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180 SOLAR GRADE SILICON FEEDSTOCK<br />

Temperature<br />

[ºC]<br />

T 0<br />

T 1<br />

X s X 0<br />

X 1<br />

Fractional composition X<br />

(a)<br />

Solid<br />

Liquid<br />

1<br />

2<br />

X 0<br />

Composition<br />

k 0 X 0<br />

Position Z<br />

(b)<br />

Figure 5.6 (a) Left side of a phase diagram with k 0 < 1 and (b) composition development in<br />

solid and liquid along a rod solidified from the left end under “normal freezing”<br />

the solid and liquid are X s and X l , respectively. The equilibrium distribution coefficient<br />

k 0 at T 1 is defined as the ratio of the equilibrium solid and liquid compositions:<br />

k 0 = X s /X l<br />

(at equilibrium both the solid and the liquid have homogeneous compositions X s and X l ,<br />

respectively).<br />

During normal freezing the solid and the liquid are not in equilibrium. This principle<br />

can be used to purify the material. If (1) the solid–liquid interface is flat, (2) the

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