Sintering activation energy MoSi2-WSi2-Si3N4 ceramic

The activation energy of sintering process was calculated based on dilatometric studies of shrinkage processes (Mo,W)Si2 + Si3N4 composite ceramic. (Mo,W)Si2 powders was obtained by solid-phase solutions of 70 wt% MoSi2 and 30 wt% WSi2 by SHS in the ISMAN RAS. The concentration rate Si3N4 was from 1 to 15 wt.%. The sintering was carried out to 1850°C in Ar atmosphere the heating rate of 5, 10, 12 and 15°C/min by the way of dilatometer tests. Based on the differential kinetic analysis method (Friedman’s method), the sintering process activation energy of (Mo,W)Si2 + Si3N4 were calculated. The two-stage sintering process and the dependence of the activation energy on the Si3N4 content was shown. Average value of 370 kJ/mol for Q was obtained.

Since the earliest studies of sintering processes many models have been developed to relate the sintering rate to particle characteristics, density, atmosphere and sintering temperature. The kinetic parameters determination is necessary to predicting the thermal ageing process development: at what temperature and for how long can a given substance be used without impairing its properties. Computer data processing allows modeling and predicting even overlapping multi-stage processes. There are three main modifications of the iso-conversion method: − differential (Friedman) [-]; 10 − integral(Flynn-Ozawa-Wall) [---]; 11 12 − improved integral, based on non-linear procedures (Vyazovkin) [-]. 13 The determining kinetic parameters by Friedman method is based on the iso-conversion principle, that the reaction rate at a constant conversion degree α is only a function of temperature. This method allows us to find the activation energy (E) (or the dependence of E on α) without knowing the exact form of the dependence f(α).
In previous work [---], it was shown that composites based on molybdenum disilicide with 30 14 15 and 50 wt% WSi2 addictive are characterised by a decrease in porosity and an increase in the flexural strength. The influence of tungsten disilicide in the MоSi2 -WSi2 system on the properties of ceramic samples MoxW1-xSi2, (where x varied from 1 to 0.3) was studied in detail in the paper [14]. It has been established that during solid-phase sintering of components mechanical mixtures at 1650-1800 °C for 30 minutes, complete interaction between disilicides of molybdenum and tungsten with formation a solid solution does not occur. Ceramic samples have greater strength and low porosity sintered from Mo0.7W0.3Si2 powder (obtained by comminuting of cast sample and synthesised by SHS).
This work is aimed at dilatometric properties studying of Mo0.7W0.3Si2 solid solution depending on the content of α-Si3N4 reinforcing additive in Mo0.7W0.3Si2 + Si3N4 composite. Conclusions are made about the sintering rate influence on the sintering start point displacement, relative shrinkage. The activation energy of the sintering process for Mo0.7W0.3Si2 + Si3N4 (from 1 to 15 wt.%) are calculated.

2.Materials and methods of researches
The cast mixture 70 wt% MoSi2 and 30 wt% WSi2 (Mo0.7W0.3Si2) [14], was obtained by the SHS method at the Institute of Structural Macrokinetics and problems of materials science of the Russian Academy of Sciences (ISMAN RAS) in Chernogolovka Russia and characterised by SEM, X-ray and granulometric analyzes. The dominant fraction in powder Mo0.7W0.3Si2 is 10÷20 μm particles.
The Si3N4 powder was presented by well-crystallized silicon nitride whiskers, with an average length about 2 μm and a thickness up to 200 nm. The α-Si3N4 content is not less than 95%, the specific surface area of the powder is 8.2 m 2 /g. The impurities content are O2 = 1.64 wt%, Fe = 0.023 wt%. The powder was obtained by SHS method at the ISMAN RAS in Chernogolovka.
The mixtures were formed in the cylinders about 6x10 mm at 200 MPa uniaxial pressing on a hydraulic press in a metal form at room temperature. The weight of each sample was about 1 g.
The microstructure and phase composition were examined on an electron microscope (Supra 50 VP (LEO, Germany) with an INCA Energy + Oxford microanalysis system with a prefix for local X-ray spectroscopy) and X-ray (Rigaku D/MAX 2500 with a rotating anode, Japan).
Dilatometric studies were carried out on a dilatometer (DIL 402C Netzsch, Germany), capable of recording up to 2000°C [-]. The sample was placed in a horizontal graphite holder equipped with a 16 graphite pusher with a high-precision displacement transducer (measuring range 500-5000 μm). The thermocouple (tungsten-rhenium alloy) was in close proximity to the sample and accurately recorded its temperature, the second thermocouple (tungsten-rhenium alloy) is in the chamber with a heater. This chamber has an independent of the working chamber argon atmosphere. The flow of argon introduced into the furnace was 70 ml/min, the heating rate was 5, 10, 12 and 15 °C/min, the heating was continued to 1850 °C, the isothermal section was 60 minutes, it was cooled to room temperature at a rate of 20 °C/min. The samples obtained after dilatometric studies density determined by archimedean method. Distilled water was used as a liquid.
Assuming isotropy in densification of all the specimens, the relative density of the sintered specimen (ρs) was calculated using the following equation [-] 17 where dL/L 0 is instantaneous linear shrinkage obtained by the dilatometer test, L 0 is the initial length of the specimen, T is the measured temperature, T 0 is the room temperature, ρ g is the green density, and α is the coefficient of thermal expansion. From a practical point of view, α is determined from the cooling steps of the dilatometer run [-,-,-]. An average value α as a function of 18 19 20 temperature T by the following estimation equations was determined from the cooling steps of the dilatometer runs performed with the different heating rate adopted during our investigations [17]. where T is absolute temperature, C the heating rate, dρ/dT the densification rate, Q the activation energy, R the universal constant of gases, f(ρ) the function of density, K the numerical constant, γ the surface energy, Ω the atomic volume, D 0 the frequency factor, k b the Boltzmann's constant, a the particle radius, dL(=L 0 -L) the change in length of the compacts, L 0 the initial length of the compacts, and the parameters n and p the order depending on the diffusion mechanism. Eqs. (2) and (3) is applicable to the fractional shrinkages of <4%, which fulfill the initial or early stage sintering condition.
Using CRH experiments, the analysis method that is able to determine the diffusion mechanism at the initial sintering step is derived as follows: in Eq. (2), using the slope S 1 of the Arrhenius -type plot of against at same density, the activation energy is expressed as: In equation (3), using the slope S 2 of the Arrhenius -type plot of against , the apparent activation energy is expressed as: Equations (3) (1)

3.Results and discussion
In this paper cast Mo0.7W0.3Si2 solid solution dilatometric studies were carried out depending on the α-Si3N4 reinforcing additive content in the composite. The dilatometry was carried out at rate of 5, 10, 12 and 15 °C/min to 1800 °C. Figures 1 and 2 highlight the change of the shrinkage Mo0.7W0.3Si2 with Si3N4 additive (from 1 to 15 wt.%). The figure below shows the change of the shrinkage and shrinkage rate of Mo0.7W0.3Si2 + 1 and 15 wt.% Si3N4 compact during non-isothermal sintering at three different heating rates of 5, 10 and 15 °C/min, respectively (figure 3). In the previous work [14][15] it was shown that Si3N4 additive concentration increase led to shift the composite sintering beginning point from 1150 °C to 1697 °C and the composite shrinkage changed from 6.75% to 20.21% (respectively, at 1 and 15 wt.% Si3N4). The comparative data of the sintering response is summarised in Table 1.  Increasing the heating rate increased the temperatures at which sintering starts (arbitrary set to 0.5% shrinkage, T Onset ) and proceeds. For example, T Onset 1234 and 1261 °C for Mo0.7W0.3Si2 + 1 wt.% Si3N4 when heating rates increased from 5 to 15 °C/min. It is a usual behaviour for this systems [17]. For the same reason, the shrinkage rate curves of specimens shifted to higher temperature, as the heating rate increased. The maximum shrinkage rate was found to be dependent on heating rate, i.e. the higher the heating rate, the higher is the instantaneous shrinkage rate whatever is the temperature. (2) is applied in the following way. For each heating rate (dT/dt)=c, both T and (dT/dt) at the same relative density were determined, and their values were plotted as ln[Tc(dρ/dT)] against 1/T ( figure 4). The Q at each relative density was determined from the slope of the straight line and as summarised in Table 2. On the other hand, Eq. (3) is applied in the following way. In the fractional shrinkage range of <4%, the nQ was determined from the slope of the straight line in the plot of ln[Td(dL/L 0 )/dt] versus using the shrinkage curve of each heating rates. The proper plots at different heating rate are shown in figure 5. As summarised in Table 2.
The activation energy for each concentration of the composites was calculated. It was shown that activation energy decreased to when the concentration of Si3N4 increase. Average value of 370 kJ/mol for Q was obtained. All values of the activation energy are given in Table 2. The average value of 440 kJ/mol for nQ was obtained.

4.Conclusion
Sintering in Ar atmosphere of Mo0,7W0,3Si2 + 1; 2.5; 5; 10 and 15 wt.% Si3N4 powder has been investigated by the way of dilatometer tests. Using the constant rates of heating technique and applying the analytical method, the activation energy value as Q = 370 kJ mol. The activation energy decrease when the concentration of Si3N4 increase in the composite.