Analyti Cal Inst Rument S

U M E NT S
L IN ST R
A L YT IC A
AN
ANALYTICAL INSTRUMENTS
• In mineral processing, there are several analytical
instruments used for various purposes; such as the
following
1. X-ray fluorescence (XRF)
2. X-ray diffraction (XRD)
3. Scanning electron microscopy (SEM)
4. Transmission electron microscopy (TEM)
5. Raman spectroscopy
6. Fourier Transform Infrared (FTIR)
7. Atomic absorption spectroscopy (AAS)
8. Inductively Coupled Plasma (ICP)
X-ray diffraction (XRD)
• The atomic planes of a crystal cause an incident
beam of Xrays to interfere with one another as they
leave the crystal. The phenomenon is called X-ray
diffraction.
Measure the average Measure the size,

spacing’s between shape and internal
layers or rows of stress of small
atoms crystalline regions
What can XRD do?
Determine the Find the crystal

orientation of a single structure of unknown
crystal or grain material
Fundamental Principles of X-ray
Diffraction (XRD)
• Max von Laue, in 1912, discovered that crystalline substances act
as three-dimensional diffraction gratings for X-ray wavelengths
similar to the spacing of planes in a crystal lattice.
• X-ray diffraction is now a common technique for the study of crystal
structures and atomic spacing.
• X-ray diffraction is based on constructive interference of
monochromatic X-rays and a crystalline sample.
• These X-rays are generated by a cathode ray tube, filtered to
produce monochromatic radiation, collimated to concentrate, and
directed toward the sample.
• The interaction of the incident rays with the sample
produces constructive interference (and a diffracted ray)
when conditions satisfy Bragg's Law (nλ=2d sin θ).
• This law relates the wavelength of electromagnetic
radiation to the diffraction angle and the lattice spacing in
a crystalline sample.
• These diffracted X-rays are then detected, processed and
counted. By scanning the sample through a range of
2θangles, all possible diffraction directions of the lattice
should be attained due to the random orientation of the
powdered material.
• Conversion of the diffraction peaks to d-spacings allows
identification of the mineral because each mineral has a
set of unique d-spacings.
• Typically, this is achieved by comparison of d-spacings
with standard reference patterns.
Basics of Crystallography
• The atoms are arranged in a regular
pattern, and there is as smallest
volume element that by repetition
in three dimensions describes the
crystal. This smallest volume
element is called a unit cell.
• Crystals consist of planes of atoms
that are spaced a distance d apart,
but can be resolved into many
atomic planes, each with a different
d spacing.
• The dimensions of the unit cell is
described by three axes : a, b, c
and the angles between them α, β ,
and γ are lattice constants which
can be
• Lattice determined by XRD.
Lattice
(001)
(010)
Atomic Planes
(hkl)
d-interspacing
distance
Units= pm (peak meters)/

Å=angstrom
The crystal lattice planar distances d
(right).The ray paths ABC and A'B'C' is
an integer multiple of the wavelength,
constructive interference will occur
for a combination of that specific
wavelength, crystal lattice planar
spacing and angle of incidence (Θ).
Each rational plane of atoms in a
crystal will undergo refraction at a
single, unique angle (for X-rays of a
fixed wavelength).
The relationship between the wavelength of the incident X-rays, angle of incidence
and spacing between the crystal lattice planes of atoms is known as Bragg's Law,
expressed as:
n λ = 2d sinΘ
where n (an integer) is the "order" of reflection, λ is the wavelength of the incident X-
rays, d is the interplanar spacing of the crystal and Θ is the angle of incidence.
Derive Bragg’s law
xy + yz = nλ ……… (1)
Substitute xy & yz
xy + yz = nλ ……… (1)
dSin Ө + dSin Ө = nλ
λ
}
Ө Ө
Ө Ө
d d
X Z
Ө Ө
Y
Ө Sin Ө = Opp/Hyp Sin Ө =
Ө
Sin Ө = xy/d Opp/Hyp
X d xy = dSin Ө Sin Ө = yz/d
d
z yz = dSin Ө BRAGG’S LAW
Y Y 2dSinӨ = nλ
BRAGG’S LAW
Typical questions
2dSinӨ = nλ
1. X-ray with wavelength of 125 pm (peak meters) was used to
study a crystal which was produced a reflection at an angle
of 17.4 degrees . Assuming first order diffraction, what is the
distance between planes of atoms
2. The second order diffraction for a certain crystal was 18.4
degrees using X-ray with a wavelength of 1.42 angstrom.
What is the interplanar spacing of atoms in this crystal?
3. Crystal XYZ has an interplanar spacing of 94.3 pm. Using first
order diffraction, what is the X-ray wavelength that should
be used to produce a reflaction with an angle of 19.5 degrees
Answ: λ= 62.96
X-ray Powder Diffraction (XRD) Instrumentation - How
Does It Work?
The set up includes X-ray source, a detector and sample mount

The rotation occurs during analysis (x-ray source and detector)
X-rays are generated in a cathode ray tube by heating a filament to produce
electrons, accelerating the electrons toward a target by applying a voltage,
and bombarding the target material with electrons. When electrons have
sufficient energy to dislodge inner shell electrons of the target material,
characteristic X-ray spectra are produced.
Planes are aligned not the peak
Single crystal- one set of peak does not sure
observed when planes are
aligned
XRD Pattern/ results
• As x-ray source and detector are rotated, the intensity of the reflected X-
rays is recorded.
• When the geometry of the incident X-rays impinging the sample satisfies the
Bragg Equation, constructive interference occurs and a peak in intensity
occurs.
• A detector records and processes this X-ray signal and converts the signal to
a count rate which is then output to a device such as a printer or computer
monitor.
XRD Applications
XRD is most widely used for the identification of unknown
crystalline materials (e.g. minerals, inorganic compounds).
Includes
• characterization of crystalline materials
• identification of fine-grained minerals such as clays and mixed
layer clays that are difficult to determine optically
• determination of unit cell dimensions
• measurement of sample purity
To determine crystal structures using Rietveld refinement

• determine of modal amounts of minerals (quantitative
analysis)
XRD strengths/ Advantages
• Powerful and rapid (< 20 min) technique for identification of

an unknown mineral
• In most cases, it provides an unambiguous mineral
determination
• Minimal sample preparation is required
• XRD units are widely available
• Data interpretation is relatively straight forward
XRD limitations / disadvantages
• Homogeneous and single phase material is best for
identification of an unknown
• Requires tenths of a gram of material which must be ground
into a powder
• For mixed materials, detection limit is ~ 2% of sample
• For unit cell determinations, indexing of patterns for non-
isometric crystal systems is complicated
• Peak overlay may occur and worsens for high angle
'reflections'

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U M E NT S

Measure the average Measure the size,

Determine the Find the crystal

Units= pm (peak meters)/

The set up includes X-ray source, a detector and sample mount

To determine crystal structures using Rietveld refinement

• Powerful and rapid (< 20 min) technique for identification of

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