JOURNAL OF MATERIALS SCIENCE LETTERS 4 (1985) 746 -750
Non-steady state nucleation process in KDP solutions in
the presence of X04 impurities
M. SHANMUGHAM, F. D. GNANAM, P. RAMASAMY
Crystal Growth Centre, Anna University, Madras 25, India
Nomenclature
AG Energy of formation of nucleus.
a Interfacial tension of crystal.
r Radius of sphere inscribed in the crystal
nucleus in equilibrium with solution.
Slope oftine plot In ~" against 1/ln 2 (X/Xo).
Avogadro's number.
Gas constant.
Temperature (K).
Molar volume of crystal.
Mole fraction of solute in the supersaturated
salt solution at temperature t.
Mole fraction of solute in the salt solution
saturated at temperature t.
m
N
R
T
V
x
x0
Nucleation is the initial and important phenomenon
in liquid-solid phase transition. The number of
nuclei forming in a supersaturated medium within
a time interval is a random quantity. The time of
formation of the first nucleus is also a random
quantity. Based on the probabilistic approach to
the nucleation process, the steady-state nucleation
rate is inversely related to the induction time or
the non-steady state time lag, the time of formation
of first nuleus [1]. After preparing supersaturated
solutions there is often a period where no phase
change can be observed, the induction period; then
minute nuclei appear and grow into visible crystals.
Classical nucleation theory can be applied to
evaluate certain parameters of the resulting crystal-
line solid. The rate of homogeneous nucleation
(J) is indirectly computed by measuring induction
period (T) and taking J c~ z -1 [2-5]. The presence
of impurities affects the nucleation rate in super-
saturated solutions [6-12]. Many surface prop-
erties in the solution are also affected due to the
presence of impurities. In the present study, the
induction period has been measured for super-
saturated potassium dihydrogen orthophosphate
solution in the presence of XO4 (X = Cr, S, C1,
Mn, I, V) impurities. The experimental method to
746
measure the induction period is simlar to that used
by Mullin and Osman [13] and Joshi and Antony
[14].
If the interfacial tension a between a solid and
a saturated solution is considered. The concept of
cr is not so well established [15] and o can not be
determined by direct unambiguous experiments
in most cases. Despite these difficulties, a plays
an important role in all theoretical expressions
describing the rates of crystal growth and
nucleation. The interfacial tension can be inferred
from the nucleation kinetics. Though o values
derived from nucleation and crystallization of a
solvent-solute system can be questioned as to
their true significance, they are fully justified for
use in crystallization [16]. It is expected that dif-
ferent solids would cause nuclei to form at different
temperatures [17-19] for constant induction
time and certainly at temperatures different from
those when there are no solids present. This may
be looked upon as being dependent upon the
energy of formation for nucleation [20]. If the
energy of formation is smaller, there will be a
greater tendency for nucleation to occur in the
solid. The induction period can be used to evaluate
the interfacial tension of the crystal relative to the
solution, the energy of formation and the radius
of critical nucleus [ 12].
The interfacial tension of the solid relative to
its solution has been calculated from the slope of
the line in r against 1/ln z (X/Xo) as
[3m11/3
c~ = RT ~167rV2N ] (1)
The energy of formation of a critical nucleus has
been estimated from the experimental data as
RTm
2xa - In 2 (X/Xo) (2)
The radius of the nucleus in equilibrium with its
solution has been given by
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