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2. METHODS OF CRYSTAL GROWTH
The ideal crystal is an infinite lattice of atoms arranged in patterns, which
repeat in all three dimensions with repeated distances (lattice spacing). In general, a
single crystal is a periodic array of atoms arranged in three dimensional structure with
equally repeated distance in a given direction. Natural crystals have often been
formed at relatively low temperatures by crystallisation from solutions, sometimes in
the course of hundreds and thousands of years. Now a days, crystals are produced
artificially to satisfy the needs of science and technology. Crystal growth is rather an
art than a science [28]. Many attempts have been made for a long time to produce
good crystals of desired material. Presently, crystal growth specialists have moved
from the periphery to the center of the materials-based technology. This Chapter
briefly describes the different methods of crystal growth and various experimental
techniques which are employed to obtain good quality crystals.
Crystal growth methods are generally classified into four categories:
i) growth from solid, ii) growth from melt, iii) growth from vapour and iv) growth
from solution.
2.1 Growth From Solid
The job of the crystal grower is to prepare large specimens of crystalline
material such that there is a complete crystallographic continuity across a given
specimen in all directions is achieved. There are two principal reasons for the
deliberate growth of single crystals.
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i) Many physical properties of solids are obscured or complicated by the effect of
grain boundaries.
ii) The full range of tensor relationships between applied physical causes and
observed effect can be obtained only if the full internal symmetry of the crystal
structure is maintained throughout the specimen.
Solid state growth technique can be considered as the conversion of a
polycrystalline material into a single crystal by causing the grain boundaries to be
swept through and pushed out of the material due to atomic diffusion. But this is very
slow at ordinary temperatures and is only rarely used.
2.2 Growth From Melt
Melt growth can be achieved by a variety of techniques (e.g. free melt surface
of confined configurations) depending on the specific properties of the material (e.g.
contraction or expansion during solidification) and requirements. The growth from
melt can be subgrouped into various techniques. The main techniques are:
i) Czochralski technique
ii) Bridgman-Stockbarger technique
iii) Vernueil technique
iv) Zone melting technique
v) Skull melting process
vi) Shaped crystal growth technique
The major factor to be considered during the growth of crystals from the melt
is volatility or dissociability, the chemical reactivity and the melting point.
Czochralski method is the most commonly used technique to grow good quality
crystals from melt.
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2.2.1 Czochralski method
In this method, the charge material is contained in a crucible which is heated
to a temperature above the melting point of the charge. A pull rod with a chuck
containing a seed crystal at its lower end is positioned above the crucible. The seed
crystal is dipped into the melt and the melt temperature is adjusted until a meniscus
can be supported by the seed crystal. The pull rod is then slowly rotated and lifted and
by carefully adjusting the power supplied to the melt, a crystal of the desired diameter
can be grown. The whole assembly is maintained in an envelope which permits
control of the ambient gas and enables the crystal to be observed visually. The
technique has been applied to an extremely wide range of materials from elemental
metals and semiconductors to complex refractory high melting point oxides. Crystal
pullers have revolutionized in the semiconductor industry with the development of the
liquid encapsulation techniques. The important semiconducting compounds like
GaAs, InP and GaP are grown by this method [29].
2.2.2 Bridgman-Stockbarger technique
In this process the material to be grown is taken in a vertical cylindrical
container, tapered conically with a point bottom and made to melt using a suitable
furnace. The furnace consists of two halves. The upper half maintains the little above
the melting point and lower half keeps just below the melting point. The crucible is
made of platinum quartz and has pointed lower end. The crucible is filled with the
material and it is lowered slowly. The temperature gradient between halves is made as
steep as possible. When the crucible crosses the zone corresponding to the freezing
point of material, single crystal forms at the lower end of the crucible. The main
advantage is to grow single crystal of any desired shape and size which can be
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obtained by choosing the appropriate crucible. This method is more suitable for
growing single crystals like GaAs, silver halides, etc [30].
2.2.3 Vernueil technique
In this method, chemically pure fine powder of 1-20 microns emerges through
an oxy-hydrogen flame and falls onto the fused end of an oriented single crystal seed
fixed to a lowering mechanism. The powder charge is fed from a bunker by means of
a special tapping mechanism. Coordinating the consumption of the charge, hydrogen
and oxygen with the rate of decent of the seed ensures crystallization at a prescribed
level of the apparatus.
2.2.4 Zone melting technique
Zone melting is a generic title given to a large family of techniques (float-
zone, traveling solvent zone, zone-pass, etc) which have in common the following
feature: “A liquid zone is created by melting a small amount of material in relatively
large or long solid charge or ingot. It is then made to traverse through a part or the
whole of the charge”. A seed crystal can be introduced at the starting end to grow
single crystals.
2.2.5 Skull melting process
The skull melting process is used for the growth of high melting point
materials. This process is currently widely used for the growth of zirconium oxide.
Zirconium oxide is a material with a melting point of about 2750°C. The high melting
point and extreme chemical reactivity of the melt make it impossible to melt and
crystallize zirconium oxide in conventional metallic or graphite crucibles. In the early
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1970’s the Russians (Aleksandrov Osiko, Tatarinstev) devised an ingenious method
whereby zirconium oxide is fused in a container or “skull” of its own substance.
Zirconium oxide, cubic stabilized with yttrium oxide is an interesting material
for an application as diamond imitation because of its high refractive index (2.15),
dispersion (0.060) combined with its hardness [31]. This method is used to produce
zirconium up to 10 cm long.
2.2.6 Shaped crystal growth technique
Shaped growth of crystals from the melt has been practised for over a half
century. In this method, the crystal is grown from a thin film of liquid on the top of a
suitable die surface. The shape of the film and therefore of the crystal is determined
by the external shape of the film and therefore of the crystal is determined by the
external shape of the die. Unlike the more conventional crystal pulling techniques,
growth rates are extremely high being in the range 1-5 cm/min as compared to 0.01 –
0.05cm/min for conventional crystal pulling.
2.3 Growth From Vapour
Single crystals of high purity can be grown from the vapour by sublimation
and chemical vapour deposition. In these processes, the source material which is a
solid or one or two components of the phase to be crystallized is provided from the
vapour phase. The ampoule must be translated through the temperature gradient at a
rate equal to the linear growth rate of the crystal. This ensures that the supercooling
conditions remain constant so that spurious nucleation does not occur. The most
widely known sublimation method is the so called Piper-Polich technique for the
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preparation of cadmium sulphide. Small size crystals of better quality can be grown
like CdS, Al2O3 and Hgl2 [32].
2.4 Growth From Solution
The method of growing crystals from solutions may be used for substances
fairly soluble in a solvent and not reactive with it. Moreover, growth of crystals from
solutions is the only method for the crystallization of substances which undergo
decomposition before melting.
2.4.1 Criteria for growth
Crystals intended for practical and technical applications should have a well
developed morphology and contain a low density of defects (such as inclusions,
dislocations, etc). These requirements may be predicted from a consideration of
thermodynamic (e.g. crystal-medium interface) and kinetic (e.g. equilibrium solute
concentration, supersaturation, growth temperature and stirring rate) parameters
which characterize the overall growth conditions. Thermodynamic parameters
determine the growth mechanism while kinetic parameters determine the growth
kinetics and generation of defects.
2.4.2 Metastable zone width
Crystal growth takes place in the metastable supersaturated zone without the
occurrence of three dimensional nucleation. The metastable zone width is an
experimentally measurable quantity, although it is well known that a number of
factors (such as stirring rate, cooling rate of the solution, presence of additional
crystals or impurities) affect its value.
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2.4.3 Crystal-medium interface
The development of a crystal involves the incorporation of growth units on its
surface. A crystal with well developed polyhedral morphology is obtained, when the
crystal medium interface is smooth, so that the surface grown by the lateral
displacement of layers (i.e. layers growth). When the surface is rough, integration of
grown species into the crystal is continuous (continuous growth), and this results in
the growth of dendrites and hopper crystals without technical applications. Whether
an interface is rough or smooth may be known from the value of the surface entropy
factor.
The growth rate of crystal depends on the values of kinetic parameters and
increases with solution supersaturation, growth temperature and crystal solubility.
Higher the values of equilibrium solute concentration (solubility) and supersaturation
lower the value of the surface entropy factor, which consequently lead to the
generation of dislocations and capture of inclusions. Higher temperatures not only
enhance growth rates but also lead to decrease in the generation of defects. Thus to
ensure good crystal growth it is useful to have a sufficiently high value of the surface
entropy factor of the system, medium supersaturation, elevated temperatures and non-
turbulent stirring.
2.4.4 Impurities
Growth aids which modify the properties of a growth system may be taken as
impurities. Additives are present in the solution as ions (metal-ions, oxy-ions and dye-
ions). Small amounts of these ions are known either to produce improvements in
crystal growth which is otherwise difficult from solutions or to change the growth
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habit. In general highly polarizable metal-ions and oxy-ions are the most effective
impurities, and the habit of crystals of ammonium and alkali metal compounds is
readily modified in the presence of these impurities.
2.4.5 Stirring
For the successful and relatively fast growth of a substance from solution
containing a reasonably high soluble concentration and having a high viscosity,
effective stirring is an important operation. The rate of stirring is to sweep off the
depleted solution at the crystal surface, providing it with fresh supersaturated solution
which would otherwise have been supplied by diffusion. Stirring may be achieved by
various types of stirrers, at a rate greater than the optimum, induces turbulence at a
point in the system, which favours trapping of inclusions on the crystal surface.
The simplest method of stirring is unidirectional rotation of the crystal fixed at
the holder of a stirrer. This type of stirring leads to the formation of cavities in the
central regions of a crystal face because of malnutrition of the solute there is
comparison with edges and corners which receive more solute supply. Periodic
rotation of the crystal in opposite directions suppresses eddy formation but does not
eliminate the formation of the central cavity. Consequently, eccentric reversive
rotation is often used.
2.4.6 Growth temperature
In order to grow the crystal of a substance in a given phase and / or
composition at a resonable rate, the choice of an optimum temperature interval is
important. As in the use of other processes, growth at elevated temperatures takes
place faster. However, at elevated temperatures, smooth growth necessitates better
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temperature control while increased vapour pressure creates problems of control of
supersaturation and spurious nucleation. These difficulties may be overcome during
crystal growth from boiling solutions.
2.4.7 Solubility and supersaturation
Solubility corresponding to saturation, is the equilibrium between a solid and
its solution at a given temperature and pressure. Thermodynamically this means that
the chemical potential of the pure solid A is equal to the chemical potential of the
same solute in saturated solution. Solubility changes with temperature and pressure. A
solvent in which the solute has solubility between 10-60% may be considered suitable
for crystal growth.
Crystals grow only if solution is out of equilibrium, i.e. if it is supersaturated.
Supersaturation can be achieved by solvent evaporation, solution cooling (or heating,
in the case of reverse solubility), change of pH, adding of a common ion, mixing of
soluble reactants. Supersaturation can be expressed in different ways. For soluble
compounds, if CS and Ce are the actual and equilibrium concentrations, we have:
∆C = CS – Ce (absolute supersaturation),
β = CS / Ce (supersaturation ratio), and
σ = (CS – Ce) / Ce = β – 1 (relative supersaturation).
When β = 1, the system is saturated; when β > 1, it is supersaturated and the crystal
can grow; when β < 1, it is undersaturated, and the crystals dissolve. Figure 4 shows
the solubility diagram showing different levels of saturation.
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BB′ - Solubility curve AB″C″ - Evaporation and cooling
CC′ - Super solubility curve D - Crystallization point
Figure 4: Solubility diagram showing different levels of saturation
2.4.8 Choice of solvent
Once the method and high purity starting material are ensured, the next
requirement is that a solvent should be chosen which allows prismatic growth and in
which the solute has high solubility. The ideal solvent should yield a prismatic habit
in the crystal and also have the following characteristics: i) high solute solubility,
ii) high positive temperature coefficient of solubility, iii) low viscosity, iv) low
volatility, v) density less than that of the bulk solute, vi) low toxicity, vii) low vapour
pressure at the growth temperature, viii) cheap in the pure state and readily available,
etc.
D
III
II
B″
B A C
B′
I
Stable
Temperature
C″
C′
Metastable C
once
ntr
atio
n
Labile
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A simple rule of thumb in the proper selection of solvent is the chemical
similarity between the solvent and the material to be grown. For example, crystals of
nonpolar organic compounds easily grow from nonpolar organic solvents. The
chemical similarity also determines crystal solubility in the solvent. Consequently,
because of the interaction of the surface of growing crystals and the solvent
molecules, the solvent also provides a control over the crystal habit.
2.4.9 Methods of crystal growth
Low temperature solution growth can be subdivided into the following
methods:
i) Slow cooling method,
ii) Slow evaporation method, and
iii) Temperature gradient method.
2.4.9.1 Slow cooling method
This is the best method to grow bulk single crystals from solution. In this
method, supersaturation is created by a change in temperature usually throughout the
whole crystallizer. The crystallalization process is carried out in such a way that the
point on the temperature dependence of the concentration moves into the metastable
region along the saturation curve in the direction of lower solubility. Since the volume
of the crystallizer is finite and the amount of substance placed in it is limited, the
supersaturation requires systematic cooling. It is achieved by using a thermostated
crystallizer. The temperature at which such crystallization can begin is usually within
the range 45-75°C and the lower limit of cooling is the room temperature. The
apparatus used for the growth of single crystals by this method is shown in Figure 5.
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L - Heater, B - Constant temperature bath F - Flask
S - Stirrer, T - Thermometer SG - Stirring gland
Figure 5: Schematic diagram of the apparatus for the slow cooling method
2.4.9.2 Slow (free) evaporation method
In this method the solution loses particles which are weakly bound to other
components and, therefore, the volume of the solution decreases. An excess of a given
solute is established by utilizing the difference between the rates of evaporation of the
solvent and the solute. Normally, the vapour pressure of the solvent above the
solution is higher than the vapour pressure of the solute and, therefore, the solvent
evaporates more rapidly and the solution becomes supersaturated. It is sufficient to
allow the vapour formed above the solution to escape freely into the atmosphere. This
method of crystal growth is the oldest and technically it is very simple. For nontoxic
solvents such as water evaporation is permissible into the atmosphere but for toxic
and inflammable solvents precautions are taken to avoid the leakage of solvent vapour
in the atmosphere.
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Figure 6: Schematic diagram of a simple apparatus for the slow (free)
evaporation method
The simplest apparatus used for the growth of single crystals by this method is
the one shown in Figure 6 with a few holes in the lid to allow solvent evaporation.
The rate of crystallization depends on the rate of solvent evaporation which may be
governed by changing the total area of the holes. In sophisticated crystallizers
evaporation is controlled by passing air or an inert gas at a controlled rate over the
solution. Good control of evaporation rate can also be obtained by using some sort of
condenser to allow the removal of condensed solvent at a controlled rate.
2.4.9.3 Temperature gradient method
In this method, the materials are transported from a hot region containing the
source material to be grown to a cooler region where the solution is supersaturated
and the crystal grows. The main advantages of this method are:
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i) Crystal grows at fixed temperature;
ii) This method is insensitive to change in temperature provided both the source
and the growing crystal undergo the same change;
iii) Economical use of solvent and solute; etc.
On the other hand, changes in the small temperature difference between the
source and the crystal zones have a large effect on the growth rate. In crystal growth
systems, the cool growth zone is separated from the hot saturator and the solution is
pumped from one vessel to the other. Supersaturated solutions tend to nucleate when
pumped. If he solution saturated at T + ∆T pumped directly to growth vessel, un-
dissolved particles are transferred to the growth region. To overcome such problems
crystallizers having three-vessel growth system is normally used. The temperature in
the saturator vessel will be 10°C above the crystallizer and the solution temperature in
the super heater vessel will be much higher than the saturator. During the crystal
growth run the solution flows from super heater vessels to the crystallizer and then to
the saturator and returns to the super heater vessel. The solution pumps fitted in the
saturator and super heater vessels are fitted with filters of size 100 µm respectively.
The apparatus used for the growth of single crystals by this method is shown in
Figure 7.
Figure 7: Schematic diagram of the apparatus for the temperature
gradient method
Thermostat for
dissolution at a
temperature T1
Nutrient
Thermostat for
growth at a
Temperature T2,
T2 < T1
Vane type agitator
Growing crystal