Quantitative analysis of planar faulting
Ernesto Estevez Rams, Raimundo Lora-Serrano, A. Pentón-Madrigal, H. Fueß · Acta Crystallographica Section A Foundations of Crystallography · 2002
Stacking faults in structures built from identical layers are important twinning mechanisms.Occurring in sufficient concentration, they also produce rods of diffuse scattering.A well-known example is the (111)-twinning in the cubic closest sphere packing, …ABC|BAC… Another example is the monoclinic structure of piperazine hexahydrate [1] where polytypic fourfold twinning results in a tetragonal diffraction picture with extraordinary absence rules.Such twinning may lead to important ambiguities, as shown by the following two examples.The polytypic structure of the metastable orange phase of HgI2 [2] is built from layers of corner-linked super-tetrahedra Hg4I10, layer symmetry pm2.Successive layers may be stacked in two ways that result in identical interlayer contacts.The two corresponding periodic Maximum Degree of Order (MDO) structures are both tetragonal: I41/amd with a 4-layer repeat (f) and P42/nmc with a two-layer repeat (t).It turns out that a structure composed of extended domains …ffff…tttt… with average volume ratio 1:1 is indistinguishable from an orthorhombic alternating stacking …ftftft… twinned through stacking faults …tftf|ftft… , independently of the average domain size and the number of stacking faults.The polytypic structure of tris(bicyclo[2.2.1]hexeno)benzene [3] shows layers with symmetry p31m.The two MDO-structures have symmetries C2/c (1) and P6122/P6522 (2); corresponding repeat distances are 4 and 6 layers, respectively.Highly disordered crystals, and ordered crystals with structure MDO-1 have been observed [4].Interestingly, 6-fold equal-volume twins of MDO-1 give exactly the same diffraction pictures, including diffuse scattering, as left-right twins of MDO-2 for any number of stacking faults.