# Schmid's Law F r = F cos λ A 0 = Acos ψ τ r = σ cos ψ cos λ

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Schmid's Law

Fr = F cos A0= Acos r = cos cos Strain HardeningSolid Solution StrengtheningGrain Size strengtheningPrecipitation Strengthening

StrengtheningStrain Hardening

Solid Solution Strengthening

Grain Size Strengthening

CRYSTALLIZATION OF METALS & ALLOYSIntroduction:-The transformation of metal/alloys from the liquid to the solid crystalline state is called crystallization or solidification.

During solidification the disordered structure of the liquid state transform to an orderly array of atom.

When the disordered structure is frozen the change is called glass transition(transition state betn disordered and ordered condition of phases).

Condition for crystallization to occur:-Crystallization proceeds under the conditions in which system is converted to a more stable thermodynamic state with lesser free energy or thermodynamic potential E.Here free energy is the portion of total energy that is reversibly changed upon or available as work.the free energy of the crystal is less than that of liquid phase.If:- H = total energy of the system T = absolute temperature S = Entropy E = H TS

Condition for crystallization to occur:-At temp. above Tm, Liquid metal is more stable with less free energy.At temp. below Tm, solid metal is more stable with less free energy.At temp. Tm, the amount of energy is equal in solid and liquid phase.

Condition for crystallization to occur:-The solidification process does not begin at this temperature Tm. It proceeds if difference in free energy between solid metal in comparison to that of liquid metal.Consequently the solidification process is initiated & proceeds only when metal is super cooled below the equilibrium temperature Tm.

T = Tm-Tk = Degree of Super coolingTm = Temp. At which equal free energy in solid and liquid phaseTk = temp. at which solidification start

SupercoolingDuring the cooling of a liquid, solidification (nucleation) will begin only after the temperature has been lowered below the equilibrium solidification (or melting) temperature Tm. This phenomenon is termed supercooling (or undercooling)The driving force to nucleate increases as T increasesSmall supercooling slow nucleation rate - few nuclei - large crystalsLarge supercooling rapid nucleation rate - many nuclei - small crystals.11Condition for crystallization to occur:-The amount of under cooling or Super cooling required to form nuclei or seed crystals may be reduced by the presence of solid impurities in the pure metal. The purer the metal the more is tendency to be super cooled.

Formation of nuclei and grain structure:-The process of solidification begins with the formation of crystalline nuclei or embryos so called center of Crystallization, and proceed with the growth.

Nucleation refers to the formation of the smallest particle of a new phase that is stable in a exiting phase.Growth refers to the increase in size of the nuclei.

Nucleation and growth - the main mechanism ofphase transformations in materials

Formation of nuclei and grain structure:-Cooling of a liquid metalCrystallisation occurs around small nuclei, which may be impurity particles. The first crystals have the crystal shape into which the metal would naturally solidify.for example face-centred cubic in the case of copper. However, as the crystal grows, it tends to develop spikes and its shape changes into a tree-like form called a dendrite.Formation of nuclei and grain structure:-

Two-dimensional ice dendrites on windows

Formation of nuclei and grain structure:-As the dendrite grows, the spaces between its arms fill up. Outward growth stops when growing arms meet others. Eventually the entire liquid solidifies, and there is little trace of the original dendritic structure, only the grain into which the dendrites have grown.

Formation of nuclei and grain structure:-

Formation of nuclei and grain structure:-As long as crystal grow freely they may be more or less regular in shape. These are termed as crystal.But as soon as growing crystal begin to obstruct one another their regular shape is spoiled because further growth of their faces stops at phase where they interface each other.So growth now continues only in the direction in which free liquid is still available & accessible.Now so this regular shape crystal becomes irregular shaped is called crystallites or grains and structure is called grain structure.

NucleationNucleation can beHomogeneous solid nuclei spontaneously appear within the under cooled phase.Heterogeneous the new phase appears on the walls of the container, at impurity particles, etc.

Homogeneous NucleationThis is simplest case of nucleation.It occurs in liquid metals when metal itself provide the atom to form nuclei.When a pure liquid metal is cooled below its equilibrium freezing temperature to a sufficient degree numerous homogenous nuclei are created by slow moving of atom bonding together.For a nucleus to be stable so that it can grow into a crystal. it must reach the critical size.When a cluster of metal bonded together which is less than critical size is called an embryo and more than critical size is called nucleus.Volume free energyThe free energy available from the solidification process which depends upon the volume of a particle form.

Due to change in phase from molten metal to solid a free energy decrease. In case of spherical particle, if the temp. is suddenly dropped below the freezing point,Then the free energy for sphere nucleus of radius r is

is the change in the free energy between the liquid and solid For unitvolume of metal

Liquid

Liquid Solid phase transformationSolid (GS)Liquid (GL)TmT G TGVLiquid stableSolid stableT - Undercooling tFor sufficientUndercooling On cooling just below Tm solid becomes stable But solidification does not start E.g. liquid Ni can be undercooled 250 K below TmGv veGv +veSurface free energyThe second factor is energy required to form liquid solid interface.Particle formed in the melt have some surface area. Solid liquid phases possess a surface in between the two. Such a surface has a positive free energy per unit area.The creation of a new interface is associated with free energy increase proportional to surface area of the particle.The energy needed to create a surface for this spherical particles DGS ,Is equal to ,Where,

Liquid

g = surface tensionTotal energy of NucleationThe total free energy associate with the formation of embryo or nucleus,

=

DGT = total free energy change r = radius of embryo or nucleusDGv =Volume free energyg =Specific surface free energy

DGT = Total Free Energy = DGS + DGV

r* = critical nucleus: for r < r* nuclei shrink; for r >r* nuclei grow (to reduce energy) Homogeneous Nucleation & Energy EffectsDGT = Total Free Energy = DGS + DGV Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface)

g = surface tensionVolume (Bulk) Free Energy stabilizes the nuclei (releases energy)

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Heterogeneous nucleation:-Occurs at surfaces, imperfections, severely deformed region, etc. which lower the critical free energy.

In molten metals,Usually foreign particles are present as impurities which lower the liquid solid interface energy and help in nucleation and reduce the amount of supercooling needed to actuate nucleation.

Basic Requirement:-The heterogeneous nucleation lies in the ability of the liquid metal to wet the foreign particle.

Heterogeneous nucleation:-After the initial nuclei are formed-More solid may be deposited upon the first nuclei or,More nuclei may form or,A difference phase may occur in the melt.

Heterogeneous nucleation:-Balancing the interfacial tensions in the plane of the container wall gives LC = SC + LS cos() and the wetting angle is defined by cos() = (LC - SC)/ LSThe surface energy of heterogeneous nucleation is equal to the S-L surface energy minus net energy decrease.

Heterogeneous nucleation:-The heterogeneous nucleation rate curve is similar to that of homogeneous nucleation with the only difference that heterogeneous nucleation starts at much higher temperature.

Growth mechanisms :-The next step after the nucleation is growth.Growth may be define as the increase of the nucleus in size.It determines the final crystallographic structure of the solid.

Types of growth :-Planer GrowthDendrite growth

Solidification of an Casting

Solidification of an Casting

Solidification Defects

Solidification Defects

Solidification Defects

Solidification DefectsShrinkageCavityPipeInterdendrite shrinkageGas porosity