Lecture 26: Crystallization

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Lecture 26 Crystallization

• PHYS 430/603 material
• Laszlo Takacs
• UMBC Department of Physics

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Nucleation

• Heterogeneous nucleation Nuclei form at
  pre-existing surfaces, so that little extra
  surface is created, the energy barrier is small.
  The most typical places for heterogeneous
  nucleation are the wall of the container and
  high-melting particles present in the melt.
  Temperature independent.
• Homogeneous nucleation Nuclei form due to the
  random motion of atoms in the melt. Increases
  with lowering temperature, dominates far below
  the melting point.
• In order to achieve large undercooling,
  heterogeneous nucleation has to be avoided. The
  best is a small droplet with no room for a seed
  particle, levitated freely in a rf magnetic
  field. In industrial settings only a few degrees
  of undercooling take place, but 15 of Tm is
  possible in the laboratory.
• Nucleation and crystallization can be avoided
  with fast cooling between Tm, where the formation
  of nuclei can start, to T0, where diffusion
  becomes negligible.

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The nucleation rate
Finish Start
Crystallization - can be avoided, by fast enough
cooling to avoid the nucleation line. This is how
metallic glasses are made.
A deep eutectic point often makes the formation
of a glassy phase possible. Ni-P is an
interesting system because it can also be made
amorphous by mechanical alloying and Ni-P
coatings deposited by electrochemical methods can
also be amorphous.
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STM images of a crystalline Zr and a glassy
Zr-Ni-Al-Cu alloy
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Mechanical property comparison for a bulk
metallic glass
Notice the very competitive properties and the
uniquely high elastic limit.
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• Stability and phase transformation - always of
  interest in the case of metastable materials.
• Crystallization of Fe(80)B(20) glass ? Fe Fe4B
  ? Fe Fe3B ? Fe Fe2B
• It takes place in several steps, with the
  formation of simpler (thus easier-to-nucleate)
  but still metastable intermediate phases.
• Magnetism - promising for soft magnetic material
  no crystal structure, no magnetocrystalline
  anisotropy stress sensitivity (anisotropy due to
  magnetostriction) can be minimized by varying the
  composition
• E.g. (Fe1-xCox)75Si15B10 shows zero
  magnetostriction at about x 0.9
• Even if rapid quenching from the melt does not
  result in a glassy phase, the first phase to form
  is not the most stable one but the one that
  nucleates the most easily. Quite often metastable
  crystalline compounds form. An interesting case
  is quasicrystals, alloys that have no
  translational periodicity but possess five-fold
  rotational symmetry.
• Nucleation is also an important component of
  solid-solid phase transformations e.g. during
  recrystallization.

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Ordinary crystallization at moderate cooling
ratesThe role of heat flow during solidification

• Heat flow is an important component of
  solidification. Heat has to be conducted away to
  lower the temperature to below the melting point.
  Solidification is an exothermic process, the
  latent heat has to be take away also. Heat
  balance of dx
• heat flow into crystal - heat flow from liquid
  latent heat

Heat flows toward the (colder) solid stable
solidification front Heat flows toward the liquid
(colder due to undercooling and latent heat)
instability
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• Undercooling and the warming from solidification
  can lead to inverse temperature gradient even if
  the melt is solidifying in a cold container. The
  resulting instability leads to the formation of
  dendrites - a very common phenomenon, not a rare
  occurrence.

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The mechanism behind crystal habit

• These Wulff diagrams show the direction
  dependence of the surface energy and the
  resultant external shape of the crystal. The
  lowest energy faces grow the fastest during
  crystallization. This is the reason behind
  crystal habit, the most obvious external feature
  of crystals. Historically, crystallography
  developed from the study of habit way before the
  existence of atoms had been proven.

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The crystallization of alloys1. Fast diffusion
in both S L system is always in
equilibrium.2. Fast diffusion in L, little in
S coring3. Slow diffusion in L S
constitutional supercooling,
dendrites.Solidification results in
concentration differences.

• Initial Sn concentration is 23 at.. On cooling
• Pb-Sn(12) crystallizes first.
• The (uniform) Sn content of the liquid increases.
  The concentration of the solid also shifts, the
  (Pb) phase develops coring.
• The liquid reaches the eutectic point, the solid
  is Pb-Sn(29).
• Simultaneous crystallization of Pb-Sn(29) and
  Sn-Pb(1.4) usually in a lamellar structure.

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Zone melting

• Suppose we have a PbSn(23 at.) rod, melt a short
  section at the left end and move the molten
  region (the heater) to the right. The Sn content
  of the left end will be only 12 the Sn will
  move to the right.
• Repeating the process several times purifies the
  left end and concentrates the Sn (or any other
  impurity) on the right.
• This is one of the most important methods of
  material purification (electro-refining is
  another.)

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Solidification in a mold

• Heat flow, cooling rate, variation of impurity
  concentration determines the micro-structure of
  cast metals
• Chill zone, fast cooling fast nucleation, many
  small grains.
• Columnar growth in the direction of the heat
  flow. Only grains with low-energy face in the
  right direction grow.
• Impurities are swept toward the middle, more
  random nucleation and the formation of equiaxed
  grains can take place.
• Volume decrease results in a shrinkage pipe.

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Nucleation in the solid state

• Most transformations in the solid state - such as
  precipitation - begin with nucleation also.
• Interface energy is the smallest for coherent
  boundaries, larger for semi-coherent boundaries,
  the largest for incoherent phase boundaries. A
  phase with low interface energy can form, even if
  it is not the phase with the lowest free energy.
• Other factors Direction dependence of the
  interface energy.
• Volume change and related elastic energy.

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Spinodal decomposition

• Consider the free energy of a two-component alloy
  system that shows phase separation in
  equilibrium.
• If it is cooled very quickly from the melt
  (quenched) solid solution may be obtained with a
  concentration outside the equilibrium solubility
  range.

At a concentration where the G(C) curve is convex
from below, e.g c1, decomposing the solid
solution to two regions with slightly different
concentrations increases G, it will not happen.
(Notice that the equilibrium state at c1 is a
two-phase state.) But at a concentration where
the G(C) curve is concave from below, e.g c3,
decomposing the solid solution to two regions
with slightly different concentrations decreases
G. There is a driving force for phase separation
by gradual change of concentration distribution.
Usually a lamellar microstructure develops -
Gunier-Preston zones.
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• For a regular solution with HAA HBB, the Gibbs
  free energy as a function of concentration is

Spinodal decomposition is possible between the
inflection points - the zeros of the second
derivative
Decomposition is energetically favorable anywhere
between the two end-points of the common tangent.
But outside the spinodal range, it can only start
with nucleation.
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Nucleation versus spinodal decomposition