Lecture 1: Introduction to Electronic Structure and Chemistry of Solids

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Electronic Structure and Chemistry of Solids
A course given as part of the joint Masters
programme Condensed Matter Science of the
Universiteit van Amsterdam and the Vrije
Universiteit, Amsterdam. Mark Golden (UvA)
Bernard Dam (VU)
Lecture 1 Introduction
Mark S. Golden, Van der Waals-Zeeman Institute,
Universiteit van Amsterdam, Room 262,
Valckenierstraat 65, 1018 XE Amsterdam, Tel. 020
525 6363. mgolden_at_science.uva.nl
http//www.science.uva.nl/research/wzi/cmp
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Electronic Structure and Chemistry of Solids
Bernard Dam Mark Golden
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Research at the WZI
atom manipulation using light atom
chips dynamics of BEC quantum information
structure dynamics polymers, colloidal
particles, micelles, biological systems
WZI
strongly correlated electron systems ns and nm
magnetisation dynamics semicon. photonics
optoelectronics novel magnetic materials
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Research at the WZI Condensed Matter Physics
Group
CMP
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Lecture 1 Introduction toElectronic Structure
and Chemistry of Solids

• Introduction - MSG BD
• Spectroscopic methods - MSG
• Electronic energy levels and chem. bonding - BD
• Elementary band theory - MSG
• The effects of electron repulsion - MSG
• Lattice distortions - BD
• Defects, impurities and surfaces - BD
• Closing workshop with presentations - MSG BD

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Lecture 1 Introduction
real, complex solids.. PT should be
familiar !
www.webelements.com
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Lecture 1 Introduction
Importance of solids
Chemical classification of solids
Molecular solids Ionic solids Covalent solids
Metallic solids 'Real', complex solids
Electrons in solids
Orbitals in atoms, molecules and solids Bands and
bonds
Metals, insulators and semiconductors
Metallic and non-metallic solids Thermal
excitation of electrons Semiconductors
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Lecture 1 Introduction
Solids . . . . . . s o w h a t ?
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Lecture 1 Introduction
Solids
we couldn't live without their mechanical
properties
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Lecture 1 Introduction
Solids
we couldn't live without their electronic
properties
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Lecture 1 Introduction
Solids
Cutting edge physics
1023 particles per cm3 this is tough! It is THE
challenge true many body physics with real
structure and dynamics covering nanoscale,
through mesoscopic to macroscopic with full
interactions realistic models for real materials
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Lecture 1 Introduction
Solids
Chemical classification
bonding
molecular ionic covalent metallic
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Lecture 1 Introduction
'Electronic' properties of solids .those
dominated by the behaviour of the electrons
Electrical conduction insulating,
semiconducting, metallic, superconducting
Can we understand this huge variation in
conductivity ?
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Lecture 1 Introduction
'Electronic' properties of solids .those
dominated by the behaviour of the electrons
Optical properties absorption, emission,
amplification and modification of light
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Lecture 1 Introduction
'Electronic' properties of solids .those
dominated by the behaviour of the electrons
Magnetic properties paramagnetism,
ferromagnetism, antiferromagnetism
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Lecture 1 Introduction
'Electronic' properties of solids .those
dominated by the behaviour of the electrons
Surface properties catalysis, electrochemistry
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Lecture 1 Introduction
Types of solid
Bonding classification
Molecular solids Ionic solids Covalent solids
Metallic solids
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Lecture 1 Introduction
Bonding classification
Molecular solids
Atoms or molecules which keep their identity Van
der Waals' forces low boiling points, low
sublimation energies
Non-polar London dispersion force
Polar electrostatic interaction e.g. H bonds
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Lecture 1 Introduction
Molecular solids
interaction of fluctuating dipoles (due to
electronic motion)
Non-polar London dispersion force
Edisp - (3/16 p e0) hwo a 2 / R6
R
hwo average electronic excitation energy a
electronic polarisability
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Lecture 1 Introduction
C60 , buckminsterfullerene sp2 intramolec.
bonding world record C-based superconductivity at
33K
Molecular solids
Non-polar solid C60
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Lecture 1 Introduction
Polarity
Molecular solids
directionality electrostatic interaction via
permanent dipoles hydrogen bonding
Polar e.g. boric acid, B(OH)3
2D network (Cox Fig. 1.1b)
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Lecture 1 Introduction
Types of solid
Bonding classification
Molecular solids Ionic solids Covalent solids
Metallic solids
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Lecture 1 Introduction
Ionic solids
Electrostatic interaction between ions
Coulomb law
Z
Z -
ECoul z1 z2 e 2 / (4 p e0 R)
R
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Lecture 1 Introduction
ECoul z1 z2 e 2 / (4 p e0 R)
Ionic solids
e.g. rock salt
Each cation (Na) has 6 anions (Cl-) at r 12
anions at ?2r 8 anions at ?3r etc..
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Lecture 1 Introduction
Ionic solids
Lattice energy in an ionic model balance
attractive Coulomb force with short range
repulsive force from overlap of closed-shell ions
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Lecture 1 Introduction
Ionic solids
Lattice energy in an ionic model Add attractive
and repulsive terms, and differentiate to give
minimum energy (should correspond to the
observed distance!)
U lat - N z1 z2 e 2 Am (1 - 1/n) / (4 p e0 R)
For ionic solids such as halides and oxides,
agrees well with experimental estimates of Ulat
from Born-Haber cycles
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Lecture 1 Introduction
ECoul z1 z2 e 2 / (4 p e0 R)
Ionic solids
Play off co-ordination vs. ion mismatch ECoul
favours maximal Am via maximal co-ordination
e.g. rock salt Each ion is surrounded by a
octahedron of other ions first co-ordination
shell is 6
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Lecture 1 Introduction
Types of solid
Bonding classification
Molecular solids Ionic solids Covalent solids
Metallic solids
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Lecture 1 Introduction
Covalent solids
Atoms held together by covalent bonds
C-C bond length and energy in diamond is ca. same
as in alkanes row 1 multiple bonding lower rows
single bonding
diamond (C)
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Lecture 1 Introduction
Types of solid
Bonding classification
Molecular solids Ionic solids Covalent solids
Metallic solids
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Lecture 1 Introduction
Metallic solids
Delocalised sharing of electrons between many
atoms
..also found on smaller scale in (metal)
clusters..
elements with a deficiency of electrons form
metallic structures ..analogies with covalent
sharing of e- in molecules
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Lecture 1 Introduction
..or nearly close packed
Metallic solids
Close-packed structures
FCC HCP BCC
pics scottv_at_asu.edu
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Lecture 1 Introduction
'Real' (interesting) solids
Bonding classification
Molecular Ionic Covalent Metallic
Metallic Ionic Molecular Covalent
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Lecture 1 Introduction
'Real' solids
Bonding classification
ionic metallic NbO, TiO ionic
covalent CdS, TiO2, cuprates covalent
, van der Waals, metallic graphite, NT ionic,
covalent, metallic, van der Waals K3C60
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Lecture 1 Introduction
Carbon
sp2 sp2 pure sp2 pure sp3
covalent C-C bonds within 'molecule'
variable sp hybridisation
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Lecture 1 Introduction
Electrons in solids
Orbitals in atoms, molecules and solids
Schrödinger equation for H atom atomic
orbitals Many electron atoms correlation
between electrons Approximate solution orbital
is solution of Schrödinger equation.
potential from (a) nucleus and (b)
other electrons in same orbital
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Lecture 1 Introduction
Orbitals in atoms, molecules and solids
Pauli exclusion principle max. two electrons per
orbital, spins opposed Degeneracy and relative
energy 1 x 1s, 1 x 2s, 3 x 2p, 1 x 3s, 3 x 3p, 1
x 4s, 5 x 3d Aufbau principle fill 'em up !
two e- at a time
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Lecture 1 Introduction
Orbitals in atoms, molecules and solids
Hund's rules 1) maximise spin multiplicity,
S e- in different orbitals, with parallel
spin 2) maximise total orbital angular
momentum, L 3) maximise total angular
momentum, J
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Lecture 1 Introduction
Orbitals in atoms, molecules and solids
Molecular orbitals from LCAO's (an approximation)
H2 linear combination of 1s orbitals H atoms far
apart ?2 same on both atoms ?S ?A ?B ?A
?A - ?B
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Lecture 1 Introduction
Orbitals in atoms, molecules and solids
H H2 H
MO's homonuclear diatomic H2
?A
Energy
bonding depends on degree of overlap
?S
(i) ?A and ?B fairly similar E (ii) correct
relative symmetry
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Lecture 1 Introduction
Orbitals in atoms, molecules and solids
A AB B
MO's heteronuclear diatomic AB
?A
Energy
?S
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Lecture 1 Introduction
Orbitals in atoms, molecules and solids
Core vs. valence atomic orbitals valence outer
most, generally partially filled core
previously filled shells smaller r than
valence orbitals little bonding
influence exception ! lanthanide 4f
levels partially filled 'valence' highly
contracted almost no overlap
'core'
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Lecture 1 Introduction
Orbitals in atoms, molecules and solids
From atom to solid no. of MO's no. of atomic
orbitals used to make them
Larger the system, the more tightly spaced the
MO's will become in energy If we consider a
solid as a very large molecule, we now have
continous bands
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Lecture 1 Introduction
Orbitals in atoms, molecules and solids
Example fcc C60 solid (p states only)
N(E) density of states
no. of allowed energy levels per unit vol. in the
range E to EdE
band gap
bands
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Lecture 1 Introduction
Electrons in solids
Bands and bonds
How does one resolve the band and the bond
? .wavefunctions behind it all are identical
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Lecture 1 Introduction
Metals, insulators and semiconductors
Metallic and non-metallic solids
Metals conduct electricity down to lowest
T's Non-metals may conduct at ?T, but cond. ?
as T?
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Lecture 1 Introduction
Metallic and non-metallic solids
Confirmation from spectroscopy such as absorption
of radiation (light)
empty levels filled levels
Energy
Absorption
Absorption
Photon energy
Photon energy
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Lecture 1 Introduction
Metallic and non-metallic solids
Band gap in a non-metal from spectroscopy
Band gap 0.1 eV to 12 eV (1 eV 8065
cm-1 visible light 1.5 to 3 eV)
Absorption
Photon energy
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Lecture 1 Introduction
Metallic and non-metallic solids
Conduction in sytems with a band gap
high T ionic conductivity (e.g. NaCl) - low
cond. cf. metallic conductivity electronic cond.
needs e- excited to the conduction band -
thermal excitation (small gap) - optical
excitation photoconductivity (Xerox)
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Lecture 1 Introduction
Metallic and non-metallic solids
Band picture works fairly well
ionic system - cation levels empty (e.g.
Na) - anion levels full (e.g.
Cl-) molecular solid - gap between HOMO and
LUMO
Egap
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Lecture 1 Introduction
Metals, insulators and semiconductors
Thermal excitation of electrons
Many properties depend on thermal excitation of
e- from ground state No. particles in excited
state at temperature T ni ? exp (- Ei / kT
) Boltzmann distribution BUT .can't use
Boltzmann for electrons in a solid !
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Lecture 1 Introduction
Thermal excitation of electrons
Electrons obey the Pauli exclusion
principle Electrons are indistinguishable
(exchange of electrons between two occupied
levels does not lead to a different arrangement)
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Lecture 1 Introduction
Thermal excitation of electrons
Fermi-Dirac distribution
filled empty
f (E )
T0 Fermi-Dirac distribution
E
top filled level in band EF
Fermi-Dirac distribution can be measured directly
using photoemission
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Lecture 1 Introduction
Thermal excitation of electrons
4kT
Fermi-Dirac distribution
Width ca. 4 kT
room temp. 4kT is ca. 0.1 eV
Total width of bands often eV only small no. of
total e- are thermally excited
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Lecture 1 Introduction
Metals, insulators and semiconductors
Semiconductors
Non metals
conduct via thermal excitation of carriers
across gap
missing e- in valence band (holes) e- in the
conduction band
Egap
ca. 1 eV
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Lecture 1 Introduction
Semiconductors
Thermal excitation of electrons
Fermi level now lies in the gap
EF
CB
VB
pure solid n-type p-type
EF
Fermi-Dirac distribution
EF
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Lecture 1 Introduction
Semiconductors
Thermal excitation of electrons
Bottom of conduction band E - E F E gap / 2 E
- E F usually much larger than kT exponent
dominates no. of exited electrons n ? exp (-E
gap / 2kT)
Arhhenius behaviour
? cf. intrinsic behaviour of pure materials
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Lecture 1 Introduction toElectronic Structure
and Chemistry of Solids
O U T L O O K

• Introduction - MSG BD
• Spectroscopic methods - MSG
• Electronic energy levels and chem. bonding - BD
• Elementary band theory - MSG
• The effects of electron repulsion - MSG
• Lattice distortions - BD
• Defects, impurities and surfaces - BD
• Closing workshop with presentations - MSG BD

59
Lecture 1 Introduction
give Bernard and I
feed back