Solidification, Crystallization

1
Solidification, Crystallization Glass Transition

• Crystallization versus Formation of Glass
• Parameters related to the formation of glass ?
  Effect of cooling rate ? Glass transition
  temperature
• Structure of Glasses ? Radial distribution
  function

2
Glasses and Amorphous Materials

• The word glass and amorphous material can be
  interchangeably used in most circumstances?
  though there is a small technical difference
  (which we will consider later).
• Based on atomic structure it is one of the 3
  fundamental states of matter. In glasses the
  atoms do not have long range order (LRO), though
  they may have short range order (SRO).
• The SRO could be very different from that
  encountered in crystals (even the crystals formed
  out of the same composition). E.g. one may find
  local icosahedral clusters.
• In a simplistic picture, glass can be thought of
  as a time snapshot of the liquid.
• Typically glasses have a higher free-volume as
  compared to the crystal (the preferred crystal
  structure that the material is expected to form
  for a given T P).
• Concepts like Lattice and motif thus cannot be
  used in glasses. This automatically implies that
  many of the properties of a glasses will be
  drastically different as compared to the
  corresponding crystal (thought he composition may
  be identical and the density not very different).
  For example, dislocations (in the usual sense)
  cannot be defined in glasses and hence the
  plastic deformation of glasses have to take place
  by other mechanisms (e.g. shear banding).

Matter
STATE / VISCOSITY
One kind of glass is the window pane glass, but
glasses come in many forms (based on bonding,
etc.). Many of these glasses are not transparent.
SOLID
GAS
LIQUID
LIQUID CRYSTALS
STRUCTURE
AMORPHOUS
QUASICRYSTALS
CRYSTALS
3

• It is assumed that glasses are metastable and
  there exists at least one crystal structure which
  has a lower Gibbs free energy (at constant, T,P).
  This implies if sufficient activation energy is
  provided (usually by heating), then glasses will
  tend to crystallize. At low temperatures the
  glass in frozen in a disordered state and may
  remain so for a long time (e.g. glass used in the
  window panes are not expected to crystallize in
  geological time scales).
• On heating glasses (see page on heating of
  glass more on this) they tend to crystallize.
  This process occurs by nucleation and growth of
  crystallites in the amorphous matrix. Many
  materials like long chain (and branched) polymers
  are difficult to crystallize completely (more on
  this soon). As we shall see soon, in some
  circumstances a partially crystallized
  microstructure can give us better properties.
• Many different kinds of materials can be obtained
  in the amorphous state. These include polymers,
  inorganic materials, organic materials, metals
  and alloys, semiconductors, etc. In fact if we
  look around us, most of the materials we see
  (like wood, building walls, etc.) are not fully
  crystalline.
• From the above it is clear that the term
  amorphous (which is based on atomic level
  structure) is used for a wide class of materials
  and based on the specifics of the material
  involved, the properties will be varied. As
  expected, polymeric glasses will have poor
  tolerance to heat, while inorganic glasses may
  withstand high temperatures.

4
Formation of Glass

• Certain materials are easy glass formers (e.g.
  silicates, long chain polymers, etc.), which
  others are difficult to amorphize (e.g. pure
  metals, simple alloys, etc.).
• Glasses can be synthesized in many ways. Three
  typical ways are listed below.
• 1) From the vapour state? By condensing the
  vapour of the material onto a cold substrate.
• 2) From the liquid state? Quenching from the
  melt (usually fast cooling from the molten
  state). The rate of quenching required depends on
  the material (and parameters to be discussed
  soon). To amorphize certain alloys cooling rates
  of the order of 106 K/s needs to be employed,
  while certain special alloys and silicate
  materials can be slowly cooled to get glass (even
  1 K/s).
• 3) In the solid state? By severely deforming the
  crystals (say a polycrystal) amorphous state can
  be obtained. Ball milling has been one of the
  popular examples for this method (for alloys).

5
Glass Forming Ability Resistance to
Crystallization

• Glass Formation Ability (GFA) should be
  differentiated with Resistance to Crystallization
  (RTC) also called Glass Stability (GS). GFA is in
  the cooling direction (i.e. how slowly can I
  cool to still get a glass?), while RTC is in the
  heating direction (i.e. to how high a
  temperature can I heat and still retain a
  glass?). Many parameters have been developed to
  characterize materials with respect to GFA and
  RTC.
• Crystallization is favoured by high enthalpy of
  fusion (?Hfusion) and a low viscocity (?). ? The
  critical Gibbs free energy for the nucleation of
  a crystal is related to the enthalpy of fusion as
  in the equation below. Large ?Hfusion implies a
  lower ?Gcrystallization, which further implies
  ease of crystallization. ? An embryo becomes a
  nucleus by jump of atom across the interface from
  liquid to crystal. This requires a activation
  enthalpy (?Hd). The activation enthalpy is
  related to the log of viscosity. This implies
  that a lower viscosity allows for easier atomic
  jumps, which in turn favours crystallization.

Click here to revise concepts on nucleation
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• Metals (in molten state) with a high enthalpy of
  fusion (10 kJ/mole) and low viscosity (1-10
  poise) are difficult to amorphize. Pure metals
  (like Al, Cu) are virtually impossible to
  amorphize by quenching from the liquid state.
  Some alloys (one popular brand name is Metglas?)
  can be cooled at a high cooling rate (using
  processes like melt-spinning or splat quenching)
  of 106 K/s to obtain a foil of amorphous
  material. one popular commercial composition of
  metallic glass is Metglas? is Fe 85 wt., Si 10
  wt., B 5 wt..
• Needless to say one dimension of the sample will
  have to be thin for fast heat extraction (which
  implies that we end up with foils).
• Inorganic glasses on the other hand, with low
  ?Hfusion and high viscosity are easily
  amorphized. In fact some oxides may have to be
  added promote crystallization. E.g. Borosilicate
  glass 81 SiO2, 13 B2O3, 4 Na2O/K2O, 2 Al2O3
  softening point of 820?C.

High ? (10-15) kJ / mole
Low
? ?Hfusion
Thermodynamic
Silicates
Metals
Crystallization favoured by
High ? (1000) Poise
Low ? (1-10) Poise
? ?Hd ?? Log Viscosity (?)
Kinetic
Enthalpy of activation for diffusion across the
interface
Very fast cooling rates 106 K/s are used for the
amorphization of alloys
Easily amorphized
Difficult to amorphize metals
7

• In contrast to metals silicates, borates and
  phosphates tend to form glasses
• Due to high cation-cation repulsion these
  materials have open structures
• In silicates the difference in total bond energy
  between periodic and aperiodic array is small
  (bond energy is primarily determined by the first
  neighbours of the central cation within the unit)

8
Measures of Glass Forming Ability (GFA)

• There are many parameters used to characterize
  the glass forming ability of a material. Most
  important of these are Critical Cooling Rate
  (qcr) and Critical Diameter (dcr).
• These two parameters are related to one another

9
Heating of Glass

• As pointed out before, a glass will tend to
  crystallize on heating.
• If crystallization does not intervene, then
  glasses will slowly soften (i.e. the viscosity
  will decrease) and will begin to flow. This is
  what enables glow blowing operations, wherein
  silicate glass is heated and blown to form
  bottles. This is what we observe when we heat wax
  candles.
• This implies that glasses do not have a well
  defined melting point like crystals.
• The crystallization of glass can be studied by
  using Differential Scanning Calorimetry (DSC). In
  DSC a sample is heated at a constant rate (say 20
  ?C/min) and hence the origin of the word
  scanning. The heat absorbed or evolved (with
  respect to a reference pan and hence called
  differential) is measured as a function of
  temperature. Typical plot in the next page.
• In a DSC plot (where Y axis is exothermic) (i)
  glass transition appears as a step, (more about
  glass transition later)(ii) crystallization(s)
  as exothermic peak(s) and (iii) melting as a
  endothermic valley. More than one
  crystallization peaks may be observed if more
  than one type of crystal forms during the heating.

10

• Materials which show glass transition (as
  indicated in the DSC plot) are called glasses and
  those which do not are referred to as Amorphous
  materials. In amorphous materials it is assumed
  that crystallization masks the glass transition
  (the presumed reason as to why we do not observe
  glass transition).
• The temperature interval between Tg and Tx
  (Tx?Tg) is called the supercooled liquid region.
  The properties of the material below Tg will be
  different (often drastically) from that above.

Crystal
Supercooled liquid region
Glass
Tg
Tx
Tg
Tg
Amorphous solid
Glass
Glass
Glass
Cool liquid
Cool liquid
Crystal
Heat Amorphous solid
Crystal
Heat glass
Tx
Tx
Often metallic glasses crystallize first (in a
viewpoint before Tg) Hence the glass transition
temperature in heating is masked by
crystallization (hence not observed
experimentally)
11

• DSC is a versatile tool to study phase
  transformations.
• By using various scanning rates (temperature
  scanned per unit time, K/s or ?C/min) in
  conjunction with the Kissinger analysis the
  activation energy for the phase transformations
  can be determined.
• The crystallization temperature (Tx) and glass
  transition temperature (Tg) are determined from
  the DSC plot as shown in the figure.
• The crystallization process is exothermic (as the
  system is going from a higher internal energy
  amorphous structure to a lower energy crystal),
  while the melting process is endothermic (energy
  has to be supplied to break the bonds in a
  crystal and to cause melting). The glass
  transition is step-like in the DSC plot.

Differential Scanning Calorimetry (DSC)
Glass transition step
Note crystallization peak(exothermic)
Material gives out heat during crystallization
Note melting valley(endothermic)
Material absorbs heat to melt (the latent heat)
Sample heated at constant rate
12
Glass Transition

• We have seen as to how glass transition is
  indicated in a DSC plot. But, typically glass
  transition is understood first in the cooling
  direction.
• When a liquid is cooled slowly and its volume is
  plotted as a function of the temperature, there
  is a sudden shrinkage at the melting point when
  crystallization takes place.
• On the other hand if crystallization is avoided
  and the material is freezes into a glass.

Liquid
All materials would amorphize on cooling unless
crystallization intervenes
Slow change in volume
Sudden shrinkage in volume during crystallization
Instead of V we can plot other extensivethermodyn
amic quantities (i.e. they all show same
behvaiour) ? S, H, E
Glass
Volume ?
Crystal
Tm
Tg
T ?
Glass transition temperature
13
Change in slope
Volume ?
T ?
Tf
Fictive temperature (temperature at which glass
is metastable if quenched instantaneously to this
temperature) ? can be taken as Tg
14
Effect of rate of cooling
As more time for atoms to arrange in closer
packedconfiguration
Volume ?
Slower cooling
Lower volume
T ?
Slower cooling
Higher density
Lower Tg
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• On crystallization the viscosity abruptly
  changes from 100 ? 1020 Pa s
• A solid can be defined a material with a
  viscosity gt 1012 Poise

If the glass crystallizes on heating (at Tx),
before Tm then ?T Tx ? Tg is a measure of the
glass formability. The region between Tg and Tx
is the supercooled liquid region in this case.
Crystal
Glass
Log (viscosity) ?
Supercooledliquid
Liquid
T ?
Tm
Tg
16
Glass transition temperature of various types of
glasses

• Note that there are elemental, alloy and compound
  glasses. Boding varies from covalent to Van der
  Waals type. Glass transition temperature ranges
  from low values (65 K) to high values (1430 K).

Material Bonding Tg (K)
SiO2 Covalent 1430
Pd0.4Ni0.4P0.2 Metallic 580
BeF2 Ionic 570
Polystyrene mixed 370
Se 310
H2O Hydrogen 140
As2S3 Covalent 470
Isopentane Van der Waals 65
R. Zallen, Physics of Amorphous Solids, John
Wiley and Sons, 1983.
17
Glass-ceramic (pyroceram)

• A composite material of glass and ceramic
  (crystals) can have better thermal and mechanical
  properties (especially spalling resistance).
• But glass itself is easier to form (shape into
  desired geometry).

Heterogenous nucleating agents (e.g. TiO2) added
(dissolved) to molten glass
Shaping of material in glassy state
TiO2 is precipitated as fine particles
Held at temperature of maximum nucleation rate (I)
Heated to temperature of maximum growth rate
18

• Even at the end of the heat treatment the
  material is not fully crystalline
• Fine crystals are embedded in a glassy matrix
• Crystal size 0.1 ?m (typical grain size in a
  metal 10 ?m)
• Ultrafine grain size ? good mechanical properties
  and thermal shock resistance
• Cookware made of pyroceram can be heated directly
  on flame.

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Radial Distribution Function

• In crystals interatomic distances are well
  defined. In a CCP crystal the distances are
  a?2/2, a, a?6/2, a?2, etc. These vectors are
  shown in the figure below.
• In glasses this is not so. The minimum approach
  distance is (r1 r2), however the distances
  after that are not discrete. Hence we have to
  come up with measures as to how the distribution
  of atoms varies from a given reference atom. One
  such measure is the Radial Distribution Funtion.
• For a distribution of atoms the Radial
  Distribution Function (g(r), RDF), describes how
  density varies as a function of distance from a
  reference atom. This reference atom could be any
  atom, as there are no preferred sites in a glass
  and things average out due to the randomness of
  atomic positions.
• RDF is a measure of the probability of finding an
  atom at a distance of r in a spherical shell,
  relative to that for an ideal gas (i.e. the
  probability is normalized w.r.t. to an ideal
  gas).
• Fourier transform of the RDF is related to the
  structure factor.

Can also be defined for molecules, etc. RDF
is closely related to the Pair Correlation
Function
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RDF continued

• RDF (g(r)) is defined as in the formula below.

• ? ? number density- number of atoms/volume
• n ? number of atoms in the volume between r (r
  dr)

Note that the discrete peaks found in the case of
crystals has become diffuse
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(No Transcript)
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Solidification and Crystallization
23
Metals
? ?Hfusion
High ? (10-15) kJ / mole
Thermodynamic
Crystallization favoured by
Low ? (1-10) Poise
? ?Hd ?? Log Viscosity (?)
Kinetic
Enthalpy of activation for diffusion across the
interface
Difficult to amorphize metals
Very fast cooling rates 106 K/s are used for the
amorphization of usual alloys ? splat cooling,
melt-spinning.
24
Silicates
? ?Hfusion
low
Thermodynamic
Crystallization favoured by
High ? (1000) Poise
? ?Hd ?? Log Viscosity (?)
Kinetic
Enthalpy of activation for diffusion across the
interface
Easily amorphized
Certain oxides can be added to silica to promote
crystallization