# magnetic properties

Urban and Civil

Nov 15, 2013 (4 years and 7 months ago)

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UNIT

IV

Chapter
-
2

MAGNETIC PROPERTIES

Dr.P.Sarah

S.Shashi

Devi

C.Venkata

subbaiah

Magnetic Permeability

Since the permeability influences the magnetic
induction (flux density),

It impacts how good of a magnet you can make.

In a vacuum, the permeability is a universal
constant,
μ
o

=
1.257*10
-
6

H/m.

H
B

H
B
o
o

Other magnetic terms

The
relative permeability (
µ
r
)
is sometimes
used to describe the magnetic properties of
a material (like
ε

for dielectrics)
.

The
magnetization (M)

represents the
magnetic moments within a material in the
presence of a magnetic field of strength H

(akin to polarization, P, for a dielectric).

The magnitude of M is proportional to the
applied field according to the
magnetic
susceptibility (

m
)
.

There are thus four main ways to represent
B, the magnetic induction (also called the
flux density).

Note that units get very confusing. Just stick
with one system (SI).

1

r
m
m
H
M

H
B
M
H
B
H
B
H
B
o
m
o
o
o
r

1
H
B
H
B
o
r
o
r

M
H
B
o
o

on
polarizati
dielectric
o
P
E
D


Magnetic Orbital Moments

Magnetic moments arise due to two mechanisms:

Orbital motion of an electron around the nucleus.

Essentially a small current loop, generating a very small
magnetic field.

A magnetic moment is established along the axis of rotation.

m
l

is the magnetic quantum number for the electron.

2
24
*
10
*
27
.
9
m
A
b

b
l
orbital
m
moment
magnetic

The magnetic quantum number indicates the type of
orbital (shape and usually orientation).

Orbital

m

Total
orbitals

Total
electrons

s

0

1

2

p

-
1,0,1

3

6

d

-
2,
-
1,0,1,2

5

10

Magnetic Spin Moments

2
nd

source of a Magnetic Moment

Direction that an electron spins.

Only two directions are possible.

The moment resulting from these spinning
electrons are along the spin axis, either UP
or DOWN.

The combination of orbital and spin
moments for every electron
throughout a crystal define its
magnetic properties.

b
spin
moment
magnetic

Diamagnetism

Nonmagnetic (only occurs in the presence of an external
magnetic field, H)

Even in an external magnetic field, very weak form of
magnetism

Non
-
permanent

Occurs
opposite to

external field.

Relative permeability < 1

(
≈0.99999)

Found in
all

materials, just usually too weak to matter.

So weak that only noticed if no other form of magnetism
exists for the atom and/or crystal.

Most common for atoms with completely filled orbitals (no
unmatched electrons that could have spin moments).

Inert gases

Some ionic structures (H
2
O, Al
2
O
3
)

Noble metals (Au, Cu, Ag, Hg, Zn)

H
B
o
r

Paramagnetism

If the orbitals are not completely filled
or spins not balanced, an overall small
magnetic moment may exist.

Without an external magnetic field, the
moments are randomly oriented.

No
net
macroscopic magnetization.

“NonMagnetic”

In an external field, the moments align
with

the field, thus enhancing it (only a
very small amount, though).

There is
no interaction
dipoles.

Permeability (
μ
r
) > 1 (barely,
≈ 1.00001 to
1.01.

Examples include Al, Cr, Cr
2
Cl
3
, MnSO
4
)

H
B
o
r

Ferromagnetism

Unlike paramagnetism with incompletely balanced orbital or spin moments
which are randomly aligned, for some materials unbalanced spin can lead to
significant permanent magnetic moments
.

Fe (BCC alpha), Co, Ni, Gd.

The permanent moments are further enhanced by coupling interactions
between magnetic moments of adjacent atoms so that they tend to align even
without an external field.

Maximum possible magnetization for these materials is the saturation
magnetization (M
s
, usually quoted per volume).

There is a corresponding saturating flux density (B
s
).

atoms

*

M
B
atoms

*

M
M
atom
per
s
atom
per
s
o

M
per atom

Fe

Co

Ni

B

2.22

1.72

0.6

Anti
-
Ferromagnetism

Magnetic moment coupling (for each individual atom)
does not always align constructively as for
ferromagnetism.

For some materials, the alignment of the spin
moments of adjacent atoms is in opposite directions.

MnO

O
2
-

has no net moment.

Mn
2+

have a spin based net magnetic moment.

Overall, there is
no net magnetic moment

even though
at the atomic level there is a local moment.

Anti
-
Ferromagnetism

Ordered arrangement of spins of the Mn
2+

ions in MnO
determined by neutron diffraction. The 0
2
-

ions are not shown.

Temperature dependence

Saturation magnetization M
S

is the maximum
magnetization in a material assuming perfect magnetic
dipole alignment.
This happens only at T=OK
.

Increasing T increases thermal vibrations

and
decreases
M
S

due to diminished (exchange) coupling between
dipoles.

This is
VERY

important for
ferro
-
,
ferri
-
, and
anti
-
ferromagnets
.

Thermal vibrations also cause the dipoles to spend more
time pointing in the ‘wrong’ direction,
reducing M
s
.

Above a critical temperature called the Curie (or Ne
è
l)
point (
T
C
or T
n
),
ferro
-

and
ferrimagnetic

materials no
longer possess a spontaneous magnetization. They
become
PARAELECTRIC
.

The Curie (or Ne
è
l) Temperature

T
n
(Fe
3
O
4
)

T
C
(Fe)

Temperature dependence

T
C

or T
n

Above a critical temperature called the Curie point (
TC
),
ferro
-

and
ferrimagnetic

materials no longer possess a spontaneous magnetization. They
become
PARAMAGNETIC
. So do
anti
-
ferromagnetic

materials.

ferromagnetic

anti
-
ferromagnetic

ferrimagnetic

T=0K

paramagnetic

20.5(a),
Callister 6e
.

20.5(b),
Callister 6e
.

20.7,
Callister 6e
.

MAGNETIC MOMENTS FOR 3 TYPES

Ferri
-

and
Anti
-
FerroMagnets
?

ferrimagnetic
? Similar to
Ferromagnets

antiferromagnetic
? Similar to Paramagnets

Classification Summary

c18f11

18.7 Domains and Hysteresis

Domains in a ferromagnetic or ferrimagnetic
material; arrows represent atomic magnetic
dipoles.

Within each domain, all dipoles are aligned,
whereas the direction of alignment varies from
one domain to another.

orientation across a domain wall.

c18f12

Hysteresis

MSE
-
630

H

increases until
B
s

and
M
s

are
reached. Upon removal, some
magnetism, call
remanence
,
remains at
B
r
. H

field must be
reversed to

H
c

to eliminate
residual magnetism. This is called
the
coercivity
.

The area in the hysteresis loop
represents work or energy
expended in going from (+) to (
-
)
H

and back. The product of
B*
H

is measured in
kJ/m
3
or
gauss
-
oersted (MGOe)

1 MGOe = 7.96 kJ/m
3

The Science….

The understanding of superconductivity was advanced in 1957
by three American physicists
-
John Bardeen, Leon Cooper, and
John Schrieffer, through their Theories of Superconductivity,
know as the
BCS Theory
.

Pictures of Bardeen, Cooper, and Schrieffer, respectively.

(Source: Nobel

Foundation)

The BCS theory explains superconductivity at temperatures
close to absolute zero.

Cooper realized that atomic lattice vibrations were directly
responsible for unifying the entire current.

They forced the electrons to pair up into teams that could pass
all of the obstacles which caused resistance in the conductor
.

The Science….

The BCS theory successfully shows that electrons can be
attracted to one another through interactions with the
crystalline lattice. This occurs despite the fact that electrons
have the same charge.

When the atoms of the lattice oscillate as positive and
negative regions, the electron pair is alternatively pulled
together and pushed apart without a collision.

The electron pairing is favorable because it has the effect of
putting the material into a lower energy state.

When electrons are linked together in pairs, they move
through the superconductor in an orderly fashion.

SUPERCONDUCTING MATERIALS

Superconductivity

-

The

phenomenon

of

losing

resistivity

when

sufficiently

cooled

to

a

very

low

temperature

(below

a

certain

critical

temperature)
.

H
.

Kammerlingh

Onnes

1911

Pure

Mercury

Resistance (
Ω
)

4.0 4.1 4.2 4.3 4.4

Temperature (K)

0.15

0.10

0.0

T
c

Transition Temperature or Critical Temperature (T
C
)

Temperature

at

which

a

normal

conductor

loses

its

resistivity

and

becomes

a

superconductor
.

Definite

for

a

material

Superconducting

transition

reversible

Very

good

electrical

conductors

not

superconductors

eg
.

Cu,

Ag,

Au

Types

1.
Low

T
C

superconductors

2.
High

T
C

superconductors

Occurrence of Superconductivity

Superconducting Elements

T
C

(K)

Sn (Tin)

3.72

Hg (Mercury)

4.15

7.19

Superconducting Compounds

NbTi (Niobium Titanium)

10

Nb
3
Sn (Niobium Tin)

18.1

Properties of Superconductors

Electrical Resistance

Zero Electrical Resistance

Defining Property

Critical Temperature

Quickest test

10
-
5
Ω
cm

Effect of Magnetic Field

Critical magnetic field (H
C
)

Minimum magnetic field
required to destroy the
superconducting property at
any temperature

H
0

Critical field at 0K

T
-

Temperature below T
C

T
C

-

Transition Temperature

Superconducting

Normal

T (K)

T
C

H
0

H
C

Element

H
C

at 0K

(mT)

Nb

198

Pb

80.3

Sn

30.9

2
0
1
C
C
T
H H
T
 
 
 
 
 
 
 
 
MEISSNER EFFECT

When

the

superconducting

material

is

placed

in

a

magnetic

field

under

the

condition

when

T
≤T
C

and

H

H
C
,

the

flux

lines

are

excluded

from

the

material
.

Material

exhibits

perfect

diamagnetism

or

flux

exclusion
.

Deciding property

χ

= I/H =
-
1

Reversible (flux lines penetrate when T
↑ from T
C
)

Conditions for a material to be a superconductor

i.
Resistivity
ρ

= 0

ii.
Magnetic Induction B = 0 when in an uniform magnetic field

Simultaneous existence of conditions

Applications of Meissner Effect

Standard test

proof for a superconductor

Repulsion of external magnets
-

levitation

Magnet

Superconductor

Yamanashi MLX01 MagLev train

Types of Superconductors

Type I

Sudden loss of magnetisation

Exhibit Meissner Effect

One H
C

= 0.1 tesla

No mixed state

Soft superconductor

Eg.s

Pb, Sn, Hg

Type II

Does not exhibit complete
Meissner Effect

Two H
C
s

H
C1
& H
C2
(
≈30 tesla)

Mixed state present

Hard superconductor

Eg.s

Nb
-
Sn, Nb
-
Ti

-
M

H

H
C

Superconducting

Normal

Superconducting

-
M

Normal

Mixed

H
C1

H
C

H
C2

H

Applications

Large

distance

power

transmission

(
ρ

=

0
)

Switching

device

(easy

destruction

of

superconductivity)

Sensitive

electrical

equipment

(small

V

variation

large

constant

current)

Memory

/

Storage

element

(persistent

current)

Highly

efficient

small

sized

electrical

generator

and

transformer

Medical Applications

NMR

Nuclear Magnetic Resonance

Scanning

Brain wave activity

brain tumour, defective
cells

Separate damaged cells and healthy cells

Superconducting solenoids

magneto
hydrodynamic power generation

plasma
maintenance

THANK YOU