SOLIDIFICATION OF METALS(To be completed)

Prof. H. K. Khaira

Professor, Deptt. of MSME

M.A.N.I.T., Bhopal

Contents

• Solidification of Metals• Cooling Curves

Solidification of Metals

Solidification of a pure metal.

Solidification of Metals1. During solidification, the liquid changes in to solid during cooling.2. The energy of liquid is less than that of the solid above the melting point. Hence liquid is stable above the melting point.3. Below the melting point, the energy of liquid becomes more than that of the solid.4. Hence below the melting point, the solid becomes more stable than the liquid.5. Therefore at the melting point, liquid gets converted in to solid during cooling.6. This transformation of liquid into solid below melting point is known as solidification.

Solidification of Metals1. Thermodynamically, both liquid and solid have equal energy at melting point and therefore both are equally stable at melting point.2. Therefore, no solidification or melting will take place at the melting point. Liquid will remain liquid and solid will remain solid.3. Some under-cooling will be essential for solidification.4. This transformation occurs by nucleation and growth.

Cooling curve for a pure metal showing possible undercooling.

• The transformation temperature, as shown on the equilibrium diagram, represents the point at which the free energy of the solid phase is equal to that of the liquid phase.

• Thus, we may consider the transition, as given in a phase diagram, to occur when the free energy change, ΔGV , is infinitesimally small and negative, i.e. when a small but positive driving force exists due to undercooling.

Nucleation and Growth of Crystals

Nucleation and Growth of Crystals• At the solidification temperature, atoms

from the liquid, such as molten metal, begin to bond together and start to form crystals.

• The moment a crystal begins to grow is know as nucleus and the point where it occurs is the nucleation point.

• When a metal begins to solidify, multiple crystals begin to grow in the liquid.

• The final sizes of the individual crystals depend on the number of nucleation points.

• The crystals increase in size by the progressive addition of atoms and grow until they impinge upon adjacent growing crystal.

a)Nucleation of crystals, b) crystal growth, c) irregular grains form as crystals grow together,

d) grain boundaries as seen in a microscope.

Cooling Curve

Cooling Curve

• A cooling curve is a graphical plot of the changes in temperature with time for a material over the entire temperature range through which it cools.

Cooling Curve for Pure Metals

• Under equilibrium conditions, all metals exhibit a definite melting or freezing point.

• If a cooling curve is plotted for a pure metal, It will show a horizontal line at the melting or freezing temperature.

Cooling Curve of Alloys• In this method, alloys with different compositions are melted and then the

temperature of the mixture is measured at certain time intervals while cooling back to room temperature.

• A cooling curve for each mixture is constructed and the initial and final phase change temperatures are determined.

Cooling Curve

• Then these temperatures are used for the construction of the phase diagrams

Cooling curve for the solidification of a pure metal.

Undercooling during

Cooling curve for a solid solution.

• In case of alloys, the solidification does not take place at a constant temperature.

• In such cases, the solidification occure in a range of temperature.

Series of cooling curves for different alloys in a completely soluble system. The dotted lines indicate the form of the phase

diagram

Phase Diagram of Solid Solution

Cooling Curves for Solid Solution

Mechanism of Solidification of Metals

• The solidification of metals occur by nucleation and growth transformation.

• In nucleation and growth transformation, the nuclei of the solid phase are formed and then they grow.

Nucleation and Growth Transformation

• Nucleation – The physical process by which a new phase is produced in a material. In the case of solidification, this refers to the formation of tiny stable solid particles in the liquid.

• Growth - The physical process by which a new phase increases in size. In the case of solidification, this refers to the formation of a stable solid particle as the liquid freezes.

Nucleation and Growth Transformation

• The Nucleation and Growth Transformation may be of two types

• 1. Homogeneous Nucleation • 2. Heterogeneous Nucleation

Homogeneous Nucleation

• Homogeneous Nucleation – Formation of a critically sized solid from the liquid by clustering together of a large number of atoms at a high undercooling (without an external interface).

Solidification of Metals

• The transformation temperature, as shown on the equilibrium diagram, represents the point at which the free energy of the solid phase is equal to that of the liquid phase.

• Thus, we may consider the transition, as given in a phase diagram, to occur when the free energy change, ΔGV , is infinitesimally small and negative, i.e. when a small but positive driving force exists.

Cooling curve for a pure metal showing possible

undercooling.

Energy barrier separating structural states.

Free Energy Changes

• The second phase has lower free energy than the first phase

• Activation energy may be required for the transformation to occur as shown above.

Nucleation and Growth Transformation

(1) The volume free energy ΔGV – free energy difference between the liquid and solid

Δ GV = 4/3πr3ΔGv

(2) The surface energy ΔGs – the energy needed to create a surface for the spherical particles

ΔGs = 4πr2γ

γ → specific surface energy of the particle

Total free energy Change ΔGT = ΔGV + ΔGs

Nucleation and Growth Transformation

• Embryo - An embryo is a tiny particle of solid that forms from the liquid as atoms cluster together. The embryo is unstable and may either grow in to a stable nucleus or re-dissolve.

• Nucleus – It is a tiny particle of solid that forms from the liquid as atoms cluster together. Because these particles are large enough to be stable, nucleation has occurred and growth of the solid can begin.

Critical Size of Nucleus

• The minimum size that must be formed by atoms clustering together in the liquid before the solid particle is stable and begins to grow.

r* : critical radius(where ΔGT reaches the maximum)

• liquid metal is cooled below freezing point, slow moving atoms bond together to createhomogeneous nuclei

• Nucleus – larger than critical size, can grow into a crystal

• Embryo – smaller than critical size, continuously being formed and redissolved in the molten metal

• For Critical size of nucleusd(ΔGT)/dr = 0 when r = r*

Or r* = - 2γ/ΔGv

critical nucleus size

• Critical nucleus size mainly determined by ΔGV

• Amount of undercooling increases, the critical nucleus size decreases the relationship is

R* = 2γTm / ΔHf ΔT

Where γ: surface free energyTm: freezing temperatureΔHf : latent heat of fusionΔT: amount of undercooling

critical radius versus undercooling

critical nucleus size - Example

• calculate the critical radius of homogeneous nucleus forms from pure liquid Cu.

• AssumeΔT = 0.2ΔTm , γ = 1.77 × 10-7 J/cm2

Tm = 1083oC, Δ Hf = 1826 J/cm3

• calculate the number of atoms in criticalsized nucleus at this undercooling

critical nucleus size - Solution• ΔT = 0.2ΔTm = 1356 K × 0.2 = 271 K

2γTm 2(1.77 × 10-7 J/cm2)(1356 K )• r* = ─── = ───────────── = 9.70 × 10-8 cm

ΔHf ΔT (1826 J/cm3)(271 K)

• volume of nucleus = 4/3 π (9.70 × 10-8 cm) 3

= 3.82 × 10-21 cm3

• Cu: FCC structure, unit length a = 3.61 × 10-8 cm• 4 atoms per unit cell• volume of unit cell = (3.61 × 10-8 cm) 3

= 4.70 × 10-23 cm 3

3.82 × 10-21 cm 3

• number of atoms = ─────── × 4 = 325 atoms 4.70 × 10-23 cm 3

critical nucleus size

• d(ΔGT)/dr = 0 when r = r*

• r* = - 2γ/ΔGv

(a) Effect of nucleus size on the free energy of nucleus formation. (b) Effect of undercooling on the rate of

precipitation.

Homogeneous Nucleation

• Quantitatively, since ∆ Gv depends on the volume of the nucleus and ∆ GS is proportional to its surface area, we can write for a spherical nucleus of radius r

∆ G = (4 π r3 /3) ∆ Gv + 4 π r2γ

• where ∆ Gv is the bulk free energy change involved in the formation of the nucleus of unit volume and γ is the surface energy of unit area.

Critical Size of Nucleus• When the nuclei are small the positive surface energy term predominates, while when

they are large the negative volume term predominates, so that the change in free energy as a function of nucleus size. This indicates that a critical nucleus size exists below which the free energy increases as the nucleus grows, and above which further growth can proceed with a lowering of free energy; ∆ Gmax may be considered as the energy or work of nucleation W. Both rc and W may be calculated since

d ∆G/dr = 4 π r2∆Gv + 8 π rγ = 0 when r = rc and thus

rc = -2γ / ∆G v

• Substituting for rc gives

W =16 π γ 3/3 ∆Gv2

• The probability of an atom having sufficient energy to jump the barrier is given, from the Maxwell–Boltzmann distribution law, as proportional to exp [Q/kT] where k is Boltzmann’s constant, T is the temperature and Q is usually expressed as the energy per atom in electron volts.1

• The rate of reaction is given byRate = A exp [- Q/kT]

where A is a constant

• The surface energy factor is not strongly dependent on temperature, but the greater the degree of undercooling or supersaturation, the greater is the release of chemical free energy and the smaller the critical nucleus size and energy of nucleation.

• This can be shown analytically since∆Gv = ∆H - T∆S,

• and at T = Te, ∆Gv = 0, so that ∆H = Te ∆S.

It therefore follows that ∆Gv =(Te -T) ∆S = ∆T∆S

• and because ∆Gv is proportional to ∆T, thenW is proportional to ∆S3 / ∆T2

Heterogeneous Nucleation

• Heterogeneous Nucleation – Formation of a critically sized solid from the liquid on an impurity surface.

• heterogeneous nucleation occurs in a liquid on the surface of its container, insoluble impurities and other structural materials that lower the critical free energy required to form a stable nucleus

Heterogeneous Transformation

• In practice, homogeneous nucleation rarely takes place and heterogeneous nucleation occurs either on the mould walls or on insoluble impurity particles.

• A reduction in the interfacial energy would facilitate nucleation at small values of ∆T.

• This occurs at a mould wall or pre-existing solid particle

Chill-cast ingot structure

crystal growth and grain formation

• nuclei → crystals → grains• polycrystalline – solidified metal containing many crystals• grains – crystals in solidified metal• grain boundaries – the surfaces between the grains• two major types of grain structures:

(1) equiaxed grains – crystals grow about equally in all directions, commonly found adjacent to a cold mold wall

(2) columnar grains – long, thin, coarse grains, created when metal solidifies rather slow in the presence of a steep temperature gradient. columnar grains grow perpendicular to the mold surface

Ingot Structure

Al ingot

Nucleation and Growth Transformation in solid solution

Nucleation and Growth Transformation in solid solution

• wt% Ni• 20

• 120• 0

• 130• 0

• 3• 0 • 4• 0 • 5• 0• 110• 0

• L (liquid)

• a• • (solid)

•L• + •a

•L• + •a

• T(°C)

• A

• 35• C0

• L: 35wt%Ni

• 46• 35• 43• 32

• a: 43 wt% Ni • L: 32 wt% Ni

• B• a: 46 wt% Ni• L: 35 wt% Ni

• C

• E• L: 24 wt% Ni• a: 36 wt% Ni

• 24 • 36• D

Nucleation and Growth Transformation

• The factors which determine the rate of phase change are:

• (1) the rate of nucleation, N (i.e. the number of nuclei formed in unit volume in unit time) and

• (2) the rate of growth, G (i.e. the rate of increase in radius with time)

Dendrites• In metals, the crystals that form in the liquid during freezing

generally follow a pattern consisting of a main branch with many appendages. A crystal with this morphology slightly resembles a pine tree and is called a dendrite, which means branching.

• The formation of dendrites occurs because crystals grow in defined planes due to the crystal lattice they create.

• The figure to the right shows how a cubic crystal can grow in a melt in three dimensions, which correspond to the six faces of the cube.

• For clarity of illustration, the adding of unit cells with continued solidification from the six faces is shown simply as lines.

• Secondary dendrite arms branch off the primary arm, and tertiary arms off the secondary arms and etcetera.

Dendrites

Dendrites

• During freezing of a polycrystalline material, many dendritic crystals form and grow until they eventually become large enough to impinge upon each other.

• Eventually, the interdendriticspaces between the dendrite arms crystallize to yield a more regular crystal.

• The original dendritic pattern may not be apparent when examining the microstructure of a material.

• However, dendrites can often be seen in solidification voids that sometimes occur in castings or welds, as shown in the next slide..

Dendrites

Computer simulated image of dendritic growth using a cellular automata technique. Notice the branching on the dendrites. Photograph courtesy of the Institute of

Materials, based on the work of U. Dilthey, V. Pavlik and T. Reichel, Mathematical Modelling of Weld Phenomena III, eds H. Cerjak and H. Bhadeshia, Institute of

Materials, 1997.

Steady-state patterns formed at the crystal–melt interface of a binary alloy of succinonitrile and coumarin 152 during directional solidification.

Losert W et al. PNAS 1998;95:431-438

©1998 by National Academy of Sciences

(A) Time evolution of the interface morphology for SCN/rhodamine 6G at constant pulling speed V (V = 3.11 μm/s, G = 2.8 K/cm, C∞ = 0.325 wt%).

Losert W et al. PNAS 1998;95:431-438

©1998 by National Academy of Sciences

Shrinkage• Most materials contract or shrink during solidification and cooling. Shrinkage is

the result of:– Contraction of the liquid as it cools prior to its solidification – Contraction during phase change from a liquid to solid – Contraction of the solid as it continues to cool to ambient temperature.

• Shrinkage can sometimes cause cracking to occur in component as it solidifies. • Since the coolest area of a volume of liquid is where it contacts a mold or die,

solidification usually begins first at this surface. • As the crystals grow inward, the material continues to shrink. • If the solid surface is too rigid and will not deform to accommodate the internal

shrinkage, the stresses can become high enough to exceed the tensile strength of the material and cause a crack to form.

• Shrinkage cavitation sometimes occurs because as a material solidifies inward, shrinkage occurred to such an extent that there is not enough atoms present to fill the available space and a void is left.