SAMPLE XRD PATTERNS MATERIALS SCIENCE &ENGINEERING Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur URL: home.iitk.ac.in/~anandh AN INTRODUCTORY E-BOOK Part of A Learner’s Guide

 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

d [nm] 2  [de] Int.h k lMul 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 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

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

NiAl pattern from  (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

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.

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

Fe 3 C Cementite Fe 3 C (Cementite) Lattice parameter(s)5.089 Å, Å, 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

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

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

Al 3 Ni Superlattice reflections (weak) SC 5