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2-fold Screw Axes. Along b have –x,1/2+y,-z For points on the axis (i.e. 0,y,0) this looks like a translation only. Just like 1-d centered cell Result for 0k0 h=2n systematic presence If the screw does not run through origin the same presences exit because cannot detect the origin shift!.

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2 fold screw axes
2-fold Screw Axes
  • Along b have –x,1/2+y,-z
  • For points on the axis (i.e. 0,y,0) this looks like a translation only.
  • Just like 1-d centered cell
  • Result for 0k0 h=2n systematic presence
  • If the screw does not run through origin the same presences exit because cannot detect the origin shift!
3 1 along c axis
31 Along C axis
  • In this case only waves with l=3 are allowed
  • Thus the condition is 00l, l=3n
glide perpendicular to b
Glide perpendicular to b
  • As before, points in the ac plane see only translation.
  • Translate ½ along c
  • Allowed h0l l=2n
  • For n glide translation is ½ along the ac diagonal resulting in h0l h+l=2n
centering
Centering
  • C centering adds (1/2,1/2,0) to all points.
  • Therefore for all hkl h+k=2n
  • I centering adds (1/2,1/2,1/2) to all points
  • Therefore for all hkl h+k+l=2n
data equivalence
Data Equivalence
  • The symmetry of the data is given by the Laue group.
  • Friedels law F(hkl)=F(-h-k-l)
space group determination
Space Group Determination
  • By Hand
  • Automatically by programs
  • NOTE—Space Group determination canNOT be done until after the data is collected.
test crystal ambi
Test Crystal (ambi)
  • Orthorhombic
  • Must check

h,0,0 0,k,0 0,0,l h,k,0 h,0,k h,k,0 and h,k,l

Data file is called xl.hkl

(Note LINUX is case sensitive)

programs
Programs

Find pattern and weight by frequency of known space groups.

This approach can find patterns that are not there—P2/c vs P21/c P212121 vs P21212

Look for weak reflections I/sigma(I)

Use some high cutoff i.e. 10sigma

This at time fails to find absences

programs14
Programs
  • xprep—part of SHELXTL
  • Uses method 1
  • Does all processing
  • absen
  • Uses method 2
space group determination15
Space Group Determination
  • To refine the structure satisfactorily the correct space group must be used.
  • If there is a centric-accentric pair try the centric space group first unless there are reasons to rule it out.
  • Sometimes you can refine in an incorrect space group. This results in a mess and you can get “Marshed”