Lecture 9: Metal oxides
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Magnetism
– Susceptibility
– Temperature dependence
– Magnetic moments
Transition metal oxides
– Bonding
– Important structural types
– Magnetism
– Functionalities
Figures: AJK
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Magnetism
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Ref: West p. 445-446
Diamagnetism is a property of all substances
– Induced magnetic field is created in a direction opposite to an external field
Inorganic solids that have unpaired electrons in their outer valence shells can
exhibit magnetic effects other than diamagnetism
– Electrons in inner core levels are always paired in fully occupied orbitals
Unpaired electrons are usually located on metal cations (d- or f-metal)
The unpaired electrons can have both spin and orbital motion, which together
generate a magnetic moment associated with the electrons
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Family tree of
magnetism
Ref: HP Meyers
(1997). Introductory
solid state physics /
Wikipedia
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Magnetic susceptibility
Ref: West p. 446
High M = high χ
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Classification based on χ
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The different kinds of magnetic behaviour may be distinguished by the values of χ
For diamagnetic substances, χ is very small and slightly negative
– Diamagnetism is associated with orbital motion of electrons in atoms. This
orbital motion generates a small electric field
– In the presence of an external field, the orbital motion is modified slightly to
give a magnetic moment that opposes the applied field leading to a slight
repulsion effect which is explained by Lenz’s law of electromagnetism.
– Superconductors represent a special, extreme type of diamagnetism since
they repel magnetic fields completely
Ref: West p. 447
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Para-, ferro-, and antiferromagnetism
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For paramagnetic substances, χ is small and positive
– Thus, when placed in a magnetic field, the number of lines of force passing
through a substance is greater if it is paramagnetic and slightly less if it is
diamagnetic than would pass through a vacuum
– Consequently, paramagnetic substances are attracted by a magnetic field
whereas diamagnetic substances experience a slight repulsion
Diamagnetic
Since superconductors show perfect
diamagnetism, they expel magnetic fields
completely, leading to levitation
In ferromagnetic substances, χ > 1 and such
materials are strongly attracted to
a magnetic field.
Paramagnetic
In antiferromagnetic substances, χ is positive
and comparable to or somewhat less than
that for paramagnetic substances.
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Pauli paramagnetism
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In addition to the strong ferro- and antiferromagnetic coupling shown by some
transition metals, most metals display a weak paramagnetism in the presence of a
magnetic field, known as Pauli paramagnetism
Only small number of
electrons near EF contribute
to the Pauli paramagnetism
Ref: West p. 458
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The effect of temperature:
Curie and Curie–Weiss laws
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The susceptibilities of different kinds of
magnetic material are distinguished by both
their temperature dependences and their
absolute magnitudes
Ordered magnetic structures, whether ferro-,
ferri-, antiferro-, heli-magnetic or spin glass,
lose their ordered structures above a certain
temperature
– Curie temperature, Tc for ferro- and ferrimagnets
– Néel temperature, TN for antiferro- and
heli-magnets
The spins become disordered and the
materials are therefore paramagnetic
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Examples of
behavior
close to Tc
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Magnetic moments (1)
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Magnetic properties are often expressed in terms of the magnetic moment
μ = M/V (M = magnetization, V = unit volume)
The magnetic properties of unpaired electrons arise from two causes, electron
spin and electron orbital motion
Of most importance is the spin component. An electron may be considered as a
bundle of negative charge spinning on its axis.
The magnitude of the resulting spin moment, μS , is 1.73 BM, Bohr Magneton:
where s is the spin quantum number, ½, and g is the gyromagnetic ratio ~2.00.
Substituting for s and g gives μS = 1.73 BM for one electron
Ref: West p. 451
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Magnetic moments (2)
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For atoms or ions that contain more than one unpaired electron, the overall spin
moment is given by
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Antiferromagnetic ordering:
superexchange
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One process, by which spins couple to give antiferromagnetism in, e.g. NiO, is
superexchange
The unpaired
electrons in these
Ni2+ in NiO has 8 d
eg orbitals couple
electrons (two in eg
with electrons in
orbitals dz2 and dx2-y2
the p orbitals of
pointing directly
the O2− ions
at adjacent oxide O
ions
Ni
Figure: AJK
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Transition metal oxides
TiO2
ZnO
FeO
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The Pauling EN of O is 3.44
EN differences (EN average):
– FeO = 1.61 (2.63)
– ZnO = 1.79 (2.55)
– TiO2 = 1.9 (2.49)
Mixed ionic-covalent bonding,
but due to actual band
structure features:
– Some TM oxides are
metallic (e.g. CrO2)
– Some are half-metals
(only other spin channel)
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Important structure types for
transition metal oxides
”Non-oxide types”
• Rocksalt (NaCl)
• Wurtzite (ZnS)
• Not important:
– CsCl
– Zinc blende (ZnS)
– NiAs
”Oxide-types”
• Rutile (TiO2)
• Perovskite (CaTiO3)
• Spinel (MgAl2O4)
• Corundum (Al2O3)
• Olivine (Mg, Fe)2SiO4
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Interstitial sites in close-packed
lattices of oxygen anions
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Rutile
Ti
O
TIO2 (P42/mnm)
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Spinel
Many oxides, sulfides and halides
have the spinel structure and
Al
different cation charge
combinations are possible:
O
Mg
MgAl2O4 (Fd-3m)
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Perovskite ABO3
Ca
Ti
O
CaTiO3 (Pm-3m –
high temperature)
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Ferroelectricity
A
O
B
Wikipedia
Ideal perovskite structure
(ABO3, e.g. BaTiO3)
Switchable polarization P
Spontaneous polarization Ps
related to the displacement
of the B atom (Ti)
Halasyamani et al. Chem. Soc. Rev. 2006, 35, 710.
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BaTiO3 phases
Pm-3m
Paraelectric
P4mm
Amm2
Ferroelectric
R3m
Nayak et al. RSC Adv. 2014, 4, 1212.
Spontaneous
polarization
Ps (μC cm-2):
Vanderbilt et al. Phys. Rev. Lett. 1994, 73, 1861.
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Al2O3 corundum
O
Al
Al2O3 (R-3c)
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b
a
c
Example of magnetism in FexOy
Fe
O2
O2
O
FeO (wüstite)
Iron(II) oxide
(Fm-3m)
Paramagnetic
Fe3O4 (magnetite)
Iron(II,III) oxide
(Fd-3m)
Ferrimagnetic
γ-Fe2O3 (maghemite)
Iron(III) oxide
(P4132)
Ferrimagnetic
“Normal” iron(III) oxide α-Fe2O3
(hematite), corundum structure,
weak ferromagnet at room temp.:
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Some functionalities of
transition metal oxides
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Catalysts (PdO, PtO2, etc.)
Li-ion battery materials (LiNixMnyCozO2, LiMn2O4, LiFePO4, Li4Ti5O12, etc.)
High-temperature superconductors (YBa2Cu3O7-x, etc.)
Ferromagnets (magnetite Fe3O4, magnetic storage)
Ferroelectrics – many perovskite oxides (BaTiO3, etc.)
– Dielectrics (capacitors)
– Piezoelectrics
– Pyroelectrics
High-temperature thermoelectrics
(NaCo2O4, ZnO, etc.)
Solid oxide fuel cells
(YSZ, ZrO2-Y2O3 etc.)
Thermal barrier coatings (e.g. YSZ)
Protective coatings (e.g. Al2O3)
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Some everyday oxides
Inert, non-toxic, abundant!
TiO2 (sunscreen,
white pigment)
ZnO (pigment,
food additive,
medicine, …)
Native oxides the surface of
metals (here Al2O3)
Hydrated α-Fe2O3 . H2O
(rust)
CuO (dietary supplement for
animals, colourful pigments)
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YBCO
Figure: Nina Heinig + Wikipedia
Defect perovskite structure
Non-stoichiometry, highest Tc (95 K) for x = 0.07
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