Abstract
The travelling heater zone-refining process and its relation to the travelling solvent and travelling heater methods of growing single crystals are described.
The variation of the zone composition during the zone passage is derived, proceeding from the solute-impurity-solvent diagrams, and the impurity distribution along the crystallisate, after a zone passage, is derived, by considering that the solute and the impurity form either a solid solution or an eutectic. The influence of the parameters which determine the distribution is discussed. The impurity distribution along the crystallisate after a number of zone passages is derived.
The application of the process is suitable in the case of a sub-unity distribution coefficient, the zone passage efficiency being higher, the smaller the distribution coefficient and the steeper the slope of the dissolution straight line. The process is particularly advantageous when the solute and the impurity form an eutectic. It is advantageous to select a high dissolution temperature, close to the solvent boiling temperature, and a crystallisation temperature as near as possible to the dissolution temperature, when the solute and the impurity form either a solid solution or an eutectic.
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Abbreviations
- A:
-
the solute
- B:
-
the impurity
- S:
-
the solvent
- ρA, ρB, ρS:
-
the solute, impurity and solvent densities
- t :
-
the crystallisation temperature
- T :
-
the dissolution temperature
- z:
-
the co-ordinate of the heater
- Z :
-
the co-ordinate of the trailing edge
- z′ :
-
the reduced co-ordinate of the heater
- l′ or subscript l :
-
the solvent zone length
- l′ or subscript l′ :
-
the solvent reduced zone length
- L :
-
the solution zone length
- L′ :
-
the solution reduced zone length
- a :
-
the quantity of solute dissolved in the solvent zone
- b :
-
the quantity of impurity dissolved in the solvent zone
- s :
-
the quantity of zone solvent
- a s :
-
the quantity of solute dissolved, at saturation, in the solvent zone, at the crystallisation temperature, and in the absence of impurity
- A s :
-
idem, but at the dissolution temperature
- b s :
-
the impurity quantity dissolved, at saturation, in the solvent zone, at the crystallisation temperature and in the absence of solute
- B s :
-
idem, but at the dissolution temperature
- x :
-
the gravimetric ratio between the quantity of solute dissolved in the solvent zone (at saturation, and at the crystallisation temperature) and the solvent zone quantity
- X :
-
idem but at the dissolution temperature
- x s, Xs :
-
the same significance as x and X but in the absence of impurity
- y :
-
the gravimetric ratio between the quantity of impurity dissolved in the solvent zone (at saturation, and at the crystallisation temperature) and the zone solvent quantity
- Y :
-
idem, but at the dissolution temperature
- Y 0 :
-
idem, for z=0
- y s, Ys :
-
the same significance as y and Y but in the absence of solute
- g A :
-
the experimental function that gives the solubility of the solute in the solvent as a gravimetric ratio, in the absence of impurity, as a function of temperature
- g B :
-
the experimental function that gives the solubility of the impurity in the solvent as a gravimetric ratio, in the absence of solute, and as a function of temperature
- mt :
-
the solvent melting temperature
- bt :
-
the solvent boiling temperature
- α, β :
-
proportionality coefficients of solubility for the solute and impurity, respectively
- (D):
-
the dissolution straight line
- (d):
-
the crystallisation straight line
- M :
-
the slope of the dissolution line
- m :
-
the slope of the crystallisation line
- k :
-
the impurity distribution coefficient between the crystallisate and the solution zone
- h :
-
the exponential function constant
- R :
-
the gravimetric ratio impurity/solute in the crystallisate
- R 0, Re, RE idem:
-
but in the zone solution corresponding to the points P 0, Pe and p E
- Γ :
-
the curve described by the return point of the saturation solubility isotherms as a function of the temperature for the case when A and B form an eutectic
References
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W. G. Pfann, Trans. AIME 194 (1952) 747.
N. W. Lord, ibid 197 (1953) 1531.
H. Reiss, ibid 200 (1954) 1053.
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Nicolau, I.F. Purification process by solution zone passages. J Mater Sci 5, 623–639 (1970). https://doi.org/10.1007/BF00549746
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DOI: https://doi.org/10.1007/BF00549746