Transcript Magnetism

Magnetism
Overview of magnetic materials
Magnetic objects
Magnetic field lines
Molecular magnetism, example 1
Paramagnets are attracted to magnetic fields
Paramagnetic gases
Organic radicals are magnetic
Zeeman splitting and NMR
gap = g mz B
Certain nucleii have a
magnetic spin, and are
therefore active in NMR
experiments
g = Lande g-factor (~2 for eˉ)
mz = magnetic moment
B = magnetic field strength
Nuclear gap energy
corresponds to radio
frequencies
Metals
• Many metals have unpaired electrons due to the
high d-orbital degeneracy.
n=3
unpaired spins
S = 3/2 magnetic moment
octahedral Cr3+ has 3 d-electrons
Metals
• Multiple spin arrangements (HS, LS) are
possible for a given number of d-electrons (in
this case, 7 valence electrons).
n=3
unpaired spins
S = 3/2 magnetic moment
n=1
unpaired spins
S = 1/2 magnetic moment
halides < OHˉ < C2O42- < H2O < NCSˉ < py < NH3 < en < phen < NO2ˉ < CNˉ < CO
Zeeman splitting and NMR
gap = g mz B
Certain nucleii have a
magnetic spin, and are
therefore active in NMR
experiments
g = Lande g-factor (~2 for eˉ)
mz = magnetic moment
B = magnetic field strength
Nuclear gap energy
corresponds to radio
frequencies
paramagnet
(disordered spins)
ferromagnet
(co-aligned spins)
antiferromagnet
(anti-aligned spins)
Ferromagnets have a persistent
moment, even without a magnetic field
cM vs T for ferromagnets
ferromagnetic paramagnetic
The math of magnetism
cM – Molar susceptibility
meff – Effective moment
mB – Bohr magneton
Useful experimental quantity
• Molar magnetic susceptibility, cM
• Magnetic susceptibility per mole
– Why use “molar” and not the “gram” susceptibility?
Moment per metal atom
meff  g S ( S  1)
S = total spin (1/2 per e ˉ)
meff  n(n  2)
n = # unpaired eˉ
meff = moment in Bohr magnetons (mB)
g = magnetogyric ratio (Landé g-facor, ~2)
mB = 9.27 x 10-24 J / T
Magnetic susceptibility, cM
N A meff mB
2
cM 
meff
2
(Curie Law – assumes no spin-spin interactions)
3kT
3kTc M

2
N AmB
meff  7.997c M T
(units are slightly fudged)
cM = measurable quantity (M / H)
Can calculate meff from cM
Can calculate # of unpaired electrons from meff
Magnetic susceptibility, cM
N A meff mB
2
cM 
cM 
3kT
Cmeff
2

Cmeff
2
(Curie Law)
T
2
T 
(Curie-Weiss law)
Simple approximations break down when spins are not isolated from each other