1. Introduction

2. Experimental Studies of Metal-Ceramic Materials and Coatings Production

2.3. Thermal Stability

One of the essential requirements to structural materials is thermal stability at high temperatures, the absence of significant grain growth of the structure, which is the key to maintaining high mechanical characteristics at these temperatures.

The study of the thermal stability of two-phase alloys (heterogeneous structures synthesized from unmelted components) is becoming increasingly important due to the increased use of such materials in modern engineering. At present, a significant number of studies on the growth rate of dispersed particles in composite materials have been performed [18,19,20].

The study of thermal stability of the metal-ceramic coatings obtained by us has shown [3,4] that they retain their structure during annealing up to temperatures of 1400°С. The study of thermal stability of two-phase metal-ceramic systems was of particular interest, since the microstructure evolution can lead to changes not only in mechanical, but also in electrophysical properties of materials.

From the obtained data extremely high stability of metal-ceramic compositions follows. The size of ceramic particles even after annealing at 1900°C for 5 hours does not exceed 1 μm. While type II stresses are almost completely removed as a result of such heat treatment, type Ш stresses remain significant. The microhardness of metal ceramics decreases with increasing temperature and annealing time, but remains sufficiently high even after annealing at 1900°С (1100-1800 kg/mm²).

The phase composition does not change in the process of annealing. The uniformity of ceramic distribution over the layer thickness does not change as compared to the original samples. In the process of annealing a significant decrease in the grain size of metal-ceramics is observed due to the effect of ceramic particles on the recrystallization process.

Most researchers process the experimental results using formula (1) and draw conclusions about the growth process mechanism during annealing based on the obtained values of п and ΔН

$$\overline{r}=Atexp(-\frac{∆H}{RT})$$

(1)

However, often the $\overline{r}$ values obtained in different heat treatment modes refer to different mechanisms, which can lead to incorrect conclusions, so criteria for selecting experimental results referring to a single mechanism are needed.

In composite materials, the growth of dispersed particles can occur by the following mechanisms: 1) growth of a supersaturated solid solution; in this case the number of particles in the system remains unchanged, only their sizes increase. This mechanism may occur if supersaturation of solution is large; 2) coagulation (agglomeration) - association of particles as a whole; 3) coalescence itself - diffusive growth of large particles at the expense of small ones.

Given the very low solubility of refractory oxides in refractory metals, as well as the significant size of dispersed particles (~50 A), it should be assumed that the role of the first two mechanisms is small.

The main mechanism of particle growth in refractory metal-metal oxide systems at high temperatures is coalescence [19].

The coalescence process may be limited by the following stages: a) dissociation of the oxide on the surface of the smallest particles; b) dissolution of the oxide components in the metal matrix; c) its diffusion in the matrix; d) adsorption and chemical reaction on the surface of large particles.

For each of these stages theoretically obtained expressions for particle growth rate.

Following [4], we will consider the methods of processing the experimental data on the growth of precipitates during high-temperature annealing and their interpretation based on different models.

To study the growth parameters in the Mo-ZrO₂ system, samples with zirconium dioxide content of 5-30 wt % were annealed in vacuum at temperatures of 1500-1900°C for 1-20 h. The dimensions of zirconia particles were measured from electron microscopic photographs. Since r - the average particle size is a statistical parameter, it is necessary to perform a large number of measurements, processing of which requires the use of a computer. For each sample, 400-500 measurements were taken and processed using statistical methods. Average particle size was determined for each standard in thermal treatment mode by using a computer

$$\overline{r}=\frac{1}{N}{\sum }_{i=1}^N{r}_i$$

and their dispersion

$${\mathsf{\sigma }}^2=\frac{1}{N-1}{\sum }_{i=1}^N{(r_i-\overline{r})}^2$$

The values of $\overline{r}$ = f (t, T) were processed by the least-squares method using equation (1).

The obtained values of parameters п and ΔН for different samples differing in the initial particle size distribution function and ZrO₂ concentration are presented in Table 4. The available scatter in values of parameters п ~2 - 4.5 and ΔН ~20 - 100 kcal/mol does not allow making unequivocal conclusions on the mechanism of coalescence process in the system studied.

Let us consider in more detail the processing of experimental data and the interpretation of the results based on some theoretical models. As the initial distribution function we used a narrow Gaussian curve and a lognormal distribution, which is often realized in engineering during milling, crushing, etc., and is therefore quite possible in composite materials obtained by powder metallurgy methods.

The most reasonable regarding coalescence in such systems are the Exner-Fischmeister [21], Wagner [22], and Lifshitz-Slezov [23] models.

The above models differ both in the values of p and ΔH parameters and in the type of the particle size distribution function. In order to process experimental data for any of the models, it is first necessary to establish the closeness of the experimental distribution function to the selected theoretical difference of heights of two neighboring columns, a very large number of measurements (in our case, 8000-10 000 for each sample) is required, which is extremely laborious without automation of the one and only for the points where there is such agreement, to determine п and ΔН.

The easiest way to check the closeness of the experimental distribution to the selected theoretical distribution is to construct histograms. However, in order for statistical fluctuations not to exceed the measurement process.

Comparison of experimental distribution functions with theoretical distributions mentioned above was performed by us on a computer using Pearson's goodness-of-fit criterion (χ² criterion) [24].

The calculations were performed as follows. An ordered sample r containing experimental values r_i was divided into L intervals with an equal number of points т_i and the function was defined

$${\mathsf{\chi }}^2=\sum _{i=1}^L\frac{{(m_i-n{p}_i)}^2}{n{p}_i}$$

where $p_i=\underset{a_i}{\overset{b_i}{\int }}f\left(x\right)dx$ is the probability of finding points in the i-th interval given by the tested theoretical distribution function f (х).

If χ² < (χ²)₀ , where (χ²)₀ is the table function at a certain confidence probability P, then with probability P we can say that the theoretical distribution function describes the experimental data well.

The results of testing different theoretical models using Pearson's goodness-of-fit test are presented in Table 5. As can be seen from this table, at no point in the coalescence process can the distribution function be represented by a lognormal distribution. At the initial sites of coalescence, the experimental distribution is close enough to the normal Gaussian distribution. As the particles grow, the distribution function becomes blurred and departs from the normal distribution more and more. This suggests that the formation of dispersed particles during crystallization of the material in our case obeys Gaussian law.

At later stages, coalescence is very well described by the asymptotic Lifshitz-Slezov distribution, and, as can be seen from Table 5, starting from some point, the process can be described by a single mechanism (u₀=0 corresponds to volume diffusion).

Figure 1a. Dependence of the variability coefficient µ on temperature (a) and annealing time (b).

Figure 1a. Dependence of the variability coefficient µ on temperature (a) and annealing time (b).

The theoretical values of the coefficients µ₃ and µ₄ were calculated on a computer.

$${\mu }_i=\frac{{\int }_0^{a_i}{u}^2{P}_{i}du}{{\int }_0^{a_i}{P}_{i}du}-1(i=\mathrm{3,4};a_s=\frac{3}{2},a_4=\frac{4}{3})$$

Only those points that correspond to the same mechanism should be processed by the least-squares method.

It is easier to determine whether different points belong to the same mechanism by examining the behavior of the coefficient of variability µ(T, t) = σ/r. If this coefficient remains constant within a wide range, it indicates that the distribution function is unchangeable.

Figure 1а shows experimental coefficients of variability µ obtained on a computer. As can be seen, not all points correspond to the same coalescence mechanism. Hence, the source of errors in processing the experimental results is clear. If we process all points corresponding to different mechanisms by the method of least squares, we obtain some average values of п and ΔН that do not make any physical sense.

At the same time the least squares processing of points corresponding to one mechanism of coalescence gives п = 3 and ΔН = 56 kcal/mol. The value of p is in very good agreement with the predictions of the Lifshitz-Slezov theory [23]. The value of ΔН can be compared with the activation energy of zirconium diffusion mass transfer in molybdenum.

3. Theoretical Aspects

4. Conclusions

• Experimental studies on the development of processes of obtaining ultradisperse metal-ceramic materials and coatings Mo-ZrO₂, Mo-Al₂O₃, W- ZrO₂, W- Al₂O₃CVD method of deposition from the gas phase in the so-called CO₂ process using low-temperature nonequilibrium plasma have been conducted.

2.

The methods of processing experimental data on coalescence by the example of the Mo- ZrO2 system are considered. The use of statistical methods (Pearson's agreement criterion and variability coefficient behavior to establish the closeness of the experimental and theoretical distribution functions) makes it possible to select points that are related to the same mechanism of coalescence. At later stages, the coalescence process is well described by the Lifshitz-Slezov theory.

3.

High-temperature X-ray studies of "molecular" two-phase alloys Mo- Al2O3 and Mo- ZrO2 have been conducted. It is shown that, depending on the elastic and thermal properties of the matrix materials and dispersed particles, the molybdenum matrix can be in a tensile or comprehensively compressed state.

4.

Temperature dependences of specific electrical resistance and thermal emfs of two-phase disperse-strengthened alloys Mo- ZrO2, Mo- Al2O3, W- ZrO2, W- Al2O3have been studied. It has been established that in the region of temperatures 1023...1273K, anomalous changes of resistance and instability of thermal emf in magnitude and sign apparently connected with the presence of internal stresses in material caused by ultradisperse particles are observed.

5.

Theoretical aspects of the problem of carriers density increasing in nanocomposite materials are discussed

6.

Possibilities of creation of ultradisperse compositions with the use of radiation-plasma methods are considered.

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