MSE 421/521 Structural Characterization
Structure
Structural Characterization
Material science is essentially the study of the relationships between the structure, processing,
and properties of materials.
Physical characterisation of a material can be achieved by examining its:
Composition
Structure
What is the chemical make up of the material?
What is the architecture of the material like?
Both composition and structure (which itself is partly dependent upon processing) will dictate
most of the properties of a material. A material can then further be characterised...
How will the properties (physical, electrical, thermal, chemical, optical, etc.) relate to
performance in terms of mechanical deformation, fracture, wear, permittivity, dielectric loss,
corrosiveness, reactivity, opacity, etc.?
Various levels of structure exist.
Levels of Structure
Atomic structure
The position of atoms relative to one another, closely related to crystal structure. If structure
describes the architecture of a material, then the atomic structure is the way the bricks are
arranged. The mortar between the bricks is analogous to atomic bonding (covalent, ionic,
metallic, etc.). As atoms have diameters on the order of just a few Angstroms, this level of
structure can only be examined using diffraction methods, high-resolution electron microscopy,
or atomic force microscopy.
A lattice is an infinite array of points in space in which each point has identical surroundings to
all others. Crystals can be described by associating a group of atoms (basis or motif) with each
lattice point. Crystals are therefore periodic arrangements of atoms and can be described in
differing degrees of detail according to one’s need. Most generally, a crystal will belong to one
of seven possible crystal systems (cubic, hexagonal, etc.). More specifically, the crystal can be
described in one of 14 possible space lattices, also called Bravais lattices (fcc, bcc, etc.), in
which case we automatically know both the crystal system and type of centering (primitive,
body-centred, face-centred, or base-centred). Looking deeper still, combinations of various
symmetry operations create 32 unique point groups, which indicate the crystal system and
contain information about the macroscopic behaviour of the crystal. By simply combining these
32 point groups (symmetries about a fixed point) with the 14 Bravais lattices, the 73
symmorphic space groups are obtained. By additionally considering symmetry operations
which involve non-primitive translations (srews and glides), an additional 157 nonsymmorphic
space groups can be derived, giving a total of 230 possible space groups in all. A summary of
crystal information is shown below.
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MSE 421/521 Structural Characterization
Crystal System
Cubic
Four 3 or 3
Tetragonal
One 4 or 4
Axial lengths and angles
a = b = c, α = β = γ = 90°
Centring
Simple
Body-Centered
Face-Centered
Simple
Bravais
Lattice
cP
cI
cF
tP
Body-Centered
Simple
Body-Centered
Base-Centered
Face-Centered
Simple
tI
oP
oI
oS
oF
hP
a = b, α = β = γ = 90°
Orthorhombic
Three 2 or 2
α = β = γ = 90°
Trigonal
One 3 or 3
(Rhombohedral)
One 3 or 3
Hexagonal
One 6 or 6
Monoclinic
One 2 or 2
Triclinic
1 or 1
a=b
α = β = 90°, γ = 120°
a = b = c, α = β = γ
Simple
hR or rP
a=b
α = β = 90°, γ = 120°
Simple
hP
α = γ = 90°
(second setting)
Simple
Base-Centered
Simple
mP
mS
aP
No restrictions
Symmorphic Space Groups
P23, Pm3, P432, P 43m , Pm3m
I23, Im3, I432, I43m , Im3m
F23, Fm3, F432, F4 3m , Fm3m
P4, P 4 , P4/m, P422, P4mm
P42m, P 4 m2 , P4/mmm
I4, I4 , I4/m, I422, I4mm
P222, Pmm2, Pmmm
I222, Imm2, Immm
C222, Cmm2, Amm2, Cmmm
F222, Fmm2, Fmmm
P3, P 3 , P312, P321, P3m1, P31m,
P 3 1m , P 3 m1
R3, R 3 , R32, R3m, R 3 m
P6, P 6 , P6/m, P622, P6mm,
P 6m2 , P 62m , P6/mmm
P2, Pm, P2/m
C2, Cm, C2/m (second setting)
P1, P 1
Note: Although “rhombohedral” is a lattice system which describes the geometry of a
rhombohedrally-centred hexagonal lattice, it is not a crystal system but only a subset of the
trigonal crystal system.
The 14 Bravais lattices
Rhombohedral - P
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Note: The rhombohedral lattice (rP) could also
be - and is more usually - described as a
rhombohedrally-centred hexagonal lattice (hR),
in which case there are three lattice sites per
unit cell.
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MSE 421/521 Structural Characterization
Polymers and biological matter form molecules at this level, which are in turn characterized by
their type and side groups. Such materials can also form crystals, but are often poorly
crystallised.
All real crystals contain flaws – imperfections in the symmetries caused by dislocations,
substitutions, vacancies, stacking faults, internal strain, etc. The degree of crystallinity is
determined by the density of such defects. Single line defects like dislocations or planar defects
like stacking faults can be imaged via transmission electron microscopy (TEM), but other forms
of crystal defect are only detectable by TEM if they form periodic arrays. Crystals which exist in
polycrystalline materials are typically referred to as grains.
Crystallographic planes (Miller Indices)
Individual planes are denoted (hkl)
Fractional axis intercepts are 1/h, 1/k, 1/l
If plane does not intercept an axis, 1/∞ = 0
If plane intercepts axis origin, origin must be moved
hkl are normally integers, negative values indicated with a bar, e.g., (11 1 ) , read as “one,
one, bar one” or “one, one, one bar”.
Crystallographic directions
These are actually vectors used as unit vectors only for their direction, but their magnitudes will
technically not be unity.
Any vector u can be represented as a linear combination of the basis vectors a, b, c of the
unit cell: u = ha + kb + lc
Once the unit cell is defined, any direction u within the lattice can be identified uniquely
by its components [hkl], and these components are called the Miller indices.
[hkl] is a specific direction
<hkl> is a family of crystallographically equivalent directions
Origin is arbitrary
As magnitude is unimportant, always reduce hkl to lowest terms
e.g., [222] - [111]
Show negative values with a bar, e.g., [11 1 ] , read as “one, one, bar one” or “one, one,
one bar”
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MSE 421/521 Structural Characterization
Microstructure
Microstructure includes structures made by assemblies of many crystals and span the size range
from around 1 µm to 1 mm. On this size scale materials are characterised by their grain sizes,
grain size distribution, phase assemblage, and porosity. Optical microscopes are often sufficient
to examine this level of structure, but very fine structures may require the use of an electron
microscope. Very fine-grained materials, with grains below 1µm in diameter, are described in
terms of their nanostructure, whereas materials with grains much larger than 1 mm can be
described (sometimes with the unaided eye) by their macrostructure.
Characterizing Structure
To characterise materials it is necessary to perturb or interact with them in some way. Even the
photons of light with which we see the world interact with it (e.g., they warm the earth, make
green plants grow, etc.). The energy of photons of visible light are fairly low (1.8 – 3.1 eV), but
even their interaction with matter can cause damage (which is essentially the way photographic
film works). X-rays (~124 eV – ~124 keV) can ionise atmospheric gases (this is how many xray detectors work) and cause damage in crystalline materials. For a closer look, a microscope is
needed to aid our eyes, and anyone who has ever used a magnifying glass to burn the wings off
insects knows that these devices can also be damaging.† For still higher magnification, an
electron microscope is required, in which the photon source is replaced with electrons with
energies typically from 10 – 300 keV. Such beams are more damaging than photons. The
objective of characterisation is to obtain the maximum information whilst causing the least
amount of damage.
Two kinds of interaction: elastic and inelastic
Elastic – any process in which the energy of the primary electron is unchanged,
e.g., diffraction, Rutherford scattering (back scattering), reflection, Rayleigh scattering.
Inelastic – processes in which the primary electron loses a detectable amount of energy.
Involve interaction between the primary-beam electrons and orbital electrons of the
atoms in the specimen, e.g., EDS, CL, SEI, absorption (tricky term), etc.
Microscopy – 2D or 3D image of specimen is obtained (real space)
Distances in image are directly proportional to distances in object
M is the proportionality constant
Microanalysis –
a spectrum is obtained in which signal intensity is recorded as a function
of either energy or wavelength.
Diffraction – signal displayed as either an image (diffraction pattern) or graphically, typically
as a function of diffraction angle (B&K call this a diffraction spectrum, but that
term is misleading and never actually used).
Scattering angle of diffracted radiation/electrons is inversely proportional to scale
of features in object
†
Please do NOT try this at home!
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