Inorganic Materials, Vol. 37, No. 3, 2001, pp. 257–263. Translated from Neorganicheskie Materialy, Vol. 37, No. 3, 2001, pp. 323–330. Original Russian Text Copyright © 2001 by Zyryanov, Gusev.
Mechanochemical Reactions in Mixtures of Lead Oxides V. V. Zyryanov and A. A. Gusev Institute of Mechano- and Solid-State Chemistry, Siberian Division, Russian Academy of Sciences, ul. Kutateladze 18, Novosibirsk, 630128 Russia Received January 12, 2000
Abstract—The mechanochemical processes, including mechanochemical synthesis of mixed-valence lead oxides, in mixtures of PbO, Pb3O4 , and PbO2 were studied by x-ray diffraction. The results demonstrate that the reduction of Pb4+ is accompanied by the formation of Pb2O3 , Pb3O4 , and possibly PbO1.37 . Phases of variable composition close in structure to minium, Pb3O4 , are shown to coexist during mechanical processing. The 2+
4+
structure of the metastable oxide Pb3O4 – x with Pb2+ : Pb4+ > 2 ( Pb 2 + x Pb 1 – x O4 – 2x) is tentatively determined. The sequence of the observed transformations is interpreted in terms of the model for the reaction zone, with consideration for primary and secondary interactions.
INTRODUCTION The study of mechanochemical reactions in oxide mixtures is of interest in developing a mechanochemical ceramic processing method for the preparation of nanopowders [1]. This approach yields fine-grained materials with unique, and often unpredictable, properties [2] and ensures controlled synthesis of new metastable compounds and nanopowders with complex morphology for nanocomposites [3]. The method includes: mechanical processing in a planetary mill with a horizontal rotation axis at ~60g; disaggregation of the resultant powder in an electrical gravitational classifier to obtain ultrafine aggregates of nanoparticles [4, 5]; and mechanical processing in a steel mill, ensuring a small particle size and high homogeneity of the powder [6]. According to the model for the reaction zone [7], mechanochemical interaction has a threshold character and involves a transient state—a layer of rolls and voids between reacting particles subjected to a pressure + shear combination. In the course of mechanochemical synthesis, mass transfer follows two fundamentally different mechanisms: by rolls and via diffusion in the deformation intermixing regime [8]. The contribution of the former mechanism is much larger [7]. The composition of the material in the transient state [7], A(solid) + B(solid)
(ABx)*
A1 – δB(solid) + B*(solid), is (ABx)* (or D* in the general case) and is determined by the difference in Mohs’ hardness between the reagents. The final product is the result of relaxation of the transient state D* in the course of quenching. For
this reason, the primary crystallizing phase is close in structure to D*. The critical difference in hardness for the formation of a transient state was shown to be ∆M = 4 [7]. Starting at this level, a thin layer of the softer reagent is formed on the surface of harder grains, so that all the supplied energy is absorbed by the softer reagent, without initiating contact reactions. The mechanochemical yield is governed by the enthalpy of the process and the molecular weight of the reagents. The latter is proportional to the density of the material and inversely proportional to its heat capacity and thermal conductivity. The enthalpy of the process is not always known; in terms of molecular weight, mechanochemical synthesis is more suitable for the preparation of compounds of heavy elements: at high molecular weights, the impact zone is smaller and, hence, the material is heated to higher temperatures, and the rate of heat removal is slower; that is, the supplied mechanical energy, necessary for surmounting the threshold for roll formation, is concentrated in smaller regions. Mechanochemical reactions in mixtures of lead oxides would be expected to have a high yield owing to the high molecular weight of Pb and the insignificant difference in hardness, ∆M < 4. Mohs’ hardnesses of PbO, Pb3O4, and PbO2 are 2, 2.5, and 5, respectively [9]. The structure of a mechanochemical product is difficult to predict. In most cases, mechanochemical synthesis in oxide systems yields perovskite phases, but exceptions are not rare. For example, the crystalline product in the PbO–VO2 system has another structure [10]. On the whole, the available information is insufficient for reliably predicting the structure type of mechanochemical products. In this context, there is considerable interest in studying mechanochemical processes in mixtures of lead oxides.
0020-1685/01/3703-0257$25.00 © 2001 MAIK “Nauka /Interperiodica”
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EXPERIMENTAL The starting reagents used were pure-grade PbO2 and analytical-grade PbO and Pb3O4 . Mechanochemical synthesis was performed in an AGO-2 planetary mill with water-cooled steel jars and steel balls [6]. Before processing, the yellow and red forms of PbO (Y- and R-PbO) were heated at 800 and 600 K, respectively, to remove the intercalated oxygen, which otherwise might give rise to a transformation into the orange form, O-PbO [11], complicating the x-ray diffraction (XRD) pattern by additional reflections. We used two samples of PbO2 of different origins, containing different amounts of plattnerite (claret red β-PbO2 with the rutile structure) and β-PbO2 (black high-pressure phase with the columbite structure). No significant difference in mechanochemical behavior between the two PbO2 samples was detected. The surfaces of the steel balls (10-mm diameter, total weight of 200 g) and jars were coated with lead oxides as described earlier [5]. The sample weight was 15 g. Every 30 s, the mill was shut off, and positive mixing was performed. This procedure kept the coating intact and prevented contamination (the Fe content of the resulting powders was within 0.02%). In addition, it allowed accurate determination of the mechanochemical yield, ensured a low (≤300 K) background temperature in the mill, and a high homogeneity of the resulting material, which is of prime importance for XRD analysis. The coating prevented direct oxidizer–metal contact, thereby decreasing the rate of PbO2 reduction (mechanolysis) [12]. The decomposition of oxides with high Pb4+ contents manifested itself by a rise in pressure. The resultant powders were characterized by XRD analysis (DRON-3M powder diffractometer, CuKα radiation). Relative XRD intensity was determined as the product of the peak height with the full width at half maximum. In XRD data processing, we used the Powder Cell-1.0 program. In view of the small contribution from oxygen to XRD intensities, its positional parameters were evaluated using ionic radii and/or by analogy with compounds having similar structures. RESULTS AND DISCUSSION High-energy mechanical processing is known to give rise to a reduction of metal oxides in the highest possible oxidation state [12–14]. This process involves charge separation in anions with the formation of holes and free electrons [14]. Hole recombination leads to irreversible oxygen removal, and the electrons are captured by traps, among which polyvalent cations are the most effective. According to Avvakumov et al. [12], mechanical processing of PbO2 not only reduces the
oxygen content but also gives rise to the following sequence of phase transformations: β-PbO2 α-PbO2 PbO1.57 PbO1.44
PbO.
The half-conversion time of PbO2 mechanically processed in vacuum is .10 min. However, XRD data [13] reveal with certainty only the β-PbO2 α-PbO2 transformation, accompanied by a slight oxygen loss. At longer processing times, reflections from Pb2O3 emerge and persist up to compositions close to PbO. It seems likely that the samples studied in [12, 13] contained an x-ray amorphous phase close in composition to PbO, and the crystalline Pb2O3 detected by XRD constituted only a small portion of the sample. The high inhomogeneity of those samples was due to the inappropriate mechanochemical processing (the presence of a dead zone in the jar of the planetary mill). Mechanical processing of minium, Pb3O4 , gives rise to broadening of XRD peaks and changes in relative intensities. The structure of minium is relatively stable: peaks from other phases appear only after τ * 10 min of processing at .30 MJ/kg. Mechanical processing of PbO leads to the tribochemical equilibrium R-PbO Y-PbO, independent of the starting form of PbO. The equilibrium ratio R-PbO : Y-PbO . 3 is attained in τ . 5 min of processing at .15 MJ/kg [11]. Thus, we observe phase transformations and partial reduction of Pb4+ with a halfconversion time (specific energy) from .2 min (.5 MJ/kg) in the case of the tribochemical equilibrium to .10 min (30–60 MJ/kg) in the case of PbO2 reduction. Milling PbO + PbO2 mixtures leads to the formation of intermediate oxides and Pb4+ reduction (Fig. 1). We observe the known phases Pb2O3 and Pb3O4 and a new phase Pb3O4 – x close in composition to minium. The hexagonal phase PbO1.37 also seems to form, as suggested by the shoulder on the reflection with d = 3.053 Å (Fig. 1b). The XRD patterns contain, along with sharp reflections from crystalline phases, an amorphous halo, typical of mechanochemical products (Figs. 1a, 1b). Lower energy processing of the same powder mixtures (at 20g or in a Fritsch planetary mill) yields only an x-ray amorphous phase (halos in the ranges d . 3–4 and 1.5–2 Å). Figure 2 displays a semiquantitative dependence of the phase composition on the supplied mechanical energy. The curves were obtained using nonoverlapping reflections normalized to 100%: 50% reflection ( 204 + 220) from Pb2O3 , 30% reflection (202) from Pb3O4 (Table 1), and 21% reflection (312) from Pb3O4 – x (Table 2). The milling time was from 30 s to 16 min. The R-PbO + PbO2 mixture differed from Y-PbO + PbO2 only by a higher mechanochemical yield of Pb2O3 . The same phases, but in other amounts, were obtained by milling the Pb3O4 + INORGANIC MATERIALS
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259
(a)
(b)
(c)
(d)
12
16
20
24
28
32
36
40 44 2θ, deg
48
52
56
60
64
68
72
Fig. 1. XRD patterns of (a) R-PbO + PbO2 after 2 min of processing at .4 MJ/kg (the arrows indicate reflections from Pb2O3) and (b) Y-PbO + PbO2 after 10 min of processing at .33 MJ/kg (the arrow indicates the 100% reflection from the hexagonal phase 2+
4+
2+
4+
PbO1.37). (c, d) Schematic XRD patterns calculated for the metastable phases Pb 2 – x Pb 1 + x O4 + 2x and Pb 2 + x Pb 1 – x O4 – 2x , respectively.
PbO2 mixture. The lattice parameters of the monoclinic phase Pb2O3 prepared by mechanochemical synthesis followed by heat treatment differ slightly from the JCPDS Powder Diffraction File data (given in parentheses): a = 7.80 (7.814) Å, b = 5.63 (5.625) Å, c = 8.45 (8.466) Å, and β = 124.8° (124.8°). The samples with a high Pb2O3 content were red-brown or, after heat treatment, black. According to the model for the reaction zone, if the difference in Mohs’ hardness between the reagents is ∆M . 3, the composition of the material in a transient state forming in the contact region must be close to PbO : PbO2 = 2. Therefore, the most likely initial product is minium, Pb3O4 . Each particle experiences, on the average, one impact per second [7]. The characteristic time of the mechanochemical processes under discusINORGANIC MATERIALS
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I, arb. units 350
PbO2
300 250
Pb2O3
PbO
Pb3O4
200 150 100 50
Pb3O4 – x
PbO1.37
0 0
2
4
6 8 E1/2, (MJ/kg)1/2
Fig. 2. Phase composition of the Y-PbO + PbO2 sample as a function of the supplied mechanical energy.
260
ZYRYANOV, GUSEV 2+
4+
Table 1. XRD data for Pb3O4 ( Pb 2 – x Pb 1 + x O4 + 2x at x = 0) prepared by mechanical processing (sp. gr. P42 /mbc (135), tetragonal system, a = 8.815 Å, c = 6.53 Å, Z = 4, red-brown color) I obs2
I obs3
18*
12
16
2
2
4
2
3.37
100
100
100
100
3.2650
3.26
5
. 20*
8
8
220
3.1166
3.10
17
31*
20
18
112
2.8922
2.89
33
73*
50
45
310
2.7875
2.79
48
. 40
45
37
202
2.6236
2.62
35
31
30
27
320
2.4448
2.44
3
1
2
2
222
2.2544
2.25
4
8
6
411
2.0318
2.03
17
.4
12
7
420
1.9711
1.96
13
5
12
8
213
1.9055
1.91
21
21*
20
18
402
1.8266
1.82
21
6
20
13
332
1.7529
1.75
32
36*
30
26
004
1.6325
1.63
8
10*
1
1
521
1.5878
1.59
12
6
12
7
440
1.5583
1.55
4
10*
8
5
512
1.5278
1.52
10
8
413
1.5253
8
5
530
1.5118
1.51
5
5
2
2
600
1.4692
1.47
8
2
4
2
224
1.4461
1.45
4
4*
2
2
314
1.4087
1.41
13
9
14
9
541
1.3471
1.35
6
5*
4
2
hkl
dcalc, Å
dobs, Å
Icalc
110
6.2331
6.20
15
201
3.6532
3.65
211
3.3749
002
I obs1
14*
7
Notes: I obs refers to the Y-PbO + PbO2 sample after 10 min of processing at .33 MJ/kg; I obs and I obs are JCPDS PDF data (cards 8-19 1
2
3
and 41-1493, respectively). * Contribution from Pb3O4 – x .
sion is on the order of 102 s. Clearly, the final products result from secondary impacts. In an A + B mixture, the fraction of the material passing through a transient state in the contact region is no higher than 6 vol % per impact (the conversion is 2% in the A + B contact regions in the most reactive oxide mixtures with an insignificant difference in hardness, high molecular weights, and a large contribution of the enthalpy (PbO + MoO3) [7] and is below 2% in the A + A and B + B contact regions, because there is no enthalpy contribution). The characteristic time of mechanical processing, necessary for the consumption of the starting reagents, is ≥20 s. With consideration for secondary
interactions, the reaction scheme of mechanochemical synthesis is as follows: Primary interactions Pb3 O *4 , (1) PbO + PbO2 (2) PbO + PbO PbO*, (3) PbO2 + PbO2 α-PbO *2 . Secondary interactions (4) PbO + α-PbO *2 Pb2O *3 , (5) PbO + Pb3O *4 (6) PbO2 + Pb3O *4
a-Pb O *1 + x , Pb2O *3 ,
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(7) PbO2 + PbO* Pb3 O *4 . Tertiary interactions (8) PbO* + α-PbO *2 Pb3O *4 , (9) Pb3O *4 + α-PbO *2
2+
α-Pb O *2 – x ,
(11) PbO* + Pb3O *4
Pb3 O *4 – x ,
(12) PbO* + Pb2O *3
Pb3O *4 ,
(13) a-Pb O *1 + x + Pb2O *3 (14) a-Pb O *1 + x + α-PbO *2
Pb3O *4 , Pb2O *3 ,
(15) Pb3O *4 + Pb2O *3 Pb O *1.37 , etc., where asterisks label the phases originating in the transient state D*, that is, crystalline (or quasicrystalline) vacancy-rich phases. This origin is equivalent to a decrease in Mohs’ hardness (or mechanical activation of a reagent via roll growth). In MO + M'O3 systems, the fraction of cation vacancies in the products with the scheelite structure attains 10% [15]; in lead titanate with the perovskite structure, the fraction of vacancies in two of the four sublattices attains about 30% [16]. Direct density measurements with a helium pycnometer demonstrate that mechanical processing reduces density by 9.3% [17]; that is, even without an enthalpy contribution, a transient state may occur in the contact region at a sufficiently high rate of mechanical processing. To simplify the description of the mechanochemical process, the composition of the forming phase is taken to be the same as that of the crystalline phase observed by XRD. Actually, the compositions of all the products may vary somewhat, and the crystalline product can be detected by XRD only after coherently scattering domains become large enough—a process which is also due to secondary interactions. The mechanism of mechanically induced “crystallization” is reminiscent of nanoparticle self-assembly; larger blocks are nonconvex formations [18] which are, during mechanical processing, in a dynamic equilibrium (similar to the Hüttich equilibrium in comminution processes [19]) with smaller blocks or individual crystallites 5–20 nm in size, which is close to the roll diameter [7, 17]. The probability of one or another process is determined by the probability that two dissimilar particles will come into contact, which, in turn, depends on the composition of the starting mixture. Mechanical processing of 2PbO + PbO2 mixtures yields, for the most part, minium; at a specific energy of .4 MJ/kg, Pb2O3 is present in trace amounts, whereas, after mechanical processing of PbO + PbO2 mixtures with the same specific energy, Pb2O3 is the major phase (Fig. 2). The long-term coexistence of amorphous and a few crystalline phases (Pb3O4 and Pb2O3 in our case) during mechanical processing is termed mechanochemical INORGANIC MATERIALS
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4+
Table 2. XRD data for Pb3O4 – x ( Pb 2 + x Pb 1 – x O4 – 2x at x = 0) in the Y-PbO + PbO2 sample after 10 min of processing at .33 MJ/kg (sp. gr. P42 /mbc (135), tetragonal system, a = 8.79 Å, c = 7.65 Å, Z = 4, red-brown color)
Pb2O *3 ,
(10) α-PbO 2* + α-PbO 2*
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hkl
dcalc, Å
Icalc
Iobs
110
6.215
42
8±5
200
4.395
12
5±5
210
3.931
9
3±5
112
3.258
9
37 ± 25
220
3.108
56
35 ± 15
202
2.885
100
100
312
2.249
21
25 ± 10
400
2.197
15
10 ± 5
410
2.132
8
32*
004
1.913
11
0 ± 10
412
1.862
14
15*
422
1.748
36
10 ± 25
224
1.629
18
5 ± 15
* Overlapping with reflections from Pb2O3 .
equilibrium. It was first found in the system 2PbO + MoO3 = PbMoO4 + Pb2MoO5 [20] and was later observed in the oxide systems 2PbO + WO3 [3] and PbO + V2O5 [10, 17] and also in apatite synthesis [21]. The essence of mechanochemical equilibrium in a statistical ensemble of particles is that the structure types stable against deviations from stoichiometry compete for the deficient reagent (PbO2 in our case and water in the case of apatite [21]). Mechanochemical equilibrium is a manifestation of the inherent thermodynamic features of open nonequilibrium systems, and the resulting crystalline phases are typical dissipative systems exhibiting self-organization and spatial variations in composition and structure in response to above-threshold mechanical impulses. The relaxation of the transient state to one or another structure type, close in stoichiometry to D*, is directed by random composition fluctuations or a combination of stresses [17]. The crystal structure of Pb3O4 is shown in Fig. 3. It can be seen that the (000) site can be partially occupied by oxygens; that is, the oxygen stoichiometry of min2+ 4+ ium may vary to some extent: Pb 2 – x Pb 1 + x O4 + 2x (0 ≤ x < 0.5). This is supported by the marked discrepancy between the XRD intensities calculated for Pb3O4 using the Pb–O distances obtained in neutron diffraction studies [22] and the observed intensities (Table 1). Note that the Pb2+ in the structure of minium is in a very atypical coordination, CN = 3, and the Pb2+–O distances are
262
ZYRYANOV, GUSEV
Pb2+ Fig.
3.
Crystal
Pb4+ structure
of
O minium,
Pb2+
O
Pb3O4
2+ 4+ ( Pb 2 – x Pb 1 + x O4 + 2x).
2+
4+
Fig. 4. Crystal structure of Pb3O4 – x ( Pb 2 + x Pb 1 – x O4 – 2x).
1 × 2.13 and 2 × 2.18 Å [22], while the normal Pb2+–O distance in oxygen octahedra is 2.54 Å [23]. At Pb2+ : Pb4+ < 2, minium has a different structure but belongs to the same space group: the Pb2+–Pb2+ chain becomes linear, the c cell parameter increases drastically, and a decreases slightly (Table 2). The XRD patterns of pure minium and mixtures of minium and Pb3O4 – x differ insignificantly. The presence of Pb3O4 – x is evidenced by the too high relative intensities of the reflections with d = 6.23, 3.11, 2.89, and 2.25 Å. Thus, mechanical processing of the sample with Pb2+ : Pb4+ . 2 yields an inhomogeneous mixture of phases of variable composition. The idealized structures of Pb3O4 and Pb3O4 – x displayed in Figs. 3 and 4 are probably the end-members of a continuous series of metastable solid solutions. Table 3. Positional parameters in the structure of Pb3O4 – x 2+
Pb4+
4+
( Pb 2 + x Pb 1 – x O4 – 2x at x = 0) Position Multiplicity
x
y
z
Occupancy
0.25
1
Pb4+
4
0
Pb2+
8
0.772 0.222 0
1
O(1)
8
0.394 0.106 0
1
O(2)
16
0.16
0.5
0.5
0.92
0.25
2+
4+
In the Pb3O4 ( Pb 2 – x Pb 1 + x O4 + 2x) synthesized mechanochemically, the coordination of Pb4+ remains unchanged (distorted octahedron), but the coordination number of Pb2+ may increase to 4 upon partial substitution of Pb4+ for Pb2+, resulting in distorted trigonalpyramidal coordination. The distance between Pb2+ and oxygen in position (000) is fairly small (2.007 Å), but, at a high concentration of cation vacancies, oxygen may occupy interstices, which is inconsistent with the space group of minium. In the proposed structure of 2+ 4+ Pb3O4 – x ( Pb 2 + x Pb 1 – x O4 – 2x), Pb4+ is in square-planar coordination, with a metal–oxygen distance of 2.32 Å, and Pb2+ is in distorted octahedral coordination, with two M–O distances equal to 2.14 and 3.05 Å and four distances, those in the square plane (on the average, two sites are vacant), equal to 2.51 Å (Table 3). The tolerance factor of a hypothetical ABO3 perovskite phase with A = Pb2+ and B = Pb4+ is 0.94, which satisfies the crystal-chemical criterion for this structure type [24]. However, no perovskite phase results from mechanochemical synthesis, just as in the case of PbVO3 . This is related mainly to the electronic structure of Pb2+, which has a lone electron pair. CONCLUSION High-energy milling of mixtures of lead oxides leads to mechanochemical synthesis of mixed-valence INORGANIC MATERIALS
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lead oxides and Pb4+ reduction. Pb2O3 is found to be in mechanochemical equilibrium with a number of phases of variable composition with the general formula 2+ 4+ Pb 2 ± x Pb 1 ± x O4 ± 2x, close in structure to minium, Pb3O4 . These crystalline phases are dissipative systems resulting from self-organization during relaxation of the transient state. The threshold character of the mechanochemical synthesis of crystalline phases is due to the development of a transient state in the contact regions between particles in response to mechanical impulses. ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research, grant no. 99-03-32733. REFERENCES 1. Zyryanov, V.V., Sysoev, V.F., and Boldyrev, V.V., Mechanochemical Ceramic Processing, Dokl. Akad. Nauk SSSR, 1988, vol. 300, no. 1, pp. 162–165. 2. Gleiter, H., Nanocrystalline Materials, Prog. Mater. Sci., 1989, vol. 33, pp. 223–315. 3. Zyryanov, V.V., Mechanochemical Ceramic Processing: Developments and Prospects, Mekhanokhimicheskii sintez v neorganicheskoi khimii (Mechanochemical Synthesis in Inorganic Chemistry), Avvakumov, E.G., Ed., Novosibirsk: Nauka, 1991, pp. 102–125. 4. Zyryanov, V.V., USSR Inventor’s Certificate no. 1403439, 1988. 5. Zyryanov, V.V., RF Patent 2065768, 1996. 6. Zyryanov, V.V., Sysoev, V.F., Boldyrev, V.V., and Korosteleva, T.V., USSR Inventor’s Certificate no. 1375328, Otkrytiya, Izobret., 1988, no. 7, p. 39. 7. Zyryanov, V.V., A Model for the Reaction Zone in Powders Mechanically Activated in a Planetary Mill, Neorg. Mater., 1998, vol. 34, no. 12, pp. 1525–1534 [Inorg. Mater. (Engl. Transl.), vol. 34, no. 12, pp. 1290–1298]. 8. Butyagin, P.Yu., Physical and Chemical Relaxation Processes in Solids: Mechanochemical Reactions in Binary Systems, Mekhanokhimicheskii sintez v neorganicheskoi khimii (Mechanochemical Synthesis in Inorganic Chemistry), Avvakumov, E.G., Ed., Novosibirsk: Nauka, 1991, pp. 32–52. 9. Fleischer, M., Wilcox, R.E., and Matzko, J.J., Microscopic Determination of Nonopaque Minerals, US Geol. Surv. Bull., 1984, no. 1627. Translated under the title Mikroskopicheskoe opredelenie prozrachnykh mineralov, Leningrad: Nedra, 1987.
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10. Zyryanov, V.V. and Lapina, O.B., Mechanochemical Synthesis and Structure of New Phases in the Pb–V–O System, Neorg. Mater., 2001, vol. 37, no. 3, pp. 331–337 [Inorg. Mater. (Engl. Transl.), vol. 37, no. 3, pp. 264–270]. 11. Zyryanov, V.V., Mechanically Induced Phase Transformations in PbO, Neorg. Mater., 1997, vol. 33, no. 10, pp. 1228–1234 [Inorg. Mater. (Engl. Transl.), vol. 33, no. 10, pp. 1039–1045]. 12. Avvakumov, E.G., Kosova, N.V., and Aleksandrov, V.V., Effect of Mechanical Activation on the Decomposition of Lead Dioxide, Izv. Sib. Otd. Akad. Nauk SSSR, Ser. Khim. Nauk., 1983, vol. 3, no. 7, pp. 25–30. 13. Avvakumov, E.G., Mekhanicheskie metody aktivatsii khimicheskikh protsessov (Mechanical Methods for Activating Chemical Processes), Novosibirsk: Nauka, 1979. 14. Zyryanov, V.V., Lyakhov, N.Z., and Boldyrev, V.V., ESR Study of Titania Mechanolysis, Dokl. Akad. Nauk SSSR, 1981, vol. 258, no. 2, pp. 394–397. 15. Zyryanov, V.V., Mechanochemical Synthesis of MM'O4 Oxides with the Scheelite Structure, Neorg. Mater., 2000, vol. 36, no. 1, pp. 63–69 [Inorg. Mater. (Engl. Transl.), vol. 36, no. 1, pp. 54–59]. 16. Zyryanov, V.V., Mechanochemical Synthesis of Lead Titanate, Neorg. Mater., 1999, vol. 35, no. 9, pp. 1101−1107 [Inorg. Mater. (Engl. Transl.), vol. 35, no. 9, pp. 935–940]. 17. Zyryanov, V.V., Mechanochemical Effects in Oxide Systems, Extended Abstract of Doctoral (Chem.) Dissertation, Novosibirsk, 2000. 18. Bokhonov, B.B., Konstanchuk, I.G., and Boldyrev, V.V., Structural and Morphological Changes during the Mechanical Activation of Nano-Size Particles, Mater. Res. Bull., 1995, vol. 30, no. 10, pp. 1277–1284. 19. Heinike, G., Tribochemistry, Berlin: Akademie, 1984. Translated under the title Tribokhimiya, Moscow: Mir, 1987. 20. Zyryanov, V.V., Mechanochemical Equilibrium in Pb2MoO5 Synthesis, Izv. Sib. Otd. Akad. Nauk SSSR, Ser. Khim. Nauk., 1990, vol. 2, pp. 101–106. 21. Gol’dberg, E.L. and Shapkin, V.L., Vibrational Instability of Mechanochemical Equilibrium, Sib. Khim. Zh., 1991, vol. 6, pp. 120–127. 22. Wells, A.F., Structural Inorganic Chemistry, Oxford: Clarendon, 1986, vol. 3, 5th ed. 23. Urusov, V.S., Teoreticheskaya kristallokhimiya (Theoretical Crystal Chemistry), Moscow: Mosk. Gos. Univ., 1987. 24. Venevtsev, Yu.N., Politova, E.D., and Ivanov, S.A., Segneto- i antisegnetoelektriki semeistva titanata bariya (Ferro- and Antiferroelectrics of the Barium Titanate Family), Moscow: Khimiya, 1985.
