Lecture: Solid State Chemistry
(Festkörperchemie)
Part 1
H.J. Deiseroth, SS 2004
Lattice Energy and Chemical Bonding in
Solids
Lattice enthalpy
The lattice enthalpy change H L is the standard
molar enthalpy change for the following process:
0
M+(gas) + X-(gas)  MX(solid)
H L
0
Because the formation of a solid from a „gas of ions“ is
always exothermic lattice enthalpies (defined in this
way !!) are usually negative numbers.
If entropy considerations are neglected the most
stable crystal structure of a given compound is the one
with the highest lattice enthalpy.
Lattice enthalpies can be determined by a thermodynamic
cycle  Born-Haber cycle
A Born-Haber cycle for KCl
(all enthalpies: kJ mol-1 for
normal conditions  standard
enthalpies)
delete
standard enthalpies of
-
sublimation: +89 (K)
ionization: + 425 (K)
atomization: +244 (Cl2)
electron affinity: -355 (Cl)
lattice enthalpy: x
Calculation of lattice enthalpies
0
 L
 V AB  V Born
VAB = Coulomb (electrostatic) interaction between all cations and
anions treated as point charges (Madelung part of lattice
enthalpy („MAPLE“)
VBorn = Repulsion due to overlap of electron clouds
(Born repulsion)
Calculation of lattice enthalpies
1. MAPLE (VAB)
(Coulombic contributions to lattice enthalpies, MADELUNG part of
lattice enthalpy, atoms treated as point charges )
2
V AB
z z e
 A
N
4 0 rAB
Coulomb potential
of an ion pair
VAB: Coulomb potential (electrostatic potential)
A: Madelung constant (depends on structure type)
N: Avogadro constant
z: charge number
e: elementary charge
o: dielectric constant (vacuum permittivity)
rAB: shortest distance between cation and anion
Calculation of the Madelung constant
Cl
Na
typical for 3D ionic
solids:
Coulomb attraction
and repulsion
Madelung constants:
CsCl: 1.763
NaCl: 1.748
ZnS: 1.641 (wurtzite)
ZnS: 1.638 (sphalerite)
ion pair: 1.0000 (!)
12 8 6 24
A 6

 
... = 1.748... (NaCl)
2
3 2
5
(infinite summation)
2. Born repulsion (VBorn)
(Repulsion arising from overlap of
electron clouds, atoms do not behave as
point charges)
Because the electron density of atoms
decreases exponentially towards zero
at large distances from the nucleus
the Born repulsion shows the same
behaviour
VAB
r0
r
approximation:
V Born 
VAB
B
r
n
B and n are constants for a given
atom type; n can be derived from
compressibility measurements (~8)
Total lattice enthalpy from Coulomb
interaction and Born repulsion
0
 L
 Min.(V AB  V Born)
(set first derivative of the sum to zero)
2
z
z
e
1
0


   A
N (1  )
L
4 0 r0
n
Measured (calculated) lattice enthalpies (kJ mol-1):
NaCl: –772 (-757); CsCl: -652 (-623) ...
(measured means by Born Haber cycle based on the known
enthalpy of formation !!)
Applications of lattice enthalpy calculations:
 lattice enthalpies and stabilities of „non existent“
compounds and calculations of electron affinity
data (see next transparencies)
 Solubility of salts in water (see Shriver-Atkins)
Calculation of the lattice enthalpy for NaCl
z z e 2
1
   A
N (1  )
L
4 0 r0
n
0
0 = 8.8510-12 As/Vm; e = 1.610-19 As (=C); N = 6.0231023 mol-1
A = 1.746; r = 2.810-10 m;
1/40 = 8.992 109
n = 8 (Born exponent)
e2N = 1.54210-14 (only for univalent ions !)
HL = -1.387  10-5  A/r0  (1-1/n)
(only for univalent ions !)
------------------------------------------------------------------------------------------------------------Vm A2s2
VAs
Dimensions: ------------------ = ----------- = J/mol
As m mol-1
mol
NaCl: HL‘ = - 865 kJ mol-1 (only MAPLE)
HL = - 756 kJ mol-1 (including Born repulsion)
Can MgCl (Mg+Cl-) crystallizing in the rocksalt
structure be a stable solid ?
HFormation ~ -126 kJ mol-1 (calculated from Born Haber cycle
based on similar rAB as for NaCl !!)
MgCl should be a stable compound !!!!!
However: Chemical intuition warns that there is a risk of
disproportionation:
2 MgCl2(s)  Mg(s) + MgCl2(s)
--------------------------------------------
HDisprop = ????????
2 MgCl  2 Mg + Cl2 HF = +252 kJ
Mg + Cl2  MgCl2
HF = -640 kJ
-----------------------------------------------------------------------
(twice the enthalpy of formation)
(from calorimetric measurement)
 2 MgCl  Mg + MgCl2 HDispr = -388 kJ
(Disproportionation reaction is favored)
Calculation of the electron affinity for Cl from the
Born-Haber cycle for CsCl
Standard enthalpy of formation
sublimation
½
atomization
ionization
Lattice enthalpy
- 433.0 kJ/mol
70.3
121.3
373.6
- 640.6
HFormation = Hsubl + ½ HDiss + HIon + HEA + HLattice
HEA = HF – (HS + ½ HD + HI + HL)
HEA = - 433 – (70.3 + 121.3 +373.6 –640.6) = -357.6
Chemical bonding in solids
 bonding theory of solids must account for their
basic properties as:
- mechanism and temperature dependence of the
electrical conductivity of isolators, semiconductors,
metals and alloys
(further important properties: luster of metals, thermal
conductivity and color of solids, ductility and malleability of
metals)
...
Temperature dependence of the electrical
conductivity of metals and semiconductors
(isolators)
key to nderstanding: „band model“
= alloy
 increasing resistivity
 resistivity below Tc = 0 !!
 decreasing resistivity
= isolator
The origin of the simple band model for solids:
Band formation by orbital overlap
(in principle a continuation of the Molecular Orbital model)
the overlap of atomic orbitals in a
solid gives rise to the formation of
bands separated by gaps
(the band width is a rough measure of
interaction between neighbouring
atoms)
E << kT
~ 0.025 eV
s- and p-bands in a one-dimensional solid
Energy
s-band
p-band
- Whether there is in fact a gap between bands (e.g. s
and p) depends on the energetic separation of the
respective orbitals of the atoms and the strength of
interaction between them.
- If the interaction is strong, the bands are wide and
may overlap.
Isolator, Semiconductor, Metal (T = 0 K)
electrical conductivity
requires easy accessible
free energy levels above EF
Energy
conduction
band (empty)
band overlap
e-
EF
hole:+
o
valence band
(filled with e-)
Isolator (> 1.5 eV)
Semiconductor
(< 1.5 eV)
Metal (no gap)
(at T = 0 K no conductivity)
EF = Fermi-level (energy of highest occupied electronic state,
states above EF are empty at 0 K)
A more detailed view for metals:
The Fermi level
At T = 0 K the lowest ½ N electronic states in a
solid with N atoms are occupied (each level is
occupied by 2 electrons with opposite spin).
At T > 0 K states above EF
are also occupied to a
certain extend. The
population P is given by
the Fermi Dirac statistics
a special version of the
Boltzmann statistics
which takes into account
that no more than two
electrons can occupy any
level
Origin and temperature dependence of electronic
conductivity in metals
- Electrons with energies
close to the Fermi level can
easily be promoted to nearby
empty levels.
- they are mobile and can
easily move through the solid
in an electric potential
gradient („free electrons“)
At elevated temperatures thermal vibrations of the atoms
reduce the mobility of the „free electrons“ . As a
consequence the electrical conductivity decreases with
increasing temperature
A more detailed view not only for metals:
(DOS = Densities of states)
E << kT
~ 0.025 eV
The number of electronic
stes in a range divided by
the width of the range is
called the density of states
(DOS).
- simplified, symbolic shapes for DOS
representations !!
Typical DOS representation
for a metal
Typical DOS representation
for a semimetal
Semiconductors
conduction band
band gap
thermal excitation of electrons
valence band
T=0K
T>0K
Semiconductors
The electrical conductivity  of a semiconductor:

~
qcu
[-1cm-1]
q: elementary charge
c: concentration of charge carriers
u: electrical mobility of charge carriers [cm2/Vsec]
- charge carriers can be electrons or holes (!)
Semiconductors
conduction band
Temperature dependence of the
electrical conductivity ( [-1cm-1])
(Arrhenius type behaviour):

band gap
 0
 Ea
 e kT
Ea
ln   
 ln 0
kT
valence band
 ln  = f(1/T)  linear
Typical band gaps (eV): C(diamond) 5.47, Si 1.12, GaAs 1.42
Semiconductors
Electrical conductivity  as a function of the
reciprocal absolute temperature for intrinsic silicon.
T,K
A semiconductor at room
temperature usually has a
much lower conductivity
than a metallic conductor
because only few electrons
and/or holes can act as
charge carriers
, -1m-1
1/T,K-1
Ea
ln   
 ln 0
kT
 slope gives Ea
A more detailed view of semiconductors:
Intrinsic and extrinsic Semiconduction
Intrinsic semiconduction
corresponds to the
mechanism just described:
charge carriers are based
on electrons excited from
the valence into the
conduction band (e.g. very
pure silicon).
conduction band
Acceptor band
valence band
band gap
Extrinsic semiconduction
appears if the
semiconductor is not a
pure element but „doped“
by atoms of an element
with either more or less
electrons (e.g. Si doped by
traces of phosphorous [ntype doping] or traces of
boron [p-type doping]
Intrinsic and extrinsic Semiconduction
Intrinsic range
slope:
-EA2/kT
Ea
ln   
 ln 0
kT
Extrinsic range
slope:
-EA1/kT
Semiconductors: Comparison of
conductivity to metals and insulators
Advanced structural chemistry
Metal structures based on sphere packings
ccp
hcp
bcc
 deviations from the ideal symmetry (e.g. , elongation or compression
along the body diagonal (c-axis) in case of ccp (hcp))
Unusual structures of metals without direct relation
to simple sphere packings
1. -Ga
~270 pm
247 pm
strongly distorted („puckered“) hexagonal
layers with short dGa-Ga = 247 pm between
adjacent layers
Special structures of metals without direct relation
to simple sphere packings
2. -Mn
complex network of CN 16 polyhedra (Friauf polyhedra)
interpenetrated by additional atoms (similar -Mn)
(notice: in metals and intermetallic compounds cordination
numbers 12, 14, 16 and more are common)
Further examples for „anomalies“ in the structural
chemistry of metallic elements are:
 polymorphism of manganese (-Mn, -Mn, -Mn, -Mn)
 polymorphism of iron (-Fe, -Fe, -Fe, -Fe)
(important for steel processing)
 the cubic primitive structure of -Po
Possible reasons for structural anomalies of metallic
elements:
 special interactions between magnetic atoms (e.g. Fe, Mn)
 deviations of atoms from spherical symmetry (special
electronic interactions due to d-orbitals)
The structures of some representative non
metallic elements
- Phosphorous: several polymorphs with complex stability
relations (only black phosphorous thermodynamical stable under
normal conditions)
- Boron: electron deficiency, icosahedra or symmetrically related
polyhedra
- Carbon: polymorphism fulleren – graphite – diamond
(thermodynamic relations and stability)
- Sulfur: variety of molecular structures
P(white): a = 18,51 Å, I-43m, Z = ??
2,3 Å
P (black): a=3.314 Å, b=10.478 Å, c=4.376 Å
Z = 8, Cmca
2,2 Å
3,6 Å
P (black): a=3.314 Å, b=10.478 Å, c=4.376 Å
Z = 8, Cmca
The purple modification of phosphorous
system of tubes based
on five membered rings;
each P atom acts with
three covalent bonds
Boron
The structural chemistry of boron is dominated by
icosahedral B12 units or fragments of such icosahedra
B12 icosahedra with the topology of a close
packed layer in tetragonal boron-T50 (Z=50)
B12-icosadron in the center of B60-cage with the
topology of a fulleren (Boron-R105)
Further advanced aspects of structures of
non-metallic elements:
thermodynamical
relations between
the polymorphs
of carbon (p/T
diagram of carbon)
Structures of sulfur molecules
S
S
S
S
S
S
S6
S
S
S
S
SS
S
S
S
8
S
S
S S
S
S
S
S7
S10, S11, S12 ...
Tin (Sn)
-Sn (non-metal)
d = 5,75 gcm-3
CN = 4 (281 pm)
cubic
diamond structure
13 oC
-Sn (metal)
d = 7,3 g cm-3
CN = 4+2 (302, 318 pm)
tetragonal
compressed diamond
structure
Specific aspects of the structural chemistry of
alloys (intermetallic compounds)
- classical alloys do not obey simple valence rules
(8-N, noble gas configuration etc.): Zr4Al3, Cu5Zn8 ...
- alloys in many cases are characterized by variable
chemical compositions („homogeneity ranges“)
with statistical atom distribution
 phase diagrams  order-disorder-transitions
- electronegativity differences are generally small !
however, if larger electronegativity differences occur
they favor smaller homogeneity ranges (e.g. CsAu =
Cs+Au-, „polar alloy“ with CsCl structure, NaTl = Na+Tl-,
ZINTL-phase )
The most important groups of alloys
1. Hume-Rothery phases: (valence electron concentration favors
certain structures, e.g. brass)
2. Laves-phases: relative atomic sizes favor certain structure
types (classical examples: MgCu2 a cubic Laves-phase)
3. Frank-Kasper-Phases: 3D interpenetration of „Frank-Kasperpolyhedra“ favors complex alloy structures which correspond to
a 3D-packing of (distorted) tetrahedra only. (e.g. Zr4Al3)
4. Zintl Phases: alloys of metals with moderate electronegativity
differences show complete electron transfer (idealized) from the
less electronegative to the more electronegative partner.
 NaTl = Na+Tl- (Tl- as „pseudo element“ of main group 4 and
forms a diamond structure
Brass: Cu – Zn (Hume-Rothery-Phases
bcc
fcc
complex
hcp
Cu
Zn
The Laves phase
MgCu2
Mg (160 pm)
Cu (128 pm)
r(Mg)/r(Cu) = 1.25
3/ 2 = 1.22 (ideal value)
from R.C. Evans, Crystal Chemistry
Frank Kasper-phases (topological close packings)
(not to be confused with classical close packings)
distorted icosahedra in the Frank-Kasper-phase
Zr4Al3
icosahedra must be distorted due to symmetry
reasons
 5-fold symmetry is impossible in crystalline
solids
„Classical“ close packings:
- Space filling: (<74%)
- 3D systems of interpenetrating cuboctahedra and
anti-cuboctahedra (both CN 12)
- defines a system of tetrahedra and octahedra
„Topological“ close packings (Frank-Kasper-phases):
(„tetrahedral close packings“)
- Space filling: ??? (>74%)
- 3D systems of interpenetrating Frank-Kasper-polyhedra
(CN 12, 14, 15, 16)
- defines a system of distorted tetrahedra
Zintl phases
Na
- If one assumes a complete
electron transfer from Na to
Tl the latter one becomes a
„pseudo element“ of group
14 and forms a diamond
structure.
- Typical for Zintl phases: the
„pseudo element“ forms a
structure (1D, 2D or 3D)
which is found in real
elements of the respective
group of the periodic table.
(LiIn, NaSi, Ba3Si4, NaP ...)
Tl
NaTl = Na+Tl-: Tl- forms a diamond
structure (Tl- is a „pseudo element“ of
group 14)
- The Zintl model is an idealized
assumption which accounts for
the structural but in many cases
not for the physical properties of
the respective alloys
The perovskite structure (CaTiO3)
BaTiO3
BaTiO3 is a dielectric material that
shows „Ferroelectricity“
Ti4+
O2-
- Displacive phase transition below the
ferroelectric Curie temperature
(Tc = 393 K for BaTiO3)
- Piezoelectricity (pressure induced),
Pyroelectricity (temperature induced)
are dielectric properties with a similar
physical origin in other materials
Ba2+
- In an electric field and below 393 K all cations (Ba2+, Ti4+) move in
one and the anions (O2-) move in the opposite direction (see
arrows); the structure becomes tetragonal (inversion center gets
lost !) and shows a permanent electrical polarisation
Different views of
the perovskite
structure
The structural relation between the structure of the high
temperature superconductor YBa2Cu3O7-x (x<1) and the
perovskite structure
oxygen atoms are
omitted
perovskite
unit
„BaCuO3“
„YCuO3“
„BaCuO3“
oxygen deficient !!
The spinell structure: MgAl2O4
- In a ccp arrangement of O2- the
Mg2+ occupiy 1/8 of the tetrahedral
and Al3+ ½ of the octahedral holes
- TA2+ O(B3+)2 O4: normal spinell
- TB3+
O(A2+B3+)
O4 :
inverse spinell
e.g. Fe3O4 (magnetite)
TFe3+ O(Fe2+Fe3+)
O4
Different view of the spinell structure
The rutile structure
(TIO2)
Scanning Electron Microscopy
Photo emission spectroscopy
Impedance spectroscopy
Moessbauer spectroscopy
CamScan 44
Interaction of a high energy electron beam with material
Primary Beam
Backscattered
Electrons
Cathode
Luminescence
Auger
Electrons
Characteristic X-Ray
Spectrum
Secondary
Electrons
X-Ray Retardation
Spectrum
Specimen
Absorbed Current
Electron Gun
Magnetic Lens
Anode
Scanning Coils
Energy
Dispersive
X-Ray Detector
Objectiv Lens
Backscattered
Electron
Detector
Wave length
Dispersive
X-Ray Detector
Secondary
Electron
Detector
Stage with
Specimen
to the Vacuum
Pump
Comparison of W-, LaB6-, and Field emission-cathods
W
LaB6
FE
work function /eV
4,5
2,7
4,5
crossover /µm
(important for high
resolution images)
20-50
10-20
3-10
Tcathod /K
2700
<2000
300
1-3
25
105
gun Brightness
/A/cm2 sr
105-106
107
109
vacuum /mbar
10-5
10-7
10-9
service life /h
40-100
1000
>2000
emission current
density /A/cm2)
Electron Gun (W-Cathode)
Cathode
Heating
Current
Tungsten
Wehnelt Cylinder
(500 V more negative
than the Cathode,„Bias“)
20000 V
Crossover (20-50 µm)
Electron beam source
Anode
grounding
The crossover is projected on the sample in a reduced size
by the electronic-optical system
(minimal diameter of the beam: ca. 5 nm)
LaB6-Cathode (also: CeB6):
Graphite
LaB6 single crystal
- indirect heating (because of the low conductivity of LaB6)
- lower work function than the W-cathode ( higher brightness)
- demageable by ionic shooting ( high vacuum necessary)
- expensive!
Field Emission-Cathode
- W – cathode with a fine apex
- two anodes:
1. one to bring up the work function
2. one for the acceleration
- high brightness
- high vacuum necessary
Interaction volume of the electron beam (pear-like)
primary beam
Auger-electrons (up to 0,001m)*
Secondary Electrons (up to 0,01m)*
Backscattered Electrons (up to 0,1m)*
X-Ray (1-5m)*
*information depths
Dependence of the information depth
on the acceleration voltage and material
(simulations)
Fe (10 kV)
Au (20 kV)
Fe (20 kV)
Al (20 kV)
1m
Fe (30 kV)
Secondary Electrons:
- inelastic scattered PE (Primary Electrons)
- energy loss by interaction with valence
electrons or with the atomic nucleus
- Energy: < 50 eV
- maximal emission depth: 5-50 nm
- leads to high resolution images
Backscattered Electrons:
- elastic and inelastic scattered PE
- Energy: 50 eV – Energy of the PE (e.g. 20 keV)
- maximal emission depth: 0.1 - 6µm (dependent on the
specimen)
- Intensity depends on the average atomic number of the
material ( material contrast images)
- high interaction volume ( low resolution images)
Cu-wire imbedded in solder
SE-Image
(high resolution)
BE-Image
(high Z-contrast)
Cu
Cu
Cu
Cu
ZPb > ZSn > Z Cu
Backscattered electron images are less
sensitive on charging:
BE-image
SE-image
reason: the average energy of the backscattered electrons is higher
Auger Electrons:
- Energy characteristic for the Element
 Auger Electron Spectroscopy (AES)
3.
EAuger-Electron = E1-E2-E3
E3
E2
1.
2.
E1
Comparison Auger / X-Ray
Rate
of
yield
Auger
X-Ray
Z
 small X-Ray yield for light elements (B, C, N, O, F)
Cathode Luminescence
- not for metals
- visible and UV radiation
- special detectors necessary
PE
h
conduction band
valence band
X-Ray Retardation Spectrum
Intensity
Energy /keV
- primary electrons are retarded by the electron clouds
of the atoms
- Emax of the X-Ray‘s: e × Uaccelerating voltage
Characteristic X-Ray Spectrum
(without fine structure)
L
O
L
N
K
M
L
K
K
L
M
M
Energy range of the main series as a function of
the atomic number:
energy
K
K
L
L
M
Mosley‘s law: 1/ = K
(Z-1)2
atomic number
(K: constant, Z = atomic number)
Typical (characteristic) X-Ray spectrum (EDX)
intensity
Spectrum of Ag6GeS4Cl2
energy /keV
- sulfur (Z = 16) and chlorine (Z = 17) easily distinguishable
(in contrast to X-Ray diffraction)
Electron Detectors
1. Secondary Electron (SE-) Detector
Szintillator-Photomultiplier-Detector
(Everhart-Thornley-Detector)
Amplifier
PhotoMultiplier
Light conductor
VideoSignal
Scintillator
Metal net (+ 400V)
SE-Detektor:
SE-D
SE-D
Principle of an EDX-Detector
P-
i-
n-conducting
Si (Li)
+
3,8 eV
h + Si

Si+ + e-
-
e.g. Mn K: 5894 eV
X-Ray
- +
high voltage
5894/3.8 = 1550
electron hole pairs
WDX-Spectrometer:
Scanning of a -range with one monochromator crystal
Rowland
circle
Detector
Axis of
Crystal
movement
Monochromator
Crystal
Specimen
(X-Ray source)
WDX Detector
4 Monochromator
crystals
Proportional
counter
Comparison EDX - WDX
Irel
Ga L
Ga L
EDX
Ge L
Ge L
Irel
Ga L
WDX
Ga L
Ge L Ge L

(compound: GeGa4S4)
1.1
1.2
energy /keV
Detector‘s for WDX:
two proportional counter switched in series
1: FPC, Flow proportional counter (for low energy X-Ray‘s)
- the counting gas (Ar / CH4) flows through the counter
(very thin polypropylen window, not leak-free for
the counting gas)
2. SPC, Sealed proportional counter (for high energy X-Ray‘s)
- counting gas: Xenon / CO2
Comparison of EDX and WDX
EDX
WDX
spectral resolution
110-140 eV
10 eV
specimen current
10-10 A
10-7 A
analysis time
1-2 min
30-100 min
simultaneous
sequential
spectrum develops
Sensitivity
of EDX and WDX
atomic
percent
EDX
Be - window
WDX
atomic
number
Applications:
I) High resolution Images
II) Qualitative and quantitative analysis
Principle of the image formation
synchronised scanning coils
Beam
Amplifier
Television image
Signal-Detector
(SE or BE)
Specimen
Twinning of Crystals
PbS
Na2Zn2(SeO3)3 3H2O
Morphology of crystals
CuGa3S5
K2In12Se19
SnIn4S4
CsIn3S5
Quality control of small technical objects
Compact disc
Cantilever
of an AFM
Large area mapping (X-Ray-images)
SE-Image
Cu-Kmapping
Ni-Kmapping
Zn-Kmapping
256x256 pixel, moving of the specimen holder
typical sample holder equipment
typical preparation of
small crystals
conducting tabs
(adhesive plastic
with graphite)
Special preparation for insulating material:
-metallisation with gold (sputtering process)
better for high resolution images
-carbon deposition (evaporation process)
better for quantitative analysis
Impedance spectroscopy (basic aspects)
Purpose: Exploring the electrical behavior of a microcrystalline
solid sample as function of an alternating current (ac) with a
variable frequency.
three basically different
regions for the exchange
interactions between
current and sample:
a) inside the grains
(„bulk“)
b) at grain boundaries
c) surface of the
electrodes
the elecrcical behavior is simulated by a suitable combination of RC
circuits: R = resistivity, C = capacity
Impedance spectroscopy (electrical quantities)
The direct current (dc) resistance (R) is defined as:
U
R
I
U: applied voltage (V), I: curent (A)
R: resistance ()
The alternative quantity for an alternating current (ac) is the
impedance (Z*) which, however, is a more complex quantity than R
because there is a phase shift between U and I in general.
ac-voltage: U(t) = U0sint
I(t) = I0 sin(t+)
(t: time,  = 2 with : frequency)
(: phase angle)
Impedance spectroscopy (U(t), I(t))
If only capacities are present the phase shift between voltage and
current amounts to /2 = 900.
Photoemission spectroscopy
UV or
X-Ray
e-
UPS spectrum
UHV
DOS
solid
Band
structure
The energy spectrum of the
emitted electrons is analyzed
energy
Moessbauer Spectroscopy
 the nucleus of the specific isotope of an atom embdedded
in a solid (e.g. 57Fe) is excited by -rays emitted by an instable
isotope of a neighbor element (e.g. 57Co)
source:
57Co
e.g.
(tunable)
absorber:
e.g.
57Fe
frequently applied for
 57Fe, 119Sn, 127J ...
 chemical surrounding (symmetry,
coordination number, oxidation
state, magnetism) of atoms with
these nuclei in a solid can be probed
in a highly sensitive way (~10-8 eV)