XRD, microstructural and EPR susceptibility characterization of combustion synthesized nanoscale Mg1-xNixO solid solutions

Article abstract of DOI:10.1016/j.jpcs.2007.08.006

The lattice parameter a(x) of the stoichiometric Mg_1-xNi_xO (0≤x≤1) solid solutions prepared by urea-based combustion synthesis with fuel to oxidizer ratio (ψ=1) was determined by X-ray diffraction. It was found that the dependence of the lattice parameter a(x) on the composition deviated more from the linear Vegard's model (VM) when compared to Kuzmin-Mironova (KM) model. a(x) in the Mg_1-xNi_xO system differs nontrivially from the predictions of both VM and KM models. For x=0.4 (Mg_0.6Ni_0.4O), the maximum deviation was about 2 and 1.7 pm, respectively. The increase in the intensity of (1 1 1) peak in XRD with increase of nickel concentration confirms that the substitution induces changes at the unit cell level. Nelson-Riley function (NRF) and Williamson-Hall plots are used to calculate micro strain in the solid solution. This analysis indicates that the micro strain is maximum for the compositions 60-40 (Mg_0.6Ni_0.4O), 50-50 (Mg_0.5Ni_0.5O) and 40-60 (Mg_0.4Ni_0.6O). The crystallite size was estimated using Williamson-Hall plot. We conclude that almost similar sized crystallite is formed in all the compositions studied. Porosity determined using XRD increases with a raise in the nickel concentration. The SEM morphology provides corroborative evidence. EPR susceptibilities of solid solution Mg_1-xNi_xO are determined at room temperature. Variable temperature of EPR allowed to check the Curie-Weiss law for solid solution. The linearity of C_M(x) and Θ(x) with concentration of nickel has ruled out chemical clustering in the samples.

Full text of DOI:10.1016/j.jpcs.2007.08.006

ARTICLE IN PRESS
Journal of Physics and Chemistry of Solids 69 (2008) 87–96
www.elsevier.com/locate/jpcs
XRD, microstructural and EPR susceptibility characterization of
combustion synthesized nanoscale Mg1ꢀxNixO solid solutions
Ã
K. Venkateswara Raoa,b, C.S. Sunandanab,
aJNTUCEH, Jawaharlal Nehru Technological University, Hyderabad 500085, India
bSchool of Physics, University of Hyderabad, Science Complex Building, Opp. DST Seminar Complex, Hyderabad 500046, AP, India
Received 30 March 2007; received in revised form 28 July 2007; accepted 3 August 2007
Abstract
The lattice parameter a(x) of the stoichiometric Mg1ꢀxNixO (0pxp1) solid solutions prepared by urea-based combustion synthesis
with fuel to oxidizer ratio (c ¼ 1) was determined by X-ray diffraction. It was found that the dependence of the lattice parameter a(x) on
the composition deviated more from the linear Vegard’s model (VM) when compared to Kuzmin–Mironova (KM) model. a(x) in the
Mg1ꢀxNixO system differs nontrivially from the predictions of both VM and KM models. For x ¼ 0.4 (Mg0.6Ni0.4O), the maximum
deviation was about 2 and 1.7 pm, respectively. The increase in the intensity of (1 1 1) peak in XRD with increase of nickel concentration
confirms that the substitution induces changes at the unit cell level. Nelson–Riley function (NRF) and Williamson–Hall plots are used to
calculate micro strain in the solid solution. This analysis indicates that the micro strain is maximum for the compositions 60–40
(Mg0.6Ni0.4O), 50–50 (Mg0.5Ni0.5O) and 40–60 (Mg0.4Ni0.6O). The crystallite size was estimated using Williamson–Hall plot. We
conclude that almost similar sized crystallite is formed in all the compositions studied. Porosity determined using XRD increases with a
raise in the nickel concentration. The SEM morphology provides corroborative evidence. EPR susceptibilities of solid solution
Mg1ꢀxNixO are determined at room temperature. Variable temperature of EPR allowed to check the Curie–Weiss law for solid solution.
The linearity of CM(x) and Y(x) with concentration of nickel has ruled out chemical clustering in the samples.
r 2007 Elsevier Ltd. All rights reserved.
Keywords: A. Nanostructures; B. Chemical synthesis; C. X-ray diffraction; D. Electron paramagnetic resonance (EPR)
1. Introduction
ionic radii of Ni2+, Mg2+ ions 0.083 and 0.086 nm,
respectively [4]. The lattice constant of the solid solution
varies from 0.4209 nm in pure MgO (x ¼ 0) to 0.4177 nm in
pure NiO (x ¼ 1), close to the linear dependence [5]. Thus,
the variation of lattice parameter is about 0.8% in
Mg1ꢀxNixO system. Therefore, the crystal structure does
not change upon dilution [6]. Pure NiO in the paramag-
netic phase has a rock-salt-type crystal structure with
nickel ions located at the center of the NiO octahedra. In
the antiferromagnetic phase, the structure of NiO under-
goes a weak cubic-to-rhombohedral distortion due to the
magnetostriction effect [7]. Substitution of nickel ions by
magnesium stabilizes the cubic structure [7]. Magnetic
ordering of these compounds depends on the concen-
tration and site distribution of magnetic ions as well as on
the signs and relative strengths of JNN and JNNN super-
exchange interactions between two Ni2+ ions via an
oxygen ion [8,9].
Diluted antiferromagnets represent an interesting class
of materials whose crystallographic structures are closely
related to their magnetic properties [1]. The MgO–NiO
solid solution belongs to the class of the diluted face-
centered cubic (fcc) antiferromagnets. While NiO is a type-
II antiferromagnet and a charge-transfer insulator with
Neel temperature TN ¼ 523 K [2,3], MgO is a diamagnetic
ionic insulator with fcc structure. The Mg1ꢀxNixO
(0oxo1) system is ideal for studying the effects of dilution
on the magnetic properties. This system forms a contin-
uous series of solid solutions with rock-salt crystal
structure due to a small difference, of about 3 pm, in the
Ã
Corresponding author. Tel.: +91 40 23134324; fax: +91 40 23010227.
E-mail addresses: csssp@uohyd.ernet.in, csssp75@yahoo.co.in
(C.S. Sunandana).
0022-3697/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jpcs.2007.08.006

ARTICLE IN PRESS
K. Venkateswara Rao, C.S. Sunandana / Journal of Physics and Chemistry of Solids 69 (2008) 87–96
88
The NN interactions, having ferromagnetic and anti-
[18]. In the present work, nickel nitrate, magnesium nitrate
and an organic fuel, typically urea (NH2CONH2) have
been used. The mechanism of combustion reaction is quite
complex. The parameters that influence the reaction
include type of fuel, fuel to oxidizer ratio, use of excess
oxidizer, ignition temperature and water content of the
precursor mixture.
For the preparation of these samples of Mg1ꢀxNixO
(0pxp1) in the present study, the required amounts of
two nitrates Mg(NO3)2 ꢁ 6H2O and Ni(NO3)2 ꢁ 6H2O
(MERCK Ltd.) were dissolved in distilled water along
with fuel urea (NH2CONH2) (QUALIGENS). Stoichio-
metric compositions of the metal nitrates and fuel are
calculated based on the propellant chemistry. Thus, heat of
combustion is the maximum for the fuel to oxidizer ratio
(c) that equals 1 [17]. Based on the concepts used in the
propellant chemistry, the elements C, H, Mg, Ni and or
any other metals are considered as reducing elements with
valences 4+, 1+, 2+, 2+ (or valency of metal ion in that
compound), respectively. Oxygen is an oxidizer having the
valency of 2ꢀ. The valency of nitrogen is taken as zero
because of its convertibility into molecular nitrogen during
the combustion. The fuel to oxidizer ratios (c) [17] are
calculated using the equation
ferromagnetic characters, occur within the three atom
chains Ni2+–O2ꢀ–Ni2+ with angle Ni–O–Ni ¼ 901, while
the NNN interactions having antiferromagnetic character
with in linear atom chains Ni2+–O2ꢀ–Ni2+ with angle
Ni–O–Ni ¼ 1801. The values of JNN and JNNN for NiO are
34 and 202 K [5,10]. A reduction in the particle size of these
solid solutions from micrometer to nanometer dimensions
is expected to modify their magnetic behavior by way of
increased surface and interface ions and a reduction in the
crystalline anisotropy. A change from bulk-like to cluster-
like behavior with enhanced magnetic moment and
magnetization is anticipated in the systems with well-
defined magnetic phase transitions. A change in the
transition temperature could arise. In general, the magnetic
behavior would show size dependence in addition to
dilution dependence. In this work, we described and
discussed structural and magnetic characterization of the
Mg1ꢀxNixO (0oxo1) system samples by chemical com-
bustion method for the first time instead of the commonly
employed solid state reaction. Thus, we were able to
prepare selected compositions of the Mg1ꢀxNixO system as
a more homogeneous product in a short time. Our
synthesis results in highly crystalline products without the
nfð1 ꢂ 4CÞ þ ð4 ꢂ 1HÞ þ ð2 ꢂ 0NÞ þ ð1 ꢂ ꢀ2OÞg
a½ð1 ꢂ 2MgÞ þ 2ðð1 ꢂ 0NÞ þ ð3 ꢂ ꢀ2OÞÞꢃ þ b½ð1 ꢂ 2NiÞ þ 2ðð1 ꢂ 0NÞ þ ð3 ꢂ ꢀ2OÞÞꢃ
c ¼
,
(1)
use of high temperature furnace. Due to evolution of a
large amount of gases produced during combustion
processes, nanosized, porous and foamy products are
obtained [11] which are not easily achieved in other
methods. Our results unambiguously show that the
composition dependence of the lattice parameter a(x) of
Mg1ꢀxNixO system deviates from the linear system
assumed within Vegard’s and Kuzmin–Mironova models.
where n is mole of fuel and a, b are mole fractions of Mg
and Ni nitrates, respectively.
The aqueous solution is thoroughly stirred with a
magnetic stirrer to achieve complete dissolution of all solid
reagents and the clear solution is placed on a hot plate to
initiate the reaction. As the temperature reached 100 1C,
water started to boil and evaporate from the solution,
which increased the solution viscosity substantially. Mean-
while, the compound caught fire and finally a black, light-
weight powder was obtained. This is the precursor. The
precursor and the precursor annealed for 2 h at 250 1C
(75 1C) are both characterized. The combustion is self-
propagating, i.e., once ignited, it automatically goes to
completion without supply of additional heat from an
external sources. The reaction equations assuming com-
plete combustion of the redox mixture used for synthesis of
Mg1ꢀxNixO solid solution may be written as
2. Samples preparation and experimental techniques
Various techniques are available for the preparation of
nanomaterials. They include dividing or breaking down of
a bulk solid or building up process. Some of the well-
known methods are laser ablation, plasma synthesis,
chemical vapor deposition, mechanical alloying or high-
energy milling and sol–gel synthesis [12]. All these
techniques involve and require special chemicals and
equipments. We prepared Mg1ꢀxNixO solid solutions by
employing the low temperature initiated self-propagating,
gas producing combustion method [13,14]. Combustion
synthesis involves an exothermic reaction between an
oxidizer (metal nitrates) and fuel (urea for example). It is
an important powder processing technique generally used
to produce complex oxide nanomaterials, aluminates [15],
ferrites [16], and chromites [17]. We already used this
method in the past to make PbZrO3 using citric acid as fuel
MgðNO3Þ2 ꢁ 6H2O þ NH2CONH2
! MgOðsÞ þ 2H2OðgÞ þ CO2ðgÞ þ 2N2ðgÞ
(2)
(3)
(4)
NiðNO3Þ2 ꢁ 6H2O þ NH2CONH2
! NiOðsÞ þ 2H2OðgÞ þ CO2ðgÞ þ 2N2ðgÞ
NiðNO3Þ2 ꢁ 6H2O þ MgðNO3Þ2 ꢁ 6H2O þ NH2CONH2
! MgNiOðsÞ þ H2OðgÞ þ CO2ðgÞ þ 3N2ðgÞ

ARTICLE IN PRESS
K. Venkateswara Rao, C.S. Sunandana / Journal of Physics and Chemistry of Solids 69 (2008) 87–96
89
Structural characterization on these samples was per-
3. Results and discussion
formed using Philips X-ray diffractometer with Cu Ka1
radiation. The principle of operation of this diffractometer
can be understood as follows. The sample is spread on a
glass plate which is supported on a table rotating about on
a particular axis to the plane of drawing. The X-ray tube is
normal to the plane of the drawing, therefore parallel to
diffractometer axis. X-rays diverge from the source and are
diffracted by the specimen to form a convergent beam
which comes into focus at a slit and enters into a counter.
The intensity of the diffracted beam is measured directly by
an electronic counter which converts the incoming X-rays
into electric pulses counted by X-ray detector placed on the
circumference of a centered circle. The counter is power-
driven at a constant angular velocity about the diffract-
ometer axis. The range of 2y (30–901) of interest is covered
in this fashion and the curve of intensity versus 2y is finally
plotted on a computer. Microstructure studies were carried
out using Philips XL-30 SERIES SEM by spreading as-
prepared and the ultrasonicated (10 min in toluene)
samples over a thoroughly cleaned and dried microscopic
slide after applying vacuum grease. EPR spectra were
obtained from samples containing 4 mm quartz tube. In the
EPR experiment, a highly uniform and reasonably stable
static magnetic field H, in the range 0–0.5 T, is applied to
the sample placed in a rectangular microwave resonance
cavity. The microwave magnetic field component perpen-
dicular to the direction of the static field causes magnetic
dipole transitions when the microwave energy quantum hn
is equal to the Zeeman splitting gbH, of the two spin status
(M ¼ 1/2 and ꢀ1/2) of the paramagnetic, i.e., n ¼ gbH.
The parameter g is the spectroscopic splitting factor
representing the nature of unpaired electrons and b is the
basic unit of electronic moment called Bohr magnetic
moment which is Bohr magnetron. Magnetic dipole
transitions in a paramagnetic material are observed in
EPR by sweeping the magnetic field intensity rather than
sweeping the microwave frequency which is technically
impracticable. A typical X-band EPR spectrometer is used
here. This contains the Gunn oscillator whose frequency
and the intensity of the microwaves produced thereby are
controlled and accurately measured by appropriate cir-
cuits. The cavity system includes the components, which
hold the sample and direct and control the microwave
beam to and from the sample. The detection and
modulation system-monitor amplifies and records the
signal. The EPR spectra of the combustion synthesized
solid solution in this work were recorded on a JEOL JES-
FA 200X-band EPR spectrometer under optimized condi-
tions of modulation amplitude, receiver gain, time constant
and scan time. The instrument is computerized so that data
can be retrieved for convenient analysis. JOEL DVT
controller was used (323–453 K) for controlling the
temperatures while heating and cooling. The spectrometer
setting used in recording the spectra were as follows:
modulation frequency ¼ 100 kHz; modulation amplitu-
de ¼ 1 mT; frequency ¼ 9.15966 GHz; power ¼ 0.998 mW.
3.1. Structure and micro strain of Mg1ꢀxNixO solid solution
versus crystallite size from X-ray diffraction
The XRD patterns obtained on annealed samples, at
250 1C (75 1C) for 2 h, Mg1ꢀxNixO system are shown in
Fig. 1. The patterns were recorded over a range of 2y
angles from 301 to 901 and crystalline phases were
identified using the JCPDS data (78-0430, 78-0643). The
XRD peaks of MgO are very similar to those of NiO. The
peak intensities of (1 1 1), (2 0 0), (2 2 0), (3 1 1) and (2 2 2)
reflections are comparable with JCPDS values. The lattice
parameters of the solid solution are in agreement with the
earlier work [1]. One can notice a strong variation of the
(1 1 1) peak intensity for solid solutions in Table 1
occurring due to the difference between the X-ray
scattering intensities of the nickel and magnesium sub-
lattices. The intensity of (1 1 1) peak in compounds with the
NaCl-type crystal structure, which is the structure type of
the Mg(1ꢀx)NixO series, depends on the difference between
the number of electrons of the anions and cations [15]. This
explains the smaller magnitude of the (1 1 1) peak for MgO
as compared to that of NiO. Table 1 shows the intensity
variation of (1 1 1) peak when the concentration varies
from 0% to 100%. We can see significant variation of the
increase in the intensity of the peak. We can further notice
(111)
(111)
(200)
(200)
(220)
(220)
(311)
(311)
(222)
(222)
(222)
k
j
(111)
(200)
(200)
(220)
(220)
(220)
(311)
(311)
i
(111)
(111)
(222)
(222)
h
(200)
(311)
(311)
g
(111)
(111)
(220)
(220)
(200)
(200)
(222)
(222)
f
(311)
e
(111)
(111)
(220)
(200)
(200)
(222)
d
(311)
(220)
(220)
(220)
(311)
(311)
(311)
(222)
(222)
(222)
c
(200)
(200)
(111)
(111)
b
a
30
40
50
60
2°
70
80
90
Fig. 1. X-ray diffractograms of Mg1ꢀxNixO solid solutions at 300 K: (a)
MgO (x ¼ 0), (b) Mg0.9Ni0.1O, (c) Mg0.8Ni0.2O, (d) Mg0.7Ni0.3O, (e)
Mg0.6Ni0.4O, (f) Mg0.5Ni0.5O, (g) Mg0.4Ni0.6O, (h) Mg0.3Ni0.7O, (i)
Mg0.2Ni0.8O, (j) Mg0.1Ni0.9O and (k) NiO (x ¼ 1).

ARTICLE IN PRESS
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90
Table 1
The intensity and area under the (1 1 1) peak
aNM(x) ¼ f(b1+b2x) and finally they got the expression
aðxÞKM ¼ x2aNiO þ 2xð1 ꢀ xÞðb1 þ b2xÞ
%Ni
Intensity of (1 1 1) peak
Area under (1 1 1) peak
2
þ ð1 ꢀ xÞ ðxaNiO þ ð1 ꢀ xÞaMgOÞ.
ð5Þ
0 (MgO)
6573
5673
7774
4473
8075
Taking into account the displacement of nickel atoms
upon dilution by magnesium, here b1 and b2 are determined
by the least-square fit to Eq. (5). x is concentration of Ni
varying from 0 to 1 and aNiO, aMgO are lattice parameters
of pure NiO and MgO. Using Eq. (5) for the present
system, we achieved the values b1 ¼ 4207.6733 pm and
b2 ¼ ꢀ13.5170.108 pm. The present results for pure NiO
and MgO are in fair agreement with the known values
published by others [1,2]. The value of lattice parameter (a)
for pure NiO is close to that of Ref. [19]. The ideal cubic
cell of NiO, however exists only in the paramagnetic phase
that is above the Neel temperature TN ¼ 532 K. The NiO
structure at room temperature experiences rhombohedral
distortion, which however, is small. This distortion is
reduced and cubic structure is stabilized due to the Mg2+
ion substitution. A careful examination of Fig. 2, the
differences a(x)ꢀa(x)VM and a(x)ꢀa(x)KM show that the
deviation is less in the case of KM model when compared
to VM. This is because in Vegard’s model the values of the
Ni–O and Mg–O bond lengths in the solid solutions are
considered to be constant as in NiO and MgO. Therefore,
the lattice parameter a(x) of solid solution becomes equal
to the additive sum of the lattice parameter of individual
components weighted with concentrations of each other,
whereas the KM model takes into account the off-center
displacements of nickel ions [1] and is in good agreement
with our experimental values.
10
20
12377
12677
192711
247715
251715
267715
265716
267716
270716
30
40
12976
198710
213711
289714
335717
367718
368718
360718
50
60
70
80
90
100 (NiO)
2.0
1.5
a) a(x)EXP-a(x)VM
b) a(x)EXP-a(x)KM
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
b
a
0
20
40
60
% of Ni
80
100
Fig. 2. Lattice parameter a(x) compared to Vegard’s and Kuzmin–
Mironova models: (a) a(x)EXPꢀa(x)VM and (b) a(x)EXPꢀa(x)KM
The variation of the lattice parameter a(x) versus the
nickel concentration x is given in Table 2. A least-square fit
to the experimental data yields the equation
.
the increase in the area of (1 1 1) peak results with the
increase in the concentration of Ni in Table 1 before and
after annealing. We can conclude that the increased
concentration of nickel in the Mg1ꢀxNixO solid solution
results in a homogeneous dense phase. It was believed for a
long time that lattice parameter of Mg1ꢀxNixO system
depends linearly on the composition and follows the
Vegard’s rule a(x)VM ¼ xaNiO+(1ꢀx)aMgO [1,16]. How-
ever, the results of the X-ray diffraction strongly suggest
deviation from Vegard’s model. This is due to a deviation
of the local environment around Ni2+ ions from the
Vegard’s model. The lattice parameters measured from
XRD are comparable to the previous work [1]. The values
obtained for the lattice parameter a(x) and their total
uncertainties Da are reported in Fig. 2 along with those
calculated using Vegard’s a(x)VM ¼ xaNiO+(1ꢀx)aMgO
and Kuzmin–Mironova models. To explain the experi-
mental behavior of a(x), Kuzmin and Mironova suggested
a model that assumes that the Ni–Ni inter-atomic distance
remains nearly constant at all compositions. Therefore,
they supposed that aNN(x) ¼ aNiO ¼ Constant. The aver-
age Ni–Mg inter-atomic distance varies linearly with
concentration and it can be given as a linear function
aðxÞ ¼ ð420:77 ꢀ 3:10xÞ pm.
It was observed that the values of lattice parameter a(x) in
the Mg1ꢀxNixO series differ from those predicted by
the Vegard’s model (VM) and Kuzmin–Mironova model.
(6)
Table 2
The variation of lattice parameter a(x) in Mg(1ꢀx)NixO in solid solution
with Ni concentration
%Ni
0 (MgO)
10
a(x)vm (nm)
a(x)km (nm)
a(x)EXP (nm)
0.42091
0.42060
0.42028
0.41996
0.41964
0.41933
0.41901
0.41869
0.41838
0.41806
0.41774
0.42091
0.42057
0.42025
0.41993
0.41962
0.41931
0.41901
0.41870
0.41839
0.41807
0.41774
0.4209170.00336
0.4204570.00336
0.4201270.00336
0.4198170.00336
0.4193070.00335
0.4190470.00335
0.4188770.00335
0.4186170.00335
0.4182770.00335
0.4180270.00334
0.4177470.00334
20
30
40
50
60
70
80
90
100 (NiO)
(a) Predicted from Vegard’s model a(x)VM, (b) predicted from Kuzmin–
Mironova model a(x)KM, and (c) experimental values a(x)EXP.

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91
The maximum deviation is about 2 and 1.7 pm, respec-
WH(a)
LS(b)
70
60
50
40
30
20
10
0
a
tively, for x ¼ 0.4 (Mg0.6Ni0.4O). This can be explained
based on the type of local deformation around impurity
ions in the MgO and NiO host lattices. To decide on the
type of local deformation, one can compare the value of
aNM calculated from the coefficient bi to the host lattice
parameter a(x) when x ¼ 0 (MgO) and x ¼ 1 (NiO). At
these end compositions, the impurity of Ni(Mg) can be
considered to be isolated in the host MgO(NiO) matrix. At
x ¼ 0, aNM ¼ 0.42075 nm which is smaller than MgO
lattice constant (0.42123 nm) but larger than the sum of
undistorted Ni–O and Mg–O distances (0.41948 nm). Thus,
the local environment in Ni-doped MgO partially relaxes in
the direction of impurity ions. In other words, the host
lattice MgO shrinks upon Ni-substitution.
b
-10
0
20
40
60
% of NI
80
100
Fig. 4. Micro strain calculated (a) Williamson–Hall plot, (b) least-squares
regression line (2W)2 cos2 y as a function of sin2 y.
3.1.1. Strain analysis
The Nelson–Reily function (NRF) versus Dd/d curves
[20,21] and least-squares regression line (2W)2 cos2 y as a
function of sin2 y [22,23] for Mg1ꢀxNixO system obtained
from the XRD data are plotted in Fig. 3. Systematic lattice
transformation of all the crystal planes upon Ni substitu-
tion is clearly evident (Fig. 3). Dd/d values increase up to
C ¼ 0.5 and thereafter it starts decreasing all the way up to
undoped NiO(x ¼ 1). In the case of Mg-rich and Ni-rich
compositions, Dd/d values lie on a horizontal line, almost
parallel to NRF axis, which indicates the absence of
stacking faults in the cubic structure. But, the rather large
scatter observed in Dd/d values for the intermediate
60–40 (Mg0.6Ni0.4O), 50–50 (Mg0.5Ni0.5O) and 40–60
(Mg0.4Ni0.6O) samples are a measure of the high concen-
tration of stacking faults present in these compositions.
Ni-rich and Mg-rich samples show less scatter with small
slope values whereas intermediate (40%, 50%, 60% Ni
doped) compositions give larger slope values. Average
micro strain is calculated for all compositions of
Mg1ꢀxNixO by measuring slopes of the least-squares
regression line. Maximum strain values are observed only
in the intermediate 40%, 50% and 60% of Ni doped MgO
but not other. Using the Williamson–Hall equation [24], we
determined the micro strain. The micro strain calculated
using above two methods is as shown in Fig. 4. Obviously,
the micro strain is the maximum for intermediate
compositions, as is observed in NRF function. This could
arise from local distortions which are maximum for
compounds with 0.4oxo0.6. Both methods of XRD
analysis, i.e., NRF and Williamson–Hall plots bring this
out and the latter method more prominently.
g
f
3.1.2. Crystallite size
All samples produce appreciable diffraction broadening
and it is reasonably assumed that this arises from the
crystallite size and internal stresses. Diffraction theory
predicts that the breadth due to crystallite size varies with
angle as sec y and that due to elastic strain as tan y [22]. The
additional broadening in diffraction peaks beyond the
inherent peak widths due to instrumental effects can be
used to measure crystallite size as low as 1.0 nm. The
crystallite size of as-prepared and annealed compositions
were calculated from the full width at half maximum
(FWHM) of all the peaks (1 1 1), (2 0 0), (2 2 0), (3 1 1) and
(2 2 2) using the Debye–Scherrer formula [25]
e
d
c
b
a
0:9l
B cos y
t ¼
.
(7)
1
2
3
4
5
The Gaussian function gives a better fit to the FWHM of
all the peaks than the Lorentzian function. Therefore, the
observed XRD peaks are essentially Gaussian, pointing to
a uniform crystallite size distribution. We also used another
method, the Williamson–Hall equation to calculate strain
NRF
Fig. 3. Strain analysis from NRF of solid solution of Mg1ꢀxNixO
obtained from XRD: (a) MgO(x ¼ 0), (b) Mg0.8Ni0.2, (c) Mg0.6Ni0.4, (d)
Mg0.5Ni0.5, (e) Mg0.4Ni0.6, (f) Mg0.2Ni0.8O and (g) NiO (x ¼ 1).

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92
and particle size of the each composition [24]. The
Williamson–Hall equation is expressed as follows:
Table 4
Porosity calculated from the X-ray diffraction before annealing and after
annealing
Kl
t
B cos y ¼
þ 2ꢀ sin y,
(8)
% Ni
Porosity before annealing
Porosity after annealing
where B is the full-width at half-maximum (FWHM) of the
XRD all peaks, K is Scherrer constant, t is the crystalline
size, l the wavelength of the X-ray, e the lattice strain and y
the Bragg angle. In this method, B cos y is plotted against
2 sin y. Using a linear extrapolation to this plot, the
intercept gives the particle size Kl/t and slope gives the
strain (e). According to Table 3, the crystallite size of pure
MgO is 2171 nm and it decreases as the concentration of
the Ni increases. At first, the size is decreased to 1271 nm
for Mg0.8Ni0.2O concentration and subsequently the size
increases very slowly to 2971 nm for Mg0.2Ni0.8O and then
decreases to 2671 nm for pure NiO. As the fuel to oxidizer
ratio c ¼ 1 is used to prepare all the compositions, the heat
of combustion is maximum for c ¼ 1 [17] and hence the
size of the particle is minimum. We obtained nearly the
same average crystallite size for all the investigated
compositions and hence we can conclude that there is no
appreciable effect of size on the XRD of Mg(1ꢀx)NixO solid
solutions. This is understandable because of the nearly
equal lattice parameters of MgO and NiO.
0 (MgO)
1.145270.0458
1.103170.0441
0.962370.0385
0.838770.0335
2.09717.00839
3.123970.1250
2.929770.1172
2.460370.0984
2.770970.1108
2.931970.1173
2.927470.1171
0.248670.0099
0.489070.0196
0.540070.0216
0.680470.0272
0.885770.0354
1.111570.0445
1.339470.0536
1.492170.597
1.701070.0680
1.821070.0728
2.025070.0810
10
20
30
40
50
60
70
80
90
100 (NiO)
un-annealed samples the variation of porosity is not
uniform, whereas after annealing porosity increases uni-
formly with Ni doping. This can be explained by taking the
density of NiO (6.67 g/cm3) into account which is more
when compared to MgO (3.58 g/cm3). Mainly, the porosity
depends on the density and hence the porosity is more for
rich Ni solid solutions. This is directly seen in scanning
electron micrographs (SEM).
3.2. Porosity measurement
3.3. Scanning electron microscopy
Products of combustion synthesis are highly porous.
They possess much less densities compared to theoretical
values [26]. The density of prepared and annealed samples
was determined by the XRD. The percentage of porosity
was calculated from the measured and theoretical density,
according to the following equation:
Secondary electron images show qualitatively the differ-
ence in the surface morphology of chemical combus-
tion prepared samples of Mg0.9Ni0.1O, Mg0.8Ni0.2O,
Mg0.7Ni0.3O, Mg0.5Ni0.5O, Mg0.3Ni0.7O and Mg0.1Ni0.9
O
as in Fig. 5(a–f). The samples were ultrasonicated in
toluene for 10 min to disperse the particles and the SEM
micrograph is as shown in Fig. 6(a–c). It is very interesting
that in Fig. 5 as the concentration of the Ni is increased the
porosity of the samples is increased, same phenomenon
was observed in the calculation of porosity from XRD in
Section 3.2. Therefore, the same reasoning may be given
for the increase of porosity. Fig. 6 shows that all the
compositions of uniform and spherical average size are in
the range of 100–170 nm.
ꢀ
ꢁ
D
porosity; P ¼ 1 ꢀ
ꢂ 100,
(9)
DT
where DT is theoretical density, and D is the density of the
samples measured using XRD. Using Eq. (9) the porosity
values are calculated. It is clear from Table 4 in
Table 3
Crystallite size calculated from XRD using Debye–Scherrer formal and
Williamson–Hall plot
%Ni
Crystalline size from
Debye–Scherrer
(nm)
Crystalline size from
Williamson–Hall plot
(nm)
3.4. Magnetic ions exchange interactions in Mg1ꢀxNixO
solid solution
For diluted antiferromagnets [27,28] in the high-
temperature limit (T4TN), the leading term for w yields
the Curie–Weiss law
0 (MgO)
2070.6
2170.42
1470.28
1270.24
1370.26
1970.38
2070.4
2170.42
2270.44
2970.58
2470.48
2670.52
10
20
1370.39
1170.33
1370.39
1470.42
1470.42
1670.48
1870.54
2270.66
2370.69
2470.72
30
40
CðxÞ
wðxÞ ¼
,
(10)
50
60
T þ YðxÞ
70
80
where C(x) is the Curie constant and Y(x) is the
Curie–Weiss temperature. Here, one should understand
that wg, the susceptibility per gram, and the variations
of Cg(x) and molar CM(x) with x are different. It can
90
100 (NiO)

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93
Fig. 5. Scanning electron micrographs of solid solution Mg1ꢀxNixO as-prepared (a) Mg0.9Ni0.1, (b) Mg0.8Ni0.2, (c) Mg0.7Ni0.3, (d) Mg0.5Ni0.5
(e) Mg0.3Ni0.7O and (f) Mg0.1Ni0.9O.
,
be shown that
(assuming no significant change in lattice constant). Thus,
the experimental variations of Y(x) with x provide a check
on the quality of random dilution of the samples. If Y(x) is
too large, it would indicate chemical clustering. Since the
maximum change in the lattice constant between x ¼ 0 and
1 in Mg1ꢀxNixO is about 0.8%, change in J1 and J2 with
dilution should be quite negligible [29].
CMðxÞ ¼ CMð1Þꢄx,
(11)
(12)
CMðxÞ
CgðxÞ ¼
W
and
YðxÞ ¼ Yð1Þꢄx,
(13)
3.5. Susceptibility of the Mg1ꢀxNixO solid solution at room
temperature
where W is the molecular weight of Mg1ꢀxNixO. Thus,
although CM(x) and Y(x) vary linearly with x, Cg(x) varies
nonlinearly with x. A plot of 1/w* against T may be used to
determine CM(1) and Y(x). Y(x) in a randomly diluted
system measures the sum of all magnetic interactions. It
should vary linearly with x if there is no chemical clustering
In their work, Mironova-Ulmane et al. [7] have identified
four domains in the Mg1ꢀxNixO solid solution: (1) a
homogeneous antiferromagnet (0.63pxp1); (2) a tricriti-
cal region or a frustrated antiferromagnet (0.4pxp0.63);

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94
Fig. 6. Scanning electron micrographs of solid solutions: (a) Mg0.3Ni0.7O, (b) Mg0.7Ni0.3O, (c) NiO.
(3) a spin-glass state (0.25pxp0.4) and (4) a diamagnet
(xp0.2) [30]. It was found that the regular domain
structure is more sensitive to the concentration of
magnesium ion than the temperature and appears upon
the cooling at temperature well below TN. We did EPR at
room temperature for all the samples and calculated the
number of spins participating in resonance with the help of
reference (standard) CuSO4 ꢁ 5H2O by using the following
formula [31,32]:
where N is the number of spins per M3, the rest of the
symbols have their meaning. N can be calculated using
Eq. (14) and g taken from the EPR data. The line width of
the solid solution is increased for Mg0.9Ni0.1
O
(73.570.1 G) and goes on increasing to (36570.1 G) for
Mg0.1Ni0.9O with increase in Ni concentration. The
number of spins (N) is also increasing with the concentra-
tion of the Ni, for Mg0.9Ni0.1O (0.4763) and it increases
(100.25) for Mg0.3Ni0.7O. It is decreased for other two
compositions 23.4 and 18.6 for Mg0.2Ni0.8
O
and
2
2
1=2
AxðScanxÞ GstdðBmÞstdðgstdÞ fsðs þ 1ÞgstdðPstdÞ
Mg0.1Ni0.9O, respectively. These observations are in accord
with the paramagnetic and antiferromagnetic natures of
compositions. While paramagnetic nature is exhibited by
the compositions x ¼ 40, 50, 60, 70 (%Ni) antiferromag-
netic character is displayed by the compositions x ¼ 80, 90
(%Ni), respectively. Using the above Eq. (15) susceptibil-
ities were calculated at room temperature. The normalized
susceptibility wꢄg ¼ wg=x, where wg is the measured suscept-
ibility per gram for each sample of Mg1ꢀxNixO. The
calculated susceptibility with concentration is drawn in
Fig. 7 and is comparable with the previous results. Fig. 7
shows the variation of the susceptibility of the solid
solution with concentration of nickel. The susceptibility is
increased as the concentration of Ni is increasing till 60%
of Ni ((Mg0.4Ni0.6O) and it decreases. The susceptibility of
(Mg0.9Ni0.1O) is 21 ꢂ 10ꢀ6 M3/kg and it iꢀs6 going to a
maximum for (Mg0.4Ni0.6O) and is 576 ꢂ 10 M3/kg. It is
decreasing for Ni-rich (Mg0.1Ni0.9O) 113 ꢂ 10ꢀ6 M3/kg.
The above results can be understood in the light of the
Nx ¼
Nstd
,
2
2
1=2
AstdðScanstdÞ GxðBmÞxðgxÞ fsðs þ 1ÞgxðPxÞ
(14)
where Ax is the area under the absorption curve which can
be obtained by double integrating the first derivate curve of
signal after least-square fits to asymmetric Gaussian
function. Scan is the magnetic field corresponding to the
unit length of the chart; G is the gain; Bm is the modulation
field width; g is the splitting factor; S is the spin of the
system in its ground state and P is the microwave power.
The subscripts ‘x’ and ‘std’ represent the corresponding
quantities for the unknown samples (Mg1ꢀxNixO) and
reference, respectively.
The paramagnetic susceptibilities can be calculated from
the EPR data by using the formula
Ng2b2JðJ þ 1Þ
3KBT
w ¼
,
(15)

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95
900
600
500
400
300
200
100
0
Data
Linear fit
800
700
600
500
400
300
200
100
0
0
20
40
60
Ni%
80
100
0
20
40
60
80
100
%Ni
Fig. 8. Variation of molar Curie constant C(x)M plotted against x
concentration of Ni which is determined from slope of Eq. (10) (see text).
Fig. 7. Susceptibility of the solid solution Mg1ꢀxNixO obtained form EPR
verses Ni concentration.
350
previous work as follows. The whole compositional region
is divided into four parts: (1) the Mg-rich compositions
(Mg0.9Ni0.1O, Mg0.8Ni0.2O) exhibit diamagnetic behavior
because MgO is diamagnetic martial and Ni content is very
small; (2) the compositions (Mg0.7Ni0.3O, Mg0.6Ni0.4O) are
said to be in spin-glass state as the Ni concentration is
moderate; (3) the compositions (Mg0.5Ni0.5O, Mg0.4Ni0.6O)
are having maximum susceptibility and it is named as
tricritical region or anti ferromagnetic frustrated region as
the concentration of Ni is increased; (4) the Ni-rich
compositions are named as homogeneous antiferromag-
netic region.
data
linear fit
300
250
200
150
100
50
0
0
20
40
60
Ni%
80
100
3.5.1. Susceptibility of the Mg1ꢀxNixO solid solution at
different temperatures (323–453 K)
Using Eqs. (14) and (15), the susceptibilities of all the
solid solutions are calculated at different temperatures
ranging from 323 to 453 K as in the above method (the
temperature range is limited because of EPR instrument).
Here, the number of spins participating in resonance were
calculated first using Eq. (14). The spins are increasing with
increase in the temperature. This could be due to
progressive breakup of antiferromagnetic coupling and a
corresponding increase in the number of (uncoupled)
paramagnetic spins, also possibly due to diamagnetic
dilution and defect creation. The temperature dependence
of the normalized susceptibility wꢄg ¼ wg=x, where wg is the
measured susceptibility per gram for each sample of
Mg1ꢀxNixO. To check the validity of the Curie–Weiss
(CW) law in Mg1ꢀxNixO and to determine the Cg(x) and
Y(x) according to equation (CW) (Eq. (10)) a plot of 1/wg*
versus T can be used in the region 323–453 K. The values of
Cg(x) and Y(x) so determined are plotted against
composition concentration (x) of Ni in Figs. 8 and 9,
respectively. An examination of Figs. 8 and 9 enables us to
conclude that Cg(x) and Y(x) are linearly varying with
concentration of Ni. This linearity of Cg(x) and Y(x) is
very important because it rules out chemical clustering in
these compositions. Thus, the experimental variation of
Fig. 9. Variation of the Curie–Weiss temperature Y(x) plotted against the
x which is determined the from the intercept of Eq. (10) (see text). The
solid line is least-square fit to present data.
Y(x) and Cg(x) with x provides a check on the quality of
random dilution of the samples. Least-square fit to the data
yield for Y(x) versus x is Y(x) ¼ 3.174xꢀ7.24 which is in
agreement with previous result [8,29]. Least-square fit to
the data yield for Cg(x) versus x is Cg(x) ¼ 8.28x which is
agreement with previous results where x is concentration
Ni [29]. Here, Y(x) is not too large and thus there is
apparently no chemical clustering in the prepared solid
solutions of Mg1ꢀxNixO [29].
4. Conclusions
XRD, SEM and EPR susceptibility measurements of
combustion synthesized MgO–NiO solid solutions have
been described and discussed in this work. The lattice
parameter a(x) of the stoichiometric Mg1ꢀxNixO (0pxp1)
solid solutions prepared by urea-based combustion synth-
esis with fuel to oxidizer ratio (c ¼ 1) was determined by
X-ray diffraction. It was found that the composition
dependence of the lattice parameter a(x) deviates more

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96
from the linear Vegard’s model (VM) when compared to
Kuzmin–Mironova (KM) model. It was observed that a(x)
in the Mg1ꢀxNixO system differs nontrivially from the
predictions of both VM and KM models and the maximum
deviation is about 2 and 1.7 pm for x ¼ 0.4 (Mg0.6Ni0.4O)
in the two models, respectively. The increase in the
intensity of (1 1 1) peak in XRD with increase of nickel
concentration confirms substitution changes at the unit
cell. Micro strain is calculated in the solid solutions using
Nelson–Riley function (NRF) and Williamson–Hall plot.
It was observed that in both methods the micro strain is
maximum for the compositions 60–40 (Mg0.6Ni0.4O), 50–50
(Mg0.5Ni0.5O) and 40–60 (Mg0.4Ni0.6O). The crystallite size
was estimated using Williamson–Hall plot and was
observed that almost same crystalline size with all the
compositions. Porosity, as determined using XRD, in-
creases with an increase of nickel concentration. The SEM
morphology provides corroborative evidence. EPR sus-
ceptibilities of solid solution Mg1ꢀxNixO are determined at
room temperature. Variable temperature EPR is allowed to
check the Curie–Weiss law for solid solution and the
linearity of CM(x) and Y(x) with concentration of nickel
has ruled out chemical clustering in the samples.
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Acknowledgments
One of the authors K.V. Rao wants to thank the JNT
University and the Department of Physics, JNTU College
of Engineering, for encouragement.
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