1st lecture

1
MENA3100

• 1st lecture
• Øystein Prytz
• General information, what to learn and
• some repetition of crystallography

2
General information

• Lectures
• Based on D. Brandon and W. D. Kaplan
  "Microstructural characterization of materials".
  Second edition, published by Wiley, 2008.
• Some parts of the Brandon and Kaplan book will be
  regarded as self study material and other parts
  will be taken out of the curriculum.
• Project work
• Energy related projects will be announced by the
  end of January
• Two students will work together, rank projects
  with 1st-3rd priority
• Written report, oral presentation and individual
  examination
• Counts 40 of final grade
• Laboratories
• Three groups A, B, C
• Individual reports
• All reports have to be evaluated and found ok
  before final written exam

3
What to learn about

• Imaging/microscopy
• Optical
• Electron
• SEM
• TEM
• Scanning probe
• AFM
• STM
• Diffraction
• X-rays
• Electrons
• ED in TEM and EBSD in SEM
• Neutrons

• Spectroscopy
• EDS
• X-rays
• EELS
• Electrons
• XPS, AES
• Electrons (surface)
• SIMS
• Ions
• Sample preparation
• Mechanical grinding/polishing
• Chemical polishing/etching
• Ion bombardment
• Crushing etc

Different imaging modes.
Mapping of elements or chemical states of
elements.
The same basic theory for all waves.
4
Probes used

• Visible light
• Optical microscopy (OM)
• X-ray
• X-ray diffraction (XRD)
• X-ray photo electron spectroscopy (XPS)
• Neutron
• Neutron diffraction (ND)
• Ion
• Secondary ion mass spectrometry (SIMS)
• Cleaning and thinning samples

• Electron
• Scanning electron microscopy (SEM)
• Transmission electron microscopy (TEM)
• Electron holography (EH)
• Electron diffraction (ED)
• Electron energy loss spectroscopy (EELS)
• Energy dispersive x-ray spectroscopy (EDS)
• Auger electron spectroscopy (AES)

5
Who is involved?

• Øystein Prytz oystein.prytz (at)fys.uio.no,
  93201512 (General, TEM, ED)
• Johan Taftø johan.tafto(at)fys.uio.no (waves
  optics, TEM, EELS)
• Ole Bjørn Karlsen obkarlsen(at)fys.uio.no (OM,
  XRD)
• Harald Fjeld harald.fjeld(at)smn.uio.no (SEM)
• Anders Skilbred awlarsen(at)ifi.uio.no (SEM)
• Sissel Jørgensen sissel.jorgensen(at)kjemi.uio.no
  (EDS, XPS)
• Spyros Diplas spyros.diplas(at)smn.uio.no (XPS)
• Lasse Vines Lasse.vines(at)fys.uio.no (SIMS)
• Terje Finnstad terje.finnstad(at)fys.uio.no
  (SPM)
• Oddvar Dyrlie oddvar.dyrlie(at)kjemi.uio.no
  (SPM)
• Magnus Sørby magnus.sorby(at)IFE.no (ND)
• Geir Helgesen geir.helgesen(at)IFE.no (ND)

6
Student contact information
7
Laboratory groups
Laboratoratory work is mandatory! The trip to
IFE, Kjeller is planned for Wednesday 11th of
February!
8
Basic principles, electron probe
Electron
Auger electron or x-ray
Characteristic x-ray emitted or Auger electron
ejected after relaxation of inner state. Low
energy photons (cathodoluminescence) when
relaxation of outer stat.
Secondary electron
9
Basic principles, x-ray probe
X-ray
Auger electron
Secondary x-rays
M
L
K
Characteristic x-ray emitted or Auger electron
ejected after relaxation of inner state. Low
energy photons (cathodoluminescence) when
relaxation of outer stat.
Photo electron
10
Basic principles
Electrons
X-rays
Ions
(SEM)
(XD) X-rays
X-rays (EDS)
(XPS)
BSE
Ions (SIMS)
PE
AE
SE
AE
(Also used for cleaning/thinning samples)
You will learn about - the equipment -imaging -di
ffraction -the probability for different events
to happen -energy related effects -element
related effects -etc., etc., etc..
EltEo (EELS)
SE
EEo
(TEM and ED)
11
Introduction to crystallography

• We divide materials into two categories
• Amorphous materials
• The atoms are randomly distributed in space
• Not quite true, there is short range order
• Examples glass, polystyrene (isopor)
• Crystalline materials
• The atoms are perfectly ordered
• Short range and long range order
• Deviations from the perfect order are important

12
Introduction to crystallography
13
Introduction to crystallography
Scattering angle 2Theta
14
Introduction to crystallography
15
Introduction to crystallography
16
Basic aspects of crystallography

• Crystallography describes and characterise the
  structure of crystals
• Basic concept is symmetry
• Translational symmetry if you are standing at
  one point in a crystal, and move a distance
  (vector) a the crystal will look exactly the same
  as where you started.

17
The lattice

• In the previous example we had a group of atoms
  that was repeated in (1D) space
• This can be described as a set of mathematical
  points in space called the lattice
• In each of these points we put a group of atoms,
  the basis

Basis Lattice crystal structure
18
The Bravais lattices

• In dealing with crystals we use lattices in three
  dimensions
• It can be shown that 14 different types of
  lattices are needed to describe all crystalline
  arrangements of atoms in space
• These are the Bravais lattices
• They are classed in terms of the vectors a, b and
  c, or rather their lengths a, b and c, and angle
  between them ?, ? and ?
• Seven crystal systems Cubic, Tetragonal,
  Orthorhombic, Rhombohedral, Hexagonal,
  Monoclinic, Triclinic

19
Bravais lattices
Seven crystal systems Cubic Tetragonal Orthorhomb
ic Rhombohedral Hexagonal Monoclinic Triclinic
Lattice centering (Hermann-Mauguin symbols) P
(primitive) F (face centered) I (body centred)
A, B, C (base or end centered) R
(rhombohedral)
20
Exaples of materials with a face centered cubic
lattice
Copper
21
Exaples of materials with a face centered cubic
lattice
Silicon
22
Exaples of materials with a face centered cubic
lattice
ZnS
23
What about other symmetry elements?

• We have discussed translational symmetry, but
  there are also other important symmetry
  operations
• Mirror planes
• Rotation axes
• Inversion
• Screw axes
• Glide planes
• The combination of these symmetry operations with
  the Bravais lattices give the 230 space groups

24
Mirror planes and rotation axes, a 2D example

• Imagine a 2D rectangular centered lattice
• Basis number 1 atom in (0,0) relative to each
  lattice point
• Basis number 2 atoms in (0,0) and (1/4,1/4)
  relative to each lattice point

Lattice
Lattice basis
What mirror planes and rotation axes are present
in the two cases?
25
The unit cell

• Elementary unit of volume!

- Defined by three non co-planar lattice vectors
a, b and c -The unit cell can also be
described by the length of the vectors a,b and c
and the angles between them (alpha, beta,
gamma). - The unit cell is the smallest unit of
volume in the material that contains all the
symmetry elements characteristic of the crystal
structure
The unit cell !
26
Space groups

• A space group can be referred to by a number or
  the space group symbol (ex. Fm-3m is nr. 225)
• Structural data for known crystalline phases are
  available in books like Pearsons handbook of
  crystallographic data. but also electronically
  in databases like Find it.
• Pearson symbol like cF4 indicate the axial system
  (cubic), centering of the lattice (face) and
  number of atoms in the unit cell of a phase (like
  Cu).

• Crystals can be classified according to 230 space
  groups.
• Details about crystal description can be found in
  International Tables for Crystallography.
• Criteria for filling Bravais point lattice with
  atoms.
• Both paper books and online

Figur M.A. White Properties of Materials
27
Lattice planes

• Miller indexing system
• Crystals are described in the axial system of
  their unit cell
• Miller indices (hkl) of a plane is found from the
  interception of the plane with the unit cell axis
  (a/h, b/k, c/l).
• The reciprocal of the interceptions are
  rationalized if necessary to avoid fraction
  numbers of (h k l) and 1/8 0
• Planes are often described by their normal
• (hkl) one single set of parallel planes
• hkl equivalent planes

28
Directions

• The indices of directions (u, v and w) can be
  found from the components of the vector in the
  axial system a, b, c.
• The indices are scaled so that all are integers
  and as small as possible
• Notation
• uvw one single direction or zone axis
• ltuvwgt geometrical equivalent directions
• hkl is normal to the (hkl) plane in cubic axial
  systems

(hkl)
uhvkwl 0
29
Reciprocal vectors, planar distances

• The reciprocal lattice is defined by the vectors
  
• Planar distance (d-value) between planes hkl in
  a cubic crystal with lattice parameter a

• The normal of a plane is given by the vector
• Planar distance between the planes hkl is given
  by