**3.2. The results of calculations**

For distinguished stages, basing on the TG function, the conversion degree was calculated. The formula (23) was used.

Methodology of Thermal Research in Materials Engineering 159

**Figure 15.** Total conversion degree. Stage III; a) time dependency b) temperature dependency.

**Figure 16.** Conversion degree dependencies on temperature and time. Purification and carbonization of

The dependencies of α(T) determined for stages I, II and III under non-isothermal conditions, at a linear heating rate of the samples, were evaluated by neural networks method. The α(T) was the described variable and the sample heating rate and temperature were the describing variables. For each stage all the measurements series were analyzed

According to the theory of non-isothermal processes kinetics, the α(T) dependencies, determined for the stages, describe with high accuracy two parameters: sample heating rate

nc-TiC/C in argon. Stage II. a) non-isothermal conditions b) isothermal conditions.

simultaneously. The results are listed in Table 7

During the measurements weight changes of the samples were as follows: in stage I: 10 Kmin-1 (1.6%), 20 Kmin-1 (1.7%) and 50 Kmin-1 (2%). In stage II, the sample weight changes equaled: 10 Kmin-1 (0.089%), 20 Kmin-1 (0.047%). Whereas in whole the range of the course of stage III weight changes were: 10 Kmin-1 (13.47%), 20 Kmin-1 (13.23%) and 50 Kmin-1 (13.66%). The obtained relations of α(T) for stages I and II are shown in Figure 14.

**Figure 14.** Temperature dependencies of α(T) function; a) stage I, b) stage II.

In accordance with the theory of kinetics of heterogeneous processes the plots of α(T) are shifted into higher temperature range along with the increase in samples heating rate.

Due to the measurements in different regimes the dependencies of α(T) determined for stage III required a more detailed discussion. The conversion degree in stage III was changing regularly in time (Fig. 15a). Irregular changes were observed in the trajectories of the curves of conversion degree dependencies on temperature (Fig. 15b). It was also found that in the transient area a significant increase in conversion degree took place.

The results presented in Figure 16a were elaborated according to the rules of non-isothermal processes theory and in Figure 16b according to the isothermal processes theory.

The plots of α(T) determined for non-isothermal conditions concern the pyrolysis process.

At low temperatures, there is no carbonisation of nc-TiC, and at temperature above 1573 K pyrolysis proceeded much faster than carbonisation. Under the non-isothermal conditions, the transition from one temperature range to the other was short. As a result the influence of carbonisation on the recorded samples weight loss was not revealed.

158 Heat Treatment – Conventional and Novel Applications

For distinguished stages, basing on the TG function, the conversion degree was calculated.

During the measurements weight changes of the samples were as follows: in stage I: 10 Kmin-1 (1.6%), 20 Kmin-1 (1.7%) and 50 Kmin-1 (2%). In stage II, the sample weight changes equaled: 10 Kmin-1 (0.089%), 20 Kmin-1 (0.047%). Whereas in whole the range of the course of stage III weight changes were: 10 Kmin-1 (13.47%), 20 Kmin-1 (13.23%) and 50 Kmin-1

(13.66%). The obtained relations of α(T) for stages I and II are shown in Figure 14.

**Figure 14.** Temperature dependencies of α(T) function; a) stage I, b) stage II.

In accordance with the theory of kinetics of heterogeneous processes the plots of α(T) are shifted into higher temperature range along with the increase in samples heating rate.

Due to the measurements in different regimes the dependencies of α(T) determined for stage III required a more detailed discussion. The conversion degree in stage III was changing regularly in time (Fig. 15a). Irregular changes were observed in the trajectories of the curves of conversion degree dependencies on temperature (Fig. 15b). It was also found

The results presented in Figure 16a were elaborated according to the rules of non-isothermal

The plots of α(T) determined for non-isothermal conditions concern the pyrolysis

At low temperatures, there is no carbonisation of nc-TiC, and at temperature above 1573 K pyrolysis proceeded much faster than carbonisation. Under the non-isothermal conditions, the transition from one temperature range to the other was short. As a result the influence of

that in the transient area a significant increase in conversion degree took place.

processes theory and in Figure 16b according to the isothermal processes theory.

carbonisation on the recorded samples weight loss was not revealed.

**3.2. The results of calculations** 

The formula (23) was used.

process.

**Figure 15.** Total conversion degree. Stage III; a) time dependency b) temperature dependency.

**Figure 16.** Conversion degree dependencies on temperature and time. Purification and carbonization of nc-TiC/C in argon. Stage II. a) non-isothermal conditions b) isothermal conditions.

The dependencies of α(T) determined for stages I, II and III under non-isothermal conditions, at a linear heating rate of the samples, were evaluated by neural networks method. The α(T) was the described variable and the sample heating rate and temperature were the describing variables. For each stage all the measurements series were analyzed simultaneously. The results are listed in Table 7

According to the theory of non-isothermal processes kinetics, the α(T) dependencies, determined for the stages, describe with high accuracy two parameters: sample heating rate

#### 160 Heat Treatment – Conventional and Novel Applications

and sample temperature. These results could therefore be used in further calculations, i.e., during the identification of kinetic models (determination of the form of g(α) function) ) and during determination of Arrhenius parameters A and E.

Methodology of Thermal Research in Materials Engineering 161

process rate increases from zero for α(T) equal zero, reaches the maximum in temperature Tm, and then usually decreases to zero at α(T)→1. The temperature ranges for stages runs are consistent with the ones determined experimentally. The α(T), and r(α,T) plots for a stage do not come to an end, because at high conversion degrees process ran according to

> A [1/min]

<sup>10</sup>8,48

<sup>50</sup>1,95

**Figure 17.** Comparison of α(T) calculated and determined from experiments. Stage I, model D3.

E [kJ/mol]

10 2,2 E-6 15,8 487,4 0,03-

20 1,2E-6 16,5 524,9 0,035-

50 3,5E-7 16,3 539,5 0.005-

10 6,81 E4 125,25 1128 0.002-

20 7,74 E6 160,8 1156 0.002-

20 3 E10 318,8 1559 0.005-

E09 306,8 1530 0.005-

E12 364,5 1590 0.004-0.29 1370-

Tm

[K] Δα <sup>Δ</sup><sup>T</sup>

0.9995

0.999

0.999

0.639

0.508

[K]

298- 1319

935- 1271

1007- 1291

1321- 1564

1345- 1560

1551

0.9989 299-826

0,9969 299-937

[K/min]

<sup>2</sup> <sup>1</sup> 3

α

α

 − − 

> α<sup>−</sup> − −

**Table 9.** List of kinetic parameters for the stages.

the different kinetic models.

I D3 ( )

II F2 ( ) <sup>1</sup> 1 1

III F1 − − ln 1( )

stage Model g(α) <sup>β</sup>

<sup>3</sup> 1 1 2


**Table 7.** Estimation of α(T) dependencies determined for stage I, II and III with use of artificial neural networks method.

First, the values of these parameters were estimated by linear regression method. Each series were analysed separately. The obtained results for stage III are given, as an example, in Table 8.


**Table 8.** List of kinetic parameters. Stage III, model F1.

r\* - correlation coefficient, F – Snedecor statistic

Using the determined values of A and E parameters, the values of α(T) were calculated from the Coats-Redfern equation. They were compared with the data determined from the measurements. The systematic error in the order of 4.5% has been noted. The accuracy was improved by correcting the value of E parameter. There was required that the error in the series, i.e. the mean square error between the values determined from the measurements

and calculated ( ) <sup>2</sup> ln *<sup>g</sup> T* α , was close to zero. The calculations for the remaining stages were

performed in the same way. The results are given in Table 9.

The results have been verified. Using the kinetic parameters given in Table 9 the conversion degrees were calculated from the Coats-Redfern equation for the e stages and compared to the ones determined from measurements. As an example, in Figure 17 the results for stage I are shown. A good consistency was obtained.

The kinetic parameters determined for the stages have been used for simulation calculations. The α(T) and r(α,T) dependencies on temperature and sample heating rate were investigated. The results are presented in Figure 18.

The determined dependencies are in accordance with the theory. With the increase in sample heating rates the α(T) curves are shifted into the higher temperature range. The process rate increases from zero for α(T) equal zero, reaches the maximum in temperature Tm, and then usually decreases to zero at α(T)→1. The temperature ranges for stages runs are consistent with the ones determined experimentally. The α(T), and r(α,T) plots for a stage do not come to an end, because at high conversion degrees process ran according to the different kinetic models.


**Table 9.** List of kinetic parameters for the stages.

160 Heat Treatment – Conventional and Novel Applications

[K/min] r\* F <sup>E</sup>

**Table 8.** List of kinetic parameters. Stage III, model F1. r\* - correlation coefficient, F – Snedecor statistic

performed in the same way. The results are given in Table 9.

were investigated. The results are presented in Figure 18.

networks method.

and calculated ( )

<sup>2</sup> ln *<sup>g</sup> T* α 

are shown. A good consistency was obtained.

Table 8.

β

during determination of Arrhenius parameters A and E.

and sample temperature. These results could therefore be used in further calculations, i.e., during the identification of kinetic models (determination of the form of g(α) function) ) and

Parameter Stage I , MLP 2/2 Stage II Stage III, MLP 2/15

S.D. Ratio 0.0361 0.0355 0.0364 0.0269 0.0274 0.0284 0.0728 0.0820 0.0784 Correlation 0.999 0.999 0.999 0.999 0.999 0.999 0.997 0.997 0.997 **Table 7.** Estimation of α(T) dependencies determined for stage I, II and III with use of artificial neural

First, the values of these parameters were estimated by linear regression method. Each series were analysed separately. The obtained results for stage III are given, as an example, in

10 -0,988 50029,7 315,09 8,48 E09 1530 0.005-0.639 1321-1564 20 -0,988 47245,7 327,77 3 E10 1559 0.005-0.508 1345-1560 50 -0,989 20219,0 375,62 1,95 E12 1590 0.004-0.29 1370-1551

Using the determined values of A and E parameters, the values of α(T) were calculated from the Coats-Redfern equation. They were compared with the data determined from the measurements. The systematic error in the order of 4.5% has been noted. The accuracy was improved by correcting the value of E parameter. There was required that the error in the series, i.e. the mean square error between the values determined from the measurements

The results have been verified. Using the kinetic parameters given in Table 9 the conversion degrees were calculated from the Coats-Redfern equation for the e stages and compared to the ones determined from measurements. As an example, in Figure 17 the results for stage I

The kinetic parameters determined for the stages have been used for simulation calculations. The α(T) and r(α,T) dependencies on temperature and sample heating rate

The determined dependencies are in accordance with the theory. With the increase in sample heating rates the α(T) curves are shifted into the higher temperature range. The

[kJ/ mol]

Tr We Te Tr We Te Tr We Te

A [1/min] Tm

, was close to zero. The calculations for the remaining stages were

[K] Δα <sup>Δ</sup><sup>T</sup>

**Figure 17.** Comparison of α(T) calculated and determined from experiments. Stage I, model D3.

Methodology of Thermal Research in Materials Engineering 163

high conversion degrees in stage III the change of kinetic model (form of g(α) function) took place. Under the isothermal conditions, at lower conversion degrees, the process first proceeded according to the F1 model (similarly as under the non-isothermal conditions), then at high conversion degrees (higher than 0.98) according to the D3 (three-dimensional diffusion Jander's model). This concerns the removal of remaining products of pyrolysis.

The charts of α (T) were obtained from about 25,000 measurement points for each case. The value of k(T) was calculated by linear regression method for the subsequent sets, each containing 1100 values of the g(α) function. The results were evaluated using several measures. The values of R2 measure were determined. The calculation results for all measurement series are given in Table 5. The temperature, the mean values of k(T) determined for the entire sets, the time of obtaining the isothermal conditions t1, counted from the beginning of the measurement, and the conversion degree α1 obtained for this time

series β [K/min] T [K] k\*103 [1/min] t1 α1 R2 1443 K 10 1440,9 13,61 158,4 0,7092 99,72 20 1440,9 14,41 99,98 0,69 99,92 1503 K 10 1501,1 14,75 203,92 0,9553 99,68 20 1501 35,18 92,85 0,872 99,59 1543 K 10 1541,4 9,39 201,72 0,9331 99,72 20 1541,3 12,48 142,69 0,9539 99,87 1573 K 10 1568,5 6,94 199,19 0,9303 99,36 20 1568,2 8,3 131,15 0,938 99,85 1623 K 10 1620,2 40,63 162,6 0,9653 99,91 20 1619,7 61,84 91,8 0,9615 99,95 1673 K 10 1669,4 54,28 160,2 0,9699 99,69 20 1669,1 104,31 86 0,9883 99,39 1773 K 10 1770,5 219,28 154,2 0,9831 99,72 20 1770 242,24 83,6 0,9831 99,52

**Table 10.** The results of kinetic calculations for isothermal conditions. F1 model.

In the considered range of temperature two processes preceded simultaneously; pyrolysis of organic compounds, contained in the raw samples and proceeding with their participation carbonisation of nc-TiCx/C. The bounded carbon remains in the system. As a result the lesser sample mass losses were observed. In lower temperature proceeds also pyrolysis, as shown by the values of k(T) given in Table 10. Carbonisation starts at temperature of about 1541 K and becomes a dominating process at temperature of about 1570 K. At 1610 K pyrolysis becomes a dominating process again. With regard to carbonisation effectiveness, the process should be carried out at temperature of about 1570 K. The minimum on the curve k(T) has

are given.

R2 – statistical measure

been observed in Figure 19.

**Figure 18.** Plots of α(T) and r(α,T) functions; a) stage I, model D3; b) stage II, model F2; c) stage III, model F1.

Under the isothermal conditions the last phase of stage III and whole the stage IV proceeded. The results presented earlier, obtained in the series up to 1573, 1673 and 1773 K, were not sufficient for description of the course of stage III under isothermal conditions. They have been complemented by additional measurements. During the investigations samples were heated up to 1343, 1503, 1543 and 1623 K using the following heating rates: 10, 20 Kmin-1.

While elaborating these results the calculations for stages I, II and III were also performed. There were obtained similar results as before (Table 9). These data are not provided. At the high conversion degrees in stage III the change of kinetic model (form of g(α) function) took place. Under the isothermal conditions, at lower conversion degrees, the process first proceeded according to the F1 model (similarly as under the non-isothermal conditions), then at high conversion degrees (higher than 0.98) according to the D3 (three-dimensional diffusion Jander's model). This concerns the removal of remaining products of pyrolysis.

162 Heat Treatment – Conventional and Novel Applications

model F1.

20 Kmin-1.

**Figure 18.** Plots of α(T) and r(α,T) functions; a) stage I, model D3; b) stage II, model F2; c) stage III,

Under the isothermal conditions the last phase of stage III and whole the stage IV proceeded. The results presented earlier, obtained in the series up to 1573, 1673 and 1773 K, were not sufficient for description of the course of stage III under isothermal conditions. They have been complemented by additional measurements. During the investigations samples were heated up to 1343, 1503, 1543 and 1623 K using the following heating rates: 10,

While elaborating these results the calculations for stages I, II and III were also performed. There were obtained similar results as before (Table 9). These data are not provided. At the The charts of α (T) were obtained from about 25,000 measurement points for each case. The value of k(T) was calculated by linear regression method for the subsequent sets, each containing 1100 values of the g(α) function. The results were evaluated using several measures. The values of R2 measure were determined. The calculation results for all measurement series are given in Table 5. The temperature, the mean values of k(T) determined for the entire sets, the time of obtaining the isothermal conditions t1, counted from the beginning of the measurement, and the conversion degree α1 obtained for this time are given.


**Table 10.** The results of kinetic calculations for isothermal conditions. F1 model. R2 – statistical measure

In the considered range of temperature two processes preceded simultaneously; pyrolysis of organic compounds, contained in the raw samples and proceeding with their participation carbonisation of nc-TiCx/C. The bounded carbon remains in the system. As a result the lesser sample mass losses were observed. In lower temperature proceeds also pyrolysis, as shown by the values of k(T) given in Table 10. Carbonisation starts at temperature of about 1541 K and becomes a dominating process at temperature of about 1570 K. At 1610 K pyrolysis becomes a dominating process again. With regard to carbonisation effectiveness, the process should be carried out at temperature of about 1570 K. The minimum on the curve k(T) has been observed in Figure 19.

Methodology of Thermal Research in Materials Engineering 165

basis of the mechanism of Shimada [26], the formation on the surface of nc-TiC particles of amorphous TiO2 layer, blocking access of oxygen to the reaction zone. The given values of k(T) indicate that the samples obtained at heating rates of 10 K/min oxidized slower than at the heating rates of 20 and 50 K/min. It is also visible that the final temperature of the process affects the properties of carbonised nc-TiC. Basing on the series up to 1673 and 1773 K there was found that after the completion of carbonisation and purification process of nc-TiC, at higher temperatures oxidation of the carbonised nc-TiC by oxygen present in argon

The removal of carbon from the matrix and carbonisation of nc-TiCx proceeded most preferably in a series up to 1573 K, at the heating rate of 20 K/min. The results of

**Figure 20.** Dependency of nc-TiC mean lattice parameters (a) and mean particles diameters (D) on

Carbonisation resulted in an increase of lattice parameter of titanium carbide. The largest increase in lattice parameter was observed for the series up to 1573 K. Under these conditions, the average particle size was in the order of 40 nm. Mean values of lattice parameters of nc-TiC and the average particle size determined after the carbonisation processes are shown in Figure 20. The measurement of crystallites size by Scherrer method and on the basis of TEM images showed that the mean size of TiC crystallites after carbonisation was approximately 30% higher in relation to the size before the heat treatment process at temperature of 1573 K. The results of microscopic examination were confirmed by the results of the X-ray diffraction. The analysis of chemical composition and phase composition showed an increase in the fraction of carbon in titanium carbide from TiC~ .68 to TiC~ .8 ÷.85 and removal of carbon from the matrix. The results of this step of research are

in trace amounts takes place.

temperature [32].

given in [6,32].

investigations concerning this series are therefore given.

**Figure 19.** Dependency of reaction rate constant on temperature for β = 20 K/min. F1 model (g(α) = [ ln(1 - α)]); ♦– mean value of k(T)

In the same manner were obtained the results presented in Table 11, concerning the desorption process of volatile products after the completion of carbonisation process.


**Table 11.** The results of kinetic calculations for isothermal conditions. D3 model

In the third column the values of k(T) are given, and in the subsequent columns time t2 from which desorption becomes the dominant factor, and the corresponding conversion degree.

Under the measurement conditions the oxidation of carbonised nc-TiC, by the oxygen contained in trace amounts in argon, occurred in series up to 1673 and 1773 K. This process proceeded according to the R2 model (reaction at the interface, cylindrical symmetry) or R3 model (reaction at the interface, spherical symmetry). The weight gain of the sample was less than 1%. Inhibition of oxidation process of carbonised nc-TiC can be explained on the basis of the mechanism of Shimada [26], the formation on the surface of nc-TiC particles of amorphous TiO2 layer, blocking access of oxygen to the reaction zone. The given values of k(T) indicate that the samples obtained at heating rates of 10 K/min oxidized slower than at the heating rates of 20 and 50 K/min. It is also visible that the final temperature of the process affects the properties of carbonised nc-TiC. Basing on the series up to 1673 and 1773 K there was found that after the completion of carbonisation and purification process of nc-TiC, at higher temperatures oxidation of the carbonised nc-TiC by oxygen present in argon in trace amounts takes place.

164 Heat Treatment – Conventional and Novel Applications

ln(1 - α)]); ♦– mean value of k(T)

**Figure 19.** Dependency of reaction rate constant on temperature for β = 20 K/min. F1 model (g(α) = [-

desorption process of volatile products after the completion of carbonisation process.

**Table 11.** The results of kinetic calculations for isothermal conditions. D3 model

In the same manner were obtained the results presented in Table 11, concerning the

series β [K/min] T [K] k\*103 [1/min] t2 α2 R2 1543 K 10 1541,4 0,255 402,3 0,989 97,82 20 1541,3 0,354 326,2 0,9933 95,03 1573 K 10 1568,5 1,47 221,76 0,9412 99,59 20 1568,2 2,34 150,98 0,9486 99,65 1673 K 10 1669,4 9,5 160,2 0,9699 99,69 20 1669,1 16,07 87 0,9892 99,45 1773 K 10 1770,5 41,08 154,18 0,9831 99,66 20 1770 49,36 84,1 0,9854 99,57

In the third column the values of k(T) are given, and in the subsequent columns time t2 from which desorption becomes the dominant factor, and the corresponding conversion degree.

Under the measurement conditions the oxidation of carbonised nc-TiC, by the oxygen contained in trace amounts in argon, occurred in series up to 1673 and 1773 K. This process proceeded according to the R2 model (reaction at the interface, cylindrical symmetry) or R3 model (reaction at the interface, spherical symmetry). The weight gain of the sample was less than 1%. Inhibition of oxidation process of carbonised nc-TiC can be explained on the The removal of carbon from the matrix and carbonisation of nc-TiCx proceeded most preferably in a series up to 1573 K, at the heating rate of 20 K/min. The results of investigations concerning this series are therefore given.

**Figure 20.** Dependency of nc-TiC mean lattice parameters (a) and mean particles diameters (D) on temperature [32].

Carbonisation resulted in an increase of lattice parameter of titanium carbide. The largest increase in lattice parameter was observed for the series up to 1573 K. Under these conditions, the average particle size was in the order of 40 nm. Mean values of lattice parameters of nc-TiC and the average particle size determined after the carbonisation processes are shown in Figure 20. The measurement of crystallites size by Scherrer method and on the basis of TEM images showed that the mean size of TiC crystallites after carbonisation was approximately 30% higher in relation to the size before the heat treatment process at temperature of 1573 K. The results of microscopic examination were confirmed by the results of the X-ray diffraction. The analysis of chemical composition and phase composition showed an increase in the fraction of carbon in titanium carbide from TiC~ .68 to TiC~ .8 ÷.85 and removal of carbon from the matrix. The results of this step of research are given in [6,32].

## **4. Oxidation of the nc-TiCx/C and nc-TiCx**

The possibility of implementing purification of TiCx/C composites by burning out the elementary carbon, composing matrix, was considered. The results of oxidation of nc-TiCx/C system have been presented. Oxidation of the TiCx/C powders, being an intermediate product of sol-gel synthesis, and of the TiCx powders obtained by reduction with hydrogen was investigated. The reduction of TiCx/C powders with hydrogen aimed at removing from the system the carbon from the matrix. Purification with hydrogen according to the reaction C+H2→CH4 was carried out at temperature of 1173K, under pressure of 16MPa, for 4.5 h [6,32]. The measurements were carried out using thermogravimetric method, under nonisothermal conditions. The samples unreduced with hydrogen were studied at the following heating rates: 5Kmin-1 (sample weight of 18.749 mg), 10 Kmin-1 (sample weight of 16.049 mg), 15 Kmin-1 (sample weight of 13.322 mg), 20 Kmin-1 (sample weight of 15.908 mg). The powders after reduction with hydrogen instead were studied at 5 Kmin-1 (sample weight of 17.768 mg), 10 Kmin-1 (sample weight of 17.174 mg), 15 Kmin-1 (sample weight of 17.544 mg), 20 Kmin-1 (sample weight 17.544 mg). During the measurements temperature of samples, TG, DTG, and HF were recorded. In one series several dozen thousands of each variable values were recorded. During the measurements the linear change of sample temperature over time was maintained, as required by the theory of non-isothermal kinetics. The normalized TG curves of the samples unreduced and reduced with hydrogen are shown in Figure 21.

Methodology of Thermal Research in Materials Engineering 167

weight gain of the sample started at temperature in the order of 600 K. This means that

In the DTG curves, there are three peaks (Fig. 22). The first peak is associated with start of the oxidation of nc-TiCx. The subsequent weight loss is associated with the burning out of the elemental carbon, produced during the oxidation of the nc-TiCx. This process proceeds simultaneously with the further oxidation of nc-TiCx. The next peak concerns the oxidation of unreacted nc-TiCx. The elemental carbon, contained in nc-TiCx/C samples unreduced with

under these conditions the oxidation of nc-TiCx started.

hydrogen, burns out in the final stage of the process.

**Figure 22.** Dependency of DTG curves on temperature, a) for TiCx/C, b) for TiCx

process, is associated with the terminating oxidation of nc-TiCx.

Two distinct maxima were observed in the HF plots (Fig. 23). The first one is associated with the beginning of oxidation process of nc-TiCx and the second one with burning out of the elemental carbon, produced during the oxidation of the nc-TiCx, and further course of the nc-TiCx oxidation. The apparent increase in the value of HF function, in the final stage of the

The results have been confirmed by the identification of CO2, formed in the system, by mass spectrometry. There was also found that while increasing sample heating rates the plots of mass spectra of CO2, originating from the nc-TiC oxidation process and from burning out of the formed carbon, overlapped. The carried out experiments have shown that the nc-TiC, obtained by sol-gel process, cannot be purified by burning out in the air the carbon

The performed studies indicated also the possibility of occurring during the description of oxidation of ceramic nc-TiC/C powders in the air, some difficult issue related to the simultaneous proceeding, in a certain range of temperature, of metal carbide oxidation and burning out of the carbon. The following manner of kinetics description of the both

concurrent reactions, based on thermogravimetric studies, has been proposed.

(after reduction with H2)

admixtures contained in the system.

**Figure 21.** Plots of TGu curves for TiCx/C samples and TiCx (after reduction with H2) samples, a) 5, b) 20 Kmin-1

The normalized TGu curves of the samples reduced with hydrogen are shifted upward to the same degree for different heating rates (ΔTG in the order of 0.03 mg), because in the TiCx powders (after reduction with hydrogen), the relative content of titanium increased as a result of removing elemental carbon by acting with hydrogen. This resulted in greater weight gain of TiCx during the oxidation in comparison with TiCx/C. In both cases the weight gain of the sample started at temperature in the order of 600 K. This means that under these conditions the oxidation of nc-TiCx started.

166 Heat Treatment – Conventional and Novel Applications

shown in Figure 21.

Kmin-1

**4. Oxidation of the nc-TiCx/C and nc-TiCx** 

The possibility of implementing purification of TiCx/C composites by burning out the elementary carbon, composing matrix, was considered. The results of oxidation of nc-TiCx/C system have been presented. Oxidation of the TiCx/C powders, being an intermediate product of sol-gel synthesis, and of the TiCx powders obtained by reduction with hydrogen was investigated. The reduction of TiCx/C powders with hydrogen aimed at removing from the system the carbon from the matrix. Purification with hydrogen according to the reaction C+H2→CH4 was carried out at temperature of 1173K, under pressure of 16MPa, for 4.5 h [6,32]. The measurements were carried out using thermogravimetric method, under nonisothermal conditions. The samples unreduced with hydrogen were studied at the following heating rates: 5Kmin-1 (sample weight of 18.749 mg), 10 Kmin-1 (sample weight of 16.049 mg), 15 Kmin-1 (sample weight of 13.322 mg), 20 Kmin-1 (sample weight of 15.908 mg). The powders after reduction with hydrogen instead were studied at 5 Kmin-1 (sample weight of 17.768 mg), 10 Kmin-1 (sample weight of 17.174 mg), 15 Kmin-1 (sample weight of 17.544 mg), 20 Kmin-1 (sample weight 17.544 mg). During the measurements temperature of samples, TG, DTG, and HF were recorded. In one series several dozen thousands of each variable values were recorded. During the measurements the linear change of sample temperature over time was maintained, as required by the theory of non-isothermal kinetics. The normalized TG curves of the samples unreduced and reduced with hydrogen are

**Figure 21.** Plots of TGu curves for TiCx/C samples and TiCx (after reduction with H2) samples, a) 5, b) 20

The normalized TGu curves of the samples reduced with hydrogen are shifted upward to the same degree for different heating rates (ΔTG in the order of 0.03 mg), because in the TiCx powders (after reduction with hydrogen), the relative content of titanium increased as a result of removing elemental carbon by acting with hydrogen. This resulted in greater weight gain of TiCx during the oxidation in comparison with TiCx/C. In both cases the In the DTG curves, there are three peaks (Fig. 22). The first peak is associated with start of the oxidation of nc-TiCx. The subsequent weight loss is associated with the burning out of the elemental carbon, produced during the oxidation of the nc-TiCx. This process proceeds simultaneously with the further oxidation of nc-TiCx. The next peak concerns the oxidation of unreacted nc-TiCx. The elemental carbon, contained in nc-TiCx/C samples unreduced with hydrogen, burns out in the final stage of the process.

**Figure 22.** Dependency of DTG curves on temperature, a) for TiCx/C, b) for TiCx (after reduction with H2)

Two distinct maxima were observed in the HF plots (Fig. 23). The first one is associated with the beginning of oxidation process of nc-TiCx and the second one with burning out of the elemental carbon, produced during the oxidation of the nc-TiCx, and further course of the nc-TiCx oxidation. The apparent increase in the value of HF function, in the final stage of the process, is associated with the terminating oxidation of nc-TiCx.

The results have been confirmed by the identification of CO2, formed in the system, by mass spectrometry. There was also found that while increasing sample heating rates the plots of mass spectra of CO2, originating from the nc-TiC oxidation process and from burning out of the formed carbon, overlapped. The carried out experiments have shown that the nc-TiC, obtained by sol-gel process, cannot be purified by burning out in the air the carbon admixtures contained in the system.

The performed studies indicated also the possibility of occurring during the description of oxidation of ceramic nc-TiC/C powders in the air, some difficult issue related to the simultaneous proceeding, in a certain range of temperature, of metal carbide oxidation and burning out of the carbon. The following manner of kinetics description of the both concurrent reactions, based on thermogravimetric studies, has been proposed.

Methodology of Thermal Research in Materials Engineering 169

On the basis of TGu curves, complemented by the results of calculations, the α(T) dependencies for the oxidation process of nc-TiCx in the whole temperature range were

The conversion degree for the process of burning out the elemental carbon was determined as follows. By subtracting the experimental values from the calculated TGu values, ΔTG was determined, and then, integrating numerically, TGu curves for the process of burning out the carbon were determined. The α(T) dependencies obtained for both processes, are presented

**Figure 25.** The α(T) dependencies. Oxidation of unreduced nc-TiCx/C in air, a) oxidation of nc-TiCx,

According to the theory, along with the increase in sample heating rates, the plots of α(T)

The conversion degree for the process of burning out the carbon in the matrix (the second temperature range) was calculated in the same way. In the case of the oxidation process of nc-TiCx (after reduction with hydrogen) two stages occurred: nc-TiCx oxidation and burning out of the elemental carbon formed at the beginning of the oxidation process of nc-TiC. The α(T) dependence was determined for all the stages in the same way. The determined α(T) dependencies were the basis of kinetic studies. The Coats-Redfern equation was used. For

These data contain the full information about the kinetics of analysed processes. There should be noted that the kinetic parameters (the forms of g(α) functions and the values of A and E) determined on the basis of experimental data, should correspond to their physicochemical meaning. In the analysed case, the F2 model [g(α) = (1-α)-1-1], having a theoretical justification, was used, and the determined activation energy values are similar

all the stages kinetic models and Arrhenius parameters were determined (Table 12).

determined.

in the form of graphs in Figure 25.

b) burning out of elemental carbon

are shifted into the higher temperature range.

to those found in many chemical reactions.

**Figure 23.** Dependency of HF on temperature, a) for TiCx/C, b) for TiCx (after reduction with H2)

To obtain the normalized TGu curve, corresponding to the oxidation process of TiCx in the whole range of temperature the neural networks method was applied. Basing on the results registered before burning out of the formed carbon and after the end of this process the network was fitted. Then the fitted network was used to generate the segment of normalized TGu curve for the temperature range in which both transformations proceeded simultaneously. The multi-layer MLP networks were used. The described variable was TGu function, and the describing variable was temperature. Each measurement series was analysed separately. Using these models sections of TG curves corresponding to the oxidation process of nc-TiC, in the temperature range in which this process proceeded simultaneously with the burning out of the carbon, were generated. The TGu plots generated by the network and determined experimentally are shown in Figure 24.

**Figure 24.** Plots of TGu function, calculated and experimental. Oxidation of nc-TiCx/C samples, unreduced by hydrogen, in air, a) 5 Kmin-1, b) 20 Kmin-1

On the basis of TGu curves, complemented by the results of calculations, the α(T) dependencies for the oxidation process of nc-TiCx in the whole temperature range were determined.

168 Heat Treatment – Conventional and Novel Applications

**Figure 23.** Dependency of HF on temperature, a) for TiCx/C, b) for TiCx (after reduction with H2)

by the network and determined experimentally are shown in Figure 24.

**Figure 24.** Plots of TGu function, calculated and experimental. Oxidation of nc-TiCx/C samples,

unreduced by hydrogen, in air, a) 5 Kmin-1, b) 20 Kmin-1

To obtain the normalized TGu curve, corresponding to the oxidation process of TiCx in the whole range of temperature the neural networks method was applied. Basing on the results registered before burning out of the formed carbon and after the end of this process the network was fitted. Then the fitted network was used to generate the segment of normalized TGu curve for the temperature range in which both transformations proceeded simultaneously. The multi-layer MLP networks were used. The described variable was TGu function, and the describing variable was temperature. Each measurement series was analysed separately. Using these models sections of TG curves corresponding to the oxidation process of nc-TiC, in the temperature range in which this process proceeded simultaneously with the burning out of the carbon, were generated. The TGu plots generated The conversion degree for the process of burning out the elemental carbon was determined as follows. By subtracting the experimental values from the calculated TGu values, ΔTG was determined, and then, integrating numerically, TGu curves for the process of burning out the carbon were determined. The α(T) dependencies obtained for both processes, are presented in the form of graphs in Figure 25.

**Figure 25.** The α(T) dependencies. Oxidation of unreduced nc-TiCx/C in air, a) oxidation of nc-TiCx, b) burning out of elemental carbon

According to the theory, along with the increase in sample heating rates, the plots of α(T) are shifted into the higher temperature range.

The conversion degree for the process of burning out the carbon in the matrix (the second temperature range) was calculated in the same way. In the case of the oxidation process of nc-TiCx (after reduction with hydrogen) two stages occurred: nc-TiCx oxidation and burning out of the elemental carbon formed at the beginning of the oxidation process of nc-TiC. The α(T) dependence was determined for all the stages in the same way. The determined α(T) dependencies were the basis of kinetic studies. The Coats-Redfern equation was used. For all the stages kinetic models and Arrhenius parameters were determined (Table 12).

These data contain the full information about the kinetics of analysed processes. There should be noted that the kinetic parameters (the forms of g(α) functions and the values of A and E) determined on the basis of experimental data, should correspond to their physicochemical meaning. In the analysed case, the F2 model [g(α) = (1-α)-1-1], having a theoretical justification, was used, and the determined activation energy values are similar to those found in many chemical reactions.


Methodology of Thermal Research in Materials Engineering 171

According to the theory of kinetics of non-isothermal processes the reaction rate should increase along with the increase in sample heating rates. This condition is not well fulfilled for the oxidation process of nc-TiCx unreduced with hydrogen (Fig.26a). This means that the samples used in measurement series differed. For the both processes of burning out the carbon the results consistent with theory were obtained. There should be noted that according to the theory, in each stage the process rate increases from zero for α(T)=0, reaches the maximum in temperature Tm, and then decreases to zero at α(T)→1. The temperature ranges determined for the stages runs on the basis of calculations are consistent with the

The analogous plots obtained for the oxidation process in air of nc-TiCx reduced with

**Figure 27.** Plots of r(α,T). Oxidation in air of nc-TiC reduced with hydrogen; a) oxidation of nc-TiCx, b)

In this case, full consistency with the theory was obtained. The plots in Figure 27a show that nc-TiCx after reduction with hydrogen was uniform, the process rate increased along with the increase in sample heating rate, and the maximum was shifted into the higher temperature range. In both cases, the process rate, according to the theory, increases from zero for α(T)=0, reaches its maximum at the temperature Tm, and then decreases to zero at α(T)→0. The temperature ranges determined for the stages runs in measurement series on

The obtained results show that the proposed description method of the kinetics of two reactions proceeding simultaneously in a certain range of temperature, allows obtaining a satisfactory accuracy. This method was developed for the needs of processes of oxidation in air of nanocrystalline TiC and nanocomposites of TiC/C with varying carbon content in the matrix, for evaluating the protective qualities of carbon matrix, and also to evaluate and compare the resistance to oxidation of carbide ceramics [17]. In Figure 28 the use of the kinetics knowledge for comparative evaluation of the rate of TiC/C nanocomposite

the basis of calculations are consistent with the ones determined experimentally.

oxidation, depending on the carbon content in the matrix is shown as an example.

burning out of elemental carbon formed during the oxidation of nc-TiCx

ones determined experimentally.

hydrogen are shown in Figure 27.

**Table 12.** List of kinetic data for the transformations in oxidation processes of titanium carbide samples before and after the reduction with H2.

Basing on the obtained results an analysis of the process has been performed. The r(α,T) dependencies on sample heating rates and sample temperature for the stages were studied. The plots of r(α,T) obtained for the nc-TiCx/C not-reduced with hydrogen are shown in Figure 26.

**Figure 26.** Plots of r(α,T). Oxidation of nc-TiCx/C unreduced with hydrogen; a) oxidation of nc-TiCx, b) burning out of the carbon formed during the oxidation process of nc-TiC, c) burning out of the carbon contained in the samples

According to the theory of kinetics of non-isothermal processes the reaction rate should increase along with the increase in sample heating rates. This condition is not well fulfilled for the oxidation process of nc-TiCx unreduced with hydrogen (Fig.26a). This means that the samples used in measurement series differed. For the both processes of burning out the carbon the results consistent with theory were obtained. There should be noted that according to the theory, in each stage the process rate increases from zero for α(T)=0, reaches the maximum in temperature Tm, and then decreases to zero at α(T)→1. The temperature ranges determined for the stages runs on the basis of calculations are consistent with the ones determined experimentally.

170 Heat Treatment – Conventional and Novel Applications

TiC F2

Celemental F2

TiC F2

Celemental F2

before and after the reduction with H2.

[K/min] A [1/min] <sup>E</sup>

[kJ/mol] Tm [K] Δα <sup>Δ</sup>T [K]

5 26343,35 88,31 810,45 0,01-0,99 648-1147 10 291522,00 99,20 822,77 0,01-0,99 671-1141 15 16689,12 86,70 903,79 0,02-0,99 691-1245 20 22863,39 89,26 923,22 0,01-0,99 690-1295

5 1,76E+10 185,04 902,35 0,02-0,99 803-1058 10 8,27E+09 177,71 916,13 0,02-0,99 809-1085 15 4,74E+12 222,13 932,37 0,02-0,98 827-1046 20 7,1E+12 223,18 936,23 0,01-0,99 817-1042

20 7,22E+16 392,43 1246,63 0,02-0,99 1138-1373

5 1,01E+06 106,33 809,11 0,01-0,99 645-983 10 1,37E+05 95,18 838,82 0,01-0,99 649-1134 15 1,70E+05 98,51 892,95 0,01-0,99 673-1153 20 3,19E+05 100,63 886,78 0,01-0,99 668-1144

5 6,98E+09 178,41 902,90 0,02-0,99 803-1063 10 6,44E+09 174,85 908,97 0,02-0,99 810-1078 15 1,55E+12 214,49 933,09 0,02-0,99 832-1063 20 5,19E+11 204,20 930,08 0,02-0,99 830-1071

Cmatrix F2 15 5,24E+16 391,91 1243,06 0,02-0,98 1142-1366

**Table 12.** List of kinetic data for the transformations in oxidation processes of titanium carbide samples

Basing on the obtained results an analysis of the process has been performed. The r(α,T) dependencies on sample heating rates and sample temperature for the stages were studied. The plots of r(α,T) obtained for the nc-TiCx/C not-reduced with hydrogen are shown in

**Figure 26.** Plots of r(α,T). Oxidation of nc-TiCx/C unreduced with hydrogen; a) oxidation of nc-TiCx, b) burning out of the carbon formed during the oxidation process of nc-TiC, c) burning out of the carbon

Sample Conversion Model <sup>Β</sup>

TiCx/C

TiCx after reduction

Figure 26.

contained in the samples

The analogous plots obtained for the oxidation process in air of nc-TiCx reduced with hydrogen are shown in Figure 27.

**Figure 27.** Plots of r(α,T). Oxidation in air of nc-TiC reduced with hydrogen; a) oxidation of nc-TiCx, b) burning out of elemental carbon formed during the oxidation of nc-TiCx

In this case, full consistency with the theory was obtained. The plots in Figure 27a show that nc-TiCx after reduction with hydrogen was uniform, the process rate increased along with the increase in sample heating rate, and the maximum was shifted into the higher temperature range. In both cases, the process rate, according to the theory, increases from zero for α(T)=0, reaches its maximum at the temperature Tm, and then decreases to zero at α(T)→0. The temperature ranges determined for the stages runs in measurement series on the basis of calculations are consistent with the ones determined experimentally.

The obtained results show that the proposed description method of the kinetics of two reactions proceeding simultaneously in a certain range of temperature, allows obtaining a satisfactory accuracy. This method was developed for the needs of processes of oxidation in air of nanocrystalline TiC and nanocomposites of TiC/C with varying carbon content in the matrix, for evaluating the protective qualities of carbon matrix, and also to evaluate and compare the resistance to oxidation of carbide ceramics [17]. In Figure 28 the use of the kinetics knowledge for comparative evaluation of the rate of TiC/C nanocomposite oxidation, depending on the carbon content in the matrix is shown as an example.

Methodology of Thermal Research in Materials Engineering 173

α

 α= = ÷ .

= = ÷ , which is the value determined experimentally. The

kinetic models were assigned for the stages. The stages I and III are well-described by model A2, and the stage II by model A4. It has been also shown that the influence of heating rate of the sample on the course of the process can be compensated, at constant activation energy,

In case of the investigated process applying the isoconversional method the following results were obtained. The E values for the stages I and III (assimetric plots of DTG and HF) changed constantly along with the change of conversion degree. However, in the case of stage II (symmetric plots of DTG and HF), E was practically constant. It seems probable that the isoconversional method compensates the influence of βi on the course of the process by changing the activation energy. Theoretically much more interesting is the possibility to

While carrying out the calculations using the Coats-Redfern method the activation energies determined by Kissinger's method were used as the base values. Almost constant values of the A and E parameters were obtained for the stages for different heating rate of the samples. The verifying calculations were performed. The α(T) and r(α,T) dependencies were determined. The good consistency with experimental data was obtained. The obtained results show that the Coats-Redfern equation is of great importance for the studies of the

Describing kinetics of the TiCx carbonisation and their oxidation, Coats-Redfern's equation was applied kinetic models of stages were identified based on statistical evaluation and compliance to a large extent, of degrees of transformation for stages calculated and determined from measurements. Building the kinetic models of processes, the results of measurements were treated as statistic values. A system of a complex analysis of measurements results was developed with the use of artificial neurone networks. Based on the TG curves four stages have been distinguished. The first, endothermic stage proceeding with mass loss, corresponded to desorption of volatile products, D3 model. The second, exothermic stage proceeding with mass growth, was assigned to oxidation of uncarbonized nc-TiCx/C by the oxygen present in argon at trace level, F2 model. The third endothermic stage, proceeding with mass loss, referred to carbonization of nc- TiCx/C and pyrolysis of organic compounds, contained in the raw samples. The pyrolysis of admixtures and carbonization of nc-TiCx/C proceeded simultaneously. After completing the carbonization process at the temperature above 1573 K, oxidation of carbonized TiCx/y by oxygen present

The third, basic stage preceded in non-isothermal and isothermal conditions; at lower conversion degrees F1 model (first-order reaction) and at the higher conversion degrees (above 0.98) D3 model (three-dimensional diffusion, spherical symmetry, Jander equation)

Adapting to the description of the processes which took place with the participation of nc-TiCx/C the parameters for the process of purification were determined together with the simultaneous carbonization of nc-TiCx in argon, in conditions which make impossible their

compensate the βi, at constant activation energy, with temperature range 0 1 *T T*

by temperature range 0 1 T T

α

temperature ranges were given for the stages.

kinetics of heterogeneous non-catalytic processes

in argon at trace level was observed, R2 model.

was applied.

 α

**Figure 28.** Dependence of conversion degree on time - α(t). T= 823 K. Oxidation of TiC commercial and TiC/C nano-composites (30 nm) in air. 50, 10, 3 % by wt. of the carbon contents in composites respectively [17].

## **5. Conclusions**

The results of thermal decomposition of NH4VO3 in dry air have been presented. The measurements were carried out by TG – DSC method. The gaseous products were determined by MS method. Solid products were identified by XRD method. On the basis of measurement results the division of the process into stages has been made and the temperature ranges for stage courses and changes of sample masses in stages were determined. There was demonstrated that decomposition of NH4VO3 proceeds according to the following equation

$$\text{(6NH}\_4\text{VO}\_3 \rightarrow \text{(NH}\_4)\_3\text{ V}\_6\text{O}\_{16} \rightarrow \text{(NH}\_4)\_2\text{ V}\_6\text{O}\_{16} \rightarrow \text{3V}\_2\text{O}\_5\text{I}$$

In all the stages at different sample heating rates NH3, H2O, NO and N2O were evolved, which were formed as a result of NH3 oxidation. NO2 did not occur among the evolved gases. There should be added that N2O was formed mainly during the stage II and III.

While performing the measurements the emphasis was placed on the possibility of obtaining experimental data for description of kinetics of investigated process, in accordance with ICTAC Kinetics Committee recommendations.

In the case of the investigated process, the necessary results for isothermal conditions were not obtained because the measurements for the stage could be performed only in a few temperatures, while at higher temperatures the results were obtained at high conversion degrees.

For non-isothermal conditions the needed data have been obtained. Kinetic calculations were performed using Kissinger's method, isoconversional method and Coats-Redfern method. Applying Kissinger's method the activation energies were determined and the

kinetic models were assigned for the stages. The stages I and III are well-described by model A2, and the stage II by model A4. It has been also shown that the influence of heating rate of the sample on the course of the process can be compensated, at constant activation energy, by temperature range 0 1 T T α α = = ÷ , which is the value determined experimentally. The temperature ranges were given for the stages.

172 Heat Treatment – Conventional and Novel Applications

respectively [17].

degrees.

**5. Conclusions** 

**Figure 28.** Dependence of conversion degree on time - α(t). T= 823 K. Oxidation of TiC commercial and

The results of thermal decomposition of NH4VO3 in dry air have been presented. The measurements were carried out by TG – DSC method. The gaseous products were determined by MS method. Solid products were identified by XRD method. On the basis of measurement results the division of the process into stages has been made and the temperature ranges for stage courses and changes of sample masses in stages were determined. There was demonstrated that decomposition of NH4VO3 proceeds according to the following equation

() () 4 3 4 6 16 4 6 16 2 5 3 2 6NH VO NH V O NH V O 3V O →→→

In all the stages at different sample heating rates NH3, H2O, NO and N2O were evolved, which were formed as a result of NH3 oxidation. NO2 did not occur among the evolved gases. There should be added that N2O was formed mainly during the stage II and III.

While performing the measurements the emphasis was placed on the possibility of obtaining experimental data for description of kinetics of investigated process, in

In the case of the investigated process, the necessary results for isothermal conditions were not obtained because the measurements for the stage could be performed only in a few temperatures, while at higher temperatures the results were obtained at high conversion

For non-isothermal conditions the needed data have been obtained. Kinetic calculations were performed using Kissinger's method, isoconversional method and Coats-Redfern method. Applying Kissinger's method the activation energies were determined and the

accordance with ICTAC Kinetics Committee recommendations.

TiC/C nano-composites (30 nm) in air. 50, 10, 3 % by wt. of the carbon contents in composites

In case of the investigated process applying the isoconversional method the following results were obtained. The E values for the stages I and III (assimetric plots of DTG and HF) changed constantly along with the change of conversion degree. However, in the case of stage II (symmetric plots of DTG and HF), E was practically constant. It seems probable that the isoconversional method compensates the influence of βi on the course of the process by changing the activation energy. Theoretically much more interesting is the possibility to compensate the βi, at constant activation energy, with temperature range 0 1 *T T* αα= = ÷ .

While carrying out the calculations using the Coats-Redfern method the activation energies determined by Kissinger's method were used as the base values. Almost constant values of the A and E parameters were obtained for the stages for different heating rate of the samples. The verifying calculations were performed. The α(T) and r(α,T) dependencies were determined. The good consistency with experimental data was obtained. The obtained results show that the Coats-Redfern equation is of great importance for the studies of the kinetics of heterogeneous non-catalytic processes

Describing kinetics of the TiCx carbonisation and their oxidation, Coats-Redfern's equation was applied kinetic models of stages were identified based on statistical evaluation and compliance to a large extent, of degrees of transformation for stages calculated and determined from measurements. Building the kinetic models of processes, the results of measurements were treated as statistic values. A system of a complex analysis of measurements results was developed with the use of artificial neurone networks. Based on the TG curves four stages have been distinguished. The first, endothermic stage proceeding with mass loss, corresponded to desorption of volatile products, D3 model. The second, exothermic stage proceeding with mass growth, was assigned to oxidation of uncarbonized nc-TiCx/C by the oxygen present in argon at trace level, F2 model. The third endothermic stage, proceeding with mass loss, referred to carbonization of nc- TiCx/C and pyrolysis of organic compounds, contained in the raw samples. The pyrolysis of admixtures and carbonization of nc-TiCx/C proceeded simultaneously. After completing the carbonization process at the temperature above 1573 K, oxidation of carbonized TiCx/y by oxygen present in argon at trace level was observed, R2 model.

The third, basic stage preceded in non-isothermal and isothermal conditions; at lower conversion degrees F1 model (first-order reaction) and at the higher conversion degrees (above 0.98) D3 model (three-dimensional diffusion, spherical symmetry, Jander equation) was applied.

Adapting to the description of the processes which took place with the participation of nc-TiCx/C the parameters for the process of purification were determined together with the simultaneous carbonization of nc-TiCx in argon, in conditions which make impossible their coalescence and growth to micron sizes. Kinetics and by the same, the mechanism of the processes of oxidation of nanocrystalline TiCx in form of powder were tested, and they were subjected to evaluation based on the comparison of the rate of oxidation.

Methodology of Thermal Research in Materials Engineering 175

*Institute of Materials Science and Engineering West Pomeranian University of Technology,* 

This work it concerns were partially generated in the context of the MULTIPROTECT project, funded by the European Community as contract No. NMP3-CT-2005-011783 under the 6th Framework Programme for Research and Technological Development. Financial support of part of the work by the Ministry of Science and Higher Education within the Projects No N N507 444334, 2008–2011 and No NR15-0067-10/2010-2013, is gratefully

The scientific support of my teacher professor Jerzy Straszko throughout this work is

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**Author details** 

*Szczecin, Poland* 

acknowledged.

**7. References** 

Anna Biedunkiewicz

**Acknowledgements** 

gratefully acknowledged.
