Phenomenology , Kinetics and Application of Abrasive-Reactive Wear during Comminution ( Overview ) †

Valuable information on the phenomenology of mechanical activation will be obtained from the accurate characterization of wearing processes that take place within mechanochemical reactors. Favoring the contamination of reactant powders with material from a reactor’s debris, for a long time such processes represented one of the greatest limitations to practical mechanochemistry applications. We will focus on two related aspects of mechanochemical processing by grinding in a ball mill: (i) nanoscale wear of the treated substances and of the milling tools (balls and container wall); and (ii) deposition of a powder coating on the surface of the milling tools (self-lining phenomenon). A new technology called abrasive-reactive wear (ARW) has been developed that utilizes wear debris as an integral component of the reaction system rather than treating it as a harmful impurity. This technology is applied to the preparation of nanocomposites and to the processing of mineral raw materials and industrial byproducts. This review includes preparation experiments, material characterization, ARW kinetics and simulation. Besides developing new technologies, ARW will contribute to a better understanding of the mechanochemical or mechanical alloying process in general.


Introduction
The mechanical activation (MA) of powders, usually carried out in suitably designed ball mills that are considered mechanochemical reactors (MR) essentially consists of the repeated mechanical loading of powders trapped between the colliding surfaces of the milling tools [1][2][3][4] . Te local compressive and shear events create hot spots and induce plastic deformation and fracturing of the particles [5][6][7] .Under such circumstances, powder particles undergo continuous comminution associated with interface renewal processes.These promote the occurrence of physicochemical transformations including microstructural refinement down to nanometer size [8][9][10][11][12] .
Contamination due to the abrasion of milling tools is an inevitable problem of conventional MA in MR; the level of contamination can reach several percent and can rarely be kept below a few tenth of a percent 4) .Many authors mentioned this problem in their works on mechanochemistr y.Moreover, some concrete examples of the possible participation of the milling tools' material in mechanochemical processes were reported [13][14][15][16][17][18][19][20][21] , but these works have not been followed up on. I 13) , the Mössbauer ef fect was used for studying MA processes of quartz.The metal iron, which contained 2.17% of isotope 57 Fe, was introduced into quartz during the process of MA as a result of the steel milling tools of a disintegrator (pin disc mill or UDA) being worn by the particles of quartz at their relative linear speed of impact up to 270 m/s.Experiments on the mechanical activation of quartz were carried out in a vacuum and in air.It is shown that the Mössbauer effect can be used successfully for studying the mechanochemical reactions of quartz with an Phenomenology, Kinetics and Application of Abrasive-Reactive Wear during Comminution (Over view) † 1 akademik Koptyug av., 3, Novosibirsk 630090, Russia ＊ Corresponding author TEL: +7 (383) 333-2007, FAX: +7 (383) 333-2792 E-mail address: urakaev@uiggm.nsc.ru iro material of disintegrator milling tools.In 14) , the quantitative characteristics of the steel material wear of milling tools dependent on MA time were determined for the first time with the purpose of mechanochemical opening of sulfide and arsenide minerals.
In 15) , the participation of the milling tools' steel material in the process of mechanochemical sulfidizing of some oxidized copper minerals in the presence of water was shown and the sulfidizing mechanism was established for the first time.In 16) , the influence of mill power and grinding environment on the contamination of quartz by iron during vibration grinding was studied.It was found that the Fe content in ground powders increased with increasing specific milling energy.The specific contamination expressed as the ratio of Fe content to newly created surface area depended upon the physical properties of the grinding environment.The influence of grinding conditions on the state of the iron in the products of grinder wear was investigated by Mössbauer spectroscopy and by measuring the magnetic susceptibility of the ground powders.It was shown that the iron produced from grinder wear is present in two main forms: as a magnetically ordered form identical with the basic material of the grinder and in a form of finely dispersed iron compound showing superparamagnetic behavior.Based on the results obtained, the formation of a silica-supported iron or iron oxide catalyst was presumed.
In 17) , the wear of high-carbon low-alloy cast steel balls during the grinding of a chalcopyrite ore was evaluated under different experimental conditions.The role of oxygen in enhancing ball wear during wet grinding is emphasized.Contributions from corrosion and abrasion towards ball wear are quantified in terms of ball wear rates as a function of time, particle size and gaseous atmosphere in the mill.In 18) , quartz powders prepared by MA in a planetary mill in the presence of monohydric or dihydric alcohols were found to exhibit magnetic properties as the result of abrasive wear of the material of the steel milling tools.Tile magnetic susceptibility of milled quartz depends on the milling time and the amount of additions.The material was shown to undergo aging: its susceptibility and electron paramagnetic resonance spectrum vary during storage.The magnetization of quartz is interpreted in terms of Fe-containing clusters present in tile amorphized surface layer.In 19) , the interaction of the sample with wear products from milling tools made of steel, tungsten carbide and strengthened ball bearing steel (ShKh15) is investigated by means of Mössbauer spectroscopy, X-ray diffraction and gravi-metric measurements.It is stated that under identical conditions, ShKh15 steel is the most resistant to wear and the least prone to participate in mechanical alloying.It is shown that when choosing materials for milling bodies for the investigations of mechanical alloying, one should take into account a condition that ensures the deliver y of reliable information: an increase of the mass of the sample under investigation should not exceed 10% during mechanical treatment.
Research of new nanocomposites prepared by the non-conventional mechanochemical route under the abrasive-reactive wear conditions was stimulated by the works of 20,21) .
In the work of Goya et al. 20) , who followed the phase evolution of CuFe2O4 during high-energy ball milling in a steel vial, it was shown that a two-phase mixture consisting of magnetite and a spinel solid solution (CuxFe3-XO4) yields the final product of the mechanical treatment of Cu-ferrite.This indicates that the high-energy milling of the oxide generates a complex series of solid-state transformations, including mechanochemical decomposition and reduction.
In view of the fact that the milling is done in air, the appearance of reduced phases in an oxide matrix is a surprising experimental result.Although several mechanisms have been proposed for the reduction processes occurring during high-energy milling, to the best of our knowledge, no conclusive explanation for mechanically induced redox reactions has been given yet.Identification of the factors representing the main driving force for mechanically induced redox processes in complex oxides, the elucidation of the microscopic mechanism(s), and the determination of rate-determining steps of reduction therefore represent a major challenge for research in mechanochemistry and require further efforts.
In 21) , the product of ball milling magnetite and amorphous silica (40-mole % Fe3O4 in SiO2) for an extended period of time (800 h) in a closed vial was investigated by Mössbauer spectroscopy, X-ray diffraction and infrared spectroscopy.It was found that the milling induces an extensive reduction of Fe(III).The material constitutes a mixture of ultrafine Fe-rich spinel particles (magnetite/maghemite) and amorphous Fe(II)-containing silicate with a magnetic transition temperature of approximately 25K.The amorphous phase has a rather high Fe content and is distinctly different from the initial amorphous silica.
On the other hand, for example, the chemical activity of ammonium thiocyanate or the high hardness of boron resulted in wear to the steel material of the milling tools of the MR, the particles of abraded iron entered into mechanochemical reactions with the treated mix of reagents [22][23][24][25] , and the quartz and other mineral particles were modified by abrasion from iron compounds [13][14][15][16][17][18][19][20][21] .
From these scattered repor ts it is evident that regular research of the participation of a material of milling tools in the course of mechanochemical reactions was not carried out.A novel strategy for their exploitation as an effective synthetic route will be described which will permit the preparation of fine materials for high-tech purposes 26) .The choice of focusing on abrasive-reactive materials is motivated by the possibility of synthesizing them via both gradual 4) and combustive 5) mechanochemical reactions starting from elemental powders.The prospect of their realization does not cause doubts.In a method offered by us of obtaining nanocomposite powders on a copper, graphite and diamond basis, only copper fittings will be used.As against the traditional realization of mechanochemical reactions in mixes of powders with the sizes of initial particles ~50 microns 4,5,27,28) , the synthesis, for example, of nanocr ystalline final products proceeds for hundreds of hours of MA 27) , and owing to participation of the nanosized material resulting from the abrasive wear of milling tools, a significant reduction of this time could be expected.
Recently begun intensive research of mechanochemical reactions with the participation of a material of milling tools not only confirmed this assumption, but also revealed many other advantages and prospects of their realization 29) .Sometimes it is possible to select the material of the milling tools in such a way that the wear debris becomes a beneficial component of the intended product.We plan to carry this possibility to the extreme: We will develop a new technique called abrasive-reactive wear (ARW) that uses the material of the milling tools as a reactant that becomes a major component of the product, not just a tolerable impurity.This innovative new approach has not been considered by any other laboratory.It opens the door to applications of the ARW phenomenon to obtain nanocomposite powders and for carrying out the synthesis of chemical compounds, functional materials, and for processing mineral and man-made raw materials.It will be shown here how the wearing of milling tools could instead provide an alternative synthetic route to materials of technological interest 26,29) such as the Cu-diamond composites that possess a high thermal conductivity 30) .
We must note that throughout the world, there is currently no direction of research analogue to that pursued by us.From the viewpoint of its application for the preparation of new functional materials, the work will be innovative and useful.The probable scopes of the ARW method stated in the paper lead us to believe that it can find specific application in various areas of modern technical mineralogy and tribology.

Planetar y mills with steel fittings and MA
The relative velocity W of collisions between milling tools is given by the equation 2,6,[31][32][33][34][35][36] ) where cosϕ=−(1+k)/m determines the angle of ball rebound from walls.The geometric factor m = l1/l2, where l1 and l2 are the radii of the carrier and drum, respectively; the kinematic factor k = ω2/ω1, where ω2 and ω1 are the number of revolutions of the drum and the opposite number of carrier revolutions, respectively.An analysis of the interaction of milling tools must be performed taking into account both the normal component Wn and the tangential component Wt of the W 33) .Wn determines the conditions of the interaction of particles in the layer.Wt determines the conditions of abrasive wear and mechanochemical processes on the frictional contact between milling tools and treated particles.For the mechanical treatment (the process time τ was varied over the range 5-240 min), we used: ・ A three-drum planetar y mill from "NPO Mekhanobr" , the characteristics of the mill were 33,34) : m = 2.3 (l1 =11.5 cm and l2 =5.0 cm); k =−1.7(ω2 =20 s -1 and ω1 =11.7 s -1 ); W ≈ 1700 cm/s, Wn ≈ 500 cm/s, Wt ≈ 1600 cm/s; the drum volume V = 450 cm 3 ; and the working part of the surface of the drum Πd = πl2(2h+l2) ≈ 250 cm 2 , where h =5.5 cm is the drum height.The ball radius was R =0.5 cm, their density ρ=7.8 g/cm 3 , number N, and the totaled surface area Πb = 4πR 2 N. ・ An AGO −2 water-cooled two-drum planetary mill with the characteristics 25,35,36) : m =1.7 (l1 =5.3 cm and l2 =3.1 cm); k =−2.4 (ω2 =29 s -1 and ω1 =12 s -1 ); W ≈ 1100 cm/s, Wn ≈ 900 cm/s, Wt ≈ 630 cm/s; V = 140 cm 3 , Πd ≈ 150 cm 2 (h = 4.6 cm); R = 0.2 cm.To provide more efficient processing, we used all four possible orientations of the mill axis: vertical, horizontal and ±15 to the latter in each case.・ An EI −2×150 two-drum planetary mill characterized by 2,26) m =1.8 (l2 = 2.9 cm), k = −1 ( ω2 = ω1 = 14 s -1 ), cosϕ= 0 and W = Wn ≈ 850 cm/s, V =150 cm 3 , Πd ≈ 130 cm 2 (h = 5.6 cm); R = 0.2 cm.The powdered mixtures had previously been ground and homogenized for 15-30 min in a Fritsch Pulverisette mill fitted with steel (a mortar of diameter 9.5 cm + 1 ball of diameter 5.2cm) or agate (9.2 cm and 7.1cm, respectively) 37,38) elements.We selected preparation of nanocomposites under various conditions of MA of the A (material of milling tools) −B (abrasive) and A−B−C (reagent) systems (e.g.iron-quartz; iron-diamond, iron-quartz-sulfur, ironquartz-graphite, copper-diamond-graphite, etc.) in a MR as an example of ARW, cf. 39).The ratio between the weight of the treated substances (M = MA +MB +MC) and the mass of the ball load (Mb) was varied.Let ρA, ρB, and ρC be the densities.The uniform selflining of milling tools (balls and inside drum walls) by a batch mixture layer occurs during MA 2,40,41) .The calculated lining thickness is 12,34,39) δ= (3) Here, the porosity of the lining p is taken to equal that of a close packing of differently sized spherical particles ( p≈ 1−π/4).In a number of cases, C−substance (e.g.graphite or sulfur), as the most plastic and pliable components, covers all metallic (A) and abrasive (B) surfaces with a continuous layer with a thickness calculated by Eq. ( 3), where the areas A and B particles are ПA+B 39,42) .

Product and process characterization
The initial mean particle size (R0) was determined by optical microscopy (NU-2E) on parts of the starting homogenized specimens for MA, and was in the range 0.01-0.025cm.MA products were studied by the standard XRD, DTA, Mössbauer (MC1104EM), Raman (Dilor/OMARS), infrared (Satellite FTIR) and electron microscopy (JSM-6380 and LEO-1550) methods.MA amorphous samples were also isothermally annealed (2 h) in a flow of argon (~1cm 3 /s) in alundum crucibles with graphite plugs and titanium sponge placed upstream of the crucibles in the heated area of the quartz tube to remove the possible oxygen impurity from argon using a new heating stage for high-temperature (up to 1600℃) investigations 43) .The degree of grinding was determined by the thermal desorption of argon with additional disaggregation 15,34) .Possible iron forms in some specimens (e.g. in quartz particles) were determined by acid etching of the material according to 33) .Washed samples were studied by routine analysis methods.ARW kinetics was studied by two methods: weight, with accurate measurement of drum weight and ball loading before and after experiments not less than 0.01 g; and volumetric in the case of diamond-containing MA products, on reaction of samples with an acid.

ARW processes caused by the MA of quartz
One of the purposes of this work was to study the influence of the material of milling tools on the MA of quartz in MRs with steel fittings.We selected these objects of study because MA quartz and mixtures based on it exhibit ferromagnetic properties and are distinguished by good sorption ability toward organic substances, the synthesized sorbents were used to collect petroleum spill over water, high water purification, etc. 44,45) .A ball mill from "NPO Mekhanobr" was used, the ratio between the weight of ball loading Mb to that of quartz M was set equal to 4 at Mb + M = 480 + 120 = 600 g.The number of balls N = 120, and the totaled surface area Πb = ≈ 370cm 2 .According to Eq. ( 1), abrasion conditions should be given preference over impact conditions for this mill.In several control tests (Fig. 1), we also used an AGO-2 mill and fused quartz (from the standpoint of interpretation of XRD data, amorphous materials are the most suitable abrasive components).It follows from 33) that ~90% of iron is present in quartz in an acid-soluble (metallic and magnetic) form.The total wear of steel mill fittings can amount to ~5% (~7 g), and the dependence of the amount of worn iron on the time of processing is not linear (Fig. 2).The deviation from linearity is caused by the self-lining of milling tools to a degree that increases as the specific surface area of the material under Fig. 1 X-ray pattern of fused quartz (3 g) processed for 12 min in an AGO-2 mill (number of balls N = 400).The size of worn particles for a material of milling tool ~10 nm 33,34) .
Temperature and pressure pulses 2,3,7) favor the occurrence of chemical reactions involving the material of milling tools, substance being processed, and medium 33,34) .As the reaction between Fe and SiO2 is forbidden, we consider the possibility of steel oxidation by air; the drums of our mill did not have vacuum gaskets, and processing occurred under air access conditions, as distinguished from control tests with the AGO-2.As a result of abrasive and oxidative wear, Fe and FeO are formed as nanoscale particles and should be adsorbed on much larger quartz particles.
On the other hand, part of the surface layer of quartz particles subjected to MA becomes amorphous (Fig. 3).The mechanism of the transition to the amorphous state and the thickness of the amorphous layer have long been the subject of discussions 1,33,34) .The question of the form in which iron is contained in activated quartz particles is the most interesting one.For this reason, along with modeling, we used the most informative methods for quartz studying, namely Mössbauer and infrared spectroscopy.
MA samples washed to remove the elemental iron only contain quartz particles with a very insignificant iron content in an acid-insoluble form (up to ~0.6% or ~0.75 g based on iron).It follows that acid-insoluble 33) iron silicates formed during processing approximately in an amount of 2 g can only occur on the surface of quartz particles.The estimated mean thickness of this layer is ~1 nm 34) .The Mössbauer spectra, Fig. 4 (see also infrared, Fig. 5), of iron atoms in iron oxides are characteristic sextets resulting from the magnetic splitting of nucleus levels.
Our samples give additional lines, which are evidence of changes in the character of bonds between iron atoms and their environment.A quadrupole doublet, whose hyperfine coupling parameters show that iron occupies two nonequivalent sites in the quartz lattice, describes the internal part of the spectrum.
For the first doublet, the isomeric shift and quadrupole splitting parameters show that iron Fe 3+ ions have an octahedral oxygen environment characteristic of iron oxides in the super paramagnetic state.
The hyperfine coupling parameters of the second doublet can be attributed to Fe 2+ ions in the high-spin state.The population of these two sites by iron ions depends on the duration of MA, and the presence of such iron forms in quartz can only be explained by the formation of iron silicates.The infrared spectra of the initial quartz samples and MA samples for 15 min indirectly substantiate the formation of iron silicates.There were no differences between the Si−O −Si and O−Si−O bands in the spectra of different samples.However, a band at ~833cm -1 appeared in the MA sample; this band was assigned to the Si−O −Fe bond in 33) .
At high temperatures 34) , the formation of iron metasilicate (FeO + SiO2 = FeSiO3) in the FeO−SiO2 system is more favorable thermodynamically and kinetically than the formation of iron orthosilicate (2FeO + SiO2 = Fe2SiO4), because the reaction occurs in the presence of excess quartz.As a separate phase of iron silicates is not observed, they can only occur in the amorphous layer on activated quartz particles.The empirical mean thickness of the layer of iron silicates on the surface of quartz particles if iron silicates are distributed uniformly is ~2 nm 33) .

ARW in abrasive−graphite/sulfur systems
Extending the ARW method is of particular interest as regards the use of carbon 26,35) , in particular graphite 37) , and sulfur 38) , which have unique physicochemical and mechanical properties 29,36,47) .Carbon and sulfur in ARW can open up a new line in making nanocomposite materials on a carbide 4,19,24,25,31) or sulfide 1,5,8,9,14,15,27,28,39) basis.This method can also be successfully used in the utilization of dust formed in decarbonization and desulfurization of the coke-oven gas formed in the coke and by-product industries 37) .The accumulation of sulfur at oil refineries and plants processing natural gas also makes its utilization a matter of current interest.Cementite (Fe3C) is commonly obtained by the MA of mixtures of iron and carbon powders, with subsequent thermal or arc-plasma processing of the MA products 48,49) .Sulfides are, as a rule, obtained from elements on MA and heating 5,8,9,27,28) .However, the morphology and the homogeneity of the target products are not always of the required level.It depends on a number of factors and, in particular, on the area and state of the surface of the starting reagents.The use of MR eliminates these drawbacks.At present, iron sulfides, especially those of nanosize 8,9,27,28) , are applied in power cells with a high energy density, in photoelectrolysis and solar power engineering, and in the synthesis of superconducting, diagnostic and luminescent materials and chalcogenide glasses.
The results of the simulation of mechanochemical reactions involving sulfur 42) show that the most important process for the synthesis of sulfides, e.g., ZnS 50) , is the plastic flow of sulfur.The heat pulse in the shock displacement of molten sulfur is determined by the thickness of layers on the surface of Zn particles lined with softer sulfur.The thinner this layer, the higher the temperature and the faster the amorphization of sulfur (polymerization with a transition to the glassy state).However, the occurrence of this process has not been confirmed experimentally.Therefore, to substantiate the theory 42) , it was necessary to choose a system for MA that would contain an inert amorphous component alongside crystalline sulfur.Ordinary glass and fused silica are suitable for this purpose.Confirmation of the mechanochemical polymerization of sulfur is also the goal of this study.
The MA was performed in an AGO-2 mill (N = 400, Πb ≈ 200cm 2 ).Graphite or sulfur were introduced in amounts of 0.3-1.6 g into a crushed amorphous (slide glass or fused silica) or crystalline (quartz) abrasive taken in an amount of 3.0 g.The annealing temperatures chosen were considerably lower than the temperature of cementite formation 36) , i.e. were equal to 660±5℃ and 960±10℃.
The XRD patterns of the system constituted by fused quartz and graphite after MA is shown in In both low-(660℃) and high-temperature (960 ℃, Fig. 6c) annealing, cementite crystallizes (PDF 75-910) from the amorphous phase.However, the degree of cementite crystallization from the amorphous phase for samples annealed at 660℃ is lower than that for the samples annealed at 960℃.The presence of residual nanoscale iron particles in the samples (Fig. 1) is confirmed by the following: the peak of cementite at 2Θ = 44.72 overlaps the base reflection of α−Fe, but not its reflection at 2Θ = 82.42-82.5 .
In annealing, a partial crystallization of graphite also occurs (halo at 2Θ = 26 in Fig. 6).Similar results were obtained for the system with quartz.It can be stated that the nanocomposite Fe−Fe3C−C−SiO2 is formed in the course of the MA of quartz-graphite systems.
Experiments on the MA of sulfur crystals (weighed portion 2 g) only were carried out under identical conditions.The XRD data for samples of MA sulfur (MA duration of up to 180 min) show that no structural transformations in sulfur take place [38].All the reflections are preser ved without any appreciable change in their shape and relative intensity (PDF 83-2285), except for the absence of a halo associated with the presence of amorphous particles of fused quar tz or glass.The situation changes (Fig. 7a) when sulfur is treated in the presence of inert glass particles.
Fundamental changes occur in the MA of samples based on fused quartz: Pyrite is formed (FeS2, PDF 71-2219; Fig. 7b).The hardness of quartz particles is considerably higher than that of steel, and its softenning point substantially exceeds that of glass.In this case, amorphization of sulfur (absence of reflections of excess sur fur in Fig. 7b) and its chemical reaction with iron nanoparticles (which have already appeared in a significant amount as a result of the ARW of steel accessories) to form pyrite FeS2 occur simultaneously.The formation of just FeS2 is due to the excess of sulfur in the MA samples.
Using the method 4,27) and the XRD data, we also calculated the sizes of crystal blocks and the extents of distortion in the structure of the resulting pyrite (and Fe particles).The parameters of fine cr ystal structure were calculated from the half widths of the diffraction peaks ( 220) and ( 440), which are commonly associated with FeS2 47) .To determine the instrumental broadening, we used the profile of lines of crystalline FeS2.The resulting size of blocks in FeS2 was about 24 nm (~10 nm for iron particles), and the extent of distortion 1%.Similar results were obtained in 27) , but after more than 110 h of MA of a 1:2 mixture of powders of Fe (starting particle size ~0.05cm) and S.

ARW processes caused by the MA of diamond
From the point of view of enhancing the possibilities of the ARW method, the use of diamond is of special interest owing to its unique mechanical and abrasive proper ties 35) and ability to interact with transitional metals and alloys, i.e., a combination of properties of both abrasives and reagents.It should also be noted that mechanochemical synthesis could in the future provide a more efficient utilization of both natural and synthetic diamonds as the result of introducing the low-grade raw material into the technological process.This section is devoted to the study of the influence of the MA of diamond on the synthesis of cohenite (Fe,Ni)3C, which is a very rare but well-described 51) mineral.It exists in two forms (Pbnm, PDF 23-1113; Pnma, PDF 35-772).Generally, this mineral has a man-made or extraterrestrial origin 35) .Its synthetic analogue in the Pbnm structure is cement-ite (Fe3C).The diamond used in the experiments was obtained in the (Fe,Ni)−C system on a multianvil highpressure split-sphere apparatus at 6 GPa and 1500℃ 52,53) .Polycrystalline diamond aggregates left as byproducts in prolonged experiments 53) with the growth of coarse diamond monocrystals are used.The obtained powder, with a particle size of ~0.011cm, was treated with a heated mixture of nitric and hydrochloric acids to remove impurities.MA of the diamond was conducted in an AGO-2 mill with N = 400 for M = 2.85g and N = 150 for M = 1.75g.We determined the ARW kinetics, see Fig. 9 (straight lines 2, 3) and Fig. 10a, and the next values of wear of the material of milling tools, i.e. drum (D) and balls (B), for the systems under study 35) :

ARW in copper-diamond-graphite system
The MA of copper-diamond-graphite mix was carried out in an EI −2×150 milling 46) .XRD data show that the MA product represents a composite powder containing besides initial components (Cu, diamond, C) of the mix (graphite becomes amorphous and reacts with iron, forming cementite Fe3C 35,36) ), some nanopar ticles of Fe and Fe3C of ARW.Annealing this product in an argon atmosphere at 600℃ and 900℃ does not result in the formation of new phases, but rather only the ordering of lattices of mix components.As expected, annealing the MA product during DTA on air up to 1030℃ results in the burning-out of carbon and the formation of an appropriate mix of copper and iron oxides.
A specific example of a property of technological relevance that characterizes materials prepared by techniques studied in the present paper is the heat conductivity.Linked to this, the problem of heat removal is very important for the semiconductor industry.For this reason, the improvement of thermal properties of materials used for manufacturing microelectronic components becomes crucial 30,54) .The "ADS" company offered nanocomposite materials on a Cu and diamond basis that have a higher heat conductivity in comparison with traditionally used  materials on a Cu or Al basis.Moreover, particles of diamond in copper-diamond composites show a high degree of stability to graphitization under sintering at temperatures up to 1150-1250K, and thus this composite material can be used for the creation of contacts and high-current electric contacts in the lowvoltage equipment 55) .
In order to prepare such nanocomposites, the method based on ARW by MA in MRs (with cupric milling tools) using par ticles of substandard diamonds appears interesting and very able to replace various labor-and power-consuming processes, see Fig. 13-17 and details in 26) .
After the MA of diamond and diamond-graphite mixture (1:1), the XRD data virtually did not differ under identical measurement conditions (Fig. 14): the MA of both samples does not produce carbon and copper compounds, see also Fig. 17.Analysis of MA samples in atmosphere by the DTA method (thermogravimetr y -TGA, heating rate 10℃/min) yielded important information (Fig. 15).The TGA data can be used to decipher constituents of composites.For example, based on the TGA, the composite in sample 2 contains 24% carbon (7.3% amorphous carbon and 16.7% diamond).Hence, the Cu content should be 76%, which is very close to the weight analysis data.
Based on the high-resolution SEM data, the relatively large agglomerates of particles have the cauliflowerlike internal structure with block dimension similar to certain dimensions of Cu crystallites.

ARW in abrasive-mineral systems
Recently, a high increase has been obser ved for the research processing of geological materials in MRs [56][57][58] . O specific interest for extending the potential of the ARW method is also the processing of mineral and technological raw materials 29,33,37,47,59,60) .MA of quartz mixes with tenorite (CuO) or galena (PbS) was carried out with the purpose of their reductive processing by iron of the milling tools to obtain copper-or lead-containing composites 33,59) .Tenorite or galena was introduced in amounts of 1.5 g into a crushed fused silica abrasive in an amount of 3.0g.MA time τ in an AGO-2 mill (N = 400) varied from 15 to 210 min. ARW at 60 min in te investigated systems amounted to about 1 g (Fig. 11).MA of ilmenite (FeTiO3) concentrate and its mixes with coke were carried out with the purpose of concentrate reduction to obtain iron and coke, rutile and/or anatase 58) .Conditions of MA in a "Mekhanobr" mill were the following:  powder of a composite material is formed.
The results obtained in studying the products of MA of the systems under study by XRD and isothermal annealing methods indicate the occurrence of various processes.These are the abrasive wear of steel milling tools, amorphization, and reduction of copper from tenorite and lead from galena.There are no crystalline phases of other products (iron oxides and sulfides) of reduction reactions, e.g.CuO + Fe = Cu + FeO (ΔrG =−28.0 kcal/mol).Fig. 18b indicates that an X-ray-amorphous product is formed in the system with tenorite and iron wear occurs (peak at 44 -45 ).The degree of amorphization increases as the processing duration becomes longer, even the Fe peak is broadened.Metallic copper is the only product formed during annealing of this sample at ~700℃ : reflections of all other products that can be formed in the exchange reaction, namely iron oxides, are completely absent (Fig. 18c).Fig. 19b illustrates a similar phenomenon of abrasive wear of Fe and reduction of galena by this iron, which occurs in this case directly during the course of MA.It should be noted here that there are no reflections of other possible products of the reductionexchange reaction, namely iron sulfides.If the MA duration is raised to 120 min, the spectrum remains virtually unchanged: only the reflections of the α− SiO2 admixture in natural galena disappear (because of amorphization).Annealing of these products does not change the situation either: only the relative intensities change insignificantly and the corresponding reflections become considerably narrower.If the MA duration is increased further, abrasive wear of Fe starts to prevail over all other processes (Fig. 19c).
The data obtained confirm that the self-lining of milling tools prevents their abrasive wear and, consequently, hinders the reduction reaction of tenorite with the material of milling tools in the course of MA.By contrast, the complete absence of self-lining of milling tools in the system with galena results in a fast breakdown of galena by iron formed in the abrasive wearing of milling tools.
It is difficult to give an unambiguous interpretation of the fact that those reflections of iron oxides or sulfides disappear after the reductive breakdown of tenorite or galena without thoroughly studying the MA of quartz with the material of steel milling tools 33) .The results of 33) suggest that the surface of quartz particles can be modified not only by amorphous iron silicates (after annealing of MA tenorite samples), but also by iron sulfides after the MA of ga-lena together with fused quartz particles.In the case of galena, a nanosize surface layer on quartz particles must be formed of a certain amorphous compound of the system FexSy−SiO2.An even more complex compound of green color, which is formed upon the MA of tenorite and which contains nanosize particles produced by abrasive wear of the steel accessories (Fig. 18b), is the amorphous compound CuxFeyOz− SiO2 on the surface of quartz particles.
The following aspect is associated with dimensional effects.In the case of the conventional MA reduction of, e.g.copper sulfides 1,28) with metallic Fe powders with an initial particle size of about 0.05 cm, the duration of MA is tens of hours.In the new ARW method of breakdown of, e.g.galena 59) , suggested here, the size of initial particles formed during the abrasive wear of Fe is close to 10 nm (Fig. 1), which is several orders of magnitude shorter than that in the conventional mechanochemical exchange reaction.Therefore, the rate of the breakdown reaction involving the material of steel milling tools is also higher and, consequently, the time of the MA breakdown of minerals becomes shorter.The XRD data were used to calculate by the known method 4,27,61) the structure of crystalline blocks in metal particles obtained in the course of MA in the system with galena.The parameters of the fine cr ystal structure were calculated from the half width of diffraction peaks (Figs.19b, c) for an MA duration of 60, 210, and 120 min (XRD spectrum is not shown).To determine the instrumental broadening of the lines, we used the profiles of the corresponding reflections after the annealing of these samples.The resulting size of Pbblocks was (nm): 83 (MA, 60 min), 61 (MA, 120 min), and 46 (MA, 210 min); the corresponding data for particles formed during the wear of Fe were 24, 19, and 12 nm.Thus, we obtained metal-oxide/sulfide nanocomposite powders based on the quartz matrix in the course of the MA of minerals mixed with an abrasive in an AGO-2 mill with steel accessories.

Kinetics and Simulation of ARW
Determination of the ARW kinetic laws of MR milling tools in the MA process of various substances and systems with an abrasive component is of current interest and comes out to the foreground.ARW kinetics was studied by two methods: weight, with an accuracy of measurement of the drum and ball loading weights before and after experiments of not less than 0.01g; volumetric (on hydrogen for diamond-containing MA products), in reaction of samples with HCl.Data on ARW kinetics in the MA process of the following kinds of mineral raw materials into nanocomposite powders were obtained 46) .Fig. 2 -quartz (preparation of a magnetic composite 18,33,34,44,45) ).MA time varied from 5 to 90 minutes.The size of wear at 5 min, ARW in grams, came to 1.43, and at 90 min ARW = 5.14g.The self-lining phenomenon of the surfaces of milling tools by МА quartz is observed.Fig. 8 -mixes of quartz and fused quartz with graphite or sulfur (preparation of cementite-or pyrite-bearing composites 36,38) ).MA of the system with graphite results in a self-lining of the milling tools.By contrast, the self-lining phenomenon is completely absent in the system with sulfur.Fig. 9 -diamond (to obtain cohenite 35) ) and a powder mix of diamond, graphite, and copper (to obtain high-heat-conducting composite materials 26,30) ).During diamond MA, a self-lining of the milling tools is barely visible.During the mix MA, the self-lining takes place.Fig. 11 -mixes of fused quartz with tenorite or galena (preparation of copper-or lead-bearing composites 1,14,15,33,59) ).MA of the system with tenorite results in a self-lining of the milling tools.By contrast, the self-lining phenomenon is completely absent in the system with galena.Fig. 12 -ilmenite concentrate of the arm filters of titanium-magnesium manufacture and mixes of concentrate with coke (for reduction of concentrate to obtain iron, rutile and anatase 60) ).The appreciable self-lining of milling tools surfaces by MA materials was only observed in case (C).
The linear law of ARW growth with MA time τ in the absence of a self-lining phenomenon is established and the ARW power law in the presence of the self-lining with an exponent less then unity.Mathematical processing of measured ARW(τ) values in various mills and MA systems gives the following empirical dependence: ARW (g) = K×τ n , where K is a rate constant of ARW, and n is an exponent 46) .We see that both a rate constant (K, from 0.0050g/min for MA system sulfur-fused quartz up to 1.8g/min 0.23 for quartz MA) and an exponent (n, from 0.17 for MA tenorite up to 1 for systems in which the self-lining does not take place) vary in sufficiently wide numerical intervals.It is evident from an example of the MA of diamond and ilmenite that K depends on the MA conditions (n = 1).For diamond K = 0.0135g/min at M = 2.85g and number of balls N = 400, K = 0.0097 g/min at M = 1.75g and N = 150.For ilmenite K = 0.0078g/min at M/Mb = 0.5, and K = 0.0083g/min at M/Mb = 0.25.
Under identical MA conditions, the K and n values essentially depend not only on the specificity of chemical reactions but also on a phase state of an abrasive.For tenorite K = 0.53g/min and n = 0.17, for galena K = 0.007g/min and n = 1.For a mix of graphite with quartz K = 0.091g/min and n = 0.37, for a mix of graphite with fused quar tz K = 0.26 g/min n and n = 0.33.For a mix of sulfur with fused quartz K = 0.005g/min n and n = 1.
As regards the problem of ARW simulation, in our opinion, it necessary to discuss the approaches to this problem recently proposed in 48,62) .In these works, the authors considered the athermic (diffusion 48) and deformation 62) ) mechanisms of the formation of cementite (Fe3C) upon MA of an iron and carbon powder mixture.Note that the role of local heating due to the impact-friction interactions in the course of MA 2) was ignored completely.This contradicts the practice of mankind 36) throughout the ages, which has been aimed either at decreasing the heating of materials upon their mechanical treatment or at using a released heat, including the primitive ways of making fire.The modeling of the MA process associated with the development of short pressure or temperature pulses or the so-called t-P-T conditions 2,3,7) is based on the rigorous thermodynamic basis.In our opinion, this basis can be complemented by invoking diffusion and deformation processes, but cannot under any circumstances can be replaced by them.Details of ARW simulation with the account of the t-P-T conditions both on contact with the treated particles and on contact with the milling tools are given in 12,[34][35][36]42,61) .

Conclusion
The study performed demonstrated that the steel material of milling tools can be involved in a direct breakdown of minerals and synthesis of nanocomposites under utilization of the abrasive properties of diamond and different boron and quartz modifications.The chemical interaction between the material of milling tools and the substance being processed was simulated numerically for the example of quartz processing in a planetary ball mill.It was shown that quartz processing resulted in the synthesis of iron silicates from silica and iron oxides.Nanoscale iron and iron oxide particles were formed as a result of the abrasive-reactive wear of steel mill fittings by quartz particles.The estimated thickness of the layer of silicates on the surface of quartz particles was ~2 nm.The mechanical activation of mixtures of quartz (or diamond) and reagents (copper, graphite, sulfur, tenorite and galena) yielded nanocomposites in a time one to two orders of magnitude shorter than that in the case of the mechanical activation of mixtures of iron powders with the reagents.We have substantiated a new field of low-grade diamond utilization, namely an abrasive-reactive synthesis based on the material of the milling tools of mechanochemical reactors.A scrap of any metal and ceramic product can be used as milling tools, which makes it possible to considerably extend the potential of the abrasivereactive wear method and the range of treated compounds.The kinetics and mechanism of abrasivereactive wear of steel milling tools in the planetary mills were investigated experimentally and modeled numerically under defined conditions of mechanical activation.

Fig. 10
Fig. 10 XRD patterns illustrating the phase composition: (a) Dynamics of the abrasive wear of the steel milling tools during the diamond MA (M = 1.75 g); (b, c) after the diamond MA (1.75g) for 2 h with subsequent annealing for 2 h in the Ar atmosphere at 660 and 960℃, respectively.
weight of the drum Md = 953.65g,ball charge Mb = 109.056g(R = 0.2cm, N = 400).The following powdered sample was subjected to MA (МА time τ varied up to τ= 60min): diamond (1.3g)-copper (1.3g)-graphite (1.3 g).After the experiment, the weight of the drum was Md* = 952.76g, the difference being Md − Md* = 0.89 g.The weight of the ball charge was Mb* = 106.78g the difference being Mb−Mb* = 2.27g.The total wear of the steel material of the EI−2×150milling tools appeared equal m* = 0.89 + 2.27 = 3.166g, i.e. close to the weight of the initial charge.The ARW kinetics for this system is presented by curve 1 in Fig. 9.

Fig. 16
Fig. 16 Results of processing the XRD data on Cu reflections by the Williamson-Hall method.

Fig. 17
Fig. 17 Raman spectrum of the MA copper−diamond−graphite sample.The line of 1334 cm -1 corresponds to diamond.