1. SAMPLE XRD PATTERNS MATERIALS SCIENCE &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-BOOK Part of http://home.iitk.ac.in/~anandh/E-book.htm A Learner’s Guide

2.  We have already seen the selection rules in Chapter_3c_X_Ray_Diffraction.ppt.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

3. d [nm] 2  [de] Int.h k lMul. 10.335926.5201000.01 0 06 20.237537.840797.21 1 012 30.193946.800294.41 1 18 40.168054.600141.32 0 06 50.150261.700394.22 1 024 60.137168.360292.72 1 124 70.118880.88094.02 2 012 80.112086.94040.33 0 06 90.112086.940161.32 2 124 100.106292.960144.53 1 024 110.101399.040135.03 1 124 120.0970105.20043.72 2 28 130.0932111.560132.53 2 024 140.0898118.200277.63 2 148 150.0840133.06043.24 0 06 160.0815142.000211.34 1 024 170.0815142.000211.33 2 224 180.0792153.280150.23 3 012 190.0792153.280300.34 1 124 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

4. Probabilistic occupation of each BCC lattice site: 50% by Cu, 50% by Zn NiAl Disordered structure True composition of the phase giving rise to the XRD pattern Ni 0.4 Al 0.6 Compare with ordered structure in upcoming slides BCC 2

5. SC NiAl Superlattice reflections (weak) Calculated Pattern Ordered structure 3 NiAl

6. NiAl pattern from 0-160  (2  ) Superlattice reflections (weak) Calculated Pattern

7.  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

8. In BCT 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.

9. Ni 3 Al Ni Al Superlattice reflections (weak) SC 5

10. Fe 3 C Cementite Fe 3 C (Cementite) Lattice parameter(s)5.089 Å, 6.7433 Å, 4.5235 Å Space GroupP 2 1 /n 2 1 /m 2 1 /a (62) Strukturbericht notationDO 11 Pearson symboloP16 Other examples with this structure Fe 3 B, Co 3 C OR 6 Interstitial compound

11. Al 2 O 3 Lattice parameter(s) a=4.7593 Å, c=12.9925 Å (c/a=2.7299) Space Group R  3 2/c (167) Pearson symbolhR30 Al 2 O 3 Trigonal 7

12. High Intensity Peaks Al 2 O 3 XRD pattern (Polycrystalline Sample) Experimental Pattern

14. Al 3 Ni Superlattice reflections (weak) SC 5