Physical Chemistry

O. K. SHABALINA, Corresponding Member of the Academy of Sciences of the USSR G. I. CHUFAROV

KINETICS OF THE DECOMPOSITION OF WÜSTITE

The kinetics of the decomposition of wüstite was studied, by means of magnetic analysis as in \((^{1,2})\), on samples with lattice parameter \(4.032\) Å. The isothermal decomposition of wüstite was carried out in vacuum at various temperatures in the range \(200\)—\(500^\circ\). The specific saturation magnetization of the samples \(\sigma_s\) as a function of time \(t\) clearly reflected the existence of two consecutive reactions (I—pre-eutectoid precipitation of magnetite and II—eutectoid decomposition of metastable wüstite) at temperatures not exceeding \(400^\circ\), and one reaction (III—overall eutectoid decomposition of the initial wüstite) at temperatures above \(400^\circ\) (Fig. 1a and b). From the curves \(\sigma_s(t)\), the kinetic curves \(\alpha(t)\) were calculated for reactions I, II, and III, where \(\alpha\) is the fraction of substance transformed by time \(t\). The most complete and accurate data were obtained for the kinetics of reaction II; therefore this process was considered first.

The decomposition of wüstite is accompanied by the appearance of diffusion porosity \((^{1,2})\), which apparently is what mainly determines the kinetics of the transformation. At first, decomposition occurs at certain initial defects in the wüstite crystals, but very soon the numerous newly appearing defects—pores—become reaction centers, and the rate of the whole process \(d\alpha/dt\) becomes substantially dependent on their number \(N\).

Fig. 1. Dependence of the specific saturation magnetization of samples of decomposing wüstite on the time of isothermal annealing at temperatures: \(a\)—not exceeding \(400^\circ\), \(b\)—above \(400^\circ\)

Since \(N \sim \alpha\), then, to a first approximation, \(d\alpha/dt \sim N \sim \alpha\). In addition, \(d\alpha/dt\) is proportional to the number of unreacted regions, i.e., to the fraction of unreacted substance \((1-\alpha)\). We obtain

\[ \frac{d\alpha}{dt}=k\alpha(1-\alpha), \tag{1} \]

whence

\[ \frac{\alpha}{1-\alpha}=e^{kt-b_1} \tag{1′} \]

(\(k\) and \(b_1\) are constants).

The experimental data for reaction II satisfy (1′), but only up to \(\alpha \approx 1/2\) (Fig. 2a).

The decomposition of wüstite is followed by processes of pore growth and recrystallization \((^2)\). It may be assumed that these processes occur even

Fig. 2. Verification of the kinetic equations for the decomposition of wüstite using the experimental data for reaction II:
a—equation (1′) in the form

\[ \lg \frac{\alpha}{1-\alpha}=(k_{\mathrm{II}}\lg e)t-(d_1)_{\mathrm{II}}\lg e, \]

b—equation (2′) in the form

\[ \lg \frac{\alpha}{1-\alpha}=(b_2)_{\mathrm{II}}\lg e-(2n_{\mathrm{II}}\lg e)t^{-1/2} \]

at low temperatures (in the temperature range studied), since the specimen is in a state of increased free energy owing to its considerable porosity. The influence of these secondary processes on the overall course of the reaction evidently appears only after substantial development of the reaction (\(\alpha \approx 1/2\)). Treating a micropore as a nonstationary source of diffusion (vacancies), we obtain \((^3)\) that the pore loses vacancies and decreases (grows) with time proportionally to \(1/(Dt)^{3/2}\), where \(D\) is the diffusion coefficient. If it is assumed that the number of pores \(N\) in the decomposed regions in the second half of the reaction changes with time approximately according to the same law, i.e., \(N \sim \alpha/(Dt)^{3/2}\), then for the overall rate of the process we have

\[ \frac{d\alpha}{dt}=\frac{k'}{(Dt)^{3/2}}\,\alpha(1-\alpha)=\frac{n}{t^{3/2}}(1-\alpha), \tag{2} \]

whence

\[ \frac{\alpha}{1-\alpha}=e^{b_2-2nt^{1/2}},\quad \text{where } n=\frac{k'}{D^{3/2}} \tag{2′} \]

(\(k'\), \(n\), \(b_2\) are constants).

The experimental data satisfy (2′) for \(\alpha \gtrsim 1/2\) (Fig. 2b). Reactions I and III are very close in mechanism to reaction II; therefore equations (1′) and (2′) also describe these transformations well ((1′)—for \(\alpha \lesssim 1/2\), (2′)—for \(\alpha \gtrsim 1/2\)).

Temperature changes in the kinetic parameters \(k, n, b_1, b_2\) are regular (Fig. 3) and can be explained on the basis of the same ideas about the role of diffusional porosity in the decomposition of wüstite.

The parameter \(k\) characterizes the rate in the first stage. For reactions I and II, the corresponding quantities \(k_{\mathrm{I}}\) and \(k_{\mathrm{II}}\) increase with temperature, since the mobility of ions in the wüstite lattice increases, which facilitates the crystallochemical transformation. As the temperature approaches \(400^\circ\), the increase in \(k_{\mathrm{I}}\) and \(k_{\mathrm{II}}\) slows down, while for reaction III, proceeding at still higher temperatures, the corresponding quantity \(k_{\mathrm{III}}\) already decreases (Fig. 3). The latter is probably explained by the fact that at elevated temperatures (above \(400^\circ\)) there may be a larger number of vacancies in the crystal lattice (of wüstite, magnetite), and consequently fewer micropores are formed, i.e., a given value of \(\alpha\) already corresponds to a smaller number \(N\) (see the justification of equation (1)).

Fig. 3. Temperature changes in the kinetic parameters \(k\) and \(n\)

The parameter \(n\) characterizes the rate in the second stage and, by definition (equation (2)), \(n = k'/D^{3/2}\), where \(k'\) has approximately the same meaning as \(k\), and \(D\) is the diffusion coefficient. The value of \(n\) for all three reactions changes hardly at all (Fig. 3). Assuming that \(k'\) changes with temperature in the same way as \(k\), we find that \(D\) also first increases with temperature and then decreases. The reason for this is that diffusion takes place mainly along the pore surface, while above \(400^\circ\) the porosity begins to decrease noticeably.

The parameter \(b_1\) characterizes the initial degree of decomposition

\[ \left(\frac{\alpha}{1-\alpha} \to e^{-b_1}\ \text{as}\ t \to 0\right), \]

i.e., the degree of decomposition of wüstite at the initial defects; after this degree is reached, the kinetics is already determined by new defects—pores. The changes in this quantity with temperature are insignificant and, given the low accuracy of the present investigation, cannot be discussed.

The parameter \(b_2\) characterizes the final degree of decomposition

\[ \left(\frac{\alpha}{1-\alpha} \to e^{b_2}\ \text{as}\ t \to \infty\right), \]

i.e., the maximum amount of decomposition that could be attained if only one mechanism operated—the one associated with porosity. With increasing temperature this quantity naturally increases, since the mobility of the particles of the decomposing substance increases, and then decreases, since the number of pores (reaction sites for this decomposition mechanism) becomes ever smaller.

Institute of Metallurgy
Ural Branch of the Academy of Sciences of the USSR

Received
1 X 1962

CITED LITERATURE

1. G. I. Chufarov, O. K. Shabalina, DAN, 140, No. 6 (1961); O. K. Shabalina, G. I. Chufarov, Fiz. met. i metalloved., 12, No. 5 (1961).
2. O. K. Shabalina, G. I. Chufarov, DAN, 142, No. 2 (1962); O. K. Shabalina, G. I. Chufarov, Fiz. met. i metalloved., 13, issue 5 (1962).
3. S. D. Gertsriken, I. Ya. Dekhter, Diffusion in Metals and Alloys in the Solid Phase, Moscow, 1960.