KRP Chapter 5 - Information and Library Network Centreshodhganga.inflibnet.ac.in/bitstream/10603/10158/18/18_chapter 5.pdf · A sample of liquid metal is removed from the furnace

Chapter 5 Thermal study of the crystal

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CHAPTER 5

THERMAL STUDY OF CRYSTAL

PART A: THERMOGRAVIMETRIC ANALYSIS

5.A.1 INTRODUCTION

Thermal analysis is a branch of materials science where the properties of

materials are studied as they change with temperature. Several methods are

commonly used - these are distinguished from one another by the property

which is measured[1-7]

:

Differential thermal analysis (DTA): temperature difference

Differential scanning calorimetry (DSC): heat difference

Thermogravimetric analysis (TGA): mass

Thermomechanical analysis (TMA): dimension

Dilatometry (DIL): volume

Dynamic mechanical analysis (DMA) : mechanical stiffness & damping

Dielectric thermal analysis (DEA): dielectric permittivity & loss factor

Evolved gas analysis (EGA) : gaseous decomposition products

Thermo-optical analysis(TOA) : optical properties

Thermal Conductivity

Simultaneous Thermal Analysis (STA) generally refers to the

simultaneous application of Thermogravimetry (TGA) and Differential

scanning calorimetry (DSC) to one and the same sample in a single instrument.

The test conditions are perfectly identical for the TGA and DSC signals (same

atmosphere, gas flow rate, vapor pressure of the sample, heating rate, thermal

contact to the sample crucible and sensor, radiation effect, etc.). The

information gathered can even be enhanced by coupling the STA instrument to

an Evolved Gas Analyzer (EGA) like Fourier transform infrared spectroscopy

(FTIR) or Mass Spectometry (MS). Other, less-common, methods measure the

sound or light emission from a sample, or the electrical discharge from a


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dielectric material, or the mechanical relaxation in a stressed specimen. The

essence of all these techniques is that the sample's response is recorded as a

function of temperature (and time). It is usual to control the temperature in a

predetermined way - either by a continuous increase or decrease in temperature

at a constant rate (linear heating/cooling) or by carrying out a series of

determinations at different temperatures (stepwise isothermal measurements).

More advanced temperature profiles have been developed which use an

oscillating (usually sine or square wave) heating rate (Modulated Temperature

Thermal Analysis) or modify the heating rate in response to changes in the

system's properties (Sample Controlled Thermal Analysis)[8]

. In addition to

controlling the temperature of the sample, it is also important to control its

environment (e.g. atmosphere). Measurements may be carried out in air or

under an inert gas (e.g. nitrogen or helium). Reducing or reactive atmospheres

have also been used and measurements are even carried out with the sample

surrounded by water or other liquids. Inverse gas chromatography is a

technique which studies the interaction of gases and vapours with a surface -

measurements are often made at different temperatures so that these

experiments can be considered to come under the auspices of Thermal

Analysis[9]

. Atomic force microscopy uses a fine stylus to map the topography

and mechanical properties of surfaces to high spatial resolution. By controlling

the temperature of the heated tip and/or the sample a form of spatially resolved

thermal analysis can be carried out. Thermal Analysis is also often used as a

term for the study of Heat transfer through structures. Many of the basic

engineering data for modelling such systems comes from measurements of heat

capacity and Thermal conductivity.

5.A.1.1 Thermal analysis of pharma materials

DSC and TGA are often used for characterisation of pharma materials.

DSC is able to differentiate between different polymorphic structures and, by

using different heating rates, can investigate the transformations which occur

during the polymorphic transformation. By using appropriate heating rates,


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polymorphic purity can be determined, and can involve heating rates up to

750°C/min. TGA is often used to measure residual solvents and moisture, but

can also be used to determine solubility of pharma materials in solvents.

Analysis of pharma materials is probably the largest area of application for

thermal analysis.

5.A.1.2 Thermal analysis of polymers

Polymers represent another large area in which thermal analysis finds

strong applications[8-11]

. Thermoplastic polymers are commonly found in

everyday packaging and household items, but for the analysis of the raw

materials, effects of the many additive used (including stabilisers and colours)

and fine-tuning of the moulding or extrusion processing used can be achieved

by using DSC. An example is oxidation induction time (OIT) by DSC which

can determine the amount of oxidation stabiliser present in a thermoplastic

(usually a polyolefin) polymer material. Compositional analysis is often made

using TGA, which can separate fillers, polymer resin and other additives. TGA

can also give an indication of thermal stability and the effects of additives such

as flame retardants Thermal analysis of composite materials, such as carbon

fibre composites or glass epoxy composites are often carried out using DMA or

DMTA, which can measure the stiffness of materials by determining the

modulus and damping (energy absorbing) properties of the material. Aerospace

companies often employ these analysers in routine quality control to ensure

that products being manufactured meet the required strength specifications.

DSC is used to determine the curing properties of the resins used in composite

materials, and can also confirm whether a resin can be cured and how much

heat is evolved during that process[8-11]. Application of predictive kinetics

analysis can help to fine-tune manufacturing processes. Another example is

that TGA can be used to measure the fibre content of composites by heating a

sample to remove the resin by application of heat and then determining the

mass remaining.


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5.A.1.3 Thermal analysis of metals

Production of many metals (cast iron, grey iron, ductile iron, compacted

graphite iron, 3000 series aluminium alloys, copper alloys, silver, and complex

steels) are aided by a production technique also referred to as thermal analysis.

A sample of liquid metal is removed from the furnace or ladle and poured into

a sample cup with a thermocouple embedded in it. The temperature is then

monitored, and the phase diagram arrests (liquidus, eutectic, and solidus) are

noted. From this information chemical composition based on the phase diagram

can be calculated, or the crystalline structure of the cast sample can be

estimated. Strictly speaking these measurements are cooling curves and a form

of sample controlled thermal analysis whereby the cooling rate of the sample is

dependent on the cup material (usually bonded sand) and sample volume which

is normally a constant due to the use of standard sized sample cups.

Advanced techniques use differential curves to locate endothermic

inflection points such as gas holes, and shrinkage, or exothermic phases such as

carbides, beta crystals, inter crystalline copper, magnesium silicide, iron

phosphide's and other phases as they solidify. Detection limits seem to be

around 0.01% to 0.03% of volume. In addition, integration of the area between

the zero curve and the first derivative is a measure of the specific heat of that

part of the solidification which can lead to rough estimates of the percent

volume of a phase. (Something has to be either known or assumed about the

specific heat of the phase versus the overall specific heat.) In spite of this

limitation, this method is better than estimates from two dimensional micro

analysis, and a lot faster than chemical dissolution.

5.A.2 THERMO-GRAVIMETRIC ANALYSIS OR TGA

Thermogravimetric analysis or thermal gravimetric analysis (TGA) is a

type of testing that is performed on samples to determine changes in weight in

relation to change in temperature. Such analysis relies on a high degree of

precision in three measurements: weight, temperature, and temperature change.

As many weight loss curves look similar, the weight loss curve may require


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transformation before results may be interpreted. A derivative weight loss

curve can be used to tell the point at which weight loss is most apparent. Again,

interpretation is limited without further modifications and deconvolution of the

overlapping peaks may be required. TGA is commonly employed in research

and testing to determine characteristics of materials such as polymers, to

determine degradation temperatures, absorbed moisture content of materials,

the level of inorganic and organic components in materials, decomposition

points of explosives, and solvent residues[10-18]

. It is also often used to estimate

the corrosion kinetics in high temperature oxidation. Simultaneous TGA-

DTA/DSC measures both heat flow and weight changes (TGA) in a material as

a function of temperature or time in a controlled atmosphere. Simultaneous

measurement of these two material properties not only improves productivity

but also simplifies interpretation of the results. The complementary information

obtained allows differentiation between endothermic and exothermic events

which have no associated weight loss (e.g., melting and crystallization) and

those which involve a weight loss (e.g., degradation).

Analysis is carried out by raising the temperature of the sample

gradually and plotting weight (percentage) against temperature. The

temperature in many testing methods routinely reaches 1000°C or greater, but

the oven is so greatly insulated that an operator would not be aware of any

change in temperature even if standing directly in front of the device. After the

data are obtained, curve smoothing and other operations may be done such as

to find the exact points of inflection. A method known as hi-resolution TGA is

often employed to obtain greater accuracy in areas where the derivative curve

peaks. In this method, temperature increase slows as weight loss increases. This

is done so that the exact temperature at which a peak occurs can be more

accurately identified. Several modern TGA devices can vent burnoff to an

infrared spectrophotometer to analyze composition Thermogravimetric analysis

(TGA) is one of the members of the family of thermal analysis techniques used

to characterise a wide variety of materials. TGA provides complimentary and


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supplementary characterisation information to the most commonly used

thermal technique, DSC. TGA measures the amount and rate (velocity) of

change in the mass of a sample as a function of temperature or time in a

controlled atmosphere. The measurements are used primarily to determine the

thermal and/or oxidative stabilities of materials as well as their compositional

properties. The technique can analyze materials that exhibit either mass loss or

gain due to decomposition, oxidation or loss of volatiles (such as moisture). It

is especially useful for the study of polymeric materials, including

thermoplastics, thermosets, elastomers, composites, films, fibres, coatings and

paints. A schematic of TGA analysis equipment is shown in fig – 5.1

Figure 5.1 - Schematic of TGA Analysis Equipment

TGA measurements provide valuable information that can be used to

select materials for certain end-use applications, predict product performance


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and improve product quality. The technique is particularly useful for the

following types of measurements[19-21]:

Compositional analysis of multi-component materials or blends

Thermal stabilities

Oxidative stabilities

Estimation of product lifetimes

Decomposition kinetics

Effects of reactive atmospheres on materials

Filler content of materials

Moisture and volatiles content

5.A.2.1 differential scanning calorimetry (DCS)

Differential Scanning Calorimetry (DSC) is widely used to characterize

the thermophysical properties of materials. DSC can measure important

thermoplastic properties including[22-25]:

Melting temperature

Heat of melting

Percent crystallinity

Tg or softening

Crystallization

Presence of recyclates/regrinds

Plasticizers

Polymer blends (presence, composition and compatibility)

Differential scanning calorimetry or DSC is a thermoanalytical

technique in which the difference in the amount of heat required to increase the

temperature of a sample and reference are measured as a function of

temperature. Both the sample and reference are maintained at very nearly the

same temperature throughout the experiment. Generally, the temperature

program for a DSC analysis is designed such that the sample holder

temperature increases linearly as a function of time. The reference sample


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should have a well-defined heat capacity over the range of temperatures to be

scanned. The basic principle underlying this technique is that, when the sample

undergoes a physical transformation such as phase transitions, more (or less)

heat will need to flow to it than the reference to maintain both at the same

temperature. Whether more or less heat must flow to the sample depends on

whether the process is exothermic or endothermic. For example, as a solid

sample melts to a liquid it will require more heat flowing to the sample to

increase its temperature at the same rate as the reference. This is due to the

absorption of heat by the sample as it undergoes the endothermic phase

transition from solid to liquid. Likewise, as the sample undergoes exothermic

processes (such as crystallization) less heat is required to raise the sample

temperature. By observing the difference in heat flow between the sample and

reference, differential scanning calorimeters are able to measure the amount of

heat absorbed or released during such transitions. DSC may also be used to

observe more subtle phase changes, such as glass transitions. DSC is widely

used in industrial settings as a quality control instrument due to its applicability

in evaluating sample purity and for studying polymer curing. The result of a

DSC experiment is a heating or cooling curve shown in fig – 5.2[25-27]. This

curve can be used to calculate enthalpies of transitions. This is done by

integrating the peak corresponding to a given transition. It can be shown that

the enthalpy of transition can be expressed using the following equation:

ΔH = KA

where ΔH is the enthalpy of transition, K is the calorimetric constant, and A is

the area under the curve. The calometric constant will vary from instrument to

instrument, and can be determined by analyzing a well-characterised sample

with known enthalpies of transition[26].


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Figure 5.2 - A schematic DSC curve demonstrating the appearance of

several common features.

Differential scanning calorimetry can be used to measure a number of

characteristic properties of a sample. Using this technique it is possible to

observe fusion and crystallization events as well as glass transition

temperatures (Tg). DSC can also be used to study oxidation, as well as other

chemical reactions. Glass transitions may occur as the temperature of an

amorphous solid is increased. These transitions appear as a step in the baseline

of the recorded DSC signal. This is due to the sample undergoing a change in

heat capacity; no formal phase change occurs. As the temperature increases, an

amorphous solid will become less viscous. At some point the molecules may

obtain enough freedom of motion to spontaneously arrange themselves into a

crystalline form. This is known as the crystallization temperature (Tc). This

transition from amorphous solid to crystalline solid is an exothermic process,

and results in a peak in the DSC signal[29]. As the temperature increases the

sample eventually reaches its melting temperature (Tm). The melting process

results in an endothermic peak in the DSC curve. The ability to determine

transition temperatures and enthalpies makes DSC an invaluable tool in

producing phase diagrams for various chemical systems. Using differential


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scanning calorimetry to study the oxidative stability of samples generally

requires an airtight sample chamber. Usually, such tests are done isothermally

(at constant temperature) by changing the atmosphere of the sample. First, the

sample is brought to the desired test temperature under an inert atmosphere,

usually nitrogen[30-32]. Then, oxygen is added to the system. Any oxidation

that occurs is observed as a deviation in the baseline. Such analyses can be

used to determine the stability and optimum storage conditions for a

compound. DSC is widely used in the pharmaceutical and polymer industries.

For the polymer chemist, DSC is a handy tool for studying curing processes,

which allows the fine tuning of polymer properties. The cross-linking of

polymer molecules that occurs in the curing process is exothermic, resulting in

a positive peak in the DSC curve that usually appears soon after the glass

transition. In the pharmaceutical industry it is necessary to have well-

characterised drug compounds in order to define processing parameters. For

instance, if it is necessary to deliver a drug in the amorphous form, it is

desirable to process the drug at temperatures below those at which

crystallization can occur[33]. In food science research, DSC is used in

conjunction with other thermal analytical techniques to determine water

dynamics. Changes in water distribution may be correlated with changes in

texture. Similar to material science studies, the effects of curing on

confectionery products can also be analyzed.

DSC curves may also be used to evaluate drug and polymer purities.

This is possible since the temperature range over which a mixture of

compounds melts is dependent on their relative amounts. This effect is due to a

phenomenon known as freezing point depression, which occurs when a foreign

solute is added to a solution. Consequently, less pure compounds will exhibit a

broadened melting peak that begins at lower temperature than a pure

compound[34].


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5.A.3 EXPERIMENTAL

Figure 5.3 - Thermal Analysis System (DSC, TGA, DTA)

at SICART, V.V.Nagar

Make Model

Perkin Elmer Pyris-1 DSC, Pyris-1 TGA, DTA-7

Small Description:

Thermal Analyzer (DSC, TGA, DTA), PerkinElmer Pyris1 DSC, Pyris1

TGA, DTA 7, Temp.

Range: TGA: Room Temperature to 1000ºC; DSC: -100ºC to 600ºC and DTA:

Room Temperature to 1200ºC. All types of thermal analysis studies /testing.


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Specifications:

(TGA)

Temperature Range: Ambient to 1000º C

Sensitivity: 0.1m gm (0.0001mg)

Atmosphere: N2, or Air

(DSC)

Temperature range: -100 °C to 600 °C

Temperature Accuracy: ± 0.2 °C

Heating Rate: 0.1 to 100 °C / min

(DTA)

Temperature range: -Ambient to 1200 °C

Heating Rate: 0.1 to 100 °C / min

Atmosphere: Air or Nitrogen

Applications:

Thermal Analysis (DSC,TGA,DTA)

Thermal Gravimetric Analyzer measures the change in mass of a sample as a

function off time or temperature in inert or oxidative atmosphere.

Chemical changes occurring in an oxidative atmosphere provide useful

information regarding characterization of the sample.

TGA-1 is based on a rugged microbalance which is sensitive to measure

even a few micrograms of weight loss.

It employs computer controlled gas switching to regulate furnace

atmosphere.

There are preset programs to allow compete separations, Decomposition

studies, proximate analysis of coal, auto stepwise analysis of filled

polymers, curing characteristics High temperature studies, Thermal

stability and compositional analysis are possible with this instrument.

Used for Melting, Crystallization, Glass Transitions Temperature,

Polymorphism, Kinetic Studies, Curing Reaction.


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Endothermic and Exothermic effects

Isothermal Cure kinetics studies.

Characterization of polymorphism of pharmaceuticals.

Characterization of pharmaceuticals formulations.

Characterization of multicomponent materials by TGA.

Thermal decomposition study

Widely used in polymer, pharmaceuticals, cosmetics industry etc.

5.A.4 RESULT AND DISCUSSION

Thermo gravimetric analysis or thermal gravimetric analysis (TGA) is a

type of testing that is performed on samples to determine changes in weight in

relation to change in temperature. Such analysis relies on a high degree of

precision in three measurements: weight, temperature and temperature change.

As many weight loss curves look similar, the weight loss curve may require

transformation before results may be interpreted. A derivative weight loss

curve can be used to tell the point at which weight loss is most apparent. Again,

interpretation is limited without further modifications and deconvolution of the

overlapping peaks may be required.TGA is commonly employed in research

and testing to determine characteristics of materials such as polymers, to

determine degradation temperatures, absorbed moisture content of materials,

the level of inorganic and organic components in materials, decomposition

points of explosives and solvent residues. It is also often used to estimate the

corrosion kinetics in high temperature oxidation. Simultaneous TGA-

DTA/DSC measures both heat flow and weight changes (TGA) in a material as

a function of temperature or time in a controlled atmosphere. Simultaneous

measurement of these two material properties not only improves productivity

but also simplifies interpretation of the results. The complementary information

obtained allows differentiation between endothermic and exothermic events

which have no associated weight loss (e.g., melting and crystallization) and

those which involve a weight loss (e.g., degradation). The factors that influence

the thermogram of a sample fall into two categories:

http://en.wikipedia.org/wiki/Weight

http://en.wikipedia.org/wiki/Temperature

http://en.wikipedia.org/wiki/Precision

http://en.wikipedia.org/wiki/Polymers

http://en.wikipedia.org/wiki/Explosives

http://en.wikipedia.org/wiki/Solvent

http://en.wikipedia.org/wiki/Corrosion

http://en.wikipedia.org/wiki/Kinetics

http://en.wikipedia.org/wiki/High_temperature_oxidation


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(A) Instrumental factors

1. Furnace heating rate

2. Recording or chart speed

3. Furnace atmosphere

4. Geometry of sample holder and furnace

5. Sensitivity of recording mechanism

6. Composition of sample container

(B) Sample characteristics

1. Amount of sample

2. Solubility of evolved gases in sample

3. Particle size

4. Heat of reaction

5. Sample packing

6. Nature of the sample

7. Thermal conductivity

In present investigation, thermogravimetric analysis of the crystals was

carried out in air by heating at a constant rate of 10oC per minute using a

Perkin-Elmer TGA-7DSC-PYRIS-1-DTA-7 thermal analysis system. The

thermograms of crystals are presented in Figure: 5.4 to 5.6. Under the

conditions employed in this analysis, the crystals lost weight gradually during

every phase of the experiment, then the samples underwent an accelerated

weight loss and finally, in the temperature range of about 500-600oC the rate of

weight loss become much more moderate. Thermo gravimetric analysis data of


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the crystals are presented in Table: 5.1. The cumulative weight loses of crystals

at 50oC, 100

oC, 150

oC, 200

oC and 250

oC are presented in Table: 5.2.

The following important observations have been made:

(i) The Schiff base used in this study starts decomposing from 170oC and

its complete decomposition takes place 300oC (Observed by V.D.Patel,

SGVU, Jaipur).

(ii) Decomposition of all crystals starts above 350oC.

(iv) The rate of decomposition of crystals is lower than that of the ligand

suggested that there may be weak intermolecular hydrogen bonding.

(v) The presence of two water molecules is also seen in Fe(III) crystal and

continuous systematic and equivalent loss in weight is observed at above

150oC and between 200 to 250

oC is 12 to 19%. It indicates two water

molecules as coordinated.

(vi) Again presence of water molecules is observed in Cu(II) crystal. These

crystal show loss 5 to 8% equivalent to two water molecules at 100 to

150oC.

(vii) The final product is found to be metal oxide in all the crystals.

Thermo gravimetric analysis shows that all synthesized crystals are

hydrated and have water molecules associated to them. Ni(II) has four

while Fe(III) and Cu(II) has two water molecules as part of their

structure. Loss of this water of hydration is not instant but a continuous

process with sustainability.


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Table 5.1 - Cumulative % Weight Loss Data of Crystals

Crystals

% Weight loss at temperature (oC)

50 100 150 200 250 300 350 400 450 500 550 600

[Fe·L2·2H2O] ·Cl3 0.1 5 9 12 19 26 34 46 52 56 56 56

[Ni·L2]. 4H2O

. Cl2

0.1 9 15 18 23 29 34 39 47 54 56 58

[Cu·L2] . 2H2O·Cl2

0.1 5 8 12 18 23 32 36 38 39 41 42


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Table 5.2 - Cumulative Weight Loss Data of Crystals at 50oC to 250

OC

Crystal

Found

50oC 100

oC 150

oC 200

oC 250

oC

g % g % g % g % g %

[Fe·L2·2H2O]·Cl3

0.67 0.1 33.79 5 60.82 9 81.10 12 97.02 19

[Ni·L2].4H2O

.Cl2

0.678 0.1 61.08 9 101.80 15 122.16 18 156.1 23

[Cu·L2].2H2O·Cl2

0.64 0.1 32.37 5 51.80 8 77.70 12 116.55 18


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Figure 5.4 - Thermogram of [Ni·L2].4H2O

.Cl2 Crystal


~ 134 ~

Figure 5.5 - Thermogram of [Fe·L2·2H2O]·Cl3 Crystal


~ 135 ~

Figure 5.6 - Thermogram of [Cu·L2].2H2O·Cl2 Crystal


~ 136 ~

5.A.5 Activation Energy and Thermodynamic Parameters studies

The Broido method was used to evaluate the kinetic parameters from the

TGAcurves. Plots of ln(ln 1/y) versus 1000/T (where y is the fraction not yet

decomposed) for four stage of the thermal degradation of the complexes are shown

in figure – 5.7 to 5.9 . The slope of the plot ln(ln 1/y) versus 1000/T is related to

the energy of activation as

Ea = –2.303 ×R ×slope

Where, R = gas constant.

The parameters, enthalpy (H#), entropy (S#) and Gibbs energy (G#) of

activation were calculated using the following standard equations

H # = Ea – R Td

S# = H

#/T – 4.576 log T/K’ – 47.22

where K’ = –ln(ln 1/y)

G# = H

# –TS

#

The activation energies of decomposition were the range (15.41-98.57),(15.93-

37.55),and (17.34-67.65) kJ mol−1

in Fe(III), Cu(II) and Ni(II) respectively.The

high values of the activation energies reflect the thermal stability of the

complexes[12-14]

. The entropy of activation (S#) and enthalpies of activation(H

#)

values for four steps of all the complexes are negative. and the negative values of

the entropies of activation are compensated by the values of the enthalpies of

activation leading to almost the same values

(27827-28731 kJ mol–1

) for the free energies of activation(G#). The data were

summarized in Table – 5.3 The entropy of activation had negative values in all the

complexes, which indicates that the decomposition reactions proceed with a lower

rate than normal ones.


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Figure 5.7 - Thermogram of [Fe·L2·2H2O]·Cl3 Crystal


~ 138 ~

Figure 5.8 - Thermogram of [Ni·L2].4H2O

.Cl2 Crystal


~ 139 ~

Figure 5.9 - Thermogram of [Cu·L2].2H2O·Cl2 Crystal


~ 140 ~

Table -5.3 Activation energy and Thermodynamic parameters some metal complexes

complexes stage Temp

range oC

Ea kJ mol-1 (H#) (S

#) (G

#)

[Fe·L2·2H2O]·Cl3

i 60-90 88.95061 -6587.19 -9.93543 -42.0454

ii 90-270 11.40068 -6664.74 -10.0524 -42.1624

iii 270-500 16.70053 -6659.44 -10.0444 -42.1544

[Ni·L2].4H2O

.Cl2

i 60-130 30.86655 -6645.28 -42.0595 28716.94

ii 130-220 15.93904 -6660.2 -42.0814 28731.84

iii 220-490 37.55796 -6638.58 -42.0497 28710.25

iv 490-640 20.33129 -6655.81 -42.075 28727.46

[Cu·L2].2H2O·Cl2

i 60-100 48.44321 -5879.44 -41.4362 27877.8

ii 100-130 98.57009 -5829.31 -41.3617 27827.75

iii 130-370 40.5706 -5887.31 -41.4479 27885.66

iv 370-640 15.41761 -5912.46 -41.4852 27910.78


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PART B: THERMAL CONDUCTIVITY

5.B.1 INTRODUCTION

Thermal conductivity is defined as:

(5.1)

where Q is the amount of heat passing through a cross section, A, and causing a

temperature difference, ΔT, over a distance of ΔL shown fig – 5.10. Q / A is

therefore the heat flux which is causing the thermal gradient, ΔT / ΔL.

The measurement of thermal conductivity, therefore, always involves the

measurement of the heat flux and temperature difference[15]

. The difficulty of the

measurement is always associated with the heat flux measurement. Where the

measurement of the heat flux is done directly (for example, by measuring the

electrical power going into the heater), the measurement is called absolute. Where

the flux measurement is done indirectly (by comparison), the method is called

comparative.

Figure 5.10 - Comparative Heat Flux Measurement


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In addition to these two main methods, other secondary methods usually

transient in nature can also yield thermal conductivity. In all cases, the entire heat

flux must be uniaxial, that is it has to flow through the sample (and the references,

in the comparative case). Thus, the heat losses or heat gains must be minimized in

the radial direction. To some degree, this can be accomplished with packing

insulation around the sample, or, at higher temperatures, where such simple

solutions become inefficient, with installation of a "guard". If the guard is

controlled to have the identical temperature gradient as the sample, then the radial

heat flow will be minimized. The configuration of a given measurement system

and of the specimen itself is influenced most prominently by the magnitude of the

thermal conductivity. When the thermal conductivity is high, the specimens are

usually "long" (for example, in the form of cylinders). When the conductivity is

low, the specimens are usually "flat" (for example, in the form of plates or disks).

Simple thermal considerations indicate why this is so. When the specimen

conductivity is high, the heat flux is usually fairly high so that, relatively speaking,

heat losses from the large lateral surface area of the specimen are small; a long

specimen in the direction of flow helps establish a reasonably high temperature

gradient which can then be accurately measured. When the specimen conductivity

is low and the heat flux correspondingly low, only a relatively small thickness is

required to generate a large, accurately measurable gradient. With this low

specimen heat flux, lateral losses are of concern, thus a plate-type specimen itself

tends to minimize these spurious flows since the lateral surface area is small. As a

matter of fact, in some cases the lateral surfaces of the specimen are surrounded by

pieces of the same specimen material to provide self-guarding. Another

independent parameter of fundamental importance is the magnitude of specimen

conductivity relative to the surroundings. It is generally desired that the specimen

effective conductance be as high as possible relative to that of the surrounding

insulation. This generally becomes more of a problem as the temperature of the

measurement system rises. With some measurement techniques used at very high


~ 143 ~

temperatures, which will be discussed, the lateral losses are allowed to be high, but

they are accounted for quantitatively in the conductivity measurement. The

following section covers the principal methods of measuring this property from

subambient temperatures up to 1500°C on solid materials exhibiting a very wide

range of conductivity. These techniques are axial flow, radial flow, guarded hot

plate, and hot-wire method[16-19]

.

1.) Axial Flow Methods Axial flow methods have been long established and have

produced some of the most consistent, highest accuracy results reported in the

literature. It is the method of choice at cryogenic temperatures. Key measurement

issues center mainly on reduction of radial heat losses in the axial heat flow

developed through the specimen from the electrical heater mounted at one end (the

power dissipation of this heater is used in calculating column heat flux). These

losses are minimal at low temperatures. As the specimen temperature moves above

room temperature, control of heat losses becomes more and more difficult. Thus a

great deal of attention centers on important experimental parameters such as the

ratio of effective specimen conductance to lateral insulation conductance (the

higher the better) and to the quality of guarding (that is the match of the axial

gradient in the specimen to that of the surrounding insulation). In practice only,

cylindrical symmetry heat transfer is used. In addition to guarded and unguarded

solutions, other categories are separated:

a.) Absolute axial heat flow, which is mostly used in subambient environments.

Systems of this nature require very precise knowledge of the electrical power

feeding the heater. Consequently, the losses from the hot heater surfaces also play

a major role.

b.) Comparative cut bar (ASTM E1225 Test Method). This is perhaps the most

widely used method for axial thermal conductivity testing. In this, the principle of

the measurement lies with passing the heat flux through a known sample and an


~ 144 ~

unknown sample and comparing the respective thermal gradients, which will be

inversely proportional to their thermal conductivities. Most commonly, the

unknown is sandwiched between two known samples, "the references", to further

account for minor heat losses that are very difficult to eliminate (Figure 5.11).

Figure 5.11 - Comparative Cut bar

Where KR is the thermal conductivity of the references. From this, the thermal

conductivity of the unknown sample can be calculated as[17]

:

(5.2)

c.) Guarded or unguarded heat flow meter method (ASTM C518, E1530 Test

Methods). Involves the use of a flux gauge. The flux gauge is very similar, in its

purpose, to the references in the comparative cut bar method. In practice, the

reference material has a very low thermal conductivity and, therefore, it can be

made very thin. Usually, a large number of thermocouple pairs are located on both


~ 145 ~

sides of the reference plate, connected differentially to yield directly an electrical

signal proportional to the differential temperature across it[18]

.

(5.3)

The assembly is cast into a protective coating for durability. This type of flux

gauge is mostly used with instruments testing very low thermal conductivity

samples, such as building insulations. In a similar fashion, flux gauges can be

constructed from just about any material, thick or thin, depending on the material’s

thermal conductivity. Common requirements for all flux gauges are that the

material used for the measuring section be stable, not affected by the thermal

cycling, and the gauge be calibrated by some method independently. A very large

variety of testing instruments use this method

2.) Guarded Hot Plate Method (ASTM C 177 Test Method) guarded hot plate is a

widely used and versatile method for measuring the thermal conductivity of

insulations. Although the specimens are often rather large, this usually presents no

difficulty. A flat, electrically heated metering section surrounded on all lateral

sides by a guard heater section controlled through differential thermocouples,

supplies the planar heat source introduced over the hot face of the specimens. The

most common measurement configuration is the conventional, symmetrically

arranged guarded hot plate where the heater assembly is sandwiched between two

specimens (Figure 5.12). In the single sided configuration, the heat flow is passing

through one specimen and the back of the main heater acts as a guard plane

creating an adiabatic environment.


~ 146 ~

Figure 5.12 - Guarded Hot Plate Method

This is an absolute method of measurement and its applicability requires:

(a) the establishment of steady-state conditions, and (b) the measurement of the

unidirectional heat flux in the metered region, the temperatures of the hot and cold

surfaces, the thickness of the specimens and other parameters which may affect

the unidirectional heat flux through the metered area of the specimen. Three

different categories of measurement systems can be distinguished: apparatus

working around room temperatures, apparatus working below room temperatures

(down to about -180°C), and apparatus working at high temperature (600°C or

above). A given apparatus is most often best adopted for measurement in one of

these temperature ranges. Hot wire methods are most commonly used to measure

the thermal conductivity of "refractories" such as insulating bricks and powder or

fibrous materials[16]

. Because it is basically a transient radial flow technique,

isotropic specimens are required. The technique has been used in a more limited

way to measure properties of liquids and plastics materials of relatively low

thermal conductivity.

3.) Relatively recent modification of this long-established technique is the

"probe" method. This configuration is particularly practical where the specimen

conductivity is determined from the response of a "hypodermic needle" probe

inserted in the test specimen. Thus the method is conveniently applied to low-


~ 147 ~

conductivity materials in powder or other semirigid form. A probe device can be

used to measure the thermal properties of soils in situ, but most commonly a

closely controlled furnace is used to contain the sample and produce the base

temperatures for the tests. The probe contains a heater and a thermocouple

attached to it. When a certain amount of current is passed through the heater for a

short period of time, the temperature history of the heater’s surface will take on a

characteristic form. In the initial phase, the temperature will rapidly rise, and as

the heat begins to soak in, the rate of rise becomes constant. When the thermal

front reaches the outer boundary of the sample, the rise will slow down or stop

altogether due to losses into the environment. From the straight portion of the rate

curve (temperature vs. time) the thermal conductivity can be calculated. For

conductivity, there are steady-state methods (up to 1200 K) and pulse methods (in

particular over 1500 K). If the material under test is a conductor the specimen can

be self-heated by passage of an electric current. Measuring diffusivity requires an

accurate recording of the time dependence of temperature following a transient or

periodic temperature perturbation at a specimen boundary. For diffusivity

measurement, transient methods are usually preferred. As a consequence of the

wide ranges of thermal property there is no single method of measurement that can

be used for measurement of either property, in particular thermal conductivity. To

obtain acceptable values for the measured property, the material type and its range

of property value over its operational temperature range will influence particularly

the type of method used and the size and conjunction of the test specimen and

apparatus. In general, thermal conductivity is measured by steady-state techniques

and thermal diffusivity by transient techniques. It is possible to use some of the

latter in a modified way to also measure thermal conductivity. A measurement

method has to be selected depending on the following criteria:

possible sample size and shape

temperature range, which is limited for individual techniques


~ 148 ~

thermal conductivity range, because low conductivity materials like

insulating materials or foams need different methods than for high

conductivity materials such as metals

The information below provides short descriptions of the most commonly used

measurement methods.

5.B.2 Common thermal conductivity or thermal diffusivity measurement methods[20-

22, 27-36]

1. Comparative technique

Short description: A secondary method of thermal conductivity

measurement in which steady-state linear heat flow is established in a stack

consisting of a specimen sandwiched between two references and

surrounded by a cylindrical guard heater.

Material type: all solids

T range in °C: 0 to 1000

Property range in W/(m.K): 0.2 to 200

2. Four-probe technique

Short description : Thermal conductivity is determined from measurement

of the electric resistivity; current and voltage are normally measured with

four probes

Material type: metals and metallic alloys

Temp range in °C: 20 to 1600

Property range in W/(m.K): 10 to 800

3. Guarded heat flow method

Short description : Similar in principle to the heat flow meter method but

used to measure much smaller higher conductivity specimens using

different calibration materials and cylindrical guard around the test stack

Material type: polymers, rocks, ceramics, foods, some metals and alloys


~ 149 ~



4. Guarded hot-plate

Short description: Steady-state linear heat flow established in a large flat

sample (usually in two nominally identical pieces) sandwiched between a

controlled and guarded central hot plate and cold plates operating at a

controlled lower temperature. A well-established absolute technique having

high accuracy, especially at ambient temperatures.

Material type: solid, opaque, homogeneous, composites, insulation

materials

Temp range in °C: -180 to 1000


5. Heat-flow meter method

Short description : A secondary steady-state method using a similar

configuration to the guarded hot plate but normally using one large self-

guarding specimen in conjunction with a heat flux transducer and with the

apparatus calibrated with one or more reference materials or transfer

standards

Material type: insulation materials


Property range in W/(m.K): 0.007 to 1.0

6. Hot-box apparatus, either guarded or calibrated (thermal resistance)

Short description : Not generally used for materials but for measuring the

steady-state thermal transmission properties (U-value) or the thermal

conductance of building envelope components and systems. A large

specimen is placed between a hot and a cold chamber operating at fixed

temperatures, humidity and air flow conditions. A guarded metering box is

attached to the central section of the specimen in the guarded hot box while


~ 150 ~

in the calibrated version a well insulated much larger box is calibrated with

a transfer standard

Material type: systems containing insulation, wood, masonry, glass and

other materials and products used for the building envelope


Property range in W/(m.K): Thermal conductance range of 0.2 to 5

(m²K)/W

7. Hot strip method

Short description : Very similar in principle to the hot wire method but

uses a narrow thin metal foil pressed directly between two specimen pieces

as the power source

Material type: glasses, foods ceramics, etc



8. Hot wire method

Short description : Three forms available, either a single or crossed

resistive wire or two parallel wires a small distance apart. A quasi-steady

state method where the thermal properties are obtained from the

temperature v. time response due to a heat flux generated by the wire

embedded in the specimen. The curve is analysed in accordance with a

model based on a solution of the time-dependent heat equation under a

particular set of boundary conditions. In principle an absolute method

Material type: refractory materials, many solid types including earth

minerals, glasses, plastics granules and, powders, plus fluids and gases

Temp range in °C: --40 to 1600



~ 151 ~

9. Laser flash method

Short description : Thermal diffusivity is determined from an analysis of

the temperature rise v. time response induced by absorption of a pulse of

laser energy

Material type: metals, polymers, ceramics



10. Angstrom method

Short description : A long thin (0.3 - 0.9 mm diameter,100 - 300 mm

long) radiating rod, tube or bar of a good conducting material, assumed to

behave as a semi-infinite medium, is heated at one end by a sinusoidal heat

source with a period of typically 100 to 150 s. Temperature sensors are

attached at two or more positions along the rod axis. Thermal diffusivity is

determined from the resulting velocity and amplitude decrease using one of

a number of solutions to the mathematical model.

Material type: Metals, alloys, graphite, ceramics


Property range in W/(m.K): above 0.5

11. Modified Angstrom method

Short description : The partially masked blackened surface of a thin

rectangular specimen is irradiated by uniform chopped light at fixed

frequencies and the ac temperature excursion on the opposite face

monitored as the specimen is moved in small increments. The in-plane

thermal diffusivity is then determined from the linear amplitude decay and

phase shift curves.

Material type: diamond, metals, semiconductors, ceramics and polymer

multi-layered composites


Property range in W/(m.K): Covers a range of six orders of magnitude


~ 152 ~

12. Modulated beam technique

Short description : Thermal diffusivity is determined from the temperature

modulation induced by absorption of the modulated light beam from a

xenon lamp or other source.

Material type: metals, polymers, ceramics


Property range in W/(m.K): 1 to 500

13. Needle probe

Short description: A modification of the hot wire technique whereby the

heat source and temperature measurement sensor(s) are together sealed into

a long thin tube which is then directly embedded in the specimen or fixed in

grooves cut across the matching surfaces of two specimen pieces. Can be

used for in-situ measurements. Some versions use reference materials for

calibration although in principle the technique is an absolute one.

Material type: soils, minerals, solid and molten polymers and foods,

rubber, particulates, powders



14. Photothermal methods

Short description : Intensity modulated light is directed onto the specimen

surface and the run-time behaviour of the resultant thermal waves is

detected. The amplitude and phase change are evaluated as a function of the

modulation frequency using appropriate models to obtain the thermal

diffusivity or thermal conductivity

Material type: small specimens of most solid material types


Property range in W/(m.K): 0.1 to 200. Methods also very useful in a

qualitative NDT mode


~ 153 ~

5. B.3 HOT WIRE METHODS FOR THE THERMAL CONDUCTIVITY

MEASUREMENT

5.B.3.1 Description of the method

The hot wire method is a standard transient dynamic technique based on the

measurement of the temperature rise in a defined distance from a linear heat

source (hot wire) embedded in the test material. If the heat source is assumed to

have a constant and uniform output along the length of test sample, the thermal

conductivity can be derived directly from the resulting change in the temperature

over a known time interval [21]

. The hot wire probe method utilizes the principle of

the transient hot wire method. Here the heating wire as well as the temperature

sensor (thermocouple) is encapsulated in a probe that electrically insulates the hot

wire and the temperature sensor from the test material[22]

. The ideal mathematical

model of the method is based on the assumption that the hot wire is an ideal,

infinite thin and long line heat source, which is in an infinite surrounding from

homogeneous and isotropic material with constant initial temperature. If q is the

constant quantity of heat production per unit time and per unit length of the

heating wire (W.m-1

), initiated at the time t=0, the radial heat flow around the wire

occurs. Then the temperature rise T(r,t) at radial position r from the heat source

conforms to the simplified formula

Cr

at

k

qtrT

2

4ln

4),(

(5.4)

where k is the thermal conductivity (W.m-1

.K-1

), a thermal diffusivity (m2.s

-1)

(a=k/cp, with is the density (kg.m-3

) and cp the heat capacity (J.kg-1

.K-1

) of the

test material and C=exp(), =0,5772157 is the Euler’s constant.


~ 154 ~

Figure 5.10 - Schematic view of the sample

The equation (1) is valid only when r2/4at<<1 is fulfilled, i.e. for a sufficiently

long time t larger than certain minimum time tmin and for a small distance r. Thus

the measurement of temperature rise T(r,t) as a function of time is be employed

to determine of the thermal conductivity k, calculating of the slope K of the linear

portion of temperature rise T(r,t) vs. natural logarithm of the time (lnt) evolution

from

K

qk

4 (5.5)

The hot wire temperature rise reaches usually up to 10ºC and its time evolution

has typically the form as shown in the Fig. 5.11.

Figure 5.11 - Typical temperature rise curve (a - ideal, b – non-ideal case)


~ 155 ~

The hot wire method can be applied in several experimental modifications.

In the standard cross technique the wire cross is embedded in ground grooves

between two equally sized specimens. The cross consists of a heating wire and the

legs of a thermocouple, which acts as the temperature sensor. The hot spot of the

thermocouple is in direct contact with the heating wire. In the resistance technique

the heating wire acts also as the temperature sensor. Here the temperature is

measured by the change in resistance caused by the heating-up of the hot wire. In

the measurement of electrically conducting materials the heating wire and

thermocouple wires, or potential leads, are insulated from the sample. This is done

either by making of a non-conducting coating on the wires, or to enclose the heater

and temperature sensor in a thin sheath or needle probe, which is inserted into the

test material, respectively. The second approach is called as the hot-wire-probe

method.

5.B.3.2 Experimental apparatus

The home-made computer controlled hot wire apparatus allows the

determination of thermal conductivity of solids, powders, sands and granular

materials.. Three measuring techniques are there available: standard cross wire

technique, resistance - potential lead method, that is based on the four point

principle and the probe modification of the hot wire method. In the cross wire

technique the platinum (Heraeus) or kanthal (Bulten Kanthal AB) wires, with

various diameter (0,1 – 0,4 mm), depending on the measured material and the

measurement temperature act as the linear heat source. The temperature rise vs.

time evolution is measured by the spot welded K type thermocouple, made from

Ni-NiCr wires (Heraeus), or S type – Pt/PtRh 90/10% (Heraeus). The hot spot of

the thermocouple is in direct contact with the heating wire and is placed in the

center of sample. The reference junction is immersed in the Dewar cup at 0°C. In

the resistance technique the platinum wire acts as the heating wire as well as the

temperature sensor. Potential leads consist of thin platinum wires, fixed to the


~ 156 ~

heating wire at about 1,5 cm from the end of the sample. The probe method uses

home-made cylindrical probe original construction, consisting of the heating wire

and the temperature sensor, both placed in the ceramic microcapilar (Degussa).

The apparatus currently allows performing in-situ measurements of solid materials

in the temperature range 20 – 1200 ºC. Details concerning the apparatus can be

find in[43]

Figure 5.12 - Typical experimental temperature rise vs. time evolution.

5.B.3.3 Sample sizes

The solid samples consist either of two cuboids, or of two cylinder halves,

respectively. They dimensions are up to 10x10x5 mm or the cylinder should be up

to 10 mm in diameter with length 100 mm, all depending on the thermal

diffusivity of the measured material. The sand, powder and granular materials are

usually put into cube container of 10x10x10 mm. A transient short hot wire

technique (SHWT) is developed for simultaneous determination of the thermal

conductivity and thermal diffusivity of various materials such as liquids, gases or

powders. A metal wire with (or without) insulation coating serves both as a

heating unit and as an electrical resistance thermometer and the wire is calibrated

using water and toluene with known thermo physical properties. This SHWT

includes correlation of the experimental data with numerically simulated values


~ 157 ~

based on a two-dimensional heat-conduction model. For the measurements with

proportional relation between temperature rise and logarithmic heating time

interval, the thermal conductivity and thermal diffusivity are obtained from the

slope and the intercept of the measured temperature rise and those of calculated

non-dimensional temperature rise by including the heat flux and the properties of

the wire. For the measurements with nonlinear relation between temperature rise

and logarithmic heating time interval, the thermal conductivity and thermal

diffusivity are extracted from a curve fitting method by using the downhill simplex

method to match the experimental data and the numerical values. This technique is

applied here using air as a testing sample. The effect of natural convection is

investigated and the accuracy of this measurement is estimated to be 2% for

thermal conductivity and 7% for thermal diffusivity[24]

. The theory of the transient

hot-wires technique for thermal conductivity measurements is reassessed in the

special context of thermal diffusivity measurements. A careful examination of the

working equation and an error analysis are employed to identify the principal

sources of error. Notwithstanding earlier claims to the contrary, the best precision

that can be attained in thermal diffusivity measurements is of the order of ±3%,

while the accuracy is inevitably poorer. Experimental evidence is adduced from

two different instruments that support the analysis given here. Although the

technique cannot yield values of the thermal diffusivity, k, as accurate as can be

achieved by the use of the best possible individual values of , , and C p in the

relation k= /C p, the simplicity of the technique makes it attractive for many

purposes. It is even possible to derive values of the isobaric heat capacity C p for

many fluids not available from other methods[25]

. A hot wire should be put in the

interfacial space between couples of solid materials. The clearance at the interface

becomes the third phase which is not considered in the theory of hot wire method,

and would cause some errors in the measurement of thermal conductivity. This

paper gives solutions to a heat conduction problem of solids with a thin interfacial


~ 158 ~

clearance, with the aid of heat source theory, and with the aid of numerical

calculation. It is found and experimentally proved that the temperature increase

rate develops slowly on account of the existence of the clearance but it reaches

finally the rate which indicates the right thermal conductivity of solid material.

Some means to make the temperature development fast are discussed[26]

.

5.B.4 EXPERIMENTAL

Thermal Conductivity of All the materials were measured at Laljibhai Chaturbhai

Institute of Technology, Gujarat. Thermal conductivity measured in powder form with

hot-wire method with presision measurement. The meaurment was done at equal interval

of 5K.

Figure 5.13 - Quick Thermal Conductivity Meter

Model No. : QTM-500

Brand Name: KEM

Country: Japan


~ 159 ~

Specification:

Thermal conductivity of all types of sample materials can be measured quickly

and easily. Just place the probe on sample surface of temperature equilibrium and wait

for 60 seconds. You will obtain the results. For thin sample materials like film (30 -

100µm), sheet or board (0.1 - 8mm), use the optional software for measurement of thin

films

Measurement method Hot Wire Method

Range 0.023 - 12W/m • K (standard probe)

Precision ±5%/reading value per reference plate

Reproducibility ±3%/reading value per reference plate

5.B.5 RESULT AND DISCUSSION

The thermal conductivity of all crystals was measured using Hot Wire Method

and measured on Quick Thermal Conductivity Meter. Thermal conductivity of all crystals

measured between 283K to 373K with equal interval of 5K. Thermal conductivity

increased as temperature increased in all the crystals which indicate that all the crystals

are good conductor of heat. In Fe(III) Crystal a thermal conductivity increased

continuously up to 363K and then become constant. The rate of increased in thermal

conductivity of Fe(III) Crystal is higher and it is near about metal. This is observed

because crystal synthesized by metal of Fe(III). The maximum value of thermal

conductivity observed in this work was 0.828 W/cmK. The tabulation and graphical

result shown in Table –5.3 and Figure 5.14 respectively. In Ni(II) Crystal a thermal

conductivity increased continuously but the rate of change observed very lower than the

Fe(III) crystal. The maximum value of thermal conductivity of Ni(II) Crystal was

observed in this work is 0.8161 W/cmK. The tabulation and graphical result shown in

Table – 5.3 and Figure 5.15 respectively. In Cu(II) Crystal a thermal conductivity

increased continuously but the rate of change observed very lower than the Fe(III) crystal

and similar to the Ni(II) crystal. The maximum value of thermal conductivity of Cu(II)

Crystal was observed in this work is 3.0314W/cmK. The tabulation and graphical result


~ 160 ~

shown in Table – 5.3 and Figure 5.16 respectively. The rate of change in thermal

conductivity is higher in Fe(III) crystal and lower in Ni(II) crystal and Cu(II) crystal

because of in Fe(III) crystal a composition of metal is higher than the Ni(II) crystal and

Cu(II) crystal


~ 161 ~

Table 5.3 - Thermal Conductivity of Crystals

Temperature

in C

Temperature

in K

Thermal Conductivity of Crystal

in W/cmK

[Fe·L2·2H2O] ·Cl3 [Ni·L2] ·4H2O Cl2 [Cu·L2] ·2H2O·Cl2

10 283 0.672 0.8005 3.0235

15 288 0.682 0.8015 3.024

20 293 0.692 0.8025 3.0245

25 298 0.702 0.8035 3.025

30 303 0.712 0.8045 3.0255

35 308 0.722 0.8055 3.026

40 313 0.732 0.8065 3.0265

45 318 0.742 0.8075 3.027

50 323 0.752 0.8085 3.0275

55 328 0.762 0.8095 3.028

60 333 0.772 0.8105 3.0285

65 338 0.782 0.8115 3.029

70 343 0.792 0.8125 3.0295

75 348 0.802 0.8135 3.03

80 353 0.812 0.8145 3.0305

85 358 0.822 0.8155 3.031

90 363 0.825 0.816 3.0312

95 368 0.827 0.8163 3.0313

100 373 0.828 0.8161 3.0314


~ 162 ~

Figure 5.14 – Thermal conductivity of [Fe·L2·2H2O] ·Cl3 crystal


~ 163 ~

Figure 5.15 – Thermal conductivity of [Ni·L2] ·4H2O Cl2 crystal


~ 164 ~

Figure 5.16 – Thermal conductivity of [Cu·L2] ·2H2O·Cl2 crystal


~ 165 ~

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KRP Chapter 5 - Information and Library Network Centreshodhganga.inflibnet.ac.in/bitstream/10603/10158/18/18_chapter 5.pdf · A sample of liquid metal is removed from the furnace