Inorganic Materials, Vol. 41, No. 4, 2005, pp. 378–392. Translated from Neorganicheskie Materialy, Vol. 41, No. 4, 2005, pp. 450–464. Original Russian Text Copyright © 2005 by Zyryanov.
Ultrafast Mechanochemical Synthesis of Mixed Oxides V. V. Zyryanov Institute of Solid-State Chemistry and Mechanochemistry, Siberian Division, Russian Academy of Sciences, ul. Kutateladze 18, Novosibirsk, 630128 Russia e-mail:
[email protected] Received April 26, 2004
Abstract—Based on experimental data on the structure of disordered milling products in MO–M'O3 systems, a theory is proposed for ultrafast mechanochemical synthesis in oxide systems, considered as a threshold process. The key points of the theory are (1) the development of a transient dynamic state (D)* in contact regions via mass transfer by the roll mechanism in primary loading events and the formation of rotation regions (D)*2 in secondary events; (2) the formation of ordered reaction products supersaturated with vacancies as a result of the relaxation of the (D)* and (D)*2 states under unloading and quenching conditions; (3) the formation, as a result of secondary events, of a nanocomposite through mechanochemical equilibrium due to diffusion between the ordered and disordered states of different compositions; and (4) rapid charge separation and recombination, leading to reduction of oxides during milling concurrently with the disintegration of particles and mechanochemical interactions. The principal factors influencing the dynamics of mechanochemical synthesis (established by linearizing the dependence of the chemical response of the system on mechanical load) are the molecular weight of the simple oxides involved, the enthalpy of the reaction, and the difference in Mohs’ hardness between the reactants. The typical structures of mechanochemical synthesis products (solid solutions) are stable to disordering and compositional changes. The theory is supported by the trimodal mechanochemical synthesis rate distribution for mixed oxides and the mechanically induced electron–hole ferromagnetism. Ways of controlling the dynamics of mechanochemical synthesis and the structure of the products are discussed.
INTRODUCTION The reaction zone model for processes in planetary mills, a first step on the way to the theory of ultrafast mechanochemical synthesis of mixed oxides, was proposed in 1998 [1]. That model proved very useful in the mechanochemistry of oxides. In particular, it allowed earlier findings on the mechanism and dynamics of the process to be systematized [2]. After the development of that model, about a hundred new oxide compounds have been obtained, and the structures of most of them have been identified. For several oxide systems, the first mechanochemical phase diagrams have been mapped out, which differ drastically from equilibrium phase diagrams. The key points of that model—the development of a dynamic state (D)* via mass transfer by the roll mechanism, the formation of a material supersaturated with vacancies as a result of the relaxation of the (D)* state under unloading and quenching conditions, and the formation of primary and secondary products—have been substantiated in studies of various oxide systems. Some of the consequences of the model have been confirmed in independent structural studies of mechanochemical synthesis products and also by statistical analysis of dynamic results. For the development of the theory of ultrafast mechanochemical synthesis, analysis of new data in unified terms is needed. Mechanochemical synthesis can justly be called an ultrafast process because, even in oxide systems with a
melting point on the order of 3000 K, room-temperature mechanical processing (MP) ensures half-conversion in 30–300 s. The loading time is as short as ~10−3 s, since the impact time is τs ~ 10–5 s. On the average, each particle in the reaction zone experiences one impact over a time τMP ~ 1 s [2]. Note that ultrafast solid-state reactions were also observed earlier. For example, ultrafast reactions are induced in organic systems by a pressure + shear combination in Bridgman anvil cells [3]. Such reactions also occur during shock compression [4] and milling of energy-rich materials with explosive kinetics [5]. All of these processes, however, differ markedly in reactants and reaction mechanism from the mechanochemical synthesis of mixed oxides [1]. In recent years, mechanochemistry has been the subject of ever increasing attention, motivated by the wide range of systems studied and the application of high-energy milling in new areas of chemistry, physics, metallurgy, materials research, geochemistry, mining, environmental protection, biology, pharmacology, etc. [6]. Modern mechanochemistry includes various areas of research: from the study of phase transitions under hydrostatic pressure and processes leading to deviations from the Hooke law to cold fusion. A major problem in mechanochemistry is the irreproducibility of results obtained with different apparatuses or even with the same mill, which makes quanti-
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ULTRAFAST MECHANOCHEMICAL SYNTHESIS OF MIXED OXIDES
tative comparison difficult. Nevertheless, the methodological aspect of mechanochemistry is receiving insufficient attention [6–9]. Even the semiquantitative approach proposed by Butyagin [10] for characterizing the processes induced by milling has not yet become generally accepted. Ultrafast mechanochemical synthesis of mixed oxides—the most interesting area in mechanochemistry—is of great practical importance in connection with the explosively growing development of nanomaterials technology. The study of this process, accompanied by mass transfer, will ensure a better understanding of other intricate processes, e.g., mechanical activation (MP-induced changes in properties) of compounds and mechanical alloying. Kinetic studies are a standard tool for clarifying the reaction mechanism. In mechanochemistry, however, quantitative studies of process kinetics (more precisely, dynamics as a function of supplied energy, because the MP time has no physical meaning) depend on the type of the milling apparatus. The study of the mechanochemical synthesis mechanism can be thought of as the “double black box” problem. The algorithm solution was described in [1, 2]. THEORY OF ULTRAFAST MECHANOCHEMICAL SYNTHESIS General concepts. The most important objectives of the theory of ultrafast mechanochemical synthesis are (1) to establish the principal factors influencing the dynamics of mechanochemical synthesis and (2) to ensure the possibility of controlling the reaction dynamics and the structure of the product. These objectives imply that the mechanochemical method is considered primarily as a tool for creating new states of solids. To address this issue, it will suffice to use relative, rather than absolute, mechanical quantities. This approach allows one to avoid a broad range of complex loads in planetary and other ball mills and apparatuses, description of which is a separate issue, unrelated to chemistry proper. A simple approach to eliminating the mechanical “black box” is to use identical MP conditions [1]. If the response of chemical systems to milling is studied under fixed MP conditions, the energy supplied to the system is equivalent to a certain number of average impacts. Identical milling conditions can be ensured by an appropriate procedure [11]. The principal factors of mechanochemical synthesis can then be established using a model reaction and a variety of chemical systems with known physical and chemical parameters. To elucidate the process mechanism, the number of factors to be examined, which have been reported to have a significant effect on the dynamics of mechanochemical INORGANIC MATERIALS
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synthesis, is almost 20. Therefore, to establish the principal factors, the number of chemical systems of the same type must be at least 20. As shown earlier [1], the only model reaction meeting all the above requirements is MO + M'O3 = MM'O4,
(1)
where M'O3 = MoO3 or WO3 . Experimental technique for obtaining kinetic data. All experimental data on the mechanochemical synthesis of powders were obtained in an AGO-2 planetary mill at 60g [12]. The power supplied to the reaction system was about 0.5 kW per vessel. The AGO-2 mill is exceeded in parameters by some other mills [13], but owing to its simple design and the fact that the volume of the water-cooled vessels (2 × 150 cm3) is ideally suited to laboratory studies, this is widely used. The speed of the balls in the AGO-2, determining the feasibility of a given mechanochemical process, is no higher than 8 m/s. Such speeds can be achieved in various types of mills [13, 14]. Therefore, the results obtained with AGO-2 and other apparatuses can, in principle, be compared, after comparing the performances of the mills, e.g., using special tests [15]. In all experiments, we used identical milling conditions (10-mm-diameter steel balls, 220-g ball load, initial sample weight of 15 g) and an appropriate procedure [11], which involved a number of consecutive steps: 1. The surfaces of the balls and vessels were coated with the material to be processed, which ensured a large friction coefficient for the balls and a stable regime of their motion. 2. The mill was stopped at regular intervals to allow the balls to cool. 3. To eliminate material from dead zones and ensure uniform powder density or voidage, we performed periodic positive mixing. Figure 1 illustrates the effect of powder voidage on the effectiveness of milling [2, 15]. The broadening of the EPR signal from a paramagnetic probe is associated with variations in the lattice strain produced by dislocations and grain boundaries in agglomerates. Whereas the initial tap density of the powder is typically 30– 40%, the density of milled oxide materials, e.g., BaTiO3 , near the wall may attain 70–80%. The efficiency of milling, quantified by the derivative of the response with respect to the energy supplied, decreases by more than one order of magnitude upon powder densification. Thus, one reason for the poor reproducibility of results is that, without stabilizing the voidage, any measurements give inaccurate results. The strong effect of voidage on the milling efficiency is due to the fact that a reduction in voidage is accompanied by an increase in the number of interparticle contacts and
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τMP , min
n
12
12
(2) to improve the macrohomogeneity of the powder to the level suitable for x-ray diffraction (XRD) examination; (3) to decrease the reduction of oxides, inevitable during MP;
2 1 10
10
(4) to prevent thermal annealing of metastable reaction products (by reducing the average ball temperature to about 320 K); and
8
8
(5) to achieve acceptable MP reproducibility even in frictional planetary mills.
6
6 3
4
4
4
2
2
0
0 0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 ∆ H × 10–4, T
Fig. 1. Broadening of EPR lines of Mn2+ in MgO during (1) rolling on a simulator and (2–4) milling in AGO-2: (2) continuous milling, (3, 4) mixing every 60 and 30 s, respectively.
total contact area. The distribution of the mechanical load over a large number of contacts reduces the probability of energy concentration in local regions. As a result, the main processes are elastic deformation and lower threshold processes, and most of the mechanical energy supplied is converted to heat. Mechanochemistry can be thought of as a science dealing with threshold phenomena in the dependence of physicochemical responses on mechanical loads, including deviations from the Hooke law and irreversibility of elastic deformation. The mixing step restores the voidage of the powder and makes it possible to quantitatively analyze the response as a function of the energy supplied to the system, which becomes a linear function of the MP time (Fig. 1, curve 3). To examine the dynamics of mechanochemical synthesis, we took five or six samples (~1 g) close in voidage each time the mill was stopped. The described procedure makes it possible (1) to reduce the contamination level of the powder by two to three orders of magnitude, to ≤0.05% in AGO-2 and to ~10–3% in M-3 and PM-1 mills [13];
Contamination of powders during milling in steel vessels with steel media is thought to be inevitable. To reduce contamination, it is recommended to use wearresistant corundum and zirconia ceramics or WC/Co composites [9]. This, however, markedly reduces the MP rate because of the brittle fracture of ceramic media, and mechanochemical synthesis of crystalline materials is then possible in only a limited number of systems and requires a long time [16, 17]. In most works where strong mechanochemical effects were observed during ball milling, the MP procedure and compositional changes due to contamination, reduction of oxides, oxidation of alloys, or reactions with the gaseous ambient were not described. Monitoring the chemical composition of the material during MP is crucial for understanding and controlling mechanochemical processes. Loading parameters and response. To establish the principal factors governing the process, it is necessary to select the loading and chemical response parameters: the calculated temperature of the reaction zone (powder) due to an average impact and the yield K = 1/E1/2 , where the half-conversion energy E1/2 (MJ/kg) is an average parameter which can be determined from the amounts of the starting reagents and reaction products. Data on the dynamics of reaction (1) were obtained in 1987 [18], but attempts to find correlation between the load and response using normalization per 1 mol of substance, common in chemistry, proved unsuccessful: the linear correlation coefficient was r = 0.47 (Fig. 2a). In 1997, we attempted “physical” normalization and obtained, in all of the systems studied, linear (rather than exponential) correlation between the load and chemical response, with r = 0.64. In evaluating the temperature of the reaction zone, one can use only the physical and chemical parameters of the substance in a normal state. Since mechanical loading changes the parameters of the material, one has to compare the temperature increment calculated for the first impact with the chemical response after 10−100 impacts. To assess the accuracy of such extrapolation, consider typical curves for the dynamics of mechanochemical synthesis (Fig. 3). Extrapolation to a conversion α = 0.5 yields correction coefficients ki ~ 1.05–1.10; if different systems are compared ki/kj ≅ 1. INORGANIC MATERIALS
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ULTRAFAST MECHANOCHEMICAL SYNTHESIS OF MIXED OXIDES Tz*, K
α 1.0
(a)
381
(a)
0.8
200
0.6
1 2 3
0.4 100
0.2 0 0
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Tz*, K (b) 200
α 1.0
100
200
300
400
(b)
0.8 0.6 1 2 3
0.4 0.2 100
0 0
0 Tf*, K
0.2
0.1
0.3
0.4
0.5
0.6
0.7
(c)
400 300
50
100
150
200
250 300 Time, s
Fig. 3. Kinetic curves of mechanochemical synthesis inferred from XRD intensities for the (1) reactants and (2) reaction product with a (a) small and (b) large error of determination of E1/2 in the HgO–MoO3 and BaO2–MoO3 systems, respectively; (3) average curve obtained using spline functions.
Structure of the theory. Generally, a theory of the mechanochemical synthesis process must include the following:
200
(1) Spatial model on macroscopic (ensemble of particles), mesoscopic (contact between particles), and microscopic (individual particle) scales;
100
0
500
0.2
0.4
0.6
0.8
1.0
K*, kg/MJ
(2) Mesomodel for a mixture of substances, describing a primary event and secondary events; and (3) Time evolution of the processes.
Fig. 2. Chemical response (heating of the reaction zone) as a function of mechanical load for MO–M'O3 systems; Tz is the average increase in temperature due to the supplied mechanical energy, linear correlation coefficient r = (a) 0.47 and (b) 0.67; T * is the relative increase in temperature at
These points differ in importance from the viewpoint of the purpose formulated above; nevertheless, we consider all of them in order to maintain a logical sequence.
interparticle contacts with allowance made for the deviation from stoichiometry in the reaction product, (c) r = 0.9437.
Macromodel. We consider an average impact of a ball on a flat powder layer, whose thickness depends on the sample volume, the tap density of the powder, and the working surface area inside the vessel. The ball velocity in an average impact, vs, is equal to the velocity of fall from a height equal to the ball diameter D in a gravitational field equal to the centrifugal factor of the
f
The accuracy in determining E1/2 by XRD is at best ±15% and may be as low as ±30%. For this reason, the contribution of extrapolation to the error of determination of E1/2 is insignificant. INORGANIC MATERIALS
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mill (g): vs = (2gD)1/2 = 3.8 m/s. The average impact energy is given by Es = 1/6πD4ρg,
(3)
where ns is the number of average impacts. The average temperature in the reaction zone due to the mechanical energy of a ball in an average impact is Tz = Es(MA + MB)/(Camz),
(4)
where MA and MB are the molecular masses of MO and M'O3 , respectively; Ca is the average molar heat capacity; and mz = ρaVz is the mass of the material in the reaction zone (ρa is the average density). The volume of the material in the reaction zone is Vz = πLz(D – Lz)L0P0 ,
(5)
where L0 is the initial thickness of the powder layer (relative density P0 = 0.45) and Lz is the depth of the pit produced in the powder layer by the impact. If a powder sample of weight m is evenly spread over the vessel wall (S ~ 0.03 m2), the thickness of the powder layer is L0 = 2/3m/(P0Sρa),
(6)
where the factor 2/3 is introduced because, in the appropriate MP procedure, some of the material rotates together with the balls. Since Lz cannot be evaluated theoretically, it was determined using the relation Lz/L0 = P0/Pz , (7) where, for Pz , we used experimental data on the density of aggregates forming during MP in the planetary mill in question. In materials with Mohs’ hardness HM = 6, the relative density of aggregates is ~0.80, as determined by mercury porosimetry, and increases with decreasing hardness. To evaluate the relative density, we used a simple linear relation normalized to unity at zero hardness of the reactants, Pz = 1 – (HM)av/30.
(8)
Here, the average hardness of a mixture of reactants is HMav = (VA(HM)A + VB(HM)B)/(VA + VB), where VA and VB are the volumes of the reactants. From the above values, the impact time τs = 2Lz/vs,
NτMP = Esm/mz.
(2)
where ρ is the density of the ball material. In our experiments, Es ≅ 0.03 J. The mechanical energy supplied to the material is Ö0 = nsEs = τMPN,
appears in the reaction zone at τMP ~ 2 s intervals, which can be found from the relation
(9)
in the systems studied lies in the range (2.4–4.7) × 10−5 s. On the average, each particle in the vessel
(10)
The table presents data on the average increase in the temperature of the reaction zone, Tz, due to the mechanical energy supplied to the powder. In systems with incongruent melting of MM'O4 , mechanochemical interaction is very weak or missing (CuO–WO3 and NiO–WO3), which may be due, e.g., to reduction [18]. Interaction is also missing in the MgO–MoO3 system because of the very large difference in Mohs’ hardness between the reactants: ∆(HM) = 4.5. In systems with congruent melting of MM'O4 , the dependence of the yield K on Tz (Fig. 2b) is described by a linear correlation coefficient r = 0.67. Note also the well-defined threshold for mechanochemical synthesis. Primary and secondary events in the mesomodel. Mechanochemical synthesis occurs at interparticle contacts created by impacts. The relatively low mechanical energy supplied to the system is concentrated owing to the small contact area between solid particles and gives rise to local changes in physical parameters, including temperature. In the course of MP, the energy required for mass transfer is delivered directly to interparticle contacts, which ensures a high efficiency of mechanochemical synthesis (as in the case of radiothermal synthesis) compared to thermal synthesis, where, at high temperatures, most of the substance is beyond the diffusion front. Ultrafast mass transfer during mechanochemical synthesis cannot be accounted for by diffusion [2] upon deformation intermixing activated owing to the reduction in diffusion distance and increase in vacancy concentration by the deformation creep mechanism [19]. A primary mechanochemical event is described by the general equation proposed in [1], A+B
(AxB)*
A1 – δB* + B*
(11.1)
where (AxB)* designates a so-called dynamic state (D)* in the form of a flat layer composed of growing rolls and voids (Fig. 4); A and B are the hard and soft (on Mohs’ scale) reactants, respectively; and B* is a particular form of reactant B, resulting from the relaxation of the dynamic state (e.g., with an amorphous or turbostratic structure). The formation of B* with a turbostratic structure in the course of MP has been observed so far only in the PbO–2MoO3 system. Given that mechanochemical powders are always composites made up of ordered regions in a disordered matrix, Eq. (11.1) can be simplified to A+B
(A1 – δB)*
A1 – δB*,
(11.2)
where the primary product is always deficient in the hard component, which ensures a high vacancy concentration in the case of structural ordering in [AB], and INORGANIC MATERIALS
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383
Parameters of MO–M'O3 systems (congruent melting of MM'O4) System
(HM)A–(HM)B
K, kg/MJ
αz , %
Tz , K
Tch , K
Y-PbO–MoO3
2–1.5
0.652
1.78
166
757
R-PbO–MoO3
2–1.5
0.638
1.70
163
744
Pb3O4–MoO3
2.5–1.5
0.652
1.66
156
576
BaO2–MoO3
2.5–1.5
0.254
0.55
94
1299
ZnO–MoO3
5–1.5
0.021
0.043
74
135
CdO–MoO3
3–1.5
0.349
0.81
106
700
HgO–MoO3
2–1.5
0.362
1.03
172
444
CaO–MoO3
3.5–1.5
0.075
0.121
56
1412
SrO2–MoO3
3–1.5
0.182
0.33
75
1452
Y-PbO–WO3
2–5
0.526
1.61
233
509
R-PbO–WO3
2–5
0.556
1.69
229
496
Pb3O4–WO3
2.5–5
0.395
1.16
219
341
BaO2–WO3
2.5–5
0.289
0.68
142
1847
ZnO–WO3
5–5
0.231
0.54
129
255
CdO–WO3
3–5
0.231
0.63
167
567
HgO–WO3
2–5
0.319
1.02
242
55
CaO–WO3
3.5–5
0.176
0.37
105
1426
MgO–WO3
6–5
0.192
0.43
107
688
MnO–WO3
5.5–5
0.210
0.48
120
586
SrO2–WO3
3–5
0.194
0.43
122
1236
CoO–WO3
5–5
0.146
0.36
117
430
Note: HM is Mohs’ hardness.
the symbol * denotes that the product originates from the dynamic state. The validity of Eq. (11) has been confirmed by various methods. 1. The difference in Mohs’ hardness between the reactants can be taken into account by introducing a small correction (the larger the difference, the smaller the yield), K* = (1/E1/2)exp(γ∆(HM)),
(12)
where γ is a parameter drastically improving the correlation between the load and response, up to r = 0.847. 2. XRD analysis of crystalline mechanochemical synthesis products with scheelite structure at conversions in the range α = 0.5–0.9 attests not only to qualitative agreement with theoretical predictions (crystalline product deficient in the harder component) but also to good correlation between the composition and difference in hardness, r = 0.91 [20]. 3. According to XRD data, mixed oxides always contain high vacancy concentrations [21]. INORGANIC MATERIALS
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4. According to He pycnometry results, the relative density of BaTiO3 after MP is 0.908 [2]. 5. From simple geometric considerations, the density of products originating from the dynamic state must be ~ 0.9 g/cm3 [20]. 6. Independent evidence of high vacancy concentration (loosening of the structure) in FeTiO3 was reported by Maksutov et al. [22], who observed, along with a sharp increase in dissolution rate, a reduction in zerophonon gamma absorption (Mössbauer effect): by a factor of 2 after 10 min and by a factor of 2.5 after 60 min of MP in an AGO-2. Their results demonstrate that Mössbauer spectroscopy is no less selective in probing the structure of MP powders than are NMR and EPR [23], which, however, was not taken into account in [24, 25]. In connection with this, it is reasonable to assume that Eq. (11) has a higher degree of generality and is also applicable in the case A = B (mechanical activation of individual compounds). Indeed, mechanochemical
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(a)
e–
(b) e–
(c)
Fig. 4. Two-dimensional scheme illustrating the development of a dynamic state (D)* in the contact region as a result of a primary loading event: (a) initial state; (b) roll growth until collision, accompanied by emission processes, (c) relaxation of (D)* to the primary product.
reactions between preactivated simple oxides follow a different path [2]: [Pb2WO5], (13.1) PbO + WO3 PbO + WO *3
[PbWO4],
(13.2)
CdO + PbO2
[Cd2PbO4],
(14.1)
CdO + PbO *2
[CdPbO3]
(14.2)
(in parentheses, we indicate the structure type of the product). The change in reaction path is equivalent to a reduction in the Mohs’ hardness of reactant A*. The heat of chemical reaction also increases the temperature of the contact region. This contribution can be thought of as internal, in contrast to the mechanical contribution. To reveal correlation with the mechanochemical yield K*, the equation describing heating INORGANIC MATERIALS
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with consideration for heat removal and the internal character of the heat of reaction can be written in the form M T * = [ T z + βα z T ch ] -------^ + βα z T ch , M
(15)
where β is a parameter, and Tch is the increase in temperature due to the chemical reaction. The correction for heat removal has the form of the ratio of the molecular weight of the reaction product to that of the probe: ^ M/ M = (MA + MB)/361. As the probe, we used the HgO–MoO3 system, in the center of the sample, with a small difference in hardness between the reactants: ∆(HM) = 0.5. The simple expression M/M^ replaces the modified Debye equation for the phonon contribution to thermal conductivity, 3/2
λph ~ T m ρ2/3/(M2/3T)
(16)
with a correlation coefficient r = 0.96 for MO oxides. If the kinetic curves of mechanochemical synthesis are similar, conversion αz in the first event is given by αzVz/(VA + VB) = Es/(2E1/2).
(17)
The curves are indeed similar, and systems with unusual kinetic curves make the main contribution to the reduction in correlation coefficient. The values of αz and Tch are listed in the table. The correlation between T* in Eq. (15) and the normalized yield K* improves: r = 0.9378. Deviations of the composition of the crystalline product from stoichiometry must also be corrected for. In the case of Tch , one can use the same correction for the difference in hardness, exp(γ∆(HM)). The proposed correction for changes in the molecular weight of the reaction product contains no new parameters and does not exceed the error of determination of E1/2, k = ∆(HM)(MB – MA)/[(HM)max(MA + MB)], where MB and MA are the molecular weights of the soft and hard reactants, respectively. The final equation for the relative heating of the contact region, with allowance made for deviations from stoichiometry, has the form M T *f = [ T z + βα z T ch exp ( – γ∆ ( HM ) ) ] -------^ ( 1 + k ) M (18) + βα z T ch exp ( – γ∆ ( HM ) ). The correlation between K* and T *f improves notably and attains r = 0.9437 (Fig. 2c). Note for comparison that the values of r achieved in [1, 2] were 0.92 and 0.94, respectively, with a more intricate form of Eq. (18) and with the use of the ZnO–WO3 system as INORGANIC MATERIALS
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the probe. In this system, the end-embers are close in hardness, but it lies away from the center of the sample. Given that Mohs’ hardness is a semiquantitative characteristic and that a number of approximations were made, the achieved value of r is rather high. For example, the density of the MO oxides studied is obviously dependent on their molecular weight, with a correlation coefficient r = 0.96. The parameter γ = 0.144 reflects the reduction in mechanochemical interaction because of the difference in hardness between the reactants and the associated decrease in heat effect due to deviations from stoichiometry. Parameter β has a simple physical meaning: β = 1 if no mechanical energy is spent for comminution, defect formation, or aggregation because the contribution of the heat of reaction to the heating of the reaction zone must be twice as large as that of mechanical energy since half of the A–A and B–B contacts are chemically inert but consume mechanical energy. The best correlation between K* and T *f is achieved at β = 10.2. In other words, only one-tenth of the theoretically possible mechanical energy is delivered to reactive contacts. Thus, linearizing the dependence of the response on load, we established the principal factors influencing the dynamics of mechanochemical synthesis: the molecular weight of the simple oxides involved (determining their density, thermal conductivity, and heat capacity), the enthalpy of the chemical reaction, and the difference in Mohs’ hardness between the reactants (which also determines the compositions of the dynamic state and primary reaction product). A difference in hardness ∆(HM) = 4 is a threshold for mechanochemical synthesis in terms of the mechanical properties of the reactants. In contrast to what was concluded in [7, 8], the particle size of the starting materials is unimportant in ultrafast mechanochemical synthesis because the main contribution to mass transfer comes from the roll mechanism. Indeed, we varied the particle size of the starting materials by three orders of magnitude but the load–response correlation coefficient remained rather large. Contact interactions can be evaluated theoretically only for the first loading event. Since the products of mechanochemical synthesis can be identified by XRD only after 10–100 loading events, we conclude that examination of secondary events is an important area of the theory under discussion. This issue, however, has not been addressed in published reports, even though secondary events are responsible for a number of interesting effects during MP, including the formation of coherently scattering domains up to 100 nm in size [26] and the so-called mechanochemical equilibrium [27, 28]. In earlier studies [1, 2], to emphasize the development of (D)*, primary and secondary loading events were assumed to differ markedly. The mass transfer in primary events was assumed to follow an ultrafast roll mechanism with the formation of (D)*, while secondary events slowly (through diffusion mixing) brought
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α 1.0 2
0.5
1 3 E Fig. 5. Dynamics of mechanochemical synthesis in systems with intermediate primary products (XRD data): (1) primary product, (2) secondary product, (3) starting reagents.
N 40
1
30 20
2
10
3 1
2
4
8
16
32 64 128 E1/2, MJ/kg
Fig. 6. Mechanochemical synthesis rate distributions in oxide systems: (1) primary, (2) secondary, and (3) reduction products.
the composition of the reaction product to the composition of the mixture. Actually, deformation mixing can be thought of as the formation of rotation regions with diffusion mass transfer upon rotation cessation and unloading. Rotation regions occur under shear loading in both liquids (where so-called Quette flows develop [29]) and solids at high plastic strain levels, leading to discontinuity and loosening [30]. It is reasonable to expect that the contribution of rotations (rolls) to mass transfer gradually decreases with increasing number of loading cycles, which implies that Eq. (11) is also applicable to secondary processes: A x B* + A y B*
( D )*
2
[ A n B m ]* + B*
( A* or A k B *l ).
In this approach, the differences in mass transfer efficiency between primary and secondary events may be related to a reduction in the probability of the system surmounting the threshold for the formation of a dynamic state, in particular because of the decrease in the contribution of the enthalpy. The large difference in the efficiencies of mass transfer by different mechanisms may be revealed by different techniques, in particular by determining the composition of crystalline mechanochemical synthesis products at various conversions, as was done in a number of works [2, 31]. Studies of mechanochemical synthesis in mixtures of oxides differing markedly in composition from (D)* and forming broad ranges of crystalline solid solutions reveal dynamics typical of mechanochemical synthesis, with the formation and consumption of the primary product (Fig. 5). The E1/2 of primary products is independent of the mixture composition, and that of secondary products can be determined in the systems represented in Fig. 5. Figure 6 shows the synthesis rate distribution obtained with an appropriate MP procedure. It is clear from these data that, on the average, primary and secondary products differ in the dynamics of formation by one order of magnitude, which lends support to the view that the roll and diffusion mechanisms make different contributions to mass transfer in primary and secondary events. Secondary processes include transformations with the participation of mechanochemical synthesis products or reactants after loading, i.e., those originating from (D)*. Among such processes are syntheses with an activated reactant, which only lead to changes in the composition of the primary product: A + B*
A1 – δ – xB*,
(19.1)
A* + B
A1 – δ + xB*.
(19.2)
Such reactions appear, however, unlikely at α < 0.5 because the enthalpy does not contribute to the threshold process of A* and B* formation. Secondary products are formed by the reactions A + A1 – δB*
A2 – γB*,
(20.1)
B + A1 – δB*
A1 – γ B *2 ,
(20.2)
A* + A1 – δB*
A2 – εB*,
(20.3)
B* + A1 – δB*
A1 – ε B *2 ,
(20.4)
which become important when a sufficient amount of the primary product is accumulated. These reactions are accompanied by coalescence of the primary product,
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and secondary products, A2 – γB*+ A2 – γB*
[A2 – γB*],
(21.2)
A1 – γ B *2 + A1 – γ B *2
[A1 – γ B *2 ],
(21.3)
A2 – εB* + A2 – εB*
[A2 – εB*],
(21.4)
[A1 – ε B *2 ],
(21.5)
A2 – γB* + A2 – εB*
[A2 – νB*],
(21.6)
A1 – γB* + A1 – εB*
[A1 – νB*],
(21.7)
A1 – ε B *2 + A1 – ε B *2 and reactive coalescence,
etc. (brackets indicate an increase in the size of coherently scattering domains). The energy supplied to an inhomogeneous chemical system during loading favors atomic-scale homogenization of the system. During unloading, the system relaxes, dissipating energy, which may be accompanied by both further diffusion homogenization and segregation. After numerous cycles, the system reaches equilibrium, except for slow compositional changes due to reduction (or reaction with the gaseous ambient). The relaxation path of the transient dynamic state (D)* or (D)*2 depends on its composition and size. If the size (thickness) of (D)* is below some limit, the transient state may decompose into the constituent phases, without formation of the intended product. This accounts for the absence of mechanochemical synthesis products in many systems, even if there are grounds to expect mechanochemical interaction at interparticle contacts. If the dynamic state is close in composition to some structure type, relaxation follows Eq. (11.3) and reaches that ordered state, which can then be identified by diffraction techniques. If the composition does not correspond to any structure type or differs markedly from that of the nearest structure type, a disordered (amorphous), energy-rich state is formed. This effect differentiates mechanochemical synthesis from thermal synthesis. If the mixture composition is close to two structure types, secondary events bring the system to mechanochemical equilibrium. Earlier, mechanochemical equilibrium was given attention because of the unusual product composition. For example, MP of a 2PbO + MoO3 sample yielded a mixture of two phases with [PbMoO4] and [Pb2MoO5] structures [27]. In the system 2PbO + WO3 , very close in phase relations to the Mo system, the intended product with the [Pb2WO5] structure first appeared together with [PbWO4] and then disappeared entirely. The unusual phase composition of mechanochemical synthesis products at mechanochemical equilibrium was tentatively attributed to the formation of far-from-stoichiometry compounds and the competition between two structure types for the deficient reactant (M'O3 in the instance under consideration) [2]. INORGANIC MATERIALS
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As pointed out earlier, there is no fundamental difference between mechanochemical processes resulting in conventional and unusual phase compositions. All processes follow Eq. (11.3), and the key feature of equilibria, including tribochemical and mechanochemical ones, is the competition between different structure types (which persist in the form of ordered grains during loading) for the disordered, amorphous state during unloading. Ordering leads to thermal energy release at the reaction front. The released energy is comparable to the crystallization energy, which increases the relaxation time and the size of coherently scattering domains. In about half of the processes studied, mechanochemical synthesis products differ in structure from solid-state thermal synthesis products. Mechanochemical synthesis products crystallize in a limited number of structure types. Perovskite and fluorite phases were obtained in about half of the systems studied [16, 21, 28, 32]. Among other phases obtained by milling are pyrochlores [32], scheelites [20], spinels [25], rocksalt-structure (fcc) phases [26], sillenites [26], columbite, clinobisvanite, the simplest layered phases (K2NiF4 , Cd2PbO4 [26], γ-Bi2VO5.5 , and Bi2GeO5 (Aurivillius phases)), and several structure types represented each by one compound. It is easily seen that mechanochemical synthesis products have structures that are favorable for the formation of solid solutions. The mechanism of mechanochemical synthesis almost rules out the formation of stoichiometric compounds, and even XRD single-phase materials are extremely inhomogeneous [26, 32]. Thus, statistical analysis of structures resulting from mechanochemical synthesis lends support to the mechanism inferred from analysis of the process dynamics. Micromodel. Disintegration and plastic deformation of individual particles in reaction mixtures are accompanied by mechanochemical processes at contacts between particles. Such processes are well studied and are not related directly to mechanochemical synthesis, but they are accompanied by electron emission. The effect of emission on these processes is essentially unexplored since its intensity, as measured by external detectors, is very low. At the same time, the mechanically induced two-dimensional electron–hole ferromagnetism revealed in magnetic resonance studies of many nonmagnetic dielectrics, including TiO2 (anatase), Al(OH)3 [2], NaF [33], KBr, and NH4I [34, 35], as well as by static magnetic measurements on anatase, indicates that loading gives rise to effective charge separation with the formation of free electrons. Because of the short-range exchange interaction, ferromagnetically ordered states may only develop at a very high density of spin hole centers. The concentration of paramagnetic centers resulting from disintegration is typically low, on the order of 10–7 to 10–5 cm–3, owing to effective recombination [36, 37]. However, at a high two-dimensional density of spin centers, these may
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||
⊥
0.26
0.30
0.34 H, T
Fig. 7. Ti3+ FR (two sample orientations) and EPR (inset) spectra of anatase after four impacts.
undergo ferromagnetic ordering, with spin-forbidden ↓↑ ↑↑ electron–hole recombination, k 0 k 0 [38]. The room-temperature lifetime of mechanically induced ferromagnetic states in nonmagnetic dielectrics is several weeks. Optimization of impact processing conditions in [33–35] made it possible to detect, in some samples, signals of the envelope of a noiselike ferromagnetic resonance (FR) spectrum (Fig. 7) with a signal-to-noise ratio of ~104 and a peak height of up to ~103 m (maximum signal amplification on a 9.4-GHz RE-1306 X-band spectrometer). Ferromagnetic ordering ensures a resonance amplification factor of ~103 compared to an analogous ensemble of unpaired spins because of the different temperature dependences of magnetization [39]. This strong FR is due to the fact that pressed samples remember the impact direction owing to oriented ferromagnetic zones. Powdering reduces the signal by several orders of magnitude owing to the strong anisotropy. The maximum spin concentration estimated from the FR intensity is ~10–5 to 10–4, and the supplied mechanical energy (~4 × 104 J/mol) is converted with an efficiency of ~1%. According to estimates under the assumption that the narrow (~10–4 T), orientation-dependent resonances are due to individual two-dimensional ferromagnets, their size is 10 µm, which exceeds the particle size. Impact-processed samples can be thought of as polycrystals with a ferromagnetic “network” of electron and hole centers on grain boundaries and dislocation lines. This picture is consistent with the model proposed by Kosevich and Shklovskii [40] for interpreting the sensational results on dislocation ferromagnetism, which were not confirmed later [41]. Analogous noiselike RF spectra were observed after heat treatment (500°C, air)
of kaolinites from deposits containing mixed-layer Fe minerals [42], which provides further evidence for the two-dimensional character of the ferromagnets in question. Note that similar FR spectra were also reported for hydrothermally synthesized Fe-containing zeolites, but those spectra were attributed to ferromagneticexchange-coupled superparamagnetic structures in the zeolite host [43]. That interpretation does not account for the anisotropy of the spectra and sharp lines. At the same time, hydrothermal conditions are favorable for the formation of layered clay minerals of the same composition, with Fe-enriched layers, since only a limited amount of Fe can be incorporated isomorphically into the kaolinite structure. The spin density on the inner surface, which remembers the loading process owing to magnetic ordering, is ~1018 m–2. Upon brittle fracture of NaF crystals, the charge density around the crack tip is 2 × 1016 m–2 [7], while the calculated charge density on the (111) face is 5.5 × 1018 m–2, which indicates that the charge density during loading may be two orders of magnitude higher than the experimentally determined value by virtue of recombination processes. It seems likely that shortterm, local disturbance of electroneutrality during loading may enhance the plasticity of the material (electroplastic effect). One possible consequence is acceleration of mass transfer, in particular owing to electricfield-enhanced diffusion. Estimates of the emission intensity in the above micromodel point to the possibility significant reduction of oxides at supplied energies on the order of ~E1/2. During milling, plastic deformation in dislocation slip planes and friction between particles give rise to charge separation, leading to the formation of holes and free electrons of various energies [44]. The system of chemical equations for redox reactions, describing the dynamics of paramagnetic centers, was first illustrated by the example of anatase [37]: O2–
O– + e–,
e– + Ti4+
(22)
Ti3+,
(23)
Ti i ,
3+
(24)
M2+,
(25)
e– + [ ]
[e–],
(26)
e– + O–
O2–,
(27)
O2– + O↑,
(28)
4+
e– + Ti i
e– + M3+
O– + O– O+O
O2↑.
(29)
The EPR spectrum of high-purity anatase processed in an AGO-2 with corundum vessels showed hole centers 3+ assignable to O–, Ti i interstitials, and [e–] electronic centers with an MP time delay because of the reactions INORGANIC MATERIALS
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with Ti ions (23) and (24) and, more importantly, charge transfer between impurities (25). A similar, but 3+ stronger Ti i EPR spectrum was observed, together with sharp FR lines, for anatase after four impacts (Fig. 7). The reduction of the oxide follows reactions (28) and (29). Some of the neutral oxygen remains in the sample and can only be removed by heating. Reactions (23)–(29) must be supplemented by O–↑ + Ti3+↓
O2– + Ti4+.
(30)
For a triplet state, this reaction is spin-forbidden: O–↑ + Ti3+↑ ≠ O2– + Ti4+.
(31)
Smirnov et al. [45] revealed an orienting surface effect on parallel spin ordering in an Fe3+ monolayer on SiO2 . The O– and Ti3+ paramagnetic centers have low mobility and may form primary ferromagnetically ordered states [ O–↑ Ti3+↑ O–↑ ], which are then stabilized by electrons after energy losses in Ti3+↑ e–↑ O–↑ ]. the lattice: [ O–↑ Experimentally, FR was only observed in high-purity samples after three to five impacts of a shot-filled hammer (after the first impact, FR was only detected in very plastic NH4I), which ensured shock compression of the powders and formation of grain boundaries. The new interfaces generated electron–hole pairs during loading and acted as a system of electron traps during relaxation. The first mechanical impulses seem to result in the filling of deep electron traps. If the material contains significant levels of impurities, reaction (25) prevails, and the electron concentration is too low to stabilize ferromagnetic states. The thermal behavior of milled anatase also depends strongly on impurity concentration. During heating, high-purity anatase loses up to ~40 mol % oxygen and turns black, whereas its conductivity remains low. Anatase samples containing significant levels of impurities and milled under the same conditions have a different EPR spectrum. During heat treatment, they lose 1 to 20 mol % oxygen and range in color from yellow to dark brown [2, 46]. Thus, mechanochemical processes may be very sensitive to impurities, which requires careful control over the purity of raw materials and sample. The important role of emission processes in mechanochemical synthesis is illustrated by the complex mechanochemical redox reaction Pb3O4 + Cu2O = [Y-PbO] + [R-PbO] + [CuO]. (32) The dynamics of this reaction (E1/2 = 90 MJ/kg) is on the same order as the electron emission intensity in systems exhibiting FR. One possible path of reaction (32) INORGANIC MATERIALS
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is through amorphous states with the formation of (D)*2: Pb3O4 + Cu2O
(D)*
am-(Pb2+, Pb4+, Cu+, Cu2+)O am-(Pb2+, Cu2+)O
(D)*2
(D)*2
(33)
[PbO] + [CuO].
In some systems, prolonged milling leads to the formation of new phases, containing cations in lower oxidation states. The rate of such processes is limited by electron emission (Fig. 6). Recent studies [47] have revealed milling-induced formation of an incongruently melting Aurivillius phase: 2Bi2O3 + V2O5 = [Bi2VO5.5] + clinobisvanite.
(34)
This mechanochemical reaction (which should not take place under ordinary conditions) seems due to the reduction of oxides. Indeed, when VO2 was used as a starting reagent, mechanochemical synthesis yielded single-phase Bi2VO5 . Time evolution of processes. The characteristic length scale of impacts in the reaction zone and subsequent relaxation is 10–4 to 10–3 s. The effective temperature profile in the contact region can be found by solving the heat equation
∑
λ i ( T ) ∂ 2 T ( x, τ ) ∂T ( x, τ ) -, -------------------- = -------------------- --------------------2 ρc ∂τ ∂x
(35)
for a semi-infinite body, with a boundary condition ∂T ( 0, τ ) λ -------------------- + q = 0, ∂x where the heat flux density is q = ξpv (ξ is the friction coefficient) [48]. Given that the dimensions of the contact region are comparable to the lattice parameter a, the ball velocity is expected to be a periodic function: v = v[1 + λ sin(vτ/a)]. Because of the surface roughness and collisions between rolls (Fig. 4), the friction coefficient is a fluctuating function of time and temperature, ξ = ξ[1 + F(τ, T)], as is the contact pressure, because the contacts compete for the energy supplied, p = p[1 + G(τ)]. Although Eq. (35) becomes very sophisticated, the general behavior of its solution is obvious [2]. In contrast to the solution at constant ξ, p, and v, the maximum temperature decreases to below the eutectic temperature owing to feedback and the development of slight
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ZYRYANOV
oscillations, which depend on the size of the system and the statistical ensemble of particles. Urakaev [48] considered an impact of a ball moving at 8 m/s with a dense NaCl polycrystal. Under certain assumptions, the solution to Eq. (35) admits short-term (~10–8 s) local heating to temperatures on the order of 103 K. Without casting doubt on the possibility of local heating to such temperatures, note that, for the purpose formulated above, the effective mean temperature, determining the formation of metastable materials and their properties, is more important. During milling of powder by an appropriate procedure, temperatures close to the melting point cannot be attained because of the competition of contacts for the energy being supplied. This is evidenced by the experimental result that, in oxides prepared by mechanochemical synthesis, structural transformations begin in the range 570– 620 K [26, 28, 32]. The case when the ball energy is sufficient for melting all of the material in the reaction zone is of no interest for mechanochemistry. CONCLUSIONS A theory is proposed for ultrafast mechanochemical synthesis in oxide systems, considered as a threshold process. The key points of the theory are as follows: 1. In a statistical ensemble of particles, primary mechanical loading events with an intensity above some threshold lead to the development of a dynamic state (D)* in the contact region via mass transfer by the roll mechanism: A+B
(A1 – δB)*
tions obtained by mechanochemical synthesis results in structures (perovskite, fluorite, and others) which are stable to disordering and compositional changes. The dynamics of mechanochemical synthesis and the structure of the product can be controlled by selecting the appropriate polymorphs of the oxides involved and oxidation states of the constituent cations and also by varying the milling conditions. The threshold character of mechanochemical synthesis offers the possibility of controlling the dynamics of the process by varying the milling parameters and MP conditions. The theory is supported by the trimodal mechanochemical synthesis rate distribution for mixed oxides, associated with the contributions of the roll mechanism in primary and secondary events to mass transfer and the reduction due to emission processes, whose importance was underestimated earlier. ACKNOWLEDGMENTS I am grateful to V.V. Boldyrev for his support of the mechanical loading studies in model systems; M.A. Kvantov for performing the static magnetic measurements; A.L. Buchachenko for helpful discussions about the nature of FR at the Ampere School; and Yu.D. Tret’yakov, N.N. Oleinikov, and other researchers of Moscow State University for their interest in this work and useful comments on the reaction zone model. This work was supported by the Russian Foundation for Basic Research, grant nos. 95-03-080068, 99-03-32733, and 02-03-33330.
A1 – δB*.
2. The formation of a primary product supersaturated with vacancies is the result of the relaxation of the (D)* state under unloading and quenching conditions. Independent of the mixture composition, the primary product is deficient in the harder reactant. 3. Secondary events, with a more important contribution of diffusion, involve the formation of rotation regions (D)*2 and their relaxation, resulting in mechanochemical equilibrium between ordered and disordered states of the secondary products, which are all close in composition to the starting mixture. 4. During milling of powders, disintegration of particles and mechanochemical interactions are accompanied by rapid charge separation and recombination, which give rise to reduction of oxides. Linearizing the dependence of the chemical response on mechanical load, we established the principal factors influencing the dynamics of mechanochemical synthesis: the molecular weight of the simple oxides involved, the enthalpy of the reaction, and the difference in Mohs’ hardness between the reactants (which also determines the composition of the dynamic state and, accordingly, the composition and structure of the primary reaction product). Ordering of solid solu-
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2005
