3 kuliah eldas 2014 - xrd.pptx

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?

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.


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


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)


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


F127 Results

Courtesy of Vikrant Urade


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


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


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


Example 1. Phase identification

Example 2. Supported metal particles


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

• 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.

3 kuliah eldas 2014 - xrd.pptx

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