ISSN 0036-0244, Russian Journal of Physical Chemistry A, 2017, Vol. 91, No. 1, pp. 10–16. © Pleiades Publishing, Ltd., 2017. Original Russian Text © S.I. Shornikov, 2017, published in Zhurnal Fizicheskoi Khimii, 2017, Vol. 91, No. 1, pp. 14–20.
CHEMICAL THERMODYNAMICS AND THERMOCHEMISTRY
Mass Spectrometric Study of the Evaporation of MgAl2O4 Spinel S. I. Shornikov* Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Moscow, 119991 Russia *e-mail:
[email protected] Received January 29, 2016
Abstract―The evaporation of MgAl2O4 spinel is studied via high-temperature Knudsen effusion mass spectrometry in the temperature range of 1850–2250 K. In the gas phase, molecular components typical of the simple oxides in the spinel and traces of gaseous complex oxide MgAlO are identified above the samples. The resulting values of the partial vapor pressures of the molecular components contained in the gas phase over the spinel are compared with those corresponding to simple oxides for the first time. Keywords: Knudsen effusion mass spectrometric method, thermodynamics of evaporation, magnesia spinel DOI: 10.1134/S0036024417010241
INTRODUCTION
of 1800–2300 K. Spinel evaporation was thought to proceed according to the reaction
The only magnesium aluminate in the MgO–Al2O3 system is MgAl2O4 spinel, which is crucial to the production of high-temperature construction ceramics due to its high melting point (2408 ± 20 K [1]) and a number of other physical and chemical properties, and to petrology as one part of multicomponent systems [2]. The spinel is of particular interest in astrochemical studies as a mineral that is part of the high-melting Ca–Al-inclusions often found in carbonaceous chondrites, which are the earliest known objects in the Solar System and have unusual isotopic characteristics [3]. Figure 1 shows a diagram of the MgO–Al2O3 system according to [4–9], where a wide range of solid solutions of the spinel with MgO [7] and Al2O3 [6, 8] can be seen.
[MgAl2O4] = (Mg) + 1/2(O2) + [Al2O3],
(1)
where the parentheses and square brackets denote the gas and condensed phases, respectively. The rate of spinel evaporation was determined from the weight loss in continuous weighting, which allowed us to calT, K 3200 2800
9 2
5
6
2400 1
The evaporation and thermodynamic properties of simple oxides MgO and Al2O3 were discussed in detail in [1, 10–12]. The gas phase over magnesium oxide consists of a number of molecular components: (O), (O2), (O3), (O4), (Mg), (MgO), and (Mg2). The gas phase over aluminum oxide consists of (O), (O2), (O3), (O4), (Al), (AlO), (AlO2), (Al2), (Al2O), (Al2O2), and (Al2O3). Experimental conditions and the results from studies of the high-temperature evaporation of spinel [13–22] are summarized briefly in Table 1.
8 4
2000
3
7
1600 1200
Early studies of spinel evaporation by Knudsen [13] and Langmuir [14–20] methods were performed using high-temperature furnaces in which the samples were placed in an alundum effusion container [13], hung on tungsten filaments [14–18] or mounted on a tungsten wire [19, 20] in vacuum [14–20] or in a helium environment [14, 15], and heated in the temperature range
0
20
40
60
80 100 Al2O3, mol %
Fig. 1. Phase diagram of the MgO–Al2O3 system [4–9]; (1) MgO (solid solution); (2) MgO + liquid; (3) MgO (solid solution) + MgAl2O4 (solid solution); (4) MgAl2O4 (solid solution); (5, 6) MgAl2O4 + liquid; (7) MgAl2O4 (solid solution) + Al2O3; (8) Al2O3 + liquid; (9) liquid. Positions of the points in the phase boundaries 4 and 7, determined here via Knudsen effusion mass spectrometry, are denoted with symbols.
10
MASS SPECTROMETRIC STUDY OF THE EVAPORATION OF MgAl2O4 SPINEL
11
Table 1. Experimental conditions and basic results of spinel evaporation [13–22] Research method High-temperature furnace (Knudsen) High-temperature furnace (Langmuir) High-temperature furnace (Langmuir) in a helium environment High-temperature furnace (Langmuir) Knudsen effusion mass spectrometry High-temperature furnace (Langmuir) Knudsen effusion mass spectrometry Knudsen effusion mass spectrometry
Container or suspension material
T, K
MgO, mol %
Al2O3 W W
2023–2273 1973–2273 2273–2573
50 50 50
W Al2O3 W W Ir, Al2O3
1833–2093 50 2038–2048 50 1973–2173 26, 50, 53 1850–2300 26, 33, 50 1773 0–10
culate roughly (up to one order of magnitude) the total vapor pressure of the spinel, depending on temperature. It would seem that the low accuracy was due to spinel evaporation in vacuum occurring not only from the surface of the test sample, as in a helium environment, but inside the sample as well, due to its porosity growing with temperature [14]. However, Rutman et al. [16, 17] showed that the rate of spinel evaporation slowed at temperatures above 2100 K because a corundum film forms on its surface, preventing evaporation. Mass spectrometric studies (by Knudsen method) of the evaporation of spinel from alundum [16, 17, 22] and tungsten [21] effusion containers were conducted in the same temperature range (1800–2300 K). Note that according to the state diagram shown in Fig. 1, the experiments by Petric and Chatillon [22] dealt with the MgAl2O4 (solid solution) + Al2O3 region. The authors of [16, 17, 21] also considered the evaporation of spinel from the viewpoint of Eq. (1) and determined only the partial vapor pressure of atomic magnesium, since a number of the spinel’s other gas phase components lay below the sensitivity of the equipment that was used. Using data reported by Yokoyama and Sato [19], Sasamoto et al. [21] found that the rate of evaporation for spinel in the crystalline state lay in the interval of 0.03–0.04 in the range of test temperatures. The information available on the processes of spinel evaporation is thus scarce and limited to determining the partial vapor pressures of the dominant component of the gas phase, atomic magnesium. Thermodynamic data obtained by evaporating the spinel in high vacuum furnace (Langmuir) are approximate because the porosity of the spinel grows along with temperature while a corundum film forms, slowing its rate of evaporation. The aim of this work was to study the high-temperature processes of the evaporation of spinel. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A
Gas phase Basic results Reference component Mg – –
pMg ptot ptot
[13] [14, 15] [14, 15]
Mg Mg, O2 Mg, O2 Mg, O2 Mg, O2
ptot pMg ptot pMg, α MgAl 2O4 pMg, pO2
[16–18] [16, 17] [19, 20] [21] [22]
EXPERIMENTAL The evaporation of stoichiometric spinel from a molybdenum container was studied via Knudsen effusion mass spectrometry in the temperature range of 1850−2250 K. An MI-1201 serial mass spectrometer equipped with a modified ion source for high temperature measurements (up to 3000 K) was used in this work. The high sensitivity of the equipment was due to the proximity of the effusion container to the field ionization source where the axes of the molecular and ion beams intersected. The design of our ion source and the methodology of the mass spectrometry experiments were described in detail in [23]. The spinel was synthesized by sintering active ultrafine powders of the mineral, obtained via the cocrystallization of magnesium and aluminum nitrates and magnesium and aluminum sulfates, and by solidphase synthesis. Mixture compositions were prepared with a stoichiometric ratio of magnesium and aluminum oxides, followed by X-ray diffraction and chemical analysis of the spinel samples. In the mass spectra of the vapor above the spinel at an ionizing electron energy of 30 eV, we observed ions characteristic of those above magnesium and aluminium oxides [12, 24], along with traces of the complex ions of gaseous oxide MgAlO. No other ions with the formula MgAliOk (i = 1, 2; k = 0–4) were observed. The choice of the ionizing electron energy was a compromise between achieving the maximum intensity of the ions in the mass spectra of the vapor and ensuring their minimal fragmentation under electron impact. The ratio of ionic current intensities (Ii) in the mass spectra of the vapor above the stoichiometric spinel at a temperature of 2046 K was IMg : IMgO : IO : I O2 : IAlO : IAl : I Al 2O : IMgAlO = 100 : 0.84 : 0.73 : 0.36 : 0.092 : 0.027 : 0.008 : 0.0006. The low intensity of the ion currents relative to the intensity of the ion current of atomic magnesium prevented us from obtaining ionization efficiency curves
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of these ions to determine their origin in the temperature range of 1851−2089 K, where the test samples corresponded to the composition of the stoichiometric spinel. The ionization efficiency curves above the ions were therefore obtained at higher temperatures (2200−2250 K) where their intensity allowed us to perform these studies. The measurements in this case corresponded to compositions of solid solutions of the spinel enriched with aluminum oxide, rather than to the composition of the stoichiometric spinel (Fig. 1). This was because there was a change in the composition of the condensed phase, which was considered in the isothermal evaporation approach developed by Sidorov [25] and requiring study of the sequence of equilibria states upon the evaporation of substances of complex composition. Energies of the emergence of ions in the mass spectra of the vapor above the spinel were determined using the Warren method [26], and were consistent with the values of the ionization energy of atoms and molecules typical of simple oxides accepted in [27]. The energy of the emergence of ion (MgAlO) in the mass spectra of the vapor above the spinel was 7.7 ± 0.6 eV, and the energy of the emergence of silver ions in the mass spectrum was used as our standard. The monotonous curves of the ionization efficiency do not display drops typical of the presence of fragment ions, though this of course does not rule out the possibility of their emergence. To estimate the possible contribution of the fragmentary ion currents to the recorded ionic currents, we calculated equilibrium constants for all independent reactions in the gas phase that can occur in an effusion container. Their coincidence with the obtained reference data [1, 10] revealed either no or negligible fragmentation caused by electron impact during ionization of the molecular forms of the vapor above the spinel. The determined molecular composition of the gas phase above the spinel suggests that spinel evaporation occurs mostly through heterogeneous reactions typical of the evaporation of individual oxides: [MgO] = (Mg) + (O),
(2)
[MgO] = (MgO),
(3)
[Al2O3] = 2(Al) + 3(O),
(4)
[Al2O3] = 2(AlO) + (O),
(5)
[Al2O3] = (Al2O) + 2(O).
(6)
The presence of small amounts of molecular MgAlO in the gas phase above the spinel indicates the possibility of the heterogeneous reaction: [MgAl2O4] = (MgAlO) + (Al) + 3(O).
(7)
The partial pressures of the gas phase components over the spinel (pi) were determined using the Hertz– Knudsen equation written in the form [28]
qi 2πRT , (8) s orC or t M i where qi is the number of the substance component with molecular weight Mi, evaporated from the effusion container in time t at temperature T through an effusion hole characterized by Clausing coefficient Cor and hole area sor . The value of the Kα constant, allowing for coefficient αi of the evaporation of the substance component associated with changes in the structure of the molecules during its transition to the gas phase with a surface area Sv, was calculated using the Komlev equation [29]: pi = K α
1 − C cα i , (9) K α = 1 + s or C or Sv α iC c where Cc is the Clausing coefficient for the effusion container. The Clausing coefficient is associated with collisions of constituents of the gas phase within the channel of the effusion hole (effusion container) and their rebounding from the channel walls; its value does not exceed unity and depends on the ratio of the effusion hole’s diameter to its thickness. Given the prevalence of gas phase components typical of MgO and Al2O3 over the spinel, rates of partial evaporation were adopted for small amounts of MgAlO, based on the results reported in [30]. The partial pressure of the gas phase above the spinel, calculated from Eqs. (8) and (9) with an error not exceeding 8%, are given in Table 2. The atomic oxygen partial pressures (Table 3) determined from these relations corresponded satisfactorily to those calculated using thermochemical data [10] on equilibrium constants Kr(T) of possible reactions occurring in the gas phase over the spinel: (MgO) = (Mg) + (O), (10) (AlO) = (Al) + (O),
(11)
(Al2O) = 2(Al) + (O),
(12)
(O2) = 2(O)
(13)
according to the equations
pO =
pMgO K 10(T ), pMg
(14)
pO =
p AlO K 11(T ) , p Al
(15)
pO =
p Al 2O 2 p Al
K 12(T ) ,
(16)
2
pO2 . (17) pO = K 13(T ) It should be emphasized that the match between the pO values over the spinel, calculated from independent reactions in the gas phase, confirms the assumed
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Table 2. Partial pressure of the spinel’s gas phase components (atm) T, K
pMg
pMgO
pAl
pAlO
p Al 2O
pO2
1851
4.68 × 10–7
9.85 × 10–10
4.47 × 10–11
1.60 × 10–10
–
3.25 × 10–9
–
1859
5.20 ×
10–7
–11
–10
–
–9
–
1.25 ×
10–6
1.70 × 10
–8
–
1.82 ×
10–6
1.88 × 10
–8
–
2.23 ×
10–6
–8
–
2.29 ×
10–6
3.00 × 10
–8
–
4.38 ×
10–6
4.82 × 10
–8
–
5.29 ×
10–6
–8
–
9.19 ×
10–6
–7
–
2047
9.15 ×
10–6
8.88 × 10
1.75 × 10
–7
2.44 × 10–10
2047
9.55 × 10–6
6.44 × 10–8
3.39 × 10–9
1.40 × 10–8
9.17 × 10–10
1.62 × 10–7
3.05 × 10–10
2089
1.67 × 10–5
1.57 × 10–7
7.65 × 10–9
3.37 × 10–8
2.48 × 10–9
2.60 × 10–7
8.89 × 10–10
1914 1938 1950 1950 1992 2005 2044
1.21 × 10
–9
4.45 × 10
–9
6.66 × 10
–9
9.53 × 10
–9
9.67 × 10
–9
2.25 × 10
–8
2.68 × 10
–8
6.07 × 10
–8
6.07 × 10
–8
5.26 × 10 1.93 × 10
–10
3.21 × 10
–10 –10
4.44 × 10 4.41 × 10 1.10 × 10
–10
–9
1.42 × 10
3.22 × 10 3.36 × 10
–9
–10
1.31 × 10
4.40 × 10
–9
1.38 × 10 4.71 × 10 1.41 × 10
2.54 × 10
–9
1.67 × 10
6.19 × 10
–9
–11
–11
3.17 × 10
–11
6.84 × 10
–9
2.31 × 10
–9
–10 –10
3.35 × 10
–8
1.45 × 10
5.29 × 10 –11
6.44 × 10
3.95 × 10
–9 –9
2.07 × 10
8.01 × 10
–8
pMgAlO
6.09 ×10
–10
1.07 × 10
–10
Table 3. Partial pressure of atomic oxygen over the spinel (atm), calculated using Eqs. (8), (9), and (14)–(17)
T, K
(8), (9)
(14)
(15)
(16)
(17)
1851
1.21 × 10–8
1.14 × 10–8
1.24 × 10–8
–
1.11 × 10–8
1859
1.43 × 10–8
1.39 × 10–8
1.57 × 10–8
–
1.52 × 10–8
1914
3.87 × 10–8
4.12 × 10–8
3.49 × 10–8
3.93 × 10–8
4.37 × 10–8
1938
6.07 × 10–8
5.58 × 10–8
6.40 × 10–8
5.61 × 10–8
5.60 × 10–8
1950
7.10 × 10–8
7.48 × 10–8
7.17 × 10–8
6.16 × 10–8
8.02 × 10–8
1950
7.09 × 10–8
7.39 × 10–8
5.96 × 10–8
6.89 × 10–8
7.80 × 10–8
1992
1.43 × 10–7
1.42 × 10–7
1.34 × 10–7
1.47 × 10–7
1.38 × 10–7
2005
1.78 × 10–7
1.61 × 10–7
1.52 × 10–7
1.96 × 10–7
1.71 × 10–7
2044
3.30 × 10–7
3.16 × 10–7
3.61 × 10–7
3.03 × 10–7
3.04 × 10–7
2047
3.49 × 10–7
3.27 × 10–7
3.74 × 10–7
3.40 × 10–7
3.97 × 10–7
2047
3.50 × 10–7
3.33 × 10–7
3.58 × 10–7
3.44 × 10–7
3.82 × 10–7
2089
6.75 × 10–7
7.05 × 10–7
7.03 × 10–7
6.37 × 10–7
6.53 × 10–7
molecular origin of the identified ions in the mass spectrum of the vapor over the spinel. As was mentioned above, there was a marked change in the spinel structure at temperatures exceeding 2000 K, due to preferential evaporation of the gas phase components belonging to magnesium oxide. Since the amount of molecular MgAlO in the gas phase above the spinel was low, the change in the composition of the residual melt spinel can be calculated using the isothermal evaporation approach [25], i.e., from the dependences of ion current intensities belonging to simple oxides on evaporation time t, which determines amount qt of the vaporized compoRUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A
nent of the condensed phase in the spinel, according to the relation t
∫ I dt i
qt =
q 0 tt==t00
,
(18)
∫ I dt i
t =0
where Ii is the total ion current of the ith component of the melt (MgO or Al2O3) and t0 is time of full evaporation of amount q0 of component i of the substance. Knowing the amount of vaporized simple oxide in the
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−4
−4
(a)
(b)
−5 1 2 3 4 5 6
−6 7 −7 1800
2000
2100
2200
2300 T, K
−7 −8 −9
10
5 8 9
−10 −11 1800 −5
(c)
−6
1900
2000
2100
2200
2300 T, K
(d)
−6 −7
logpO [atm]
logpAlO [atm]
1900
logpAl [atm]
logpMg [atm]
−6
−8 −9
6 8 9
10
−10 1800
1900
2000
2100
2200
2300 T, K
−7
7 4 5 8 9
−8 10 −9 1800
1900
2000
2100
2200
2300 T, K
Fig. 2. Partial pressure of vapor components (a) Mg, (b) Al, (c) AlO, and (d) O above (1–5) the spinel and (6, 7) magnesium and (8–10) aluminium oxides determined via (1) Knudsen effusion mass spectrometry (alundum container) [13]; (2) Langmuir method [14, 15]; (3) Knudsen effusion mass spectrometry (alundum container) [16, 17]; (4, 6) Knudsen effusion mass spectrometry (tungsten container) [21]; (5) Knudsen effusion mass spectrometry (molybdenum container) in this work; (8, 9) Knudsen effusion mass spectrometry (molybdenum container) in [24] and [28], respectively; and (7, 10) calculated in this work from thermochemical data [10].
spinel at each moment, we can determine the composition of the residual melt. Note that the change in the composition of the spinel through evaporation continued up to compositions at the boundary of spinel solid solutions and the MgAl2O4 (solid solution) + Al2O3 region, which evaporate congruently. This allowed us to clarify the position of the above boundary by selecting the temperature regime of the experiments; the evaporative trend of one of these is shown in Fig. 1. RESULTS AND DISCUSSION Values of the partial vapor pressures of the components that predominated in the gas phase over the spinel (Mg, Al, AlO, and D) determined in this work are compared in Fig. 2 to those obtained in [13–17, 21] and correlate with the evaporation of simple oxides (MgO and Al2O3) found under the reducing conditions caused by oxygen reacting with the material of the tungsten [21] or molybdenum [24, 28] effusion containers because of the heterogeneous reactions
[Me] + i(O) = (MeOi),
(19)
j 2
[Me] + (O2) = (MeOj),
(20)
where Me is the container material (tungsten or molybdenum). Figure 2 shows the corresponding partial vapor pressure of the components in the gas phase above magnesium and aluminium oxides, calculated in this work from the thermochemical data [10] obtained when there was no such interaction. Because of reactions (19) and (20), the values of pMg over the spinel found here (Fig. 2a) are slightly higher than those determined via Knudsen effusion mass spectrometry in [16, 17]. Note that the coincidence between these data and the results from our calculations for magnesium oxide (Fig. 2a, line 7) indicates there were certain reducing conditions in the alundum effusion containers as well. The values of total vapor pressure over the spinel calculated in [13– 15] and presented in Fig. 2 are not very accurate; it would seem that at temperatures above 2100 K they do
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not correspond to the stoichiometric spinel composition because of the abovementioned corundum film forming on the surface, which prevents evaporation. The values of the partial vapor pressures of atomic magnesium over the spinel and magnesium oxide obtained via Knudsen effusion mass spectrometry upon their evaporation from the tungsten container [21] (Fig. 2a, 4 and 6, respectively) contradict our data and those reported in [16, 17]. This is because the above values of pMg over the spinel are much lower, although they were found under reducing conditions stronger than those in the respective experiments [16, 17]. As expected, however, the values of pMg over magnesium oxide obtained in [21] exceed the ones calculated for nonreducing conditions. We believe these systematic differences were due to approximate calculations of the absolute values of the partial pressures of vapor components from the intensities of the corresponding ion currents [25, 31]. This was in turn due to the uncertainty of the parameters used in the calculations: ionization cross sections, the effective conversion rate on the first electrode of the second electron multiplier used in [21], and the sensitivity constant—a proportionality coefficient of the measured ion current intensity of the corresponding ion, which refers to the value of the vapor partial pressure of the gas phase component over the test substance. The values of partial pressures pAl and pAlO over the spinel determined in this work (Figs. 2b and 2c, lines 10) are consistent with those for aluminum oxide [24, 28], which are in satisfactory agreement with the results from our calculations (Figs. 2b and 2c, lines 10). Some excess of the values of pAlO relative to those of pAl can be explained by the temperature dependence of the partial pressure of atomic oxygen, which occupies an intermediate position between those of magnesium and aluminium oxides (Fig. 2d, symbols 5), and differ substantially from the estimate based on the data in [21]. The estimates of the values pO also contradict those of the partial pressures of atomic oxygen obtained for Al2O3 in the experiments of [24, 28], which were performed in a reducing environment (a molybdenum container), in contrast the reducing conditions of [21], where a tungsten container was used for evaporation of the spinel. CONCLUSIONS The evaporation of MgAl2O4 spinel from a molybdenum container at temperatures of 1850−2250 K was studied via high-temperature Knudsen effusion mass spectrometry. In the gas phase, traces of the gaseous complex oxide MgAlO and molecular components typical of the simple oxides making up the spinel were identified above it. The values of the partial vapor pressures of molecular components contained in the gas phase over the spinel were identified for the first time. A comparison of these values to the available RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A
15
experimental data and those corresponding to simple oxides testifies to the accuracy of our data. ACKNOWLEDGMENTS The author wishes to thank O.I. Yakovlev and M.A. Nazarov at the Vernadsky Institute of Geochemistry and Analytical Chemistry for discussing the results of this work. This work was supported by the Presidium of the Russian Academy of Sciences, project no. 7 (“Experimental and Theoretical Studies of Objects in the Solar System and Stellar Planetary Systems”). REFERENCES 1. M. W. Chase, J. Phys. Chem. Ref. Data, Monograph No. 9, 1951 (1998). 2. A. S. Berezhnoi, Multicomponent Systems of Oxides (Naukova Dumka, Kiev, 1970) [in Russian]. 3. D. Wark and W. V. Boynton, Met. Planet. Sci. 36, 1135 (2001). 4. D. A. Rankin and H. E. Merwin, J. Am. Chem. Soc. 38, 568 (1916). 5. H. von Wartenberg and H. J. Reusch, Z. Anorg. Allg. Chem. 207, 1 (1932). 6. D. M. Roy, R. Roy, and E. F. Osborn, Am. J. Sci. 251, 337 (1953). 7. A. M. Alper, R. N. McNally, P. H. Ribbe, and R. C. J. Doman, Am. Ceram. Soc. Bull. 45, 263 (1962). 8. D. Viechnicki, F. Schmid, and J. W. McCauley, J. Am. Ceram. Soc. 57, 47 (1974). 9. C. Ronchi and M. Sheindlin, J. Appl. Phys. 90, 3325 (2001). 10. V. P. Glushko, L. V. Gurvich, G. A. Bergman, I. V. Veits, V. A. Medvedev, G. A. Khachkuruzov, and V. S. Yungman, Thermodynamical Properties of Individual Substances, The Handbook, Ed. by V. P. Glushko (Nauka, Moscow, 1978–1982) [in Russian]. 11. I. S. Kulikov, The Thermodynamics of Oxides (Metallurgiya, Moscow, 1986) [in Russian]. 12. E. K. Kazenas and Yu. V. Tsvetkov, Evaporation of Oxides (Nauka, Moscow, 1997) [in Russian]. 13. R. L. Altman, J. Phys. Chem. 67, 366 (1963). 14. E. S. Lukin and D. N. Poluboyarinov, Ogneupory, No. 9, 418 (1964). 15. D. N. Poluboyarinov, Ogneupory, No. 11, 19 (1967). 16. D. S. Rutman, I. L. Shchetnikova, E. I. Kelareva, and G. A. Semenov, Ogneupory, No. 10, 40 (1968). 17. D. S. Rutman, I. L. Shchetnikova, T. S. Ignatova, et al., Tr. Vost. Inst. Ogneuporov, No. 9, 143 (1969). 18. D. S. Rutman, I. L. Shchetnikova, E. I. Kelareva, and G. A. Semenov, in Proceedings of the 8th Workshop on Experimental and Technical Mineralogy and Petrography (Nauka, Moscow, 1971), p. 357 [in Russian]. 19. T. Sata and T. Yokoyama, J. Ceram. Soc. Jpn. 81, 170 (1973). 20. H. L. Lee and T. Sata, J. Ceram. Soc. Jpn. 86, 136 (1978).
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21. T. Sasamoto, H. Hara, and T. Sata, Bull. Chem. Soc. Jpn. 54, 3327 (1981). 22. A. Petric and C. Chatillon, High Temp. Mater. Chem. 2, 415 (2000). 23. S. I. Shornikov, I. Yu. Archakov, and T. Yu. Chemekova, Russ. J. Phys. Chem. A 74, 677 (2000). 24. J. Drowart, G. de Maria, R. P. Burns, and M. G. Inghram, J. Chem. Phys. 32, 1366 (1960). 25. L. N. Sidorov, M. V. Korobov, and L. V. Zhuravleva, Mass-Spectrum Thermodynamic Studies (Mosk. Gos. Univ., Moscow, 1985). 26. J. W. Warren, Nature 165 (4203), 810 (1950).
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Translated by V. Avdeeva
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