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 MATERIALS SCIENCE &ENGINEERING Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur URL: home.iitk.ac.in/~anandh AN INTRODUCTORY E-BOOK Part of A Learner’s Guide

↑  H fusion ↓  H d  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 6 K/s are used for the amorphization of alloys → splat cooling, melt-spinning.

 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 ~ (10 5 – 10 6 ) 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) → TmTm 0 U I

↑  H fusion ↓  H d  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. TiO 2 ) added (dissolved) to molten glass TiO 2 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 maximum I T maximum 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

↑  H fusion ↓  H d  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 6 K/s are used for the amorphization of usual alloys → splat cooling, melt-spinning.

↑  H fusion ↓  H d  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 Liquid Glass Crystal TgTg TmTm Glass transition temperature

T → Volume → Change in slope TfTf 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 Slower cooling Higher density Lower T g Lower volume As more time for atoms to arrange in closer packed configuration

T → Log (viscosity) → Glass Crystal TgTg TmTm Supercooled liquid Liquid  On crystallization the viscosity abruptly changes from ~100 → ~10 20 Pa s  A solid can be defined a material with a viscosity > 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.

TgTg Heat glass Cool liquid TxTx Often metallic glasses crystallize before T g Hence the glass transition temperature in heating is masked by crystallization (not observed experimentally)

MaterialBondingT g (K) SiO 2 Covalent1430 Pd 0.4 Ni 0.4 P 0.2 Metallic580 BeF 2 Ionic570 Polystyrene370 Se310 H2OH2OHydrogen140 As 2 S 3 Covalent470 IsopentaneVan der Walls65 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   → number density- number of atoms/volume  n → number of atoms in the volume between r & (r + dr)