Solidification, Crystallization & Glass TransitionSolidification, 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

MATERIALS SCIENCEMATERIALS SCIENCE&&

ENGINEERING ENGINEERING

Anandh Subramaniam & Kantesh Balani

Materials Science and Engineering (MSE)

Indian Institute of Technology, Kanpur- 208016

Email: anandh@iitk.ac.in, URL: home.iitk.ac.in/~anandh

AN INTRODUCTORY E-BOOKAN INTRODUCTORY E-BOOK

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A Learner’s GuideA Learner’s GuideA Learner’s GuideA Learner’s Guide

↑ Hfusion

↓ Hd 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 ~106 K/s are used for the amorphization of alloys → splat cooling, melt-spinning.

2* 1

fusionHG

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 Tm , 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)

→

Tm

0

U

I

↑ Hfusion

↓ Hd 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

Tmaximum I

Tmaximum U

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

↑ Hfusion

↓ Hd 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 ~106 K/s are used for the amorphization of usual alloys → splat cooling, melt-spinning.

2* 1

fusionHG

↑ Hfusion

↓ Hd 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 →

Vol

ume

→

Or other extensivethermodynamic properties → S, H, E

Liquid

Glass

Crystal

Tg Tm

Glass transition temperature

T →

Vol

ume

→Change in slope

Tf

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

T →

Vol

ume

→Effect of rate of cooling

1T

2T

21 TT

Slower cooling

Slower cooling Higher density

Lower Tg

Lower volume

As more time for atoms to arrange in closer packedconfiguration

T →

Log

(vi

scos

ity)

→

Glass

Crystal

Tg Tm

Supercooledliquid 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 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.

Tg

Heat glass

Cool liquid

Tx

Often metallic glasses crystallize before Tg

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

Material Bonding Tg (K)

SiO2 Covalent 1430

Pd0.4Ni0.4P0.2 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

ng r

r dr → number density- number of atoms/volume

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