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Particle Packing

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Title: Particle Packing


1
Particle Packing
Che5700 ??????
  • Forming strongly related to particle packing
    (science and technology)
  • Results from packing packing density and
    porosity
  • Factors particle size and distribution, particle
    shape, resistance of particles to pressure
    (deformation binder effect), flow resistance
    (friction between particles) For uniform spheres
    five different packing arrangements cubic,
    orthorhombic, tetragonal, pyramidal, tetrahedral
    etc.
  • Different packing density higher coordination
    number to higher packing density, theoretical
    maximum 74.

2
In theory, we can obtain ordered packing of
mono-disperse particles in reality, it is often
to get packing as shown above (small range of
ordering)
3
Packing Density and Pore Size
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4
Packing Characteristics
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  • Tortuosity ?o for cubic packing ?o 1.0
    tetrahedral packing ?o 1.3
  • Number of particle contact Nc 3 (PF) (CN)/(? a3)
  • PF packing fraction CN coordination number
  • for nonregular packing Nc 3 (1-?)/(?a3) since
    CN ?/? (usually between 6 10)
  • Container wall effect (on packing) insignificant
    when container dia./particle dia. gt 10
  • Use two particle sizes, small one can fill into
    interstice, thus increase packing density

5
Furnas Model
Che5700 ??????
  • In theory, if three kinds particle in packing
  • PFmax PFc (1- PFc) PFm (1- PFc)(1- PFm) PFf
  • f i, w Wi/W total
  • Wc PFc ?c medium and fine the same
  • The small particle size have to be small enough,
    size ratio gt 7, to effectively increase packing
    density
  • In industry, often mix two or more particles to
    get high density packing, to reach densification
    at lower sintering temperature

6
  • ???????????????????
  • Highest density occurs when small particle fill
    completely porosity from large particles (volume
    fraction for fines 26 or porosity from large
    particles 26)
  • In reality, since the size ratio will not be too
    large, the highest point of packing density
    usually moves toward the middle point.

7
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8
Packing of Continuous Distribution
Che5700 ??????
  • E.g. log normal distribution theoretical
    calculation shows that, under random packing,
    larger geometric standard deviation , denser
    packing (spheres)
  • Andreasen cumulative distribution (1) usually n
    0.33 0.5 experience 1/n increase, packing
    density increase
  • Zheng modified distribution (2) one more
    parameter, amin

9
Taken from JS Reed, 1995 often packing density
60-69 In reality, particles not very
spherical, will affect packing density
10
Results from real particle size distributions,
sample calcined Bayer alumina it is not very
easy to rationalize
11
Hindered Packing
Che5700 ??????
  • Including external and internal factors
  • Bridging of particles and agglomerates with rough
    surface of walls (mechanical vibration tap
    density, lubrication, large force causing
    particle fracture may improve somewhat)
  • Coagulation , adhesion between particles also
    retard particle motion and hence packing into
    dense structure
  • High aspect ratio often produce high porosity
  • Adsorbed binder molecule also hinder particle
    movement

12
Ordered Structure in Suspension
Che5700 ??????
  • For monodisperse particle systems particle
    interaction gravity force ? ordered structure
    (so called order-disorder phase transition
    question a thermodynamic and mechanical
    equilibrium problem)
  • Defects point defect (vacancy), line defect
    (dislocations), planar defects (grain boundary),
    volume defects (cracks)
  • Point defect can be estimated from
    thermodynamics other defects related to
    processing
  • Measurement of ordered domain size Scherer
    equation (peak broadening) ? FWHM k?/(L cos?)
    full width at half height k constant 0.9

13
  • ????TA Ring, 1996
  • Measurement of ordered array structure light
    diffraction (iridescence) n? 2 d sin? ? can
    estimate size of structure from diffraction peaks
    (d)

14
Sinterbility of Agglomerated Powders
  • Source J. Am. Cer. Soc., 67(2), 83-89, 1984 (by
    FF Lange)
  • A new concept Pore coordination number
    thermodynamic analysis pore will disappear only
    when its coordination number is less than a
    critical value
  • Real system irregular particle size and shapes
    irregular arrangement (packing)
  • Agglomerates hard (partially sintered) soft
    (held by van der Waals forces)

15
  • General experiences soft agglomerates produce
    better sintering results than hard agglomerates
  • This author thinks particle arrangement is
    important
  • A pore has its volume, shape and coordination
    number
  • RgtRc pore surface convex RltRc concave surface
    (those pores are able to disappear)

16
  • Theoretical calculation equal-sized spheres,
    random packing, pore volume always 0.37 0.41
    (or density 059 0.63) for real powder tap
    density rarely over 30 of true density
  • Theoretical calculation different sized sphere
    can produce bulk density up to 95
  • Consolidation force to increase bulk density
    depend on resistance of particle packing unit to
    deformation (via particle rearrangement) as
    shear stress increase, agglomerate first to shear
    apart into their smaller domains, next domain
    deformation, finally, particle deform or
    fracture
  • Grain growth a method to reduce pore
    coordination number grain growth from mass
    transport (temperature effect)
  • If pore growth faster, we may get pores with
    higher coordination number

17
Transparent Alumina
  • Grain size ?500 nm residual porosity negligible
    (e.g. 0.03)
  • Possible methods (a) Use high sintering
    temperature (grain growth problem) or (b)
    through special particle coordination and low
    temperature sintering (shaping technique or
    particle size distribution key homogeneity
    e.g. no agglomerates)
  • Following data from J. Am. Cer. Soc. 89(6),
    1986-1992, 2006.
  • Raw material Al2O3, 99.99 pure, 150-200 nm

18
  • Shaping methods (a) dry pressing (uniaxial
    pressing at 200 MPa cold isostatic pressing CIP
    at 700MPa (pre-shaped at 30-50 MPa) (b)
    gel-casting (4-5 wt monomer) (c) slip casting
    into porous alumina mold
  • Binder burnout 800oC, very small shrinkage (lt
    0.2), develop neck, provide strength for Hg
    intrusion analysis
  • Mercury porosimetry better than SEM to measure
    pore size distribution
  • No large pores (gt75 nm) an indication of
    homogeneity

19
  • Gel-casting versus uniaxial pressing

20
  • Pore size distribution do not change much from
    green state to intermediate sintering stage
  • Homogeneity poor for uniaxial pressing
  • Pore size 50 nm 1/3 of particle size

21
  • Slip casting provides the best particle
    coordination pore size 35 nm 1/5 particle
    size
  • Observation Smaller and larger pore are
    eliminated at similar rates

22
  • Density grain size trajectory of different
    processing

23
  • (a) slip casting without binder, presintered at
    1200oC, then HIP 1170oC, ave. grain size 0.44
    µm
  • (b) gelcasting, presintered at 1240oC, HIP
    1200oC, ave. grain size 0.53 µm (both densities
    gt 99.9)
  • All above data taken from J. Am. Cer. Soc. 89(6),
    1985-1992, 2006.
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