# Problem Solving _DT_

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```					Review of Ball Milling

Matthew King
2/4/04
Talk Outline

   Ball Milling parameters
   Different Milling machines and their respective energies
   Overview of contamination and methods of reducing it
   Milling ball motion in a planetary mill and the effects on
collision energies
   The effect of temperature and milling ball energy on sample
evolution
   Overview of Mechanical Milling pre-alloyed intermetallics
   Overview of Mechanical Alloying of elemental powders
   Summary of Milling parameters
   Brief Conclusions
Overview of Ball Milling Parameters

   Type of mill (planetary, attrition, vibratory, rod, tumbler, etc.)
   Speed of mill, relative speeds of pot rotation to disk revolution in a
planetary mill

   Composition, size, shape and surface of pot
   Degree of filling pot
   Number, size(s), material (density, elasticity), and surface of milling balls

   Weight, shape, size and composition of starting material

   Macroscopic temperatures of pot, ball and powder
   Microscopic Temperature at collision point
   Milling atmosphere
   Milling time

Chaotic system!
Different milling machines
   Tumbler mill
   Energy depends on diameter and speed of
drum
   Primarily used for large-scale industrial
applications

   Attrition mill                            SPEX miller:
   High energy                                  High energy,
small-industry                                research-scale
scale (<100kg)
       ~10cm3

    Fritsch planetary miller
    Medium-high energy
research miller (<250g)
    What we have!
Power of different milling machines
Contamination
   Fresh atomic surfaces constantly created during mechanical
milling, so contamination by O2 & N2 is a real problem:
   Argon commonly used as an inert environment (impurities in Argon
can be a problem though)
   Can be useful – mechanical milling invented as means of creating
metals with uniform dispersion of oxide for strength.
   Milling with a liquid surface agent can lower particles’ surface
energy, allowing smaller particle sizes to develop. However,
some becomes absorbed into the sample as a contaminant.
   Other source of contamination is from pot/balls:
   Less “foreign” material tends to be introduced if sample/milling media
are dissimilar materials.
   Effect of contamination tends to be more serious if sample/milling
media are dissimilar materials
   Using milling media that are of the same material as the sample is the
solution if contamination critical, but compensation to retain balance of
alloy may be required.
Reducing cross-contamination

   Milling often results in powder being welded to the pot, and
diffused into the milling surfaces.

   This can be minimised by:
   Having designated pots for a particular material
   Skimming the milling surface
   Removing chemically (not a good option if milling media/stuck-on
sample are similar materials)
   Milling with sand – both manufacturers recommend milling with high
purity (quartz) sand to remove stuck-on material
   Milling with meths/acetone
Trajectory of milling balls in a planetary mill
   Aim is generally to have milling balls cascading across pot
and colliding with maximum energy with the opposite wall.
   In reality, there is a high slip-factor between pot and balls
(80%), so observed trajectories in a Fritsch mill are:

   25% reduction in energy transfer due to slipping
Trajectory of milling balls continued . . .
   Slip factor means higher rotation:revolution
ratio needed for cascading motion:
   Pot rotation in opposite
direction to revolution of
disk more efficient

   Too high a pot rotn:disk revn ratio leads to
milling balls being pinned to side, so a
balance is needed.

   Power input approximately given by:       P  l m 
2       2

   A higher ball elasticity should increase the efficiency with
which energy is transmitted to the powder.
Other parameters affecting the ball impact
Cr on graph means BPR. R = ball size
    Greater Ball to Powder Ratio (BPR)
generally only increases the collision
frequency (decreases the time it takes for
powders to evolve)

    However, filling the pot above 50% reduces
the milling efficiency

    Having milling balls of varying sizes can
have a chaotic effect on the ball trajectories,
preventing tracks forming (making sure all
the sample is milled uniformly), but this less
of an issue with planetary ball millers

    Heavier milling balls increase the impact
energy of collisions
Temperature Reached
   Macroscopic Pot temperature:
   Maximum temperature rise of 100-200oC is generally accepted.
   Maximum depends on milling conditions & cooling mechanisms

   Macroscopic ball temperature:
   Paper predicts milling balls will get
much hotter (600oC) than pot:
   Max temperature linked to ball size
   Heat transfer from balls to pot
relies on forced convection

   Microscopic powder collision temperature:
   Only weakly linked to ball temperature
   Can be 100oC up to 1100oC
   Temperature pulses calculated to last ~10-5s
General effects of milling powders
Generally, increasing the impact energy:
 Increases the amount of cold welding and fracture

 Collisions plastically deform the atomic structure, which:
   Introduces dislocations, vacancies, stacking faults, atomic disorder…
   Thereby increases strain, which is relieved by grain refinement (i.e.
fracture). More energetic milling reduces the grain size.
   The stored energy of cold work introduced into the sample has been
known to be up to 50% of enthalpy of fusion of a material

   Effect of temperature:
   More energetic milling increases the temperature of the powder (which
can result in recovery from disorder . . .)
   Vacancy density and fracture decrease as temperature increase
   Higher macroscopic/microscopic temperatures promote recovery from
disordered state and promote diffusion
Effect of Mechanically Milling pre-alloyed Intermetallics
   Creates disordered nanocrystalline structure,
with amorphous halos between grains.
   If the increase in the free energy (associated
with grain boundaries and atomic defects)
reaches a critical level, the formation of a meta-
stable phase becomes possible (e.g solid
solution, amorphous, or simply nanocrystalline)

   Low temperatures
generally favour
amorphous phase, as:
   Lower recovery rate
   More disorder (e.g.
smaller grain size)
produced
   Can be a maximum
temperature for
amorphous phase
formation.
Mechanical Alloying in ductile/ductile systems

In ductile/ductile systems:
   Lamellar structure develops
   Layers get thinner and thinner
   Thermal diffusion occurs
   Alloy is formed
Mechanical Alloying in ductile/brittle systems

In ductile/brittle systems alloying:
   Brittle powder fragments when hit
   Brittle powder embedded in ductile material
   If brittle material soluble in ductile material, short range diffusion
of the brittle material into the ductile and an alloy can form
Mechanical Alloying in brittle/brittle systems

In brittle/brittle systems, alloying may occur:
   Both brittle powders fragment
when hit
   When powder size reaches
“limit of comminution”,
material can become more
ductile, allowing
conglomeration and cohesion.
   Diffusion may then form
“alloy” (e.g. Si/Ge)

   Temperature generally critical. If the temperature is
below a certain limit, diffusion will be too limited to allow
alloy formation
Effect of Mechanically Alloying powder mixture

   The evolution of particle size
generally follows the trend
opposite:

   Mechanical alloying often results in a (fully mixed)
amorphous (or partially amorphous) phase, which can then
be annealed to form the crystalline intermetallic.
   However, in different milling conditions, the intermetallic
may be formed directly.
   Predicting which phase will predominate is difficult:
   There is evidence that softer (less energetic) conditions favour
amorphisation over intermetallic formation. However, the effects of
temperature on this trend cannot be ignored
   Contradictory evidence for effect of temperature exists
Summary of Milling parameters
   Mechanical Milling: Likely optimum conditions for creating
disordered (nano-crystalline then amorphous) intermetallics:
   Low temperature milling favours smaller average grain size (more
defects, less re-arrangement) but broader distribution.
   Greater ball size and BPR results in lower grain sizes, more defects
and faster grain-size reduction
   Greater pot width and higher ratio of pot rotation to disk revolution
(opposite directions) is more energetic (until milling balls stick to side).
Filling the pot too full can inhibit milling

   Mechanical Alloying:
   The process depends on how ductile the constituent powders are.
   Softer milling favours amorphous phase formation over intermetallic
   Contradictory evidence for the effect of temperature on phase

   Contamination should be controlled by use of pure Argon,
minimising milling times and by use of milling media of the
same material as the sample if possible
Conclusions

   The physics of the process is very complicated, and is
dependant on large numbers of parameters, making
comparisons between research groups difficult.
   More research is needed to understand ball milling enough to
allow accurate prediction of material phases prior to
experiment.
   However, mechanisms for mechanical milling and alloying
are broadly agreed upon in the literature, allowing general
effect of milling parameters to be predicted.
   Mechanical Milling provides a means of producing materials
that cannot be produced by other means, and so this is a
very exciting research area.
References

   Abdellaoui, “The Physics of Mechanical Alloying in a modified horizontal rod mill: mathematical treatment”, Acta Materialia 44(2) 725-734
   Atzmon, “In situ Thermal Observation of Explosive Compound-Formation Reaction during mechanical Alloying”, Physical Review Letters 64 (4)
   Begin, “Nanocrystalline oxides synthesized by mechanical alloying” J Physique III France 1997 473-482
   Burgio, “Mechanical Alloying of the Fe-Zr system. Correlation between input energy and end products”, Il Nuovo Cimento 13 D,(4) p459
   Chattopadhyay, “A mathematical analysis of milling mechanics in a planetary ball mill”, Materials Chemistry and Physics 68 84-94
   Froes, “Synthesis of Intermetallics by Mechanical Alloying”, Materials Science and Engineering A192/193 612-623
   Gaffet, “Planetary Ball-Milling – an experimental parameter phase-diagram”, Materials Science and Engineering A 132: 181-193
   Gaffet “Effects of High-Energy ball milling on ceramic oxides”, Synthesis & Properties of Mech Alloyed & nanocrystalline materials, Ismanum96
   Harris, “The Russian Doll Effect by Mechanical Alloying” J of Materials Science Letters 12 1103-1104
   Harris, “The Morphological Evolution of hollow shells during the mechanical milling of ductile metals”, Scripta Materialia, 34 (1) 67-73
   Heilmann, “Orientation determination of subsurface cells generated by sliding”, Acta metallurgic 31 (8) 1293-1305
   Hellstern, “Structural and thermodynamic properties of heavily mechanically deformed Ru and AlRu”, J Applied Physics 65(1) p305
   Huang, “Ball milling of ductile metals“ Materials Science and Engineering A199 (1995) 165-172
   Joardar, “Estimation of entrapped powder temperature during mechanical alloying”, Scripta Materialia 50 1199-1202
   Koch, “Mechanical Milling and Alloying” – review forms chapter 5 of a book ~1990
   Kwon, “Ball Temperatures during mechanical alloying in planetary mills”, Journal of Alloys and Compounds 346 276-281
   Lawn, “A model for crack initiation in elastic/plastic indentation fields” J of Materials Science 12 2195-2199
   McCormick, “The Dynamics of Mechanical Alloying”, Proceedings of the 2nd Conference on Structural Applications of Mechanical Alloying, 1993
   Mio, “Effects of Rotational Direction and rotation-to-revolution speed ratio in planetary ball milling”, Materials Science and Engineering A332 75-80
   Rigney, “Wear Processes in Sliding Systems”, Wear, 100 195-219
   Schaffer, “On the Kinetics of Mechanical Alloying”, Metallurgical Transactions A – Physical Metallurgy & Materials Science, 23A p1285
   Schaffer, “The influence of Collision energy and strain accumulation on the kinetics of mechanical alloying”, J of Materials Science 32 3157-3162
   Simoneau, “Structural and magnetic characterisation of granular YBCO nanocrystalline powders”, Journal of materials Research 9(3)
   SPEX Industries, “Handbook of sample preparation and handling”
   Suryanarayana, “Mechanical Alloying and milling”, Progress in Materials Science 46 1-184 (#954)
   Szwarc, “Low Energy Mechanochemistry Formation of Silver and Copper Metals from Hemioxides”, Journal of Solid State Chemistry
   Zhang, “Evolution of Vacancy densities in powder particles during mechanical milling”, Physica B 325 120-129
   Ziegler, “Structural and Morphological Investigations of Ceramic Powders and Compacts”, Powder Metallurgy International 10 (2) p70

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