SAMPLE XRD PATTERNSSAMPLE XRD PATTERNSMATERIALS SCIENCEMATERIALS SCIENCE

&&ENGINEERING ENGINEERING

Anandh Subramaniam & Kantesh Balani

Materials Science and Engineering (MSE)

Indian Institute of Technology, Kanpur- 208016

Email: anandh@iitk.ac.in, URL: home.iitk.ac.in/~anandh

AN INTRODUCTORY E-BOOKAN INTRODUCTORY E-BOOK

Part of

http://home.iitk.ac.in/~anandh/E-book.htmhttp://home.iitk.ac.in/~anandh/E-book.htm

A Learner’s GuideA Learner’s GuideA Learner’s GuideA Learner’s Guide

We have already seen the selection rules in Chapter_3c_X_Ray_Diffraction.ppt. Here we consider some sample patterns to identify some salient features of the patterns

and further see the differences between the patterns.

XRD powder patterns from various materials

d [nm] 2[de] Int. h k l Mul.

1 0.3359 26.520 1000.0 1 0 0 6

2 0.2375 37.840 797.2 1 1 0 12

3 0.1939 46.800 294.4 1 1 1 8

4 0.1680 54.600 141.3 2 0 0 6

5 0.1502 61.700 394.2 2 1 0 24

6 0.1371 68.360 292.7 2 1 1 24

7 0.1188 80.880 94.0 2 2 0 12

8 0.1120 86.940 40.3 3 0 0 6

9 0.1120 86.940 161.3 2 2 1 24

10 0.1062 92.960 144.5 3 1 0 24

11 0.1013 99.040 135.0 3 1 1 24

12 0.0970 105.200 43.7 2 2 2 8

13 0.0932 111.560 132.5 3 2 0 24

14 0.0898 118.200 277.6 3 2 1 48

15 0.0840 133.060 43.2 4 0 0 6

16 0.0815 142.000 211.3 4 1 0 24

17 0.0815 142.000 211.3 3 2 2 24

18 0.0792 153.280 150.2 3 3 0 12

19 0.0792 153.280 300.3 4 1 1 24

SC Po

All peaks present

Look at general trend line!(reminds one of Lorentz-Polarization factor)

Note that all hkl are present

Only elemental metal with SC structure under

‘normal’ conditions.

1

Probabilistic occupation of each BCC lattice site: 50% by Cu, 50% by Zn

NiAlDisordered structure

True composition of the phase giving rise to the XRD pattern Ni0.4Al0.6

Compare with ordered structure in upcoming slides

BCC2

SC

NiAl

Superlattice reflections (weak)

Calculated Pattern

Ordered structure

3 NiAl

NiAl pattern from 0-160 (2)

Superlattice reflections (weak)

Calculated Pattern

Comparison of this ordered structure with the disordered structures reveals the following:

1) Existence of superlattice (weak) peaks in the ordered structure

2) Slight difference in the peak positions due to a difference in stoichiometry.

Missing peaks

InBCT

Six {002}CUBIC planes are not equivalent now in tetragonal In → split into {002}2 members and {200}4 members

Similarly some other equivalent planes in cubic

become non-equivalent now

4 The selection rule is similar to BCC i.e. (h+k+l) should be even.

The (200) and (020) planes give rise to one peak, while the (002) plane gives rise to a separate peak (due to lowering of symmetry as compared to the cubic crystal).

The (101) & (011) give rise to one peak, while the (110) gives rise to a separate peak.

Ni3Al

Ni

Al

Superlattice reflections (weak)

SC5

Fe3C Cementite

Fe3C (Cementite)Lattice parameter(s) 5.089 Å, 6.7433 Å, 4.5235 Å

Space Group P 21/n 21/m 21/a (62)

Strukturbericht notation DO11

Pearson symbol oP16

Other examples with this structure

Fe3B, Co3C

OR6 Interstitial compound

Al2O3

Lattice parameter(s)a=4.7593 Å, c=12.9925 Å

(c/a=2.7299)

Space Group R 3 2/c (167)

Pearson symbol hR30

Al2O3Trigonal7

0

500

1000

1500

2000

2500

3000

10 20 30 40 50 60 70 80 90 1002

Inte

nsi

ty

Alumina (Al2O3)

012

104

110

31.65006

113

024

116

018

214300

1 0 10

0 2 100 0 12

-246128

223

No d [nm] 2 [deg.]

I h k l

1. 0.3480 25.580 620.2 0 1 2

2. 0.2551 35.140 1000.0 1 0 4

3. 0.2380 37.780 468.8 1 1 0

4. 0.2086 43.360 506.9 1 1 3, 1 1 -3

5. 0.1740 52.540 528.5 0 2 4

6. 0.1602 57.500 526.0 1 1 6, 1 1 -6

7. 0.1511 61.300 82.9 0 1 8

8. 0.1405 66.520 215.2 1 2 -4, 2 1 4

9. 0.1374 68.200 661.1 3 0 0

10. 0.1239 76.880 195.4 1 0 10

11. 0.1234 77.240 52.2 1 1 9, 1 1 -9

12. 0.1190 80.700 76.9 2 2 0

13. 0.1147 84.340 31.8 2 2 -3, 2 2 3

14. 0.1126 86.340 23.4 1 3 -2, 3 1 2

15. 0.1099 89.000 94.6 0 2 10

High Intensity Peaks Al2O3 XRD pattern (Polycrystalline Sample)

Experimental Pattern

Al3Ni

Superlattice reflections (weak)

SC5