Magnetics- Diamagnetism and Paramagnetism Flashcards
Formula for magnetic susceptibility and what’d it indicates
χ=M/H
Indicates how responsive a material is to an applied magnetic field. Most technologically useful magnetic materials have χ»1
What is χ of free space?
0
What can atoms have a magnetic moment?
Electrons orbit nucleus and have spin so behave like circulating currents. Direction of magnetic moment depends on interaction between atoms.
What is value of electron spin dipole moment?
9.3x10-24 Am^2
Equal to 1μB
Where μB has B subscript and is Bohr magneton
What does size of atomic magnetic moment depend on?
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
Five types of magnetism that occur in materials
Diamagnetism Paramagnetism Ferromagnetism Antiferromagnetism Ferrimagnetism
Lenz’s law
Currents created by a magnetic field oppose the field that created them
Is every material slightly diamagnetic?
Yes
What is diamagnetism?
Where the material responds to magnetic field with a magnetisation that opposes the applied field. It’s the weakest magnetic effect
Formula for magnetic susceptibility in diamagnetism
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 orbitalsWhat is χ of diamagnetic materials?
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
Example of diamagnetic materials
Water, Bi, Hg
Properties of diamagnetism
No magnetic moment without a magnetic field. No critical temperature or temperature dependence. Susceptibility almost constant with field
Describe paramagnetism
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
What leads to paramagnetism?
Unpaired electrons in molecules
M vs H graph for paramagnetism
Straight line through origin with small positive gradient χ
Langevin function for paramagnetism
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
For langevin theory describe graph of M/Nm vs α
Initially linear until just under 0.5 where gradient gradually decreases to 0 at M/Nm=1. Does this within α=0-4
Why is graph of M/Nm vs α like it is?
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.
Approximate langevin theory
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
Curie’s law
χ=C/T
Susceptibility inversely proportional to temperature
What does langevin theory mean for paramagnetic materials?
No critical temperature No spontaneous magnetisation χ small but positive μr a little greater than 1 χ inversely proportional to temperature
Explain the diamagnetic response to a magnetic field
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.
Explain the origins of the paramagnetic response to a magnetic field
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.
