APPLIED PHYSICS
CODE : 07A1BS05
I B.TECH
CSE, IT, ECE & EEE
UNIT-1: CHAPTER 2.2
NO. OF SLIDES : 20
1
UNIT INDEX
UNIT-I
S.No. Module Lecture PPT Slide
No. No.
9 Braggs law. L10 3-9
10 Laue method L11 10-15
11. powder method. L12 16-20
2
Lecture-10
X-Ray Powder Diffraction
3
Lecture-10
4
Lecture-10
X-Ray Powder Diffraction (XRPD) is one
of the most powerful techniques for
analyzing the crystalline nature of solids.
XRPD capabilities include micro-
diffractometry, flat plate or capillary
sample configuration, spinning and
rocking methods, variable temperature
and humidity conditions, and a unique
sample conveyor system to overcome
sample inhomogeneity effects.
5
Lecture-10
XRPD is perhaps the most widely used X-ray
diffraction technique for characterizing materials. As
the name suggests, the sample is usually in a powdery
form, consisting of fine grains of single crystalline
material to be studied. The technique provides
information that cannot be obtained any other way. The
information obtained includes types and nature of
crystalline phases present, structural make-up of
phases, degree of crystallinity, amount of amorphous
content, microstrain & size and preferred orientation of
crystallites. The technique is also used for studying
particles in liquid suspensions or polycrystalline solids
(bulk or thin film materials).
6
Lecture-10
The term 'powder' means that the crystalline domains
are randomly oriented in the sample. Therefore,
when the 2-D diffraction pattern is recorded, it
shows concentric rings of scattering peaks
corresponding to the various d spacings in the crystal
lattice. The positions and the intensities of the peaks
are used for identifying the underlying structure (or
phase) of the material. This phase identification is
important because the material properties are highly
dependent on structure (think, for example, of
graphite and diamond).
7
Lecture-10
Powder diffraction data can be collected using
either transmission or reflection geometry, as
shown below. If the particles in the powder
sample are randomly oriented, both methods
will yield the same results.
8
Lecture-10
Single crystal diffraction L
e
Laue‟s method - variable, fixed. c
t
Rotating crystal method - fixed, variable to
u
r
some extent. e
-
1
Why not single crystal methods? 0
• It may be difficult to obtain a single crystal.
• The usual form of a material may be
polycrystalline.
• Problems with twinning or phase transitions
complicate structural assignments.
9
Lecture-11
Powder diffraction
In this method the crystal is reduced to a
fine powder and is placed in a beam of
monochromatic X-rays. Each particle is a tiny
crystal or an assemblage of smaller crystals
randomly oriented with respect to the the
incident beam.
Powder methods - fixed, variable.
10
Lecture-11
The diagram shows only two scattering planes, but implicit here
is the presence of many parallel, identical planes, each of which
is separated from its adjacent neighbor by a spacing d.
Constructive interference occurs when (A+B)/ = n, coinciding
with Bragg’s law, n= 2dsin . The integer n refers to the order
of diffraction. For n = 1, (A+B) = and for n = 2, (A+B) = 2 etc.
11
Lecture-11
• Angles are used to calculate the interplanar atomic
spacings (d-spacings). Because every crystalline
material will give a characteristic diffraction pattern
and can act as a unique „fingerprint‟, the position (d)
and intensity (I) information are used to identify the
type of material by comparing them with patterns for
over 80,000 data entries in the International Powder
Diffraction File (PDF) database, complied by the Joint
Committee for Powder Diffraction Standards (JCPDS).
By this method, identification of any crystalline
compounds can be made even in complex samples.
12
Lecture-11
The position (d) of the diffracted peaks also provides
information about how the atoms are arranged within
the crystalline compound (unit cell size or lattice
parameter). The intensity information is used to
assess the type and nature of atoms. Determination
of lattice parameter helps understand extent of solid
solution (complete or partial substitution of one
element for another, as in some alloys) in a sample.
The „d‟ and „I‟ from a phase can also be used to
quantitatively estimate the amount of that phase in a
multi-component mixture.
The width of the diffracted peaks is used to determine
crystallite size and micro-strain in the sample.
13
Lecture-11
If the sample consists of tens of randomly
oriented single crystals, the diffracted beams
are seen to lie on the surface of several cones.
14
Instrument geometries Lecture-11
There are several ways of collecting XRPD patterns:
Camera methods: Guinier, Debye-Scherrer, Gandolfi,
15
The Debye – Scherrer powder camera Lecture-12
A photographic film is placed around the inner circumference of the camera body.
The incident beam enters through a pinhole and almost the whole diffraction
pattern is recorded simultaneously. At the point of entrance the angle is 180 and
at the exit the angle is 0.
16
L Lecture-12
e
Pinhole source
c
Film located on camera
t
body u
r
Rod shaped sample e
Sample rotates to give
-
better “randomness”1
0
Almost complete
angular range covered
17
View of an instrument Lecture-12
18
Lecture-10
Lecture-10
19
X-Ray Powder Diffraction Instruments
Lecture-12
20