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Pathological crystallography


Yeates TO (1997) Detecting and overcoming crystal twinning. Meth Enzymol 276:344–358
Yeates TO, Fam BC (1999) Protein crystals and their evil twins. Structure 7:R25–9
Dauter Z, et al. (2005) Pathological crystallography: case studies of several unusual macromolecular crystals. Acta Crystallogr D 61:967–975
Zwart PH, Grosse-Kunstleve RW, Lebedev AA, et al. (2008) Surprises and pitfalls arising from (pseudo)symmetry. Acta Crystallogr D 64:99–107


A typical definition of a twinned crystal is: "Twins are regular aggregates consisting of crystals of the same species joined together in some definite mutual orientation" (Giacovazzo, 1992). Space groups where it is possible to index the cell along different axes are very prone to twinning.

Types of twinning:
  1. Merohedral: lattice from distinct/twin domains completely overlap in 3D. This is possible in crystal system where lattice symmetry exceeds the underlying symmetry of the crystal. The diffraction patter looks normal. When involving only two distinct domain orientations (most macromolecules) it is called 'hemihedral'.
  2. Epitaxial (non-Merohedral): lattices of distinct domains may match in 2D by may be incompatible in 3D. Two interpenetrating lattices will be visible from the diffraction (easy to recognize).

Twinning - Random notes from the ccp4bb

- Linda Schuldt via to CCP4BB
In a monoclinic space group an orthorhombic lattice metric can be simulated when one of the following conditions is fulfilled:
i) a = c [e.g. in Wittmann & Rudolph (2007) Acta Cryst. D63, 744-749]
ii) the beta angle is close to 90° [e.g. in Larsen et al. (2002) Acta Cryst. D58, 2055-2059 ]
iii) c cos beta is about -a/2 [e.g. in Declercq & Evrard, (2002) Acta Cryst. D57, 1829-1835]The a and b axes of the orthorhombic cell are 
identical to the monoclinic a and c axes, respectively. The length of the orthorhombic b-axis can also be calculated by "c(monoclinic) 
cos(beta-90°) = 1/2b(orthorhomic)".

- Eleanor Dodson via to CCP4BB
You might like to look at this..
It tries to explain likely twinning possibilities in P21.
If you get C2222 and P21, then probably a~=c - then Beta can have any value.
C222 axes are then always possible with a* +c* , a*-c*, b* all having angles ~ 90
Without twinning you wont get 222 symmetry though. Pointless helps here.When the twinning domains are superimposable in three dimensions with twinning fraction alpha, defined as the fractional volume of domains in the second orientation;cannot be detected by examining diffraction patterns, but can be detected by examining the intensity statistics (use the "Twinning Server")

Pseudo translational or rotational symmetry

It arises when noncrystallographic symmetry (NCS) operators are close to true crystallographic symmetry.