powder consolidation method of ceramic fabrication

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POWDER CONSOLIDATION

• BY-SUMIT KIRADOO YOGIRAJ SHARMA

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INTRODUCTION

• The Powder Consolidation means how the particles
  are being packed ,when filled in any die to give
  a shape.
• The packing of particles has direct effect on
  the Variation in packing densities of green body,
  there will be heterogeneity in microstructure.
• Microstructure of consolidated powder form
  (green body) has a significant effect on the
  properties of fired product.

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GOLS OF POWDER CONSOLIDATION

• THE uniform packing of particles in the green
  body is the main goal of powder consolidation.
• THE packing density controls the green fired
  shrinkage, the high packing density is always
  desirable.

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PACKING OF PARTICLES

• Packing of particles is generally divided into
  two types

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• There are various parameters to define the
  packing arrangement but the most widely used are
•  
• 1. Packing Density
• 2. Coordination number the number of
  particles in contact with any given particles.

Volume of solids Total volume
of
arrangement(solids voids)
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• In general, the Packing of powder particles can
  be classified in four ways
• Regular Packing of Monosize spheres
• Random packing of spherical particles
• Packing of powders in practice
• Packing of Mixtures of powders and short fibers

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REGULAR PACKING OF MONOSIZE SPHERES

• The packing of Particle of monosize spheres is on
  similar pattern with packing of atoms in
  crystalline solids to produce regular, repeating,
  three- dimensional pattern such as the simple
  cubic, body-centered cubic, and hexagonal
  close-packed structures.
• He packing densities and coordination numbers for
  these crystals structures are listed in Table

Crystal structure Packing den. c. n.
1. SIMPAL CUBIC 0.524 6
2. B.C.C. 0.680 8
3. F.C.C. 0.740 12
4. H.C.P 0.740 12
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• Three dimensional packing patterns of particles
  can be visualized by
• (i) Packing spheres in two dimensions to from
  layers and then (ii) stacking the layers on the
  top of one another
• Mainly, while packing spheres in two dimensions,
  there can be two types of layers
• 1. Square type of regular packing of monosize
  spheres
• 2. Equilateral Triangular or Rhombic type of
  regular packing of monosize spheres.

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• 1. Square type of regular packing of monosize
  spheres
• Where, the angle of intersection
  between the rows has limiting values of 90
  degree.

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• 2. Equilateral Triangular or Rhombic type of
  regular packing of monosize spheres.
• Where the angle of intersection b/w row is 60
  degree.

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• Although, there are other types of layers but
  they will have angles of intersection between
  these two values are possible.
• For stacking each type of layer on the top of
  one another, There are three geometrically simple
  ways of stacking (ABABAB, ABABAB, A?B A?B A?B)
  which gives rise to six packing arrangement
  altogether for both Square rhombic type
  However, examination of the arrangements will
  show that neglecting the difference in
  orientation in space, two of the ways of stacking
  the square layers are identical to two of the
  ways of stacking the simple rhombic layers. (i)
  Therefore there are only four different regular
  packing arrangements shown

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Packing density and Coordination Number of the
Four Regular packing Arrangementof Monosize
Spheres.
Packing arrangement Packing density Coordination number
Cubic 0.524 6
Orthohomphic 0.605 8
Tetragonal- sphenoidal 0.698 10
Rhombohedral 0.740 12
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RANDOM PACKING OF SPHERICAL PARTICLES

• In general, the commonly used ceramic forming
  methods produce more random packing arrangement
  in the consolidated powder form . Keeping in view
  the spherical particles, two different states of
  random packing have been distinguished powder
  form.
• 1. If the particles are poured into a
  container and then the container is vibrated to
  settle the assembly of particles, the resulting
  packing arrangement reaches a state of minimum
  porosity referred to as dense random packing.
• 2. If the particles are simply poured into
  the container and are not allowed to rearrange
  and settle into as favorable a position as
  possible, the resulting packing arrangement is
  referred to as loose random packing.
• ?For Dense random - experimentally value is
  0.635-0.640
• Computer simulations confirm the value
  of 0.637.

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• ?For loose random packing theoretical
  calculations as well as experiments give values
  in the range of 0.57-0.61 for the packing
  density.
• ?For density fluctuations existing over such a
  small scale, uniform sintering may be achieved
  during firing of the consolidated powder form.
  Therefore, the production of regular,
  crystals-like particle, packing achievable at
  present only over very small domains may after
  all be unnecessary from the point of view of
  fabrication.
• Random Packing with binary mixture of spheres
• In dense random packing, an increase in the
  packing density can be achieved either by
• (a) Filling the interstices between large spheres
  with small spheres .
• (b) Replacing small spheres and their
  interstitial porosity by large spheres.
• (c) By inserting the each hole a single sphere
  with the largest possible diameter that would fit
  to the hole.

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Filling the interstices between
large spheres with small spheres
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• Starting with an aggregate of large (coarse)
  spheres in dense random packing, as we add fine
  spheres the packing density of the mixture
  increases along the line CR stage will be reached
  when the interstitial holes between the large
  spheres are filled with fine spheres in dense
  random packing and further additions of fine
  spheres will only serve to expand the arrangement
  of large spheres, leading to a reduction in the
  packing density.
• Assuming a packing density of 0.64 for dense
  random packing and the interstitial holes are
  filled with a large number of fine spheres in
  dense random packing
• Volume fraction of interstitial holes in the
  original aggregate of large spheres is 1 - 0.64,
  or 0.36.
• Maximum packing density is therefore 0.64 0.36
  x 0.64 0.87.

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• Fractional volumes occupied by the large spheres
  and fine spheres are 0.64 and 0.87 - 0.64,
  respectively.
• Fraction of large spheres in the binary mixture
  is therefore 0.64/0.87, or 0.735.

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• Replacing small spheres and their interstitial
  porosity by large spheres
• Alternatively, we can increase the packing
  density of an aggregate of fine spheres in dense
  random packing by replacing some of them and
  their interstitial holes by large spheres. In
  this case, the packing density of the mixture
  will increase along the line FR
• The packing of binary mixtures of
  spheres is also commonly represented in terms of
  the apparent volume (i.e. total volume of the
  solid . The apparent volume is defined as
• Va Where P is fractional volume of
  voids (i.e., the porosity).

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By inserting the each hole a single sphere with
the largest possible diameter that would fit to
the hole.
For a aggregate of monosize spheres in dense
random packing, the computer simulations reveals
the value of 0.76 for the maximum packing density
of binary mixture. Which is lower than the value
of 0.87 when filled with large no .of fine
spheres in the interstices of the large spheres.
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