Defects and x ray diffraction

Defects in Crystals
• Real crystals are never perfect.
• Always contain defects that affect their properties.
• In many situations ,defects are desirable.
• Defects, natural or man made have significant
influence on the properties of crystals.
• Defects may cause change in strength, thermal
and electrical properties
• Man – made defects – doping in semiconductors,
alloy making have advantageous effects
1

Dimensional Ranges for Different Classes of Defects
2

Imperfections in Solids
BONDING
+
STRUCTURE
+
DEFECTS
PROPERTIES
Is it enough to know bonding and
structure of materials to estimate
their macro properties ?
Defects (both natural and man made) do have a significant impact
on the properties of materials 3

CRYSTAL DEFECTS
Definition
The disturbance occurred in the regular orientation of atoms is
called crystal defect or imperfection.
Classification of crystal Defects
Crystalline defects / imperfections are classified on the basis of
their geometry as follows.
Point Defects – crystalline irregularities of atomic dimensions
(a) Vacancies (b) Interstitials (c) Impurities
Line Defects
(a) Edge dislocation (b) Screw dislocation
Surface Defects
(a) Grain boundaries (b) Tilt boundaries (c) Twin boundaries
(d) Stacking faults
Volume Defects
(a) Cracks (b) pores
4

Imperfections in Solids
Defects in Solids
0-D, Point defects
Vacancy
Interstitial
Substitutional
1-D, Line Defects / Dislocations
Edge
Screw
2-D, Area Defects / Grain boundaries
Tilt
Twist
3-D, Bulk or Volume defects
Crack, pore
Secondary Phase
MATERIALSPROPERTIES
Crystals in nature are never perfect, they have defects !
Atoms in irregular
positions
Planes or groups of
atoms in irregular
positions
Interfaces between
homogeneous regions of
atoms
5

6
Point defects
The simplest point defects are :
Vacancy – missing atom at a certain crystal lattice position;
Interstitial impurity atom – extra impurity atom in an
interstitial position
Self-interstitial atom – extra atom in an interstitial position
Substitution impurity atom – impurity atom, substituting
an atom in crystal lattice
Frenkel defect – extra self-interstitial atom, responsible for
the vacancy nearby.

Point defects
8
1. Vacancy – refers to a missing
atom or vacant atomic site.
2. Self-interstitial – in a lattice
of the same type of atoms,
an atom occupies an
interstitial space (i.e., voids)
3. Interstitial impurity – An
atom of a different kind
occupies the voids space
4 Substitution impurity- A
foreign atom is purposely
introduced in a lattice (doping
in semiconductors)

ENTHALPY OF FORMATION OF VACANCIES
 Formation of a vacancy leads to missing bonds and distortion of the
lattice
 The potential energy (Enthalpy) of the system increases
 Work required for the formaion of a point defect →
Enthalpy of formation (Hf) [kJ/mol or eV / defect]
 Though it costs energy to form a vacancy its formation leads to
increase in configurational entropy
  above zero Kelvin there is an equilibrium number of vacancies
Crystal Kr Cd Pb Zn Mg Al Ag Cu Ni
kJ / mol 7.7 38 48 49 56 68 106 120 168
eV / vacancy 0.08 0.39 0.5 0.51 0.58 0.70 1.1 1.24 1.74
9

G = H  T S
G (putting n vacancies) = nHf  T Sconfig
 Let n be the number of vacancies, N the number of sites in the lattice
 Assume that concentration of vacancies is small i.e. n/N << 1
 the interaction between vacancies can be ignored
 Hformation (n vacancies) = n . Hformation (1 vacancy)
 Let Hf be the enthalpy of formation of 1 mole of vacancies
S = Sthermal + Sconfigurational





 



n
nN
k
n
Sconfig
ln
n
S
T
n
H
nH
n
G configf
f








zero
0


n
G
For minimum
Larger contribution
10






 

kT
H
N
n f
expConsidering only configurational entropy





 


n
nN
kT
H f
ln
User R instead of k if Hf is in J/mole
Assuming n << N





 









kT
H
n
S
kN
n fthermal
exp
1
exp
Using S = Sthermal + Sconfigurational
Independent of temperature, value of ~3
?
11

T (ºC) n/N
500 1 x 1010
1000 1 x 105
1500 5 x 104
2000 3 x 103
Hf = 1 eV/vacancy
= 0.16 x 1018 J/vacancy
G(Gibbsfreeenergy)
n (number of vacancies)
Gmin
Equilibrium
concentration
G (perfect crystal)
 Certain equilibrium number of vacancies are preferred at T > 0K
At a given T
12

The number of vacancies formed by thermal agitation follows the
law:
NV = NA × exp(-QV/kT)
where NA is the total number of atoms in the solid, QV is the
energy required to form a vacancy, k is Boltzmann constant, and
T the temperature in Kelvin ,
When QV is given in joules, k = 1.38 × 10-23 J/atom-K. When
using eV as the unit of energy, k = 8.62 × 10-5 eV/atom-K.
Note that kT(300 K) = 0.025 eV (room temperature) is much
smaller than typical vacancy formation energies.
For instance, QV(Cu) = 0.9 eV/atom. This means that NV/NA at
room temperature is exp(-36) = 2.3 × 10-16, an insignificant
number.
Thus, a high temperature is needed to have a
high thermal concentration of vacancies.
Even so, NV/NA is typically only about 0.0001 at the melting
point. 13

14
Estimating Vacancy Concentration
• Find the equil. # of vacancies in 1m of Cu at 1000 ˚C.
• Given:
3
8.62 x 10 -5 eV/atom-K
0.9eV/atom
1273K
 ND
N
 exp
QD
kT






For 1m 3, N =
NA
ACu
 x x 1m 3 = 8.0 x 10 28 sites
= 2.7 · 10 -4
• Solve:
* What happens when temperature is slowly
reduced to 500 C, or is rapidly quenched to 500 C?

Ionic Crystals
 Overall electrical neutrality has to be maintained
Frenkel defect
 Cation (being smaller get
displaced to interstitial voids
 E.g. AgI, CaF2
Schottky defect
 Pair of anion and cation
vacancies
 E.g. Alkali halides
15

16
Some facts on point Defects
•Point defects are where an atom is
missing or is in an irregular place in
the lattice structure.
•Point defects include self interstitial
atoms, interstitial impurity atoms,
substitution atoms and vacancies.
•Point defects occur due to
imperfect packing of atoms
•Point defects produce distortion
inside the crystal structures
•Point defects produce strain only in
the surrounding but does not affect
the regularity in other parts of the
crystal

Schottky and Frenkel DEFECTS in IONIC SOLIDS
17
A Schottky defect is a pair of
anion and cation vacancies
in ionic crystals
Frenkel defect is a vacancy
associated with interstitial impurity.
Since the size of cations are
generally smaller it is more likely
that cations occupy interstitial sites.

Difference between Frenkel land Schottky defects
Schottky defect arises when both a positive and a negative ion
leave the lattice . This causes decrease in the atomic density .
In Schottky defect stoichiometry is maintained & density
is decreased
Frenkel defect arises when any one ion occupies the interstices
between the lattice. Since there is no change in the number of
ions the density remains unaltered.
Frenkel defects may occur on either the anion or cation sub
lattice
Cation Frenkel defects are more common than anion defects
– cations are smaller than anions and hence easier to
accommodate in interstitial positions
In Frenkel stoichiometry is not maintained & density remains
unchanged
18

Sample problem:
Ca Cl crystallizes in a face centred cubic unit cell with
a=0.556nm. Calculate the density if
i. It contains 0.1% Frenkel defects.
ii. It contains 0.1% Schottky defects.
Hint:
Frenkel defect does not affect density.
d=z M / a 3 NA
Schottky defect reduces the density by 0.1%, assuming
that volume remains constant.
d’=d( 1- 0.1/100)
d’=0.999d
19

20
Line defects
Linear crystal defects are edge and screw
dislocations.
•Edge dislocation is an extra half plane of atoms
“inserted” into the crystal lattice.
•Due to the edge dislocations metals possess high
plasticity characteristics: ductility and malleability.
Screw dislocation forms when one part
of crystal lattice is shifted (through shear) relative
to the other crystal part. It is called screw as
atomic planes form a spiral surface around the
dislocation line.
For quantitative characterization of a difference
between a crystal distorted by a dislocation and
the perfect crystal the Burgers vector is used.
The dislocation density is a total length of
dislocations in a unit crystal volume.

21
LINE DEFECTS OR DISLOCATIONS
Line defects are one-dimensional, affecting a row of atoms. The most
common line defect in crystals is called dislocation.
There are two types of line defects:
1) Edge dislocation and 2) Screw dislocation
Edge dislocation: arises when one of the atomic planes forms only
partially and does not extend through the entire crystal as shown

22
Screw dislocation in a crystal
(long black line: dislocation line;
black arrow: Burgers vector)..
SCREW DISLOCATION
Screw dislocation arises due to
displacement of atoms in one part of a
crystal relative to the rest of the crystal.
In a screw dislocation, there is a line of
atoms about which the crystal planes are
warped to give an effect similar to the
threads of a screw. The term screw is used
to represent that one part of the crystal is
moving in a spiral manner about the
dislocation line as shown in the figure.
Dislocations make a material softer
because they permit crystals to deform
without moving one entire crystal plane
over the one below.

The Burgers’ Vector:
A dislocation cannot be described just in terms of its
orientation since this can vary with position. The entire
dislocation is characterized by a vector which represents the
amount and direction of slip which is produced when that
dislocation has passed right through the crystal in a certain
direction. This vector is called the Burgers’ vector b.
The Burgers vector is found by drawing a Burgers circuit and
recording the vector that would complete the circuit
23

24
The Burgers vector is normal to an edge but parallel to a screw dislocation.
The Burgers vector is the same at all points along the dislocation line. The
dislocation is in edge orientation when normal to the Burgers vector and in screw
orientation when parallel to it.

25
The Burgers vector is a precise indicator of the magnitude and
direction of shear that a dislocation produces. It is defined by
means of a circuit around the dislocation on any surface which
intersects the dislocation These represent the 'failure
closure' in a Burger's circuit in imperfect (top) and perfect
(bottom) crystal.
Edge Screw
Vectors describing dislocation line and Burger's vector are
Perpendicular Parallel

26
Plane defects occur along a 2-dimensional
surface.
The surface of a crystal is an obvious
imperfection, because these surface atoms are
different from those deep in the crystals. When
a solid is used as a catalyst, the catalytic activity
depends very much on the surface area per unit
mass of the sample. For these powdery
material, methods have been developed for the
determination of unit areas per unit mass.
Another surface defects are along the grain
boundaries. A grain is a single crystal. If many
seeds are formed when a sample starts to
crystallize, each seed grow until they meet at
the boundaries. Properties along these
boundaries are different from the grains.

Surface Defects - Grain Boundaries
Found in Polycrystalline materials.
Present paths for atoms to diffuse into the material and
scatter light through transparent materials to make them
opaque.
the boundaries limit the lengths and motions of
dislocations that can move.
That means that smaller grains (more grain boundary
surface area) strengthens materials.
The size of grains can be controlled by the cooling rate.
Rapid cooling (quenching) produces smaller grains .
Large grains result in low strength materials.
Any defect in the regular lattice disrupts the motion of
dislocations
Motion of dislocations produces more dislocations which
impede the motion of other dislocations and increases the
strength of the material. 27

Grain Boundaries
28
Whenever the grains of different
orientations separate the general
pattern of atoms and exhibits a
boundary, the defect caused is
called grain boundary
A Grain Boundary is a general
planar defect that separates
regions of different crystalline
orientation (i.e. grains) within a
polycrystalline solid.
This type of defect generally takes
place during the solidification of
liquid metals
High Resolution Transmission Electron
Microscope (HRTEM) Image of a Grain
Boundary Film in Strontium-Titanate

29
Planar defects
Planar defect is an imperfection in form of a plane between
uniform parts of the material. The most important planar
defect is a grain boundary. Formation of a boundary between
two grains may be imagined as a result of rotation
of crystal lattice of one of them about a specific axis.
Depending on the rotation axis direction, two ideal types of a
grain boundary are possible:
Tilt boundary – rotation axis is parallel to the boundary
plane;
Twist boundary - rotation axis is perpendicular to the
boundary plane:
An actual boundary is a “mixture” of these two ideal types.

Tilt and twist boundaries
30
Grain boundaries are rather complicated
defects!
A Tilt Boundary, between two slightly mis-aligned
grains appears as an array of edge dislocations.
A Twin Boundary occurs when the crystals on
either side of a plane are mirror images of each
other. Twins are either grown-in during
crystallization, or the result of mechanical or
thermal work.
The boundary between the twinned crystals will be
a single plane of atoms.
There is no region of disorder and the boundary
atoms can be viewed as belonging to the crystal
structures of both twins
Schematic representations of a tilt boundary
(top) and a twist boundary between two
idealized grains.
twin boundaries are the most frequently
encountered grain boundaries in Silicon, but also
in many other fcc crystals
Tilt boundary
Twin boundary

31
STACKING FAULTS
In simple terms, stacking fault is a
defect in a face-centered cubic or
hexagonal close-packed crystal in
which there is a change from the
regular sequence of positions of
atomic planes.
It is a surface dislocation.
Consider stacking of layers of atoms
A, B, C by repetition to form a crystal.
If the stacking sequence ABCABCA..
has been changed to a faulty
sequence ABCABABCA.., then a
stacking fault occurs.
Stacking faults by themselves are
simple two-dimensional defects. They
carry a certain stacking fault
energy very roughly around a
few 100 mJ/m2.

32
Grain boundaries are called large-angle boundaries if misorientation of
two neighboring grains exceeds 10º-15º.
Grain boundaries are called small-angle boundaries if misorientation of
two neighboring grains is 5º or less.
Grains, divided by small-angle boundaries are also called subgrains.
Grain boundaries accumulate crystal lattice defects (vacancies,
dislocations) and other imperfections, therefore they effect on the
metallurgical processes, occurring in alloys and their properties.
Since the mechanism of metal deformation is a motion
of crystal dislocations through the lattice, grain boundaries, enriched
with dislocations, play an important role in the deformation process.
Diffusion along grain boundaries is much faster, than throughout the
grains.
Segregation of impurities in form of precipitating phases in the
boundary regions causes a form of corrosion, associated with chemical
attack of grain boundaries. This corrosion is called Inter granular
corrosion.

SCHEMATIC DIAGRAM OF X-RAY DIFFRACTION METHOD
35

36
X-Ray Crystallography
• The wavelength of X-rays is typically
1 A°, comparable to the interatomic
spacing (distances between atoms
or ions) in solids.
• We need X-rays:
eVx
mx
hchc
hE rayx
3
10
103.12
101
 



A single crystal, also called monocrystal, is a crystalline solid
in which the crystal lattice of the whole sample is continuous
and unbroken till the edges of the sample, i.e., with no grain
boundaries.
A polycrystalline sample, on the other hand, is made up of a
number of smaller crystals known as crystallites. Usually those
crystallites are connected through a amorphous material to form
extended solid.
37

38
X-RAY DIFFRACTION METHODS
X-Ray Diffraction Method
Laue Rotating Crystal Powder
Orientation
Single Crystal
Polychromatic Beam
Fixed Angle
Lattice constant
Single Crystal
Monochromatic Beam
Variable Angle
Lattice Parameters
Polycrystal (powdered)
Monochromatic Beam
Variable Angle

40
Bragg Equation
• Bragg reflection can only occur for wavelength
• This is why we cannot use visible light. No diffraction
occurs when the above condition is not satisfied.
• The diffracted beams (reflections) from any set of
lattice planes can only occur at particular angles
pradicted by the Bragg law.
 nd sin2
dn 2

The Laue method is today mainly used to find
the orientation of large single crystals.
Poly chromatic X-rays are reflected from, or
transmitted through, a sample crystal.
The diffracted beams form arrays of spots,
that lie on curves on a photo film.
The Bragg angle is fixed for every set of
planes in the crystal.
Every set of planes picks out and diffracts a
particular wavelength from the white radiation
that satisfies the Bragg law for the values
of d and θ involved.
Each curve therefore corresponds to a
different wavelength.
The spots lying on any one curve are
reflections from planes belonging to one zone.
Laue reflections from planes of the same zone
all lie on the surface of an imaginary cone
whose axis is the zone axis. 41

Transmission Laue
In the transmission Laue mode, the film is
placed behind the crystal to record x-rays
which are transmitted through the crystal.
One side of the cone of Laue reflections is
defined by the transmitted beam. The film
intersects the cone, with the diffraction
spots generally lying on an ellipse.
Back-reflection Laue
In the back-reflection method, the film is
placed between the x-ray source and the crystal.
The beams which are diffracted in a backward
direction are recorded.
One side of the cone of Laue reflections is
defined by the transmitted beam.
The film intersects the cone, with the diffraction
spots generally lying on an hyperbola.
42

43
Laue Pattern The symmetry of the
spot pattern reflects the
symmetry of the crystal
when viewed along the
direction of the incident
beam. Laue method is
often used to determine
the orientation of single
crystals by means of
illuminating the crystal
with a continuos spectrum
of X-rays;
Single crystal
Continous spectrum of x-
rays
Symmetry of the crystal;
orientation

44
Crystal structure determination by Laue
method
• The Laue method is mainly used to determine the
crystal orientation.
• Although the Laue method can also be used to
determine the crystal structure, several wavelengths can
reflect in different orders from the same set of planes,
with the different order reflections superimposed on
the same spot in the film. This makes crystal structure
determination by spot intensity diffucult.
• Rotating crystal method overcomes this problem.

45
ROTATING CRYSTAL METHOD
• In the rotating crystal method,
a single crystal is mounted
with an axis normal to a
monochromatic x-ray
beam. A cylindrical film is
placed around it and the
crystal is rotated about the
chosen axis.
As the crystal rotates, sets of lattice planes
will at some point make the correct Bragg
angle for the monochromatic incident beam,
and at that point a diffracted beam will be
formed.

46
ROTATING CRYSTAL METHOD
Lattice constant of the crystal can be
determined by means of this method; for a
given wavelength if the angle at which a
reflection occurs is known, can be
determined from:
hkld

2 2 2
a
d
h k l

 

47
Rotating Crystal Method
The reflected beams are located on the surface of
imaginary cones. By recording the diffraction patterns (both
angles and intensities) for various crystal orientations, one
can determine the shape and size of unit cell as well as
arrangement of atoms inside the cell.
Film

In the rotating crystal method, a single crystal is mounted with an axis
normal to a monochromatic x-ray beam. A cylindrical film is placed around it
and the crystal is rotated about the chosen axis. As the crystal rotates, sets
of lattice planes will at some point make the correct Bragg angle for the
monochromatic incident beam, and at that point a diffracted beam will be
formed.
The reflected beams are located on the surface of imaginary cones. When
the film is laid out flat, the diffraction spots lie on horizontal lines.
48

The powder method is used to determine the
value of the lattice parameters accurately.
Lattice parameters are the magnitudes of the
unit vectors a, b and c which define the unit
cell for the crystal.
If a monochromatic x-ray beam is directed at
a single crystal, then only one or two
diffracted beams may result.
If the sample consists of some tens of
randomly orientated single crystals, the
diffracted beams are seen to lie on the
surface of several cones. The cones may
emerge in all directions, forwards and
backwards.
49

The distance S1 corresponds to a diffraction angle of 2q. The angle between
the diffracted and the transmitted beams is always 2q. We know that the
distance between the holes in the film, W, corresponds to a diffraction angle
of q = p. So we can find q from:
• Or
We know Bragg's Law: nλ = 2dsinθ
and the equation for inter planar spacing, d, for cubic crystals is given by:
So,
where a is the lattice parameter this gives:
From the measurements of each arc we can now generate a table of S1, q and
sin2q.• If all the diffraction lines are considered, then the experimental values of
sin2q should form a pattern related to the values of h, k and l for the structure.
• We now multiply the values of sin2q by some constant value to give nearly
integer values for all the h2+k2+ l2 values. Integer values are then assigned.
50

The integer values of h2+ k2+ l2 are then equated with their hkl values to
index each arc, using the table shown in the next slide
51

52
THE POWDER METHOD
• A powder is a polycrystalline material in which there are all
possible orientations of the crystals so that similar planes
in different crystals will scatter in different directions.
If a powdered specimen is used, instead of a single crystal,
then there is no need to rotate the specimen, because
there will always be some crystals at an orientation for
which diffraction is permitted.
Here a monochromatic X-ray beam is incident on a
powdered or polycrystalline sample.
This method is useful for samples that are difficult to obtain
in single crystal form.

53
THE POWDER METHOD
 The powder method is used to determine the value of the
lattice parameters accurately.
 Lattice parameters are the magnitudes of the unit vectors
a, b and c which define the unit cell for the crystal.
 For every set of crystal planes, by chance, one or more
crystals will be in the correct orientation to give the
correct Bragg angle to satisfy Bragg's equation.
 Every crystal plane is thus capable of diffraction.
 Each diffraction line is made up of a large number of small
spots, each from a separate crystal.
 Each spot is so small as to give the appearance of a
continuous line.

54
The Powder Method
• If a monochromatic x-ray beam is directed at a single crystal,
then only one or two diffracted beams may result.
 A sample of some hundreds of
crystals (i.e. a powdered sample)
show that the diffracted beams
form continuous cones. A circle of
film is used to record the
diffraction pattern as shown. Each
cone intersects the film giving
diffraction lines. The lines are seen
as arcs on the film.

55
Debye Scherrer Camera
A very small amount of powdered material is sealed into a fine
capillary tube made from glass that does not diffract x-rays.
The specimen is placed in the
Debye Scherrer camera and is
accurately aligned to be in the
centre of the camera. X-rays enter
the camera through a collimator.
The powder diffracts the x-rays in
accordance with Braggs law to
produce cones of diffracted
beams. These cones intersect a
strip of photographic film located in
the cylindrical camera to produce a
characteristic set of arcs on the
film.

56
Powder diffraction film
When the film is removed from the camera,
flattened and processed, it shows the diffraction
lines and the holes for the incident and
transmitted beams.

Indexing a Powder Pattern
We shall now consider the powder patterns from a sample crystal.
The sample is known to have a cubic structure, but we don't know
which one.
We remove the film strip from the Debye camera after exposure, then
develop and fix it. From the strip of film we make measurements of the
position of each diffraction line. From the results it is possible to
associate the sample with a particular type of cubic structure and also
to determine a value for its lattice parameter.
• When the film is laid flat, S1 can be measured. This is the distance
along the film, from a diffraction line, to the centre of the hole for the
transmitted direct beam.• For back reflections, i.e. where 2θ > 90° you
can measure S2 as the distance from the beam entry point.
57

•For some structures e.g. bcc, fcc, not all planes reflect, so some of the
arcs may be missing.
• It is then possible to identify certain structures, in this case fcc (- the
planes have hkl values: all even, or all odd in the table above).
• For each line we can also calculate a value for a, the lattice parameter.
For greater accuracy the value is averaged over all the lines. 58

A student has made measurements of S1 from three films, from Debye
Scherrer experiments on three different samples. It is known that all three
samples are cubic. From the results determine the cubic structure type of
each sample:
Use the data sheet here to help you.
Sample1S1/m
m
Sample2S1/m
m
Sample3S1/m
m
22 35 41
31 41 59
38 59 73
45 71 87
50 75 101
56 88 114
65 99 130
70 103 153
74 116 -
78 128 -
59

60
Applications of XRD
1. Differentiation between crystalline and amorphous
materials;
2. Determination of the structure of crystalline materials;
3. Determination of electron distribution within the atoms,
and throughout the unit cell;
4. Determination of the orientation of single crystals;
5. Determination of the texture of poly grained materials;
6. Measurement of strain and small grain size…..etc
XRD is a nondestructive technique. Some of the uses
of x-ray diffraction are;

61
Advantages and disadvantages of
X-rays
Advantages;
• X-ray is the cheapest, the most convenient and widely used
method.
• X-rays are not absorbed very much by air, so the specimen
need not be in an evacuated chamber.
Disadvantage;
• They do not interact very strongly with lighter elements.

62
Other Difraction Methods
Diffraction
X-ray Neutron Electron
Neutrons and electrons can also be used in
diffraction experiments.
The physical basis for the diffraction of electron
and neutron beams is the same as that for the
diffraction of X rays, the only difference being in the
mechanism of scattering.

Electron Diffraction
Electrons are charged particles and interact strongly with
all atoms. So electrons with an energy of a few eV would
be completely absorbed by the specimen. In order that
an electron beam can penetrate into a specimen , it
necessitas a beam of very high energy (50 keV to 1MeV)
as well as the specimen must be thin (100-1000 nm)
Electron diffraction has also been used in the analysis of
crystal structure. The electron, like the neutron, possesses
wave properties;
0
2AeV
m
h
m
k
E
ee
40
22 2
222



63

64
Electron Diffraction
If low electron energies are used,
the penetration depth will be very
small (only about 50 A°), and the
beam will be reflected from the
surface. Consequently, electron
diffraction is a useful technique
for surface structure studies.
Electrons are scattered strongly in
air, so diffraction experiment must
be carried out in a high vacuum.
This brings complication and it is
expensive as well.

ELECTRON DIFFRACTION PATTERNS FOR STRUCTURE ANALYSIS
ONLY THREE TYPE SPECIMENS AND ELECTRON DIFFRACTION
PATTERNS MAY BE USED FOR ATOMIC STRUCTURE ANALYSIS
UNKNOWN PHASES
MOSAIC SINGLE CRYSTAL PLATELIKE TEXTURE POLYCRYSTAL
65

66
Neutron Diffraction
• Neutrons were discovered in 1932 and their wave
properties was shown in 1936.
• If λ ~1A°; Energy E~0.08 eV. This energy is of the same
order of magnitude as the thermal energy kT at room
temperature, 0.025 eV, and for this reason such neutrons
are called thermal neutrons.
E = p2/2m p = h/λ
where E=Energy λ=Wavelength
p=Momentum
m = Mass of neutron = 1,67.10-27kg

67
Neutron Diffraction
• Neutrons do not interact with electrons in the crystal. Thus,
unlike x-rays, which are scattered entirely by electrons, the
neutron is scattered entirely by nuclei
• Although uncharged, neutron has an intrinsic magnetic
moment, so it will interact strongly with atoms and ions in
the crystal which also have magnetic moments.
• Neutrons are more useful than X-rays for determining the
crystal structures of solids containing light elements.
• (X-rays are more useful for samples with higher Atomic
number)
• Neutron sources in the world are limited so neutron
diffraction is a very special tool.

68
Neutron Diffraction
• Neutron diffraction has several advantages over its x-ray
counterpart;
• Neutron diffraction is an important tool in the investigation
of magnetic ordering that occur in some materials.
• Light atoms such as H are better resolved in a neutron
pattern because, having only a few electrons to scatter the
X ray beam, they do not contribute significantly to the X ray
diffracted pattern.

69
X-Ray
λ = 1A°
E ~ 104 eV
interact with electron
Penetrating
Neutron
λ = 1A°
E ~ 0.08 eV
interact with nuclei
Highly Penetrating
Electron
λ = 2A°
E ~ 150 eV
interact with electron
Less Penetrating
Diffraction Methods

x-ray electron
neutron
scattering
by electrostatic
repulsion of
nucleus
by electron cloud
around nucleus
by interaction with
the nucleus
resolution moderate moderate high
penetrating power
poor (requires
thin specimens)
good good
matter interaction
high (unreliable
results)
none moderate
magnetic effects no no
yes (neutrons have
their own magnetic
field)
good for light
elements
no no yes
particular uses crystals
crystals fuel rods,
archaeological
artifacts 70

Defects and x ray diffraction

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