Kinetics of the thermal treatment of an iron-molybdenum catalyst

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stage of the thermal treatment of an iron–molybde num catalyst. The aim of this work was to study the dehydration and decomposition of impurities and phase ...

ISSN 00231584, Kinetics and Catalysis, 2014, Vol. 55, No. 5, pp. 649–655. © Pleiades Publishing, Ltd., 2014.687 Original Russian Text © A.O. Kostynyuk, F. Gutenuar, A.N. Kalashnikova, Yu.V. Kalashnikov, N.V. Nikolenko, 2014, published in Kinetika i Kataliz, 2014, Vol. 55, No. 5, pp. 681–687.

Kinetics of the Thermal Treatment of an Iron–Molybdenum Catalyst A. O. Kostynyuka, F. Gutenuarb, A. N. Kalashnikovaa, Yu. V. Kalashnikova, and N. V. Nikolenkoa, * a

Dnepropetrovsk State University of Chemical Technology, Dnepropetrovsk, Ukraine b Laboratoire des Oxydes et Fluorures, Universite du Maine, France *email: [email protected] Received September 25, 2013; in final form, March 26, 2014

Abstract—The samples of iron molybdate obtained by the mixing of the solutions of ammonium heptamo lybdate and iron nitrate were studied by thermal analysis. The temperature ranges and kinetic parameters of dehydration processes, the decomposition of impurities, and a topochemical reaction between iron and molybdenum oxides were determined. Data on the concentrations of solid phase components as functions of the temperature and duration of heat treatment were acquired. DOI: 10.1134/S0023158414050073

INTRODUCTION The oxidation of methanol in an excess of atmo spheric oxygen on an iron–molybdenum oxide cata lyst, which is a mixture of iron(III) molybdate and molybdenum trioxide with the molar ratio Mo/Fe = 2–5 in terms of chemical composition, is currently considered as the most resourcesaving method of formaldehyde production. Although this catalyst has been successfully used in industry, its studies and improvement continue until now [1–3]. The activity and selectivity of an iron–molybde num catalyst is a problem of considerable current interest for its operation. It has been reliably estab lished that the presence of an iron oxide impurity irre versibly decreases its selectivity in the partial oxidation reaction of methanol. Previously, based on a study of the thermodynamic equilibrium of the Fe 3+ −MoO 24 − system and an investigation of iron molybdate precip itates by Xray diffraction (XRD) and electronprobe analysis, Nikolenko et al. [4] demonstrated that the impurities of iron oxide compounds were present in them even at the stage of precipitation. Subsequently, it was established that the prolonged thermal treat ment of a mixed precipitate of iron molybdate with molybdenum trioxide (a Mo/Fe molar ratio of >1.5) at temperatures higher than 350°С makes it possible to decrease the iron oxide impurity content because of the occurrence of a topochemical reaction between iron and molybdenum oxides. From the practical point of view, it is of interest to study in detail the pro cesses of the thermal treatment of iron molybdate pre cipitates and to determine the optimum duration of a stage of the thermal treatment of an iron–molybde num catalyst. The aim of this work was to study the dehydration and decomposition of impurities and phase formation in the precipitates of iron molybdate obtained by the

mixing of ammonium heptamolybdate and iron nitrate solutions. For this purpose, the steps of pro cesses were examined by thermal analysis and the tem perature ranges and kinetic parameters of thermal decomposition steps were determined. Based on the results, a mathematical model of thermal treatment was developed and tested by XRD analysis and studies performed in a model flow reactor. EXPERIMENTAL The 1 M solutions of Fе(NО3)3 ⋅ 9H2O and (NH4)6Mo7O24 ⋅ 4H2O prepared from chemically pure reagents were used in the experiments. Iron molybdate was precipitated by continuous crystallization at low degrees of mother liquor supersaturation [5]: the solu tions of iron and molybdenum salts were added in small portions to 600 mL of a 0.1 M solution of nitric acid at a temperature of 70°С. The suspension was stirred with a propeller agitator at a rotation speed of 300 rpm. In the process of precipitation, the solution was adjusted to constant pH ~1 by introducing addi tional amounts of a 0.1 M solution of HNO3 if neces sary. The resulting solution with a precipitate was evaporated to a moist state and then dried in a vacuum at room temperature. Thermal analysis was performed on an SDT Q600 system (TA Instruments, United States) in a tempera ture range from 20 to 700°С in a flow of nitrogen (50 mL/min) at a heating rate of 1.5 or 10.0 K/min. Tem peratures higher than 700°С were not used because of the possible sublimation of molybdenum(VI) oxide. The kinetic studies for the determination of the mechanism of topochemical interaction between the iron and molybdenum oxides were conducted under isothermal conditions. The oxides were prepared from iron hydroxide and molybdic acid, which were obtained by the addition of ammonia and nitric acid



KOSTYNYUK et al. ΔT, °C 2 1 0

Weight, mg 32



–2 –4






same size. All of the experiments were conducted at a 3 vol % initial concentration of methanol vapor. To reach a steady state in the processes of mass and heat exchange, all of the measurements were started not sooner than 30 min after the establishment of a neces sary reaction mixture flow rate and the heating of the reactor to a specified temperature. Based on the data on the reaction product composition at the reactor outlet, a material balance was calculated, the precision of which served as a validation criterion for the cor rectness of the executed analysis.

16 –10 0


400 600 Temperature, °C


Fig. 1. Results of studying the thermal decomposition of a catalyst sample with the molar ratio Fe/Mo = 1 : 2.2 by (1) TGA and (2, 3) DTA at heating rates of (1, 3) 10.0 and (2) 1.5 K/min.

solutions to the solutions of iron nitrate and ammo nium heptamolybdate, respectively. The resulting pre cipitates were washed with distilled water on a Buch ner funnel for the removal of associated electrolytes, dried at 150°С, and thoroughly ground in a porcelain mortar. The Mo/Fe ratio was 1.9 : 1. After thoroughly mixing, the obtained samples were subjected to extru sion at a pressure of 10 MPa; then, they were calcined at temperatures of 400–500°С for 120, 180, 240, or 360 min. The rate of heating in a muffle furnace was 20 K/min. The concentration of a molybdenum oxide phase in the samples obtained after calcination was determined by quantitative XRD analysis; the mea surements were repeated three times, and the arith metic mean values were used in the subsequent calcu lations. All of the results were checked with the aid of a Qtest with a confidence coefficient of 90%. XRD analysis was carried out on an X’Pert Pro dif fractometer (PANalytical, Netherlands) using mono chromatic CuKα1 radiation with a wavelength of 1.54056 Å and a linear correction with a wavelength of 1.54433 Å. Diffraction patterns were analyzed using the Match!2 software, which makes it possible to carry out the qualitative and quantitative identification of diffractograms. The catalytic oxidation of methanol was studied in a model Ushaped flow reactor as a tube with an inside diameter of 9 mm. The bulk volume of a catalyst was 7.0 cm3. The reactor was placed in a tube furnace; the temperature was regulated automatically to within ±5°С by means of a thermoregulator. A thermocouple was located inside the reactor in the middle part of the catalyst bed. In order to obtain nearly isothermal con ditions of the experiment, a powdered catalyst with particle sizes of 0.25–1 mm was mixed with a fourfold amount of an inert filler, silicon carbide particles of the

RESULTS AND DISCUSSION In preliminary experiments, we found that the pre cipitates of iron molybdate and hydrated molybdenum trioxide were formed on the gradual addition of the solutions of iron and molybdenum salts at the molar ratio Fe/Mo = 1 : 2.2 to a relatively large volume of a 0.1 M solution of nitric acid; reflections due to an impurity phase of Fe2O3 were absent from the Xray diffraction patterns of these precipitates. At the same time, the study of the precipitates by thermal analysis showed that the impurities of precursor salts were present in their composition. It is obvious that these impurities can decompose on the subsequent thermal treatment with the formation of the oxides of iron and molybdenum. Therefore, it was of interest to study the kinetics of decomposition of the impurities in a matrix of iron molybdate for determining optimum condi tions for the calcination of contact mass to reliably ensure a decrease in the iron oxide content. For determining the kinetic parameters of impurity decomposition processes, we examined the catalyst contact mass precipitates by thermogravimetric and differential thermal analysis (TGA and DTA, respec tively). As an example, Fig. 1 shows the results of the analysis of a sample of the airdry contact mass with the molar ratio Fe/Mo = 1 : 2.2. The thermograms indicate that thermal transfor mations in the sample were accompanied by a contin uous decrease in its weight up to a temperature of 360°С. The total weight loss of the sample weighing 32 mg was 52.8%. The curve has four sections charac terized by different rates of weight changes. The differ entiation of this curve showed that maximum rates of weight changes were observed at temperatures of 113, 203, 250, and 326°C. The DTA data (Fig. 1, curve 3) indicate that changes in the sample weight occurred with either heat absorption (three endotherms with minimums at 113, 250, and 326°C) or heat release (two exothermic effects with maximums at 203 and 342°C). As is well known, heat absorption in the initial sections of the DTA curves of the airdry samples of oxides and of hydroxides obtained by precipitation from aqueous solutions is caused by the evaporation of hydration water. Therefore, the endotherm at of 113°С can be described as the dehydration of iron molybdate. It is KINETICS AND CATALYSIS

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likely that the distinct exotherm with a maximum at 203°С is caused by the decomposition of ammonium nitrate, which resulted from the interaction of iron nitrate with ammonium molybdate and remained in the precipitate after drying. Ammonium nitrate melts at 169.6°С, and it decomposes at 200°С with heat lib eration. According to published data [6], the following reactions can occur on the heating of ammonium nitrate: NH4NO3 → NH3 + HNO3, NH4NO3 → N2O + 2H2O, NH4NO3 → 0.8N2 + 1.8H2O + 0.4HNO3, NH4NO3 → N2 + 0.5O2 + 2HNO3. The origin of the endotherm at 250°С can be explained by the presence an impurity of nitrate ions bound to the cations of iron(III) in the samples: 2Fe(NO3)3 → Fe2O3 + 3N2O↑ + 6O2↑. Shaheen [7] noted the possibility of iron nitrate decomposition at 250°С. We failed to confirm the presence of iron nitrate in the samples by XRD analy sis; this was likely due to its low content. The endotherm at 326°С, like all of the above events indicated by the DTA curve, was accompanied by a sample weight loss. Hence, the additional release of volatile compounds accompanied by heat absorp tion occurred in this temperature range. It is well known that ammonium molybdates can undergo decomposition with the release of gaseous products. The exotherm with a maximum at 342°С was not accompanied by a change in the sample weight. It is likely that heat liberation in this case is caused by the interaction of iron and molybdenum oxides Fe2O3 + 3MoO3 → Fe2(MoO4)3. According to Huang et al. [8], a topochemical reac tion between Fe2O3 and MoO3 comes into play at 400°C. However, Shaheen [7] reported on the possi bility of the formation of an iron molybdate phase even at 350°С. This disagreement can be explained by the use of different precursors. The data given in Fig. 1 make it possible to deter mine the activation energies of processes accompa nied by a loss of sample weights. As is well known [9], the activation energy of a process occurring with a decrease in the sample weight whose rate obeys a first order kinetic equation can be calculated from the for mula ⎛W − Wf ⎞ E aθ (1) ln ln ⎜ i , ⎟= 2 ⎝ W − Wf ⎠ RTm where Wi and Wf are the initial and final sample weights, respectively; W is the sample weight at tem perature T; Tm is the temperature at which a maximum rate of sample weight decrease was observed; and θ = Т – Tm. As is well known, the order of a thermal decompo sition reaction can be determined based on the degree KINETICS AND CATALYSIS

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Wi – Wf ln ln   W – Wf 1.5 1.0 0.5 0 –0.5 2

–1.0 –1.5 4 1 –2.0 –40 –30

3 –20

–10 θ, °C




Fig. 2. Thermogravimetric analysis of an iron molybdate sample in the coordinates of Eq. (1). Straight lines 1–4 correspond to weight loss sections at Tm of 113, 203, 250, and 326°C, respectively.

of symmetry of peaks in the DTA curve. In accordance with Fig. 1, the symmetry factors of the endotherms and exotherms are close to unity. For this reason, all of the calculations were carried out on the assumption that the weight loss rates are described by first order rate equations. Figure 2 shows the results of a comparison of data obtained for an iron molybdate sample based on an analysis of thermoanalytical curves in the coordinates of Eq. (1). The slopes of the straight lines correspond to the following apparent activation energies: – 48.7 kJ/mol for a process with Tm = 113°C (precipi tate dehydration), –96.5 kJ/mol for a process with Tm = 203°C (ammonium nitrate decomposition), ⎯286 kJ/mol for a process with Tm = 250°C (iron nitrate impurity decomposition), and –109 kJ/mol for a process with Tm = 326°C (molybdenum salt impurity decomposition). The results of the calculation of activation energies from thermogravimetric data were confirmed by DTA data (Fig. 1, curves 2 and 3). According to the Kiss inger equation, the temperature Tm in the DTA curves depends on the rate of sample heating:

E ln F2 = K − а , RTm Tm


where F is the heating rate, Tm is the temperature cor responding to the position of an endothermic peak, K is a constant, which includes the order of reaction and the conversion at the point in time when a maximum rate of sample weight loss is reached.



phase synthesis reactions: the Jander, Ginstling– Brownstein, Zhuravlev–Lesokhin–Tempelman, and Erofeev–Avrami equations and the contracting sphere equation. The statistical treatment of the rate func tions х(t) using the Fischer dispersion relation at a confidence level of 0.05 showed that the linearity hypothesis can be applied to all of the above equations. At the same time, the coefficients of correlation in the approximation of the experimentally found functions х(t) with the use of the above rate equations were essentially different. The best results were obtained in the description of the rate of the interaction of compo nents by the Zhuravlev–Lesokhin–Tempelman equa tion [10]

F = [(1 – x)–1/3 –1]2 0.5 3

0.4 0.3 0.2





⎡(1 − x) −1 3 − 1⎤ = kt, ⎣ ⎦

0 150


250 Time, min



where k is the observed rate constant determined by the diffusion coefficients of ions in the phase of regents and/or their interaction product, and t is residence time under isothermal conditions. This equation describes solidphase interaction as a diffusioncontrolled process, whose ratelimiting stage is the threedimensional onesided diffusion of a reagent into a spherical grain of the second reagent. Unlike the Jander and Ginstling–Brownstein models, it takes into account changes in the concentrations of reactants. A comparison of the calculated rate constants with the temperatures of the oxide mixture under isother mal conditions in the coordinates of the Arrhenius equation made it possible to calculate the kinetic parameters of a topochemical reaction of the forma tion of iron molybdate. These data and the results of kinetic studies of the other steps of thermal decompo sition (see Table 1) were used to develop a mathemat ical model for the process of contact mass calcination. In the construction of the mathematical model, we assumed that all steps in an open system can be con sidered as parallel and almost irreversible. This assumption was based on the rapid removal of the gas

Fig. 3. Dependence of the rate of iron oxide conversion on the residence time of a stoichiometric mixture of Fe2O3 with MoO3 under isothermal conditions at temperatures of (1) 400, (2) 450, and (3) 500°С.

The measurement of the slopes of linear depen dences in the coordinates of Eq. (2) ln F2 − 1 at F = Tм Tм 1.5 and 10.0 K/min makes it possible to determine the activation energies of the above stages of the dehydra tion and decomposition of impurities. They almost completely coincide with the results of the calculation of activation energies based on thermogravimetric data. To determine the kinetic parameters of a topochemical reaction between iron and molybdenum oxides, we performed kinetic studies under isothermal conditions. Figure 3 shows an example of the resulting kinetic curves. In the analysis of the experimental results, we used the following rate equations of solid

Table 1. Stages of the thermal decomposition of contact mass and their kinetic parameters Stage of thermal decomposition Dehydration of iron hydroxide and molybdic acid impurities: 2B k1 B1, C k1 C1 Decomposition of an ammonium nitrate impurity: A Decomposition of an iron nitrate impurity: 2E





Decomposition of an ammonium heptamolybdate impurity: F




Topochemical reaction with impurity iron oxide: B1 + 3C1


k0, min–1

Ea, kJ/mol

1.51 × 106


1.97 × 1010


4.83 × 1028


1.17 × 109


1.05 × 107


* G refers to the products of NH4NO3 decomposition. KINETICS AND CATALYSIS

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eous products of dehydration and decomposition from the reaction zone and on a relatively large difference in temperatures at which endo and exo effects in the DTA curves and weight decrease effects in the thermo grams were detected. In accordance with the law of mass action and tak ing into account the above consideration, we can rep resent a mathematical model for the thermal decom position of contact mass in the form if the following system of differential equations: d C = − 2k C , (3) B 1 B dt d C = −k C , (4) C 1 C dt d C = − 2k C , (5) E 2 E dt d C = −k C , (6) A 3 A dt d C = −k C , (7) F 4 F dt 4 1 d C = k C + k C − k ⎡2 C −3 ⎛ C −3 − 1⎞⎤ , (8) ⎟⎥ 1 B 2 E 5⎢ B B1 ⎜ B1 dt 1 ⎣3 ⎝ ⎠⎦ 4 1 d C = k C + 7k C − 3k ⎡2 C −3 ⎛ C −3 − 1⎞⎤ , (9) ⎟⎥ 1 C 4 F 5⎢ C C1 ⎜ C1 dt 1 ⎣3 ⎝ ⎠⎦ 4 1 d C = k ⎡2 C −3 ⎛ C −3 − 1⎞⎤ , (10) ⎟⎥ 5⎢ D B1 ⎜ B1 3 dt ⎣ ⎝ ⎠⎦ where A is NH4NO3, B is Fe(OH)3, B1 is Fe2O3, C is H2MoO4, C1 is MoO3, D is Fe2(MoO4)3, E is Fe(NO3)3, and F is (NH4)6Mo7O24. The kinetic equations were set up taking into account the stoichiometric coefficients of the chemi cal reactions. The rate constants were determined from the Arrhenius equation. The calculations were conducted at different impurity contents of the con tact mass by varying them from 0.1 to 10 wt %. The dependences of the concentrations of all reac tion mixture components (in mole fractions) on calci nation time and temperature were calculated based on Eqs. (3)–(10). Figure 4 shows these dependences for calcination temperatures of 100, 250, and 380°С as examples. At 100°С (Fig. 4a), the reactions of MoO3 ⋅ nH2O and Fe(OH)3 dehydration were complete after ~20 min. At 250°С, the rapid decomposition of ammonium nitrate and iron nitrate and the relatively slow decomposition of an ammonium molybdate impurity were observed (Fig. 4b). The resulting molybdenum(VI) oxide did almost not react with iron(III) oxide; this is explained by a low value of the rate constant of this reaction at 250°С. At calcination temperatures higher than 300°С (Fig. 4c), the rela tively rapid formation of a phase of Fe2(MoO4)3 was observed as a result of a topochemical reaction between the molybdenum and iron oxides. KINETICS AND CATALYSIS

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(а) Mole fraction B1 0.06



E C1 B C


F 20

40 60 Time, min (b)







Mole fraction 0.10 B1 0.08 0.06 C1 0.04 0.02 F 0


40 60 Time, min (c)

Mole fraction 0.10 B1 0.08 C1

0.06 0.04 0.02 F 0

D 2

4 6 Time, min

Fig. 4. Dependence of the concentrations of reaction mass components in the process of annealing under isothermal conditions at temperatures of (a) 100, (b) 250, and (c) 380°C: (B) Fe(OH)3 (concentration before the onset of annealing, 5 wt %), (B1) Fe2O3 (0%), (C) H2MoO4 (1 wt %), (C1) MoO3 (0%), (D) Fe2(MoO4)3 (0%), (E) Fe(NO3)3 (2.5 wt %), and (F) (NH4)6Mo7O24 (0.7 wt %).



version was increased. The experimental data are con sistent with the results of a study of the catalytic activ ity of an iron–molybdenum catalyst over a wide range of Mo/Fe ratios [11]. House et al. [11] found a regular decrease in the selectivity of samples with increasing the iron oxide content of them.

Intensity, arb. units 1200 1000 800 600 400 200

In conclusion, it should be noted that it is impossi ble to accelerate the process of Fe2O3 impurity conver sion by increasing the temperature of contact mass 2θ, deg calcination because the recrystallization and sublima 15 25 35 45 55 1 2 tion of molybdenum oxide occurs in this case. We 3 experimentally established that the particles agglom Fig. 5. Xray diffraction patterns of contact mass samples erated and changed their color after the calcination of (a) with an impurity of 8.5 wt % Fe2O3 and (b) without an the contact mass at 600°С for 10 h, and the acicular impurity of Fe2O3. Reference data on reflections in the crystals of molybdenum oxide were formed on their diffraction patterns of (1) Fe2(MoO4)3, (2) Fe2O3, and surface. The catalytic activity of these samples in the (3) MoO3 are given at the bottom. reaction of partial methanol oxidation sharply decreased. A detailed analysis of the mathematical model of Thus, in this work, we performed a kinetic analysis the thermal treatment of an iron–molybdenum cata lyst made it possible to determine optimum time inter of impurity dehydration and decomposition processes vals in which the impurity of Fe2O3 almost completely and a topochemical reaction between the iron oxide reacts with an excess of MoO3. For example, at a cal and molybdenum oxide components of an iron– cination temperature of 500°С, the time taken for the molybdenum catalyst. The catalyst samples were pre complete conversion of Fe2О3 at its initial concentra pared by continuous chemical precipitation at the low tion of 5–10 wt % and a twofold excess of molybde degrees of mother liquor supersaturation with the use num oxide is no shorter than 15 h. of the Fe(NO3)3 and (NH4)6Mo7O24 salts for this pur This conclusion was confirmed experimentally in a pose. The threedimensional oneside diffusion of a study of the samples by XRD analysis. Figure 5 shows reagent into the spherical grain of the second reagent some of the experimental diffraction patterns, which is a ratelimiting step of the reaction between iron and are consistent with reference data for iron molybdate molybdenum oxides. We developed a mathematical (PCPDFWIN no. 350183) and molybdenum trioxide model for the thermal treatment of contact mass based (PCPDFWIN no. 350609). The computerassisted on the assumption of the parallel irreversible steps of identification of the diffraction patterns in Fig. 5a the decomposition of impurity phases and the diffu showed the presence of an iron oxide impurity in the sion inhibition of the step of formation of an iron(III) sample in an amount of 8.5 wt %. The reflections of molybdate phase in accordance with the Zhuravlev– the phase of Fe2O3 were not detected after the thermal Lesokhin–Tempelman model. treatment of this sample at 500°C for 15 h (Fig. 5b). Based on the model proposed, we were the first to We compared the catalytic activity of the synthe find the dependences of the concentrations of solid sized contact masses in the oxidation reaction of phase components on the temperature and duration of methanol vapor in the model flow reactor. Table 2 summarizes the results of the determination of meth calcination. The time intervals obtained for the occur anol conversion selectivity in two samples with differ rence of the main steps of the thermal treatment of ent iron oxide impurity concentrations. With the use iron molybdate precipitates allowed us to determine of a catalyst containing iron oxide, selectivity optimum process parameters for the synthesis of an decreased more rapidly as the degree of methanol con iron–molybdenum catalyst. а b

Table 2. Selectivity for the oxidation of methanol in a model flow reactor at a temperature of 300°C and a methanol vapor concentration of 3 vol % on the iron–molybdenum catalysts synthesized at the molar ratio Fe/Mo = 1 : 2.2 Formaldehyde formation selectivity, % Methanol conversion, % 85 90 95

sample containing 8.5 wt % iron oxide

sample with no Fe2O3 impurity

90 85 74


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REFERENCES 1. Bowker, M., Holroyd, R., House, M., Bracey, R., Bamroongwongdee, C., Shannon, M., and Carley, A., Top. Catal., 2008, vol. 48, nos. 1–4, p. 158. 2. Dias, A.P.S., Rozanov, V.V., Waerenborgh, J.C.B., and Portela, M.F., Appl. Catal., A, 2008, vol. 345, no. 2, p. 185. 3. Hernelind, M. and Augustsson, O., Catal. Today, 2006, vol. 112, nos. 1–4, p. 40. 4. Nikolenko, N.V., Kostynyuk, A.O., Kalashnikov, Yu.V., and Cheremis, E.A., Russ. J. Appl. Chem., 2012, vol. 85, no. 12, p. 1814. 5. Vasserman, I.M., Khimicheskoe osazhdenie iz rastvorov (Chemical Deposition from Solutions), Leningrad: Khimiya, 1980. 6. Kuprin, A.V., Kovalenko, I.L., Dovban’, L.V., and Teplitskaya, A.G., Vopr. Khim. Khim. Tekhnol., 2008, no. 5, p. 97.


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7. Shaheen, W.M., Mater. Sci. Eng. A, 2006, vols. 445– 446, p. 113. 8. Huang, Y., Cong, L., Yu, J., Eloy, P., and Ruiz, P., J. Mol. Catal. A: Chem., 2009, vol. 302, nos. 1–2, p. 48. 9. Shestak, Ya., Teoriya termicheskogo analiza: Fiziko khimicheskie svoistva tverdykh neorganicheskikh vesh chestv (Thermal Analysis Theory: Physicochemical Properties of Solid Inorganic Substances), Moscow: Mir, 1987. 10. Tret’yakov, Yu.D., Tverdofaznye reaktsii (SolidPhase Reactions), Moscow: Khimiya, 1978. 11. House, M.P., Carley, A.F., EcheverriaValda, R., and Bowker, M., J. Phys. Chem. C, 2008, vol. 112, no. 11, p. 4333.

Translated by V. Makhlyarchuk

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