This document reports on the synthesis and structural characterization of Ni1−xCdxFe2O4 materials. Key points: - Ni1−xCdxFe2O4 materials were synthesized using an auto-combustion technique, producing nanoparticles between 29-33 nm. - X-ray diffraction analysis confirmed the formation of a single cubic spinel phase structure with increasing lattice parameter with higher Cd content. - Fourier transform infrared spectroscopy showed absorption bands in the 400-700 cm−1 region. - Density functional theory calculations using the ATK-VNL code verified the experimental structural parameters and showed the materials have metallic electronic behavior.

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R E S E A R C H A R T I C L E
Quantum Matter
Vol. 5, 1–6, 2016
Synthesis and Structural Characterization of
Ni1−xCdxFe2O4: Experiment and Theory
Anurag Srivastava2 ∗
, Hari Shankar Tewari1
, and Aniruddha Mukherjee1
1
Department of Pure and Applied Physics, Guru Ghasidas Vishwavidyalaya, Bilaspur
2
Advanced Materials Research Group, CNT Lab, ABV-Indian Institute of Information Technology and Management, Gwalior
We have synthesized Ni1−x Cdx Fe2O4, using auto combustion technique with particles size in nanometer
(29–33 nm) range. The material was calcined at 800 C for 6 hours and sintered at three different temperatures.
The XRD analysis indicates the formation of single phase materials with six prominent peaks of Ni ferrite and
one extra due to Cadmium doping, whereas FT-IR analysis shows absorption band as well as narrow band
in fundamental vibration region (400–700 cm−1
) and few microscopic characteristics (density, porosity, size,
shape). The experimental structural parameters have been verified through density functional theory based
ab-initio analysis using revised PBE type parameterized generalized gradient approximation. The ab-initio result
also confirms the metallic behavior of Ni1−x Cdx Fe2O4 analyzed through its band structure and density of states
profiles.
Keywords: Magnetic Material, Sintering, X-ray Diffraction, FTIR, Ab-Initio Calculations, Band-Structure.
1. INTRODUCTION
The development of ferrite was first reported in 1946 by Snoeck
at Philips Laboratory in Holland, since then a number of
researchers have shown interest in synthesizing as well as char-
acterizing mixed ferrites materials. Spinel ferrites of general for-
mula M2+
Fe3+
2 O4, (M2+
especially transition metal ions, like
Ni2+
, Co2+
, Zn2+
etc.) possess special magnetic and electrical
properties with high chemical stability and mechanical hard-
ness, are important magnetic materials, suitable for operating
at higher frequency region, extensively used in electromagnetic
devices1–3
such as memories, sensors and microwaves, as well
as in our modern information technology applications.4
Ni fer-
rites are in demand for magnetic recording devices, magneto
optical recording and electronic devices. Magnetic interaction
and distribution of cations among tetrahedral (A) and octahe-
dral (B) sites have significant effects on the structural as well
as electrical and magnetic properties. The Cd doped Ni fer-
rites are the magnetic materials characterized by maximum per-
meability, minimum hysteresis losses, temperature variation of
properties between prescribed limits and low core losses at high
frequencies, depending on their microstructure (density, poros-
ity, size, shape) as well as macro structure (crystal structure
and elemental composition). Ni–Cd ferrites with nanometer size
can be synthesized through various methods, where in all the
methods, the reagents are mixed together at molecular levels
∗
Author to whom correspondence should be addressed.
that form homogeneous materials. Recently, experimental as
well as theoretical studies have been reported on Ni–Co–Mn,5
Ni–Zn,6
Mn–Zn,7
Ni–Cu–Zn,8
Ni–Cr9
, Ni–Co,10
Ni–Co–Cd,11
Ni–Cu–Cd,12
and Co–Cd13
by using various techniques. All these
reports confirms the single phase cubic spinel structure of ferrite
materials. However, not much work has been reported so far on
Ni–Cd ferrite. Hence looking to the importance of this category
of material, we thought it pertinent to explore the properties of
this material through its synthesis, characterization and theoret-
ical validation. Recently, our group has performed experimental
as well as ab-initio based theoretical analysis of variety of nanos-
tructured materials.14–17
In present manuscript we have reported
Ni–Cd ferrite prepared by auto combustion method, character-
ization by XRD and FT-IR analysis and verified the structural
parameters and electronic behavior of these materials using a
density functional theory based ab-initio approach.
2. METHODOLOGY
One of the most popular and efficient method of material prepa-
ration is combustion synthesis (CS) is generally of two types3
—
propagating mode (heated locally), and simultaneous mode (uni-
formly heating). Based on the property of matched oxidation and
reduction between the fuel and the oxidizer, the extremely safe
combustion synthesis can be controlled through initial param-
eters. Depending upon the fuel and the oxidizer the tempera-
ture rises rapidly and as a result of auto combustion, highly
Quantum Matter Vol. 5, No. 3, 2016 2164-7615/2016/5/001/006 doi:10.1166/qm.2016.1329 1

2. R E S E A R C H A R T I C L E Quantum Matter 5, 1–6, 2016
pure and crystalline nano size materials are formed. Reaction
between the mixture of nitrates and highly pure glycine results
a self-sustained exothermic process. This technique has asso-
ciated advantages of getting soft and fine crystalline materials
with high surface area and high purity at very low temperature
(<400 C).
The calculation of molar ratio (stoichiometric fuel to oxidant
ratio) has a significant role in this redox based combustion syn-
thesis. In the present price of work, the nitrates6 7 18 19
of the
materials are taken as oxidizer and glycine [NH2CH2COOH] as
fuel. The stoichiometric ratio ( ) have been calculated using fol-
lowing relation,
= summesion of oxidizing element in specific formula
×valency × −1 coefficient of reducing element
specific formula ×valency
−1
Where, valency of the starting materials for (M = +2, N = 0,
O = −2, H = +1, c = +4),
The ratio of the total nitrate to glycine ( ) is calculated from
the oxidation number of the starting materials and the valences
of the composition of the starting materials.
= M × +2 + N × 0 + O × −2
+ Fe × +3 + O × −2
× +4 ×C + −2 ×O + 0 ×N + +1 ×H −1
=
40
9
= 4 44
The flow chart of our present experimental setup for the syn-
thesis of Ni1−xCdxFe2O4 0 0 ≤ x ≤ 0 6 ferrites is given in
Figure 1. Here nitrates of the precursor materials have been taken
as oxidizer and glycine as reducing agent or fuel. First of all,
stoichiometric amount ( ) of nickel, cadmium and ferric nitrate
salts were taken in a beaker and heated at 70 C for 15–20 min
until it get totally melt. Then the glycine is added to the mixture
and heated till it melts so as to get a homogeneous mixture. The
total mixture is further heated at higher temperature (320–350 C,
Fig. 1. Flow chart representing the experimental steps for Ni1−x Cdx Fe2O4 Ferrite synthesis.
depending upon x) for 15 min so that the following reaction5
takes place results combustion.
1−x Ni NO3 2 +xCd NO3 2 +2Fe NO3 3
+
40
9
NH2CH2COOH = Ni1−xCdxFe2O4 +
100
9
H2O
+
80
9
CO2 +
56
9
N2
The structural parameter of Ni–Cd ferrite materials of different
compositions have been calculated experimentally and to verify
the same we have used a well known density functional theory
based ab-initio tool ATK-VNL.20
For the present computation,
a generalized gradient approximation (GGA)21 22
scheme has
been used as exchange correlation with revised Perdew, Burke,
Ernzerhof23
type parameterization employed with double zeta
double polarized type of basis sets. The calculation has been per-
formed on a sufficient k mesh for the inverse structure unit cell
containing 14 atoms and the optimized structure is a face cen-
tered cubic (a = b = c). The obtained theoretical lattice parameter
is in close agreement to our experimental results. Further, the
theoretical analysis has been extended to understand the behavior
of synthesized Ni–Cd ferrite in respect of its commercial appli-
cations, the electronic properties24 25
in terms of band structure
and density of states (DOS) computation have been analyzed and
discussed in results section separately.
3. RESULTS AND DISCUSSION
The present section discusses the Powder X-ray Diffraction
(XRD) and Fourier Transform Infra-Red (FT-IR) spectroscopy
results of Ni–Cd Ferrite powdered sample followed by the theo-
retical verification of structural parameters and electronic prop-
erties using ab-initio approach applied through Atomistix Tool
Kit-Virtual Nano Lab (ATK-VNL) code.
3.1. X ray Diffraction Studies
In our present work, the XRD analysis of powdered
Ni1−xCdxFe2O4 (x = 0 0, 0.2, 0.4, 0.6) ferrite system rep-
resented in Figure 2, have been performed and analyzed
through RIGAKU, MINIFLEX diffractometer (Cu K radiation,
2

3. R E S E A R C H A R T I C L EQuantum Matter 5, 1–6, 2016
20 30 40 50 60 70 80
X=0.6
X=0.4
X=0.2
X=0.0
relativeintensityrelativeintensity
2θ in degreein degree
Fig. 2. XRD patterns of Ni1−x Cdx Fe2O4 Ferrite as a function of Cd
Composition (x).
2 = 20 –80 ). Where, the most intense peak, representing (220),
(311), (400), (422), (333), (440) planes27
are for Ni ferrite, and
an additional peak (533) is due to substitutional doping of Cd.
The lattice parameters ‘aexp’ for all the samples have been deter-
mined using Eq. (1), represents the most prominent peak (311)
of the XRD pattern and tabulated in Table I as a function of the
Cd composition. The larger ionic radii of Cd2+
(0.97 Å) to that
of Ni2+
(0.69 Å) and Fe3+
(0.645 Å) results an increase in the
lattice parameter as well as X ray density and the crystalline size
of Ni–Cd Ferrite shown in Figure 3. The Ni–Cd ferrites have
been calcined at 800 C temperature for 6 hrs and sintered at
different temperatures at 1050 C, 1100 C, 1150 C, for 6 hrs.
aexp = dhkl
√
h2
+k2
+l2
sin
√
h2
+k2
+l2
(1)
Where hkl are the Miller indices and dhkl the inter planner
spacing. The average crystalline size (D in nm) in the direction
perpendicular to (hkl) plane of reflexes have been estimated by
using Scherrer Eq. (2),
D =
k
cos
(2)
Where, k = 0 9 is the Scherrer constant, proposed by Klug and
Alexander,28
= 1 540562 Å and the full wave half maxima
of the diffraction peaks at an angle for corrected instrument
broadening (in radian respectively). The (311) peak has been
chosen for calculation as the most suitable for crystalline size
Table I. Lattice parameter (a), density ( the), crystallite size of
Ni1−x Cdx Fe2O4.
Lattice parameter (Å)
Cd Crystallite Density ( the)
concentration (x) Exp Theory Others 1
size (nm) in gm/cm3
0.0 8.338 8.333 8.34 29.25 5.370
0.2 8.343 8.340 – 27.78 5.606
0.4 8.361 8.346 – 29.94 5.813
0.6 8.379 8.367 – 32.94 5.985
0.0 0.1 0.2 0.3 0.4 0.5 0.6
8.34
8.35
8.36
8.37
8.38
28.5
30.0
31.5
33.0
34.5
Latticeparameter
Cd composition(x)
Crystallitesize
Fig. 3. Lattice parameter and crystallite size of Ni1−x Cdx Fe2O4 as a func-
tion of Cd composition (x).
distribution. The theoretical density (X ray density) has been cal-
culated using the following relation
the =
ZM
Na3
=
8M
Na3
(3)
Here, Z =8 represent the number of molecules per unit cell of
the spinel lattice, M the molecular weight of the ferrite, N and a
(aexp be the respective Avogadro’s number and lattice parameter.
Generally all Ni2+
ions occupy octahedral B sites but the Cd2+
ions are preferred to occupy the tetrahedral A sites. The pre-
ferred cation distribution2 29–32
of the sample Ni1−xCdxFe2O4 is
[Cd2+
x Fe3+
1−x]A [Ni2+
1−x Fe3+
1+x]BO2−
4 . Here, the first square bracket
indicates tetrahedral A sites and the second one is octahedral B
site. The Cd2+
ion has a zero magnetic moment33
whereas Fe3+
and Ni2+
has the magnetic moment of 5 B and 2 B respec-
tively. Addition of Cd2+
ion at A site create a loss of magnetic
neighborhood of Fe3+
ions and the spin may become uncoupled
consequently more field is need to align the magnetic moments
in the direction of applied magnetic field.
The theoretical lattice parameter (ath) have been computed by
total energy minimization of the optimized structure using ATK-
VNL19
code and have a good agreement with the obtained exper-
imental values as given in Table I.
3.2. Density, Porosity and Densification Parameter
The densification parameter as shown in Figure 4 described in
terms of apparent porosity and bulk density as a function of firing
(sintering) temperature is calculated using the relation (4)
= T − O
the − O
(4)
The apparent porosity of the investigated object decreases from
1050 C to 1150 C in another observation the bulk density
decreases with increase in Cd concentration but increases with
the firing temperature. The increase of the bulk density with
increase in the firing temperature is due to the fact of decreas-
ing porosity (Table II) and the formation of Ni–Cd ferrite phase
where the reactant has high densities. A characteristic path of
the sintering process is shrinkage of the samples, are measured
for the sintered material compared to the original unfired (green
body) powder compact.
3

4. R E S E A R C H A R T I C L E Quantum Matter 5, 1–6, 2016
1040 1060 1080 1100 1120 1140 1160
42
44
46
48
50
52
54
56
58
2.60
2.65
2.70
2.75
2.80
2.85
2.90
2.95
3.00
3.05
3.10
Bulkdensity(gm/cc)
sintering temperature (ºC)
porosity
X = 0.0
X = 0.2
X = 0.4
X = 0.6
Fig. 4. Porosity and bulk density of Ni1−x Cdx Fe2 O4 as a function of sin-
tering temperature.
In the present work, increase of sintering temperature accel-
erates the linear shrinkage and increases densification. Further
increase in sintering temperature leads to shrinkage and reaching
to maximum value at 1150 C. During shrinkage, small pores
merge first and further increase in temperature results continu-
ous shrinkage. On the other hand, due to increase in temperature,
some micro-pores were merged together forming macro-pores
in the pore size distribution. High temperature treatment results
slower rate shrinkage of large pores than small pores, even
though both are associated at a grain boundary. Thus sintering
temperature has a significant effect on bulk density as well as
porosity of the materials.
3.3. FTIR Analysis
IR spectrum represents the molecular absorption and transmis-
sion, creating a molecular fingerprint of the sample. FT-IR
analysis was used to identify unknown materials as well as to
determine the quality or consistency of a sample and the amount
of components in a mixture. The spectra were recorded on a
SHIMADZU-FTIR 8400S equipment using KBr as reference in
a wave number region of 350 to 4000 cm−1
. The ratio of KBr
and samples were taken as 95:5 in a cylindrical die and measured
at room temperature. Figure 5 shows the recorded spectra in 400
to 800 Cm−1
range of Ni–Cd ferrite system. The inspection of
the spectra shows absorption band and a narrow band in that
range. It is due to the fact for these classes of compounds that
Table II. Bulk density ( T ), densification parameter ( ) and poros-
ity (P) of Ni1−x Cdx Fe2O4.
Cd Temperature 0 in T in Porosity
concentration (x) in C gm/cm3
gm/cm3
(P )
0.0 1050 2.766 2.766 0.000 48.49
1100 2.766 2.872 0.041 46.51
1150 2.766 3.050 0.109 43.20
0.2 1050 2.705 2.705 0.000 51.47
1100 2.705 2.722 0.006 51.45
1150 2.705 2.778 0.025 50.45
0.4 1050 2.674 2.674 0.000 53.99
1100 2.674 2.681 0.002 53.88
1150 2.674 2.690 0.005 53.72
0.6 1050 2.637 2.637 0.000 55.94
1100 2.637 2.648 0.003 55.76
1150 2.637 2.684 0.014 55.16
400 450 500 550 600 650 700 750 800
0
10
20
30
40
50
60
transmitance(%)
wave number cm–1
X=0.0X=0.0
X=0.4X=0.4
X=0.2X=0.2
X=0.6X=0.6
Fig. 5. FT-IR spectra of Ni1−x Cdx Fe2O4 at four different Cd compositions
at room temperature.
the absorption in that range is not restricted but occur in spectra
of most metallic oxide.34
The reason of arising of these bands
are due to lattice vibration of the oxide ions against the cations.
A gradual increase in absorption at higher frequency is observed
due to electronic transition.
The IR spectra have been used to locate the band positions, as
given in Table III. The higher frequency band is observed around
590 cm−1
and lower frequency around 410 cm−1
but a narrow
band is also observed at 460 cm−1
. The bands in 400–700 cm−1
region are assigned to the fundamental vibration of the ions of
the ferrite crystal. It is necessary to consider the vibrational spec-
tra of the periodic structure for the analysis of such spectra. By
taking into consideration this vibrational problem, a crystal can
be classified according to the continuity of bonding as (1) contin-
uously bonded, (2) discontinuously bonded and (3) intermediate.
Since Ni2+
ions occupied in octahedral B sites so the substitu-
tion of Cd2+
ion in the system decreases the amount of Ni2+
ion
and transforms Fe3+
ion from B site to A site, shifts the band
position toward lower wave number. The estimation of force con-
stant of the tetrahedral site (Kt) and octahedral site (Ko) have
been performed for these two vibrational band by employing the
method suggested by Waldron34
as given by,
Kt = 7 62×Mt ×v2
t ×10−7
Nm−1
Ko = 10 62× Mo/2 ×v2
o ×10−7
Nm−1
Where, Mt and Mo represent the molecular weight of the
cations occupying tetrahedral and octahedral sites respectively.
Table III contains the estimated values of Kt and Ko. The tetra-
hedral force constant gradually increases with Cd concentration
where as octahedral force constant decreases in this ferrite sys-
tem. Addition of Cd2+
content in tetrahedral site transform Fe3+
Table III. Absorption band frequency and force constant of
Ni1−x Cdx Fe2O4.
Cd concentration vt v vo Kt Ko
(x) cm−1
cm−1
cm−1
102
N/m 102
N/m
0.0 586 461 423 1.46 1.08
0.2 588 462 410 1.79 1.02
0.4 593 463 401 2.10 0.97
0.6 595 464 400 2.42 0.95
4

5. R E S E A R C H A R T I C L EQuantum Matter 5, 1–6, 2016
ion from tetrahedral to octahedral site results a charge imbalance
on the system increase tetrahedral force constant.
3.4. Band Structure and Density of State Analysis
In order to verify the nature of Ni1−xCdxFe2O4 0 0 ≤ x ≤ 0 6
we have performed the density functional theory based
(a)
–6 –4 –2 0 2 4 6
0
20
40
60
80
100
120
DOS(eV–1
)
Energy (eV)
x=0.0
(e)
(b)
DOS(eV–1
)
–6 –4 –2 0 2 4 6
0
10
20
30
40
50
60
70
80
Energy (eV)
x=0.2
(f)
(c)
DOS(eV–1
)
Energy (eV)
–6 –4 –2 0 2 4 6
0
10
20
30
40
50
60
70
x=0.4
(g)
(d)
DOS(eV–1
)
Energy (eV)
–6 –4 –2 0 2 4 6
0
10
20
30
40
50
60
x=0.6
(h)
Fig. 6. Band structure and DOS profile of Ni1−x Cdx Fe2O4 at different Cd concentration (x).
computation to analyze the band structure and density of state
(DOS). Figures 6(a)–(d) shows the band structure of the face
centered cubic Ni–Cd ferrite, where, number of bands are over-
lapping and crossing the Fermi level showing metallic behavior.
On substitutional doping of 20% Cd, few energy levels are cross-
ing the Fermi level and in turn show the metallicity.
5

6. R E S E A R C H A R T I C L E Quantum Matter 5, 1–6, 2016
To verify the band structure plots, the density of states profile
has also been analyzed, shown in Figures 6(e)–(h) for each Cd
concentration in Ni1−xCdxFe2O4 0 0 ≤ x ≤ 0 6 . In pure Ni fer-
rite, there are number of peaks in conduction band region with
a highest peak at 4.0 eV along with distorted peak crossing the
Fermi level and few peaks in valence band. However, on increas-
ing the Cd composition in host Ni-ferrite there is shifting of high-
est peak of conduction bands, few bands crossing the Fermi level
in band structure plot of 20% cadmium in host Ni-Ferrite. Simi-
larly, for other compositions of cadmium it can be seen that peaks
are available near both sides of the Fermi level and broadening
of the peaks occurs in the conduction band region, which in turn
confirms the metallic properties of the materials. The densities
of state plots have number peaks and as much as Cd atoms are
doped, peaks are more dispersed showing more metallic nature
of Cd doped Ni ferrite than pure Ni ferrite.
4. CONCLUSION
The present work includes the synthesis of Ni–Cd ferrite at dif-
ferent Cd concentration using auto combustion route method and
its characterization through XRD and FTIR. In the study, it has
been observed that due to continuous shrinkage of material, the
estimated bulk or green densities of the materials increases from
2.63 to 2.73 gm/cm.3
XRD patterns of the sample estimates the
lattice parameters between 8.34 Å–8.37 Å, XRD densities from
5.37 gm/cm3
to 5.98 gm/cm3
and crystallite size ranges from
27 nm to 33 nm. The structural parameters and metallic nature of
Ni–Cd ferrite material as a function of cadmium composition has
successfully been verified through ab-initio approach in terms of
its electronic band structure and density of state profiles. As not
much information is available on Ni–Cd ferrite material, hence
the present piece of work will certainly be a matter of further
investigations for the scientific community.
Acknowledgment: Authors are thankful to ABV-IIITM,
Gwalior for providing computational facilities at Advanced
Materials Research Group of CNT Lab. One of the authors,
Aniruddha Mukherjee is thankful to department of physics, G. G.
Vishwavidyalaya, Bilaspur, where, synthesis and characterization
of this material was performed.
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Received: 22 December 2013. Accepted: 30 July 2014.
6