown in Table 1.Figure 2
UDM plot for Al2O3/10wt. % SiC sample: (a) electrical resistance heating sintering and (b) microwave sintering.
(a)(b)(2) Uniform Stress Deformation Model (USDM). In numerous scenarios, the concepts of homogeneity and isotropies are not met. In order to overcome this and assimilate more practical condition, an approach of anisotropic is implemented. Consequently, anisotropic strain (ε) is used to improve the W-H equation. The stress owing to lattice distortion is assumed to be even across all directions of crystallography in the uniform stress deformation model (USDM), presuming particles have only a small microstrain. In uniform stress deformation model (USDM), stress and strain have linear relationship based on Hook’s law:(7)σ=εYhkl⇒ε=σYhkl,where σ is the crystal stress, Yhkl is the modulus of elasticity, and ε is the anisotropic microstrain. The Williamson–Hall technique is modified in the USDM method by replacing equation (7) for equation (6) [32]:(8)βhklcosθ=kλD+4σsinθYhkl.Equation (9) gives Young’s modulus for hexagonal crystal structures [33]:(9)Yhkl=h2+h+2k2/3+al/c22S11h2+h+2k2/32+S33al/c4+2S13+S44h2+h+2k2/3al/c2,where S11, S13, S33, and S44 are the elastic compliances of Al2O3 with values 2.3 × 10−12, 0.4 × 10−12, 2.2 × 10−12, and −6.8 × 10−12 m2N−1 respectively; “a” and “c” are lattice parameters [34]. By plotting, βhklcosθ along the y-axis and 4sinθ/Yhkl along the x-axis, the slope of the linear fit provides the uniform stress (σ) and the y-intercept provides the crystallite size (D). The USDM plots for electrical resistance heating-sintered and microwave-sintered Al2O3/10 wt. % SiC samples are shown in Figures 3(a) and 3(b), respectively, and the values of uniform deformation stress (σ) and crystallite size (D) are included in Table 1.Figure 3
USDM plot for Al2O3/10wt. % SiC: (a) electrical resistance heating sintering; (b) microwave sintering.
(a)(b)(3) Uniform Deformation Energy Density Model (UDEDM). The crystal energy density of the sample was calculated using the UDEDM model. Crystals were formerly thought to follow a homogeneous and isotropic model, according to traditional view. Nevertheless, the assumption of homogeneity and isotropy is false in a large number of cases. Furthermore, when examining the deformation energy density, the strain-stress connection is not independent. Hooke’s law used for an elastic system shows that u=ε2Yhkl/2 is used to calculate the density of deformation energy. As a result, equation (9) may be changed as follows based on the energy and strain relationship:(10)βhklcosθ=kλD+4sinθ2uYhkl1/2.The UDEDM plots for electrical resistance heating-sintered and microwave-sintered Al2O3/10 wt. % are shown in Figures 4(a) and 4(b). The values of anisotropic energy density (u) and average crystallite size (D), which are given in Table 1, are calculated using the slope and Y-intercept.Figure 4
UDEDM plot for Al2O3/10wt. % SiC: (a) electrical resistance heating sintering; (b) microwave sintering.
(a)(b)


### 3.3. Morphological Study

Figure5 shows the average matrix particle size and morphology of Al2O3/10 wt. % SiC-sintered powder as analysed using a field emission scanning electron microscope picture. It can be clearly confirmed that the attained sintered sample powders are spherical in shape with agglomeration of particles. The average matrix particle size can be seen as 67 ± 5 nm for electrical resistance heating-sintered Al2O3/10 wt.% SiC and 38 ± 5 nm for microwave-sintered Al2O3/10 wt.% SiC, and the results are very close to the values obtained by Debye–Scherrer and W-H plot. The reason behind the reduction of average matrix particle size of microwave-sintered sample is volumetric heating and less dwell time than electrical resistance heating sintering. The longer dwell time in electrical resistance heating sintering results in grain growth and forms coarse matrix particle, and it was evident in the previous studies [19].Figure 5
SEM image of sintered powder: (a) electrical resistance heating sintered; (b) microwave sintered.
(a)(b)


## 3.1. X-Ray Diffraction Analysis

Figure1 exemplifies the diffractogram of microwave-sintered and electrical resistance heating-sintered Al2O3/10 wt.% SiC ceramic composite sample, recorded between 10° and 90° of Bragg angle (2θ). All the observed peaks of X-ray diffraction pattern can be indexed with the rhombohedral system of α-Al2O3 and β-SiC, referenced in the JCPD’s file no. 71–1123 with space group R3c and 89–4793 with space group R3m, respectively. The R3c space group has both hexagonal and rhombohedral unit cells. The fundamental structure is made up of hexagonal oxygen planes interspersed with aluminium planes. The R3m space group of β-SiC indicates the rhombohedral polymorphs, which have zigzag atomic position of Si and C.Figure 1
XRD pattern of Al2O3/10 wt.% SiC: (a) microwave sintered and (b) electrical resistance heating sintered.
(a)(b)The lattice parameter ofα-Al2O3 matrix phase determined from the X-ray diffraction pattern of electrical resistance heating sintered sample were a = b = 4.758 Å and c = 12.998 Å and microwave sintered samples were a = b = 4.759 Å and c = 12.995 Å and those relatively close when equated with the lattice parameter of α-Al2O3 unit cell were a = b = 4.761 Å and c = 12.99 Å from the JCPD’s file no. 71–1123. In both microwave-sintered and electrical resistance heating-sintered sample, strong and sharp peaks of stable α-Al2O3 phase were present and indicate that the samples have crystalline phase, and no other phases of Al2O3 were found because the starting powder used was stable α-Al2O3. In the X-ray diffraction analysis, it was found that the microwave-sintered sample peaks were more intense than those of the electrical resistance heating-sintered sample, indicating that the microwave-sintered sample exhibits higher levels of crystallinity than the electrical resistance heating sample.


## 3.2. Crystallite Size and Strain Determination

### 3.2.1. Debye–Scherrer Method

In general, the increase in peak width in the X-ray diffractogram and in the peak profile analysis as a result of dislocation growth is by reason of an increase in lattice strain, crystallite size, and instrumental magnification as a result of dislocation growth [28]. The peak broadening caused by instrumental magnification must be taken into consideration while conducting a systematic examination for lattice strain and crystallite size effects. The X-ray diffractogram of a standard Al2O3 was obtained in order to isolate the instrumental peak widening from the sample. The corrected peak broadening corresponding to the various peaks of α-Al2O3 was calculated using the following equation [29]:(1)βhkl=βhklmeasured2−βhklinstrumental21/2.Equation (2) shows how to determine the size of a crystallite using the Scherrer formula, which is given below:(2)D=kλβhklcosθ⇒βhkl=kλDcosθ,where k is the shape factor (0.9), D is the crystallite size in nm, λ is the wavelength of X-ray (Cu Kα = 0.15406 nm), and βhkl is the full width at half maxima (FWHM) of an individual peak at 2θ. Table 1 shows the α-Al2O3 average crystallite size of electrical resistance heating-sintered and microwave-sintered Al2O3/10 wt.% SiC composite.Table 1
Results of Debye–Scherrer, WH plots and SEM image
MethodDebye–SchererW-H methodsSEMUDMUDSMUDEDMD in nmD in nmStrainD in nmStrainStressσ in MPaD in nmStrainStressσ in MPau in kJm−3D in nmElectrical resistance heating sintering67.1561.414.1E-0.570.674.3E-0.5389.8174.954.5E-0.5394.65183.3467 ± 5Microwave sintering37.7137.054.7E-0.639.634.6E-0.6388.7740.364.6E-0.6392.43189.6738 ± 5


### 3.2.2. Williamson–Hall Method

(1) Uniform Deformation Model (UDM). In addition to the strain, the crystallite size and defects in the crystallite lattice may cause X-ray diffraction peaks to be generated in a variety of other situations. By examining the full width half maximum of the peak as a function of Bragg’s angle (2θ), Williamson–Hall analysis clearly separates the peak deformation caused by the crystallite size and the lattice strain [30]. Equation (3) was used to calculate the amount of crystal defect and distortion that produces strain in the powders which results in peak broadening:(3)ε=βhkl4tanθ.It has been shown that the crystallite size-induced peak width changes as1/cosθ and that the lattice strain varies as tanθ using equations (2) and (3), respectively. The total peak widening, which is the sum of the peak broadening caused by both lattice strain and crystallite size, is given by [31](4)βhkl=βD+βε,where βD is the peak broadening on account of crystallite size, βε is the peak broadening as a result of lattice strain, and βhkl is the instrumental adjusted full width half-maximum intensity of the peak broadening. The value of the instrumentally adjusted full width half-maximum intensity of each peak is calculated using equation (1). Given the assumption of self-reliant contributions of lattice strain and crystallite size to peak broadening, the broadening of the peak is equal to the sum of equations (2) and (3), which is denoted by [32](5)βhkl=kλDcosθ+4εtanθ.We may get by rearranging equation (5) the following:(6)βhklcosθ=kλD+4εsinθ.Based on the assumption that strain is even in all crystallographic directions, as shown in equation (6), the Williamson–Hall equation, also known as the uniform deformation model (UDM), may be used to predict crystallographic direction in a variety of situations. UDM models assume that crystal nature is isotropic, with the assumption that the material’s characteristics are not affected by the direction of measurement in the crystallographic direction, as the case with conventional models. With βhklcosθ on the y-axis and 4εsinθ on the x-axis, a graph was created and a linear fit was performed. The y-intercepts of the graph represent the crystallite size (D) of the matrix and the slope represents the amount of strain (ε) in the α-Al2O3 matrix. While the UDM plots for electrical resistance heating-sintered sample and microwave-sintered sample are shown in Figures 2(a) and 2(b), respectively, and the average crystallite size and lattice strain are shown in Table 1.Figure 2
UDM plot for Al2O3/10wt. % SiC sample: (a) electrical resistance heating sintering and (b) microwave sintering.
(a)(b)(2) Uniform Stress Deformation Model (USDM). In numerous scenarios, the concepts of homogeneity and isotropies are not met. In order to overcome this and assimilate more practical condition, an approach of anisotropic is implemented. Consequently, anisotropic strain (ε) is used to improve the W-H equation. The stress owing to lattice distortion is assumed to be even across all directions of crystallography in the uniform stress deformation model (USDM), presuming particles have only a small microstrain. In uniform stress deformation model (USDM), stress and strain have linear relationship based on Hook’s law:(7)σ=εYhkl⇒ε=σYhkl,where σ is the crystal stress, Yhkl is the modulus of elasticity, and ε is the anisotropic microstrain. The Williamson–Hall technique is modified in the USDM method by replacing equation (7) for equation (6) [32]:(8)βhklcosθ=kλD+4σsinθYhkl.Equation (9) gives Young’s modulus for hexagonal crystal structures [33]:(9)Yhkl=h2+h+2k2/3+al/c22S11h2+h+2k2/32+S33al/c4+2S13+S44h2+h+2k2/3al/c2,where S11, S13, S33, and S44 are the elastic compliances of Al2O3 with values 2.3 × 10−12, 0.4 × 10−12, 2.2 × 10−12, and −6.8 × 10−12 m2N−1 respectively; “a” and “c” are lattice parameters [34]. By plotting, βhklcosθ along the y-axis and 4sinθ/Yhkl along the x-axis, the slope of the linear fit provides the uniform stress (σ) and the y-intercept provides the crystallite size (D). The USDM plots for electrical resistance heating-sintered and microwave-sintered Al2O3/10 wt. % SiC samples are shown in Figures 3(a) and 3(b), respectively, and the values of uniform deformation stress (σ) and crystallite size (D) are included in Table 1.Figure 3
USDM plot for Al2O3/10wt. % SiC: (a) electrical resistance heating sintering; (b) microwave sintering.
(a)(b)(3) Uniform Deformation Energy Density Model (UDEDM). The crystal energy density of the sample was calculated using the UDEDM model. Crystals were formerly thought to follow a homogeneous and isotropic model, according to traditional view. Nevertheless, the assumption of homogeneity and isotropy is false in a large number of cases. Furthermore, when examining the deformation energy density, the strain-stress connection is not independent. Hooke’s law used for an elastic system shows that u=ε2Yhkl/2 is used to calculate the density of deformation energy. As a result, equation (9) may be changed as follows based on the energy and strain relationship:(10)βhklcosθ=kλD+4sinθ2uYhkl1/2.The UDEDM plots for electrical resistance heating-sintered and microwave-sintered Al2O3/10 wt. % are shown in Figures 4(a) and 4(b). The values of anisotropic energy density (u) and average crystallite size (D), which are given in Table 1, are calculated using the slope and Y-intercept.Figure 4
UDEDM plot for Al2O3/10wt. % SiC: (a) electrical resistance heating sintering; (b) microwave sintering.
(a)(b)


## 3.2.1. Debye–Scherrer Method

In general, the increase in peak width in the X-ray diffractogram and in the peak profile analysis as a result of dislocation growth is by reason of an increase in lattice strain, crystallite size, and instrumental magnification as a result of dislocation growth [28]. The peak broadening caused by instrumental magnification must be taken into consideration while conducting a systematic examination for lattice strain and crystallite size effects. The X-ray diffractogram of a standard Al2O3 was obtained in order to isolate the instrumental peak widening from the sample. The corrected peak broadening corresponding to the various peaks of α-Al2O3 was calculated using the following equation [29]:(1)βhkl=βhklmeasured2−βhklinstrumental21/2.Equation (2) shows how to determine the size of a crystallite using the Scherrer formula, which is given below:(2)D=kλβhklcosθ⇒βhkl=kλDcosθ,where k is the shape factor (0.9), D is the crystallite size in nm, λ is the wavelength of X-ray (Cu Kα = 0.15406 nm), and βhkl is the full width at half maxima (FWHM) of an individual peak at 2θ. Table 1 shows the α-Al2O3 average crystallite size of electrical resistance heating-sintered and microwave-sintered Al2O3/10 wt.% SiC composite.Table 1
Results of Debye–Scherrer, WH plots and SEM image
MethodDebye–SchererW-H methodsSEMUDMUDSMUDEDMD in nmD in nmStrainD in nmStrainStressσ in MPaD in nmStrainStressσ in MPau in kJm−3D in nmElectrical resistance heating sintering67.1561.414.1E-0.570.674.3E-0.5389.8174.954.5E-0.5394.65183.3467 ± 5Microwave sintering37.7137.054.7E-0.639.634.6E-0.6388.7740.364.6E-0.6392.43189.6738 ± 5


## 3.2.2. Williamson–Hall Method

(1) Uniform Deformation Model (UDM). In addition to the strain, the crystallite size and defects in the crystallite lattice may cause X-ray diffraction peaks to be generated in a variety of other situations. By examining the full width half maximum of the peak as a function of Bragg’s angle (2θ), Williamson–Hall analysis clearly separates the peak deformation caused by the crystallite size and the lattice strain [30]. Equation (3) was used to calculate the amount of crystal defect and distortion that produces strain in the powders which results in peak broadening:(3)ε=βhkl4tanθ.It has been shown that the crystallite size-induced peak width changes as1/cosθ and that the lattice strain varies as tanθ using equations (2) and (3), respectively. The total peak widening, which is the sum of the peak broadening caused by both lattice strain and crystallite size, is given by [31](4)βhkl=βD+βε,where βD is the peak broadening on account of crystallite size, βε is the peak broadening as a result of lattice strain, and βhkl is the instrumental adjusted full width half-maximum intensity of the peak broadening. The value of the instrumentally adjusted full width half-maximum intensity of each peak is calculated using equation (1). Given the assumption of self-reliant contributions of lattice strain and crystallite size to peak broadening, the broadening of the peak is equal to the sum of equations (2) and (3), which is denoted by [32](5)βhkl=kλDcosθ+4εtanθ.We may get by rearranging equation (5) the following:(6)βhklcosθ=kλD+4εsinθ.Based on the assumption that strain is even in all crystallographic directions, as shown in equation (6), the Williamson–Hall equation, also known as the uniform deformation model (UDM), may be used to predict crystallographic direction in a variety of situations. UDM models assume that crystal nature is isotropic, with the assumption that the material’s characteristics are not affected by the direction of measurement in the crystallographic direction, as the case with conventional models. With βhklcosθ on the y-axis and 4εsinθ on the x-axis, a graph was created and a linear fit was performed. The y-intercepts of the graph represent the crystallite size (D) of the matrix and the slope represents the amount of strain (ε) in the α-Al2O3 matrix. While the UDM plots for electrical resistance heating-sintered sample and microwave-sintered sample are shown in Figures 2(a) and 2(b), respectively, and the average crystallite size and lattice strain are shown in Table 1.Figure 2
UDM plot for Al2O3/10wt. % SiC sample: (a) electrical resistance heating sintering and (b) microwave sintering.
(a)(b)(2) Uniform Stress Deformation Model (USDM). In numerous scenarios, the concepts of homogeneity and isotropies are not met. In order to overcome this and assimilate more practical condition, an approach of anisotropic is implemented. Consequently, anisotropic strain (ε) is used to improve the W-H equation. The stress owing to lattice distortion is assumed to be even across all directions of crystallography in the uniform stress deformation model (USDM), presuming particles have only a small microstrain. In uniform stress deformation model (USDM), stress and strain have linear relationship based on Hook’s law:(7)σ=εYhkl⇒ε=σYhkl,where σ is the crystal stress, Yhkl is the modulus of elasticity, and ε is the anisotropic microstrain. The Williamson–Hall technique is modified in the USDM method by replacing equation (7) for equation (6) [32]:(8)βhklcosθ=kλD+4σsinθYhkl.Equation (9) gives Young’s modulus for hexagonal crystal structures [33]:(9)Yhkl=h2+h+2k2/3+al/c22S11h2+h+2k2/32+S33al/c4+2S13+S44h2+h+2k2/3al/c2,where S11, S13, S33, and S44 are the elastic compliances of Al2O3 with values 2.3 × 10−12, 0.4 × 10−12, 2.2 × 10−12, and −6.8 × 10−12 m2N−1 respectively; “a” and “c” are lattice parameters [34]. By plotting, βhklcosθ along the y-axis and 4sinθ/Yhkl along the x-axis, the slope of the linear fit provides the uniform stress (σ) and the y-intercept provides the crystallite size (D). The USDM plots for electrical resistance heating-sintered and microwave-sintered Al2O3/10 wt. % SiC samples are shown in Figures 3(a) and 3(b), respectively, and the values of uniform deformation stress (σ) and crystallite size (D) are included in Table 1.Figure 3
USDM plot for Al2O3/10wt. % SiC: (a) electrical resistance heating sintering; (b) microwave sintering.
(a)(b)(3) Uniform Deformation Energy Density Model (UDEDM). The crystal energy density of the sample was calculated using the UDEDM model. Crystals were formerly thought to follow a homogeneous and isotropic model, according to traditional view. Nevertheless, the assumption of homogeneity and isotropy is false in a large number of cases. Furthermore, when examining the deformation energy density, the strain-stress connection is not independent. Hooke’s law used for an elastic system shows that u=ε2Yhkl/2 is used to calculate the density of deformation energy. As a result, equation (9) may be changed as follows based on the energy and strain relationship:(10)βhklcosθ=kλD+4sinθ2uYhkl1/2.The UDEDM plots for electrical resistance heating-sintered and microwave-sintered Al2O3/10 wt. % are shown in Figures 4(a) and 4(b). The values of anisotropic energy density (u) and average crystallite size (D), which are given in Table 1, are calculated using the slope and Y-intercept.Figure 4
UDEDM plot for Al2O3/10wt. % SiC: (a) electrical resistance heating sintering; (b) microwave sintering.
(a)(b)


## 3.3. Morphological Study

Figure5 shows the average matrix particle size and morphology of Al2O3/10 wt. % SiC-sintered powder as analysed using a field emission scanning electron microscope picture. It can be clearly confirmed that the attained sintered sample powders are spherical in shape with agglomeration of particles. The average matrix particle size can be seen as 67 ± 5 nm for electrical resistance heating-sintered Al2O3/10 wt.% SiC and 38 ± 5 nm for microwave-sintered Al2O3/10 wt.% SiC, and the results are very close to the values obtained by Debye–Scherrer and W-H plot. The reason behind the reduction of average matrix particle size of microwave-sintered sample is volumetric heating and less dwell time than electrical resistance heating sintering. The longer dwell time in electrical resistance heating sintering results in grain growth and forms coarse matrix particle, and it was evident in the previous studies [19].Figure 5
SEM image of sintered powder: (a) electrical resistance heating sintered; (b) microwave sintered.
(a)(b)


## 4. Conclusion

Al2O3/10 wt. % SiC ceramic composite is successfully synthesized at 1500°C by electrical resistance heating sintering and microwave sintering methods. The electrical resistance heating sintering method has a longer holding time of 5 hours, and microwave sintering has a shorter holding time of 15 minutes. Powder XRD and FESEM are used to characterise the samples from both techniques. The XRD study reveals the existence of α-Al2O3 and β-SiC phases in the samples synthesized using both methods, but the intensity of the peaks is higher in the sample synthesized by microwave sintering than in the sample synthesized by electrical resistance heating sintering, indicating that the microwave sintered sample is more densely packed. The lattice parameter of α-Al2O3 matrix phase determined from the X-ray diffraction pattern of electrical resistance heating-sintered sample were a = b = 4.758 Å and c = 12.998 Å and microwave-sintered samples were a = b = 4.759 Å and c = 12.995 Å. X-ray diffraction peak broadening was evaluated using three models of W-H techniques: the UDM, UDSM, and UDEDM. There was an acceptable degree of accuracy in estimating the values of various physical parameters such as energy density, stress, and strain using these three W-H analysis models; thus, these three W-H plot models are highly sought after for describing crystal perfection. When compared to electrical resistance heating-sintered sample, microwave-sintered sample shows fine crystallite size with less strain. When compared to the W-H techniques, the SEM findings were in close agreement with each other.



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