Powder-XRD

CRYSTAL STRUCTURE DETERMINATION FROM POWDER- XRD

BY JAYABRATA DAS

ROLL-9905PG-III NO ndash 150021

REGN NO -28-0605 UNIVERSITY OF NORTH BENGAL

OUTLINE1 WHAT ARE MILLER INDICES

2 HOW BRAGGrsquoS LAW AND REFLECTION FROM PLANES ARE RELATED

SELECTION RULES OF REFLECTIONS FOR VARIOUS LATTICES

BRIEF INTRDUCTION TO DIFFRACTOMETER

HOW TO OBTAIN LATTICE STRUCTURE FROM POWRER-XRD DATA

APPLICATIONSLIMITATIONS

MILLER INDICES (hkl)

Miller indices are notations for describing and labelling planes in crystals and lattices

BRAGGrsquoS LAW IS A NECESSARY BUT INSUFFICIENT CONDITION FOR DIFFRACTION

BRAGGrsquoS EQN IS A NEGATIVE STATEMENT-If Braggrsquos eqn is not satisfied- No Reflection can

occur

If Braggrsquos eqn is satisfied ndash Reflection lsquoMAYrsquo occur

The presence of additional atom in the unit cell

Is the reason for missing Reflection known aslsquoSYSTEMETIC ABSENCESrsquo

Reflection from some planes are missing in the below BCC unit cell path difference between green rays is λ so they are

in phase but between green and red rays are λ2so

they out of phase and reflection from 100 (red) plane is not observed

THE REFLECTIONS PRESENT AND MISSING REFLECTIONS IN CUBIC SYSTEMBRAVAIS LATTICE REFLECTIONS

WHICH MAY BE PRESENT

REFLECTION WHICH NECESSARILY ABSENT

SC ALL NONEBCC (h+ k+l ) even (h+k+l) ODDFCC h k l unmixed h k l mixed

ALLOWED REFLECTIONS IN SCBCCFCCh2+k2+l2 SC BCC FCC

1 1002 110 1103 111 1114 200 200 2005 2106 211 21178 220 220 2209 300221 31110 310 31011 311 31112 222 220 22013 32014 321 3211516 400 400 40017 41032218 411330 41133019 331 331

RATIO OF h2+k2+l2 FOR SCBCCFCCSC 1 2 3 4 5 6 8 9 10

BCC

2 4 6 8 10 12 14 16 18

FCC

3 4 8 11 12 16 19 20 24

d- spacing in cubic system ndash 1d2 =h2+k2+l2a2

and Braggrsquos eqn n λ= 2dsin θ

Combining this two sin2 θ =( λ24a2) (h2+k2+l2)

So sin2 θ is propotional to h2+k2+l2 which can be used to determine lattice parameters

MODERN DIFFRACTOMETER

ESSENTIAL PARTS OF DIFFRACTOMETER1 X-RAY TUBE2 INCIDENT BEAM OPTICS3THE GONIOMETER4 THE SAMPLE AND SAMPLE HOLDER5RECIEVING SIDE OPTICS6 DETECTOR

DETERMINING CRYSTAL STRUCTUREA Diffraction pattern cannot be analyzed until

it has been lsquoINDEXEDrsquo

1Manual Indexing 2Autoindexing

Two methods of indexinga Mathematical bAnalytical

STEPS TO FOLLOW FOR MATHEMATICAL INDEXING1 Identify the peaks

2 Determine sin2θ

3 Calculate the ratio of sin2θsin2θmin and multiply by the appropriate integers

4 Select result from (3) that yields h2+k2+l2 as integers 5Compare results with the sequences of h2+k2+l2 values to idetify the Bravais lattice

6 calculate lattice parameters

NUMBER OF PEAKS DEPENDS ONWAVELENGTH OF X-RAY

LATTICE TYPE

SYMMETRY OF THE CRYSTAL

APPLICATIONS BRAVAIS LATTICE DETERMINATION

LATTICE PARAMETER DETERMINATION

DETERMINE IF MATERIAL IS AMORPHOUS OR CRYSTALLIE

PHASE COMPOSITION OF A SAMPLE

CRYSTALLITE SIZE AND STRAIN

QUANTITATIVE PHASE ANALYSIS

LIMITATIONSELEMENTAL ANALYSIS

ONLY SMALL FRACTION OF CRYSTALLITES IN SAMPLE CONTRIBUTE TO DIFFRACTION PATTERN

ACKNOWLEDGEMENTI AM VERY GREATEFUL TO Dr ASHIS

KUMAR NANDA FOR ASSISTING ME DURING THE PREPARATION OF SEMINAR

I AM ALSO THANKFUL TO OUR HEAD OF DEPARTMENT Prof BASUDEB BASU ALL OTHER TEACHERS OF DEPARTMENT MY FRIENDS AND WELL WISHERS FOR SUPPORTING ME

REFERENCEPOWDER X-RAY DIFFRACTION MIT

(PDF)httpprismmitedux-ray

X-RAY DIFFRACTION UNIVERSITY OF NORTH CAROLLINA (PDF)

MTE CLASS17 X-RAY DIFFRACTION

THANK YOU