ELECTROPHYSICAL STUDIES OF THE THERMAL DECOMPOSITION OF SOLID SUBSTANCES

(review)

A. A. KABANOV

(Presented by the scientific seminar of the Department of Radiation Chemistry, CTF)

The study of the mechanism of solid-phase reactions is of great theoretical and practical importance, since many technically important reactions proceed with the participation of solid substances [1—3]. Thermal decomposition reactions are encountered in the metallurgical industry, in the production of ceramic articles, in the manufacture of catalysts for heterogeneous catalysis, in the synthesis of new semiconductor materials and phosphors, in the production of ferrites, and in the decomposition of explosives. As recently as 7 years ago, when solid-phase reactions were considered, attention was paid chiefly to the nature and composition of the final reaction products. The physical aspect of the decomposition process, however, has until now received insufficient attention, although the urgency of this is obvious [3—5] and there is no doubt that this has been one of the reasons why, up to the present, we do not have a complete understanding of the mechanism of the processes occurring in the decomposition even of the simplest inorganic compounds.

There are no systematic works in the literature on the use of electrophysical methods in the study of the electronic and ionic processes of which the thermal decomposition of solids is composed. The existing studies of individual stages of solid-phase reactions using electrophysical methods leave no doubt as to their effectiveness. The most important tasks of solid-state chemistry are the development of simple and reliable methods for investigating elementary reactions in the solid phase and the use of the achievements of the theory of semiconductors and dielectrics in the study of the electronic and ionic stages of such reactions. The accumulation of experimental facts in this direction and their systematization are the principal stage in developing recommendations for the directed change of the rate of solid-phase reactions, for choosing methods of changing the thermal stability and radiation stability of solid substances, and for methods of monitoring the course of reactions.

The purpose of this review is to systematize the results of studies of the thermal decomposition of ionic compounds in which the electrophysical properties of the objects of study were employed.

Studies Using Electrical Conductivity

Macdonald and Sandison [6] used measurements of electrical conductivity to evaluate the shape of reaction nuclei (germs) during decomposi-

of silver oxalate. The study was carried out together with an investigation of the kinetics of decomposition of silver oxalate. The calculations predicted a jump in the electrical conductivity of the specimens at the moment of coalescence of the metallic nuclei at 10–30% decomposition of the oxalate in the case of the formation of flat (plate-like) nuclei. Experimentally, however, a jump was recorded at about 60% decomposition of the preparation. On the basis of the results obtained, Macdonald and Sandison concluded that, during the thermal decomposition of silver oxalate, three-dimensional (spherical) silver nuclei are formed.

Bel’kevich and Osinovik [7] repeated the experiments of the authors of [6] and arrived at the opposite conclusion. In their experiments the coalescence of nuclei occurred at 17–30% decomposition of silver oxalate, which testified in favor of the formation of two-dimensional (flat) nuclei. In [6] the procedure for measuring electrical conductivity and for preparing the specimens is not described. One can only surmise that the experiments were carried out on pressed specimens under continuous application of a constant voltage. Osinovik and Bel’kevich [7] used, in their experiments, specimens pressed in the form of tablets, with a constant voltage of 1.3 V applied. In our view, the discrepancy between the results of [6, 7] may have been caused both by the use of electric fields of different magnitude and by partial tribochemical decomposition of silver oxalate during pressing and during preliminary grinding of the crystals. It is known [4, 8] that the application of an electric field can lead

Fig. 1. Results of V. Garner [11, 12] for lithium aluminum hydride, obtained at 373°K.

to the intensification of chemical reactions, and silver oxalate has a tendency to decompose when ground in a mortar [9].

On the basis of Griffith’s results [10], who, by structural studies of decomposed crystals of silver oxalate, found a layered structure of the nuclei of the new phase, the formation of flat nuclei during the decomposition of $\mathrm{Ag_2C_2O_4}$ appears more probable.

Garner [11, 12] used electrical-conductivity measurements to study the period of decomposition of lithium aluminum hydride, which decomposes at temperatures above 100°C to lithium hydride, aluminum, and hydrogen. According to their data, lithium aluminum hydride is a good semiconductor, and at the decomposition temperature the change in electrical conductivity passes through a maximum (Fig. 1). The segment $AB$ is explained by the authors as an increase in the concentration of $F'$ centers (electron donors), which may be formed during the decomposition of lithium aluminum hydride and through the loss of hydrogen atoms from the surface of the crystals.

$F'$ centers diffuse into the crystal lattice, increasing the conductivity. It is assumed that nuclei of the new phase during the decomposition of lithium aluminum hydride are formed from $F'$ centers when they associate along dislocations and internal surfaces. The decrease in the concentration of $F'$ centers explains the decrease in electrical conductivity in the segment $BC$. The jump in electrical conductivity ($DE$) is associated with the coalescence of aluminum nuclei into a continuous chain between the electrodes. However, similar anomalies in electrical conductivity may also occur when moisture is present in the specimen and during polymorphic transitions [13—16], to which the authors of [11—12] did not pay attention.

Weidenthaler [17] used the results of electrical-conductivity measurements to study the thermal decomposition of silver oxide. He expected proportionality between the degree of decomposition of silver oxide and its electrical conductivity, believing that during decomposition the process

\[ \mathrm{O}^{--} = \square^{-} + 2e + \frac{1}{2}\mathrm{O}_2, \]

takes place, where $\square^{-}$ is an anion vacancy.

As a result of reaction I the concentration of free electrons will increase, and, if silver oxide is an $n$-type semiconductor, the electrical conductivity will increase in proportion to the decomposition. According to Weidenthaler [18], the surface of silver oxide is covered with a layer of $\mathrm{Ag}_2\mathrm{O}_3$, and because of this silver oxide is an $n$-type semiconductor. It is useful to note here that, according to the literature data [19], silver oxide is classified as a $p$-type semiconductor. Weidenthaler [17] carried out experiments on pressed samples of silver oxide and obtained an increase in electrical conductivity with the degree of decomposition. He regarded this fact as evidence that, during the decomposition of silver oxide, accompanied by the formation of silver nuclei, only process I takes place. But Weidenthaler’s results refer to the solid solution $\mathrm{Ag}_2\mathrm{O} + \mathrm{Ag}_2\mathrm{O}_3$ and cannot be extended to other samples of silver oxide. According to Garner and Reeves [20], who measured the electrical conductivity of silver oxide during the thermolysis of “equilibrium” samples (calcined in oxygen), the resistance of silver oxide did not change, and the activation energy of thermolysis was 45.6—56.2 kcal/mole. According to Weidenthaler [17], the activation energy of the thermal decomposition of silver oxide is 8 kcal/mole.

In the works of Boldyrev and Zakharov [3, 21], the influence of induced ionic defects on the kinetics of the thermal decomposition of a number of ionic compounds that are ionic conductors (oxalates, azides, carbonates, etc.) was studied. The results of electrical-conductivity studies were used to assess the type of defectiveness of the structure of ionic crystals and served as one of the methods for recording the formation of solid solutions when univalent impurities were introduced. The formation of solid

substitution solutions in ionic conductors is accompanied by characteristic V-shaped curves in the relative dependence of electrical conductivity on impurity concentration at constant temperature.

The authors showed, in particular, that the electrical conductivity of silver oxalate is effected by interstitial cations. This was confirmed by a decrease in electrical conductivity upon doping silver oxalate with divalent cadmium ions (up to 5 mol%), which lower the concentration of interstitial cations. In parallel experiments on thermal decomposition, a decrease in the rate of thermolysis was found when these additives were introduced at a similar concentration. The activation energy of the electrical conductivity and thermal decomposition of silver oxalate did not change upon introduction of divalent cadmium ions at concentrations up to 5 mol%. The results obtained served to confirm the assumption that reaction nuclei form and grow in silver oxalate owing to electrons from interstitial cations and their association.

MacLaren [4], in studying the initiation of explosion of crystals by a constant electric field at room temperature, found that the resistance of the crystals before explosion fell by 10 orders of magnitude (from \(10^{14}\) to \(10^4\) ohm). The sharp drop in resistance is not associated with silver dendrites. On the basis of the results obtained, MacLaren concluded that the decrease in the resistance of silver azide crystals and their explosion are due to the intensification, by the electric field (above \(250\ \mathrm{V/cm}\)), of electronic processes in silver azide. This, in his opinion, leads to partial decomposition of silver azide and to a thermal explosion due to the energy released during the decay of \(N_3^0\) radicals. The results obtained are of great interest both with regard to the methodology of subsequent electrophysical investigations and with regard to the possibility of initiating explosions by an electric field. However, in discussing his results MacLaren regarded silver azide as an electronic conductor, which is not consistent with the experiments of Young [14], who proved that undecomposed silver azide is an ionic (cationic) conductor.

Laschoff [22], by measuring transport numbers, thermo-e.m.f., and the dependence of electrical conductivity on temperature and oxygen pressure, came to the conclusion that lead chromate is an electronic semiconductor, although its resistance at room temperature is greater than \(10^9\ \mathrm{ohm\ cm}\). In the author’s opinion, this indicates decomposition of lead chromate according to the equation

\[ 2\mathrm{PbCrO}_4 \rightarrow \mathrm{Pb}(\mathrm{CrO}_2)_2 + \mathrm{Pb}^0 + 2\mathrm{O}_2. \tag{2} \]

Laschoff considers that the electron donors in lead chromate are lead reaction nuclei, which dissociate into ions and electrons

\[ \mathrm{Pb}^0 \rightarrow \mathrm{Pb}^+ + \mathrm{e}. \tag{3} \]

In our view, such an explanation of the mechanism of conductivity in lead chromate is insufficient, since electronic conductivity may also be due to the motion of small-radius polarons through the anion sublattice, as in barium titanate, lanthanum cobaltate, and manganites [24—28].

Young [14] investigated electronic and ionic processes in pure and partially decomposed silver azide by measuring various optical and electrophysical characteristics. From the results of dark-conductivity measurements the author drew the following conclusions:

1. The powdered preparation, especially in pressed specimens, sinters without decomposition when heated above \(135^\circ\mathrm{C}\). Sintered

silver azide samples have a higher conductivity than pressed ones. Freshly prepared, undecomposed and unexposed silver azide has neither photoconductivity nor a Hall emf. From these results it was concluded that silver azide is an ionic conductor, and that the analogous samples of McLaren [29], in which photoconductivity was detected, had in all probability been partially decomposed as a result of exposure to light or of natural aging.

1. Silver azide, after partial decomposition, acquires electronic conductivity, as follows from the presence of the Hall effect and photoconductivity. The electronic conductivity in silver azide is explained by the formation of colloidal silver particles (nuclei), which are electron donors.

2. Electronic conductivity appears especially distinctly in partially decomposed pressed samples, whereas in sintered samples it is suppressed by cationic conductivity. It is asserted that, with increasing density of the samples (after sintering, for example), the conditions for the manifestation of ionic conductivity are more favorable, while this factor has practically no effect on electronic conductivity. As confirmation of this conclusion, known cases for silver iodide and silver chloride are cited. In the polymorphic transition near 145°C, the ionic electrical conductivity of silver iodide single crystals increases by 3 orders of magnitude, whereas in polycrystalline silver iodide a jump in electrical conductivity is observed only in the case of preliminary sintering of the sample at 350°C. Further, an increase in the electronic component of the electrical conductivity of silver chloride single crystals during and after photolysis by ultraviolet rays is also observed in pressed samples. But there are contrary examples. Thus, in [30] the conclusion was drawn that silver bromide single crystals are electronic conductors, while polycrystals exhibit predominantly ionic conductivity. The diffusion of different ions in the form of isotopes proceeds more intensively in polycrystals of cuprous oxide than in single crystals [31].

3. In the region of the polymorphic transition in silver azide at 190°C, Young found a jump in electrical conductivity, having a different character in samples in the form of powder poured between metal blocks (Fig. 2) and in the form of pressed tablets (Fig. 3), which agrees

Fig. 2 and 3. Young’s results [14] for silver azide

with his other conclusions (items 1—3). A temperature dependence of electrical conductivity in the form of a Z-shaped curve has also been found for single crystals of potassium nitrate and sodium nitrite [16] at polymorphic transitions, which would be interesting to verify for polycrystals. The significance of Young’s work [14] lies, above all, in its methodological aspect. Using silver azide, the author showed that the choice of a method for electrophysical—

...of studies of thermal decomposition must be approached with great caution, so as not to draw erroneous conclusions when assessing the role of electronic and ionic processes in the elementary stages of thermal decomposition.

Torkar and coauthors [32] used the results of an investigation of electrical conductivity in discussing the mechanism of thermolysis of sodium azide. When sodium azide was heated at a constant rate, several bends were found in the functional dependence of the logarithm of electrical conductivity on the reciprocal absolute temperature. The authors suggested that the low-temperature portion of the conductivity curve is due to cationic conduction by vacancies, while the high-temperature region, with a large activation energy, is due to cationic electrical conductivity by interstitials. In the high-temperature region, during the decomposition of sodium azide there is some decrease in electrical conductivity, which is associated with the consumption of some of the interstitial ions in the decomposition process. Further decomposition leads to an increase in the specific electrical conductivity owing to coalescence of the reaction nuclei (nuclei of the new phase). In measurements in vacuum, after the rise in electrical conductivity, complete coalescence of the nuclei occurs and the electrical conductivity over a certain temperature interval does not depend on temperature, after which breakdown occurs. In measurements in air, after a decrease in the temperature coefficient of electrical conductivity, the activation energy becomes the same as before nucleation, which is explained by destruction of the nuclei at the surface. These data are used to confirm the Mott mechanism of nucleation and growth of nuclei, i.e., with alternate capture of electrons and interstitial ions by nuclei of the new phase.

Thus, the use of electrical conductivity proved to be very useful in investigating the mechanism of thermal decomposition of a whole series of solid ionic compounds. From the review of the literature it is evident that the most detailed studies have been carried out on solid electrolytes, whereas there are few works on semiconductor materials with an ionic structure, although their study is no less important for obtaining, for example, catalysts of chemical reactions, crystallophosphors, and semiconductors by thermal decomposition.

Application of Photoconductivity Studies

Maclaren and Rogers [29] found photoconductivity in undecomposed silver azide in the region of the long-wavelength edge of intrinsic absorption. In partially decomposed samples the photoconductivity maximum shifts into the long-wavelength region, which is associated with the photoeffect from reaction nuclei. From the presence of photoconductivity in silver and lead azides at decomposition temperatures, the authors concluded that the first stage of their decomposition is the transition of an electron into the conduction band with its subsequent capture by an interstitial cation, which creates conditions for the exothermic decay of the radical $\mathrm{N}_3$.

In the light of the results obtained, the possibility is indicated of studying nucleation in azides by photoconductivity measurements and of explaining the causes of the autocatalytic influence of the solid decomposition product of azides. In connection with the proposed mechanism of decomposition of silver azide, a catalytic influence of electron-acceptor additives was predicted, which was confirmed by Mitchell [4]. Yang [14], by means of careful measurements, showed that in freshly prepared...

in silver azide, photoconductivity is absent and appears only upon partial decomposition of the substance. He suggested that all of MacLaren’s samples had been partially decomposed by exposure to light or as a result of natural aging.

Forty and coauthors [33] judged the processes of nucleation during the thermal decomposition of lead iodide from the change in the photoconductivity of partially decomposed samples. In lead iodide, at the moment of formation of reaction nuclei, the photoconductivity decreases, which is associated with the acceptor properties of nuclei consisting of lead atoms. It was found that the process of formation of lead embryos in lead iodide proceeds very rapidly at 180°C owing to the association of \(F\)-centers or anion vacancies with free electrons. The presence of photoconductivity was explained by the dissociation of excitons with the formation of a free electron and a hole. Two positive holes, on reacting, give an iodine molecule, which is the second product of lead iodide. The formation of lead embryos may also occur through the trapping of free electrons by interstitial cations. Stable reaction nuclei can form from four lead atoms.

Didman and Lewis [34] investigated the photoconductivity of lead azide in order to establish a correlation between electrophysical properties and the kinetics of decomposition of lead azide. It was found that the results of measuring dark conductivity and photoconductivity on poly- and single crystals of lead azide do not coincide. Thermal treatment increased the dark electrical conductivity and photoconductivity, which may be due to partial decomposition of the substance. The presence of photocurrent was explained by dissociation of excitons with the formation of free electrons. The energy of exciton dissociation was calculated from the temperature dependence of photoconductivity. The increase in photoconductivity in a partially decomposed crystal is explained by a change in the mobility of electrons.

Boldyrev and Skorik [35] investigated the photo- and gamma-conductivity of silver and barium azides under conditions of their thermal decomposition. During decomposition of barium azide, a noticeable increase in electrical conductivity was observed when the samples were irradiated with X-rays at a dose rate of 110 rad/min. In the process of decomposition of silver azide, neither gamma- nor photoconductivity was detected. In discussing the results obtained, the authors considered that the decomposition of silver and barium azides proceeds through the formation of free electrons with their subsequent capture by interstitial cations.

The authors concluded that the rate of thermal decomposition of azides may be proportional to the concentration of free electrons if their number is smaller than the number of traps capable of capturing electrons. It is assumed that such a case occurs in barium azide, the decomposition rate of which increases during decomposition under irradiation with X-rays. On the basis of the results obtained, the limiting stage of the thermal decomposition of barium azide is considered to be the excitation of an electron in the anion into the conduction band. For silver azide no change in the rate of thermolysis was found upon irradiation at the moment of decomposition. From this fact it was concluded that, in silver azide, the transfer of electrons to the conduction band is not the rate-limiting stage of decomposition.

Zakharov and Savel’ev [21, 36], from the absence of photoconductivity in silver sulfite and oxalate, concluded that the thermal decomposition of these substances proceeds with excitation of electrons from the valence band to exciton levels, and not to the conduction band. These experiments also served as one of the proofs that sulfite and oxalate belong

silver to ionic conductors. Measurements of photoconductivity were performed on pressed specimens. Photoconductivity, like the Hall effect, is undoubtedly [37, 38] among the most accurate and unambiguous methods for detecting electronic conductivity in ionic compounds; however, the fact that these effects are zero does not yet prove the absence in the material of appreciable (and often predominant) electron or hole conductivity [38]. This is due to the dependence of photoconductivity and the Hall emf [38] on the mobility of charge carriers, which limits the capabilities of modern apparatus and methods for measuring these characteristics. In [39] the value of the electron (hole) mobility is given as \(0.04\ \text{cm}/\text{V sec}\), corresponding to the sensitivity limit of modern Hall-effect setups.

Thus, conclusions about an exciton mechanism for the initial stage of thermal decomposition of ionic compounds cannot be drawn solely from the absence of photoconductivity and the Hall effect without involving additional studies—for example, transport numbers, thermoelectric emf, and measurements of electrical conductivity in an oxygen atmosphere.

Use of contact phenomena for the study of solid-phase reactions

Recently [40—43], in discussing the mechanism of catalysis and autocatalysis of solid-phase reactions, electronic effects at the metal–semiconductor contact and between semiconductors [37, 44, 45] have begun to be invoked. From the standpoint of contact phenomena, the electronic mechanism of catalysis and autocatalysis in topochemical reactions reduces to the transfer of electrons into the material with the larger work function. For example, if free electrons exert an inhibiting influence on the rate of decomposition of an ionic crystal, then their removal from the reaction zone by the contact electric field should lead to an increase in the rate of thermal decomposition of the ionic compound.

In this case, the work function of electrons from the additive or decomposition product must be higher than that of the decomposing substance. The effectiveness of the additive will be determined by the thickness of the layer of decomposing substance depleted of electrons by the contact field. The mechanism of electronic catalysis of solid-phase reactions is analyzed in greater detail in [43].

B. V. Erofeev [40] was the first to use electronic effects at a metal–semiconductor contact in discussing the mechanism of solid-phase reactions. On the basis of the assumption of the inhibiting role of free electrons, the author concluded that the rate of thermal decomposition of azides of divalent metals would increase with increasing contact potential difference between the metal (the decomposition product) and the azide. Erofeev believed that in solids with the same anion and cations similar in the structure of their electron shells, the electron work function would be the same and the rate of thermolysis should increase in sympathy with the work function from the metal—the decomposition product. As an example the author used the azides of barium, strontium, and calcium. The hypothesis itself of the autocatalysis mechanism (acceptor electronic catalysis) is quite realistic for azides [3—5], but the evidence used for it is not very convincing. First, there are no grounds, from the assumptions made, to expect equality of the electron work functions for barium, strontium, and calcium azides, which have different crystal lattices [46]. For this, direct experiments on the electron work function from the azides taken under decomposition conditions are needed; such experiments are not present in the work of [40]. Further, even assuming equality of the work functions for

azides, it is necessary to use data on the electron work function from metals—the products of azide thermolysis—taking into account not only the decomposition conditions (the author gives data on the electron work function without indicating the temperature), but also the form in which the metal is liberated into the decomposition products. Most probably [14, 29], the metal is liberated in colloidal form with a grain size of less than 100 Å. For example, during the decomposition of silver oxalate [47] the final size of the silver nuclei is 20–50 Å. It is known [48] that, beginning at 100 Å, the electron work function of solids increases exponentially as the particle size decreases, approaching the ionization potential of the corresponding element. Thus, the evidence used by Erofeev to confirm the proposed mechanism of electronic autocatalysis in barium, strontium, and calcium azides is not sufficiently rigorous, and Erofeev’s merit lies in the fact that he was the first to draw attention to the important role of contact fields in solid-phase catalysis.

Savel’ev and Zakharov [41] used electronic effects at the silver oxalate–ionic semiconductor boundary in discussing the mechanism of thermolysis of silver oxalate with additions of nickel and zinc oxides. The authors found a bell-shaped dependence between the rate of thermolysis of silver oxalate and the electron work function of the additives. Attention was drawn to the need to ensure close contact between the additive and the substance being decomposed in order to increase the probability of the manifestation of electronic catalysis. The authors achieved close contact by introducing the additive during crystallization of the silver oxalate. It was shown that, in the case of nickel oxide as an additive, the acceleration of thermolysis from simple mixing of the reaction components is much smaller.

A correlation was found between the decomposition rate of potassium permanganate, ammonium perchlorate, and potassium chlorate and the work function of a whole series of oxides in the available literature data. From these facts a conclusion was drawn that thermolysis is accelerated for all four preparations upon the addition of semiconductor electron acceptors. Among the shortcomings of [41] are (as in Erofeev’s work) the lack of attention to the possible change in the electron work function of the reaction components under decomposition conditions and the use, for comparison, of literature values of work functions obtained by different methods, since such a comparison cannot be made [49, 50].

In another work [43], Zakharov and Savel’ev gave a more detailed analysis of the electronic mechanism of catalysis in solid-phase thermal-decomposition reactions, taking into account possible stages limiting the process of decay of ionic crystals. The analysis was carried out on the basis of a thermal-decomposition scheme that includes the following electronic stages:

1. Detachment of an electron from an anion with formation of a free electron and a hole according to the scheme

\[ A^- \rightleftarrows A^0 + \overline{e} \qquad \text{or} \qquad A^- A \rightleftarrows {}^0_T + \overline{e}, \tag{4} \]

and if the reaction is irreversible, then

\[ A^- \to A^0_T + \overline{e}, \tag{5} \]

where the subscript \(T\) refers to a special state of the ion at the surface in a defective lattice site or near it.

1. Trapping of an electron by a cationic site

\[ K^+_T + \overline{e} \rightleftarrows K^0_T. \tag{6} \]

1. Formation of the final decomposition products \(P_1\) and \(P_2\) by the reactions

\[ A_T^0 \to P_1, \tag{7} \]

\[ K_T^0 \rightleftarrows P_2. \tag{8} \]

The authors believed that, upon introducing electron-acceptor additives into the decomposing substance, the rate of thermolysis would increase only in the case where the decomposition process is limited by stages 4 and 7, and would decrease in the case where the solid-phase reactions are limited by stages 6 and 8. When electron-donor additives are introduced, one should expect an increase in the thermolysis rate when decay is limited by stages 6 and 8, and a decrease when thermolysis is limited by elementary stage 7. It is assumed that contact electric fields will have no effect on the thermolysis rate if the decomposition process is limited by stage 4 with formation of an exciton rather than a free electron.

In a short communication [51], Zakharov and coauthors note a sigmoidal dependence of the thermolysis rate of silver azide, oxalate, and nitrite, and of barium and copper azides, on the work function of electrons from heterogeneous additives. A change in the activation energy of the thermolysis process upon introducing decomposition-catalyst additives was observed. The viewpoint is again expressed concerning the decisive role of contact electric fields in the catalysis of solid-phase reactions of the thermal decomposition of ionic compounds by semiconductor additives. On the basis of experimental data it is assumed that, in the case of decomposition of silver sulfite, a change in the electron concentration in the reaction zone has no effect on the rate of decomposition of silver sulfite.

In work [52], Zakharov already specifically states that the catalytic activity of additives correlates clearly with the work function of electrons from semiconductors, measured under conditions corresponding to those of decomposition of the specimen.

Boldyrev and coauthors [42], in order to confirm the proposed idea of the existence in potassium permanganate of electron-acceptor autocatalysis by manganese dioxide, used preliminary measurements of the work function of electrons from potassium permanganate and manganese dioxide, carried out at room temperature by the vibrating-capacitor method. The work function of electrons from manganese dioxide was found to be 5.48 eV and 4.76 eV for potassium permanganate. Consequently, electron-acceptor catalysis is quite possible. But such proof of the autocatalytic influence of manganese dioxide in the thermolysis of potassium permanganate raises a number of objections. For example, the assessment of the direction of electronic transitions at the \(KMnO_4\)–\(MnO_2\) boundary was made on the basis of measurements of the electron work function under conditions far removed from the conditions of decomposition of potassium permanganate. Further, in the experiments manganese dioxide of unknown modification was used, and the modification of manganese dioxide in the decomposition products of potassium permanganate was not determined.

It is known [53] that manganese dioxide has two stable modifications (\(\beta\) and \(\gamma\)), differing in electrophysical properties and catalytic activity [54]. In addition, manganese dioxide can exist in an amorphous form [53]. Thus, in the experiments of the authors of work [42] it was necessary to use manganese dioxide isolated from the decomposition products of potassium permanganate and to compare the ra-

work functions for electron emission from potassium permanganate and manganese dioxide under conditions close to decomposition.

In an amorphous decomposition product, in the case of electronic catalysis, there is a greater possibility of accelerating thermolysis due to the larger electron work function than in crystals of an analogous chemical compound. It is known [37, 44, 45] that the electron work function from a crystal consists of two components:

\[ \varphi = W + \frac{\Delta E}{2}, \tag{9} \]

where

\(W\) is the work of the electric image forces,
\(\Delta E\) is the width of the forbidden band of the semiconductor.

When an ionic compound passes into the amorphous state, owing to a decrease in density, the width of the forbidden band, as a rule, increases [37, 55]. Since there are no grounds to expect a change in the work of the electric image forces [37, 44, 56, 57] while the short-range order in the arrangement of atoms (ions) is preserved, the electron work function upon transition to the amorphous state should increase. For example, iodine, known as a semiconductor [58], has \(\varphi = 2.8\ \mathrm{eV}\) for the rhombic lattice; \(5.4\ \mathrm{eV}\) for the monoclinic lattice; and \(6.8\ \mathrm{eV}\) in the amorphous state [59]. Figure 4 presents band diagrams of various

Fig. 4. Band diagrams of semiconductors: \(E_1\)—upper level of the valence band, \(E_2\)—lower level of the conduction band, \(E_3\)—electron level in vacuum, \(F\)—Fermi level, \(A\)—acceptor levels, \(D\)—donor levels; \(a\)—\(n\)-type semiconductor, \(b\)—\(p\)-type semiconductor, \(v\)—intrinsic semiconductor, \(g\)—amorphous semiconductor.

types of semiconductors, which clearly explain the difference in their work functions [37, 38, 60, 59]. It is also interesting to note that amorphous semiconductors do not exhibit impurity conductivity [55], although they are capable of forming solid solutions with impurities.

Thus, the study of contact electric fields under decomposition conditions is necessary for proving the presence of electronic catalysis in the decomposition of solid ionic compounds with heterophase additives.

Use of Dielectric Permittivity and the Dielectric Loss Tangent in Topochemistry

In [61], by low-frequency dielectric permittivity \((\varepsilon_{\mathrm{st}})\) and \(\operatorname{tg}\delta\), the polymorphic transition in pressed specimens was evaluated—

decomposition of potassium nitrate at 129°C. At this temperature a sharp jump in \(\varepsilon_{\mathrm{st}}\) (by a factor of 2.72) and in the tangent of the dielectric-loss angle (by a factor of 136) was found. It was already known in the literature [16] that, in potassium nitrate single crystals at 129°C, the electrical conductivity increases abruptly by approximately a factor of 100. Therefore, comparison of various electrophysical characteristics facilitates elucidation of the mechanism of polymorphic transitions, which may be one of the stages of the thermal decomposition of ionic crystals.

The increase in \(\varepsilon_{\mathrm{st}}\) noted in [61] is evidently connected [62] with an increase in the coefficient of elastic ionic polarizability \((\alpha_l)\), due to weakening of the quasi-elastic bonding of ions in the lattice upon a sharp increase in the mobility of charge carriers [63] during the polymorphic transition, and to a decrease in the density of the crystal. The increase in \(\operatorname{tg}\delta\) is most likely connected with an increase in energy losses due to through conductivity [62], which agrees with the approximately equal increase in electrical conductivity. Thus, the use of \(\varepsilon_{\mathrm{st}}\) and \(\operatorname{tg}\delta\) in the study of ionic processes in solid-phase reactions may prove to be a very useful supplement to the results of electrical-conductivity measurements.

In [4, 27, 29, 34], in calculating the optical \((\Delta E_0)\) and thermal \((\Delta E_T)\) excitation energies of electrons into the conduction band, the low-frequency and high-frequency \((\varepsilon_\infty)\) dielectric constants were used. In doing so, Mott’s relation [64] was applied:

\[ \frac{\Delta E_0}{\Delta E_T} = \frac{\varepsilon_{\mathrm{st}}}{\varepsilon_\infty}. \tag{10} \]

Boldyrev and Medvinskii [65] had already noted that Mott’s formula, derived from crude assumptions without a rigorous theoretical basis, cannot be used for such calculations. In addition to the critical remarks concerning Mott’s formula already made in [65], some facts from solid-state physics may be added (Table 1). In semiconductors with covalent bonding, \(\Delta E_0 = \Delta E_T\) [37, 38]. For ionic compounds with appreciable electronic conductivity these quantities are also close. Table 1 presents ionic photoconductors. \(\Delta E_0\) was calculated by the authors of [38, 58, 67, 68] from the maximum of photoconductivity and the long-wavelength edge of optical absorption \((\lambda_g)\) by the formula

\[ \Delta E_0 = \frac{1.234 \cdot 10^4}{\lambda_g}, \ \mathrm{eV}. \tag{11} \]

where \(\lambda_g\) is in m\(\mu\).

Table 1

Experimental verification of Mott’s formula

The ionicity of the chemical bond \((i)\) was calculated by Bashanov [68], and \(\Delta E_T\) was calculated by the authors of [38, 58, 67—70] from the temperature dependence of the electrical conductivity in the region of intrinsic electronic conductivity (except for halides), using the formula [67]

\[ \Delta E_T=-3.97\,\frac{\lg\sigma_1-\lg\sigma_2}{\left(\dfrac{1}{T_1}-\dfrac{1}{T_2}\right)10^4},\ \text{eV} \tag{12} \]

In alkali-halide crystals, the electronic conductivity and the corresponding absorption band are due to \(F\)-centers [61]. Sikorskii [71] showed that the polarizability of the \(F\)-center in sodium chloride is so small that the change in \(\varepsilon_{\mathrm{st}}\) caused by coloration may be neglected, since in the best case it does not exceed \(\pm 0.02\), and in the case of coloration by X-rays it is equal to \(\pm 0.001\). Thus, the results for typical ionic photoconductors (Table 1) do not confirm Mott’s formula. The calculation of the activation energy of thermal decomposition of thermolysis from \(\Delta E_0\) using Mott’s formula has still less justification.

Zakharov and coauthors [72] found anomalies in the isotherms of \(\varepsilon_{\mathrm{st}}\) and \(\operatorname{tg}\delta\) of silver oxalate with additions of lead and cadmium ions. Similar dependences have also been found by us for silver azide with additions of \(\mathrm{CO}_3^{--}\) and \(\mathrm{Pb}^{++}\) ions [73]. Investigations in this field can provide an additional electrophysical method for evaluating the formation of solid solutions, which is necessary in studying the mechanism of reactions in the solid phase, where the method of isovalent homophase additives is widely used in connection with the possibility of creating a definite type of defects in ionic crystals [3, 21].

Because of the small number of experimental results on the use of \(\varepsilon_{\mathrm{st}}\) and \(\operatorname{tg}\delta\) in topochemical studies, it is still difficult to assess the possibilities of using these characteristics in elucidating the mechanism of thermal decomposition of ionic crystals. One may only suppose that the use of these characteristics in studies of thermal decomposition may contribute to a deeper understanding of ionic processes in the crystal and will make it possible to follow their change during the decomposition of solid ionic compounds.

Prospects for the Application of Thermo-e.m.f. in the Study of Topochemical Reactions

Up to the present time, the well-studied phenomenon of thermo-e.m.f. has hardly been used in investigating the mechanism of solid-phase reactions, although the technique for measuring thermo-e.m.f. is not complicated. The simplest analysis of the known experimental results on the thermo-e.m.f. of ionic crystals makes it possible to identify a range of questions important for topochemistry that can be solved by investigating thermo-e.m.f.

1. Registration of the formation of solid solutions in semiconductors with an ionic crystal lattice from anomalies in the isotherms of the differential thermo-e.m.f. [74, 79].

2. Distinction in semiconductors between electronic conductivity and hole conductivity by the sign of the thermo-e.m.f. [37, 38]. From the thermo-e.m.f. one can evaluate the type of conductivity even in the case when it is impossible to detect the Hall effect and photoelectric effects (for example, in the case of electronic conductivity in the form of small-radius polarons) [38, 76—78].

3. Distinction of ionic conductivity via interstitial sites from conductivity

with respect to vacancies by the sign of the thermo-e.m.f. in solid electrolytes, since these types of conductivity are in the same relation as electrons and holes in semiconductors [79].

1. Calculation, from the differential thermo-e.m.f., of the activation energy of electrical conductivity \((E_\sigma)\) in the region of intrinsic ionic conductivity [80, 81] according to the formula

\[ E_\sigma=\alpha_T T,\ \text{eV}, \tag{13} \]

where

\[ \alpha_T \]
is the differential thermo-e.m.f. in \(\text{V/deg}\),

\[ T \]
is the temperature in \({}^{\circ}\mathrm{K}\).

1. Calculation of the concentration of electrons \((n)\) and holes \((p)\) at specified temperatures, which makes it possible to follow their changes during the decomposition of ionic compounds. This is best done by the Pisarenko formula [37, 82], which, when one type of conductivity predominates, can be written for ionic semiconductors in the form

\[ \lg(n,p)=57.28-1.5\lg m^*_{n,p}+1.5\lg T-5.03\cdot10^3/\alpha_T, \tag{14} \]

where

\[ n \text{ and } p \]
are the carrier concentrations, \(\text{cm}^3\);

\[ m^*_{n,p}=\text{const}\cdot m_0 \]
is the effective mass of the electron or hole, g;

\[ m_0 \]
is the mass of the electron at rest, g; \(\alpha_T\), \(\text{V/deg}\); \(T\), \({}^{\circ}\mathrm{K}\).

Kontorova [82] showed that the Pisarenko formula may be applied up to a concentration of \(10^{20}\ \text{cm}^{-3}\) at \(300^{\circ}\mathrm{K}\). In this case, for \(n<2\cdot10^{19}\ \text{cm}^{-3}\) the calculation error is less than \(\pm 0.64\%\), while for \(n=10^{20}\ \text{cm}^{-3}\) the error is \(\pm 10\%\). The concentration of free electrons (holes) in semiconductors varies within the limits \(10^{10}\)–\(10^{21}\ \text{cm}^{-3}\) [83]. In calculations of the concentration of charge carriers by formula (14), the effective mass is usually set equal to the rest mass of the electron [84–86]. But in the region of impurity conductivity of ionic semiconductors it can also be estimated more accurately from the dielectric constant [37, 58, 67]

\[ \Delta E_{\mathrm{p}}=\frac{13.5}{\varepsilon_{\mathrm{st}}^{2}}\cdot\frac{m^*}{m_0}\ \text{eV}, \tag{15} \]

where \(\Delta E_{\mathrm{p}}\) is the ionization energy of impurity levels.

For \(\varepsilon_{\mathrm{st}}\ge 10\), the electron wave functions encompass several lattice constants [37], which makes it possible to estimate the polarization by conduction electrons of neighboring regions from a macroscopic characteristic—the low-frequency dielectric constant.

The thermo-e.m.f. effect has one essential “drawback”: unlike the Hall effect and photoconductivity, in the analysis of electronic and ionic processes it may be caused by any type of charge carrier. But even in the case of mixed (electron–ion) conductivity, by using the results of measurements of transport numbers (by the Tubandt method [80]) and electrical conductivity, one can decide the question of the type of conductivity and then carry out the necessary calculations. Owing to the extremely low mobility of ions, ionic thermo-e.m.f. usually appears in the region of intrinsic conductivity, where the concentration of ions participating in conduction and their mobility become sufficient to obtain a noticeable thermoelectric current. This is indicated by the known experimental results (which, admittedly, are very few) on the thermo-e.m.f. of sodium chloride [81], silver chloride and bromide [87].

The results of Reinhold’s thermoelectric measurements [87] for silver sulfide, selenide, and telluride, attributed to ionic thermoe.m.f., are open to doubt, since these materials are known as semiconductors [38, 79, 88, 89].

Using formula (13), one can estimate the presence of intrinsic ionic conductivity from the ratio of the activation energy of electrical conductivity to the value of the differential thermoe.m.f. For example, according to the data of [87], for silver bromide at \(127^\circ—327^\circ\text{C}\), \(\alpha_{\text{T}} = 0.6\ \text{mV/deg}\) and lies in the region of intrinsic conductivity [80] with \(E_\sigma = 0.78—0.89\ \text{eV}\) [80, 90]. From formula (13) we obtain the value \(E_\sigma = 0.84—0.6\ \text{eV}\), which agrees with the results obtained from electrical conductivity.

Among studies of the thermal decomposition of solid ionic compounds using thermoe.m.f., one can point only to the work of Yang [14], who, in addition to thermoe.m.f., used the results of studies of absorption and reflection spectra, measurements of the Hall effect, dark electrical conductivity, and photoconductivity to elucidate the mechanism of decomposition of silver azide. With the aid of thermoe.m.f., it was intended to confirm the conclusions and assumptions made by the author from other electrophysical investigations. The thermoe.m.f. was measured at a temperature difference at the contacts of \(2—3^\circ\text{C}\), on pressed specimens, in an atmosphere of oxygen and nitrogen. The specimens were clamped between two metal blocks at a pressure of \(1\ \text{kg}/\text{cm}^2\). The author studied the dependence of the differential thermoe.m.f. on the mean temperature of the specimen. The specimens studied were pressed and sintered, previously ground and unground, and also partially decomposed.

Figure 5 gives one of the curves for silver azide partially decomposed to \(1\%\) and then strongly ground in a mortar before pressing. The segment \(ab\) is explained by the dominance of electrons in the electrical conductivity of silver azide. During sintering of the particles above \(135^\circ\text{C}\), cationic conductivity begins to displace electronic conductivity (segment \(bv\)). During the polymorphic transition, the intergranular contact is disrupted owing to the decrease in volume upon transition to the high-temperature form. The contribution of electrons to the total electrical conductivity then again increases, and the thermoe.m.f. decreases, passes through zero, and gives a sharp peak at the temperature of the polymorphic transition.

Fig. 5. Dependence of thermoe.m.f. on temperature for silver azide according to Yang’s data [14]

Further, sintering of azide particles again occurs, and cations begin to dominate in the electrical conductivity (segment \(de\)). This explanation of the functional dependence shown in Fig. 5 confirms the conclusions drawn by the author from other measurements. In the method used by Yang for measuring the differential thermoe.m.f., there is a serious drawback—the use of a low temperature gradient, which can give a large error in calculating the thermoe.m.f. [91]. In studying the differential thermoe.m.f., it is best to use a temperature difference at the contacts of not less than \(10^\circ\text{C}\) [37, 92].

Thus, by studying the thermal e.m.f. one can determine a whole series of characteristics necessary for solid-state chemistry; however, for an unambiguous interpretation of the results it is necessary to bring in other electrophysical properties as well, for example: electrical conductivity, photoconductivity, transport numbers, and the Hall e.m.f.

It is quite evident from the review presented that electrophysical studies can provide substantial assistance in the study of various stages of decomposition and in elucidating very important details of the mechanism of thermal decomposition of ionic compounds. The accumulation of experimental facts in this direction, the improvement and search for new experimental methods for investigating solid-phase reactions, is an important task of the theory and practice of solid-state chemistry.

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Noted Misprints