Decomposition of Solutions in Front of the Interface Induced by Directional Crystallization

doi:10.4236/jcpt.2013.34026

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Journal of Crystallization Process and Technology, 2013, 3, 170-174

http://dx.doi.org/10.4236/jcpt.2013.34026 Published Online October 2013 (http://www.scirp.org/journal/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.

Email: [email protected]

Received October 7th, 2013; revised November 7th, 2013; accepted November 14th, 2013

cense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

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-

ture.

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

171

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

state.

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-

tion.

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

172

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

m.

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(f)).

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

173

(a) (d)

(b) (e)

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-

terconnected.

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

174

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.

13-02-91156-a.

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