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Indexing
Indexing
Qhkl = h2a*2 + k2c*2 + l2c*2 +2hka*b* cos gamma* +2klb*c* cos alpha* +2hlc*a* cos beta*
= (1/dhkl)2
Indexing
Ito's method example - Q values given
0.0310 0.34290.0457 0.33220.0730 0.33640.0769 0.34280.1165 0.34510.1187 0.35050.1239 0.36640.1649 0.37230.1699 0.38240.1816 0.40160.1957 0.40830.2077 0.44320.2123 0.44500.2386 0.44980.2436 0.46080.2517 0.46590.2563 0.47680.2793 0.48630.2884 0.49180.3065 0.4938
0.5376
Q100 = a*2 = 0.0310 a* = 0.1761
Choose first three reflectionsas basis vectors
Q100
Q010
Q001
Q200
Q300
Indexing
Ito's method example - Q values given
0.0310 0.34290.0457 0.33220.0730 0.33640.0769 0.34280.1165 0.34510.1187 0.35050.1239 0.36640.1649 0.37230.1699 0.38240.1816 0.40160.1957 0.40830.2077 0.44320.2123 0.44500.2386 0.44980.2436 0.46080.2517 0.46590.2563 0.47680.2793 0.48630.2884 0.49180.3065 0.4938
0.5376
Q100 = a*2 = 0.0310 a* = 0.1761
Choose first three reflectionsas basis vectors
Q100
Q010
Q001
Q020
Q030
Q010 = b*2 = 0.0454 b* = 0.2131
Indexing
Ito's method example - Q values given
0.0310 0.34290.0457 0.33220.0730 0.33640.0769 0.34280.1165 0.34510.1187 0.35050.1239 0.36640.1649 0.37230.1699 0.38240.1816 0.40160.1957 0.40830.2077 0.44320.2123 0.44500.2386 0.44980.2436 0.46080.2517 0.46590.2563 0.47680.2793 0.48630.2884 0.49180.3065 0.4938
0.5376
Q100 = a*2 = 0.0310 a* = 0.1761
Choose first three reflectionsas basis vectors
Q100
Q010
Q001
Q002
Q010 = b*2 = 0.0454 b* = 0.2131
Q001 = c*2 = 0.0721 c* = 0.2685
Indexing
Ito's method example - Q values given
0.0310 0.34290.0457 0.33220.0730 0.33640.0769 0.34280.1165 0.34510.1187 0.35050.1239 0.36640.1649 0.37230.1699 0.38240.1816 0.40160.1957 0.40830.2077 0.44320.2123 0.44500.2386 0.44980.2436 0.46080.2517 0.46590.2563 0.47680.2793 0.48630.2884 0.49180.3065 0.4938
0.5376
Qhkl = h2a*2 + k2c*2 + l2c*2 +2hka*b* cos gamma* +2klb*c* cos alpha* +2hlc*a* cos beta*
Q110 = 0.0310 + 0.0454 = 0.0764
Q110
Q120 = 0.0310 + 0.1816 = 0.2126Q120
Q100
Q010
Q001
Q002
Q020
Q030
Q200
Q300
Q210 = 0.1240 + 0.0454 = 0.2126
Q210
gamma* = 90°
Indexing
Ito's method example - Q values given
0.0310 0.34290.0457 0.33220.0730 0.33640.0769 0.34280.1165 0.34510.1187 0.35050.1239 0.36640.1649 0.37230.1699 0.38240.1816 0.40160.1957 0.40830.2077 0.44320.2123 0.44500.2386 0.44980.2436 0.46080.2517 0.46590.2563 0.47680.2793 0.48630.2884 0.49180.3065 0.4938
0.5376
Qhkl = h2a*2 + k2c*2 + l2c*2 +2hka*b* cos gamma* +2klb*c* cos alpha* +2hlc*a* cos beta*
But Q011 = 0.0454 + 0.0721 = 0.1175doesn't quite work
Q110
Q120
Q100
Q010
Q001
Q002
Q020
Q030
Q200
Q300
Q210
Q0kl = k2Q010 + l2Q001 +
2klb*c* cos alpha*Q0kl = k2Q010
+ l2Q001 -2klb*c* cos alpha*
Indexing
Ito's method example - Q values given
0.0310 0.34290.0457 0.33220.0730 0.33640.0769 0.34280.1165 0.34510.1187 0.35050.1239 0.36640.1649 0.37230.1699 0.38240.1816 0.40160.1957 0.40830.2077 0.44320.2123 0.44500.2386 0.44980.2436 0.46080.2517 0.46590.2563 0.47680.2793 0.48630.2884 0.49180.3065 0.4938
0.5376
But Q011 = 0.0454 + 0.0721 = 0.1175doesn't quite work
Q110
Q120
Q100
Q010
Q001
Q002
Q020
Q030
Q200
Q300
Q210
Q0kl = k2Q010 + l2Q001
ave. of Q0kl & Q0kl
Q0kl = Q0kl - 2klb*c* cos alpha*
Q011 = 0.1176 Q011 = 0.1187 & Q011 = 0.1165
alpha* = 89.5°
Q011
Q011
Indexing
Ito's method example - Q values given
0.0310 0.34290.0457 0.33220.0730 0.33640.0769 0.34280.1165 0.34510.1187 0.35050.1239 0.36640.1649 0.37230.1699 0.38240.1816 0.40160.1957 0.40830.2077 0.44320.2123 0.44500.2386 0.44980.2436 0.46080.2517 0.46590.2563 0.47680.2793 0.48630.2884 0.49180.3065 0.4938
0.5376
Q101 = 0.0310 + 0.0722 = 0.1032
Q110
Q120
Q100
Q010
Q001
Q002
Q020
Q030
Q200
Q300
Q210
Q011
Q102 = 0.0310 + 4*0.0722 = 0.3198
Q102 = 0.3198 Q102 = 0.4432 & Q102 = 0.1957
beta* = 47.9°Q102
Q102
a* = 0.1761b* = 0.2131c* = 0.2685alpha* = 89.5°beta* = 49.0°gamma* = 90°
Some SST valuesfor indexing problem
(sin (theta))2 =
WL2/4*Q
wavelength = 1.540593 Å
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