Journal of Crystallization Process and Technology, 2013, 3, 170-174 Published Online October 2013 (
Copyright © 2013 SciRes. JCPT
Decomposition of Solutions in Front of the Interface
Induced by Directional Crystallization
A. Guskov1, L. Nekrasova2
1Institute of Solid State Physics of RAS, Chernogolovka, Russia; 2A. N. Sysin Research Institute of Human Ecology and of Environ-
ment Hygiene RAMS, Mosc ow, Russia.
Received October 7th, 2013; revised November 7th, 2013; accepted November 14th, 2013
Copyright © 2013 A. Guskov, L. Nekrasova. This is an open access article distributed under the Creative Commons Attribution Li-
cense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Here we show the results of experimental observation of decomposition of the solution components into the neighbor-
ing cells. The liquid solu tion under crystallization first gets into the unstable state and then decomposes. Th e decompo-
sition result is fixed in the solid phase as inhomogeneous component distribution. Our experimental results enable to
argue that the eutectic pattern forms due to interface instability and spinodal decomposition of non-equilibrium solution
forming in front of the interface.
Keywords: Spinodal Decomposition; Directional Crystallization; Eutectic; Phase Transformation; Metastable Phases
1. Introduction
It has long been known that crystallization of liquid ho-
mogeneous solutions of near eutectic composition often
produces structures with periodic solid phase distribution.
On the one hand, such structures are attractive for ap-
plied science as materials with unique properties. On the
other hand, their formation is of interest for fundamental
science since their complicated space-time formation dy-
namics remains unclear [1-3]. The most popular theory
now in use is the Hunt-Jackson (HJ) one that enables a
quantitative description of the feasibility of periodic com-
ponent distribution upon liquid-solid phase transition of
solutions [4]. Within this model the existing periodic
solution of the diffusion equation along the interface pro-
vides a formally adequate description of the experimen-
tally obtained eutectic pattern. The undeniable advantage
of the model is the hyperbolic d ependence o f the eutectic
pattern period on the interface displacement rate. How-
ever, some statements of the H-J theory raise questions.
It is primarily the statement about periodic equilibrium
component distribution on the interface. The assumption
is a boundary condition for the diffusion problem and
plays a key role in the whole H-J theory. According to
the latter, on the interface there are three solution con-
centration jumps: two concentration jumps between each
of the two solid phases and the liquid phase and a jump
between the solid phases located periodically along the
interface. The problem is formally set similarly to the sta-
tionary one-dimensional quasi-equilibrium Burton-Prim-
Slichter (BPS) theory [5] that has a thermodynamic justi-
fication, namely, small deviation of interface temperature
and concentration from equilibrium conditions. In this
case concentratio n jump occurs due to the equality of the
chemical potentials of the co-existing phases. These con-
ditions are also fulfilled within the H-J theory, yet, there
is an additional phenomenon: periodic alternation of
solid phases along the interface which is introduced as a
formal dependence providing correct approximation of
numerous experimental data. The phase alternation pe-
riod is calculated using extra hypotheses. The periodic
boundary condition brings about decomposition of solid
solution in front of the interface. The thermodynamic
condition of decomposition of solutions is their transition
into the metastable (bino dal region) or unstab le (spinodal
region) states. Such conditions are not considered within
the H-J theory. Periodic interface distribution of concen-
tration is usually explained by instability o f the interface.
The extensive review presented in [6] considers the theo-
ries of cell crystallization. However, there are no avail-
able theories relating occurrence of a cell interface to
alternation of cells in which the phase concentration is
equal to its equilibrium values near eutectic tempera-
We present the results of experimental observation of
formation of periodic eutectic pattern of two-component
Decomposition of Solutions in Front of the Interface Induced by Directional Crystallization
Copyright © 2013 SciRes. JCPT
solution. The solution was chosen so that the digital mi-
croscope enabled visualization of decomposition of the
solution components into the neighboring cells. The de-
composition observed is explained by the transition of
the solution to the unstable state. Below it is clarified
how crystallized solution can appear to be in an unstable
2. Transition of Solution through the Region
of Spinodal Decomposition
Let us build binodal and spinodal curves for the solid
solution in the phase diagram coordinate. These bounda-
ries are shown in Figure 1. Curves aCb and dCf denote
the regions of metastable solid phase solution. The bCf
region is the spinodal one of the solid solution. It is seen
that when the concentration values are near the eutectic
point, the solid phase is in the unstable state region. The
liquid-solid phase transition involves changes of the po-
tentials of the solution component particle interaction. In
the liquid state the components of the solution whose
phase diagram is shown in Figure 1 are soluble at any
concentration. In the solid state the solution presented by
the spinodal bf region is unstable. On transition to the
solid state the change in the interaction potential can
bring the solution into the spinodal region and make it
unstable against diffusion. Whether nonequilibrium solu-
tion gets into the spinodal region depends on the condi-
tions of phase transition and configuration of the spi-
nodal region.
It is be logical to assume that nonequilibrium solution
is most likely to become equilibrium if phase transition
occurs in the shaded regions gcs1e and hcs2e of Figure 1.
Diffusion instability means that solution component par-
ticles diffuse into the region with a higher component
Figure 1. Phase diagram of the two-component solution of
the eutectic type. The dashed lines mark the spinodal bCf
and binodal aCd of the solid solution.
concentration rather than the region with a lower com-
ponent concentration, i.e., the diffusion constant is nega-
tive. It is easily seen that if the components are only
slightly soluble in the solid state, i.e., the liquidus lines
are close to concentrations of pure components, the spi-
nodal region can take a large interval of the concentration
component values. In the experiments described below
the solution was observed to decompose into phases of
different concentrations in the course of eutectic pattern
formation so that the decomposition can be explained by
the spinodal decomposition of the nonequilibrium solu-
3. Experimental
The experiments were performed using a coolant unit
composed of a package of four TEC1-127080-50-8A
Peltier elements (one is shown in Figure 2) 50 × 50 × 4.8
mm3 in size. “Extreme performance liquid CPU cooler
H100” 2 was used for heat removal from the Peltier ele-
ments. The cooler and the coolant unit were connected to
power supply 3. The heater was wood plate 7 bordering
on the cooler surface. Crystallization was carried out in
Petri dish (4 in Figure 2) 40 in diameter and 10 mm high.
A metal rod secured the Petri dish to displacement
mechanism 5 that moved it between the heater and the
cooler at a constant rate. The interface displacement was
rec ord e d by a videocamera and “Expert” or BW1008-500X
microscopes (6 i n Figure 2) depending on the magnifica-
tion required. The maximum magnification of the micro-
scopes was 100× and 500×, respectively. The video
equipment was attached to a computer so that the whole
process was visualized on the display which enabled to
choose the required survey region by way of coordinate
displacement of the video equipment. The process was
recorded as photographs and video clips.
Figure 2. Apparatus for observation movement of the in-
terface of the crystallizing solution.
Decomposition of Solutions in Front of the Interface Induced by Directional Crystallization
Copyright © 2013 SciRes. JCPT
The experiments were performed using bromthymol
blue indicator aqueous solution that is convenient due to
the dark blue color of its liquid subalkali aqueous solu-
tion. On crystallization, owing to its low solubility in the
solid phase, bromthymol blue is displaced by the solid
phase and, as a result, the latter is visually practically
pure ice. Therefore, under crystallization the interface is
a pronounced boundary between the dark liquid and
transparent solid phases. In case the freezing solution
layer is sufficiently thin, the interface is a distinct inter-
phase line. The change in the solution component con-
centration can be judged from the color intensity of the
solution. The properties of the solution are demonstrated
by the experimental volume crystallization data. A test
tube with bromthymol blue indicator liquid solution was
placed into a freezer. Following crystallization in a rap-
idly cooled zone close to the tube border, the solid phase
was practically pure ice (Figure 3). The center exhibited
volume crystallization forming crystals with the indicator
adsorbed on their borders, i.e., in the course of volume
crystallization the component was completely displaced
from the solid into liquid phase.
To observe formation of periodic eutectic pattern, the
experiments were performed in the following order. The
dish with solution was fixed so that part of the solution
was on the coolant unit. After a time that part of the solu-
tion froze and formed an interface between the liquid and
solid phases. The dish remained fixed until the interface
had become fixed. Its immobility was cond itioned by the
temperature gradient, and the interface temperature was
obviously equal to phase transition temperature. The in-
terface curvature was determined by the geometry of the
Figure 3. Bromothymol blue solution after crystallization in
tube. Pure ice on the border of the tube and the blue solu-
tion at its center is seen on the red background. In the
course of crystallization the component was displaced from
the solid into liquid phase.
solution-containing dish and, excluding the dish borders,
the boundary co uld be considered flat.
In the photographs it is a distinct flat boundary be-
tween the transparent solid phase and the dark liquid.
Then the dish was set in motion and the boun dary started
to move. The displacement rate varied within 1 - 10 m/s.
After a time morphological perturbations appeared on the
boundary (Figure 4(a)). The amplitude of the pertur-
bations increased (Figure 4(b)) and they transformed to
a periodic component distribution (Figure 4(c)), i.e.,
when growing they transformed to parallel transparent
and dark bands of specific thickness. Following crystal-
lization they produced a eutectic periodic structure. Dur-
ing its formation the structure period remained un-
changed and determined by the period of the initial in-
stability of the interface. From Figure 4(b) it is seen that
the solution is dark between many bands in front of the
interface which means that immediately in front of it the
solution has not had time to completely decompose. The
farther is the solution from the bound ary, the lighter it is,
which is indicative of its decomposition by way of
reverse diffusion. Besides, the dark solution region be-
tween the phase bands can be confined by a meniscus to
which a component from the lower concentration region
can diffuse. As a result, the meniscus may give rise to a
defect as a separate equilibrium phase buildup. Figure
4(b) and (c) show several dark and light buildups. The
experimental data enable us to claim that the solution in
the decomposition region is in unstable equilibrium.
The decomposition period is determined by the period
of the interface morphological instability. The ex-
perimental structure period values were within 40 - 80
The process of solution decomposition into equilib-
rium phases in the form of periodically located bands is
most pronounced on rapid displacement of the interface
into the lower temperature region. Figures 4(d)-(g) pre-
sent the experimental results. Subsequent to formation of
a flat interface, the solution was immediately placed into
a cooler region. As in the previous experiments, small mor -
phological perturbations occurred on the interface (Fig-
ure 4(d)). In this case the interface moved faster than in
the previous experiment and the solution was dark be-
tween the dark phase bands. With growing bands the
solution between the dark phase bands becomes lighter
(Figure 4(c)). In the established regime solution de-
composition occurs in front of the interface (Figure
4. Discussion of Experimental Results
There exist several techniques of transferring solutions
into a spinodal region, i.e., into a non-equilibrium state.
This is most commonly achieved by temperature varia-
tion. For instance, in order to transfer solid so lution from
Decomposition of Solutions in Front of the Interface Induced by Directional Crystallization
Copyright © 2013 SciRes. JCPT
(a) (d)
(b) (e)
(c) (f)
Figure 4. Formation of a periodic structure under the di-
rectional solidification of an aqueous solution bromothymol
blue. Rate of the solution movement 10 m/s (a; b; c). In a
sudden move the plane interface to the low temperature
area (d; e; f). Colored bands of dye did not appear as sharp
regions, and continuous manner. Therefore, the eutectic
pattern is formed gradually. It is assumed that this effect is
determined by the spinodal decomposition of the solution.
a one-phase region point (T1,c1) (Figure 1) to a spinodal
point (T2,c2), the solid solution should be in stantly co oled
from temperature T1 to T2. In point (T2,c2) the solution
decomposes into regions with concentrations cs1 and cs2
by the spinodal decomposition mechanism and then into
regions with concentrations cb1 and cb2 by the binodal
decomposition mechanism. The scenarios of spinodal
and bimodal decomposition are different. In the spinodal
region the solution is unstable to any slight fluctuations.
The absence of external effects during decomposition
may, for instance, give rise to interconnected nonspheri-
cal regions, their composition being time dependent.
Concentration changes are related to ascending diffusion
that tends to split the homogeneous solution into regions
with concen trations cs1 and cs2.
In the absence of external effects the size of the re-
gions is determined by internal temperature and concen-
tration fluctuations of the solution. In the binodal region
the solution is metastable: it is stable to small fluctua-
tionns. For decomposition to occur, fluctuations should
be sufficiently large to overcome the energy barrier re-
quired for occurrence of critical size particles. This is
followed by growth and nucleation of particles which
forms a system of spherical particles of constant compo-
sition exhibiting sharp interfaces that are usually not in-
terconnected. In the absence of external effects the size
of the regions is determined by internal temperature and
concentration fluctuations of the solution. In the binodal
region the solution is metastable: it is stable to small
fluctuations. For decomposition to occur, fluctuations
should be sufficiently large to overcome the energy bar-
rier required for occurrence of critical size particles. This
is followed by growth and nucleation of particles which
forms a system of spherical particles of constant compo-
sition exhibiting sharp interfaces that are usually not in-
The above scheme of solution transition into the spi-
nodal region implies a rapid change in solution tempera-
ture. We believe that under crystallization a different
transition scheme is realized. The spinod al region is cha-
racterized by a negative second concentration derivative
of the thermodynamic potential. Th e latter and its second
concentration derivative are functions of temperature,
concentration, particle interaction potentials and other
parameters. On phase transition the initial phase becomes
unstable which leads to a drastic change in the particle
interaction potential. Besides, when the solution is in
point (T2,c2) (Figure 1), but in the one-phase region of
the liquid phase, it gets into the solid phase spinodal re-
gion at constant temperature and concentration. The so-
lution decomposes in the spinodal region. Decomposi-
tion intensity is dependent on the reverse diffusivity and
solution residence time in the unstable state. In this work
we explain the cause of the unstable state of the non-
crystallized solution rather than provide any numerical
estimates of the above values.
The experiments described above as well as the ex-
planation of the feasibility of solution transfer into the
unstable state suggest that upon solidification near the
eutectic point phase transition can proceed by the spi-
nodal decompositio n mechanism. The unstable state can-
not be ignored in the description of the mass transfer
process as in the unstable region the solution decomposes
and becomes inhomogeneous. The liquid solution under
crystallization first gets into the unstable state and then
decomposes. The decomposition result is fixed in the
solid phase as inhomogeneous component distribution.
As mentioned above, in the absence of external effects
inhomogeneous component distribution is related to in-
ternal temperature and concentration fluctuations. Under
crystallization the unstab le solution region bord ers on the
interface. In case the latter is unstable, it produces mor-
phological perturbations and temporary fluctuations. In
this case the components of the unstable solution diffuse
to the regions with a higher component concentration, i.e.,
Decomposition of Solutions in Front of the Interface Induced by Directional Crystallization
Copyright © 2013 SciRes. JCPT
towards the concentration maxima of the same compo-
nent. Hence, the solution decomposes into stable phases
with an interface instab ility period. In contrast to the H-J
theory, this scheme of periodic eutectic pattern develop-
ment does not require equilibrium conditions for a peri-
odic component distribution along the interface; neither
does it require any relationship of component distribution
to virtual liquidus and solidus lines that continue the lines
of phase transition into the region of lower eutectic tem-
perature. Within the scheme presented the dependence of
eutectic pattern on the interface displacement rate is not
defined by extra hypotheses as required by the H-J theory,
but it is represented by the solution of the dispersion re-
lation of the interface stability problem under specific
conditions of phase transition.
The scheme presented is in good agreement with the
experimentally observed concentration component redis-
tribution in the process of periodic structure formation.
The latter can be described as follows. The immobile
interface is flat. In accordance with the quasi-equilibrium
problem statement, the interface separates the liquid and
solid phases and the concentrations on the interface de-
fined by the equilibrium phase diagram. In the statio nary
regime of interface displacement the excess of one of the
components is displaced from the solid phase into the
melt and, hence, a concentration jump occurs on the in-
terface. Assume that between the solid and liquid phases
there is a non-equilibrium solution layer. Then there are
two interfaces in the stationary phase transition regime:
one of them is between the stable liquid phase and the
unstable solution, the other between the unstable phase
and the solid solution. In accordance with the equilibrium
phase diagram, in the ideal case the unstable solution
between the stable liquid and stable solid phases decom-
poses into two equilibrium phases. This means that the
concentrations of the unstable solution on the stable liq-
uid and solid phase interfaces are related by the equilib-
rium distribution ratio. In this case there are no concen-
tration jumps on the interfaces. The solution concentra-
tion changes continuously from the initial concentration
of the liquid solution to the concentration of the solid
phase solution.
Let the interface between the solid phase and the
non-equilibrium layer be unstable (the diffusion coeffi-
cient is negative as the diffusion problem refers to the
non-equilibrium layer), which gives rise to increasing
morphological perturbations (Figures 4(a) and (b)). The
perturbation period is defined by the wave number with a
maximum growth increment of interface instability. Due
to ascending diffusion, the perturbations extend to the
whole non-equilibrium solution layer including the in-
terface between the liquid and instable solutions. Figure
4(b) demonstrates the change in the solution concentra-
tion between the dark bands. The dark component dif-
fuses towards the dark bands. As a result, only the light
equilibrium phase remains between the bands. Thus, the
solution in the non-equilibrium layer decomposes into
equilibrium phases with an interface instability period.
During interface displacement the regions of solution de-
composition solidify to form a periodic alternation of
equilibrium solid phase bands (Figures 4(c) and (f)). The
latter are periodic structures formed under crystallization
of eutectic solutions.
5. Conclusion
It has been shown that periodic eutectic pattern form by
way of spinodal decomposition of the solution in front of
the interface. This changes qualitatively the explanation
of eutectic pattern formation within the H-J theory. The
data obtained reveal that between the liquid and solid
phases considered in the H-J theory there exists a non-
equilibrium unstable solution layer. The eutectic pattern
is the result of spinodal decomposition of the solution
under the interface instability influence. The decomposi-
tion period is determined by the maximum of the insta-
bility growth increment.
6. Acknowledgements
The reported study was partially supported by RFBR, re-
search project No. 11-03 -01259 and research proj ect No.
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