Chapter 1: Lanthanide Intermetallic Compounds
1
CHAPTER 1
Lanthanide Intermetallic Compounds
Binary rare earth compounds as well as their derivatives have gained lot of
attention during past decades after the discovery of giant magnetocaloric effect and
simultaneous discovery of giant magnetoresistance effect. In extension to this, rare
earth intermetallic compounds with transition metals prove to be important class of
materials due to their possible potential applications towards the fabrication of
magnetic sensors, magnetic memory devices, automobile devices operated at high
temperatures, aerospace applications like the development of aircraft turbines for
commercial use. The intermetallic compounds of lanthanide with nickel are ideal
ferromagnetic materials because of their extraordinary magnetic properties used in
the generation of magnetocaloric devices, which are active materials in eco-friendly
magnetic refrigeration process. Also they have use in permanent magnets, magnetic
lasers, medical field for MRI and many more.
In this chapter we have introduced the solid state physics and introduction of
lanthanide intermetallic compounds with transition metals and their peculiar
technical applications. A description of origin of magnetism, the spin interaction
within the compounds and concept of magnetocaloric effect is included. The chapter
also includes the motivation, objectives behind the target and aim of the present
thesis.
Chapter 1: Lanthanide Intermetallic Compounds
2
1.1 Solid State Physics
Science is a systematic attempt to understand natural phenomena and use the
knowledge so gained to predict, modify and control phenomena. The curiosity to
learn about the world, unravelling the secrets of nature is the first step towards the
discovery of science. Unifying concepts that offered a genuine ability to calculate the
properties of solids had to await the coming of quantum mechanics. In order to
compute the properties of solids we can use our knowledge of atoms, Quantum
Mechanics and Statistical physics to explain what we call condensed matter physics.
Condensed matter Physics also known as solid state physics deals with the
macroscopic and microscopic physical properties of matter. It classifies materials
into two categories: Crystalline materials and Non- crystalline materials
(Amorphous materials). Solid State Physics is concerned with study of crystal
structure and behaviour of electrons in crystals. It began with the discovery of X-ray
diffraction and calculation and predictions of various crystal properties. Basically the
structure of solid can be defined in terms of lattice with a group of atoms attached to
every lattice points called basis. Such type of groups of basis, when repeated in a
space forms a crystal lattice.
In comprise manner, crystal structure can be obtained by attaching atoms,
groups of atoms or molecules which are called basis (motif) to the lattice sides of the
lattice point. The smallest component of the crystal (group of atoms, ions or
molecules) when stacked together with pure translational repetition reproduces the
whole crystal is called unit cell.
Chapter 1: Lanthanide Intermetallic Compounds
3
1.2 Types of Crystal Lattice
The study of condensed matter physics begins in the early years of the
century following the discovery of X-ray diffraction (XRD) by crystals leads to the
successful predictions of the various properties of crystal [1]. In a crystal structure
the lattice points group provides the information about the collection of symmetry
operations carried about the lattice point. There are 32 classes of crystal systems
based on their geometrical considerations (symmetry and internal system).
To understand the various types of lattices, one has to learn elements of group
theory:
Point group consists of symmetry operations in which at least one point
remains fixed and unchanged in space.
Space group consists of both translational and rotational symmetry operations
of a crystal.
For that reason, crystal systems are categorised into 7 groups on the basis on
angles between the three internal axes and intercepts of the faces along them. The
basic crystal systems are: cubic, tetragonal, orthorhombic, monoclinic, triclinic,
trigonal, and hexagonal. These seven basic crystal lattices are further divided into 14
crystal lattices by Bravais and are commonly known as Bravais Lattices. A Bravais
Lattice is a three dimensional lattice. A Bravais Lattice tiles space without any gaps
or holes. There are 14 ways in which Bravais Lattices can be accomplished. They are
shown in Figure 1.1.
Chapter 1: Lanthanide Intermetallic Compounds
4
Figure 1.1: Seven basic crystal lattices classified into Bravais Lattices
1.3 Brillouin Zone
A Brillouin Zone is defined as a Wigner-Seitz primitive cell in the reciprocal
lattice. Reciprocal lattice is a concept which is devised for tabulating both the slopes
and the interplaner spacing of the planes of the crystal lattice. If the length assigned
to each normal is proportional to the reciprocal of the interplaner spacing of the
plane, then the points at the end of their normal drawn from a common origin is
called reciprocal lattice.
Brillouin zones for a crystal lattice can be obtained by constructing the
reciprocal lattice. Then, use the same algorithm as for finding the Wigner-Seitz
primitive cell in real space (draw vectors to all the nearest reciprocal lattice points
and then bisect them. The resulting figure is gives Wigner-Seitz cell. The nice result
of this, it has a direct relation to the Bragg‟s diffraction condition.
Chapter 1: Lanthanide Intermetallic Compounds
5
22K.G G 0 or 22K.G G (1.1)
Where, K is the wave vector of an X-ray measured from the origin of reciprocal
lattice, can be written as G and –G are also vectors in the reciprocal lattice related to
original lattice structure.
Therefore, equation 1.1 concludes that the Brillouin Zone exhibits all wave vectors
K in reciprocal lattice G , which can be Bragg-reflected by a crystal.
The first Brillouin zone is the smallest volume entirely enclosed by the planes
that are perpendicular bisectors of the reciprocal lattice vectors drawn from
the origin. Or we can also define it as the volume encompassed around a
lattice point without crossing any Bragg planes.
Second Brillouin zone is the volume obtained by crossing only one plane.
Continue to higher orders…
1.4 Symmetry of a Crystal
In all the crystal lattices it is found that the angles between corresponding
faces of the lattice have same value. It means the regularity of the external structure
implies regularity of internal structure. This leads to the sense of symmetry within
the crystal lattice which is a powerful tool to study the internal structure of crystal
structures. The symmetry possessed by the crystal lattices is described by symmetry
operations.
A symmetry operation is one which carries the crystal structure into itself i.e.
leaves the crystal and its environment invariant [2]. If a body attains its position after
an operation the body is said to possesses a symmetry corresponding to that
operation. Symmetry operations performed about a point or a line define point group
symmetries and if translation is also added then the combination of rotation and
Chapter 1: Lanthanide Intermetallic Compounds
6
translation define space group symmetry elements. There are 32 point groups which
cover all the possible symmetries of a crystal with respect to a point in space which
does not move during the symmetry operations [3].
Basically there are three point group symmetry elements:
Rotation axes of symmetry: If a body remains invariant after a rotation
through any angle θ, the body is said to possess rotational symmetry.
Inversion symmetry: A crystal is said to possess centre of symmetry also
known as inversion centre or inversion symmetry, if for every lattice point at
position r, there must present an another lattice point –r.
Reflection symmetry: In this symmetry operation, a line or plane exists which
divides the crystal into two exactly identical halves.
1.5 Rare Earth Compounds
The term „rare earths‟ was proposed in 1794 [4]. The term „rare‟ was used
because when they were found they were thought to be present in the earth‟s crust in
only small amounts, and the term „earths‟ was used because as oxides they have an
earthy appearance. The rare earth elements are the 15 lanthanide elements (Ln) with
atomic numbers 57 to 71. In order of increasing atomic number, they are Lanthanum
(La), Cerium (Ce), Praseodymium (Pr), Neodymium (Nd), Promethium (Pm),
Samarium (Sm), Europium (Eu), Gadolinium (Gd), Terbium (Tb), Dysprosium (Dy),
Holmium (Ho), Erbium (Er), Thulium (Tm), Ytterbium (Yb) and Lutetium (Lu).
Yttrium (Y), Scandium (Sc) and Thorium (Th), they are f-block elements except
La57
, which belongs to d-block element with electronic configuration [Xe] 5d1
6s2.
Electronic configuration of lanthanides may be represented by a general formula
[Xe] 4f n
5dm
6s2 (n= 1, 2, 3, --- 14; m= 0 or 10). Ln‟s are classified into two groups:
Chapter 1: Lanthanide Intermetallic Compounds
7
light Ln‟s or cerium group (Lanthanum to Europium) as well as yttrium and
scandium and the heavy Ln‟s comprising Gadolinium through Lutetium. The light
Ln‟s are more abundant than the heavy Ln‟s. In these elements the 4f electrons are
deeply embedded within the atoms and encapsulated by 5s and 5p states situated
around them. The conduction bands of the metals are formed by the 5d and 6s
electrons and since these electrons encase the 4f electrons, they are drawn closer
toward the nucleus because of the increased shielding of the increasing nuclear
charge by the 4f electrons (when moving across the series from lanthanum to
lutetium). Some of the structural parameters of Lanthanide ions at room temperature
[1] are shown in Table1.1.
Table 1.1 The crystal structure, lattice constants and atomic radius of the elements
of lanthanide series at room temperature
Lanthanide Lattice structure
Lattice constants (Å) Atomic radius (a.u.)
A c
La dhcp 3.774 12.171 3.92
Ce () dhcp 3.681 11.857 3.83
Ce () fcc 5.161 3.81
Ce(α) fcc 4.850 (77K) 3.58
Pr dhcp 3.672 11.833 3.82
Nd dhcp 3.658 11.797 3.80
Pm dhcp 3.650 11.650 3.78
Sm rhom 3.629 26.207 3.77
Eu bcc 4.583 -- 4.26
Gd hcp 3.634 5.781 3.76
Tb hcp 3.606 5.697 3.72
Dy hcp 3.592 5.650 3.70
Ho hcp 3.578 5.618 3.69
Er hcp 3.559 5.585 3.67
Tm hcp 3.538 5.554 3.65
Yb fcc 5.485 4.05
Lu hcp 3.505 5.549 3.62
Chapter 1: Lanthanide Intermetallic Compounds
8
Lanthanide elements have numerous, diverse, highly specialised applications.
The largest use of lanthanide oxides is in mixed forms, principally in petroleum
fluid-cracking catalysts and in lanthanide-phosphors for television, X-ray
intensifying, and fluorescent and incandescent lighting [5]. Ln‟s have great use as
catalysts, mainly in the refining of crude oil to improve cracking efficiencies and in
automobiles to improve oxidation of pollutants. They are used in the glass and
ceramics industry as glass-polishing compounds, decolourising agents, UV
absorbers, colouring agents, in optical lenses and glasses, and additives to structural
ceramics [6]. They also have potentials applications to be used as alloying agents to
improve the properties of superalloys and magnesium, aluminium and titanium
alloys. Ln‟s and their alloys form an important class of materials due to the presence
of localized f-band electrons in these materials. These compounds have partially
localized f states which get delocalized under pressure into d states of Ln–ion and
make them strongly-correlated. Their physical properties are different from other
materials because of large atomic number. The Lanthanides have long been an
interesting and challenging subject to physicists due to their unique magnetic,
electric, thermal and optical properties. They show various fascinating physical
phenomena, such as magnetic-optical effect, heavy-fermion state, dense Kondo
effect, magnetic polaron effect, etc [7]. In addition, they are also of great importance
to the industries due to their numerous technological applications.
1.6 Lanthanide – Nickel Intermetallic Compounds
High pressure research on compounds with lanthanide elements has drawn
great attention during last decades because of their peculiar properties [8-14]. Their
interesting features have been correlated with the existence of unfilled f-electron
Chapter 1: Lanthanide Intermetallic Compounds
9
shells of the lanthanide ions, which are highly delocalized and interact strongly with
the lattice [15-16]. Correlation between f-electrons of lanthanide elements and d-
electrons of transition elements is the origin of high magnetic moments and magnetic
anisotropy and semi-metallic, half metallic and metallic character of a particular
material [17-18]. Their intermetallics with transition metals are known as promising
materials for hydrogen storage purpose which is one of the recent topic of interest in
fundamental as well as applied researches.
Intermetallic compounds in which the magnetism of the lanthanide (Ln) ions
with their partially filled localized 4f shell is combined with that of the itinerant 3d
transition (T) metals form an important class of materials, both for fundamental
studies in magnetism as well as from an applications point of view. The 4f and 3d
electron spins are coupled by exchange interactions for which three different types
are distinguished: T-T, Ln-T and Ln-Ln interactions [19]. For the iron, cobalt and
nickel rich Ln-T compounds, the T-T interaction is the strongest interaction and
primarily governs the Curie temperature. The Ln-Ln interaction is weak, although its
effect contributes to a characteristic variation of the Curie temperature with the
lanthanide element in an iso-structural series. The Ln-T interaction, which is
intermediate between the two former ones, plays an important role in the magnetism
of LnT compounds, since it couples the strongly anisotropic Ln-sublattice
magnetization to the less anisotropic T- sublattice magnetization. In this way, some
of the LnT compounds exhibit large magnetic anisotropies even at room temperature,
one of the prerequisites for potential application as permanent-magnet material. The
exchange coupling between the Ln and T electron spins is indirect. There is an intra-
atomic, ferromagnetic exchange interaction between the 4f and 5d spins of the
Chapter 1: Lanthanide Intermetallic Compounds
10
lanthanide ions and an interatomic interaction between the itinerant 5d and 3d spins.
For electrons in a less than half-filled d band (the 5d electrons of the lanthanide ions)
interacting with electrons in a more than half-filled d band (3d electrons of the
transition metal), the exchange interaction is, in general, found to lead to an anti
parallel coupling between the 5d and 3d spins. Taking into account the coupling
between the spin and orbital moments of the 4f electrons, it can be explained that the
magnetic order is ferromagnetic (parallel Ln and T magnetic moments) in LnT
compounds with light and heavy lanthanide elements. The exchange interaction
between the 3d and 4f electrons is usually represented by a molecular-field
parameter, nLnT, by which the 4f and 3d sublattice magnetic moments are coupled
[20]. Values for this molecular field for the iron, nickel or cobalt-rich LnT
compounds are typically of the order of 100 T and large magnetic fields are required
in order to induce changes in the magnetic moment configuration of the two
sublattices [3].
Here, in the present work, we considered a set of some lanthanide intermetallic
compounds; LnNi‟s (where, Ln= Ce, Pr, Nd, Sm, Gd and Dy) to perform first
principle study on their structural, magnetic, electronic and thermal properties.
1.7 Crystal Properties of LnNi’s
1.7.1 Structural Properties
When the material changes from one lattice structure to another state then
they creates minimum energy configuration. The change in crystal structure with
change in internal energy leads to the phase transformation phenomenon. Phase
transformation of a thermodynamic system causes a sudden change in one of the
Chapter 1: Lanthanide Intermetallic Compounds
11
physical quantities like specific heat or volume due to change in thermodynamic
variable like pressure or temperature. At the point of phase transition, two phases of
a substance have identical free energies and therefore are equally likely to exist. (The
process and phenomenon of phase transitions are discussed in detail in chapter 6).
The present chosen set of lanthanides intermetallic compounds i.e. CeNi,
PrNi, NdNi, SmNi, GdNi and DyNi, the lanthanide ion exists in trivalent form (Ln3+
)
[21-22] with Ni. These lanthanide intermetallic compounds exhibits base centred
chromium boride structure with space group Cmcm and No. 63. CrB structure except
DyNi compound whose ground state is orthorhombic FeB structure with space group
(62-Pnma) [23-29]. The unit cell representation of CrB and FeB structure is shown in
Figure 1.2.
Figure 1.2 The unit cell structure of CrB and FeB in which lanthanide intermetallics
compounds exists.
Chapter 1: Lanthanide Intermetallic Compounds
12
Effect of Pressure on Structural Properties
The applications of high pressure in solid state physics have become a topic
of great interest from past few decades. In crystal structure, the distribution of atoms
and / or molecules may be homogenous or non-homogeneous. Its homogenous
assembly is called phase and characterized by many thermodynamic quantities, like
volume, pressure, temperature, energy, etc. A phase is said to be meta stable, if it is
present with the intermediate minimum free energy and the actual phase is found at
further lower energy under the same thermodynamic conditions [30-31]. If such
phases do not exist, then the crystal state becomes unstable and the system
transforms to the other stable or equilibrium phase at lower Gibb‟s free energy. The
two phases of a system are distinguished from each other, if they crystallize in
different compositions or crystal structures. The phase transition in a solid occurs
when the variation of Gibb‟s free energy is associated with some changes in
structural details (atomic or electronic configuration) and the variation of energy
takes place, if the thermodynamic conditions acting on the system, like pressure,
temperature, electric or magnetic field are varied and causes smooth variation in the
Gibb‟s free energy.
1.7.2 Electronic Properties
Electronic properties of solids deals with energy band structures of the
electronic states of the valence shell electrons. It provides an idea about the basic
nature of the material whether it is metallic characteristics, insulator or semi
conductor.
Every solid has its own characteristic energy band structure. A solid can have
large number of bands. In theory, a solid can have infinitely many bands (just as an
Chapter 1: Lanthanide Intermetallic Compounds
13
atom has infinitely many energy levels). However, all but a few of these bands lie at
energies so high that any electron that attains those energies will escape from the
solid. These bands are usually disregarded. Bands have different widths, based upon
the properties of the atomic orbitals from which they arise. Also, allowed bands may
overlap, producing (for practical purposes) a single large band. On the basis of
energy band structures solids are categorise into three types shown in figure given
below:
Figure 1.3 Classification of materials on the basis of energy band gaps
Metals
Metals have free electrons and partially filled valence bands. Metals have
overlapping valence and conduction bands, therefore they are highly conductive.
They possess high density of states at the Fermi energy Level.
Semi Metals
It is the sub branch of metals. Semimetals have their highest valance band
filled. The filled valance band, however, are overlapped with the next higher band
(conduction band), therefore they are conductive but with slightly higher resistivity
Chapter 1: Lanthanide Intermetallic Compounds
14
than normal metals. They possess very low density of states at the Fermi energy
Level. Semi metals do not have free electrons.
Semi conductors
Semiconductors have similar band structure as insulators but with a much
smaller band gap (< 4 eV). Some electrons can jump to the empty conduction band
by thermal or optical excitation. Semiconductors have resistivity in between those of
metals and insulators.
Insulators
Insulators have filled valence bands and empty conduction bands, separated
by a large energy band gap (>4eV), which is a “forbidden” range of energies.
Electrons must be promoted across the energy gap to conduct, but the materials
having energy gap typically > 4eV have very high resistivity.
The knowledge of the density of states, that is, what is the probability of an
electron in an energy state, also tells about the magnetic and non magnetic behaviour
of solids.
Effect of Pressure on Electronic Properties
The high pressure applications related to electronic structure of solids become
more important phenomenon to understand the electron transfer from one orbital to
another orbital. When the pressure of higher range is applied on the solids then the
average distance between the molecules decreases which increases the tunnelling to
the mobile electrons [32-33]. As a result of which both mobility and carrier
concentration of the electrons increases. Therefore, electronic structure of the solids
can be modified by applying the pressure of appropriate magnitude.
Chapter 1: Lanthanide Intermetallic Compounds
15
1.7.3 Magnetic Properties and different types of magnetism
The magnetism is a phenomenon in which the materials assert an attractive or
repulsive force on other materials existing nearby them. Some elements like iron,
cobalt and nickel and their alloys behave like magnets. It is a property of materials
that respond to an applied magnetic field. The magnetic state / phase of a material
depends on temperature, pressure etc. So a material may exhibit more than one form
of magnetism depending on its temperature etc. When magnetic materials are placed
in magnetic field they show one of the following behaviour,
Diamagnetic: Such materials show a net but weak magnetic moment
opposite to an applied magnetic field.
Paramagnetic: Such materials show a net magnetic moment in the direction
of an applied field.
Ferromagnetic: Such materials possess a net magnetic moment even in zero
applied magnetic fields.
Antiferromagnetic: in such type of materials the magnetic moments of
atoms or molecules, usually related to the spins of electrons, align in a regular
pattern with neighbouring spins (on different sublattices) pointing in opposite
directions.
Ferrimagnetic: in such materials the magnetic moments of the atoms on
different sublattices are opposed as in antiferromagnetism but the opposing
moments are unequal and a spontaneous magnetization remains.
Magnetism in Lanthanide Compounds
The atomic configurations of the lanthanide metals are characterized by
partially filled 4f shells, which like the partially filled d shells of the transition
metals, can lead to a variety of magnetic effects. Depending upon the immediate
environment of the lanthanide atom, the magnitude of the effective magnetic
Chapter 1: Lanthanide Intermetallic Compounds
16
moments of the atom can vary, that is why a collection of lanthanide atoms generally
represent slightly different magnetic properties than in the case of a free lanthanide
ion.
The magnetic properties of the lanthanides, as well as those interesting many-
body phenomena, are intimately related to the highly localized 4f electrons of the
open shell. As early as seventy years ago, Van Vleck et al. had studied the magnetic
properties of lanthanide ions [7]. They have suggested that the 4f electrons
responsible for the magnetism of the lanthanides are sequestered in the interior of the
atom and so experience only a small crystalline field [34]. They explained why
Hund‟s rule with L-S coupling could give values of the magnetic moments of
lanthanide ions very close to experimental observations, at least in the high-
temperature region. The lanthanides generally have large magnetic moments, yet the
exchange interactions between local spins are relatively weak. Thus other factors,
such as magnetic dipole interactions, may also have significant influence on their
magnetic orderings.
Almost the entire lanthanides exhibit complicated forms of magnetism. The
most widely recognised materials are the ferromagnetic. Nickel containing
lanthanide elements belong to same class.
1.7.4 Thermal Properties
The change in the temperature of a material affects its dynamic properties.
The branch of science “Thermodynamics”, impart great help to explain the internal
characteristics of solids which cannot be explained by the transport of single particle.
Lattice dynamics is an important aspect to study properties of materials. It concerns
with the vibrations of the atoms about their mean position. These vibrations are
Chapter 1: Lanthanide Intermetallic Compounds
17
entirely responsible for thermal properties heat capacity, thermal expansion, entropy,
phonons and thermal conductivity etc [35]. The concept of phonons assumes that the
atomic vibrations are harmonic in nature, which is strictly valid at low temperatures,
typically below the Debye temperature and specific heat of solid.
In the present thesis, we have also analysed the thermal behaviour of chosen
set of lanthanide nickel intermetallic compounds (i.e CeNi, PrNi, NdNi, SmNi, GdNi
and DyNi). Various phenomenons related to thermal properties like thermal
expansion, specific heat, Gruneisen parameter, bulk modulus and equilibrium
volume by varying temperature and pressure range are studied.
1.8 Review of Literature
A plenty of literature is available based on experimental techniques as well as
theoretical approaches on lanthanide compounds. But as concerned with the topic
intermetallics of lanthanide elements they need more attention because meager
information is available about these compounds. Earlier studies on such compounds
contain the structural parameters of some Gadolinium and Dysprosium intermetallics
have been reported by Baenziger and Moriarty Jr. [23]. They have concluded that
the lanthanide intermetallics exist with either CrB structure (B33) or FeB structure
(B27) in their equilibrium state. CrB (B33) phase have orthorhombic structure with
space group Cmcm. It is denoted by space group number 63. The lattice co-ordinates
occupied by Cr and B atoms are (0, y1, 1/4) and (0, y2, 1/4) respectively. On the other
side FeB structure (B27) is also orthorhombic but with space group Pnma (space
group number 62). The atomic positions of Fe atoms in a unit cell are found at (x1,
1/4, z1) and for B (x2, 1/4, z2) atom respectively.
Chapter 1: Lanthanide Intermetallic Compounds
18
A sample of polycrystalline DyNi has been reported by Tripathy et.al [24] by
arc melting stoichio-metric proportions of the starting materials (of at least 99.9%
purity) on a water-cooled copper hearth under high purity argon atmosphere. The
crystal structure and the phase purity of the sample were analyzed from the rietveld
refinement of the powder x-ray diffraction data. In purpose to analyse the magneto
caloric effect, Magnetization measurements, in the temperature range 4-150 K were
carried out on pieces of the annealed sample using a vibrating sample magnetometer.
The study on magnetoclaoric effect concludes that the compound is ferromagnetic
with a Curie temperature (TC) of 59 K. Also the effective magnetic moment
calculated from the high temperature susceptibility is found to be 10.6μB, which is
almost equal to the free ion magnetic moment of 10.3 μB of the Dy ion. Later, the
magnetic properties of lanthanides–nickel intermetallic compounds and their relative
hydrides have been studied by Yaropolov et.al [25-26]. The intermetallic compounds
were synthesized by arc melting under argon atmosphere in a furnace with a non
consumable tungsten electrode and water-cooled copper tray. Nickel (purity of
99.99%) and lanthanide metals (99.9%) were used as a starting components and
titanium sponge as a getter. Hydrogen absorption properties were investigated on a
Sievert type volumetric apparatus at room temperature and hydrogen pressures up to
1 MPa. Authors discovered that LnNi alloys easily interact with hydrogen at room
temperature and hydrogen pressure about 0.1 MPa. But In case of GdNi and SmNi
introduction of hydrogen atoms leads to expansion of the unit cells without structure
transformation. In case of TbNi and DyNi the ternary hydrides formation is
accompanied by metal sublattice structure transformation (FeB–CrB structure
transition). The conclusion of their study is that the transition temperatures of the
LnNi intermetallic compounds and ternary hydrides appeared to be lower than liquid
Chapter 1: Lanthanide Intermetallic Compounds
19
nitrogen temperature (78 K). In 2008, Durga Paudyal and her co-workers computed
the magnetoelastic behaviour of GdNi [27]. The work has been done by using both
experimental and theoretical approaches. First of all the intermetallic compound was
prepared by arc melting of the pure metals under argon atmosphere The x-ray
powder-diffraction study at room temperature was performed using a Bragg-
Brentano diffractometer. The variation of lattice parameters and interatomic
distances between atoms with varying temperature has been analysed. All the
experimental results have also been compared with the computational studies. The
computation part of the work was based on LAPW method within the framework of
DFT by performing tight binding linear muffin tin orbital method. H. Drulis et.al,
have studied the magnetocaloric effect in magnetic SmNi by evaluating
magnetization and heat capacity measurements [28]. SmNi samples were synthesized
by the arc melting in an argon gas atmosphere of nickel (purity of 99.99%) and
samarium (99.9%) metals. The X-ray diffraction studies shows that the material is
single phase of CrB type structure with the lattice constants a = 3.782(3) Å, b =
10.375(4) Å and c = 4.301(2) Å, respectively. Magnetic measurements were carried
out in the temperature range of 1.7–300 K in an applied magnetic field up to 5 T
using a Quantum Design superconducting quantum interference device (SQUID)
magnetometer. The magnetization curve indicates the ferromagnetic nature at
temperatures lower than about 43 K. The magnetic and transport properties of PrNi
were studied by S. Matar et. al [30]. The single crystal was grown in a tri-arc furnace
by the Czochralski method under an argon atmosphere. The orthorhombic CrB-type
structure was confirmed by X-ray diffraction having unit cell dimensions, a =
0:38307, b = 1:0543, c = 0:4369 nm. They showed that the nonmagnetic singlet
ground state PrNi undergoes a ferromagnetic transition at TC = 20 K.
Chapter 1: Lanthanide Intermetallic Compounds
20
In recent decades, many efforts have been made on the investigation of
magnetism in compounds with lanthanide (Ln) elements due to the possibility of
technological application in industry (laser, luminescent materials, permanent
magnets, glasses) and medicine (contrast agents) [36], as well as the interest in basic
scientific research, because of its electric and magnetic properties and its non-usual
structures [37]. A great deal of work has been reported recently on the magnetic
properties of lanthanides and its compounds [21, 22]. On the other hand, the study of
the origin of magnetism and formation of magnetic moments in Ln atoms in such
compounds, as well as their interactions with neighbours atoms have become one of
the main objectives of basic research in magnetism.
1.9 Motivation
Lanthanide intermetallics have become a topic of great interest because of
their peculiar properties which are helpful in fabrication of lasers, luminescent
materials, permanent glasses, permanent magnets having high coercive field, nuclear
batteries etc. They are found having great variety in their structural, magnetic, and
electrical and phonon properties as they exhibit many diverse and unusual physical
properties such as large magnetic anisotropy, complex magnetic phase diagram, a
very small crystal field splitting. On the other hand the intermetallics are also used
in industrial, technological and medicinal field. They are also known as promising
materials for hydrogen storage purposes. Some of these materials are also used as
contract agent in magnetic resonance imaging (MRI) studies, X-ray tubes etc. On
realizing the importance due to their useful applications it is realized that these
systems still need to be studied widely to analyze variation in their structural,
magnetic, electronic, thermal properties.
Chapter 1: Lanthanide Intermetallic Compounds
21
1.10 Aim
Due to the advancement of the quantum mechanical approach, it is now
possible to compute various crystal properties of solids with high accuracy from
first-principles methods [38-42]. In this thesis, first principles study on the structural,
electronic, magnetic and thermal properties of LnNi (i.e. CeNi, PrNi, NdNi, SmNi,
GdNi and DyNi) compounds. The emphasis is given to study the interplay between
the localized f-electrons of lanthanide atoms and d-electrons of transition metals.
Such interactions are responsible for the high magnetic moments. It will provide the
next generation of magnetic refrigeration materials. The high pressure effect has also
been included to analyze the change in the crystallography of the structure from one
phase to another. The lanthanide compounds with Ni composition are also studied
under high temperature conditions. An understanding of the modifications of various
properties of the materials under certain conditions is desirable for novel
technological applications.
All the theoretical calculations are based on the full potential linearized
augmented plane wave approximation within the framework of density functional
theory. The complete and detailed overview about the theoretical tools and
approximations used in the present study is given in chapter 2 and 3.
Chapter 1: Lanthanide Intermetallic Compounds
22
References
[1] C. Kittel, Introduction to Solid State Physics (John-Wiley & Sons Inc., New
York, 2004).
[2] Solid state physics, H. C. Gupta, Vikas Publishing House Pvt. Ltd., New
Delhi, India].
[3] Sadao Adachi, Properties of group-ΙV, ΙΙΙ-V and ΙΙ-VΙ semiconductors.
[4] Christie T., Brathwaite B. & Tulloch A. 1998. Mineral commodities report
17- rare earths and related elements. New Zealand Institute of Geological
and Nuclear Sciences Ltd.
[5] Hedrick J.B. 2005. Rare earths. In: United States Geological Survey.
Compiler. Mineral Commodity Summaries (2005), pp. 132–133. United
States Department of the Interior.
[6] Handbook on Physics and Chemistry of Rare Earth (North-Holland,
Amsterdam (1979).
[7] J. H. Van Vleck, “The Theory of Electric and Magnetic Susceptibilities
Oxford University Press, New York, (1932), Chap. IX.
[8] A.M. Russell, Z. Zhang, T.A. Lograsso, C.C.H. Lo, A.O. Pecharsky, J.R.
Morris, Y. Ye, K.A. Gschneidner Jr. and A.J. Slager, Acta Materialia 52
4033 (2004).
[9] T. Reif, M. Doerr, M. Loewenhaupt, M. Rotter, P. Svoboda and S. Welzel,
Physica B 276 600 (2000).
[10] Rui Wang, Shaofeng Wang, Xiaozhi Wu, Intermetallics 18 1653 (2010).
[11] D. Gozzi, M. Iervolino, Intermetallics 13 1172 (2005).
[12] P.Schobinger-Papamantellos, M. Brunelli, J.Rodriguez-Carvajal,
K.H.J.Buschow, C. Ritter and F.Grammd, Journal of Magnetism and
Magnetic Materials 323 903 (2011).
[13] J.B. Goodenough and P.M. Raccah, Physical Review B 36 1031(1965).
[14] A.K. Tripathi and H.B. Lal, J. Mat. Sc. 17 1595 (1982).
Chapter 1: Lanthanide Intermetallic Compounds
23
[15] Kanchan Gaur and H.B. Lal, J. Mat. Sc. Let 2 3325 (1984).
[16] H.B. Lal, B.K. Verma and N. Dar, Ind. J. Cryogenics 2 119 (1977).
[17] Dixie P. Gautreaux , Cigdem Capan, John F. DiTusa , David P. Young and
Julia Y. Chan, Journal of Solid State Chemistry 181 1977 (2008).
[18] A.M. Mills, R. Lam, M.J. Ferguson, L. Deakin and A. Mar, Coordination
Chemistry Review 207 233 (2002).
[19] O. Sologub, P.S. Salamakha, K.A. Gschneidner, J.C.G. Bunzli and V.K.
Pecharsky, Handbook on the Physics and Chemistry of Rare Earths 33
Elsevier, Netherlands, (2003)
[20] S.M. Kauzlarich, S.M. Kauzlarich, Chemistry, Structure and Bonding in Zintl
Phases and Ions, VCH Publishers, New York, (1996)
[21] Wallace, W. E., 'Rare earth internzetullics', Acad. press, New York (1973).
[22] Gschneidner, Jr and Eyring, L (ed), 'Hand book on the physics and chemistry
of rare earths' 1&2 (1979).
[23] N. C. Baenziger and J. L. Moriarty Jr, Acta Crystallograhica 14 946 (1961).
[24] S. Tripathy, K. G. Suresh, R. Nirmala, A. K. Nigam, and S.K. Malik, Solid
State Communications 134 323 (2005).
[25] Yu. L. Yaropolov, A. S. Andreenko, S. A. Nikitin, S. S. Agafonov, V. P.
Glazkov, and V. N. Verbetsky, Journal of Alloys Compounds 509S S830
(2011).
[26] Yu. L. Yaropolov, V. N. Verbetsky, A. S. Andreenko, K. O. Berdyshev, and
S. A. Nikitin, Inorganic Materials 46 364 (2010).
[27] Durga Paudyal, Ya. Mudryk, Y. B. Lee, V. K. Pecharsky, K. A. Gschneidner
Jr. and B. N. Harmon, Physical Review B 78 184436 (2008).
[28] H. Drulis, A. Hackemera, A. Zaleski, Yu. L. Yaropolov, S.A. Nikitin and
V.N. Verbetsky, Solid State Communications 151 1240 (2011).
[29] S. Matar, Marian Mihalik, M. Zentkova and Matus Mihalik, Acta Physica
Polonica A 113 319 (2008).
Chapter 1: Lanthanide Intermetallic Compounds
24
[30] J.E. Ricci, The Phase Rule and Hetereogeneous Equilibria (Van Nostrand,
New York, 1951).
[31] R. Roy, in Phase Transitions, edited by H.K. Henisch, R. Roy and L.E.
Cross (Pergamon Press, New York, 1973).
[32] U. P. Verma, Poonam Singh and Per Jensen, Phys. Status Solidi B 248 1682
(2011).
[33] Poonam Singh, U. P. Verma and Per Jensen, Solid State Communications 152
624 (2012).
[34] J. H. Van Vleck, Rev. Mod. Phys. 50 181 (1978).
[35] T. S. Martins and P. C. Isolani, Quimica Nova 28 111 (2005).
[36] Taylor, K. N. K., Adv. Phy. 20 551 (1971).
[37] D.J. Chadi, Phys. Rev. Lett. 72 534 (1994).
[38] M. Fuchs, and M. Scheffler, Computer Phys. Commun. 119 67 (1999).
[39] G. Kresse, and D. Joubert, Phys. Rev. B 59 1758 (1999).
[40] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, and J. Luitz, in
WIEN2k, An Augmented Plane Wave + Local Orbitals Program for
Calculating Crystal Properties, edited by K. Schwarz (Technical Universitat
Wien, Austria, 2001), ISBN 3-9501031-1-2.
[41] J.M. Soler, E. Artacho, J.D. Gale, A. Gracia, J. Junquera, P. Ordejon, and D.
Sanchez-Portal, J. Phys.: Condens. Matter 14 2745 (2002).
[42] S. Scandolo, P. Giannozzi, C. Cavazzoni, S. Gironcoli, A. Pasquarello, and S.
Baroni, Z. Kristallogr 220 574 (2005).