Features of the Thermal Decomposition of Mixed Crystals

G. T. Ponov

(Presented at a scientific seminar of the Department of Radiation Chemistry)

The doping method is used for the directed alteration of the rates of reactions of thermal, photo-, and radiation decomposition, and also for elucidating the features and mechanism of reactions of this kind in solids \[1, 3\].

Systematic studies of the thermal stability of mixed crystals have been carried out for a number of systems, mainly azides \[3–15\], oxalates \[3,16–24\], and metal perchlorates \[25–27\]. However, in most of the works cited above, the initial assumptions determining the method of formation and the type of mixed crystals are used either formally or are not taken into account at all. Thus, the nature of the distribution of the impurity over the volume of the crystals and its influence on the thermal stability of mixed crystals were completely disregarded in \[4,11,16–20\]; the influence of different methods of preparation on the possibility of forming mixed crystals was not studied \[4–11,22–27\]. In \[4–8\], the type of mixed crystals and the methods of their formation were not established. It should be noted that in individual cases attempts were made to determine the type of mixed crystals \[9–11\], the method of their construction \[9–11,28\], and to take into account the nature of the distribution of the impurity over the volume of the microcrystals \[12,28\].

The absence of such information, i.e., ignorance of the model (type) of the mixed crystals and of the method of their construction, can lead to untenable conclusions when discussing the mechanism of the effect of impurities (additives) on the thermal stability of solids.

In this connection, the present work briefly considers the principal types and methods of construction of mixed crystals, me—

years of their identification and, in some cases, predict the nature of the effect of an additive (a microcomponent) on the thermal stability of the substrate (macrocomponent).

Since the conditions for the formation of mixed crystals (solid solutions) of one type or another are associated primarily with the nature of the micro- and macrocomponent and with the conditions of their cocrystallization, and have been considered in detail in works [29–31], they are not discussed here.

As for the classification of mixed crystals, it was carried out by Nikitina [29], who formally divided them into three groups.

1. True (isomorphous) mixed crystals, consisting of substances that have the same type of chemical formula and equality of the valences of the corresponding particles, as, for example:
   $SrSO_4 - BaSO_4$, $K_2SO_4 - K_2SeO_4$. The conditions for their formation, determined by the charge, radii of the substituting ions, and the type of crystal lattice, were formulated by Grimm [30, 31].

2. Mixed crystals of a new kind (Grimmoire crystals), composed of substances with the same type of chemical formula but with different valence of the corresponding particles, as, for example, $KMnO_4 - BaSO_4$, $SrSO_4 - KClO_4$.

3. Anomalous mixed crystals, consisting of substances one of whose ions is common, $CaWO_4 - Ce_2(WO_4)_3$, or of combinations of substances with different chemical formulas, $Ba(NO_3)_2$—methylene blue.

Hahn [32] also singled out internally adsorbed systems as a separate group. In this case impurity ions do not enter the lattice of the initial substance. Mixed crystals of this type, as a rule, have an upper limit of miscibility.

The types of mixed crystals listed above also correspond to different methods of their formation [1, 31]. All kinds of mixed crystals can apparently be covered by six methods of their construction.

1. Replacement of ions, atoms, or complex ions by equivalent particles at lattice sites. All true solid solutions are constructed in this way.

2. Methods of complex combined substitution.

a) substitution of several ions by an equal number of ions correspondingly similar in size but different in charge, with preservation of the sum of the charges (substitution of \(Ti\) ions for \(FeTi_2\) in the system \(FeTi_2O_5 - TiO_2\)).

b) substitution of several ions of different sign by a complex ion, with preservation of the sum of the charges (\(2NH_4^+\) and \(4Cl^-\) for \(MnCl_4 \cdot 2H_2O\) in [41]).

1. Substitution of whole portions of the crystal lattices of pure components, when they possess a definite structural analogy—three-dimensional in true solid solutions, two-dimensional in anomalous mixed crystals.

2. Incorporation of foreign particles into lattice interstices.

3. Simultaneous substitution of ions having identical sizes but different charge and incorporation into interstices of ions of the same name, for charge compensation (a Frenkel defect).

4. Replacement of an ion with a lower charge by an ion with a higher charge, with the formation of ionic vacancies (Mott defects).

By methods 2a,b some types of anomalous mixed crystals are formed. More often anomalous mixed crystals are encountered whose formation occurs by methods 4–6.

The distribution of impurities is determined first of all by the crystallization conditions [29,31–33].

A homogeneous, uniform distribution of impurities throughout the volume of crystals occurs in accordance with the Berthelot–Nernst distribution law [33,34] and, according to Khlopin [35–36], is possible in the case of true equilibrium between the solution and the solid phase. A generalized mathematical expression of the law was proposed by Henderson and Kracek [37]:

\[ \frac{x}{a-x} = D \frac{y}{b-y}, \]

where \(x,y\) are the amounts of micro- and macrocomponent in the solid phase,

\(a,b\) are the amounts of micro- and macrocomponent in the solution.

In those cases when crystallization proceeds rapidly, from supersaturated solutions without stirring or in a quiescent solution with insignificant supersaturations, inhomogeneous mixed crystals are formed; here the distribu-

the impurity likewise obeys the Derrer–Hoskins law [38].

\[ \ln \frac{x}{a} = \lambda \ln \frac{t}{b} \]

Fig. 1. Distribution of impurities over the volume of crystals

a) uniform, b) surface,
c) nonuniform, predominantly
in the center of the crystal.

In general form, the distribution of an impurity over the volume of a crystal can be represented graphically by Fig. (1), in the coordinates: concentration of the microimpurity \(C\) — crystal radius \(r\) (the crystal is conventionally taken to be spherical).

In this connection, when studying thermal stability it is important to be able to distinguish and to know the properties of the four types of mixed crystals listed above, the methods of their formation, and the distribution of impurities.

The differences between crystals of a new kind (II) and anomalous mixed crystals (III) are only formal, while the methods of substitution and the properties are to a considerable extent similar and often identical, as was shown by Nikitin and Khlopina [39]. Isomorphism of the first kind (mixed crystals) differs from anomalous mixed crystals not only formally, but also in the method of isomorphous substitution and in the properties of the mixed crystals. The differences in the crystallochemical properties of anomalous and isomorphous mixed crystals were formulated by Nikitin [29] and are presented below (Table 1).

Table I

Among the many methods of experimental discrimination of various types of mixed crystals, the most accessible, reliable, and well-developed are chemical methods.

According to Khlopin \([38]\), the dependence of the crystallization coefficient \(D\) on the amount of micro-precipitate formed and sedimenting ...

component makes it possible to distinguish three types of mixed crystals. 1. The constancy of \(D\) when the concentration of the microcomponent is varied over wide limits indicates the formation of true mixed crystals. 2. A decrease in \(D\) with a decrease in the concentration of the microcomponent is evidence of the formation of anomalous mixed crystals. 3. A decrease in \(D\) with an increase in the concentration of the microcomponent corresponds to internal-adsorption coprecipitation.

The separation of true mixed crystals and adsorption phenomena can be carried out by several other methods \([36, 40–42]\).

1. In testing the rate of establishment of equilibrium between the solution and the crystals with respect to the distributing microcomponent. For this purpose, the content of the microcomponent is analyzed after a certain time during separation of the solid phase from: a) a supersaturated solution containing the microcomponent; b) recrystallization of the solid phase (macrocomponent) in a solution containing both components. In adsorption capture, the amount of microcomponent that has passed into the solid phase is the same in both cases. In isomorphous coprecipitation, the amount of microcomponent in the precipitate will be considerably greater in case “a” than in case “b”.

2. In studying the amount of microcomponent transferred into the solid phase during recrystallization. For isomorphous cocrystallization, the amount of microimpurity in the solid phase during recrystallization practically does not change, whereas for adsorption processes it decreases sharply.

3. In studying the effect of changing the sign of the charge and the magnitude of the surface charge on the relative amount of microcomponent that has passed into the solid phase. In adsorption capture, the amount of microimpurity depends strongly on the sign of the surface charge; in isomorphous cocrystallization, it does not depend on it.

4. The presence in the solution of small amounts of polyvalent

of them, strongly adsorbed ions (\(\mathrm{Fe}^{+++}\), \(\mathrm{Zr}^{++++}\), etc.) do not affect the concentration of the macro-impurity in the precipitate during isomorphous coprecipitation and strongly increase it during adsorption coprecipitation.

In a number of cases, to establish the type of mixed crystals, the radiography method [32] may prove useful; however, its application requires large crystals, radioactive isotopes, and special grades of small-angle photomaterials.

An assessment of the possibilities for distinguishing the type of mixed crystals by several of the methods listed above is given in Table 2 [43].

Table 2

Comparative characteristics of various types of coprecipitation

To distinguish isomorphous coprecipitation from adsorption coprecipitation, Korenman [44] proposes studying the coprecipitation of unchanged amounts of the microcomponent at constant quan-

in the lattice sites of the macrocomponent. The dependence of the amount of the microcomponent in the solid phase (precipitate) on its amount remaining in solution gives an isotherm, which has the form of a characteristic curve for the adsorption type of coprecipitation and a straight line for the isomorphic type. The sensitivity of chemical methods is determined by the sensitivity of the methods of analysis for the content of individual elements—microimpurities—and sometimes makes it possible to determine less than \(10^{-9}\) mole % of a microimpurity in mixed crystals.

It should be noted that chemical methods do not provide direct information on the mode of formation of mixed crystals. Such information can be obtained in studying the electrical conductivity of mixed crystals \(\{45,47\}\). For this purpose, isotherms of the relative electrical conductivity \((\sigma_{\text{mixed crystal}}/\sigma_{\text{pure macrocomponent}})\) are plotted as a function of the concentration of the microcomponent. Analysis of such an isotherm makes it possible to determine the mode of formation of mixed crystals, the concentration and mobility of charge carriers, and the miscibility limit \(\{3,45\}\). The method of measuring electrical conductivity makes it possible to determine an impurity concentration of \(\sim 10^{-6}\) mole %. Analysis of the mode of formation of mixed crystals is possible in a number of cases for systems possessing photoconductivity.

Qualitative information on the position of impurities in mixed crystals can be obtained by studying changes in photosensitivity, the rate of photoresponse, and the broadening of the spectral region of photoconductivity of mixed crystals. Quantitative information on the position and nature of impurities in mixed crystals can be obtained by studying the change in the concentration of free carriers with temperature, the appearance of new bands in the photoconductivity spectrum, the appearance of new absorption bands associated with impurities, and certain other characteristics \(\{46\}\).

Among other electrophysical methods, one should note measurement of the dielectric constant and \(\operatorname{tg}\delta\) of mixed crystals \(\{45,47\}\), which make it possible to quan—

the destruction of defects and impurities, and also to determine the binding energy of the impurity–lattice-defect complex, which is of great importance in solid-phase reactions. Electrophysical methods for studying mixed crystals, despite the value of the information obtained with their aid, require special installations and lengthy experiments.

In this respect the E.P.R. method (electron paramagnetic resonance) is extremely simple and rapid. The EPR method is suitable for solving some of the questions listed above. Thus, it makes it possible to determine the concentration of paramagnetic impurities in mixed crystals [48, 49]. The presence of superfine structure (S.F.S.) in EPR spectra indicates the absence of dipole–dipole interaction between paramagnetic atoms and thereby testifies to the incorporation of the impurity into the substrate lattice [50]. The high sensitivity of the E.P.R. method (it detects down to \(10^{-12}\) paramagnetic impurity particles), its rapidity, the possibility of using powder-like and single-crystal substances, and its accessibility make it one of the most promising methods for analyzing mixed crystals.

The processes of formation and decomposition of mixed crystals, or the separation of impurities into a separate phase, may be detected by studying thermograms of mixed crystals, since the temperatures of dissociation, melting, phase transitions, and other changes in mixed crystals accompanied by thermal effects differ from those for the pure components [51].

For identifying the type of mixed crystals and the manner of their formation, it is apparently advisable to apply the methods indicated above in the order in which they were listed. In a number of cases it is useful, in order to obtain additional information about the properties of mixed crystals, to use measurements of optical spectra, X-ray diffraction analysis, measurements of hygroscopicity and density, visual observations of changes in color, etc. [47, 52].

When considering the question of the influence of impurities on the thermal stability of mixed crystals, one should expect,

that for isomorphous mixed crystals (solid solutions) thermal stability is determined by the degree of lattice deformation, which depends on the size of the impurity ion. The character of the impurity distribution apparently should not have a substantial effect on the kinetics and rate of decomposition.

For compounds belonging to the first group of Boldyrev’s classification [53], one should apparently expect in this case a decrease in thermal stability; however, in some cases an increase in thermal stability is also possible as a result of the donor–acceptor properties of the impurity [54,55]. For compounds of the second group, both an increase and a decrease in thermostability are possible; this will correlate with changes in the optical and other physical characteristics of the solid solution.

As was already indicated above (Table 1), the laws of distribution can formally be applied also to anomalous mixed crystals; therefore all our subsequent reasoning will also apply to them.

For anomalous mixed crystals formed by methods 2a, 4, 5, and 6, with uniform distribution of the microcomponent throughout the volume of the crystals and in the absence of its adsorption on the surface, nonisovalent impurities, according to Mott–Wagner disorder theory [56,57], cause corresponding changes in the concentration of ionic and electronic defects, as well as deformation and distortion of the lattice at the sites of impurity incorporation. In this case thermal stability is determined first of all by the type and concentration of ionic and electronic defects [58,60], and then by lattice deformation as well. The influence of the impurity will be manifested throughout the entire course of the thermal and photochemical decomposition reaction and will also lead to changes in the rates of formation and growth of nuclei, their concentration, and possibly will cause a change in the decomposition kinetics.

Thus, for the system \(AgC_2O_4-Cu(C_2O_4)_2\), the effect of the additive was manifested up to 80% decomposition, while the rate of formation and growth of nuclei during thermal decomposition substantially

changed [21].

The role of contact phenomena in such mixed crystals is apparently negligibly small; however, they (contact phenomena) may play a competing and even predominant role for systems with limited miscibility, in the adsorption of a portion that has not entered the impurity lattice on the surface of microcrystals. In the case of significant differences in the thermal stability of the impurity and the substrate in such systems, one should expect two rate maxima on the kinetic curves of thermal decomposition, as well as an influence of the decomposition products of the unstable component on the decomposition of the entire system, according to electronic concepts [58, 60]. It is possible that precisely these causes explain the lowering of the melting point and the decrease in photoconductivity and sensitivity to excitation by an exploding flash lamp in crystals of thallium azide doped with potassium cyanide [51]. Characteristically, orange spots are clearly visible on the doped crystals, which is most likely due to the separation of $\mathrm{Tl_2CN_2}$ into a separate phase. As a result of the separation of the impurity into a separate phase, even the nature of the impurity’s influence may change. Thus, Sviridov [62] gives a number of examples of the diverse influence of homophase impurities $\mathrm{Tl}^{++}$, $\mathrm{Pb}^{++}$, $\mathrm{Cu}^{++}$ on the photosensitivity and photolysis rate of silver halides. These impurities either had no effect, or accelerated or decreased the photolysis rate and the photosensitivity of silver halides. This behavior of impurity ions, which is incomprehensible at first glance, is presumably explained by the different influence of impurities that have entered the lattice and those adsorbed on the surface of the crystals.

When the impurity concentration is greatest in the center of the crystal (Fig. 1c), the influence of additives will be manifested at late stages of decomposition, which will cause a change in the growth rate of nuclei and in the value of the maximum reaction rate.

With a surface distribution of a microimpurity (Fig. 1b), the action of additives will be most effective at the initial moment of time, which will change the duration of the induction period owing to a change in the rate of formation of nuclei and their concentration. Apparently, a similar case occurs in work [25], where the action of the homophase impurity $\mathrm{Cu}^{++}$, intro—

in \(NH_4ClO_4\), manifested itself only up to 20% decomposition of ammonium perchlorate. The rate of formation of nuclei and their number per unit surface increased in comparison with “pure” ammonium perchlorate. The rate of growth of the nuclei, according to microscopic observations, did not change.

For mixed crystals formed by method 3, substitution proceeds not ion for ion, but by regions of the lattice, each of which as a whole is electroneutral. Consequently, in such a system we are dealing with microdispersed mosaic structures, whose thermal stability is determined primarily by contact phenomena (melting, mutual diffusion of the reacting particles, electronic processes, etc.) at the boundaries between microheterogeneous regions [58–60], by deformation and distortion of the lattice of the macrocomponent, and by the appearance of an additional number of dislocations.

The distribution of the impurity will not play a significant role here. It should only be noted that, when the impurity has lower thermal stability than the substrate, the impurity will “burn out,” i.e., decompose first. This will lead to anomalous effects on the kinetic curves (the appearance of a second rate maximum), while the thermal stability of such a system will apparently change as a result of processes occurring at the boundary between the substrate and the product of the thermal decomposition of the impurity.

For mixed crystals formed by methods 2 and 6, depending on the synthesis conditions, as occurs for the system \(NH_4Cl{-}CoCl_2{-}H_2O\) [63], both the presence of a miscibility gap and its absence are possible. In the first case, it should be expected that the thermal stability of these mixed crystals will be determined by the same factors as for crystals formed by method 3. In the second case, in their mode of construction these crystals are indistinguishable from true (isomorphic) mixed crystals and, apparently, their thermal stability will be determined by the same factors. The decomposition of individual impurity molecules is also not excluded, especially when the impurity is distributed at the surface.

months (Fig. 1, b).

In conclusion we note that, under real conditions, the picture of the influence of impurities on the thermal stability of solids may be considerably complicated by a possible change in the valence of the additive [64, 65] and by the interaction of adsorbed gases [66] and gaseous decomposition products [67] with the initial substance.

CONCLUSIONS

1. The types of mixed crystals, methods of their formation, and the methods and sequence of their application for identifying mixed crystals have been considered.

2. The possible influence of a microcomponent and of impurity distribution on the thermal decomposition of mixed crystals has been discussed.

The author expresses gratitude to Associate Professors G. G. Savel'ev and M. A. Zakharov for their valuable comments and interest in the work.

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