Kuliah Xrd Mr
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Analisis Difraksi Sinar-X
(X-Ray Diffraction Analysis)
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Crystal Structure
LATTICE = Kisi susunan titik dalam ruang yang memiliki lingkungan identik antara
satu dengan lainnya
CRYSTAL STRUCTURE = Susunan atom (kelompok atom) yang berulang .
It can be described by associating with each lattice point
a group of atoms called the MOTIF (BASIS)
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Primitive Cell: simplest cell, contain one lattice point
Not necessary have the crystal symmetry
UNIT CELL = The smallest component of the crystal, which when
stacked together with pure translational repetition reproduces the
whole crystal
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5 Kisi Bravais dalam 2D
P P NP
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Definition:
Bravais Lattice: an infinite array of discrete points with an
arrangement and orientation that appears exactly the same from
whichever of the points the array is viewed.
Name
Number of Bravais lattices
Conditions
Triclinic
1 (P)
a1 a2 a3
Monoclinic
2 (P, C)
a1 a2 a3
= = 90°
Orthorhombic
4 (P, F, I, A)
a1 a2 a3
= = = 90°
Tetragonal
2 (P, I)
a1 = a2 a3
= = = 90°
Cubic
3 (P, F, I)
a1 = a2 = a3
= = = 90°
Trigonal
1 (P)
a1 = a2 = a3
= = < 120° 90°
Hexagonal
1 (P)
a1 = a2 a3
= = 90°
= 120°
3D: 14 Bravais Lattice, 7 Crystal System
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Kisi FCC
Logam Cu memiliki kisi face-centered cubic Atom-atom identik terletak pada sudut dan pada bagian muka kisi
Jenis Kisi adalah type F
also Ag, Au, Al, Ni...
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BCC Lattice
-Fe merupakan sebuah kisi body-centered cubic
Atom-atom Identik terletak pada sudut dan body center (nothing at face centers)
Lattice type I
Also Nb, Ta, Ba, Mo...
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FCC Lattices
Sodium Chloride (NaCl) - Na is much smaller than Cs
Face Centered Cubic
Rocksalt structure
Lattice type F
Also NaF, KBr, MgO….
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Unit cell contents Counting the number of atoms within the unit cell
Many atoms are shared between unit cells
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Atoms Shared Between: Each atom counts:
corner 8 cells 1/8
face center 2 cells 1/2
body center 1 cell 1
edge center 4 cells 1/4
lattice type cell contents
P 1 [=8 x 1/8]
I 2 [=(8 x 1/8) + (1 x 1)]
F 4 [=(8 x 1/8) + (6 x 1/2)]
C
2 [=(8 x 1/8) + (2 x 1/2)]
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e.g. NaCl
Na at corners: (8 1/8) = 1 Na at face centres (6 1/2) = 3
Cl at edge centres (12 1/4) = 3 Cl at body centre = 1
Unit cell contents are 4(Na+Cl-)
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CRYSTAL STRUCTURE
DETERMINATION BY X-RAY DIFRACTION (XRD)
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Bravais lattices Crystals possess a regular, repetitive
internal structure. The concept of symmetry
describes the repetition of structural features.
Symmetries are most frequently used to classify the
different crystal structures. In general one can generate 14
basic crystal structures through symmetries. These are called
Bravais lattices. Any crystal structures can be reduced to one
of these 14 Bravias lattices.
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CRYSTAL STRUCTURE DETERMINATION
The determination of an unknown structure
proceeds in three major steps:
1. The shape and size of the unit cell are deduced
from the angular positions of the diffraction
lines.
2. The number of atoms per unit cell is then
computed from the shape and size of the unit cell,
the chemical composition of the specimen, and
its measured density.
3. Finally, the position of the atoms within the unit
cell are deduced from the relative intensities of
the diffraction
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Size and Shape of the Unit Cell This step is same as the indexing of power diffraction pattern. It involves: • The accurate determination of peak positions. • Determination of the unit cell parameters from the peak positions.
Bragg’s Law Interplanar d-spacing Systematic Absences
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Bragg's Law When x-rays are scattered from a crystal lattice, peaks of scattered intensity are observed which correspond to the following conditions: 1. The angle of incidence = angle of scattering.
2. The pathlength difference is equal to an integer number of
wavelengths. The condition for maximum intensity contained in Bragg's
law above allow us to calculate details about the crystal structure, or if the crystal structure is known, to determine the wavelength of the x-rays incident upon the crystal.
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Indexing Tetragonal system:
2
2
2
22
2
1
c
l
a
kh
dhkl
hkld2/sin
222
2
2
2
2222
2 )(42
sin ClkhAc
l
a
kh
dhkl
2222 4/;4/ cCaA
The value of A is obtained from hk0 lines.
When l = 0,
Possible values for h2 + k2 are 1, 2, 4, 5, 8, 9, 10, …
The rest of lines are
Possible values for l2 are 1, 4, 9, 16, …
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Indexing Hexagonal system:
2
2
2
22
2 3
41
c
l
a
khkh
dhkl
222
2
22
2
2222 )(
43sin ClkhkhA
c
l
a
khkh
2222 4/;3/ cCaA
Possible values for h2 + hk + k2 are 1, 3, 4, 7, 9, 12, …
The rest of lines are
Possible values for l2 are 1, 4, 9, 16, …
2222
2222
)(sin
)(sin
ClkhkhA
atau
ClkhkhA
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yCxAClkhkhA 2222 )(sin
l h,k
0,0 1,0 1,1 2,0 2,1 2,2 3,0 3,1
0 0 x 3x 4x 7x 12x 9x 13x
1 y x + y 3x + y 4x + y 7x + y 12x + y 9x + y 13x + y
2 4y x + 4y 3x + 4y 4x + 4y 7x + 4y 12x + 4y 9x + 4y 13x + 4y
3 9y x + 9y 3x + 9y 4x + 9y 7x + 9y 12x + 9y 9x + 9y 13x + 9y
4 16y x + 16y 3x + 16y 4x + 16y 7x + 16y 12x + 16y 9x + 16y 13x + 16y
h,k
1,0 1,1 2,0 2,1 2,2 3,0 3,1
Sin2 Sin2 /3
Sin2 /4
Sin2 /7 Sin2 /12 Sin2 /9 Sin2 /13
1 0,097 0,032 0,024
2 0,112 0,037 0,028
3 0,136 0,045 0,034
4 0,209 0,070 0,052
5 0,332 0,111 0,083
6 0,390 0,130 0,098 7 0,434 0,145 0,109 8 0,472 0,157 0,118 9 0,547 0,182 0,137
10 0,668 0,223 0,167 11 0,722 0,241 0,180
A = 0,112
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Example:
sin2 sin2/3 sin2/4 sin2/7
0.097 0.032
0.112 0.037
0.136 0.045
0.209 0.070
0.332 0.111
0.390 0.130
0.434 0.145
0.472 0.157
0.547 0.182
0.668 0.223
0.722 0.241
0.024
0.028
0.034
0.052
0.083
0.098
0.109
0.118
0.137
0.167
0.180
0.014
0.016
0.019
0.030
0.047
0.056
0.062
0.067
0.078
0.095
0.103
100
110
Let’s say A = 0.112
1
2
3
4
5
6
7
8
9
10
11
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sin2 sin2-A sin2-3A
0.097
0.112
0.136
0.209
0.332
0.390
0.434
0.472
0.547
0.668
0.722
0.806
0.879
0
0.024
0.097
0.220
0.278
0.322
0.360
0.435
0.556
0.610
0.694
0.767
0.054
0.098
0.136
0.211
0.332
0.386
0.470
0.543
0.097 belongs to Cl2.
What is the l?
There are two lines
between 100 and 110.
Probably, 10l1 and
10l2
0.024 and 0.097
are different ls.
0.097/0.024 ~ 4
0.220/0.024 ~ 9
0.390/0.024 ~ 16
C = 0.02441
1
2
3
4
5
6
7
8
9
10
11
12
13
100
110
101
102
002
112
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0 2 4 6 8 10 12 14 16 18
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Cl2
l2
Slope = C = 0.02441
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Indexing orthorhombic system:
222
2
2
2
2
2
222
4sin ClBkAh
c
l
b
k
a
h
More difficult! Consider any two lines having indices
hk0 and hkl Cl2; get a guesses value C then put it back
and get A and B. If the guess is right, the number will be
consistent. If not try another guesses value of C.
Indexing Monoclinic and Triclinic system:
Even more complex, 6 variables, must have enough
diffraction lines for the computer to indexing.
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Effect of Cell distortion on the powder Pattern:
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Determination of the number of atoms in a unit cell:
After establishing shape and size we find the number
of atoms in that unit cell.
M
NVn C 0
VC: unit cell volume; : density
N0: Avogodro’s number;
M: molecular weight;
n: number of molecules in a unit cell
We need to index the powder pattern in order to obtain
the unit cell parameters unit cell volume
66054.1)10022.6()()10( 23
03
338 C
C
VN
cm
gcmVnM
in Å3
in g/cm3
A
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MENENTUKAN INTENSITAS PUNCAK
DIFRAKSI SINAR X
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Multiplicity factor
Lattice Index Multiplicity Planes
Cubic
(with highest
symmetry)
(100) 6 [(100) (010) (001)] ( 2 for negatives)
(110) 12 [(110) (101) (011), (110) (101) (011)] ( 2 for negatives)
(111) 12 [(111) (111) (111) (111)] ( 2 for negatives)
(210) 24* (210) 3! Ways, (210) 3! Ways,
(210) 3! Ways, (210) 3! Ways
(211) 24 (211) 3 ways, (211) 3! ways,
(211) 3 ways
(321) 48*
Tetragonal
(with highest
symmetry)
(100) 4 [(100) (010)] ( 2 for negatives)
(110) 4 [(110) (110)] ( 2 for negatives)
(111) 8 [(111) (111) (111) (111)] ( 2 for negatives)
(210) 8* (210) = 2 Ways, (210) = 2 Ways,
(210) = 2 Ways, (210) = 2 Ways
(211) 16 [Same as for (210) = 8] 2 (as l can be +1 or 1)
(321) 16* Same as above (as last digit is anyhow not permuted)
* Altered in crystals with lower symmetry
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Cubic hkl hhl hk0 hh0 hhh h00
48* 24 24* 12 8 6
Hexagonal hk.l hh.l h0.l hk.0 hh.0 h0.0 00.l
24* 12* 12* 12* 6 6 2
Tetragonal hkl hhl h0l hk0 hh0 h00 00l
16* 8 8 8* 4 4 2
Orthorhombic hkl hk0 h0l 0kl h00 0k0 00l
8 4 4 4 2 2 2
Monoclinic hkl h0l 0k0
4 2 2
Triclinic hkl
2
* Altered in crystals with lower symmetry (of the same crystal class)
Multiplicity factor
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If atom B is different from atom A the amplitudes must be weighed by the
respective atomic scattering factors (f)
The resultant amplitude of all the waves scattered by all the atoms in the UC gives
the scattering factor for the unit cell
The unit cell scattering factor is called the Structure Factor (F)
Scattering by an unit cell = f(position of the atoms, atomic scattering factors)
electronan by scattered waveof Amplitude
ucin atoms allby scattered waveof AmplitudeFactor StructureF
[2 ( )]i i h x k y l zE Ae fe 2 ( )h x k y l z In complex notation
2FI
[2 ( )]
1 1
j j j j
n ni i h x k y l zhkl
n j j
j j
F f e f e
Structure factor is independent of the shape and size of the unit cell
For n atoms in the UC
If the UC distorts so do the planes in it!!
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nnie )1(
)(2
Cosee ii
Structure factor calculations
A Atom at (0,0,0) and equivalent positions
[2 ( )]j j j ji i h x k y l z
j jF f e f e
[2 ( 0 0 0)] 0i h k lF f e f e f
22 fF F is independent of the scattering plane (h k l)
nini ee
Simple Cubic
1) ( inodde
1) ( inevene
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B Atom at (0,0,0) & (½, ½, 0) and equivalent positions
[2 ( )]j j j ji i h x k y l z
j jF f e f e
1 1[2 ( 0)]
[2 ( 0 0 0)] 2 2
[ 2 ( )]0 ( )2 [1 ]
i h k li h k l
h ki
i h k
F f e f e
f e f e f e
F is independent of the ‘l’ index
C- centred Orthorhombic
Real
]1[ )( khiefF
fF 2
0F
22 4 fF
02 F
e.g. (001), (110), (112); (021), (022), (023)
e.g. (100), (101), (102); (031), (032), (033)
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X-Ray Fluorescence Analysis
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Analisis X-ray Fluoresensi
Pendahuluan
Prinsip Kerja
Skema Cara Kerja Alat
Preparasi Sampel
Instrumen XRF
Contoh spektra
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Radiasi Elektromagnetik
1Hz - 1kHz 1kHz - 1014Hz
1014Hz - 1015Hz
1015Hz - 1021Hz
Extra-Low Frequency
(ELF)
Radio Microwave Infrared
Visible Light
X-Rays,
Gamma Rays
Low energy High energy
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Pendahuluan
Teknik fluoresensi sinar x (XRF) merupakan suatu teknik analisis yang dapat menganalisa unsur-unsur yang membangun suatu material, dengan dasar interaksi sinar-X dengan materi analit.
Teknik ini juga dapat digunakan untuk menentukan konsentrasi unsur berdasarkan pada panjang gelombang dan jumlah sinar x yang dipancarkan kembali setelah suatu material ditembaki sinar X.
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Fitur XRF
• Akurasi yang relative tinggi
• Dapat menentukan unsur dalam material tanpa adanya standar (bandingkan dg. AAS)
• Dapat menentukan kandungan mineral dalam bahan biologis maupun dalam tubuh secara langsung.
Kelebihan
• tidak dapat mengetahui senyawa apa yang dibentuk oleh unsur-unsur yang terkandung dalam material yang akan kita teliti.
• tidak dapat menentukan struktur dari atom yang membentuk material itu.
Kelemahan
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Prinsip Kerja
Menembakkan radiasi foton elektromagnetik
ke material yang diteliti.
Radiasi elektromagnetik yang
dipancarkan akan berinteraksi dengan
elektron yang berada di kulit K suatu unsur.
Elektron yang berada di kulit K akan
memiliki energi kinetik yang cukup untuk
melepaskan diri dari ikatan inti, sehingga
elektron itu akan terpental keluar.
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Peristiwa pada tabung sinar-X.
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Prinsip Kerja XRF
Pada teknik XRF,
• dienggunakan sinar-X dari tabung pembangkit sinar-X untuk mengeluarkan electron dari kulit bagian dalam untuk menghasilkan sinar-X baru dari sample yang di analisis.
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Prinsip Kerja XRF
• Untuk setiap atom di dalam sample,
intensitas dari sinar-X karakteristik tersebut
sebanding dengan jumlah (konsentrasi)
atom di dalam sample.
• Intensitas sinar–X karakteristik dari setiap
unsur, dibandingkan dengan suatu standar
yang diketahui konsentrasinya, sehingga
konsentrasi unsur dalam sample bisa
ditentukan.
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Skema Cara Kerja Alat
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Instrumen XRF
Instrumen XRF terdiri dari :
• Sumber cahaya
• Optik
• Detektor
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Syarat Sampel
Serbuk Ukuran serbuk < 4 00 mesh
Padatan Permukaan yang dilapisi akan meminimalisir efek
penghamburan Sampel harus datar untuk menghasilkan analisis kuantitatif
yang optimal
Cairan Sampel harus segar ketika dianalisis dan analisis dilakukan
secara cepat jika sampel mudah menguap Sampel tidak boleh mengandung endapan
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Sumber Cahaya
• Tabung Sinar X
• End Window
• Side Window
• Radioisotop
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Tabung sinar x
• End Window
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Side Window
Be W indow
Silicone Insulation
Glass En v elope
Filament
Electron beam
Target (Ti, Ag,
Rh, etc.)
Copper Anode
H V Lead
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Radioisotop
Isotope
Fe-5 5
Cm-244
Cd-109
Am-241
Co-57
Energy (keV)
5.9
14.3, 18.3
22, 88
59.5
122
Elements (K-lines)
Al – V
Ti-Br
Fe-Mo
Ru-Er
Ba - U
Elements (L-lines)
Br-I
I- Pb
Yb-Pu
None
none
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Optik
Source Detector
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Filter
Detector
X-Ray
Source
Source Filter
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Contoh Spektra
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Contoh Spektra
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Detektor
• Si(L i)
• P N Diode
• Silicon Drift Detectors
• Proportional Counters
• Scintillation Detectors
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Si ( Li) Detektor
WIndow
Si(Li)
crystal
Dewar
filled with
LN 2
Super-Cooled Cryostat
Cooling: LN2 or Peltier
Window: Beryllium or Polymer
Counts Rates: 3,000 – 50,000 cps
Resolution: 120-170 eV at Mn K-alpha
FET
Pre-Amplifier
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PIN Diode
• Cooling: Thermoelectrically cooled (Peltier)
• Window: Beryllium
• Count Rates: 3,000 – 20,000 cps
• Resolution: 170-240 eV at Mn k-alpha
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Silicon Drift Detector
Packaging: Similar to PIN Detector Cooling: Peltier Count Rates; 10,000 – 300,000 cps Resolution: 140-180 eV at Mn K-alpha
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Proportional Counter
Anode Filament
Fill Gases: Neon, Argon, Xenon, Krypton
Pressure: 0.5- 2 ATM
Windows: Be or Polymer
Sealed or Gas Flow Versions
Count Rates EDX: 10,000-40,000 cps WDX: 1,000,000+
Resolution: 500-1000+ eV
Window
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Scintillation Detector
PMT (Photo-multiplier tube) Sodium Iodide Disk Electronics
Connector Window: Be or Al Count Rates: 10,000 to 1,000,000+ cps Resolution: >1000 eV
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(0,0,0)
(0, ½, ½)
(½, ½, 0)
(½, 0, ½)
Fractional Coordinates
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Cs (0,0,0)
Cl (½, ½, ½)
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Density
Calculation
AC NV
nA
n: number of atoms/unit cell
A: atomic mass
VC: volume of the unit cell
NA: Avogadro’s number
(6.023x1023 atoms/mole)
Calculate the density of copper.
RCu =0.128nm, Crystal structure: FCC, ACu= 63.5 g/mole
n = 4 atoms/cell, 333 216)22( RRaVC
3
2338/89.8
]10023.6)1028.1(216[
)5.63)(4(cmg
8.94 g/cm3 in the literature
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(100) (111)
(200) (110)
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2
222
2
1
a
lkh
dhkl
For cubic system
Lattice spacing
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Bragg’s Law
For cubic system:
But no all planes have the
diffraction !!!
sin2
sinsin
hkl
hklhkl
d
dd
QTSQn
222 lkh
adhkl
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• X-ray diffraction from a crystal: Bragg’s Law
sin2 hkldn
222 lkh
adhkl
X-Ray Diffraction
n: order of
diffraction peak
dhkl: interplanar
spacing
(hkl): Miller
indices of plane
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Crystal Structures [OGN 21.2] • Body-centered
cubic (BCC)
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(200) (211)
Powder diffraction
X-Ray
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Phase purity. In a mixture of compounds each crystalline phase present will contribute to
the overall powder X-ray diffraction pattern. In preparative materials
chemistry this may be used to identify the level of reaction and purity of the
product. The reaction between two solids Al2O3 and MgO to form MgAl2O4
may be monitored by powder X-ray diffraction.
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•At the start of the reaction a mixture of Al2O3 and MgO will produce an X-
ray pattern combining those of the pure phases. As the reaction proceeds,
patterns (a) and (b), a new set of reflections corresponding to the product
MgAl2O4, emerges and grows in intensity at the expense of the reflection
from Al2O3 and MgO. On completion of the reaction the powder diffraction
pattern will be that of pure MgAl2O4.
•A materials chemist will often use PXRD to monitor the progress of a
reaction.
•The PXRD method is widely employed to identify impurities in materials
whether it be residual reactant in a product, or an undesired by-product.
•However the impurity must be crystalline.
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Observable diffraction
peaks
222 lkh Ratio
Simple
cubic
SC: 1,2,3,4,5,6,8,9,10,11,12..
BCC: 2,4,6,8,10, 12….
FCC: 3,4,8,11,12,16,24….
222 lkh
adhkl
nd sin2
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Ex: An element, BCC or FCC, shows diffraction peaks
at 2: 40, 58, 73, 86.8,100.4 and 114.7.
Determine:(a) Crystal structure?(b) Lattice constant?
(c) What is the element?
2theta theta (hkl)
40 20 0.117 1 (110)
58 29 0.235 2 (200)
73 36.5 0.3538 3 (211)
86.8 43.4 0.4721 4 (220)
100.4 50.2 0.5903 5 (310)
114.7 57.35 0.7090 6 (222)
2sin222 lkh
a =3.18 A, BCC, W
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0
5
10
15
20
25
30
0 20 40 60 80
Bragg Angle (, degrees)
Lo
ren
tz-P
ola
riza
tio
n f
act
or
Polarization factor Lorentz factor
2
1
2
1
SinCos
SinfactorLorentz 21 2CosIP
CosSin
CosfactoronPolarizatiLorentz
2
2 21
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Intensity of powder pattern lines (ignoring Temperature & Absorption factors)
CosSin
CospFI
2
22 21
Valid for Debye-Scherrer geometry
I → Relative Integrated “Intensity”
F → Structure factor
p → Multiplicity factor
POINTS
As one is interested in relative (integrated) intensities of the lines constant
factors are omitted
Volume of specimen me , e (1/dectector radius)
Random orientation of crystals in a with Texture intensities are
modified
I is really diffracted energy (as Intensity is Energy/area/time)
Ignoring Temperature & Absorption factors valid for lines close-by in
pattern
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