15/1-08 MENA3100

MENA3100

1st lecture

General information, what to learn and

some repetition of crystallography

15/1-08 MENA3100

Student contact information Name E-mail Phone

Jørn Eirik Olsen Jorneo(a)student.matnat.uio.no 41100739

Jack Bonsak Jackb(a)ulrik.uio.no 97649877

Kai K Lange Kaikl(a)student.matnat.uio.no 95141689

Joakim Aardal Joakimaa(a)student.matnat.uio.no 41479008

Magnus Kvalbein Magnuskv(a)student.matnat.uio.no 90533341

Einar Vøllestad Einarvo(a)student.matnat.uio.no 41107628

Halvard Haug Halvarha(a)gmail.com 99486757

Kristine Kostøl Kristbko(a)student.matnat.uio.no 41634468

15/1-08 MENA3100

Who is involved?

• Anette E. Gunnæs: eleonora(at)fys.uio.no, 91514080 (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)

• Sissel Jørgensen: sissel.jorgensen(at)kjemi.uio.no (SEM, 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)

15/1-08 MENA3100

General information

• Lectures– Based on “Microstructural characterization of materials” + by Brandon and

Kaplan. SPM lecture based on chapter 7.8 in second edition of “Physical methods for materials characterisation” by Flewitt and Wild. EBSD will be based on separate text.

– 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 (chapter 7 + some sub chapters).

• 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

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Laboratory groups

A B C

Laboratory work will mainly take place on Tuesdays.

The trip to IFE, Kjeller has been rescheduled to Wednesday 13th of February!

15/1-08 MENA3100

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– Crunching etc……

Mapping of elements or chemical states of elements.

The same basic theory for allwaves.

Different imaging modes.

15/1-08 MENA3100

Probes used

• Visible light– Optical microscopy (OM)

• X-ray– X-ray diffraction (XD)– 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)

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Basic principles, electron probeValence

K

L

M

Electronshell

Characteristic x-ray emitted or Auger electron ejected after relaxation of inner state. Low energy photons (cathodoluminescence)when relaxation of outer stat.

K

L

M

1s2

2s2

2p2

2p43s2

3p2

3p4

3d4

3d6

Auger electron or x-ray

Secondary electron

Electron

15/1-08 MENA3100

Basic principles, x-ray probe

K

L

M

Auger electron

Photo electron

X-ray Valence

K

L

M

Electronshell

Characteristic x-ray emitted or Auger electron ejected after relaxation of inner state. Low energy photons (cathodoluminescence)when relaxation of outer stat.

Secondary x-rays

15/1-08 MENA3100

Basic principles

Electrons X-rays Ions

E<Eo(EELS)

BSE

SEAE

X-rays (EDS)Ions (SIMS)

AE PE

(XD)X-rays

E=Eo

(XPS)

(Also used forcleaning/thinning samples)

SE

(SEM)

(TEM and ED)

You will learn about:- the equipment-imaging-diffraction -the probability for different events to happen-energy related effects-element related effects-etc., etc., etc……..

15/1-08 MENA3100

Basic aspects of crystallography

• Crystallography describes and characterise the structure of crystals

The unit cell !

a

c

bα

βγ

- Defined by three non 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).

Elementary unit of volume!

15/1-08 MENA3100

Unit cell

• The crystal structure is described by specifying a repeating element and its translational periodicity

– The repeating element (usually consisting of many atoms) is replaced by a lattice point and all lattice points have the same atomic environments.

– The whole lattice can be described by repeating a unit cell in all three dimensions. The unit cells are the smallest building blocks.

– A primitive unit cell has only one lattice point in the unit cell.

a

c

bα

βγ

Replaces repeating element(molecule, base etc.)

15/1-08 MENA3100

Axial systems

The point lattices can be described by 7 axial systems (coordinate systems)

x

y

z

a

b

c

α

γ

β

Axial system Axes Angles

Triclinic a≠b≠c α≠β≠γ≠90o

Monoclinic a≠b≠c α=γ=90o ≠ β

Orthorombic a≠b≠c α= β=γ=90o

Tetragonal a=b≠c α= β=γ=90o

Cubic a=b=c α= β=γ=90o

Hexagonal a1=a2=a3≠c α= β=90o

γ=120o

Rhombohedral a=b=c α= β=γ ≠ 90o

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Bravais lattice

The point lattices can be describedby 14 different Bravais lattices

Hermann and Mauguin symboler:P (primitiv)F (face centred)I (body centred) A, B, C (bace or end centred) R (rhombohedral)

15/1-08 MENA3100

Hexagonal unit cell

a1

a2

a3

a1=a2=a3

γ = 120o

(hkil)h + k + i = 0

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Space groups

• 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

• 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 “Pearson’s 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).

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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/∞ = 0

– Planes are often described by their normal

– (hkl) one single set of parallel planes

– {hkl} equivalent planes

Z

Y

X

(010)

(001)

(100)

Z

Y

X

(110)

(111)

Z

Y

X

y

z

x

c/l

0a/h b/k

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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

– <uvw> geometrical equivalent directions

• [hkl] is normal to the (hkl) plane in cubic axial systems

uaa

b

x

z

c

y

vb

wc

[uvw]

Zone axis [uvw]

(hkl)

uh+vk+wl= 0

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Stereographic projection

• Plots planes and directions in a 2D map

Fig 6.5 of Klein (2002) Manual of Mineral Science, John Wiley

and Sons

All poles in a zone are on the same great circle!!

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Wulff net

Fig 6.8 of Klein (2002) Manual of Mineral Science,

John Wiley and Sons

15/1-08 MENA3100

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:

222 lkh

ad hkl

Vbac

Vacb

Vcba

/)(

/)(

/)(

*

*

*

–The normal of a plane is given by the vector:

–Planar distance between the planes {hkl} is given by:

*** clbkahg hkl

hklhkl gd /1