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