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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
Chapter 5 Thermal study of the crystal
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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
Chapter 5 Thermal study of the crystal
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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
Chapter 5 Thermal study of the crystal
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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
Chapter 5 Thermal study of the crystal
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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
Chapter 5 Thermal study of the crystal
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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].
Chapter 5 Thermal study of the crystal
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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
Chapter 5 Thermal study of the crystal
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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].
Chapter 5 Thermal study of the crystal
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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.
Chapter 5 Thermal study of the crystal
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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.
Chapter 5 Thermal study of the crystal
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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:
Chapter 5 Thermal study of the crystal
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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
Chapter 5 Thermal study of the crystal
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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.
Chapter 5 Thermal study of the crystal
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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
Chapter 5 Thermal study of the crystal
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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
Chapter 5 Thermal study of the crystal
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Figure 5.4 - Thermogram of [Ni·L2].4H2O
.Cl2 Crystal
Chapter 5 Thermal study of the crystal
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Figure 5.5 - Thermogram of [Fe·L2·2H2O]·Cl3 Crystal
Chapter 5 Thermal study of the crystal
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Figure 5.6 - Thermogram of [Cu·L2].2H2O·Cl2 Crystal
Chapter 5 Thermal study of the crystal
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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.
Chapter 5 Thermal study of the crystal
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Figure 5.7 - Thermogram of [Fe·L2·2H2O]·Cl3 Crystal
Chapter 5 Thermal study of the crystal
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Figure 5.8 - Thermogram of [Ni·L2].4H2O
.Cl2 Crystal
Chapter 5 Thermal study of the crystal
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Figure 5.9 - Thermogram of [Cu·L2].2H2O·Cl2 Crystal
Chapter 5 Thermal study of the crystal
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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
Chapter 5 Thermal study of the crystal
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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
Chapter 5 Thermal study of the crystal
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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
Chapter 5 Thermal study of the crystal
~ 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
Chapter 5 Thermal study of the crystal
~ 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
Chapter 5 Thermal study of the crystal
~ 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.
Chapter 5 Thermal study of the crystal
~ 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-
Chapter 5 Thermal study of the crystal
~ 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
Chapter 5 Thermal study of the crystal
~ 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
Chapter 5 Thermal study of the crystal
~ 149 ~
Temp range in °C: 100 to 300
Property range in W/(m.K): 0.2 to 20
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
Property range in W/(m.K): 0.0001 to 2
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
Temp range in °C: -100 to 200
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
Chapter 5 Thermal study of the crystal
~ 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
Temp range in °C: -20 to 40
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
Temp range in °C: -50 to 500
Property range in W/(m.K): 0.1 to 5
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
Property range in W/(m.K): 0.001 to 20
Chapter 5 Thermal study of the crystal
~ 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
Temp range in °C: -100 to 3000
Property range in W/(m.K): 0.1 to 1500
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
Temp range in °C: -25 to 1300
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
Temp range in °C: -100 to 500
Property range in W/(m.K): Covers a range of six orders of magnitude
Chapter 5 Thermal study of the crystal
~ 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
Temp range in °C: 300 to 2000
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
Temp range in °C: -50 to 500
Property range in W/(m.K): 0.05 to 20
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
Temp range in °C: -50 to 500
Property range in W/(m.K): 0.1 to 200. Methods also very useful in a
qualitative NDT mode
Chapter 5 Thermal study of the crystal
~ 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.
Chapter 5 Thermal study of the crystal
~ 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)
Chapter 5 Thermal study of the crystal
~ 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
Chapter 5 Thermal study of the crystal
~ 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
Chapter 5 Thermal study of the crystal
~ 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
Chapter 5 Thermal study of the crystal
~ 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
Chapter 5 Thermal study of the crystal
~ 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
Chapter 5 Thermal study of the crystal
~ 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
Chapter 5 Thermal study of the 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
Chapter 5 Thermal study of the crystal
~ 162 ~
Figure 5.14 – Thermal conductivity of [Fe·L2·2H2O] ·Cl3 crystal
Chapter 5 Thermal study of the crystal
~ 163 ~
Figure 5.15 – Thermal conductivity of [Ni·L2] ·4H2O Cl2 crystal
Chapter 5 Thermal study of the crystal
~ 164 ~
Figure 5.16 – Thermal conductivity of [Cu·L2] ·2H2O·Cl2 crystal
Chapter 5 Thermal study of the crystal
~ 165 ~
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Chapter 5 Thermal study of the crystal
~ 166 ~
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Chapter 5 Thermal study of the crystal
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