Vertical stirred mills are usually charged with media occupying 80% of the mill volume which is in sharp contrast to tumbling mills that are seldom charged more than 40% of their volumes to allow space for the tumbling action to develop. The stirred mills are charged with a media size of 1012mm and operated at a maximum tip speed of 38m/s. The Metso detritor mill, however, has a maximum tip speed of 1112m/s. Even though a finer ground product is obtained with higher speeds, a limit has to be imposed. This is to allow the separation of media and mineral particles at the top of the mill where a settling zone develops. The ultrafine ground product is usually discharged as it passes through the separating screen. It also takes with it fine media product. The Metso detritor mill uses a screen size of 300m to retain sand when used as a media.

During operation a small amount of heat is generated. This affects the viscosity of the slurry. According to Kwade [7], if the viscosity of the slurry is too high the grinding efficiency is reduced as activity in the grinding chamber is inhibited and the contact between the grinding media and the particles is decreased resulting in less abrasive action on the mineral particles. Thus, the heat generated during media stirring could assist in lowering the slurry viscosity and hence benefit grinding efficiency.

The stress intensity and the number of stress events determine the specific energy to achieve a certain product fineness. The number of stress events is a function of mill operating parameters such as grind time, stirrer speed, percent solids and media size. The relationship between stress intensity and specific energy was shown by Kwade as indicated in Figure10.10.

The stress energy available to particle breakage is distributed in different sections of the mill, being maximum near the tip of the stirrer. For a satisfactory grind and size reduction of all particles, the residence time of the slurry in the mill is the prime factor. Experience so far indicates that about 3060seconds of travel time through a mill is adequate.

It may be noted that all the stress energy generated are not transferred to the mineral particles and the media hardness and media size affects the product size. The portion of the stress energy transferred to the particles depends on the Youngs modulus of both the grinding media and the particles [8].

The Vertimill is a vertical stirred mill that uses a helical screw to impart motion in the charge. Mechanically, the Vertimill is a very simple machine with an agitating screw suspended into the grinding chamber, supported by spherical roller bearings, and driven by a fixed speed motor through a planetary gearbox. Figure 8.14 presents a schematic diagram of the Vertimill. The screw rotates slowly such that the ball charge and slurry are not fluidized, but settle under gravity. The screw action pulls the ball charge up the center of the mill, and the charge eventually cascades over the edge of the screw, creating a general downward flow pattern at the mill perimeter. This pattern of flow, coupled with the low velocities involved, ensures that the grinding media and particles stay in contact with one another, thus enabling the efficient transfer of the drive energy into attrition and abrasion breakage throughout the charge. The operating conditions of the Vertimill are very similar to those of the conventional ball mill in the sense that the percentage solids of the feed should be kept in the range of between 65% and 75% by mass. The power draw of the mill is directly linked to the mass of balls within the mill. The distinct advantage that the VTM has over the conventional ball mill is its ability to use media smaller than 25mm more effectively.

In the past 20 years, more than 60 Vertimill machines have been sold for iron ore applications, with more than 20 of those in the last 2 years alone. Table 8.2 lists examples of the Vertimill in Brazilian iron ore applications. The Metso Vertimill is very common in regrind applications, but the industry quickly realized its potential in coarser applications as well.

where P is the shear power (W), the viscosity of the mill contents (N.s m2) (for which a relationship was given), the angular velocity (rad s1), and V the shear volume (referring to all the shear surface pairs between an impeller and the mill chamber). With appropriate calibration the predicted power matched the measured power for the data of Gao et al. (1996) and Jankovic (1998).

The IsaMill milling technology is a large-scale commercial high-speed stirred mill that is currently under development for coal micronising applications. The technology achieves very high energy efficiencies by using small milling balls in a high intensity configuration (>300 kWmm3). It is claimed that the technology (Fig.15.7) can produce coal with 90% of the particles less than 20m.

IsaMill technology is receiving serious consideration as part of a CSIRO investigation into preparing micronised coal for coal/water fuel in a diesel engine to deliver base-load power (see Section15.10.1).

Vibratory mills use oscillatory motion of the mill shell to agitate the media. As for the stirred mills, the active grinding zone encompasses the entire mill volume. The grinding energy is supplied by the inertia of the media and is not limited by gravity. In principle, high energy can be supplied to quite fine media, making these devices attractive for ultrafine grinding applications. By very careful matching of media size, powder size, and energy input (based on vibrational amplitude and frequency) it should be possible to achieve quite high grinding efficiencies. Unfortunately, mechanical design for reliability and low maintenance is not simple. Problems in these areas have tended to limit their large-scale application.

Different kind of mills are suitable for grinding, mechanical alloying and mechanical milling such as horizontal mills (tumbler ball mill), stirred mill (attritor, e.g. Szegvari attrition mill1), planetary ball mill, vibrating mill (tube vibrating mill, Sweco vibrating mill and shaker vibrating mill (e.g. Spex is a lab-scale mill3)). Their working principles and operating conditions are summarised in Fig. 12.1 and Table 12.1. The classification on a scale of increasing mill energy is: horizontal ball mill, attritor, planetary ball mill and vibrating ball mill. For example, a process that takes only a few minutes in the SPEX mill can take hours in an attritor and a few days in a commercial tumbler ball mill.

The choice of a milling technique is determined by many parameters. For example, attrition mills are more efficient than tumbler ball mills for mixing and blending WC-Co cutting tool powders because of short milling time, production of fine particle size (submicron sized) and enhanced smearing of Co onto carbide particles. However, as the product output is relatively low with attrition mills, tumbler ball mills are usually used for production runs of over 100kg/day. Moreover, powder contamination, which is an important criterion for many applications, can be due to the initial purity of the powder, the milling equipment (design), the milling operating conditions (mill speed, balls size and material, atmosphere) and/or the use of process control agent. It increases with milling time, milling intensity and with the reduction of the difference of strength/hardness between the powder and the milling balls.

There are in general two methods by which nanoparticles can be produced using high-energy milling: (i) milling alone and (ii) combining chemistry and milling (referred to as chemical-mechanical milling or mechanochemical processing). It is suggested that these methods offer the advantage of being easily scaled. References [19 and 20] are good starting points for further reading.

High-energy milling processes involve the comminution of bulk materials. The principle of comminution is centred on applying physical forces to bulk material so as to effect breakage into smaller sizes. The forces required to effect breakage are usually a combination of either impact or shear. Material is introduced into a milling chamber in which grinding (milling) media are contained. Milling occurs when the media is made to move either by stirring (using a rotor) or by shaking/vibrating the chamber and contacts the bulk material thus imparting, depending on the milling parameters, either impact or shear forces on it. Breakage can occur through a variety of mechanisms and are generally described as attrition, abrasion, fragmentation or chipping and occur both at the macro and microscopic level [21]. This is illustrated in Figs 1.3 and 1.4

The rate at which comminution occurs is dependent on the size and frequency with which forces are applied. Breakage is influenced by both extrinsic and intrinsic factors. Intrinsic factors include such things as material properties (hardness, density, size) whilst extrinsic factors are determined by the amount of energy put into the system and the efficiency with which that energy is translated to the milling process. The latter is determined by variables such as vibrating frequency (in a rotorless mill), rotor speed (in a stirred mill), mill design, media size and loading, solids loading and whether the milling is performed dry or wet. These variables dictate which force regime predominates (i.e. shear or impact) which in turn dictate milling rate and efficiency. In high-speed stirred mills the effect of mill tip speed, media size and density can be evaluated simultaneously using the grinding media 'stress intensity' approach and an illustration of this is summarised in Fig. 1.5 which shows a plot of product particles size (starting size 45 m, product size 26 m) versus stress intensity for a pin mill using a zinc concentrate.

A variety of mills are commercially available and range from tumbling, shaker, vibratory, planetary and stirred ball mills. Production of nanoparticles using this technique is sometimes limited by the need for extended milling times, material properties and contamination issues. Attrition methods allow the production of alloys and composites that cannot be synthesised by conventional casting methods. They have also gained attention as non-equilibrium processes resulting in solid state alloying beyond the equilibrium solubility limit and the formation.

The types of nanoparticles produced by the attrition milling technique are generally alloys or single-phase powders. When a single-phase elemental powder (or intermetallic) is milled, grain size asymptotically reduces to a range of 330 nm [19]. For alloys produced by this method, unstable intermediate substances are formed, from mixing and diffusion as a consequence of repeated deformation and folding of the different metals. These intermediates allow the chemical reactions necessary for alloy formation to occur [11].

For non-metallic compounds (carbides, oxides, etc.) the reduction in grain size is consequent on fracturing and cold welding and the limit to minimum grain size is determined by the minimum size that does not support nucleation and propagation of cracks within the grain. For metallics, on the other hand, it is thought that the reduction in grain size is a process where localised plastic deformation is induced, subgrains are formed (by eradication of dislocations) which combine (through intimate mechanical contact) to form discrete grains. The latter process is analogous to recrystallisation observed during hot forming of metals and alloys but in these circumstances at low temperatures. In intermetallics, the process is thought to be different again in that grain formation is due to nucleation (on a nanoscale) followed by a limited growth of the generated phase [20,23]. There are numerous examples in the literature of alloy and mixed metal oxide production using this technique [20,28]. Few examples can be found where single-phase powders or particles are produced at the nanoscale level [24,25].

In this technique, a large number of small grinding media are agitated by impellers, screws, or disks in a chamber. Breakage occurs mainly by the collision of the media. There are designs of the mill with a vertical or horizontal rotating shaft with wet or dry systems (Fig. 2.19).

The medium agitating mill is one of the most efficient devices for micronizing materials and has been in regular use for the production of fine particles and mechanical alloying processes. A typical stirred mill with a vertical rotating shaft and horizontal arms is shown in Fig. 2.20. This stirring action causes a differential movement between balls and the material being milled, thus a substantially higher degree of surface contact than is achieved in tumbling or vibratory mills is ensured. Milling takes place by impact and shear forces. The rotating charge of balls and milling product form a whirl where the milling product is impacted by balls moving in various trajectories.

The attrition mill agitator rotates at speeds ranging from 60rpm for production units to 300rpm for laboratory units and uses media that range from 3 to 6mm while ball mills use large grinding media, usually 12mm or larger, and run at low rotational speeds of 1050rpm. Power input to attrition mills is used to agitate the medium, not to rotate or vibrate heavy drums. Therefore, specific energy consumption of attrition mills is significantly less than with ball mills. Table 2.4 offers a comparison of grinding mills by rotational velocity. In the attrition grinding process, grinding time is related to medium diameter and agitator speeds [12], within given limits, as:

where t is grinding time required to reach a certain medium particle size; k is a constant that varies with the suspension being processed and the type of medium and mill being used; d is the diameter of the grinding medium; and n is shaft movement, in rpm.

Attrittion mills are classified as batch-, continuous-, or circulation-type mills. In the batch mill, material is loaded into the chamber and ground until the desired dispersion and particle size are achieved. Chamber walls are jacketed so that either hot or cold water can be circulated to control and maintain the temperature of the charging. The batch attrition mills can process high-density material, such as tungsten carbide, as well as viscous materials. They are also suitable for dry grinding and for producing dispersion-strengthened metals by means of mechanical alloying.

Continuous attrition mills, more appropriate for large production output, consist of a tall, jacketed chamber through which previously prepared slurry is pumped in at the bottom and discharged at the top. Grids located at the bottom and top retain the grinding medium, as shown in Fig. 2.21.

The circulation grinding system comprises an attrition mill and a large holding tank, generally 10 times the volume of the grinding unit. The attrition mill contains grids that restrain the medium while the slurry passes through. Usually, the contents of the holding tank are passed through the system at a rate of 10 times per hour. The slurry can be monitored continuously and processing is stopped when the desired particle size dispersion is achieved.

Dry milling can provide reduced transportation costs compared to wet grinding because 50% of the gross weight is liquid in many wet slurry processes. Because the removal of the liquid from a wet grinding process involves not only another process step but also requires large amounts of energy, dry grinding can provide reduced energy costs. Another advantage is the elimination of waste liquid disposal.

Attrition mills find application for hard materials such as carbides and hard metals where conventional tumbling and vibratory ball mills are less efficient. The principal advantages of attrition mills for mixing and blending tungsten carbide with cobalt as binder metal cutting tool powders include a short milling time, the production of fine particle size (submicron sizes), and the enhanced coating of cobalt onto the surface of tungsten carbide particles [25]. Attrition mills effectively grind metals in inert atmospheres, such as in solid state or mechanical alloying.

Previous work (Heitzmann [8]) performed with coloured tracer experiments in a glass body version of a four blades Dyno mill showed that the action of the stirrer - beads system was first to delimit four perfectly mixed cells centered on each of the four blades. Further, it has been shown that classical models (plug flow, cascade of perfectly mixed cells, dispersion models) were unable to correctly represent RTD experiments. An internal recirculation loop model, with a single adjustable parameter R (see Figure 1), was considered and gave very good results in continuous milling of suspensions of known grinding kinetics (Berthiaux et al. [9]).

Another important conclusion of this work was concerned with the physical meaning of the recirculation ratio R which is undoubtedly linked with the local hydrodynamic conditions, such as porosity, stirrer speed of rotation N, and perhaps mill flow-rate Q. It was also suggested that there exists an optimum value of R that leads to the best continuous grinding conditions (see Figure 2). For example, low values of R benefits the flow itself as it approaches plug flow through tanks in series, while it clearly slows down the kinetics of grinding because the bead - particle collisions are of a lower intensity. In the absence of kinetic data, typical R-values should then range between 0.5 and 5.

The procedure followed to obtain these RTD curves becomes tedious when dealing with a greater number of perfectly mixed cells, or better said a greater number of stirring blades, as it is the case for other types of mills. In general, the analytical or numerical derivation of the RTD from any complex model is in fact highly subjected to errors when done by the classical transfer function method. Particularly, many problems can be incurred when hypotheses are made to simplify the mathematical equations, which may lead to unrealistic dynamic behaviour (see Gibilaro et al. [10]). The advantage of using the Markov chain approach lies in the fact that it is systematic, and its application does not depend on the complexity of the flow scheme.

A Markov chain is a system which can occupy various states, and whose evolution is defined once an initial state and the probability transitions between the states are fixed. It can therefore be said that a Markov chain does not have memory. In the case of flow problems (Fan et al. [11]), the system is a fluid element, the states are the perfectly mixed cells of the flow model (as plug flow can be represented by a series of such cells), and the probability transitions are fixed by elementary mass balances.

For example (Figure 3), the probability pii of remaining in cell i is exp(t/i), where t is the time interval under which the system is observed, and i is the geometric residence time corresponding to cell i. The other transitions pij depend then on the flow rate ratios and on the value of 1- exp(t/j), which is the probability of getting out of cell i during t. All these information are then collected in a probability transitions matrix P, whose rows (i) and columns (j) are the pijs. Further, the initial state of the system is represented by a single row E0, being En the state of system after n transitions (steps of duration t), which is available from the following matrix product (Eq.1):

The last element of En, which is the collecting cell or outlet of the network, represents therefore the dynamic response of the system to a perturbation that may be a tracer impulse: E0=[1 0 0]. Simulation of the RTD curve of the model is further performed by letting t become smaller and smaller until the stability of the solution is ensured.

The ball mill accepts the SAG or AG mill product. Ball mills give a controlled final grind and produce flotation feed of a uniform size. Ball mills tumble iron or steel balls with the ore. The balls are initially 510 cm diameter but gradually wear away as grinding of the ore proceeds. The feed to ball mills (dry basis) is typically 75 vol.-% ore and 25% steel.

The ball mill is operated in closed circuit with a particle-size measurement device and size-control cyclones. The cyclones send correct-size material on to flotation and direct oversize material back to the ball mill for further grinding.

Grinding elements in ball mills travel at different velocities. Therefore, collision force, direction and kinetic energy between two or more elements vary greatly within the ball charge. Frictional wear or rubbing forces act on the particles, as well as collision energy. These forces are derived from the rotational motion of the balls and movement of particles within the mill and contact zones of colliding balls.

By rotation of the mill body, due to friction between mill wall and balls, the latter rise in the direction of rotation till a helix angle does not exceed the angle of repose, whereupon, the balls roll down. Increasing of rotation rate leads to growth of the centrifugal force and the helix angle increases, correspondingly, till the component of weight strength of balls become larger than the centrifugal force. From this moment the balls are beginning to fall down, describing during falling certain parabolic curves (Figure 2.7). With the further increase of rotation rate, the centrifugal force may become so large that balls will turn together with the mill body without falling down. The critical speed n (rpm) when the balls are attached to the wall due to centrifugation:

where Dm is the mill diameter in meters. The optimum rotational speed is usually set at 6580% of the critical speed. These data are approximate and may not be valid for metal particles that tend to agglomerate by welding.

The degree of filling the mill with balls also influences productivity of the mill and milling efficiency. With excessive filling, the rising balls collide with falling ones. Generally, filling the mill by balls must not exceed 3035% of its volume.

The mill productivity also depends on many other factors: physical-chemical properties of feed material, filling of the mill by balls and their sizes, armor surface shape, speed of rotation, milling fineness and timely moving off of ground product.

where b.ap is the apparent density of the balls; l is the degree of filling of the mill by balls; n is revolutions per minute; 1, and 2 are coefficients of efficiency of electric engine and drive, respectively.

A feature of ball mills is their high specific energy consumption; a mill filled with balls, working idle, consumes approximately as much energy as at full-scale capacity, i.e. during grinding of material. Therefore, it is most disadvantageous to use a ball mill at less than full capacity.

The ball mill is a tumbling mill that uses steel balls as the grinding media. The length of the cylindrical shell is usually 11.5 times the shell diameter (Figure 8.11). The feed can be dry, with less than 3% moisture to minimize ball coating, or slurry containing 2040% water by weight. Ball mills are employed in either primary or secondary grinding applications. In primary applications, they receive their feed from crushers, and in secondary applications, they receive their feed from rod mills, AG mills, or SAG mills.

Ball mills are filled up to 40% with steel balls (with 3080mm diameter), which effectively grind the ore. The material that is to be ground fills the voids between the balls. The tumbling balls capture the particles in ball/ball or ball/liner events and load them to the point of fracture.

When hard pebbles rather than steel balls are used for the grinding media, the mills are known as pebble mills. As mentioned earlier, pebble mills are widely used in the North American taconite iron ore operations. Since the weight of pebbles per unit volume is 3555% of that of steel balls, and as the power input is directly proportional to the volume weight of the grinding medium, the power input and capacity of pebble mills are correspondingly lower. Thus, in a given grinding circuit, for a certain feed rate, a pebble mill would be much larger than a ball mill, with correspondingly a higher capital cost. However, the increase in capital cost is justified economically by a reduction in operating cost attributed to the elimination of steel grinding media.

In general, ball mills can be operated either wet or dry and are capable of producing products in the order of 100m. This represents reduction ratios of as great as 100. Very large tonnages can be ground with these ball mills because they are very effective material handling devices. Ball mills are rated by power rather than capacity. Today, the largest ball mill in operation is 8.53m diameter and 13.41m long with a corresponding motor power of 22MW (Toromocho, private communications).

Planetary ball mills. A planetary ball mill consists of at least one grinding jar, which is arranged eccentrically on a so-called sun wheel. The direction of movement of the sun wheel is opposite to that of the grinding jars according to a fixed ratio. The grinding balls in the grinding jars are subjected to superimposed rotational movements. The jars are moved around their own axis and, in the opposite direction, around the axis of the sun wheel at uniform speed and uniform rotation ratios. The result is that the superimposition of the centrifugal forces changes constantly (Coriolis motion). The grinding balls describe a semicircular movement, separate from the inside wall, and collide with the opposite surface at high impact energy. The difference in speeds produces an interaction between frictional and impact forces, which releases high dynamic energies. The interplay between these forces produces the high and very effective degree of size reduction of the planetary ball mill. Planetary ball mills are smaller than common ball mills, and are mainly used in laboratories for grinding sample material down to very small sizes.

Vibration mill. Twin- and three-tube vibrating mills are driven by an unbalanced drive. The entire filling of the grinding cylinders, which comprises the grinding media and the feed material, constantly receives impulses from the circular vibrations in the body of the mill. The grinding action itself is produced by the rotation of the grinding media in the opposite direction to the driving rotation and by continuous head-on collisions of the grinding media. The residence time of the material contained in the grinding cylinders is determined by the quantity of the flowing material. The residence time can also be influenced by using damming devices. The sample passes through the grinding cylinders in a helical curve and slides down from the inflow to the outflow. The high degree of fineness achieved is the result of this long grinding procedure. Continuous feeding is carried out by vibrating feeders, rotary valves, or conveyor screws. The product is subsequently conveyed either pneumatically or mechanically. They are basically used to homogenize food and feed.

CryoGrinder. As small samples (100 mg or <20 ml) are difficult to recover from a standard mortar and pestle, the CryoGrinder serves as an alternative. The CryoGrinder is a miniature mortar shaped as a small well and a tightly fitting pestle. The CryoGrinder is prechilled, then samples are added to the well and ground by a handheld cordless screwdriver. The homogenization and collection of the sample is highly efficient. In environmental analysis, this system is used when very small samples are available, such as small organisms or organs (brains, hepatopancreas, etc.).

The vibratory ball mill is another kind of high-energy ball mill that is used mainly for preparing amorphous alloys. The vials capacities in the vibratory mills are smaller (about 10 ml in volume) compared to the previous types of mills. In this mill, the charge of the powder and milling tools are agitated in three perpendicular directions (Fig. 1.6) at very high speed, as high as 1200 rpm.

Another type of the vibratory ball mill, which is used at the van der Waals-Zeeman Laboratory, consists of a stainless steel vial with a hardened steel bottom, and a single hardened steel ball of 6 cm in diameter (Fig. 1.7).

The mill is evacuated during milling to a pressure of 106 Torr, in order to avoid reactions with a gas atmosphere.[44] Subsequently, this mill is suitable for mechanical alloying of some special systems that are highly reactive with the surrounding atmosphere, such as rare earth elements.

A ball mill is a relatively simple apparatus in which the motion of the reactor, or of a part of it, induces a series of collisions of balls with each other and with the reactor walls (Suryanarayana, 2001). At each collision, a fraction of the powder inside the reactor is trapped between the colliding surfaces of the milling tools and submitted to a mechanical load at relatively high strain rates (Suryanarayana, 2001). This load generates a local nonhydrostatic mechanical stress at every point of contact between any pair of powder particles. The specific features of the deformation processes induced by these stresses depend on the intensity of the mechanical stresses themselves, on the details of the powder particle arrangement, that is on the topology of the contact network, and on the physical and chemical properties of powders (Martin et al., 2003; Delogu, 2008a). At the end of any given collision event, the powder that has been trapped is remixed with the powder that has not undergone this process. Correspondingly, at any instant in the mechanical processing, the whole powder charge includes fractions of powder that have undergone a different number of collisions.

The individual reactive processes at the perturbed interface between metallic elements are expected to occur on timescales that are, at most, comparable with the collision duration (Hammerberg et al., 1998; Urakaev and Boldyrev, 2000; Lund and Schuh, 2003; Delogu and Cocco, 2005a,b). Therefore, unless the ball mill is characterized by unusually high rates of powder mixing and frequency of collisions, reactive events initiated by local deformation processes at a given collision are not affected by a successive collision. Indeed, the time interval between successive collisions is significantly longer than the time period required by local structural perturbations for full relaxation (Hammerberg et al., 1998; Urakaev and Boldyrev, 2000; Lund and Schuh, 2003; Delogu and Cocco, 2005a,b).

These few considerations suffice to point out the two fundamental features of powder processing by ball milling, which in turn govern the MA processes in ball mills. First, mechanical processing by ball milling is a discrete processing method. Second, it has statistical character. All of this has important consequences for the study of the kinetics of MA processes. The fact that local deformation events are connected to individual collisions suggests that absolute time is not an appropriate reference quantity to describe mechanically induced phase transformations. Such a description should rather be made as a function of the number of collisions (Delogu et al., 2004). A satisfactory description of the MA kinetics must also account for the intrinsic statistical character of powder processing by ball milling. The amount of powder trapped in any given collision, at the end of collision is indeed substantially remixed with the other powder in the reactor. It follows that the same amount, or a fraction of it, could at least in principle be trapped again in the successive collision.

This is undoubtedly a difficult aspect to take into account in a mathematical description of MA kinetics. There are at least two extreme cases to consider. On the one hand, it could be assumed that the powder trapped in a given collision cannot be trapped in the successive one. On the other, it could be assumed that powder mixing is ideal and that the amount of powder trapped at a given collision has the same probability of being processed in the successive collision. Both these cases allow the development of a mathematical model able to describe the relationship between apparent kinetics and individual collision events. However, the latter assumption seems to be more reliable than the former one, at least for commercial mills characterized by relatively complex displacement in the reactor (Manai et al., 2001, 2004).

A further obvious condition for the successful development of a mathematical description of MA processes is the one related to the uniformity of collision regimes. More specifically, it is highly desirable that the powders trapped at impact always experience the same conditions. This requires the control of the ball dynamics inside the reactor, which can be approximately obtained by using a single milling ball and an amount of powder large enough to assure inelastic impact conditions (Manai et al., 2001, 2004; Delogu et al., 2004). In fact, the use of a single milling ball avoids impacts between balls, which have a remarkable disordering effect on the ball dynamics, whereas inelastic impact conditions permit the establishment of regular and periodic ball dynamics (Manai et al., 2001, 2004; Delogu et al., 2004).

All of the above assumptions and observations represent the basis and guidelines for the development of the mathematical model briefly outlined in the following. It has been successfully applied to the case of a Spex Mixer/ Mill mod. 8000, but the same approach can, in principle, be used for other ball mills.

The Planetary ball mills are the most popular mills used in MM, MA, and MD scientific researches for synthesizing almost all of the materials presented in Figure 1.1. In this type of mill, the milling media have considerably high energy, because milling stock and balls come off the inner wall of the vial (milling bowl or vial) and the effective centrifugal force reaches up to 20 times gravitational acceleration.

The centrifugal forces caused by the rotation of the supporting disc and autonomous turning of the vial act on the milling charge (balls and powders). Since the turning directions of the supporting disc and the vial are opposite, the centrifugal forces alternately are synchronized and opposite. Therefore, the milling media and the charged powders alternatively roll on the inner wall of the vial, and are lifted and thrown off across the bowl at high speed, as schematically presented in Figure 2.17.

However, there are some companies in the world who manufacture and sell number of planetary-type ball mills; Fritsch GmbH (www.fritsch-milling.com) and Retsch (http://www.retsch.com) are considered to be the oldest and principal companies in this area.

Fritsch produces different types of planetary ball mills with different capacities and rotation speeds. Perhaps, Fritsch Pulverisette P5 (Figure 2.18(a)) and Fritsch Pulverisette P6 (Figure 2.18(b)) are the most popular models of Fritsch planetary ball mills. A variety of vials and balls made of different materials with different capacities, starting from 80ml up to 500ml, are available for the Fritsch Pulverisette planetary ball mills; these include tempered steel, stainless steel, tungsten carbide, agate, sintered corundum, silicon nitride, and zirconium oxide. Figure 2.19 presents 80ml-tempered steel vial (a) and 500ml-agate vials (b) together with their milling media that are made of the same materials.

Figure 2.18. Photographs of Fritsch planetary-type high-energy ball mill of (a) Pulverisette P5 and (b) Pulverisette P6. The equipment is housed in the Nanotechnology Laboratory, Energy and Building Research Center (EBRC), Kuwait Institute for Scientific Research (KISR).

Figure 2.19. Photographs of the vials used for Fritsch planetary ball mills with capacity of (a) 80ml and (b) 500ml. The vials and the balls shown in (a) and (b) are made of tempered steel agate materials, respectively (Nanotechnology Laboratory, Energy and Building Research Center (EBRC), Kuwait Institute for Scientific Research (KISR)).

More recently and in year 2011, Fritsch GmbH (http://www.fritsch-milling.com) introduced a new high-speed and versatile planetary ball mill called Planetary Micro Mill PULVERISETTE 7 (Figure 2.20). The company claims this new ball mill will be helpful to enable extreme high-energy ball milling at rotational speed reaching to 1,100rpm. This allows the new mill to achieve sensational centrifugal accelerations up to 95 times Earth gravity. They also mentioned that the energy application resulted from this new machine is about 150% greater than the classic planetary mills. Accordingly, it is expected that this new milling machine will enable the researchers to get their milled powders in short ball-milling time with fine powder particle sizes that can reach to be less than 1m in diameter. The vials available for this new type of mill have sizes of 20, 45, and 80ml. Both the vials and balls can be made of the same materials, which are used in the manufacture of large vials used for the classic Fritsch planetary ball mills, as shown in the previous text.

Retsch has also produced a number of capable high-energy planetary ball mills with different capacities (http://www.retsch.com/products/milling/planetary-ball-mills/); namely Planetary Ball Mill PM 100 (Figure 2.21(a)), Planetary Ball Mill PM 100 CM, Planetary Ball Mill PM 200, and Planetary Ball Mill PM 400 (Figure 2.21(b)). Like Fritsch, Retsch offers high-quality ball-milling vials with different capacities (12, 25, 50, 50, 125, 250, and 500ml) and balls of different diameters (540mm), as exemplified in Figure 2.22. These milling tools can be made of hardened steel as well as other different materials such as carbides, nitrides, and oxides.

Figure 2.21. Photographs of Retsch planetary-type high-energy ball mill of (a) PM 100 and (b) PM 400. The equipment is housed in the Nanotechnology Laboratory, Energy and Building Research Center (EBRC), Kuwait Institute for Scientific Research (KISR).

Figure 2.22. Photographs of the vials used for Retsch planetary ball mills with capacity of (a) 80ml, (b) 250ml, and (c) 500ml. The vials and the balls shown are made of tempered steel (Nanotechnology Laboratory, Energy and Building Research Center (EBRC), Kuwait Institute for Scientific Research (KISR)).

Both Fritsch and Retsch companies have offered special types of vials that allow monitoring and measure the gas pressure and temperature inside the vial during the high-energy planetary ball-milling process. Moreover, these vials allow milling the powders under inert (e.g., argon or helium) or reactive gas (e.g., hydrogen or nitrogen) with a maximum gas pressure of 500kPa (5bar). It is worth mentioning here that such a development made on the vials design allows the users and researchers to monitor the progress tackled during the MA and MD processes by following up the phase transformations and heat realizing upon RBM, where the interaction of the gas used with the freshly created surfaces of the powders during milling (adsorption, absorption, desorption, and decomposition) can be monitored. Furthermore, the data of the temperature and pressure driven upon using this system is very helpful when the ball mills are used for the formation of stable (e.g., intermetallic compounds) and metastable (e.g., amorphous and nanocrystalline materials) phases. In addition, measuring the vial temperature during blank (without samples) high-energy ball mill can be used as an indication to realize the effects of friction, impact, and conversion processes.

More recently, Evico-magnetics (www.evico-magnetics.de) has manufactured an extraordinary high-pressure milling vial with gas-temperature-monitoring (GTM) system. Likewise both system produced by Fritsch and Retsch, the developed system produced by Evico-magnetics, allowing RBM but at very high gas pressure that can reach to 15,000kPa (150bar). In addition, it allows in situ monitoring of temperature and of pressure by incorporating GTM. The vials, which can be used with any planetary mills, are made of hardened steel with capacity up to 220ml. The manufacturer offers also two-channel system for simultaneous use of two milling vials.

Using different ball mills as examples, it has been shown that, on the basis of the theory of glancing collision of rigid bodies, the theoretical calculation of tPT conditions and the kinetics of mechanochemical processes are possible for the reactors that are intended to perform different physicochemical processes during mechanical treatment of solids. According to the calculations, the physicochemical effect of mechanochemical reactors is due to short-time impulses of pressure (P = ~ 10101011 dyn cm2) with shift, and temperature T(x, t). The highest temperature impulse T ~ 103 K are caused by the dry friction phenomenon.

Typical spatial and time parameters of the impactfriction interaction of the particles with a size R ~ 104 cm are as follows: localization region, x ~ 106 cm; time, t ~ 108 s. On the basis of the obtained theoretical results, the effect of short-time contact fusion of particles treated in various comminuting devices can play a key role in the mechanism of activation and chemical reactions for wide range of mechanochemical processes. This role involves several aspects, that is, the very fact of contact fusion transforms the solid phase process onto another qualitative level, judging from the mass transfer coefficients. The spatial and time characteristics of the fused zone are such that quenching of non-equilibrium defects and intermediate products of chemical reactions occurs; solidification of the fused zone near the contact point results in the formation of a nanocrystal or nanoamor- phous state. The calculation models considered above and the kinetic equations obtained using them allow quantitative ab initio estimates of rate constants to be performed for any specific processes of mechanical activation and chemical transformation of the substances in ball mills.

There are two classes of ball mills: planetary and mixer (also called swing) mill. The terms high-speed vibration milling (HSVM), high-speed ball milling (HSBM), and planetary ball mill (PBM) are often used. The commercial apparatus are PBMs Fritsch P-5 and Fritsch Pulverisettes 6 and 7 classic line, the Retsch shaker (or mixer) mills ZM1, MM200, MM400, AS200, the Spex 8000, 6750 freezer/mill SPEX CertiPrep, and the SWH-0.4 vibrational ball mill. In some instances temperature controlled apparatus were used (58MI1); freezer/mills were used in some rare cases (13MOP1824).

The balls are made of stainless steel, agate (SiO2), zirconium oxide (ZrO2), or silicon nitride (Si3N). The use of stainless steel will contaminate the samples with steel particles and this is a problem both for solid-state NMR and for drug purity.

However, there are many types of ball mills (see Chapter 2 for more details), such as drum ball mills, jet ball mills, bead-mills, roller ball mills, vibration ball mills, and planetary ball mills, they can be grouped or classified into two types according to their rotation speed, as follows: (i) high-energy ball mills and (ii) low-energy ball mills. Table 3.1 presents characteristics and comparison between three types of ball mills (attritors, vibratory mills, planetary ball mills and roller mills) that are intensively used on MA, MD, and MM techniques.

In fact, choosing the right ball mill depends on the objectives of the process and the sort of materials (hard, brittle, ductile, etc.) that will be subjecting to the ball-milling process. For example, the characteristics and properties of those ball mills used for reduction in the particle size of the starting materials via top-down approach, or so-called mechanical milling (MM process), or for mechanically induced solid-state mixing for fabrications of composite and nanocomposite powders may differ widely from those mills used for achieving mechanically induced solid-state reaction (MISSR) between the starting reactant materials of elemental powders (MA process), or for tackling dramatic phase transformation changes on the structure of the starting materials (MD). Most of the ball mills in the market can be employed for different purposes and for preparing of wide range of new materials.

Martinez-Sanchez et al. [4] have pointed out that employing of high-energy ball mills not only contaminates the milled amorphous powders with significant volume fractions of impurities that come from milling media that move at high velocity, but it also affects the stability and crystallization properties of the formed amorphous phase. They have proved that the properties of the formed amorphous phase (Mo53Ni47) powder depends on the type of the ball-mill equipment (SPEX 8000D Mixer/Mill and Zoz Simoloter mill) used in their important investigations. This was indicated by the high contamination content of oxygen on the amorphous powders prepared by SPEX 8000D Mixer/Mill, when compared with the corresponding amorphous powders prepared by Zoz Simoloter mill. Accordingly, they have attributed the poor stabilities, indexed by the crystallization temperature of the amorphous phase formed by SPEX 8000D Mixer/Mill to the presence of foreign matter (impurities).

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