Materials for engineering, 3rd Edition - (Malestrom)

1.2 Microstructure
Structure of engineering materials 7
Microstructure refers to the size and arrangement of the crystals, and the
amount and distribution of impurities in the material. The scale of these
features is typically 1–100 µm. Microstructure determines many of the
properties of metals and ceramics.
1.2.1 Introduction to phase transformations
The transition from the liquid state to the solid state is known as ‘crystallization’,
and the mechanism by which the process takes place controls the microstructure
of the final product. A phase transformation, such as the change from liquid
to solid, occurs by the mechanism of nucleation of small ‘seed’ crystals in
the liquid, which then grow by the addition of more material from the liquid.
The driving force for this change can be obtained by considering the change
in free energy on solidification. For example, if a liquid is undercooled by
∆T below its melting point (T m ) before it solidifies, solidification will be
accompanied by a decrease in the Gibbs free energy of ∆G. The Gibbs free
energy of a system is defined by the equation
G = H – TS
where H is the enthalpy, T the absolute temperature and S the entropy of the
system. The free energies of the liquid and solid at temperature T are given
by
G L = H L – TS L
G S = H S – TS S
so that at temperature T, the change in free energy/unit volume upon
solidification may be written:
∆G v = ∆H – T∆S [1.1]
where ∆H = H L – H S and ∆S = S L – S S
At the equilibrium melting temperature T m , ∆G v = 0, thus
∆S = ∆H/T m = L/T m [1.2.]
where L is the latent heat of fusion. Combining equations [1.1] and [1.2]
gives
∆G v = L – T(L/T m )
Thus, for an undercooling ∆T,
∆G v = L∆T/T m [1.3]