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XRD applications and interpretation
10 20 30 402
PowderCell 2 .0
Atomic distribution in the unit cell
Peak relative intensities
Unit cell Symmetry and size
Peak positions
a
cb
Peak shapes
Particle size and defects
Background
Diffuse scattering, sample holder,
matrix, amorphous phases, etc...
X-ray Powder Diffraction
ANATOMI DIFRAKTOGRAM XRD
Sinyal yang diinginkan
Noise
Background
X-Ray Powder Diffraction (XRPD) uses information about the position, intensity, width, and shape of diffraction peaks
in a pattern from a polycrystalline sample.
The x-axis, 2theta, corresponds to the angular position of the detector that rotates around the sample.
You can use XRD to determine• Crystalline phase and sample identification• Phase Composition of a Sample
– Quantitative Phase Analysis: determine the relative amounts of phases in a mixture by referencing the relative peak intensities
• Unit cell lattice parameters and Bravais lattice symmetry– Index peak positions– Lattice parameters can vary as a function of, and therefore give you information
about, alloying, doping, solid solutions, strains, etc.• Residual Strain (macrostrain)• Crystal Structure
– By Rietveld refinement of the entire diffraction pattern• Epitaxy/Texture/Orientation• Crystallite Size and Microstrain
– Indicated by peak broadening– Other defects (stacking faults, etc.) can be measured by analysis of peak shapes
and peak width • in-situ studies (evaluate all properties above as a function of time,
temperature, and gas environment)
Phase Identification• The diffraction pattern for every phase is as unique as your
fingerprint – Phases with the same chemical composition can have drastically
different diffraction patterns.– Use the position and relative intensity of a series of peaks to match
experimental data to the reference patterns in the database
Databases such as the Powder Diffraction File (PDF) contain d-I lists for thousands of crystalline phases.
• The PDF contains over 200,000 diffraction patterns.• Modern computer programs can help you determine what phases are
present in your sample by quickly comparing your diffraction data to all of the patterns in the database – database XRD pattern matching
• The PDF card for an entry contains a lot of useful information, including literature references.
XRD patterns of furnace materials and reference patterns of identified phases
Pengolahan data XRD
• Raw data• Background substraction• Smoothing• K substraction
The wavelength of X rays is determined by the anode of the X-ray source.
• Electrons from the filament strike the target anode, producing characteristic radiation via the photoelectric effect.
• The anode material determines the wavelengths of characteristic radiation.• While we would prefer a monochromatic source, the X-ray beam actually
consists of several characteristic wavelengths of X rays.
KL
M
Spectral Contamination in Diffraction PatternsK1
K2
KbW L1
K1
K2 K1
K2
• The K1 & K2 doublet will almost always be present– Very expensive optics can remove the K2 line– K1 & K2 overlap heavily at low angles and are more
separated at high angles•W lines form as the tube ages: the W filament
contaminates the target anode and becomes a new X-ray source•W and Kb lines can be removed with optics
Wavelengths for X-Radiation are Sometimes UpdatedCopperAnodes
Bearden(1967)
Holzer et al.(1997)
CobaltAnodes
Bearden(1967)
Holzer et al.(1997)
Cu K1 1.54056Å 1.540598 Å Co K1 1.788965Å 1.789010 ÅCu K2 1.54439Å 1.544426 Å Co K2 1.792850Å 1.792900 ÅCu Kb 1.39220Å 1.392250 Å Co Kb 1.62079Å 1.620830 Å
MolybdenumAnodes
ChromiumAnodes
Mo K1 0.709300Å 0.709319 Å Cr K1 2.28970Å 2.289760 Å
Mo K2 0.713590Å 0.713609 Å Cr K2 2.293606Å 2.293663 ÅMo Kb 0.632288Å 0.632305 Å Cr Kb 2.08487Å 2.084920 Å
• Often quoted values from Cullity (1956) and Bearden, Rev. Mod. Phys. 39 (1967) are incorrect. – Values from Bearden (1967) are reprinted in international Tables for X-Ray
Crystallography and most XRD textbooks.• Most recent values are from Hölzer et al. Phys. Rev. A 56 (1997)• Has your XRD analysis software been updated?
x
23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 412 (deg.)
Inte
nsity
(a.u
.)
00-043-1002> Cerianite- - CeO2
Crystallite Size and Microstrain
• Crystallites smaller than ~120nm create broadening of diffraction peaks– this peak broadening can be used to quantify the average crystallite size of
nanoparticles using the Scherrer equation– must know the contribution of peak width from the instrument by using a
calibration curve• microstrain may also create peak broadening
– analyzing the peak widths over a long range of 2theta using a Williamson-Hull plot can let you separate microstrain and crystallite size
b
cosKD
b
cosKD
Center for Materials Science and Engineeringhttp://prism.mit.edu/xray
The Scherrer Constant, K
• The constant of proportionality, K (the Scherrer constant) depends on the how the width is determined, the shape of the crystal, and the size distribution– the most common values for K are:
• 0.94 for FWHM of spherical crystals with cubic symmetry• 0.89 for integral breadth of spherical crystals w/ cubic symmetry• 1, because 0.94 and 0.89 both round up to 1
– K actually varies from 0.62 to 2.08• For an excellent discussion of K, refer to JI Langford and AJC
Wilson, “Scherrer after sixty years: A survey and some new results in the determination of crystallite size,” J. Appl. Cryst. 11 (1978) p102-113.
cos2
LKB
cos94.02
LB
Different crystallite sizes
Quantitative Phase Analysis
• With high quality data, you can determine how much of each phase is present– must meet the constant volume assumption
(see later slides)• The ratio of peak intensities varies linearly
as a function of weight fractions for any two phases in a mixture– need to know the constant of proportionality
• RIR method is fast and gives semi-quantitative results
• Whole pattern fitting/Rietveld refinement is a more accurate but more complicated analysis
0
10
20
30
40
50
60
0 0,2 0,4 0,6 0,8 1
X(phase a)/X(phase b)I(p
hase
a)/I(pha
se b) ..
Unit Cell Lattice Parameter Refinement
• By accurately measuring peak positions over a long range of 2theta, you can determine the unit cell lattice parameters of the phases in your sample– alloying, substitutional doping, temperature and pressure, etc
can create changes in lattice parameters that you may want to quantify
– use many peaks over a long range of 2theta so that you can identify and correct for systematic errors such as specimen displacement and zero shift
– measure peak positions with a peak search algorithm or profile fitting• profile fitting is more accurate but more time consuming
– then numerically refine the lattice parameters
determination and refinement of lattice parameters (indexing)
)(4
sin 2222
22 lkh
a
)(sin 2222 lkhC
dividing the above equation with the first reflection angle gives the ratio of hkl
relationship between Miller indices and diffraction angles
)()(
sinsin
21
21
21
222
12
2
lkhlkh
the ratio of hkl define the possible Miller indices: ratio = h2 + k2 + l2if there are some possible hkl, the highest number comes firstAfter indexing, one of the peaks can be used to calculate the cell parameters.As the error in measuring the diffraction angles is a systematic error, the last reflection data will be used
exercise 1: indexing XRD data (cubic)2 sin2 ratio Miller indices19.213 0.0279 1 10027.302 0.0557 2 11033.602 3 11138.995 4 20043.830 5 21048.266 6 21156.331 8 22060.093 9 22163.705 10 31067.213 11 31170.634 12 222
1. define the Miller indices
2. calculate the lattice parameters
Answer:ao = 4.6138 Ǻ
lattice type and systematic absences on cubic system
destructive interferences occurring between the diffracted waves intensity cancels outeg:
topics
Evaluation of the intensities of X-rays diffracted from polycrystalline samples;
Evaluating crystallinity
taking the sum total of relative intensities of ten individual characteristic peaks1 then taking the ratio over the corresponding relative intensities of standard materials E.g.:Comparing crystallinity of flyash-based zeolite-A using XRD and IR spectroscopy
1CURRENT SCIENCE, VOL. 89, NO. 12, 25 DECEMBER 2005
% crystallinity = (AD4R)/(ATO4)
% crystallinity = (ΣIR sample)/(ΣIR standard)
72.8% 85%
98.6%
98.6%
98.6%
100%
72.8%83.2%
92%
93.3%
96.2%
100%
Crystallinity = (A ratio of 560 over 464 cm-1 bands of sample/reference) x 100%
Preferred Orientation (texture)
• Preferred orientation of crystallites can create a systematic variation in diffraction peak intensities– can qualitatively analyze using a 1D diffraction pattern– a pole figure maps the intensity of a single peak as a function of
tilt and rotation of the sample• this can be used to quantify the texture
(111)
(311)(200)
(220)
(222)(400)
40 50 60 70 80 90 100Two-Theta (deg)
x103
2.0
4.0
6.0
8.0
10.0
Inte
nsity
(Cou
nts)
00-004-0784> Gold - Au
• For example MoO3 crystallizes in thin plates (like sheets of paper) these crystals will pack with the flat surfaces in a parallel orientation.
• Comparing the intensity between a randomly oriented diffraction pattern and a preferred oriented diffraction pattern can look entirely different.
• Quantitative analysis depend on intensity ratios which are greatly distorted by preferred orientation.
• Careful sample preparation is most important to deal with preferred orientation samples
• The following illustrations show the Mo O3 spectra's collected by using transmission , Debye-Scherrer capillary and reflection mode.
ZnO nanorod
In-situ XRD can yield quantitative analysis to study reaction pathways, rate constants, activation energy, and phase
equilibria
N NaAlH 4N NaAlH 4
0 e k1t
N Na3AlH 6
13
N NaAlH 4
0 k1k2 k1
e k1t e k2t
N Na3AlH 6
0 e k2t
N Al N NaAlH 4
0 23
13
k2k2 k1
1 e k1t
13
k1k2 k1
1 e k2t
N Na3AlH 6
0 1 e k2t
N Al
0
NaAlH4
AlNaCl
Na3AlH6
Ways to prepare a powder sample
• Top-loading a bulk powder into a well – deposit powder in a shallow well of a sample holder. Use a
slightly rough flat surface to press down on the powder, packing it into the well.• using a slightly rough surface to pack the powder can help minimize
preferred orientation• mixing the sample with a filler such as flour or glass powder may
also help minimize preferred orientation• powder may need to be mixed with a binder to prevent it from falling
out of the sample holder– alternatively, the well of the sample holder can be coated with a
thin layer of vaseline
• Dispersing a thin powder layer on a smooth surface– a smooth surface such as a glass slide or a zero background holder
(ZBH) may be used to hold a thin layer of powder• glass will contribute an amorphous hump to the diffraction pattern• the ZBH avoids this problem by using an off-axis cut single crystal
– dispersing the powder with alcohol onto the sample holder and then allowing the alcohol to evaporate, often provides a nice, even coating of powder that will adhere to the sample holder
– powder may be gently sprinkled onto a piece of double-sided tape or a thin layer of vaseline to adhere it to the sample holder• the double-sided tape will contribute to the diffraction pattern
– these methods are necessary for mounting small amounts of powder– these methods help alleviate problems with preferred orientation– the constant volume assumption is not valid for this type of sample, and
so quantitative and Rietveld analysis will require extra work and may not be possible
What is polymorph?Same Chemical formula but different crystal system
Example: α phase, β phase, γ phase FormⅠ, FormⅡ,
These differences are very important for the production since some phase are stable or easy to product. Therefore originally developed company have a patent to protect their products. Competitors (Generic drug pharmaceutical company) should check their product whether they are out of these patent using XRD. Of course original drug supplier always try to check competitors products.
xrd-6000-pharma.ppt
Most popular way for polymorph identification Comparison of raw data profiles Compare raw data profiles with standard sample data using “Multi Plot” function whether abnormal appear or disappear.
*: abnormal peak
* * * ***
*
xrd-6000-pharma.ppt
Polymorph Identification(Search/Match Method)
xrd-6000-pharma.ppt
Some Meanings of Diffraction Pattern
Half Height widthCrystallizationCrystal SizeLattice Strain
Amorphous Degree of Crystallization
xrd-6000-pharma.ppt
Crystalinity calculation in XRD In a X-ray diffraction method, total intensity from certain volume of the sample are always fixed by their combination of the atoms even they are amorphous phase or crystalline phase. Sharpe profile are detected from the crystal phase are and broad peak profile from the amorphous phase area. So crystalinity degree is determined by the calculation of the ratio of these area.Crystalinity (%) Xc=K ・
IcIt
Ic: Area of crystalline phaseIt: Total area of the profile
xrd-6000-pharma.ppt
Crystalinity Calculation
xrd-6000-pharma.ppt
What is Crystallite size?
Particle sizeCrystallite size
β s= λ D ・ Cosθ Scherrer’s Formula
β s
xrd-6000-pharma.ppt
Application of the Crystallite size
xrd-6000-pharma.ppt
Acquisition concerns
Operations: Y Scale Mul 0.712 | Strip kAlpha2 0.514 | Background 1.000,1.000 | ImportQUARTZ OFFSET - File: 715Q-01.RAW - Type: 2Th/Th unlocked - Start: 15.000 ° - End: 69.990 ° - Step: 0.030 ° - Step time: 0.2 s - Temp.: 25 °C (Room) - Time Started: 0 s - 2-Theta: 15.000 ° - Theta:Operations: Strip kAlpha2 0.514 | Background 1.000,1.000 | ImportQUARTZ - File: Q091506.RAW - Type: 2Th/Th unlocked - Start: 18.000 ° - End: 72.000 ° - Step: 0.030 ° - Step time: 0.2 s - Temp.: 25 °C (Room) - Time Started: 0 s - 2-Theta: 18.000 ° - Theta: 0.000 ° -
Lin
(Cou
nts)
0
1000
2000
3000
2-Theta - Scale
15 20 30 40 50 60 70
MSE715-XRD.ppt
Operations: Y Scale Mul 0.712 | Strip kAlpha2 0.514 | Background 1.000,1.000 | ImportQUARTZ OFFSET - File: 715Q-01.RAW - Type: 2Th/Th unlocked - Start: 15.000 ° - End: 69.990 ° - Step: 0.030 ° - Step time: 0.2 s - Temp.: 25 °C (Room) - Time Started: 0 s - 2-Theta: 15.000 ° - Theta:Operations: Strip kAlpha2 0.514 | Background 1.000,1.000 | ImportQUARTZ - File: Q091506.RAW - Type: 2Th/Th unlocked - Start: 18.000 ° - End: 72.000 ° - Step: 0.030 ° - Step time: 0.2 s - Temp.: 25 °C (Room) - Time Started: 0 s - 2-Theta: 18.000 ° - Theta: 0.000 ° -
Lin
(Cou
nts)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
2200
2300
2400
2500
2-Theta - Scale
25 26 27 28
h < 100mm
Illustrate correction process later
MSE715-XRD.ppt
Interpretasi data XRD
1. Identifikasi keteraturan pori struktur meso2. Identifikasi indeks kristal heksagonal
Pore Structure Characterization X-Ray Diffraction Small angle XRD 0.6 to 3.0 degrees 2θ
Peaks in XRD pattern show d-spacing between micelles (pores) in parallel planes.
Transmission Electron Microscopy (TEM)
Example of silica XRD pattern indicating mesostructure
Self-assembled mesoporous metal oxide thin films , Heidi Springer, Purdue University MSE REU, August 5, 2004
P123 ResultsP123 Surfactant Concentration
0
2000
4000
6000
8000
10000
12000
14000
16000
0.6 1.1 1.6 2.1 2.6
Degrees 2-theta
Cou
nts
Per
Sec
ond
(CP
S)
1.2g P123
1.5g P123
1.8g P123
Best mesostructure observed at 1.8g P123.(EO):Sn molar ratio of 0.6.
Self-assembled mesoporous metal oxide thin films , Heidi Springer, Purdue University MSE REU, August 5, 2004
F127 Results
No XRD peaks observed at lowest concentrations.
Lowest Concentrations F127
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
1 2 3
Degrees 2-theta
Cou
nts
Per
Sec
ond
(CP
S)
.75g F127
1.0g F127
Self-assembled mesoporous metal oxide thin films , Heidi Springer, Purdue University MSE REU, August 5, 2004
F127 Results
Unresolved peaks, indicating poor mesostructure begin to appear at 1.25g F127.
Low Angle XRD at 1.25g F127
0
2000
4000
6000
8000
10000
12000
14000
16000
1 2 3
Degrees 2-theta
Cou
nts
Per
Sec
ond
(CP
S)
Self-assembled mesoporous metal oxide thin films , Heidi Springer, Purdue University MSE REU, August 5, 2004
XRD patterns of mesostructured tin oxide displaying an Im3m derived structure. (a) after thermal treatment at temperatures up to 250°C and (b) after calcination at 400°C for four hours.
Best structure is observed at 1.75g F127.(EO):Sn molar ratio of 1.4.
F127 ResultsC
ourtesy of Vikrant Urade
Self-assembled mesoporous metal oxide thin films , Heidi Springer, Purdue University MSE REU, August 5, 2004
F127 Results
Courtesy of Vikrant Urade
Self-assembled mesoporous metal oxide thin films , Heidi Springer, Purdue University MSE REU, August 5, 2004
Menentukan nilai a dan c heksagonal
1⁄d2 = 4⁄3((h2 + hk + k2)⁄a2) + l2⁄c2 100 a = 2d⁄√3110 a = 2d200 a = 4d⁄√3210 a = 2d⁄√5⁄3300 a = 2d√3Dengan trial and error jika pada harga d berbeda, a tetap itulah a. Panjang c dicari dari persamaan dg variasi hkl yang harga l tidak nol. Harga d sudah diketahui dari tabel.
Penentuan Struktur Kristal Kubus dan non-kubus, Sukir dkk., Tugas Matakuliah Kimia Anorganik Terapan, S2 Depag, 2010
• h, k, l are Miller indices• a, b, c are unit cell distances• , b, are angles between the lattice directions
Complexity of calculations is dependent on the symmetry of the crystal system.
Selection Rules for Observing X-ray Peaks FCC : (h k l) must all be either odd or even BCC : sum h + k + l must be even (Otherwise, an in between plane will cancel the reflection)
Sudut 2Ѳ
(derajat) Sin2ѲRasio
(Sin2Ѳ) / (Sin2Ѳ1)
Rasio x 3
(bil. bulat)
(h k l)
(ccp)
h k i l
(hcp)
30 0,0667 1 3 (1 1 1) 1 0 Ī 0
32.5 0.0783 1.17 3 (1 1 1) 1 0 Ī 0
34.5 0.0879 1.32 4 (0 0 2) 0002
36.6 0.0986 1.48 5 (0 2 1) 1 0 Ī 1
48 0.1654 2.48 8 (2 0 2) 1 0 Ī 2
57.5 0.2277 3.41 10 (3 1 0) 1 1 ˉ2 0
65.5 0.2889 4.33 12 ( √2 1 3) 10Ī3
69 0.3208 4.8 15 (√2 3 2) 1 0 ˉ2 2
70.5 0.3331 5 15 (√5 3 1) 2 0 ˉ2 1
74 0.3622 5.43 16 (0 0 4) 0004
CARA PERHITUNGAN DENGAN MODEL BERDASARKAN HARGA h k l KUBUS
Penentuan Struktur Kristal Kubus dan non-kubus, Sukir dkk., Tugas Matakuliah Kimia Anorganik Terapan, S2 Depag, 2010
a
b
c
Rasio x 3
(bil. bulat)
(h k l)
(ccp)
h k i l
(hcp)
3 (1 1 1) (1 0 Ī 0)
3 (1 1 1) (1 0 Ī 0)
4 (0 0 2) (0 0 0 2)
5 (0 2 1) (1 0 Ī 1)
8 (0 2 2) (1 0 Ī 2)
10 (3 1 0) (1 1 ˉ2 0)
12 ( √2 1 3) (1 0 Ī 3)
15 (√2 3 2) (1 0 ˉ2 2)
15 (√5 3 1) (2 0 ˉ2 1)
16 (0 0 4) (0 0 0 4)
Hubungan hkl kubus dengan hkil hcp
•Tentukan hkl sistem kubus•jika salah satu dari h atau k pada hkl ccp = 1 atau 0, maka cenderung nilai a1 = 1.•Jika baik h maupun k pada ccp ≠ 1, maka a1 = 1⁄2. Ingat , (h + k + i) = 0. •Jika l pada hkil adalah 0 maka bidang akan tegak pada sisi heksagonal.•Kubus bisa diputar.
CUBIC IN HEXAGONAL MODEL, CREATED BY SECOND GROUP, MARCH 2010
Rule
Penentuan Struktur Kristal Kubus dan non-kubus, Sukir dkk., Tugas Matakuliah Kimia Anorganik Terapan, S2 Depag, 2010
InP nanocrystals
Guzelian et al., J. Phys. Chem., 100, 7212 (1996)
Applications: Determination of Crystallite Size
Scherrer equation:
Bcrystallites = (k)/(L cos )
k constant ~ 1 (precision error 10%)L average crystal size (nm) wavelength of the X-rays used (nm) Bragg angle (radians)B full width at half maximum (FWHM,
radians)
Example: anatase TiO2Cu = 0.15406 nmL1 = 0.0061 1=25.28 B1 = 25.3 nmL2 = 0.0061 2=37.8 B2 = 25.26 nm
Particle size measurement• Diffraction line of a perfect, infinite crystal = narrow
“spike”• Smaller particles = line broadening• Scherrer formula used to calculate particle size:
where L is the dimension of the particle is the wavelengthb is the peak width is the angle of reflectionK is a constant, can be assumed to be 1
(This is a simplified analysis)
βcosθKλ
=L
karakterisering_2004.ppt
karakterisering_2004.ppt
Example 1. Phase identification
Example 2. Supported metal particles
karakterisering_2004.ppt
XRD of TiO2 Nanoparticles as a Function of Deposition Temperature
20 30 40 50 600
100
200
300
400
700 oC
600 oC
500 oC
350 oC
250 oC
R RRR
R
AA
AAA
Inte
nsity
(arb
. uni
ts)
2 (degree)
20 30 40 50 60
0
100
200
300
400A: AnataseR: RutileA
nsf.ppt
TiO2 Phase Transformation: Effect of Particle size
20nmInte
nsity
(arb
. uni
ts)
800 oC
750 oC
700 oC
as-deposited
23 nm (b)
20 30 40 50 60
R(220)R(211)800 oC
750 oC
700 oC
as-deposited
12 nm (a)
Inte
nsity
(arb
. uni
ts)
2 (deg.)
R(111)R(101)
A(211)A(105)A(200)A(004)
R(110)
A(101)
XRD patterns from as-deposited samples and samples annealed at 700, 750, and 800 oC.
The phase compositions were calculated based on formula
Particle sizes were calculated.
A. A. Gribb and J. F. Banfield, Am. Mineral. 82, 717 (1997).
RA
RRR AA
AAAW
884.00
(*)
nsf.ppt
X-ray Diffraction Patterns for TiO2 with Different Particle Sizes
20 30 40 50 60
(211)(105)(200)(004)
(101)
17 nm
23 nm
12 nm
Inte
nsity
(arb
. uni
ts)
2(deg.)
20 30 40 50 60
24.5 25.0 25.5 26.0 26.5In
tens
ity (a
rb. u
nits
)2(deg.)
24.5 25.0 25.5 26.0 26.5
Anatase (101)
12 nm
17 nm
23 nm
Effect of O2 gas flow rate on particle size.
All peaks belong to the anatase phase and no other phase is detected within the X-ray detection limit
The measured average particle sizes were 12 ±2, 17 ±2, and 23 ±2 nm for the three samples.
nsf.ppt
Activation Energy Calculation
AR=A0Exp(-Ea/KT), A0=0.884AA+AR
Ea is anatase to rutile transformation activation energy. The activation energy decreases with the particle size
and 12-nm sample has the lowest activation energy of 180.28 kJ/mol. Bulk TiO2 has activation energy of 450 kJ/mol.(*)
(*) H. Zhang and J. F. Banfield, Am. Mineral. 84, 528 (1999).
0.00092 0.00096 0.00100 0.00104-5
-4
-3
-2
-1
0
12nm (Ea=180.28kJ/mol) 17nm (Ea=236.38kJ/mol) 23nm (Ea=298.85kJ/mol) R=0.995 R=0.998 R=0.991
Ln(A
R/A
0)
1/T (K-1)
0.000 92 0.00096 0.001 00 0. 0010 4
nsf.ppt
Karakterisasi Struktur Meso
XRD sudut kecil:1. struktur heksagonal
2. struktur kubus3. struktur lamellar
MCM-41, fasa heksagonal• presents a typical 4-peak pattern:– a very strong at low angle (d100) and – 3 weaker peaks at a higher angle (d110 , d200,
d210)• can be indexed on a hexagonal unit cell (ao
= 2d100/3 )• wall thickness, t = ao – pore diameter• periodic array of mesopores gives a
crystalline character
Guo et al., Chem. Mater., 2003, 15, 2295
ao = 12.61 nm
p6mm hexagonal symmetry
ao = 12.60 nm
MCM-48, fasa kubus
MCM-50, fasa lamellar
It’s a single crystal
2
At 27.42 °2, Bragg’s law fulfilled for the (111) planes, producing a diffraction peak.
The (200) planes would diffract at 31.82 °2; however, they are not properly aligned to produce a diffraction peak
The (222) planes are parallel to the (111) planes.
111
200
220
311222
A random polycrystalline sample that contains thousands of crystallites should exhibit all possible diffraction peaks
2 2 2
• For every set of planes, there will be a small percentage of crystallites that are properly oriented to diffract (the plane perpendicular bisects the incident and diffracted beams).
• Basic assumptions of powder diffraction are that for every set of planes there is an equal number of crystallites that will diffract and that there is a statistically relevant number of crystallites, not just one or two.
111
200
220
311222
Hubungan antara tekstur tekanan pada padatan dengan pola difraktogram XRD
METHOD 1:– Diffraction will occur when Bragg law is satisfied:
– The interplanar spacing d for a cubic material is given by:
– Combining the above equations results in:
sin2d
222 lkh
adhkl
2
2
2222
sin4
lkhad
1-92
PENETAPAN PARAMETER KRISTAL
– Which gives:
– Since 2 / 4a2 is constant, sin 2 is proportional to (h2 + k2 + l2),– As increases, planes with higher Miller indices will diffract.– Writing the above equation for two different planes and diving by the
minimum plane, we get:
2222
22
4lkh
aSin
22
22
22
21
21
21
22
12
sinsin
lkhlkh
1-93
Example: indexing of Aluminium diffraction pattern by method 1
1-94
1-95
1. Identify the peaks
2. Determine sin2
3. Calculate the ratio sin2 / sin2min and multiply by the appropriate
integers (1, 2, or 3)
4. Select the result from step (3) that yields h2 + k2 + l2 as an integer
5. Compare results with the sequences of h2 + k2 + l2 values to
identify the Bravais lattice
6. Calculate lattice parameter.
Example: indexing of Aluminium diffraction pattern by method 1
1-96
1-97
1-98
• The bravais lattice can be identified by noting the systematic presence (or absence) of reflections in the diffraction pattern.
• The Table below illustrates the selection rules for cubic lattices.
• According to these rules, the (h2 + k2 + l2) values for the different cubic lattices follow the sequence:
Simple cubic : 1,2,3,4,5,6,8,9,10,11,12,13,14,16,….BCC : 2,4,6,8,10,12,14,16,18,...FCC : 3,4,8,11,12,16,19,20,24,27,32,…
1-99
Bravais lattice Reflections present for Reflections absent for
Primitive (simple cubic) All None
Body Centered Cubic (BCC)
h + k + l = even h + k + l = odd
Face Centered Cubic (FCC)
h, k, l = unmixed (all even or all odd)
h, k, l = mixed
1-100
CALCULATION OF THE LATTICE PARAMETER
– The lattice parameter,a, can be calculated from:
– Rearranging gives
2222
22
4lkh
aSin
2222
22
sin4lkha
1-101
METHOD 2:
– This method can be used to index the diffraction pattern from materials with a cubic structure. From:
– Since 2 / 4a2 is constant for any pattern and which we will call A, we can write:
2222
22
4lkh
aSin
2222sin lkhA
1-102
– In a cubic system, the possible (h2 + k2 + l2) values are: 1, 2, 3, 4, 5, 6, 8, …. (even though all may not be present in every type of cubic lattice).
– The observed sin2 values for all peaks in the pattern are therefore divided by the integers 1, 2, 3, 4, 5, 6, 8, to obtain a common quotient, which is the value of A, corresponding to (h2 + k2 + l2) =1.
– We can then calculate the lattice parameter from the value of A using the relationship:
Aaor
aA
24 2
2
1-103
Note that 0.1448 is also common in 1, 2, 3, 4, 5, 6, BUT absent in 8
It can only be FCC1-104
Smaller Crystals Produce Broader XRD Peaks
t = thickness of crystalliteK = constant dependent on crystallite shape (0.89) = x-ray wavelengthB = FWHM (full width at half max) or integral breadthB = Bragg Angle
Scherrer’s Formula
BcosBKt
Contoh 1. Modifikasi silika dilakukan dengan mensintesis ester dan amino dengan polimer silika gel (Qu, et al., 2006)
Pola difraksi sinar-X : SiO2 dan SiO2-G0SiO-G4.0. 1:SiO2 ; 2:SiO2 - G0; 3:SiO -G0.5; 4:SiO2 -G1.0; 5:SiO2 -G1.5; 6:SiO2 -G2.0; 7:SiO2 – G2.5;8:SiO2-G3.0; 9:SiO2 -G3.5; 10:SiO2 -G4.0
Dari pola difraksi sinar-X menunjukkan hasil modifikasi bersifat amorph dan secara umum puncak-puncak difraksi SiO2 dan SiO2-G0- SiO2-G4.0 disekitar 24o. Puncak lebar pada sudut 2θ antara 15-35o merupakan puncak yang karakteristik dari senyawa amorph.
Dalam senyawa amorph penyusunan atom terjadi secara acak atau dengan derajat keteraturan rendah. Puncak lebar pada sudut 22o merupakan sifat amorph dari silika (Kalaphaty, 1998).
Contoh 2. Modifikasi MCM-41oleh 5-merkapto-1-metiltetrazol (Perez-Quintanilla, et al., 2007)
Pola difraksi sinar-X a) MCM-41 dan MTTZ-MCM-41 (modifikasi MCM-41oleh 5-merkapto-1-metiltetrazol )
MCM-41 sebelum dimodifikasi menunjukkan harga 2θ yang rendah dengan sangat tajam (100) pada puncak difraksi 2,24o dan ditambah dua puncak lain, yaitu (110) pada 3,88o dan (200) pada 4,65o. Sistem ini menunjukkan kisi suatu heksagonal dengan ketebalan kristal (d) berturut-turut : 39,31; 22,47 dan 18,97Å. Parameter unit kristal ao = 45,39 Å; yang diperoleh dari persamaan : ao = 2d100/√3
Penurunan puncak 2 θ = 2,25o pada pola difraksi sinar-X (100) dalam MTTZ-MCM41 memberikan fakta bahwa terjadi grafting (pencangkokan) di dalam celah mesopori. Adanya gugus fungsional oganik di dalam celah mesopori cenderung mengurangi daya hamburan dari lapisan silika mesopori. Hal ini juga didukung oleh tingkat struktural dari sintesis material yang dipertahankan setelah fungsionalisasi (Tabel 2)
Tabel 2. Data karakterisasi MCM-41 dan MTTZ-MCM-41
Daftar Pustaka :• Cullity, B.D., 1967, Element of X- Ray Diffraction, Addison-Wisley Publishing
Company Inc, New York.• Imelik, B., dan Vedrine, J.C., 1994, Catalyst Charactherization : Physical
Tehnique for Solid Materials, Plenum Press, New York.• Jenkins, R. dan Snyder, R.L., 1996, Introduction to X-ray Powder
Diffractometry, John Wiley and Sons Inc, New York.• Kalaphaty, U., Proctor, A., and Shultz, J., 2002, An Improved Method for
Production of Silica from Rice Hull Ash, Bioresource, 85 : 285-289.• Niemantsverdriet J.W., 2000, Spectroscopy in Catalysis, Wiley-VCH,
Weinheim.• Perez-Quintanilla, D., Hierro I.D., Fajardo M., dan Sierra I, 2006, 2-
Mercaptotiazoline modified mesoporous silica for mercury removal fromaqueuos media, Journal Hazardous Materials, B134 : 245-256.
• Qu R., Niu Y., Sun C, Ji C., Wang C., dan Cheng G., 2006, Syntheses, characterization, and adsorption properties for metal ions of silica-gel functionalized by ester-and amino-terminated dendrimer-like polyamidoamine polymer, Microporous and Mesoporous Materials, 97 : 58-65.