Thermal and structural studies of carbon coated Mo2C synthesized via in-situ single step reduction-carburization

Carbon coated nano molybdenum carbide (Mo2C) has been synthesized at 800 °C through single step reduction route using molybdenum trioxide (MoO3) as a precursor, polypropylene (P.P) as a carbon source and magnesium (Mg) as a catalyst in an autoclave. The synthesized samples were characterized by X-ray diffraction (XRD), thermal analysis techniques (TG/DTA/DTG), field emission scanning electron microscopy (FESEM) and transmission electron microscopy (TEM). Williamson- Hall (W-H) analysis has been done to estimate various parameters like strain, stress and strain energy density. Multi-stage kinetic analysis of the product phase has been studied to establish the nature of the thermal decomposition. Coats-Redfern method applied to determine the mechanism involved in the decomposition of the product phase shows that initial and final stage follow F1 mechanism whereas middle stage follow F3 mechanism. The activation energy (E a) and pre-exponential factor (A) has also been determined. The morphological studies shows that the particles have partially spherical/faceted shape, with carbon coated having wide particle size distribution. The surface chemistry and surface area analysis were studied by X-ray photoelectron spectroscopy (XPS) and Brunauer-Emmet-Teller (BET), respectively. The formation mechanism of carbon coated Mo2C nano particles has been predicted based on the XRD, TG/DTA & DTG and microstructural results.


(S 1.4)
As Scherrer equation follows 1/cosθ dependency, the Williamson-Hall method varies with tanθ and allows the separation of diffracted beams when both crystallite size and strain are simultaneously involved [38]. Even though β is combination of equation (S1.3) and (S1.4), Williamson Hall plot is used to separate the individual effects: ] (S 1.5) Equation (S1.5) represents the uniform deformation model where strain was considered to be isotropic through whole crystal.
In many cases the strain homogeneity assumption and isotropy is not fulfilled, so uniform stress deformation model and uniform deformation energy density model come into consideration.
The anisotropic nature of Young's modulus is considered by both the models, hence are more realistic routes [2,39]. In uniform deformation stress model, anisotropic micro strain ε is exhibited due to isotropic stress σ. The linear proportionality between stress and strain is given by Hook's law, σ=εE hkl . Considering this, Williamson-Hall equation has been formulated as: Where E hkl is Young modulus and for hexagonal crystal phases, it can be calculated by following relation: [5] Where S 11 , S 13 , S 33 and S 44 are elastic compliances of Mo 2 C having values of 2.4×10 -3 , -0.68×10 -3 , 2.56×10 -3 and 7.353×10 -3 GPa -1 respectively [3][4]. Young modulus was calculated as 390.49 GPa which is in close approximation to earlier reported by [5]. Plotting (4 Sinθ /E hkl ) on x-axis and (β Cosθ) on y axis as shown in Fig. S2.a, the value of stress was calculated from slope of fitted line and crystallite size is extracted from intercept reported in Table A2. The uniform deformation energy density model assumes isotropic energy density as a cause of anisotropic deformation within the crystal. The energy density u as a function of strain for a system that follows Hook's law is given by u = ε 2 E hkl /2. According to energy and strain relation, the uniform deformation energy model is given by following mathematical relation: Plots were drawn with 4 Sinθ (2u/E hkl ) 1/2 and β Cosθ on x-axis and y-axis respectively and data fitted to lines as shown in (Fig. S2.b). The slope of the fitted line is used to estimate the value of energy density u while as crystallite size D is estimated from intercept as given in Table A2. The deformation stress and deformation energy density are related as u = σ 2 /E hkl .
At constant temperature, with increase in synthesis time R-4 (2h), R-5 (5h), R-3 (10h) and R-6 (12h), the strain value increases upto 10h while, the value decreases when synthesis time is increased up to 12h where the carbon drain out from the system and the product is converted back to MoO 2 , showing the reversibility of the reaction.         Where, ( ) signifies the log-normal distribution, particle diameter, is the number of particles, is the mean diameter and is the standard deviation respectively.

Kinetic Theory
The rate of solid state thermal decomposition of chemical reaction can be written as [6]: where n is the order of reaction, α is the degree of conversion, m o is the initial mass, m t is the mass at time t, m f is the final mass and k is the rate constant which can be expressed by Arrehenius equation: where, A is the pre-exponential factor, E a is the activation energy, R is the gas constant (8.314 J K -1 mol -1 ) and T is the absolute temperature. The final equation for rate of thermal decomposition process can be expressed as: If the temperature increases in a dynamic TG experiment at linear heating rate , the above equation can be written as: where, ( ) is the integral function of degree of conversion. This equation serves as a base for various kinetic methods used to determine thermal kinetic parameters.

Coats-Redfern method
This method is extensively used to determine the reaction mechanism involved in the thermal decomposition of the sample [28]. Coats and Redfern method is an integral method based on Eq.
(4) and can be expressed as: A plot between ( ( ) ) and provides information regarding the kinetic parameters of a reaction. The activation energy ( ) is determined from the slope, whereas the value of preexponential factor ( ) is calculated from the intercept. However, it is essential to calculate the accurate value of ( ) which can only be obtained by employing various reaction mechanism involved in a thermal decomposition process, as listed in Table S1 [7]. The choice of exact ( ) depends on the value of correlation factor (R 2 ).