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Chapter 3 Crystal growth

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CHAPTER 3

CRYSTAL GROWTH

3.1 INTRODUCTION

Crystallization is a separation and purification technique employed to

produce a wide variety of materials. Crystallization may be defined as a phase

change in which a crystalline product is obtained from a solution. A solution is

a mixture of two or more species that form a homogenous single phase.

Solutions are normally thought of in terms of liquids; however, solutions may

include solids suspension. Typically, the term solution has come to mean a

liquid solution consisting a solvent, which is a liquid, and a solute, which is a

solid, at the conditions of interest. The solution to be ready for crystallization

must be supersaturated. A solution in which the solute concentration exceeds

the equilibrium (saturated) solute concentration at a given temperature is

known as a supersaturated solution [1]

. There are four main methods to generate

supersaturation that are the following:

• Temperature change (mainly cooling),

• Evaporation of solvent,

• Chemical reaction, and

• Changing the solvent composition (e.g. salting out).

The Ostwald - Miers diagram shown in Fig. 3.1 illustrates the basis of

all methods of solution growth. The solid line represents a section of the curve

for the solute / solvent system. The upper dashed line is referred to as the

super-solubility line and denotes the temperatures and concentration where

spontaneous nucleation occurs [2]

. The diagram can be evaluated on the basis of

three zones:

• The stable (unsaturated) zone where crystallization is impossible.

• The Meta stable (supersaturated) zone where spontaneous nucleation is

improbable but a crystal located in this zone will grow.

• The unstable or labile (supersaturated) zone where spontaneous nucleation is

probable and so the growth.


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Crystallization from solution can be thought of as a two step process.

The first step is the phase separation, (or birth), of a new crystals. The second is

the growth of these crystals to larger size. These two processes are known as

nucleation and crystal growth, respectively. Analysis of industrial

crystallization processes requires knowledge of both nucleation and crystal

growth.

The birth of new crystals, which is called nucleation, refers to the

beginning of the phase separation process. The solute molecules have formed

the smallest sized particles possible under the conditions present. The next

stage of the crystallization process is for these nuclei to grow larger by the

addition of solute molecules from the supersaturated solution. This part of the

crystallization process is known as crystal growth. Crystal growth, along with

nucleation, controls the final particle size distribution obtained in the system. In

addition, the conditions and rate of crystal growth have a significant impact on

the product purity and the crystal habit. An understanding of the crystal growth

theory and experimental techniques for examining crystal growth from solution

are important and very useful in the development of industrial crystallization

processes. The many proposed mechanisms of crystal growth may broadly be

discussed under a few general headings [2-5]

:

• Surface energy theories

• Adsorption layer theories

• Kinematic theories

• Diffusion - reaction theories

• Birth and spread models


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Figure 3.1 - Ostwald-Miers diagram for a solute/solvent system [2]

.

3.2 THE THREE-STEP-MODEL

Modeling of crystal growth in solution crystallization is often done by

the Two- Step-Model. The Two-Step-model describes the crystal growth as a

superposition of two resistances: bulk diffusion through the mass transfer

boundary layer, i.e. diffusion step, and incorporation of growth unites into the

crystal lattice, i.e. integration step [2-5]

. The overall growth rate is expressed as:

The Two-Step-Model is totally ignoring the effect of heat transfer on the

crystal growth kinetics. In the literature there is little evidence for the effects of

heat transfer on the crystal growth kinetics in the case of crystallization from

solution. Matsuoka and Garside[8]

give an approach describing the combined

heat and mass transfer in crystal growth processes. The so called Three-Step-


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model of combined mass and heat transfer takes the above mentioned effects

into account [6-8]

. A mass transfer coefficient is defined which includes a

dimensionless temperature increment at the phase boundary constituted by the

temperature effect of the liberated crystallization heat and the convective heat

transfer. For simplicity the transport processes occurring during growth will be

described in terms of the simple film theory. This has the advantage that the

resulting equations can be easily solved and the predictions do not differ

significantly from those derived using the boundary layer theory [9,10]

.

Conditions in the fluid adjacent to the growing crystal surface are illustrated in

Fig. 3.2. The mass transfer step can be presented by the equation:

where Ci* and Cb* are the saturation concentrations evaluated at the

interface and bulk temperatures, respectively. The effect of bulk flow,

important at high mass fluxes, is neglected in Eq. 3.4. It is also assumed that

the temperature difference (Ti - Tb) is sufficiently small for the solubility curve

to be assumed linear over this temperature range. A heat balance relating heat

evolution to convective transfer gives:


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Where βd is defined by Matsuoka and Garside [8]

as a dimensionless number

for the temperature increase at the crystal surface and therefore as measure of

the heat effect on growth kinetics.

Figure 3.2 - Concentration and temperature profiles to the crystal surface

as assumed in the simple film theory [6]

.

The analogy between mass transfer and heat transfer is given by [11]

:

The general expression for the overall growth rate can be obtained by

combining Eqs. 3.1, 3.2 and 3.6:

Matsuoka and Garside [8]

give a limit βd must be > 10 -2

, for values

below which the influence of the heat transfer on the crystal growth kinetics


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can be neglected. The dissolution process is, on the contrary, quite frequently

described only by use of the diffusion step. What is not true since there is

definitely a surface disintegration step[12,13]

. In other words dissolution is the

100 % opposite of crystal growth. However, a justification for the model

assumption that dissolution can be seen as just diffusion controlled is due to

experimental results which show a linear dependence on the concentration

difference (under saturation). Furthermore, the dissolution process is happening

according to literature much faster (4 to 6 times) than the crystal growth

process so that a possible surface reaction resistance is here difficult to observe

[12,13]. The assumption that the dissolution of crystals involves the sole diffusion

step is therefore, in many cases valid:

Two methods, the differential and integration method are mainly used

for the measurements of the growth rates in fluidized bed experiments [14]

. In

this study the differential method was used. In the differential method, the

crystallization is seeded by adding a few grams of crystals with a known sieve

aperture into a supersaturated solution. The seed crystals grow in the

supersaturated solution. Since the amount of crystals is small, it is assumed that

the concentration of the solution does not change during the growth. The other

assumptions are as follows:

• The number of seed crystals put into the crystallizer is equal to the number of

crystals taken out from the crystallizer.

• There is no crystal loss, an assumption which is always valid for an

experienced experiment.

• The shape factor of the growing crystals is considered to be the same.

This assumption is not always true especially in the case of surface

nucleation. In this case, growth values are thought of as average values. If the


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amount of the crystals put into the crystallizer is M1 and the amount of the

crystals taken out from the crystallizer is M2, they can be related to the size of

the crystals L as shown in the following equations[15]

:

where L1 and L2 are the characteristic size of the crystals input and the

output, respectively. The overall linear growth rate G (m/s) is defined as the

rate of change of characteristic size:

The expression for the growth rate in terms of size of the seed crystals and the

weight of the crystals can be given by:

G and RG are related to each other as follows:

where β1 and α1 are surface and volume shape factors, respectively. M1

and M2 are experimentally obtained. The growth rate, RG, and the dissolution

rate, RD, are calculated from Eq. 3.16 by knowing L1 and t.

3.3 CRYSTAL GROWTH TECHNIQUES

The mathematical models are based on the Navier-Stokes equations and

the heat & mass transport equations in the 2D and 3D approximations. Special

models are available for crystallization phenomena and chemical reactions.

The mathematical aspects of the models used for the analysis of bulk

crystal growth are described in the literature [16-31]

. The global heat transfer

calculations [16-19]

are the basis for a detailed analysis of flows, mass transfer,

and crystallization. Usually, the view-factor (surface-to-surface) method is

applied to simulate radiative heat exchange; a heat transport conservation


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equation is used to predict the temperature distribution. To simulate radiative

heat transfer in semitransparent media, we apply an original model based on a

combination of the ray-tracing and discrete ordinate approach [30,31]

.

The moving grid approach is used to find the geometry of the

melt/crystal interface. The grid is reconstructed after each step of finding the

crystallization front.

MELT GROWTH METHODS

This method is the most basic. A gas is cooled until it becomes a liquid,

which is then cooled further until it becomes a solid. Polycrystalline solids are

typically produced by this method unless special techniques are employed. In

any case, the temperature must be controlled carefully. Large crystals can be

grown rapidly from the liquid elements using a popular method invented in

1918 by the Polish scientist Jan Czochralski and called crystal pulling.

Horizontal Boat Growth Methods

Horizontal Gradient Freezing (HGF) method

Horizontal Bridgman (HB) method

Horizontal Zone Melting (HZM) method

Vertical Boat Growth Methods

Vertical Bridgman (VB) method

Vertical Gradient Freezing (VGF) method

Vertical Zone Melting (VZM) method

Pulling Methods

Czochralski (CZ) method

Liquid Encapsulated Czochralski (LEC) method

Kyropolous and Liquid Encapsulated Kyropolous (LEK)

methods

Floating Zone (FZ) Method

Other Methods

Shaped Crystal Growth Method

Heat Exchange Method (HEM)

http://www.britannica.com/EBchecked/topic/468425/polycrystal

http://www.britannica.com/EBchecked/topic/586581/temperature

http://www.britannica.com/EBchecked/topic/149253/Czochralski-method


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SOLUTION GROWTH METHODS

Simple Solution Growth Method

Traveling Heater Method (THM)

Solute Solution Diffusion (SSD) Method

Solvent Evaporation (SE) Method

Temperature Difference Method under Controlled Vapor

Pressure (TDM-CVP)

Hydrothermal Synthesis Method

VAPOR PHASE GROWTH METHOD

Direct Synthesis (DS) Method

Physical Vapor Transport (PVT) Method

Open tube method

Closed tube method

Chemical Vapor Transport (CVT) Method

Solid Phase Reaction (Solid State Re-crystallization)

MODIFICATION OF CRYSTAL GROWTH METHODS

In-Situ Synthesis

Vapor Pressure Control

Magnetic Field Application

Accelerated Crucible Rotation Technique (ACRT)

3.3.1 Solvent evaporation (SE) method for solid crystal growth

It is often necessary to remove solvent from a solution to recover either

a solid or a high-boiling liquid. There are several ways to do this.

3.3.1.1 Distillation

Simple distillation can be used to remove solvent. Distillation works

well if the solution is composed of a solid and a low-boiling solvent, or if the

solution is composed of a high-boiling liquid and a low-boiling solvent (with

boiling point differences greater than 100°). Advantages of distillation are that

the solvent can be collected and recycled and that no vapors are released into


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the atmosphere. A disadvantage is that it can take a long time. Simple

distillation is process covered on the next section.

Method 1 - Open-Dish evaporation

Solvent can be evaporated by placing the solution in an open container

(an Erlenmeyer, evaporating dish, beaker, and vial). The container is set on a

heat source (steam bath, hot plate, heating mantle, sand bath) and the solvent

boiled off. (If the solvent is water, use a heat source other than a steam bath.)

The problem with open-dish evaporation is that the solvent is released

into the air. Open-dish evaporation should always be done in a hood if the

solvent is anything other than water. Even in a hood, however, vapors are

released into somebody’s air. If the solvent is a hazardous compound (for

instance, methylene chloride), it is probably better to choose another method of

solvent removal.

Method 2 - Reduced-Pressure evaporation

You can accomplish evaporation from a solution quickly by placing it in

a side-arm flask, sealing the flask, and then applying vacuum. Under vacuum -

reduced pressure - liquids vaporize and boil off at lower temperatures;

effectively, the solvents come off a lot faster when under vacuum than at

atmospheric pressure.

In the Organic Chemistry Teaching Labs, a small (25 or 50 mL) side-arm flask

fitted with a rubber stopper is used to strip off small (5-10 mL) amounts of

solvent. As a vacuum source, we use the VacuuBrand systems. Details follow.

Procedure for crystal growth

Put the solution in a 25 or 50 mL side-arm flask. Do not fill the flask

more than one-third full, since the evaporation causes the solvent to

froth and bubble up and out of the flask.

A boiling chip is not necessary, but can be helpful, especially if not plan

to hold and swirl the flask during the process.

Stopper the flask with a black stopper. (Corks do not give a good seal.)

Clamp the flask to a ring stand to prevent it from falling over.


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Connect the flask with vacuum tubing to the VacuuBrand vacuum

source. Do NOT use Tygon tubing.

Have ready a small dish containing warm water.

Turn on the vacuum.

The solution will bubble and froth, especially when you first turn on the

vacuum.

The flask will become cool as the solvent evaporates - place it in the

warm water bath to speed up the evaporation.

Remove the flask from the clamp and hold it in your hand and

constantly swirl it during the process both to prevent bumping and to

increase the surface area to speed up the process.

First turn off the vacuum source connection at your lab bench,

Disconnect the flask from the vacuum tubing.

Method 3 - Rotary evaporators

Rotary evaporators, or roto-vaps, are standard equipment in most

organic chemistry research labs. These evaporators are designed to remove

solvent rapidly from solutions.

Procedure

The motor in the roto-vap turns the flask rapidly, providing a greater

surface from which evaporation can occur, thus speeding up the process.

Cooling coils in the roto-vap condense the vapors and drop them into a

collection flask so that they can be recycled or properly disposed. The

roto-vap is connected to a vacuum source, again, this speed up the

evaporation process.

There are three tubing outlets on the roto-vap, one for a vacuum source

and two for the cooling coils. Use vacuum tubing to connect the outlet

that evacuates the roto-vap chamber to the vacuum source. Use a piece

of Tygon tubing to connect one cooling coil outlet to the cold water


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faucet, and use another piece of Tygon tubing to connect the other

cooling coil outlet to the drain

Place the solution to be evaporated in a round bottom flask, then connect

the flask to the roto-vap. Do not fill the flask more than about one-third

full.

Use a joint clamp to secure the flask to the apparatus. Make sure the

cool water to the cooling coils is turned on.

Turn on the motor so that the flask rotates.

Usually the flask containing the solution to be evaporated is warmed by

a water bath.

Make sure the vent at the top of the cooling coils is closed.

Turn the vacuum outlet on the vacuum system on.

As the solvent evaporates, you may notice a lot of frothing and bubbling

in the evaporating flask. If it starts bubbling out of the flask, you can

open the vent a little to release some of the pressure.

The (unwanted) solvent condenses on the cooling coils and drips down

into the collection flask.

When the solvent has evaporated, turn off the motor that turns the flask

and turn the vacuum outlet to close.

Slowly open the vent to release the pressure in the roto-vap chamber.

Remove the flask from the roto-vap.

In current research work all methods were used but crystal growth from method

3 - Rotary Evaporators are used for further research work.

3.3.2 Distillation and reflux under heat

A process in which a liquid or vapour mixture of two or more

substances is separated into its component fractions of desired purity, by the

application and removal of heat.

Distillation is based on the fact that the vapour of a boiling mixture will

be richer in the components that have lower boiling points.


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Therefore, when this vapour is cooled and condensed, the condensate

will contain more volatile components. At the same time, the original mixture

will contain more of the less volatile material.

Distillation columns are designed to achieve this separation efficiently.

Although many people have a fair idea what “distillation” means, the important

aspects that seem to be missed from the manufacturing point of view are that:

Distillation is the most common separation technique

It consumes enormous amounts of energy, both in terms of cooling and

heating requirements

It can contribute to more than 50% of plant operating costs

To achieve this improvement, a thorough understanding of distillation

principles and how distillation systems are designed is essential.

Separation of components from a liquid mixture via distillation depends

on the differences in boiling points of the individual components. Also,

depending on the concentrations of the components present, the liquid mixture

will have different boiling point characteristics. Therefore, distillation

processes depends on the vapour pressure characteristics of liquid mixtures.

The vapour pressure of a liquid at a particular temperature is the equilibrium

pressure exerted by molecules leaving and entering the liquid surface. Here are

some important points regarding vapour pressure:

Energy input raises vapour pressure

Vapour pressure is related to boiling

A liquid is said to ‘boil’ when its vapour pressure equals the surrounding

pressure

The ease with which a liquid boils depends on its volatility

Liquids with high vapour pressures (volatile liquids) will boil at lower

temperatures

The vapour pressure and hence the boiling point of a liquid mixture

depends on the relative amounts of the components in the mixture


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distillation occurs because of the differences in the volatility of the

components in the liquid mixture

3.3.2.1 The boiling point diagram

The boiling point diagram shows in figure 3.3 how the equilibrium

compositions of the components in a liquid mixture vary with temperature at a

fixed pressure. Consider an example of a liquid mixture containing 2

components (A and B) - a binary mixture. This has the following boiling point

diagram.

The boiling point of A is that at

which the mole fraction of A is 1.

The boiling point of B is that at

which the mole fraction of A is 0. In

this example, A is the more volatile

component and therefore has a

lower boiling point than B. The

upper curve in the diagram is called

the dew-point curve while the lower

one is called the bubble-point curve.

Figure 3.3 - The boiling point diagram

The dew-point is the temperature at which the saturated vapour starts to

condense. The bubble-point is the temperature at which the liquid starts to

boil. The region above the dew-point curve shows the equilibrium composition

of the superheated vapour while the region below the bubble-point curve shows

the equilibrium composition of the sub cooled liquid. For example, when a sub

cooled liquid with mole fraction of A=0.4 (point A) is heated, its concentration

remains constant until it reaches the bubble-point (point B), when it starts to

boil. The vapours evolved during the boiling have the equilibrium composition

given by point C, approximately 0.8 mole fraction A. This is approximately

50% richer in A than the original liquid. This difference between liquid and

vapour compositions is the basis for distillation operations. Heating under


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reflux enables a mixture including volatile materials to be heated for a long

time without loss of solvent. The system is designed to keep materials in the

flask - it follows, therefore, that any apparatus attached to the top of the

condenser is redundant.

Many organic reactions are quite slow and need heating to achieve a

reasonable reaction rate. However, most organic chemicals are quite volatile,

and if heated they will evaporate and be lost. The solution to this problem is to

heat the reaction mixture under reflux. This involves having the reaction

mixture in a flask which is attached to a vertical, open Liebig condenser. Never

attempt to stopper the Liebig condenser. This is quite a popular idea among

students "to stop the vapour escaping". If you attempt to heat sealed glass

apparatus it may explode! There should be no problem with vapour escaping -

as it hits the cold surface of the condenser it will condense and drip back in to

the flask. The use of a hot water bath may be safer and prevent overheating, but

will limit the reaction temperature to 100 ºC.

3.4 MATERIAL AND METHOD

[1] Materials

The ligand which is a Schiff base obtained from

p- dimethylaminobenzaldehyde and o-phenylenediamine were used. The

stock solutions of FeCl3, NiCl2and CuCl2 were prepared.

[2] Preparation of schiff base

p-dimethylaminobenzaldehyde (1.4919 gm 0.1 mol) solution in ethanol

and o-phenylenediamine (1.0814 gm 0.1 mol) solution in hot water were taken

in round bottomed flask, 50 ml absolute ethanol was added and the mixture was

refluxed for 3 hour. The refluxed mixture was put in ice bath, then orange

coloured precipitate was obtained. It was suctioned filtered and washed with

distilled water. Schiff base obtained was dried and kept in vacuum desiccators.

The pure Schiff base was recrystallized from absolute ethanol


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[3] Preparation of crystals

The crystals were prepared by mixing Schiff base (0.1mol) in hot

ethanol solution to (0.1mol) metal chloride salt solution prepared in distilled

water. The schiff base solution was added slowly with continuous stirring to

metal solution. It was refluxed for 2 hours and after refluxation, the mixture

was heated for 10 minutes till the contents was reduced to half. Then the metal

crystals precipitated out after being cooled. The precipitate was filtered and

washed with the distilled water. All complexes were dried and kept in vacuum

desiccators.

3.5 CHEMISTRY OF CRYSTAL GROWTH

All chemicals used were of reagent grade. Their standard solutions were

prepared by using doubly distilled CO2 free water. Metal salt were standardized

by complexometric EDTA titration method conductivity water is used

throughout the experimental work. Digital µ 361 pH meter with readability +

0.001 with combined glass calomel electrode have been used for pH metric

study. Stoichiometrically 1:1:1 concentration of M1, M

2, L1 and L2 were

maintained in the solution. Metal ligand mixtures of following compositions

were prepared for titration keeping total volume 50ml in each case (µ=0.2 M

NaClO4). The concentration of ligand and metal solution were checked by pH

metric titration against 0.2 N carbonate free sodium hydroxide solution.

The following sets were prepared for titration.

(A) Known amount of HClO4.

(B) Free HClO4 + known amount of ligand L1.

(C) Free HClO4 + known amount of ligand L2.

(D) Free HClO4 + known amount of ligand L1 + known amount

of metal [M1] (Binary).

(E) Free HClO4 + known amount of ligand L2 + known amount of metal

[M1] (Binary).

(F) Free HClO4 + known amount of ligand L1 + known amount of

metal [M2] (Binary).


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(G) Free HClO4 + known amount of ligand L2 + known amount of metal

[M2] (Binary).

(H) Free HClO4 + known amount of ligand L1 + known amount of ligand

L2 + known amount of metal [M1] (Ternary).

(I) Free HClO4 + known amount of ligand L1 + known amount of ligand

L2+ known amount of metal [M2] (Ternary).

(J) Free HClO4 + known amount of ligand L1 + known amount of ligand

L2+ known amount of metal [M1] + known amount of metal [M

2]

(Quaternary) .

(i) M1 L1or L2 and M

2L1or L2 → 1:1 Binary mixtures.

(ii) M1L1L2 and M

2L1L2 → 1:1:1 ternary mixtures.

where M1, M

2 are Cu

II, Ni

II,Fe

III as required

L1= o-Phenylenediamine

L2= p-dimethyleaminobenzaldehyde

Crystals of ternary mixtures M1L1L2 and M

2L1L2 were used for further work.

3.6 SYSTEM USED

Instrument Name: All glass double distillation unit, with borosilicate

boiler, borosilicate condenser & Quartz Electric Heater, Vertical type.

Figure 3.4 - Photograph of Working of Rotary Reflux Distillation Setup


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Specification:

Table 3.1 – Specification of Crystal Growth Apparatus

Dist. Water o/p capacity 1.5 lt/hr

Electrical requirement

230-250 volts

Single Phase 1.5x2 Kw

Quartz heater

Cooling water consumption 100 lt/hr

Biological Activity Pyrogen free

pH 6.9 – 7

Conductivity S/cm < 1X 10-6

Distillate Temp 65-75 C

The boiler is made of high purity quartz and the condenser is of

borosilicate/quartz material. The built in heater provides of minimum loss of

heat and production of material. The unit is mounted on powder coated metal

stand with electrical connections and is easy to dismantle and assemble the

unit. Fiber glass insulated wire and silicon rubber boot resist high temperature.

Spares for this unit:

1. Borosilicate boiler with water leveler 1.5 lt.

2. Condenser 1.5 lt.

3. Quartz new type heater B-34 complete unit.

4. Flasks – Boling, round bottom, short neck with interchangeable joint.

Capacity – 250 ml and Approx Height – 140 mm

All apparatus were used have high quality and Pore size of about 90 –

150 microns. All apparatus have excellent resistant to chemical attack. All

apparatus are incorporating them are mainly design for the application of

vacuum or for passage of gases at relatively low pressure. In all cases the

differential pressure must not exceed 100 KN/m2 (15 psi). All apparatus are

particularly suited for drying to constant weight. All apparatus at room


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temperature can be placed directly 150 C, although customary practice is to

dry at 110C. It is advisable that rate of heating should not be more than

2C/min. This prevents internal strains caused by excessive temperature

differences between the surrounding glass vessel and the sintered disk, which

can lead to fracture of apparatus.

3.7 CRYSTALS SPECIFICATION

Photographs and Dimensions of all crystals were measured at Laljibhai

Chaturbhai Institute of Technology (LCIT), Mehsana. All apparatus were used

have high quality with 5 MP cameras.

Crystal of Cu(II) with O-Phenylenediamine and p-dimethyleaminobenzaldehyde

ligand

Figure 3.5 - Photograph of Crystal Cu(II)

A: Photograph of crystal in bulk form B: Photograph of crystal in single form

Size: 0.80 mm length and 0.35 mm width


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Crystal of Ni(II) with O-Phenylenediamine and p-dimethyleaminobenzaldehyde

ligand

Figure 3.6 - Photograph of Crystal Ni(II)



Crystal of Fe(III) with O-Phenylenediamine and p-dimethyleaminobenzaldehyde

ligand

Figure 3.7 - Photograph of Crystal Fe(III)




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