Izvestia Academia Of Science USSR
Inorganic Materials
1986, v.22, N 9, p. 1497-1499. (
offprint rus.)
The solution of the problem of an adequate description of the experimental data on the temperature dependencies of the linear growth rate of crystals in various melts is one of the necessary conditions for the purposeful management of the phase composition and superstructure of products in the technology of cement, steel, stone casting. A number of works [1-11] have obtained experimental dependencies of crystal growth rate on temperature in a wide super-cooling interval in various silicate melts.
In [12], experimental data on crystallization in two model silicate systems are described by approximation by a semi-empirical equation using the least squares method. It was of interest to follow the influence of small additions of oxides metals of variable valence on the temperature dependencies of the velocity growth of the crystals of monocalcium silicate chosen as a model object and to compare them with those obtained for melts that do not contain such oxides, which is also of practical importance for the directional crystallization of industrial slags containing iron, copper, manganese oxides and other metals of variable valence.
In the present work, using a high-temperature microscope [13], using the methods described in [10], the temperature dependencies of the growth rate of crystals of monocalcium silicate from melts with the ion-molecular ratio M : CaSiO_{3} = 1: 10 (M - Mn^{3+} or Mn^{2+}, Fe^{3+}, Fe^{2+}, Cu^{2+}, Cu^{+}). Metal ions were introduced in the melt in the form of the corresponding oxides.
The figure shows the temperature dependences of growth rates crystals CaSiO_{3} in the coordinates 1n v - 1/T, where v is the linear velocity growth, T - temperature. In contrast to the analogous dependencies of the growth of crystals in melts that had not previously been studied by the authors ions of metals of variable valence [10-12], approximation by the known semi-empirical formula
v = k (ΔT/T)^{c}×exp (-E/ RT) (1)
(where AT = T_{o}-T, T_{o} is the liquidus temperature, k, c, E are empirical coefficients, as can be seen from the figure (curves 1)), did not give satisfactory results in the case of additions of iron and copper oxides. Table 1 presents values of empirical coefficients of equation (1).
If, according to the interpretation of the physical meaning of the empirical of the coefficients of equation (1) [12], it can be assumed that the number of degrees of freedom along which the transition of structural elements from the melt to the crystal occurs and the sum of entropy of activation of potential barriers with respect to these degrees of freedom are, in the first approximation, linear functions of temperature
c = c_{o} + c_{1}ΔT, ΣΔS_{a} = ΣΔS_{ao} + a_{1}ΔT
then equation (1) can be rewritten in the form
v = k_{o} (ΔT/T)^{co+c1ΔT} exp (-E_{o}/RT + a_{1}ΔT) (2)
where k_{o}, c_{o}, c_{1}, E_{o}, a_{1} are empirical coefficients.Temperature dependencies of the linear growth rate of the crystals of monocalcium silicate in the melt of 100 % CaSiO_{3} (a); with additives Mn_{3}O_{4} (b), Fe_{2}0_{3} (c), FeO (d), CuO (e), Cu_{2}O (f) (curves: 1 - approximation by formula (1); 2 - by the formula (2); the upper axis of the abscissa is for a, c, e, the lower is for b, d, f) |
Approximation of the experimental data by means of equation (2) led to a fairly good coincidence of experimental and theoretical dependencies (figure, curve 2). Table. 1 gives the values of the empirical coefficients of equation (2).
The use of the approximating equation (2) as an approximating equation makes sense only in the case of a sufficiently substantial deviation of the experimental data from the form of equation (1). Otherwise, the procedure of approximating the experimental data by the method of least squares loses stability, and the error in determining the values of the empirical coefficients becomes larger than their value.
Addition | To, K | η^{2} | c | ln(k), (μm/s) | E, (kJ/mol) |
- | 1845±10 | 0.98 | 2.53±0.12 | 46±1 | 426±8 |
Mn3O4 | 1810±10 | 0.86 | 1.11±0.18 | 24±1 | 197±13 |
Fe2O3 | 1810±10 | 0.92 | 0.86±0.22 | 29±2 | 267±25 |
FeO | 1810±10 | 0.92 | 1.51±0.19 | 337±2 | 368±25 |
CuO | 1810±10 | 0.92 | 0.84±0.17 | 223±2 | 179±13 |
Cu2O | 1810±10 | 0.85 | 1.68±0.29 | 33±2 | 284±21 |
The existence of a noticeable temperature dependence of the mechanism of the crystal growth process can be explained as follows. Because the in the melt at any temperature there is an equilibrium distribution ions in different degrees of oxidation, which differs from the preset in the synthesis, the degree of deviation from the equilibrium state of the melt is a function of temperature. The number of defects in the structure of the melt is not corresponds to the Arrhenius temperature function.
Addition | To, K | η^{2} | c | c_{1}, K^{-1} | ln(k), (μm/s) | E, (kJ/mol) | a1, K-1 |
Fe2O3 | 1810±10 | 0.98 | 1.04±0.54 | 0.021±0.008 | 133±27 | 1811±360 | 0.097±0.021 |
FeO | 1810±10 | 0.98 | 1.82±0.43 | 0.027±0.006 | 175±22 | 2376±297 | 0.124±0.017 |
CuO | 1810±10 | 0.96 | 2.16±0.78 | 0.022±0.007 | 93±18 | 1113±225 | 0.056±0.012 |
Cu2O | 1810±10 | 0.93 | 2.77±1.00 | 0.034±0.009 | 150±28 | 1924±330 | 0.102±0.018 |
It is possible that the phenomenon of reversible thermal staining of the melt with admixtures of iron oxides is a consequence of a sharp increase in the concentration of defects with an increase in temperature above 1000 K.
The proposed interpretation of the experimental data allows also explain the increase in the spread of the experimental points in comparison with the growth in the melt of the stoichiometric composition, since the degree of deviation of the actual ratio of the number of ions of different degrees of oxidation from the equilibrium due to the interaction with oxygen of the air should depend on the thermal prehistory of the sample.
Conclusions
High temperature microscopy was used to study the temperature the dependence of the growth rate of the crystals of monocalcium silicate in melts with additions of metal oxides of variable valence Mn_{3}0_{4}, Fe_{2}O_{3}, FeO, CuO, Cu_{2}O. The obtained dependencies could be approximated by means of the proposed semi-empirical equation that takes into account the temperature dependence of the mechanism of the process of embedding structural elements in the crystal.
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Academy of Sciences of the USSR
Institute of Silicate Chemistry
them. I.V. Grebenshchikova,
Leningrad
Received by the Editor
Dec. 3, 1984
May. 6, 2018; 16:44 EST