Chapter - 1
Introduction
Introduction
1.1 Thermal Decomposition
A crystalline solid substance is an ordered arrangement of the constituent atoms,
molecules or ions. The bonding forces amongst the constituent units in the crystalline
solid substances form perfectly ordered three dimensional structural arrangements [1-4].
The crystalline solids are classified according to the dominant bonding forces between
the constituents in the crystal as molecular, covalent, ionic or metallic crystals. When a
solid substance is heated, the thermal energy increases the amplitude of the vibration of
the lattice constituents [5-7]. At relatively higher temperature, the solid substances
undergo various transformations such as phase transition, melting, sublimation, thermal
decomposition, etc. [5-8]. Thermal decomposition is a process which occurs when the
bonding forces within the constituent molecules or ions are weaker than those of the
constituting atomic units. In presence of sufficient thermal energy, the bonds of the
constituting atoms of the solid substance (i.e. reactant) are redistributed to produce the
product(s) which is (are) chemically different from the reactant(s) [8-10]. For example,
calcium carbonate decomposes into calcium oxide and carbon dioxide when heated:
CaCO3 → CaO + CO2. Thermal decomposition reaction is usually endothermic as heat
is required to break chemical bonds in the compound. If decomposition is sufficiently
exothermic, reactions can lead to self-sustaining combustion producing thermal
runaway and possibly an explosion [9, 10].
1.1.1 Thermal Decomposition as a Synthetic Route for Metal
Oxides
Metal oxides have been the subject of intense scientific and technological
research for many years because their unique characteristics make them the most
diverse class of materials with properties covering almost all aspects of solid state
physics and materials science [11, 12]. Indeed, the crystal chemistry of metal oxides,
i.e., the nature of the bonding varies from highly ionic to covalent or metallic [13].
They exhibit fascinating optical, electrical and magnetic properties [14]. In other words,
they show metallic, insulating or semiconducting and ferro-, ferri-or antiferromagnetic
behavior [15] combined with their overall characteristics of hardness, thermal stability
and chemical resistance [14, 16]. Some oxides possess ferroelectric or piezoelectric
properties [17], some others exhibit superconducting properties [18, 19], or colossal
2
Introduction
magnetoresistance [20]. Moreover, metal oxides are essential constituents in
technological applications such as catalysis [21], magnetic storage [22 - 24], gas
sensing [25] and energy conversion [26] to name only a few. Mixed metallic oxides are
designated as an important class of compounds and among them ferrites [27] are most
prominent by virtue of their special characteristics, such as, high electrical resistivity
[16],
thermodynamic
stability
[16],
electro-catalytic
activity
[21],
superior
magnetization properties [15, 16], lower cost and easier manufacture.
The oxides are commonly prepared by the thermal decomposition of precursor
compounds containing the desired metal ion in air or oxygen [7, 8, 16]. In addition,
various physical and chemical synthetic approaches have been developed for the
processing of metal oxide micro- or nanoparticles [14, 16, 21, 28, 29], which include
dividing a bulk solid through mechanical abrasion (crushing), electrical or thermal
erosion (laser ablation) or vapor-phase oxidation [30], thermal vapor transport and
condensing [31, 32] ions or molecules. Precipitation and co-precipitation of ions from
solutions have been used for many years in most industrial productions in fine powders
for ceramics or catalyst supports. However, most of these approaches must be
performed at relatively high temperature (500–1500 oC) to grow crystalline particles
[28]. In case of thermal decomposition process for preparing metal oxide(s), preference
is generally given to precursor compounds that decompose at low temperatures to
minimize sintering of the resulting oxide and have minimum interfering side reactions
or by-products (volatile compounds)
[16]. Carbonates, bicarbonates, hydroxides,
nitrates and oxalates are usually preferred for this reason [21, 33-35]. The
decomposition may also be carried out in vacuum to lower the decomposition
temperatures.
Among different synthetic routes the preparation of metal or mixed-metal
oxides, thermal decomposition of metal-organic complexes at relatively low
temperatures becomes increasingly important mainly due to the easy control of process
conditions, purity, phase, composition, microstructure, etc. of the resultant products [16,
21, 33-35].
3
Introduction
1.1.2 Thermal Decomposition of Oxalate-based Compounds
Leading to Metal Oxides
The judicious choice of ligand plays an important role in thermal decomposition
of metal-organic precursor compounds. For oxide synthesis, the ligand should be a
facile atomic source of oxygen and should decompose cleanly with minimum
interfering side reactions or by-products [36, 37]. Oxalate [(C2O4)2-] is a good ligand,
and can be coordinated with many transition and non-transition metals [36-38]. As a
bidentate ligand, oxalate has been of great interest in material science especially, in
coordination chemistry [36, 37]. The coordinative versatility of the oxalate ligand is
valuable as it can stabilize metal centres of different and diverse coordination
geometries. It is also a simple and useful means to bring together metals that would be
otherwise incompatible. The salts of the simple oxalates show that the oxalate ion can
be combined with a single metal ion or with more than one [36]. There are also more
complex oxalates where other organic radicals can be incorporated into the structure
[37- 39].
The thermal decomposition of oxalate ligand based compounds is relatively
complicated due to their reduction property and variable coordination modes to stabilize
a broad variety of complexes [36, 37]. The thermal decomposition of metal oxalates
strongly depends on the reducible property of the metallic cation involved [38]. The
morphology of the crystal, mainly shape, size, the presence of defects and prehistory
treatments take important role in the decomposition process of these materials [38, 39].
Nevertheless, the major advantage of selection of such ligand based complexes to the
synthesis of mono/bimetallic oxides are (i) availability of a wide range of metals, (ii)
presence of atomic source of oxygen, (iii) elimination of volatile gaseous products in
the decomposition process which oppose the formation of large complex oxide
particles, and (iv) quite easy and economic synthesis of the precursor materials [38, 39].
For these reasons, thermal decomposition of the complexes with oxalate ligand serves
as a wide and convenient source of oxide with controlled stoichiometry, high
homogeneity and reduced particle size and is of great importance to the scientific
community of material science [37-39].
The first work on the thermal decomposition of oxalate based material, PbC 2O4
leading to the formation of lead oxide was reported in 1870 [40]. Boldyrev et al.
proposed three possible decomposition schemes for simple bivalent metal oxalates,
4
Introduction
MC2O4 (M = bivalent metal) where most of these oxalates with the metal ion and the
oxalate ion exist as separate entities in the solid lattice as [41]
MCO3 + CO
MC2O4 
MO + CO + CO2
M + 2CO2
Such types of decomposition originate from breakdown of the oxalate anion due to
bond rupture: (C2O4)2- = 2CO2-. This intermediate is converted to the carbonate (due to
carbonylcarbonate intermediate) or to CO2 (by electron transfer):
2CO2-  [OCOCO2]-  CO32- + CO  O2- + CO + CO2
Or
CO2-  CO2 +2eand
M2+ + 2e-  M.
According to the said mechanism, the primary decomposition product(s) of simple
oxalates differs from material to material. Oxides are reported as main product in case
of thermal decomposition of silver, magnesium, aluminum, chromium(III), iron(III) and
zinc oxalate [38, 39]. Cobalt, nickel, cadmium, tin and lead oxalate are decomposed to
their individual metal, whereas the decomposition of lithium, sodium, calcium,
strontium, and barium oxalate results in carbonate [38, 39]. The oxalates of antimony
and bismuth give a mixture of metal and oxide [39]. The occurrence of carbon in the
solid product residues was reported particularly for the rare earth oxalates by Gallagher
[42]. Praseodymium oxalate hydrate is an example where carbon may be found in the
solid residual product. Gallagher studied the thermal decomposition of rare-earth
hexacyanocobaltates [42]. Rare-earth trioxalatocobaltates are promising precursors for
the low-temperature production of rare-earth cobaltites [42, 43].
There are three probable reaction schemes for the oxalates of trivalent metal
ions [39, 41]. Out of these three, two are analogous to the decomposition schemes for
the divalent metal oxalate, with a third to yield the trivalent oxide M2O3. These are
2MO +4CO2 + 2CO
M2(C2O4)3 
2M + 6CO2
M2O3 +3CO2 + 3CO
5
Introduction
In case of thermal decomposition of oxalate based material with crystalline
water, first of all the water molecules are dehydrated with increase of temperature and
dehydrated product may be amorphous or crystalline depending upon the vapour
pressure of the water vapour [39]. One can represent the decomposition for the low
pressure system as
MC2O4.xH2O  (MC2O4) amorphous + xH2O.
At high vapour pressures it can be written as
MC2O4.xH2O  (MC2O4) crystalline+ xH2O.
where MC2O4 represents the dehydrated product which may be amorphous or
crystalline and x is the number of crystalline water molecules. As temperature increases
the dehydrated product undergoes through several decomposition processes depending
on the materials [39].
The thermal dehydration and decomposition of CaC2O4.H2O has been rigorously
investigated and this substance has been used as a thermal analyses reference material
[44-47]. During the thermal decomposition of CaC2O4.H2O, there are three reaction
steps visible at increased temperature and corresponding to the dissociation of H 2O, CO
and CO2, respectively.
Step-I: CaC2O4.H2O (s) CaC2O4 (s) + H2O (g)
Step-II: CaC2O4 (s) CaCO3 (s) + CO (g)
Step-III: CaCO3 (s) CaO (s) +CO2 (g)
where ‘g’ and ‘s’ stands for gas and solid, respectively. However, the thermal
decomposition of ZnC2O4.2H2O and NiC2O4.2H2O takes place in two steps only. Zinc
oxalate di-hydrate decomposes in the following steps [39]:
Step-I: ZnC2O4.2H2O ZnC2O4 (s) + 2H2O
Step-II: ZnC2O4ZnO (s) + CO (g) + CO2 (g),
whereas nickel oxalate di-hydrate follows the decomposition route as [39]
Step-I: NiC2O4.2H2O NiC2O4 (s) + 2H2O
Step-II: NiC2O4Ni (s) + 2CO2 (g).
Noticeably, the thermal decomposition of CaC2O4.H2O and ZnC2O4.2H2O leads
to CaO and ZnO residue, respectively, whereas that of NiC 2O4.2H2O results in metallic
Ni as the solid final product. Al2O3, Cr2O3 and Fe2O3 are reported as the decomposed
residual products in case of the thermal decomposition of Al2(C2O4)3.4H2O,
6
Introduction
Cr2(C2O4)3.6H2O and Fe2(C2O4)3.5H2O, respectively [39]. The thermal decompositions
of oxalate based complexes of type K3[M(C2O4)3].3H2O (where M = Co, Cr, Fe, Ga,
Al) and K2[M(C2O4)2].2H2O (where M = Cu, Zn, Pd) were also studied by different
workers [48-57]. Nagase studied the potassium oxaloto metallates (III) of the type
K3[M(C2O4)3].xH2O (where M = Al, V, Cr, Mn, Rh, Co) [51]. Deb et al. investigated
the thermal decomposition of the compounds of type M[M(C2O4)2].xH2O (where M =
same metal; with CoII, CdII, CrIII, SbIII, and LaIII) and found the different intermediates
and end products in different atmosphere [53]. The generation of mixed metal oxides of
type M1M2Ox (where M1 and M2 are two different metal and x = 2 or 3) were observed
and reported as main product in case of the solid state pyrolytic decomposition of
bimetallic
oxalate
Cu[Co(C2O4)2].3H2O,
precursors
Mn[Co(C2O4)2].3.5H2O,
Cd[Co(C2O4)2].5H2O,
Fe[Co(C2O4)2].5H2O,
Ca[Co(C2O4)2].3.5H2O,
Sr[Co(C2O4)2].5H2O and Ba[Co(C2O4)2].8H2O [58, 59]. The thermal decomposition of
the compounds Ag2M(C2O4)2.nH2O (M = Co, Ni, Cu or Zn) in dynamic air and N2 flow
has been investigated and mixed oxide was reported as decomposed product [60].
Randhawa et al. reported the thermolysis of alkali tris(oxalate/malonato) ferrates(III)
[61-64]. Thermal decomposition of metal ferricarboxylate precursors was extensively
studied in their works to prepare oxide/ ferrite nanoparticles with controlled
stoichiometry, high homogeneity and reduced particle size. There are several reviews
on the chemistry of the metal oxalato complexes where the decomposition process is
well documented and oxides are reported as decomposed residual products by
numerous workers [38, 39, 65, 66]. Recently, the review of Ahmad and his co-workers
[67] discusses the synthesis of transition metal (Cu, Ni, Mn, Co and Fe) and Zn oxalate
nanorods by the reverse micelles route. The thermal decomposition of these transition
metal oxalates at low temperatures (~450–500
o
C) yields homogenous oxide
nanoparticles [67].
The reaction environment plays an important role during the course of oxalate
decomposition [5, 8]. The most obvious change by the environment is said to have
taken place when the actual product becomes different due to the influence of the
surrounding gas atmosphere. A few examples regarding this point may be mentioned:
the decomposition of manganese oxalate yields a series of different oxide products
depending on experimental conditions [68]. The product in vacuum, nitrogen or any
other inert gas is the green oxide, MnO, whereas the product in oxygen is one of the
other manganese oxides, MnO2, Mn2O3 or Mn3O4, recognized by their black or
7
Introduction
brownish-black color; the exact nature of this product depends on indigenous conditions
adjacent to the decomposing sample. In case of nickel oxalate dihydrate, the metallic
nickel is reported as residual product in nitrogen atmosphere, whereas the metal is
oxidized to nickel oxide in air [69]. Praseodymium oxalate hydrate is an example
where carbon may be found in the solid residual products. The main decomposition
route can be written as
Pr2(C2O4)3.10H2O  Pr2(C2O4)3  Pr2O(CO3)2  Pr2O2CO3
yielding Pr7O12 in a helium/oxygen mixture, Pr2O3 in helium and in carbon dioxide. The
formation of carbon is recognized to the direct decomposition of Pr2O(CO3)2 to the
oxide and carbon dioxide [70]. It may be noted that this is not necessarily a main
stoichiometric reaction but possibly only a side reaction. Thorium oxalate also
decomposes to an oxide plus a carbon [71]. Zhou et al. [72] has synthesized three most
common iron oxides by decomposing a precursor, FeC2O4.2H2O at relatively low
temperature. For the synthesis of γ -Fe2O3, the precursor was heated to 400 oC for 2h at
the heating rate of 2 oC min-1 under nitrogen atmosphere, while in air, with the other
conditions unchanged, α-Fe2O3 was obtained. Besides, in order to get Fe3O4, a 10 mg
amount of the FeC2O4.2H2O was sealed in a quart tube with 4 ml of air. Then, the tube
was heated to 400 oC for 2 h at a heating rate of 2 oC min-1. Finally, the black Fe3O4
powder was obtained [72].
There is another environmental effect which cannot be ignored sometimes,
namely the shape and size of the container crucible and the material with which it was
constructed. Simons and Newkirk [73] documented very clearly that the factors
affecting decomposition are sample size, heating rate, the atmosphere and container
geometry, and this has been confirmed several times on a variety of systems and
samples.
Thus, the thermal decomposition of oxalate ligand based metallic compounds
leads to numerous numbers of metal oxides and this is why the decomposition study
serves as the most useful tool to get insight into the mechanism of solid-state
decomposition of oxalate based materials leading to metal oxides.
8
Introduction
1.2 Thermal Decomposition Kinetics
Study of reaction kinetics of a solid state thermal decomposition describes the
movement of the molecules specially when they collide and get transformed into new
species [8, 9]. The study of reaction kinetics to describe the process of transformation
from reactant(s) to products was started in the early 20th century [74, 75]. It includes the
investigations of how different experimental conditions can influence the speed of a
chemical reaction and yield information about the reaction mechanism and transition
states. The kinetic study also deals with measurement and parameterization of the
process rates, and becomes very useful in construction of mathematical models that can
describe the characteristics of a chemical reaction. There are two principle objectives in
studying the kinetics of a chemical reaction: a) one is the determination of the rate
equation that satisfactorily describes the extent of conversion of reactant(s) or formation
of products with time as the reaction proceeds and b) to determine the influence of
temperature on the rate of reaction [76, 77]. The earliest kinetics studies were
performed under isothermal (i.e. at constant temperature) conditions. The nonisothermal methods were not used for kinetic evaluation until 1930s [78]. Therefore, the
concepts of solid state kinetics were established on the basis of experiments carried out
under the isothermal conditions.
In the isothermal kinetic study, rates of the reaction are measured at several
different constant temperatures to obtain the Arrhenius parameters (i.e. activation
energy and frequency factor). The kinetic analysis for the thermal decompositions and
other reactions of solids using isothermal methods are all based on the initial
assumption that a single conversion function and a single set of Arrhenius parameters
apply over the full range of α [76, 77]. This procedure requires the measurement of a set
of (extent of conversion (α), time (t)) values for the reaction selected for analysis at a
known and constant temperature (T). These data are then tested for accuracy of fit to the
equations listed in Table 1.1 to identify which expression represents most precisely the
systematic changes of α with time. Thus, the model so selected may describe the way in
which the reactant/product interface develops geometrically during the reaction. The
kinetic analysis of data from isothermal experiments [9, 76, 77] includes –
(i) examination of the linearity of plots of reaction mechanism, g(α) against time, t
(ii) comparison of plots of α against reduced-time with curves calculated from the rate
determining equations in Table 1.1. Reduced-time, tred is a dimensionless quantity
9
Introduction
obtained by scaling the measured time values, t appropriately to give common point on
all curves, in general t0.5 = 1.0 for α = 0.5 and tred = t/t0.5, (iii) comparison of plots of
measured (dα/dt) values against reduced-time or α with curves given by the rate
determining equations in Table 1.1 and (iv) examination of the linearity of plots of
measured (dα/dt) values against f(α) (from Table 1.1). The expression which gives the
best fit to the α-time data is often independent of temperature, while the magnitudes of
the rate constants increase with temperature [9, 76, 77].
In the field of thermal analysis, nowadays much attention has been directed
towards the problem of obtaining kinetic information from programmed temperature,
dynamic or non-isothermal experiments. These experiments usually involve
measurement of some quantity (for example mass, heat evolved, etc.), which can be
related directly to the extent of reaction at a series of different, usually constant, heating
rates [9]. The non-isothermal technique for kinetic evaluation was accepted after the
pioneering work of Flynn on non-isothermal kinetics [79]. The vast development of the
field of non-isothermal kinetics began in the late 1950s when the thermal analysis
instruments became commercially available and computational difficulties associated
with the kinetic analysis were resolved progressively [80, 81]. The practical advantage
of non-isothermal experiments over isothermal experiments is that non-isothermal
heating resolves a major problem of the isothermal experiments in which a sample
requires some time to reach the experimental temperature and by that time some
transformations are likely to affect the results of the kinetic analysis [80]. In fact, this
problem restricts someone to the use of high temperatures during an isothermal
experiment. In addition, since a single non-isothermal experiment contains information
on the temperature dependence of reaction rate, it was widely believed and accepted
that such an experiment would be sufficient to evaluate kinetic parameters [9].
The majority of kinetic methods deal with the measurement of the extent of
reaction (α) either as a function of time (t) at constant temperature, or as a function of
temperature (T) which increases according to some heating programme, (usually linear),
β
dT
. In the isothermal method, α vs. t, corresponds to the conventional curve of
dt
concentration against t, while in case of non-isothermal method measurement of α vs. T
is the basis of thermal analysis [9]. In order to study the kinetics of solid state reaction,
considering the reaction rate to be a function of only two variables, namely, the extent
10
Introduction
of reaction (α) and temperature (T), the most commonly used kinetic equation is given
as [81]
dα
 k(T)f(α)
dt
where α( 
(1.1)
mi  m t
) is the extent of reaction, i.e. the fraction of material reacted in
mi  m f
time t, with mi is the initial mass, mf the final mass, mt the mass at any instant of
reaction, k(T) the temperature-dependent Arrhenius rate constant, T the temperature in
absolute scale and f(α) is the differential conversion function depending on the
mechanism of a kinetic reaction [80-82]. The temperature-dependent Arrhenius
equation [83] in solid state transformation is typically written as
 E 
k  T   A exp  

 RT 
(1.2)
where E is the activation energy (kJ mol-1), A the frequency factor (s-1) and R is the
universal gas constant (kJ mol-1 K-1), respectively. Combining Eqn. 1.1 and 1.2 one can
get
dα
 E 
 A exp  
 f  α
dt
 RT 
(1.3).
As discussed earlier, the temperature program controlled by thermal analysis
instruments, can be isothermal (i.e. T = const.) or non-isothermal in which the
temperature varies linearly with time i.e. T = T(t) so that the linear heating
rate β 
dT
= constant, and Vallet [78] suggested the replacement of the temporal
dt
differential in Eqn. 1.1 by dt 
dT
. This transformation simply assumes that the
β
change in experimental conditions from isothermal to non-isothermal does not affect
the reaction kinetics. Thus, in constant heating rate non-isothermal conditions, the
kinetic equation (Eqn. 1.1) of solid state thermal decomposition is frequently rearranged
by well-known differential rate equation
β
dα
 E 
 Af  α  exp  

dT
 RT 
[as
dα dT
dα

β
]
dT dt
dT
On integration over the variables α and T, the Eqn. 1.4 leads to
11
(1.4).
Introduction
α
AT
1
 E
g α    f  α  dα   exp  
β 0  RT
0


where x 


dT

AE
AE  exp ( u)
p(x)
du 

2
βR
βR x u
E
RT
is
the
reduced
(1.5)
activation
energy
at
temperature
T
and
exp ( u)
α
1
u
p(x)  
d
is
the
temperature
integral.
g
α

dα is the reaction


 f  α
2
x u
0


mechanism function [76, 77, 81]. Since the value of E varies with extent of conversion,
α the activation energy, E is written as Eα*.
The general purpose of kinetic analysis of a thermal decomposition or any other
thermally stimulated process is to evaluate kinetic triplet i.e. frequency factor (A),
activation energy (Eα*) and mechanism function g(α). Each of the components of kinetic
triplet is associated with some fundamental theoretical concept [76, 77, 81]. The
magnitude of activation energy, Eα* is identified with the energy barrier to a bond
redistribution step in the transition complex or activated complex, A with the frequency
of vibrations of the activated complex and g(α) is associated with reaction mechanism
function which refers to molecular description of how the reactants are converted into
products during the reaction, and it describes what takes place at each step of a solid
state chemical transformation.
The concept of reaction model as a representative of the mechanism of a solidstate kinetics started in 1920s, when MacDonald and Hinshelwood [84] introduced the
idea of the formation and the growth of the product nuclei in the decomposing solid.
Jacobs and Tomkins [85] gave the first representative account of these rate-determining
mechanisms and their corresponding equations. A set of mechanism functions derived
for variety of kinetic models, has been in use for many years for kinetic analysis of
solid state reactions. The frequently used rate determining equations as well as
mechanisms operating in solid-state kinetics are given in Table 1.1 [8, 47, 81, 84- 87].
These expressions are grouped according to the shape of the isothermal α-time curves
as acceleratory, sigmoid or deceleratory. These groups are further sub-divided
according to the dominant controlling factor assumed in the derivation as geometrical,
diffusion or reaction order. The general rate equations which have been proposed [86,
12
Introduction
87] to cover most of the mechanism functions enlisted in Table 1.1 are often referred as
Šesták-Berggren equation, expressed as either
dα/dt = kαm(1-α)n
or dα/dt = kαm(1-α)n[-ln(1- α)]p
(1.6),
where m, n and p are the fitting parameters. The problem of compiling a complete list of
reaction models can be avoided using the above empirical model (Eqn. 1.6). Šesták has
suggested [81] that the term “accommodation coefficient” for any additional term, other
than (1-α)n, is needed to modify equations based on reaction order for application to
heterogeneous systems. Theoretically, a rational mechanistic interpretation of Eqn. 1.6
is possible only for a limited combination of m, n and p [80].
Table 1.1 The frequently used kinetic models with mechanisms operating in solid-state
reactions [47, 81, 84-87].
No. Symbol
Name of the
g(α )
f(α )
One-third order
1 - (1- α )2/3
(3/2)(1- α )2/3
Ratedetermining
function
mechanism
(A) Chemical process or mechanism non-invoking equations
1
F1/3
Chemical
Reaction
2
F3/4
3
F3/2
4
F2
Three-quarters
order
One and a half
order
Second order
1 - (1- α )1/4
4 (1- α )3/4
(1 - α )-1/2 – 1
2(1- α )3/2
(1 - α )-1 – 1
(1- α )2
Chemical
Reaction
Chemical
Reaction
Chemical
Reaction
5
F3
Third order
(1 - α )-2 – 1
(1/2)(1- α )3
Chemical
Reaction
(B) Acceleratory rate equations
6
P3/2
Mampel power law
α3/2
(2/3) α -1/2
Nucleation
7
P1/2
Mampel power law
α1/2
2α 1/2
Nucleation
8
P1/3
Mampel power law
α 1/3
3α 2/3
Nucleation
9
P1/4
Mampel power law
α¼
4α 3/4
Nucleation
10
E1
Exponential law
lnα
α
Nucleation
13
Introduction
(C) Sigmoidal rate equations or random nucleation and subsequent growth
11
-ln(1- α)
(1- α)
A1,
Avrami
Assumed random
F1
-Erofeev
nucleation and its
equation
subsequent growth,
n=1
12
A3/2
Avrami
[-ln(1- α)]2/3
(3/2)(1- α)[-ln(1-α)]1/3
Assumed random
-Erofeev
nucleation and its
equation
subsequent growth,
n=1.5
13
A2
Avrami
[-ln(1- α)]1/2
2(1- α)[-ln(1- α)]1/2
Assumed random
-Erofeev
nucleation and its
equation
subsequent growth,
n=2
14
A3
Avrami
[-ln(1- α )]
1/3
3(1- α )[-ln(1- α )]
2/3
Assumed random
-Erofeev
nucleation and its
equation
subsequent growth,
n=3
15
A4
Avrami-
[-ln(1- α )]1/4
4(1-α )[-ln(1- α )]3/4
Assumed random
Erofeev
nucleation and its
equation
subsequent growth,
n=4
16
Au
Prout-
ln[α / (1- α )]
α (1- α )
Branching nuclei
Tomkins
equation
(D) Deceleratory rate equations: Phase boundary reaction
17
R1,
F0, P1
18 R2,
F1/2
19 R3,
F2/3
Power law
α
(1- α )0
Contracting disk
Power law
1 - (1- α )1/2
2(1- α )1/2
Power law
1 - (1- α )1/3
3(1- α )2/3
Contracting cylinder
(cylindrical symmetry)
Contracting sphere
(spherical symmetry)
14
Introduction
(E) Deceleratory rate equations: Based on the diffusion mechanism
20 D1
21 D2
22 D3
Parabola
law
Valensi
equation
Jander
equation
α2
1/2α
α + (1- α)ln(1- α)
[-ln(1- α)]-1
[1- (1- α)1/3]2
(3/2)(1- α)2/3[1-(1- α)1/3]-1
23 D4
GinstlingBrounstein
equation
1-2α /3- (1- α)2/3
(3/2)[(1- α)-1/3-1]-1
24 D5
Zhuravlev,
Lesokin,
Tempelman
equation
anti-Jander
equation
antiGinstlingBrounstein
equation
antiZhuravlev,
Lesokin,
Tempelman
equation
[(1- α)-1/3-1]2
(3/2)(1- α)4/3[(1- α)-1/3-1]-1
[(1+ α)1/3-1]2
(3/2)(1+ α)2/3[(1+ α)1/3-1]-1
1+ 2α/3-(1+ α)2/3
(3/2)[(1+ α)-1/3-1]-1
25 D6
26 D7
27 D8
[(1+ α)-1/3-1]2
One-dimensional
diffusion
Two-dimensional
diffusion
Three-dimensional
diffusion,
spherical
symmetry
Three-dimensional
diffusion,
cylindrical
symmetry
Three-dimensional
diffusion
Three-dimensional
diffusion
Three-dimensional
diffusion
(3/2)(1+ α)4/3[(1+ α)-1/3-1]-1 Three-dimensional
diffusion
(F) Other kinetics equations with unjustified mechanism
28 G1
-------
1-(1- α)2
1/2(1- α)
-------
29 G2
-------
1-(1-α )3
1/3(1- α)2
-------
30 G3
-------
1-(1- α)4
1/4(1- α)3
-------
31 G4
-------
[-ln(1- α)]2
(1/2)(1- α)[-ln(1- α)]-1
-------
32 G5
-------
[-ln(1- α)]3
(1/3)(1- α)[-ln(1- α)]-2
-------
33 G6
-------
[-ln(1- α)]4
(1/4)(1- α)[-ln(1- α)]-3
-------
34 G7
-------
[1- (1- α)1/2]1/2
4{(1- α)[1- (1- α)]1/2}1/2
-------
35 G8
-------
[1- (1- α)1/3]1/2
6(1- α)2/3[1-(1- α)1/3]1/2
-------
15
Introduction
The most reliable and accurate evaluation of kinetic triplet depends very much
on the proper kinetic analysis methods used [88]. The kinetic methods which are
intended to analyze thermal analysis data can be classified as model-fitting and modelfree methods. Model fitting method is based on the assumption that the solid state
transformation is ruled by a particular reaction model, whereas the model free method
allows the activation energies to be determined independently of the particular
mechanism governing the solid-state transformation.
1.2.1 Model-fitting Method
The traditional methodology of kinetic analysis is based on fitting data to a
suitable reaction model and is an old technique used to the very first isothermal studies.
The model fitting approach is a method in which the kinetic parameters associated with
a particular reaction model assumed to represent the conversion dependence of the
reaction rate [8, 81, 85]. In general, model-fitting based on a single heating rate is not
reliable. The model-fitting methods solve Eqn. 1.3 by force-fitting experimental data to
different f(α) functions (Table 1.1) and then mechanistic interpretations are made in
terms of the best-fitting model. The kinetic parameters can be evaluated once a f(α)
function has been selected. The model-fitting methods produce highly uncertain values
of the Arrhenius parameters when applied to non-isothermal data [80, 89]. In fact,
experimental data obtained using single heating rate program can be force-fitted by
several f(α) functions, yielding Arrhenius parameters that vary by an order of magnitude
[90]. However, model-fitting methods lead to a constant value of the activation energy
for the overall process, without taking into account the multi-step nature of the solidstate reaction. The reliability and consistency of model-fitting methods depend on the
identification of an appropriate f(α) [8, 9, 77, 81]. If this is not done correctly, the
interpretation of kinetic parameters will be meaningless. The model-fitting methods are
generally classified in two categories - a) linear model-fitting method and b) non-linear
model-fitting method.
16
Introduction
1.2.1.1 Linear Model-fitting Method
Linear model-fitting methods are based on the use of linear regression
techniques and to employ this technique the rate equation should be converted to a
linear form. To describe the kinetics of thermal decomposition of solids, the following
mechanistic model-fitting equation has been used for a long time to identify the
mechanism of reaction [91]
Δ ln α'
E * Δ(1 / T )
Δ ln f(α)


Δ ln (1-α)
R Δ ln (1- α) Δ ln (1- α)
(1.7),
where f(α) is the kinetic differential function which determines the actual reaction
mechanism. A series of proposed forms of f(α) are available in Table 1.1. A plot of
(
Δ(1/T )
Δ ln α'Δ ln f(α)
) vs.
will be a straight line with a slope –E*/R, irrespective
Δ ln (1- α )
Δ ln (1- α)
of the form of f(α) employed. The form of function f(α) is selected in such a way that it
best fits the actual mechanism of the reaction corresponding to the intercept value and
correlation coefficient close to zero and unity, respectively.
In order to test the correctness and validity of the above conclusion (i.e.
selection of actual mechanism f(α) of the kinetic process using Eqn. 1.7), the Arrhenius
equation (logarithmic form of Eqn. 1.4) of following type is used [91]
ln α  - ln f(α) = ln (
A
E*
)
β
RT
[as β 
dα
dT
and α' 
]
dT
dt
(1.8)
where the symbols and terms have their usual meaning. Thus, the plot of ln α- ln f(α)
vs 1/T should be a straight line from which one can get values of the slope –E*/R, and
the intercept. Now, if the proposed mechanism on the basis of Eqn. 1.7 is correct, the
activation energy estimated from Eqn. 1.8 should be the same or close to that obtained
using Eqn. 1.7.
Combined kinetic analysis is another frequently used procedure in order to
perform linear model-fitting in its best way [92, 93]. In this analysis, the kinetic model
is determined in the following general form
f(α) = cαm(1- α )n
(1.9).
Adjusting the parameters c, m and n Eqn. 1.9 can fit very accurately various ideal and
standard kinetic models which are derived under certain mechanistic assumptions. The
combined kinetic analysis is based on the following equation [92]
17
Introduction
 d

1
E*
ln 
 ln(cA) 
m
n 
RT
 dt α (1  α) 
(1.10),
which is derived by rearranging the basis Eqn. 1.3 and replacing f(α) with the right
hand side of Eqn. 1.9. It is necessary requirement to substitute kinetic data α and dα/dt
vs. T obtained at several different temperature programs, T(t) to evaluate the kinetic
parameters. The parameters are considered to be those that yield the best linearity of a
plot of the left hand side of the Eqn. 1.10 against the reciprocal of temperature. The
linearity is evaluated as the coefficient of linear correlation whose maximum is found
through numerical optimization of the parameters n and m [92, 93]. For single-step rate
equation this method is quiet good but linearization of multi-step rate equations is
generally problematic as many of these cannot be linearized.
1.2.1.2 Non-linear Model-fitting Methods
The non-linear regression methods, which work by minimizing the difference
between the measured and calculated data, are widely applicable for fitting of either
single or multi-step kinetic reactions. This method is based on the least square
evaluation of the difference in the form of the residual sum squares (RSS) [94]
RSS   ( y exp y calc ) 2  min
(1.11).
If the values of yexp be the values of the experimentally measured rate (dα/dt) at
different temperature programs, then ycalc will be the rate values calculated by
substituting the variables (i.e. t, T, and α) and kinetic parameters (A and E*) in the right
hand side of a rate equation such as Eqn. 1.1. A minimum of RSS is found numerically
by varying the values of the kinetic parameters [94].
The traditional model-fitting approach suffers from an inability to determine the
reaction model uniquely and provides highly uncertain values of Arrhenius parameters
[80, 94]. However, according to International Confederation for Thermal Analysis and
Calorimetry (ICTAC) kinetic study based on the model-fitting methods can be as
reliable as isoconversional (i.e. model-free) method provided the proper models are
chosen and fitted simultaneously to multiple data sets obtained under different
temperature programs [94, 95].
18
Introduction
1.2.2 Model-free Method
The great advantage of the model-free method lies in its simplicity and
avoidance of errors concerning the selection of kinetic model. The model free methods
(or isoconversional methods) analyze the evolution of a given parameter at a given
extent of conversion, α. Kujirai et al. were the first to propose the isoconversional
method of kinetic evaluations [96]. Originally, isoconversional methods are based on
the assumption that the temperature and the system’s state (especially the rate of change
in the state) are described entirely by a single parameter, the extent of conversion, α
(0 < α ≤ 1). It may be noted that this assumption is generally true for spatially
homogeneous processes, for heterogeneous transformation (such as crystallization) it is
an approximation [97]. The Eqn. 1.4 does not have an analytical solution. As a result,
depending on approximations of the temperature integral and using of correct
computational programming the isoconversional (or model free) methods differ time to
time. There are large numbers of isoconversional computational methods which are
generally classified in two categories - a) integral and b) differential.
1.2.2.1 Integral Isoconversional Method
All integral isoconversional methods are based on solving the temperature
integral (see Eqn. 1.4 and eqn. 1.5) and the accuracy of this method is linked to the
approximation used in the calculation of temperature integral [88, 97, 98].
The widely used integral method to calculate the kinetic parameters is FlynnWall-Ozawa (FWO) [99, 100] method, expressed as
ln β i  ln
0.0048 Aα E*α
g α  R
E* A
 1.0516 α α
RT
α,i
(1.12)
where the subscript ‘βi’ denotes different heating rates and Tα,i is the temperature at
which an extent of reaction, α, is reached at constant heating rate, and Eα* is the
activation energy for a given α. In fact, the Eqn. 1.12 is based on Doyle’s
approximation to evaluate temperature integral [101]. Kissinger-Akahira-Sunose (KAS)
equation [102, 103] is another mostly used integral method, written as
ln
βi
AαR
E*
 ln
 α
2
g (α) E*α RTα,i
T α,i
(1.13).
19
Introduction
Murray’s approximation [104] to calculate temperature integral was used to derive
Eqn. 1.13. These two methods of plotting a linear regressive curve are used at extent of
conversion 0.1 < α < 0.9, different heating rate βi and sample masses. For a given α, the
activation energy is obtained from the slope of the plots of ln βi vs. 1/Tα,i [Eqn. 1.12]
and ln (βi/T2α,i) vs. 1/Tα,i [Eqn. 1.13], respectively. The activation energy values
obtained by the Eqn. 1.12 and Eqn. 1.13 are often found less accurate. To avoid this
problem, the iterative procedure is used to calculate the activation energy more
accurately approximating the exact value of activation energy, according to the
following equations [105]
ln
βi
2
h x  T α,
i
 ln
AαR
g α  E*α

E*α
RT
α,i
(1.14)
and
ln
βi
H  x
 ln
0.0048 Aα E*α
g α  R
E* A
 1.0516 α α
RT
α,i
(1.15)
According to the fourth Senum and Yang approximation formula [106], the h(x) is
expressed as [47, 105]:
x 4  18 x 3  88 x 2  96 x
h x   4
x  20 x 3  120 x 2  240 x  120
(1.16)
and H(x) is expressed as [47, 107]
H x  
exp   x  h x  /x 2
(1.17),
0.0048 exp   1.0516 x 
where x 
E*α
.
R T α, i
In addition to the above methods, there is another model-free (or
isoconversional) method, proposed by Vyazovkin for non-isothermal thermogravimetry
experiments in which the activation energy Eα* can be evaluated at any particular value
of α [88, 89, 108, 109]. Let the temperature integral I(Eα*, Tα,i) be expressed in form


I E*α ,T α, i 
T α, i
 E*α dT
 exp  
 RT 
0
(1.18).
With regard to Eqn. 1.5, g(α) take the form
20
Introduction
g α  
AT
A
 E 
dT  ( )I E*α ,T α, i
 exp  
β 0  RT 
β


(1.19).
Using a general assumption that the reaction model is independent of the heating rate,
the Eqn. 1.19 for a given extent of conversion α and a set of experiments performed
under different heating rates βi (i = 1, 2, 3……….n) can be written as
(Aα/ β1)I(Eα*, Tα,1) = (Aα/ β2)I(Eα*, Tα,2) = (Aα/ β3)I(Eα*, Tα,3) =………..
………………...= (Aα/ βn)I(Eα*, Tα,n)
(1.20).
From the strict fulfillment of condition, the Eqn. 1.20 takes the form [108, 109]




n n I E*α ,T α, i β j
 n(n  1)
 
*
I
,
β
i  1 j  1 E α T α, j i
i j
(1.21),
where j = 1, 2, 3, ………., n. Since the Tα values are measured with some experimental
error, the above equation (Eqn. 1.21) can only be satisfied as an approximate equality.
Thus, Eqn. 1.21 may be satisfied as a condition of minimum value




n n I E*α ,T α, i β j
|n(n-1) -  
| = min
*
i  1 j  1 I E α ,T α, j β i
i j
(1.22).
Accordingly, the activation energy Eα* can be evaluated at any particular value of α by
minimizing the following objective function [88, 89, 108, 109]




n
n I E*α ,T α, i β j
*
Ω Eα   
i  1 j  1 I E*α ,T α, j β i
i j
 
(1.23).
Substituting experimental values of Tα and β into the above equation and varying Eα* to
reach the minimum gives the value of the activation energy at a given conversion. Thus,
at each particular value of α in Eqn. 1.23, Eα* is determined as a value that
 
minimizes Ω E*α , and the temperature integral I(Eα*, Tα,i) is solved numerically.
While analysing data by integral methods, it is necessary to calculate the
temperature integral which does not have an analytical solution. The temperature
integral I(Eα*, Tα,i) has plays an important role in evaluation of kinetic parameters as
well as in the development of solid-state decomposition reaction kinetics of several
materials. There are numerous methods to evaluate this temperature integral. Órfão
21
Introduction
[110] reviewed the various approximations carried out by different workers to evaluate
temperature integral. Some of the temperature integral values, evaluated by different
workers based on several popular approximations, are enlisted in Table 1.2.
Table 1.2 Some of the temperature integral values evaluated by different workers.
Author(s)
CoatsRedfern
[111]
Gorbachev
-Lee-Beck
[112, 113]
Li ChungHsiung
[114]
Agrawal
[115]
QuanyinSu [116]
WanjunYumen
[117]
Cai-Yao
[118]
Chen-Liu
[119]
Órfão
[110]
Tα,i
 Eα*
 
exp

 RT
0
p(x)

dT

ex 
1 
x2 
E*
2
RTα,i  2 RTα,i   RTα,i
1 
e
Eα* 
Eα* 
RTα,i
2
Eα*  2 RTα,i
e

ex  1 


x  x  2
E*
RTα,i
 2
1  
e 
x
2
6 
x 
1  2 
x 


 RT  
 1  2 *α,i   E*
2

RTα,i 
 Eα   e RTα,i
2
Eα* 
1  6 RTα,i  
 E*  

 α  


 RTα,i  
 *   E*

1

2
2

RTα,i 
 Eα   e RTα,i
2
Eα* 
1  5 RTα,i  
 E*  

 α  


 RTα,i  
 *   E*

1

2
2

RTα,i 
 Eα   e RTα,i
2 
Eα* 
1  4.6 RTα,i  
 E*  

 α  

RTα,i
2

x
2
1.00198882 Eα*  1.87391198RTα,i
e
x
 2
1  
e 
x
2
5 
x 
1  2 
x 

x
 2
1  
e
x

2
x  4.6 
1  2 
x 

x

ex 
1



x  1.00198882 x  1.87391198 
E*
RTα,i
ex
x2
E*
2
RTα,i  Eα*  0.66691RTα,i   RTα,i

e
Eα*  Eα*  2.64943RTα,i 
*
ex
x2
2
E
2
2
RTα,i  3Eα*  16 Eα* RTα,i  4 R 2Tα,i   RTα,i

e
Eα*  3Eα* 2  22 Eα* RTα,i  30 R 2Tα,i 2 


*
2
2
  RTE e  x
RTα,i 
0.99997 Eα*  3.03962 Eα* RTα,i

 e α,i x 2
Eα*  Eα* 2  5.03637 Eα* RTα,i  4.19160 R 2Tα,i 2 


22
 x  0.66691 


 x  2.64943 
 3x 2  16 x  4 
 2

 3x  22 x  30 
 0.99997 x 2  3.03962 x 
 2

x

5
.
03637
x

4
.
19160


Introduction
1.2.2.2 Differential Isoconversional Method
In general, the differential isoconversional methods require the experimental
determination of the conversion rate (or a parameter directly linked to the conversion
rate) at different heating rates, βi and a given extent of conversion, α. The most common
method is that of Friedman [120] and it is exact because it does not use any
approximation
ln(
dα
E*α
) α,i  ln[ f(α) A α ] 
RT α,i
dt
(1.24).
The method is based on taking logarithms on both sides of Eqn. 1.3. Therefore, at a
given value of α, the Eα* is determined from the slope of a plot of ln(
1
T α,i
dα
) α,i against
dt
for a set of heating rates βi. For non-isothermal programs the above equation is
frequently expressed as
ln[ β i (
dα
E*
) α,i ]  ln[ f(α) Aα ]  α 
dT
RT α,i
(1.25).
This equation assumes that Tα,i changes linearly with the time according to the heating
rate βi [82, 94].
1.3 Thermodynamic Parameters
During a chemical reaction, reactants do not unexpectedly convert to products.
The formation of products is a continuous process of redistribution of chemical bonds
(i.e. breaking and forming of bonds). At some point in a reaction, a transitional species
is formed containing “partial” bonds, known as transition state or activated complex
which is highly energetic and normally very short-lived in the reaction. According to
the International Union of Pure and Applied Chemistry, the activated complex is
defined as "the assembly of atoms which corresponds to an arbitrary infinitesimally
small region at or near the col (saddle point) of a potential energy surface" [121]. The
activated complex should not be thought of as an unstable isolatable intermediate
because it is assumed to be always in the process of decomposing and decomposes
immediately into the products of the reaction or back into the reactants.
23
Introduction
The activated complex theory [121-125] studies the kinetics of reactions that
pass through a defined intermediate state with standard Gibbs free energy of formation
of products. This is a theory of the rates of elementary reactions, which assumes a
special type of equilibrium, having an equilibrium constant, to exist between reactants
and activated complexes [123]. The activation energy can be defined as the minimum
energy required to reach the transition state or activated complex of a reaction and for a
successful reaction to occur. The activated complex theory also assumes that in passing
from reactants to the products, the reactants have to pass through a crucial configuration
of highest energy [121, 123]. The whole set of events from reactants to products is often
conveniently represented in a reaction profile. For example, Fig. 1.1 represents a
reaction profile for a simple reacting system. The horizontal axis is the reaction
coordinate, and the vertical axis is the potential energy. The activated complex is the
region near the potential maximum, and the transition state corresponds to the
Activation
Energy
maximum itself.
Fig. 1.1 The reaction profile for a simple reacting system.
24
Introduction
Let A, and B are two reactants and P be the product. Then A and B form an
activated complex [AB]# and are in equilibrium with it.
A + B = [AB]#  P
The reactions proceed through an activated or transition state which has higher energy
than the reactants or the products (see Fig. 1.1). The rate depends on two factors - i)
concentration of [AB] and ii) the rate at which activated complex is decomposed. The
activated complex breaks up into products on a special vibration, along which it is
unstable. In general, the vibration of low frequency will decompose the activated
complex. The energy of vibration is given by well-known equation: E = hν. In classical
sense, the average energy of such vibrational degree freedom is E = kBT, where kB is the
Boltzmann constant, h the Plank constant and T is the equilibrium temperature. Thus,
the frequency of vibration ν = E/h = kBT/h. According to the theory of the activated
complex (or transition state) of Eyring [121-125], the rate of elementary reactions
assumes a special type of equilibrium with equilibrium constant K# exists between
reactants and activated complexes. The rate constant is given by
k
k BT # o 1m
K (C )
h
(1.26),
where Co is the standard–state concentration of 1mol L-1, and m is the order. The
equilibrium constant K# can be expressed in terms of thermodynamic parameters. Let
the activated complex be formed from the reactants and ∆G*, ∆S* and ∆H* are the
standard molar change of Gibbs free energy, entropy and enthalpy for activation,
respectively. Now, from thermodynamics
∆G* = -RTlnK#
(1.27)
and ∆G* = ∆H* -T∆S*
(1.28).
Combining Eqn. 1.27 and Eqn. 1.28, the equilibrium constant K# can be expressed for
1st order reaction (m = 1) as
K #  exp( 
H *
S *
) exp(
)
RT
R
(1.29).
Using Eqn. 1.29 the rate constant can also be expressed in form of Arrhenius equation
as
k BT
H *
S *
k
exp( 
) exp(
)
h
RT
R
(1.30).
25
Introduction
For monomolecular reactions, ∆H* ≈ E*. Thus, considering Eqn. 1.30 and comparing
with Arrhenius equation (Eqn. 1.2), from the theory of the activated complex, the
frequency factor can be written as [123, 124]
A
eχk BT
h
ΔS
exp 
 R 


*
(1.31).
where e = 2.7183 (Neper number);  : transition factor (= 1 for monomolecular
reactions).
The change of the entropy S* may be calculated according to the formula
 Ah 

ΔS *  R ln 
 eχk T 
B
p


(1.32),
Since
ΔH *  E*  RT
(1.33),
the changes in the enthalpy, H* and Gibbs free energy, G* for the activated complex
formation from the precursor can be calculated using Eqn. 1.28.
1.4 Kinetics of Thermal Decomposition of Oxalate –
based Compounds
The compounds formed by transition metals and oxalate ligands are of a
complex constitution, and they were accordingly known as complexes [36, 37]. The
thermal decomposition of oxalate-based complexes, as stated earlier, is usually
complicated and proceeds stepwise through a series of intermediate reactions [38, 39].
Therefore, it is very much difficult to describe the kinetics and mechanisms of thermal
decomposition of the precursors step by step most reliably and accurately. Generally,
collecting the thermo-analytical data of the precursors and analyzing the results of the
physical characterizations of the decomposed products, one can predict the thermal
decomposition reaction pathway as well as the reaction product(s) in case of such type
of material(s) [39].
Thermal analysis and kinetics of the thermal decomposition of pure and mixed
oxalates have drawn the interest of several investigators. Duval summarized the
thermogravimetric analysis of a wide range of metal oxalates, mainly in air but a few
cases in inert atmosphere or in vacuum [126]. He reported the decomposition of
26
Introduction
oxalates of sixteen metals at a heating rate of 8-10 oC/min with a somewhat restricted
air-supply. However his results differed from those reported by other investigators
probably owing to the conditions used [39, 68, 69, 73]. Galwey precisely demonstrated
the kinetics of thermal decomposition of a large number of metal oxalates [8]. Some of
the specific and well-studied decomposition kinetics of oxalate materials is reviewed
here.
There were three reaction steps visible in case of thermal decomposition of
CaC2O4.H2O, at increased temperature which corresponds to the dissociation of H2O,
CO and CO2, respectively [44-47]. The steps were classified as dehydration,
decarbonylation and decarbonation, respectively. The reaction kinetics of this thermal
reference material was widely studied [44-47]. The phase boundary reaction (spherical
symmetry) is reported as most probable mechanism describing the dehydration step.
The second stage of decomposition (splitting of carbon monoxide) corresponds to onethird order chemical reaction whereas the third stage of thermal decomposition
(splitting of carbon dioxide) is characterized as phase boundary reaction mechanism
function with cylindrical symmetry. The activation energy as calculated for these steps
is lower for dehydration step and much higher for decarbonylation step as compared to
decarbonation step [47].
The controlled decomposition of various metal oxalates of Zn, Mn, Co, Ni, Mg,
Fe, Ba, Pb, Cu and Ca was carried out in TGA, DSC, and DTA by Mu et al. to reveal
the kinetics of the decomposition process [127]. Various sample sizes, heating rates,
and ambient atmospheres were used to demonstrate their influence on the
decomposition results. The activation energy, order of reaction and frequency factor
were determined for these oxalate complexes. The oxalates were found to decompose
differently in nitrogen or air atmospheres, not only with respect to kinetics, but also in
terms of the specific intermediate and final products [127].
The non-isothermal decomposition of nickel oxalate dihydrate (NiC2O4·2H2O)
in dynamic atmospheres of air and nitrogen was investigated by means of TGA, DTA
and DSC [128]. It was reported that the dehydration reaction was endothermic in both
atmospheres, giving rise to anhydrous nickel oxalate which still retained some water.
On the other hand, the decomposition process was endothermic in air and exothermic in
nitrogen. The final decomposition product in air was NiO, whereas in nitrogen the final
product was found to be metallic nickel. The non-isothermal kinetic and
thermodynamic parameters for the different steps were estimated under different
27
Introduction
atmospheres and a comparative study was made. Remarkable phenomenological and
morphological changes were found to accompany the decomposition process [127,
128].
The isothermal kinetic of thermal decomposition of manganese(II) oxalate
dihydrate in helium atmosphere was studied in the temperature range from 608 to 623 K
and compared to the previous [68, 127, 129]. It has been reported that the thermal
decomposition of MnC2O4·2H2O proceeds in two stages. First stage is dehydration of
oxalate which finishes at 393 K and second stage is decomposition of anhydrous
oxalate which begins at about 523 K. Manganese(II) oxide (MnO) was found to be the
final product of reaction [130]. The Avrami–Erofeev kinetic equation was used to
describe all the experimental data in the range of extent of conversion from 0.1 to 0.9.
The activation energy was determined to be 184.7 kJ mol–1. The rate limiting step of
MnC2O4 decomposition was the nucleation of new MnO phase and the rate of nuclei
growth was rising during decomposition [127, 129, 130]. As mentioned earlier, the
decomposition of manganese oxalate yields a series of different oxide products
depending on experimental conditions [68].
As stated earlier, ZnC2O4 is obtained by dehydration of zinc oxalate dihydrate.
Decomposition of zinc oxalate is a simple one stage reaction leading to ZnO as solid
and CO and CO2 as gaseous products, respectively [127, 131-133]. In the beginning, the
rate of decomposition is determined by nucleation of new phase. The kinetics of
decomposition in the range of extent of conversion 0.2 < α < 0.85 were described in
terms of Avrami–Erofeev equation for isothermal and non-isothermal measurements.
The rate of reaction was controlled by the two-dimensional growth of nuclei. The
activation energy of ZnC2O4 decomposition was evaluated as 181.4–186.5 and 190.8 kJ
mol−1 for non-isothermal and isothermal conditions, respectively [131-133].
Similarities in decomposition scheme were found between patterns of behaviour
reported for zinc and magnesium oxalates. Decomposition of magnesium oxalate is a
simple one stage reaction leading to MgO as solid and CO and CO2 as gaseous products
[8]. Initial acceleratory step (α < 0.3), as reported, was attributed primarily to the
growth of nuclei formed during the removal of water from the dihydrate and activation
energy was evaluated to 200 kJ mol-1 [8, 127].
The sigmoid α-time curves were identified as being due to nucleation and
growth process in case of thermal decomposition of iron(III) oxalate compound [8]. The
first half of the reaction process was well represented by the Avrami–Erofeev equation
28
Introduction
(n = 2) and latter half by the contracting volume equation. The activation energy values
as evaluated were relatively low, 107 to 120 kJ mol-1 [8, 127]. The rate control process
was attributed to either electron transfer or C-C bond rupture. On the other hand, the
iron(II) oxalate decomposed between 596 and 638 K to yield FeO, as initial
decomposed product which may then disproportionate to Fe and Fe3O4. The α-time
data could be fitted, as before, with Avrami–Erofeev equation (n = 2) with calculated
activation energy 175 kJ mol-1 [8, 127]. The decomposition process was proposed to
proceed by nucleation and growth without melting [8].
The isothermal and non-isothermal studies, using TG - DTA techniques, on the
mechanism and kinetics of thermal decomposition of cobalt oxalate were reported by
several investigators [134-136]. The decomposition occurred in two main stages: (i)
removal of water and (ii) decomposition of CoC2O4 to Co. Kinetic study showed that
the increase in activation energy˛ with extent of conversion indicating decomposition of
cobalt oxalate to cobalt is a multistep process. The variation of activation energy
between 73.23 and 119 kJ mol−1 from the lowest to the highest temperature of
decomposition indicated the multi-step nature of the process [135]. Isothermal kinetics
of thermal decomposition of cobalt oxalate to cobalt was found to obey Avrami-Erofeev
equations [134-136].
The TG - DSC study was performed for the complexes K3[Cr(C2O4)3].3H2O,
K3[Al(C2O4)3].3H2O, K3[Fe(C2O4)3].3H2O and K2[Cu(C2O4)2].2H2O in nitrogen at
different heating rates to study chemical kinetics of these materials [57, 137]. The
multi-reaction mechanism and single reaction mechanism have been used to optimize
for each of these complexes. Kinetic parameters and enthalpy were estimated for the
dehydration and decomposition steps and most probable mechanism functions are
suggested for the decomposition process of these compounds [57, 137].
Deb et al. reported the thermal decomposition of a series of oxalate based
compounds of type M1[M2(C2O4)x].nH2O (where M1 / M2 = same / different metal with
x = 2 or 3) and investigated the different intermediates and end products in different
atmosphere [53-55, 58, 59]. The kinetic parameters (activation energy, pre-exponential
factor, activation entropy and the order of the reaction) have been evaluated for all the
dehydration and decomposition steps of all the compounds from non-isothermal TG
curves using non-mechanistic differential and integral rate equations. Using seven
mechanistic equations, the kind of dominance of kinetic control mechanism of the
several dehydration and decomposition steps have also been inferred [53-55, 58, 59].
29
Introduction
The decomposition product(s) (same or mixed metal oxides) was / were identified by IR
and X-Ray powder diffraction studies. Tentative scheme of decomposition pathways of
these precursors in air (some time in different atmosphere) were proposed.
The
thermal
decomposition
of
rare-earth
trioxalatocobaltates
LnCo(C2O4)3.xH2O, where Ln = La, Pr, Nd, has been studied [138] in atmospheres of
air/oxygen, argon / nitrogen, carbon dioxide and a vacuum. The decomposition process
reveals that the compounds decompose through three major steps: dehydration,
decomposition of the oxalate to an intermediate carbonate, which further decomposes to
yield rare-earth cobaltite as the final product [138]. The influence of the surrounding
gas atmosphere in the formation of the final product has been also reported.
The thermal decomposition of potassium titanium oxalate was studied using
non-isothermal TG at different heating rates under a nitrogen atmosphere [139]. The
five stage decomposition process, with elimination of CO and CO 2, leading to the
formation of final titanate was investigated by model free kinetic analyses and kinetic
parameters were evaluated [139].
The decomposition of thorium oxalate hexahydrate was investigated by evolved
gas analysis-mass spectrometry (EGA-MS) and TGA [140]. The complex indicated a
sequential loss of water molecules leading to the formation of anhydrous thorium
oxalate. Then the microcrystalline thorium oxalate anhydrate got transformed to
amorphous carbonate complex after loss of CO from oxalate ligands. The nanocrystalline thoria upon decomposition through an oxycarbonate intermediate was
investigated by powder-XRD technique. Activation energy and frequency factor were
evaluated from the non-isothermal kinetics expressions using fractional extent of the
decomposition data. The mechanism of the various conversion stages as exhibited were
controlled by random nucleation, diffusion, and phase boundary interface motion [140].
In addition, the thermal decomposition of mixture of various oxalate based
materials evokes much research interest in recent past to prepare mixed metal oxide due
to its wide application and technological importance. For example, the non-isothermal
decomposition of zinc(II) oxalate– iron(II) oxalate mixture (1:2 mole ratio) and iron(II)
oxalate–magnesium oxalate mixture (2:1 mole ratio) in air was studied by Gabal et al
[141, 142]. The dehydration and decomposition steps of these oxalate mixtures were
described. The integral methods of Coats–Redfern and Ozawa for kinetic analysis of the
dynamic thermogravimetric data showed that the oxalate decomposition reactions for
zinc and iron mixture were best described by the two-phase boundary models whereas
30
Introduction
for iron and magnesium mixture decomposition reactions were best described by the
three-phase boundary, R3 model [141, 142]. The kinetic parameters were calculated and
characterizations of the decomposed products were thoroughly discussed. The presence
of iron ions with zinc oxalate was reported to decrease the activation energy for the zinc
oxalate decomposition reaction [141].
1.5 Aim of Present Work
Polymeric
bimetallic
oxalate
complexes
of
general
formula
{XR4[MIIMIII(C2O4)3]}(where, XR4+ is the mono positive organic cation ( X = N, P,
As; R = n-alkyl, aryl ) and MII / MIII = di- / trivalent transition metal, (C2O4)– : oxalate
ligand) have been widely studied in the research field of molecule based magnetism due
to the formation of quasi-2D layers of hexagonal oxalate based magnetic networks
[143-157]. The most remarkable feature of these materials is that a wide variety of
metal ion arrangements can be combined into the same basic structure made up of
infinitely extended layers of oxalate-bridged metal pairs MII and MIII exhibiting
hexagonal symmetry and being separated by the organic cation XR4+ [143, 145-147,
152]. The non-magnetic organic cation, in such type of metal assembled complexes,
determines the creation of 2D-network as well as the interlayer separation. The oxalate
ions act as the bridging ligand for the transition-metal centres [143]. Depending on the
di- / trivalent metal, the near-neighbor exchange may be ferro- or antiferromagnetic
which is responsible for bulk ferri-, ferro- / anti-ferromagnetic behavior [143, 148, 151,
152].
Neo and co-workers reported that {XR4[MIIMIII(C2O4)3]} type of bimetallic
complexes may provide an alternative molecular source to prepare intermetallic oxide
[158]. In their report, the thermal decomposition of molecular ferromagnetic material
{N(n-C4H9)4[MnIICrIII(C2O4)3]}resulted into a spinel oxide - Mn1.5Cr1.5O4 at ~ 500°C
through an internal redox process in one step. This observation highlighted that, under
suitable conditions, both metals in such oxalate ligand based heterometallic molecular
complexes, if used as precursor, can be transformed to the metal oxides [158]. It also
suggests that composite metal oxides can be generated from hetero- and inter-metallic
oxalate complexes at relatively low temperatures, which could serve as a convenient
route for the preparation of technologically important composites. This is a convenient
‘molecular-to-materials’ pathway which is primarily favourable not only due to the ease
31
Introduction
of synthesis, lower energetic demand, less complicated product mixtures [159], but
also the potential to tune the materials’ outcome by adjusting the molecular
stoichiometry, composition and structure. The judicious choice of ligand plays an
important role for an effective ‘molecular-to-materials’ conversion. For oxide synthesis,
the ligand should be a facile atomic source of oxygen and decompose cleanly with
minimum interfering side reactions or by-products (volatile compounds). To prepare
metal oxide, as discussed earlier, oxalate ligand [(C2O4)2-] are widely used due to its
variable coordination modes [36-38] which can stabilize a variety of complexes. It
could also decompose easily to volatile CO2 and CO, and serve as a convenient source
of oxide [160].
The synthesis of {XR4[MIIMIII(C2O4)3]} type molecular magnetic materials,
which may be used as precursors for thermal decomposition, is quite easy and economic
[143-145]. Keeping in view the possibility of formation of different types of metal /
intermetallic oxide(s) through thermal decomposition route from such heterometallic
oxalate-based complexes at relatively low temperatures and their applicability as
prospective materials, we felt it interesting to explore the thermal behavior in order to
develop a strategy for preparing metal oxides of various kinds from molecular
precursors of {XR4[MIIMIII(C2O4)3]} family. Neo’s report [158] is one of the examples
to prepare metal oxides from molecular precursors in thermal decomposition route.
However, more investigation is required in this field to improve ‘molecular-tomaterials’ conversion route. Modern kinetics investigation procedure using multiheating rates for multi-step reactions [8, 77, 81] is very useful technique to get insight
of the decomposition process during such type of ‘molecular-to-materials’ conversion.
The estimation of kinetics and the thermodynamics parameters as well as the prediction
of the thermal decomposition reaction pathway and the reaction product(s) are very
essential in this regard. The evaluation of variation in kinetic and thermodynamic
parameters on the extent of reactions as well as the role of divalent metal (MII) ions,
organic cation XR4+, mixing of metals at di- / trivalent sites are also relevant to reveal
the complexity of multi-step reactions for these materials. These are the main objectives
of this experimental research work.
32
Introduction
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