Structure Elucidation From XRD 1

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Structure elucidation fromXRD

X-rays are electromagnetic waves with a wavelength in the range of interatomicdistances (0.1-10 )

topics

Structure analysis by X-ray diffraction fromcrystals

Crystallography

X-ray diffraction from polycrystalline samples(powders); Evaluation of the intensities of X-rays diffracted

from polycrystalline samples; Elucidation of simple inorganic crystal structures

starting from the model structures andcomparison of the intensities calculated for themodel structures with the observed intensities;


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What is X-ray Diffraction?


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Practical aspect

3 basic components of an X-ray dif fractometer

1.X-ray source 2. Specimen 3. X-ray detector

1. X-Ray source

Generated by directing anelectron beam of highvoltage at a metal targetinside an evacuated x-raytube

Cu K ~ 8.04 keV(=0.154184 nm) is the mostused metal target due to itshigh intensity

3. Detector

3 main types: proportional,scintillation, and solid-state

The most used isproportional

2. Specimen

Quantity ~ a few mg Grain size 50m

(passed 325 meshsieve)

Applied as a thin layer ofpowder/film onto a non-

diffracting material, suchas microscope glassslide


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Solid matter

crystalline

The atoms andmolecules are arrangedin a random way similarto the disorder we find in

a liquid do not formcrystallites. Glasses areamorphous materials.Small particles with nolong-range order (100)

The atoms arearranged in aregular pattern,and there is assmallest volume

element that byrepetition in threedimensionsdescribes thecrystal (a unitcell).

Long range order(>103 molecules)

polycrystallineSolids which containmany small, randomlyoriented and joinedcrystallites/grains

2 (o)10 20 30 40 50 60 70 80 90

Intensit

y

(a.u)

2 h

3 h

4 h

5 h

A [101]

A

AA A

Am

Bnon-crystalline(amorphous)

single crystalSolid which containssingle crystallite


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Single crystal polycrystalline amorphous

long-range order

consists of some

single crystalregion (grains)

separated bygrain boundaries

not ordered short-range

order

Polymers can also present ordered region as incrystalline materials, called crystallite

crystallite region

amorphous region


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XRD can be used to provide information about thestructure of amorphous or non-crystalline materials, such

as glass


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constructive interference results in diffraction line, but destructive interference does not


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monochromatic/single wavelength

with highest intensity is used asthe X-ray source


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In powder or polycrystalline diffraction it is

important to have a sample with a smoothplane surface.

If possible, grind the sample down to particlesof about 0.002 mm to 0.005 mm crosssection.

The ideal sample is homogeneous and thecrystallites are randomly distributed random distribution of all possible h,k,l planes

The sample is pressed into a sample holderso that we have a smooth flat surface.

Only crystallites having reflecting planes (h,k, l)parallel to the specimen surface will contribute tothe reflected intensities.

If we have a truly random sample, each possiblereflection from a given set of h, k, l planes anequal number of crystallites contributing to it.

We only have to rock the sample through theglancing angle THETA in order to produce allpossible reflections.


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X-ray Diffraction Pattern

Consists of a series of peaks

The peak intensity as the ordinate (y axis) expressedas an arbitrary units

The measured diffraction angle, 2, along the abscissa

The as-recorded XRD pattern generally have abackground, then it is usually substracted and thepeaks smoothened

Sources information: Powder Diffraction File (PDF) JCPDS (database of standard XRD pattern byInternational Centre for Diffraction Data)

Crystallography: reviews


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About 95% of all solid materials can be described ascrystalline

When X-rays interact with a crystalline substance(phase) gets a diffraction patternIn 1919 A.W.Hull gave a paper titled, A New Method ofChemical Analysis. Here he pointed out that .everycrystalline substance gives a pattern; the same substancealways gives the same pattern; and in a mixture ofsubstances each produces its pattern independently ofthe others. The X-ray diffraction pattern of a pure substance afingerprint finger print identification

The powder diffraction method is thus ideally suited forcharacterization and identification of

crystalline/polycrystalline phases

Today about 50,000 inorganic and 25,000 organic singlecomponent, crystalline phases, diffraction patterns havebeen collected and stored on magnetic or optical media asstandardsThe main use of powder diffraction is to identifycomponents in a sample by a search/match procedureThe areas under the peak are related to the amount of

each phase present in the sampleFor single-phase materials the crystal structure can beobtained directly using X-Ray diffraction (XRD)XRD can be used :

for phase identification (With the help of a database ofknown structures)

to determine crystal size, strain and preferredorientation of polycrystalline materials

the related technique of X-ray reflection enablesaccurate determination of film thickness


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Structure analysis by X-ray diffraction fromcrystals


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XRD patterns of furnace materials and reference patterns of identified phases


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Applications:

Identification

of crystallinephases

A

A A A

A

AA

TiO2 has 3 major

crystalline

phases, anatase

(A), rutile (R) and

brookite (B) with

fully anatase (A)as the crystalline

phase

TiO2 with fully

anatase (A) as thecrystalline phase

TiO2 with anatase (A) and rutile

(R) as the crystalline phases


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Peak intensitiesEvaluation of the intensities of X-rays diffracted

from polycrystalline samples evaluatingcrystallinity

taking the sum total of relative intensities of

ten individual characteristic peaks1 thentaking the ratio over the correspondingrelative intensities of standard materials

E.g.:

Comparing crystallinity of flyash-basedzeolite-A using XRD and IR spectroscopy

1CURRENT SCIENCE, VOL. 89, NO. 12, 25 DECEMBER 2005


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% crystallinity =(AD4R)/(ATO4)

% crystallinity = (IR sample)/(IR standard)

72.8% 85%

98.6%

98.6%

98.6%

100%


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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%

cos

KD =


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Applications:

Determination

of Crystal Size

Scherrer equation:

Bcrystallites = (k)/(L cos )k constant ~ 1 (precision error 10%)

L average crystal s ize (nm)

wavelength of the X-rays used (nm) Bragg angle (radians)B fu ll 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

Different crystallite sizes


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determination and refinement oflattice parameters (indexing)

)(

4

sin 222

2

22

lkh

a

++=

)(sin2222lkhC ++=

dividing the above equation with the first reflection angle gives the ratio of hkl

relationship between Miller indices and diffraction angles

)(

)(

sin

sin2

1

2

1

2

1

222

12

2

lkh

lkh

++

++=

the ratio of hkl define the possible Miller indices: ratio = h2 + k2 + l2

if 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 lastreflection data will be used


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exercise 1: indexing XRD data (cubic)

43.830

60.093

67.213

70.634

56.331

63.705

33.602

27.302

10010.027919.213

48.266

38.995

Miller indicesratiosin22 1. define the Millerindices

2. calculate thelatticeparameters

lattice type and systematic absenceson cubic system

destructive interferences occurringbetween the diffracted waves intensitycancels out

eg:


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For example MoO3 crystallizes in thin plates (like sheetsof paper) these crystals will pack with the flat surfacesin a parallel orientation.

Comparing the intensity between a randomly orienteddiffraction pattern and a preferred oriented diffractionpattern can look entirely different.

Quantitative analysis depend on intensity ratios whichare greatly distorted by preferred orientation.

Careful sample preparation is most important to dealwith preferred orientation samples

The following illustrations show the Mo O3 spectra'scollected by using transmission , Debye-Scherrercapillary and reflection mode.


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TiO2 film layered on SnO2 (S) thin f ilm

with anatase (A) as the crystalline

phases


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ZnO nanorod

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Structure Elucidation From XRD 1