Solidification, Crystallization & Glass Transition

Solidification, Crystallization & Glass Transition Solidification, Crystallization & Glass Transition

 Cooling the Melt  solidification

 Crystallization versus Formation of Glass

 Parameters related to the formaton of glass

 Effect of cooling rate

 Glass transition temperature

 Structure of Glasses  Radial distribution function

↑ H

↓ H

 Log [Viscosity ()]

Crystallization favoured by

High → (10-15) kJ / mole

Low → (1-10) Poise Metals

Enthalpy of activation for diffusion across the interface

Difficult to amorphize metals

Thermodynamic

Kinetic

Very fast cooling rates ~10

K/s are used for the amorphization of alloys

→ splat cooling, melt-spinning.

2

* 1

fusion

G H

 



 Fine grain size bestows superior mechanical properties on the material

 High nucleation rate and slow growth rate  fine grain size

 ↑ Cooling rate  lesser time at temperatures near T_m , where the peak of growth rate (U) lies

 ↑ nucleation rate

 Cooling rates ~ (10⁵ – 10⁶) K/s are usually employed

 Grain refinement can also be achieved by using external nucleating agents

 Single crystals can be grown by pulling a seed crystal out of the melt

I, U →

T (K) →

T

0

U

I

↑ H

↓ H

 Log [Viscosity ()]

Crystallization favoured by

low

High → (1000) Poise Silicates

Enthalpy of activation for diffusion across the interface

Easily amorphized

Thermodynamic

Kinetic

Certain oxides can be added to silica to promote crystallization

 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)

 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).

Glass-ceramic (pyroceram)

Shaping of material in glassy state

Heterogenous nucleating agents (e.g. TiO₂ ) added (dissolved) to molten glass

TiO₂ is precipitated as fine particles

Held at temperature of maximum nucleation rate (I)

Heated to temperature of maximum growth rate

→ T t →

Nucleation

Growth

T

T

Glass Partially crystallized Glass

 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.

Solidification and Crystallization

↑ H

↓ H

 Log [Viscosity ()]

Crystallization favoured by

High → (10-15) kJ / mole

Low → (1-10) Poise Metals

Enthalpy of activation for diffusion across the interface

Difficult to amorphize metals

Thermodynamic

Kinetic

Very fast cooling rates ~10

K/s are used for the amorphization of usual alloys

→ splat cooling, melt-spinning.

2

* 1

fusion

G H

 



↑ H

↓ H

 Log [Viscosity ()]

Crystallization favoured by

low

High → (1000) Poise Silicates

Enthalpy of activation for diffusion across the interface

Easily amorphized

Thermodynamic

Kinetic

Certain oxides can be added to silica to promote crystallization

 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)

Glass Transition

“All materials would amorphize on cooling unless crystallization intervenes”

T →

Volume →

Or other extensive thermodynamic properties → S, H, E

Liq uid

Glass

Crystal

T

T

Glass transition temperature

T →

Volume →

Change in slope

T

Fictive temperature (temperature at which glass is metastable if quenched instantaneously to this temperature) → can be taken as T_g

T →

Volume →

Effect of rate of cooling

T

T

2

1

T

T   

Slower cooling

Slower cooling Higher density Lower T

Lower volume

As more time for atoms to arrange in closer packed configuration

T →

Log (viscosity) →

Glass

Crystal

T

T

Supercooled

liquid

Liquid

 On crystallization the viscosity abruptly changes from ~100 → ~10²⁰ Pa s

 A solid can be defined a material with a viscosity > 10¹² Poise

If the glass crystallizes on heating (at T_x), before T_m then T = T_x  T_g is a measure of the glass formability.

The region between T_g and T_x is the supercooled liquid region in this case.

T

Heat glass

Cool liquid

T

Often metallic glasses crystallize before T_g

Hence the glass transition temperature in heating is masked by crystallization (not observed experimentally)

Material Bonding T_g(K)

SiO₂ Covalent 1430

Pd_0.4Ni_0.4P_0.2 Metallic 580

BeF₂ Ionic 570

Polystyrene 370

Se 310

H₂O Hydrogen 140

As₂S₃ Covalent 470

Isopentane Van der Walls 65

R. Zallen, Physics of Amorphous Solids, John Wiley and Sons, 1983.

 In crystals interatomic distances are well defined. In glasses this is not so.

 Radial distribution function (g(r), RDF, is closely related to the pair correlation function) for a distribution of atoms (can also be defined for molecules, etc.), describes how density varies as a function of distance from a reference atom.

 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).

 FT of the RDF is related to the structure factor.

Radial Distribution Function

( ) 2

4

g r n

r dr



 

 n → number of atoms in the volume between r & (r + dr)