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Magnetic Properties from
Molecules to Solids
Materials may be classified by their response to
externally applied magnetic fields as
 diamagnetic
 paramagnetic
 ferromagnetic
 antiferromagnetic
 ferrimagnetic
Magnetic Properties
Diamagnetic:
unaffected by a magnetic field
no unpaired electrons
Paramagnetic:
influenced by a magnetic field
unpaired electrons
Transition metals and their compounds are often
paramagnetic
Have unpaired d-electrons
Eg.
Ti2+
Mn2+
 diamagnetism : systems contain no unpaired electrons
Magnetic properties
Magnetic susceptibility (μ) and the spin-only formula.
Materials that are diamagnetic are repelled by a magnetic
field, whereas paramagnetic substances are attracted into
a magnetic field, i.e. show magnetic susceptibility. The
spinning of unpaired electrons in paramagnetic
complexes of d-block metal ions creates a magnetic field,
and these spinning electrons are in effect small magnets.
The magnetic susceptibility, μ, due to the spinning of the
electrons is given by the spin-only formula:
μ(spin-only) =
n(n + 2)
Where n = number of unpaired electrons.
Magnetization and Magnetic
Susceptibility
χ=∂M/∂H
where M : the molar magnetization, a vector,
H : the magnetic field strength , an axial vector,
χ: molar magnetic susceptibility, a second rank tensor.
When H is weak enough, χis independent of H, one can
write
M=χH
χ
The measurerement of magnetic susceptibility
A Gouy balance, which is used to measure the magnetic susceptibi
lities of substances
Electronic configurations of dn complexes from paramagnetism
and diamagnetism
Magnet off
Magnet on:
Paramagnetic
Magnet on:
diamagnetic
9
Sample problem
The magnetic moment of an octahedral Co(II) complex is
4.0 µB. What is its electron configuration?
Answer
µ = [N(N+2)]1/2 µB 4.0 = [N(N+2)]1/2 N 3
A Co(II) complex is d7. The two possible configu
Rations are t52ge2g (high spin) with three unpaired electron
Or t62ge1g (low-spin) with one unpaired electron.The spin
Only magnetic moment are 3.87 µB and 1.73 µB,repectively
(see Tab.).Therefore the only consistent assigment is the
High-spin configuration t52ge2g.
Magnetic Measurement
Experimental distinctiom between high-spin and low-spin
complexes is based on the dertermination of their megnetic
properties.Complexes are classified as diamagnetic if they
tend to move out magnetic field and paramagnetic if they
tend to move into magnetic field.The extent od paramagnetism
of a complexes is commonly reported in terms of the magnetic
dipol moment.the higher magnetic moment the greater the
paramagnetism of the sample.
The spin-only paramagnetism which is characteristic of many
d-metal complexes.
µ = 2[S(S+1)]1/2 µB
S: Total spin quantum number; each unpair electron has a spin
quantum number of ½, it allows that S= 1/2N, where N is the
number of unpaired electrons;therefore
µ = [N(N+1)]1/2 µB ; µB is known as Bohr magneton
its value is 9.274x10-24 JT-1
A measurement of the magnetic moment of a d-block complex can be
usually be interpreted in terms of the number of unpaired electrons it
contains, and hence the measurement can be used to distinguish between high-spin and low-spin complex. For example, Magnetic measu
Rements on d6 complex permit us to distinguish between a high-spin
t42ge2g ( N= 4, µ= 4.90) configuration and a low-spin t62g (N=0, µ=0)
configuration.
-----------------------------------------------------------------İon
N
S
µ / µB
------------------------Calc.
Exp.
------------------------------------------------------------------Ti3+
1
½
1.73
1.7-1.8
V3+
2
1
2.83
2.7-2.9
Cr3+
3
3/2
3.87
3.8
Mn3+
4
2
4.90
4.8-4.9
Fe3+
5
5/2
5.92
5.9
Magnetic properties
The spin-only formula applies reasonably well to metal ions from the
first row of transition metals: (units = μB,, Bohr-magnetons)
Metal ion dn configuration
Ca2+, Sc3+
d0
Ti3+
d1
V3+
d2
V2+, Cr3+
d3
Cr2+, Mn3+
d4
Mn2+, Fe3+
d5
Fe2+, Co3+
d6
Co2+
d7
Ni2+
d8
Cu2+
d9
Zn2+, Ga3+
d10
μeff(spin only) μeff (observed)
0
0
1.73
1.7-1.8
2.83
2.8-3.1
3.87
3.7-3.9
4.90
4.8-4.9
5.92
5.7-6.0
4.90
5.0-5.6
3.87
4.3-5.2
2.83
2.9-3.9
1.73
1.9-2.1
0
0
Example:
What is the magnetic susceptibility of [CoF6]3-,
assuming that the spin-only formula will apply:
[CoF6]3- is high spin Co(III). (you should know this).
High-spin Co(III) is d6 with four unpaired electrons,
so n = 4.
energy
eg
We have μeff
=
=
n(n + 2)
4.90 μB
t2g
high spin d6 Co(III)
Spin and Orbital contributions to
Magnetic susceptibility
For the first-row d-block metal ions the main contribution to
magnetic susceptibility is from electron spin. However,
there is also an orbital contribution from the motion of
unpaired electrons from one d-orbital to another. This
motion constitutes an electric current, and so creates a
magnetic field (see next slide). The extent to which the
orbital contribution adds to the overall magnetic moment is
controlled by the spin-orbit coupling constant, λ. The
overall value of μeff is related to μ(spin-only) by:
μeff
=
μ(spin-only)(1 - αλ/Δoct)
Diagrammatic representation of spin and
orbital contributions to μeff
spinning
electrons
d-orbitals
spin contribution – electrons are
spinning creating an electric
current and hence a magnetic
field
orbital contribution - electrons
move from one orbital to
another creating a current and
hence a magnetic field
Ferromagnetism:
In a normal paramagnetic material, the atoms containing the unpaired
electrons are magnetically dilute, and so the unpaired electrons in one atom
are not aligned with those in other atoms. However, in ferromagnetic
materials, such as metallic iron, or iron oxides such as magnetite (Fe3O4),
where the paramagnetic iron atoms are very close together, they can create
an internal magnetic field strong enough that all the centers remain aligned:
unpaired electrons
oriented randomly
Fe
atoms
a)
unpaired electrons
unpaired electrons aligned in their
own common magnetic field
a) paramagnetic,
magnetically
dilute in e.g.
[Fe(H2O)6]Cl2.
separated by
diamagnetic atoms
b)
b) ferromagnetic,
as in metallic
Fe or some
Fe oxides.
Antiferromagnetism:
electron spins in opposite
directions in alternate metal atoms
antiferromagnetism
Here the spins on the
unpaired electrons
become aligned in
opposite directions so
that the μeff approaches
zero, in contrast to
ferromagnetism, where
μeff becomes very large.
An example of antiferromagnetism is found
in MnO.
Ferromagnetism and
Antiferromagnetism
 Curie-Weiss Law
χ = C / (T-θ)
θ : Weiss constant, have the units of temperature
θ > 0, parallel (ferromagnetic) interactions
θ < 0, antiparallel (antiferromagnetic) interactions
Ferromagnet
Distribution of high- and low-spin
complexes of the d-block metal ions:
Co(III) is big exception – all low-spin except for [CoF6]31st row tend to be high-spin except for CN- complexes
2nd and 3rd row are all low-spin except for PdF2 and [PdF6]4-