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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