Pfann’s technique of zone-refining has been applied to the purification of many metals, particularly silicon and germanium. The high purity silicon required for transistors for the electronic industry is produced by the concept of purification based on zone-refining. The concept is based on the non-equilibrium behaviour during solidification of the solid solution alloys. Purification of a metal by zone-melting (i.e., melting in zones, certain thickness at a time) technique is called zone-refining.

The solidifying phase, in a solid solution type of liquid alloy (in diagrams having separate liquidus and solidus), is purer than the liquid as in evident from Fig. 3.50. The solute content in solid, Cs’ is less than solute content in liquid, CL’. This is expressed mathematically, where Ke is the equilibrium distribution coefficient,

Ke = CS’ / CL

It is a reasonable assumption that liquidus and solidus are straight lines. If solidification occurs further at lower temperature T under equilibrium conditions, even then Ke = CS/CL is a constant. If CO is the original composition of liquid, then the first solid formed had composition, CS’ = kCO. Thus, for each gram of solid formed, there are (1 – Ke) C0 gram of extra solute in the liquid shifting the liquid composition CL’ to the right. Under equilibrium conditions, the alloy cools to produce a solid of uniform composition CO.


Let us take non-equilibrium us behaviour during solidification, making a reasonable assumption that a given portion of solid solution does not change in composition once it has solidified. Let the amount of liquid alloy be Ao, and say at temperature T Fig. 3.50, the compositions of solid and liquid phases at the solidifying interface is CS and CL respectively.

And by now as illustrated in Fig. 3.51 (b) a fraction ‘g’ of the total amount AO has solidified. If now temperature drops by ΔT, the additional fraction ‘dg’ solidifies. At T, the amount of solute in the liquid was CLAO (1 – g), which gets divided in the fractional solid AOdg of solid and the remaining liquid (of changed composition), thus, we can write for this-

CLAO (1 – g) = (CL + dCL) A0(1-g-dg) + CsAO dg


On simplification and neglecting the term dCLA0dg, being very small, and as k = CS/CL, thus in terms CS.

This equation has been used to get curves for different values of k in Fig. 3.51 (a). This is based also on actual solidification behaviour, where it is assumed that liquid phase has uniform composition and that no diffusion occurs within solidified alloy. Thus, concentration of solute in the solid increases along the length of the solidified bar as Shown in Fig. 3.51 (a). If effective distribution coefficient is used instead of equilibrium distribution coefficient, the former is defined as

K = CS /CL


where CS is the composition of the solid being formed and CL, is the average- composition of all of the liquid in molten zone. The enrichment of solute, at liquid-solid interface, although still occurring, is now accounted for in the determination of k. The value of k lies between ke and unity.

Thus, using above two equations results in the following equation for concentration profile produced by one pass of the molten zone of length l:

Advantage is taken of above facts while doing zone-melting (refining). A bar of solid solution alloy of length L with initial uniform concentration of solute CO is taken. A heater is used to form a molten zone of length, l.


The heater is slowly moved from left to right. Thus, a molten zone forms initially at the left-end of the bar, and then the molten zone moves slowly towards the right. The first solid that forms at the extreme left has solute concentration, CS = k CL = kCO. As k is less than one, the solid that has formed contains less solute than the composition of the alloy, and thus solute concentration of the molten zone increases.

Its concentration in the progressively solidifying solid also increases. When the molten zone attains a solute concentration of CO/k, then the solidifying solid has Cs = kCL = k(CO/k) = CO, i.e., the concentration of the solute is the same in the solid, which is solidifying as in the solid being melted.

Fig. 3.52 (b) illustrates that the solute concentration in the last zone length (l) of the solid rises as the enriched liquid freezes. The above equation holds good for the whole length of the curve except the last zone. The curve in Fig. 3.52 (b) is obtained in one pass of the heater (i.e., one pass of the molten zone).


While doing zone-refining, the heater is passed through the bar a number of times to produce successive improvements in the purity of the solid, as also illustrated in Fig. 3.53 (a) and (b). After a large number of passes of the heater an ultimate distribution is approached as the theoretical limit. Fig. 3.53 (b) shows the effect of increasing the number of passes on the solute concentration of the bar.

As long as the value of k is less than one, the concentration of solute decreases. The value of k can be greater than one, when the initial solid is richer in solute than the liquid from which it is forming. In such cases, the concentration of solute decreases along the length of the bar, Fig. 3.54 (b).

In zone-melting, advantage is taken of the fact that purification effects of successive zone-melting is cumulative (compared to conventional melting). For example, if k = 0.5 as in Fig. 3.53, the solute concentration at x = 0 is decreased to 0.5 CO by the first pass of molten-zone. The average composition of the first zone is about 0.6 Co. In the second pass, at x = 0, the solid formed has solute concentration of about 0.5 x 0.6 CO =  0.3 CO.

The purification of the first few zone lengths, by factors ranging up to many powers of 10, is achieved in a number of passes, that depends sensitively on the values of k and L/l. In every case, an ultimate distribution appears that sets a limit to the purification possible by zone-refining.

Floating-zone melting technique, Fig. 3.54 reduces the contamination of the metal by mould material. If only limited volume of the metal is molten, surface tension is sufficient to hold the molten zone in place, if the specimen is vertical. Here, electron-bearn melting is used in vacuum. Thus, there is an additional source of purification by evaporation of impurities.