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Indexing

Indexing. Indexing Q hkl = h 2 a* 2 + k 2 c* 2 + l 2 c* 2 + 2hka*b* cos gamma* + 2klb*c* cos alpha* + 2hlc*a* cos beta* = (1/d hkl ) 2. Q 100 Q 010 Q 001. Choose first three reflections as basis vectors. Q 200. Q 300. Indexing Ito's method example - Q values given

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Indexing

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  1. Indexing

  2. Indexing Qhkl = h2a*2 + k2c*2 + l2c*2 + 2hka*b* cos gamma* + 2klb*c* cos alpha* + 2hlc*a* cos beta* = (1/dhkl)2

  3. Q100 Q010 Q001 Choose first three reflections as basis vectors Q200 Q300 • Indexing • Ito's method example - Q values given • 0.0310 0.3429 • 0.0457 0.3322 • 0.0730 0.3364 • 0.0769 0.3428 • 0.1165 0.3451 • 0.1187 0.3505 • 0.1239 0.3664 • 0.1649 0.3723 • 0.1699 0.3824 • 0.1816 0.4016 • 0.1957 0.4083 • 0.2077 0.4432 • 0.2123 0.4450 • 0.2386 0.4498 • 0.2436 0.4608 • 0.2517 0.4659 • 0.2563 0.4768 • 0.2793 0.4863 • 0.2884 0.4918 • 0.3065 0.4938 • 0.5376 Q100 = a*2 = 0.0310 a* = 0.1761

  4. Q100 Q010 Q001 Choose first three reflections as basis vectors Q020 Q030 • Indexing • Ito's method example - Q values given • 0.0310 0.3429 • 0.0457 0.3322 • 0.0730 0.3364 • 0.0769 0.3428 • 0.1165 0.3451 • 0.1187 0.3505 • 0.1239 0.3664 • 0.1649 0.3723 • 0.1699 0.3824 • 0.1816 0.4016 • 0.1957 0.4083 • 0.2077 0.4432 • 0.2123 0.4450 • 0.2386 0.4498 • 0.2436 0.4608 • 0.2517 0.4659 • 0.2563 0.4768 • 0.2793 0.4863 • 0.2884 0.4918 • 0.3065 0.4938 • 0.5376 Q100 = a*2 = 0.0310 a* = 0.1761 Q010 = b*2 = 0.0454 b* = 0.2131

  5. Q100 Q010 Q001 Choose first three reflections as basis vectors Q002 • Indexing • Ito's method example - Q values given • 0.0310 0.3429 • 0.0457 0.3322 • 0.0730 0.3364 • 0.0769 0.3428 • 0.1165 0.3451 • 0.1187 0.3505 • 0.1239 0.3664 • 0.1649 0.3723 • 0.1699 0.3824 • 0.1816 0.4016 • 0.1957 0.4083 • 0.2077 0.4432 • 0.2123 0.4450 • 0.2386 0.4498 • 0.2436 0.4608 • 0.2517 0.4659 • 0.2563 0.4768 • 0.2793 0.4863 • 0.2884 0.4918 • 0.3065 0.4938 • 0.5376 Q100 = a*2 = 0.0310 a* = 0.1761 Q010 = b*2 = 0.0454 b* = 0.2131 Q001 = c*2 = 0.0721 c* = 0.2685

  6. Q100 Q010 Q001 Q110 Q120 Q002 Q020 Q200 Q300 Q210 Q110 = 0.0310 + 0.0454 = 0.0764 Q030 Q120 = 0.0310 + 0.1816 = 0.2126 Q210 = 0.1240 + 0.0454 = 0.2126 • Indexing • Ito's method example - Q values given • 0.0310 0.3429 • 0.0457 0.3322 • 0.0730 0.3364 • 0.0769 0.3428 • 0.1165 0.3451 • 0.1187 0.3505 • 0.1239 0.3664 • 0.1649 0.3723 • 0.1699 0.3824 • 0.1816 0.4016 • 0.1957 0.4083 • 0.2077 0.4432 • 0.2123 0.4450 • 0.2386 0.4498 • 0.2436 0.4608 • 0.2517 0.4659 • 0.2563 0.4768 • 0.2793 0.4863 • 0.2884 0.4918 • 0.3065 0.4938 • 0.5376 Qhkl = h2a*2 + k2c*2 + l2c*2 + 2hka*b* cos gamma* + 2klb*c* cos alpha* + 2hlc*a* cos beta* gamma* = 90°

  7. Q100 Q010 Q001 Q110 Q120 Q002 Q020 Q200 Q300 Q210 But Q011 = 0.0454 + 0.0721 = 0.1175 doesn't quite work Q030 Q0kl = k2Q010+ l2Q001 + 2klb*c* cos alpha* Q0kl = k2Q010+ l2Q001 - 2klb*c* cos alpha* • Indexing • Ito's method example - Q values given • 0.0310 0.3429 • 0.0457 0.3322 • 0.0730 0.3364 • 0.0769 0.3428 • 0.1165 0.3451 • 0.1187 0.3505 • 0.1239 0.3664 • 0.1649 0.3723 • 0.1699 0.3824 • 0.1816 0.4016 • 0.1957 0.4083 • 0.2077 0.4432 • 0.2123 0.4450 • 0.2386 0.4498 • 0.2436 0.4608 • 0.2517 0.4659 • 0.2563 0.4768 • 0.2793 0.4863 • 0.2884 0.4918 • 0.3065 0.4938 • 0.5376 Qhkl = h2a*2 + k2c*2 + l2c*2 + 2hka*b* cos gamma* + 2klb*c* cos alpha* + 2hlc*a* cos beta*

  8. Q100 Q010 Q001 Q0kl = k2Q010+ l2Q001 ave. of Q0kl & Q0kl Q0kl = Q0kl - 2klb*c* cos alpha* Q110 Q120 Q002 Q020 Q200 Q300 Q210 Q011 Q011 Q030 Q011 = 0.1176 Q011 =0.1187 & Q011 = 0.1165 alpha* = 89.5° • Indexing • Ito's method example - Q values given • 0.0310 0.3429 • 0.0457 0.3322 • 0.0730 0.3364 • 0.0769 0.3428 • 0.1165 0.3451 • 0.1187 0.3505 • 0.1239 0.3664 • 0.1649 0.3723 • 0.1699 0.3824 • 0.1816 0.4016 • 0.1957 0.4083 • 0.2077 0.4432 • 0.2123 0.4450 • 0.2386 0.4498 • 0.2436 0.4608 • 0.2517 0.4659 • 0.2563 0.4768 • 0.2793 0.4863 • 0.2884 0.4918 • 0.3065 0.4938 • 0.5376 But Q011 = 0.0454 + 0.0721 = 0.1175 doesn't quite work

  9. Q102 Q011 Q300 Q020 Q002 Q210 Q110 Q200 Q120 Q102 = 0.3198 Q102 =0.4432 & Q102 = 0.1957 beta* = 47.9° Q102 Q030 • Indexing • Ito's method example - Q values given • 0.0310 0.3429 • 0.0457 0.3322 • 0.0730 0.3364 • 0.0769 0.3428 • 0.1165 0.3451 • 0.1187 0.3505 • 0.1239 0.3664 • 0.1649 0.3723 • 0.1699 0.3824 • 0.1816 0.4016 • 0.1957 0.4083 • 0.2077 0.4432 • 0.2123 0.4450 • 0.2386 0.4498 • 0.2436 0.4608 • 0.2517 0.4659 • 0.2563 0.4768 • 0.2793 0.4863 • 0.2884 0.4918 • 0.3065 0.4938 • 0.5376 Q100 Q010 Q001 Q101 = 0.0310 + 0.0722 = 0.1032 Q102 = 0.0310 + 4*0.0722 = 0.3198 a* = 0.1761 b* = 0.2131 c* = 0.2685 alpha* = 89.5° beta* = 49.0° gamma* = 90°

  10. Some SST values for indexing problem (sin (theta))2 = WL2/4*Q wavelength = 1.540593 Å

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