Growth:

After the formation of nuclei, growth occurs as atoms are attached

to the solid surface.

It depends on the removal of heat during solidification.

a) Specific heat of the liquid:

It is the heat required to change the temperature of a unit weight of

the material by one degree.

It must be removed either by radiation or conduction, until the

liquid cools to the freezing temperature.

b) Latent heat of fusion

It represents the energy that evolved as the disordered liquid

structure transforms to a more stable crystal structure.

Types of growth mechanisms:

The difference between the two types of growth mechanisms arises

because of the different sinks for the latent heat.

1) Planar Growth

It occurs by the movement of smooth solid-liquid interface into the

Liquid, where the container or mold must absorb the heat.

2) Dendritic Growth:

When nucleation is poor, the liquid undercools to a temperature below

the freezing temperature before the solids forms. The undercooled

liquid absorbs the heat.

Under this condition, a small solid protuberance (dendrite) forms at the interface. Secondary and tertiary dendrite arms can also form on the primary

stalks to speed the evolution of the latent heat.

In pure metals, dendritic growth normally represents only a small

fraction of the total growth.

c=specific heat of the liquid, T = heat that the undercooled liquid can absorbHf = latent heat represents the total heat that must be given up during solidification.

As the undercooling T increases, more dendritic growth occurs.

Q76) Calculate the fraction of growth that occurs dendritically in copper which (a) nucleates homogeneously and (b) nucleates heterogeneously with 100C undercooling. Where latent heat of fusion for copper is 1628x10 6 J/m3, specific heat is 4.4x106 J/m3, undercooling for homogeneous nucleation is 2360C

Solution:

(a) For homogeneous nucleation

(b) For 100 C undercooling

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