Magnetics- Diamagnetism and Paramagnetism

Question 1

Formula for magnetic susceptibility and what’d it indicates

Answer 1

χ=M/H
Indicates how responsive a material is to an applied magnetic field. Most technologically useful magnetic materials have χ»1

Question 2

What is χ of free space?

Answer 2

0

Question 3

What can atoms have a magnetic moment?

Answer 3

Electrons orbit nucleus and have spin so behave like circulating currents. Direction of magnetic moment depends on interaction between atoms.

Question 4

What is value of electron spin dipole moment?

Answer 4

9.3x10-24 Am^2
Equal to 1μB
Where μB has B subscript and is Bohr magneton

Question 5

What does size of atomic magnetic moment depend on?

Answer 5

Number of free electrons. If one free there is a 1μB spin dipole moment. If none free (maybe full outer shell) there is 1μB spin dipole moment up and 1 down so no net dipole moment

Question 6

Five types of magnetism that occur in materials

Answer 6

Diamagnetism
Paramagnetism 
Ferromagnetism
Antiferromagnetism
Ferrimagnetism

Question 7

Lenz’s law

Answer 7

Currents created by a magnetic field oppose the field that created them

Question 8

Is every material slightly diamagnetic?

Answer 8

Yes

Question 9

What is diamagnetism?

Answer 9

Where the material responds to magnetic field with a magnetisation that opposes the applied field. It’s the weakest magnetic effect

Question 10

Formula for magnetic susceptibility in diamagnetism

Answer 10

χ=(-Nμ0Ze^2/6me){r^2}av
N is number of atoms per unit volume 
e is electron charge
Z is atomic number
me with e subscript is electron mass
{r^2}av has brackets like chevron and subscript av and means average radius squared of all orbitals

Question 11

What is χ of diamagnetic materials?

Answer 11

Les than 0 as M opposes H. Superconductors repel applied field completely have χ=-1.
Means μr just less than 1 (non-superconducting) as μr=χ+1

Question 12

Example of diamagnetic materials

Answer 12

Water, Bi, Hg

Question 13

Properties of diamagnetism

Answer 13

No magnetic moment without a magnetic field. No critical temperature or temperature dependence. Susceptibility almost constant with field

Question 14

Describe paramagnetism

Answer 14

Individual atoms have weak magnetic moments at 0 field. These moments are randomly oriented. No local ordering. Weak response to applied magnetic fields which rotates moments towards field direction. Temperature disorders magnetic moments. Still stronger than diamagnetism. χ>0 maybe 10^-3 to 10^-5

Question 15

What leads to paramagnetism?

Answer 15

Unpaired electrons in molecules

Question 16

M vs H graph for paramagnetism

Answer 16

Straight line through origin with small positive gradient χ

Question 17

Langevin function for paramagnetism

Answer 17

M=Nm(coth(α)-1/α)=NmL(α)
α=μ0mH/kBT
N is number of atoms per unit volume
m is magnetic moment
T is temperature 
k subscript B is Boltzmann’ constant
H is applied magnetic field

Question 18

For langevin theory describe graph of M/Nm vs α

Answer 18

Initially linear until just under 0.5 where gradient gradually decreases to 0 at M/Nm=1. Does this within α=0-4

Question 19

Why is graph of M/Nm vs α like it is?

Answer 19

Higher fields give greater alignment and higher M. At highest fields get saturation of M because all atomic moments are aligned. Temperature disorders magnetic moments reducing M.

Question 20

Approximate langevin theory

Answer 20

For low values of α L(α) is about α/3
So M=Nmα/3=Nμ0m^2H/3kBT
Means approximate χ is Nμ0m^2/3kBT

Question 21

Curie’s law

Answer 21

χ=C/T

Susceptibility inversely proportional to temperature

Question 22

What does langevin theory mean for paramagnetic materials?

Answer 22

No critical temperature 
No spontaneous magnetisation
χ small but positive 
μr a little greater than 1
χ inversely proportional to temperature

Question 23

Explain the diamagnetic response to a magnetic field

Answer 23

Faraday’s law and Lenz’s law show moving electrons adjust their paths to produce a magnetic field that opposes any externally applied magnetic field. In atoms this means that electron orbitals will adjust to produce a magnetisation that opposes an applied magnetic field. This is diamagnetism.

Question 24

Explain the origins of the paramagnetic response to a magnetic field

Answer 24

Paramagnetic materials contain atoms with permanent magnetic moments that are disordered under zero applied magnetic field. When a magnetic field is applied the magnetic moments tend to align. Increasing the temperature increases the disorder and competes with the applied magnetic field.