Lecture 25: The Liquid State Nucleation and Metallic Glasses

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Lecture 25 The Liquid State Nucleation and
Metallic Glasses

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

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The states of matter

• Gas - relatively simple
• There is a reference state, the ideal gas, that
  can be understood in significant detail. Real
  gases are usually described as deviations from
  the ideal gas state due to interaction between
  molecules.
• Crystalline solid - relatively simple
• There is a reference state, the ideally periodic
  infinite crystal, that can be understood by
  focusing on the unit cell. Real crystals
  deviate from the ideal state due to finite
  crystallite size and defects.
• Liquid - inherently complicated
• There is no good reference state. Liquids are
  dense like solids with strong interaction between
  the molecules, but their structure is random, at
  least it has neither long range order nor unit
  cell. There is some short range order, both
  correlations in position and specific local
  geometries. The structure is dynamic, the
  molecules are in constant motion.
• Intermediate cases
• Amorphous materials - dense, random, but static
• Quasicrystals - orientational order, but no
  periodicity
• Partially ordered materials, e.g. liquid
  crystals

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Structure from diffraction experiments
The intensity of the diffracted beam depends on
the phase difference between elementary rays
scattered by individual atoms.

• Gas The relative atomic positions are random,
  constructive and destructive interference average
  out. Same as scattering by individual molecules.
• Crystal If there is constructive interference
  between corresponding atoms in two neighboring
  unit cells, the interference is constructive
  between atoms from every unit cell, diffraction
  peak is observed.
• Notice that XRD of crystals does not derive the
  structure from scratch, but only selects the
  structure from a list of possible structures
  allowed by symmetries. A 1-d (or possibly 2-d)
  measurement may not be able to reconstruct a 3-d
  structure.
• Liquids and glasses There is some short range
  order and consequently an interference pattern,
  but only statistical information can be obtained
  from diffraction, the position of every atom
  cannot be determined.

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Characterization of a liquid or amorphous
structure

• Radial distribution function the probability of
  finding an atom at a distance r from an average
  atom.

For a completely random structure (gas) or for
large distances where there is no more short
range order, RDF approaches a parabola
corresponding to the average atomic density.

• Notice that there is clear short-range order
• The nearest neighbors are quite clearly defined,
  both their distance and their number (the area
  under the first peak.)
• The second and third coordination shell are
  identifiable.
• The curve approaches the 4?r2?0 parabola.
• The bars indicate the distance and number of
  neighbors in crystalline hcp Zn. The short range
  order in the liquid is quite different - RDF
  cannot be obtained by broadening the crystalline
  distances.

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What do we measure in diffraction?

• Scattered intensity corrected for instrumental
  effects is the interference function, S(Q),
  where Q is the scattering vector (the change of
  the wave vector from the initial to the scattered
  state, Q 4?/? sin?.) From S(Q) the radial
  distribution function can be calculated

• This seems to be a straightforward procedure, but
• The interference function is known only to a
  finite Q, the integral must be truncated.
• Instrumental effects must be considered very
  carefully, as the pattern consists of broad
  features, not sharp lines.

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XRD results on amorphous FeP electrodeposited and
melt quenched alloys

• Interference functions. Notice that the top three
  curves contain a small crystalline fraction. The
  lowest two define the fully amorphous
  concentration range, 16.7 to 22.9.
• Hiltunen, Lehto, Takacs, 1986

RDF, P concentration increases down. Notice that
the short range order is similar but stronger
than in liquids. There is little variation
between samples, it is difficult to identify
trends.
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Partial correlation functions for Ni60Nb40

• The measured interference function is an average
  of the partial interference functions
  corresponding to the different atom pairs,
  weighted with the atomic scattering amplitudes.
  If three independent measurements with different
  scattering amplitudes are performed, the partial
  correlation functions can be separated.
• The three measurements here were made using XRD,
  neutron diffraction with natural Ni and neutron
  diffraction on a sample made with 58Ni isotope.
• Forgács, Hajdu, Sváb, J. Takács (1980)

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Ni60Nb40 partial RDFs

• There are clear differences between the curves,
  e.g. in the first neighbor distance and the shape
  of the split second peak. Unfortunately,
  decomposing similar curves from independent
  measurements, even different samples, results in
  large experimental uncertainties.
• Another method of obtaining similar results is
  anomalous scattering of X-rays.

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Crystallization

• It is simple Over the melting point a material
  is liquid, below it is crystalline.
• No! Starting to form a new phase also requires
  formation of a new interface!

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• Crystallization from the liquid state must always
  start from a nucleus.
• Homogeneous nucleation from a cluster within the
  liquid.
• Heterogeneous nucleation from a pre-existing
  surface, e.g. wall of the container or surface of
  impurity particle.

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The free energy balance of homogeneous nucleation
Volume free energy Surface energy ?, assumed
to be direction independent For a spherical
nucleus of radius r
If r is small, the positive surface term
dominates, the formation of a small nucleus is
not favorable. But if a large nucleus forms
against the odds, for large r the negative volume
term dominates, the nucleus is stable. The two
regions are separated by the radius of the
critical nucleus
The volume energy gain increases with increasing
undercooling, consequently the critical radius
decreases, that is random fluctuations can more
easily - and more frequently -create a nucleus
larger than the critical size. At Tm the volume
energy gain becomes zero, the critical size
approaches infinity, there is no nucleation.
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Heterogeneous nucleation

• Nucleation can start at pre-existing surfaces,
  with substantial gain in surface energy. The most
  typical places for heterogeneous nucleation are
  the surface of the container and high-melting
  particles present in the melt (seeds added
  intentionally or impurities, e.g. oxides.)
• Heterogeneous nucleation dominates close to the
  melting point, but homogeneous nucleation becomes
  important at low temperatures, as the number of
  heterogeneous nucleation sites is constant, but
  the number of homogeneous nuclei increases with
  decreasing temperature.
• 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.

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The nucleation rate

• The nucleation rate is proportional to the
  probability of forming a nucleus larger than
  critical size

Close to Tm the size and therefore the free
energy of the critical nucleus is large, the
nucleation rate is very slow, substantial
nucleation takes a very long time. At low
temperature, T in the denominator is small,
nucleation is slow because of the slow
dynamics. In between there is a degree of
undercooling where homogeneous nucleation is the
fastest. Growth is a diffusion-driven process
that has a rate according to the Fulcher equation
of
Finish Start
The fastest nucleation happens close to the
temperature a the tip of the curve.
Crystallization - can be avoided, by fast enough
cooling to avoid the nucleation line. This is how
metallic glasses are made.
The temperature variation of the nucleation and
growth rates explain the shape of the TTT -
time-temperature-transformation diagram.
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What materials can form a glass?

• Some materials - like mixtures of oxides,
  chalcogenides, complex organic materials - are
  easy glass formers. In those cases nucleation is
  very difficult because a large cluster of
  molecules must fit together by random motion to
  acct as a crystalline seed. Many of those
  materials do crystallize if cooling is very slow
  or seeds for heterogeneous nucleation are
  provided.
• The structure of metals is simpler, thus
  nucleation is easier. Until 1959 it was believed
  that metals were always crystalline. This is not
  the case. Crystallization can be avoided also in
  metallic melts, if the difference between Tm and
  T0 is small. In a typical alloy system Tm can be
  strongly temperature dependent - deep eutectic
  points are advantegous - while T0 varies
  relatively little.
• 1960 P. Duwez, Au-Si, later Pd-Si
• Late 1960s The first ferromagnetic metallic
  glasses Fe80P12C8
• 1975 The METGLAS 2605 family (Fe80B20 and
  related compositions)
• Late 1970s Ni-Nb and other early-late transition
  metal systems
• 1985-1995 a decade of decreasing interest
• 1996 Inoue (Tohoku, Sendai) and W. Johnson
  (CalTech, Pasadena), bulk metallic glasses, such
  as Al-Y-Ni, La-Al-Ni Zr-Ni-Al-Cu, Zr-Ti-Cu-Ni-Be
  and Mg-Cu-Y

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Some typical metallic glass forming systems

• Au-Si the first one Fe-B ferromagnetic
  Nb-Ni metal-metal

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Forming traditional metallic glasses requires
106 C/s cooling rate - possible only for thin
ribbons or sheets.Melt spinning is the most
frequently used method to reach such cooling
rates.
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STM images of a crystalline and glassy Zr alloy
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Mechanical property comparison for a bulk
metallic glass
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Other subjects related to metallic glasses

• Stability and crystallization
• E.g. Fe(80)B(20) melt ? Fe(80)B(20) glass ? Fe
  Fe4B ? Fe Fe3B ? Fe Fe2B
• Magnetism - no crystal structure, no
  magnetocrystalline anisotropy, stress sensitivity
  can be minimized by varying the composition
• E.g. (Fe1-xCox)75Si15B10 at about x 0.9
• Partially crystallized magnetically hard-soft
  alloys.
• Other materials produced by rapid quenching
  Quasicrystals, metastable compounds