International Tables for Crystallography (2006). Vol. D, ch. 3.3, pp. 393-448
https://doi.org/10.1107/97809553602060000644

Chapter 3.3. Twinning of crystals

Chapter index

A2BX4 structure type 3.3.7.2
ABX3 structure type 3.3.7.2
Aizu notation 3.3.10.2.1
allotwins 3.3.2.4, 3.3.9.2.4
AlMn alloys 3.3.10.2.2
ammonium sulfate [(NH4)2SO4] 3.3.7.3, 3.3.7.3
anatase (TiO2) 3.3.2.4, 3.3.10.4.1, 3.3.10.6.1
to rutile phase transition 3.3.10.6.1
annealing twins 3.3.7.1.2, 3.3.8.3
antiphase
aristotype 3.3.7.2, 3.3.9.2.4
arrowhead twin 3.3.3.1
Baveno twin 3.3.10.4.1
benzil [(C6H5CO)2] 3.3.8.6
berlinite (AlPO4) 3.3.6.3.3
bicrystallography 3.3.7.1.2, 3.3.8, 3.3.10.9
boundary contrast 3.3.10.4.2
brookite (TiO2) 3.3.2.4, 3.3.10.6.1
Burgers vector 3.3.10.8, 3.3.10.8
butterfly twin 3.3.3.1
cadmium telluride (CdTe) 3.3.6.6
cassiterite (SnO2) 3.3.3.1, 3.3.10.6.2
chalcopyrite 3.3.7.3
chirality relation 3.3.2.1, 3.3.2.2, 3.3.2.3
clamping 3.3.10.7.5
co-elastic twins 3.3.7.3
coherence
of grain boundaries 3.3.10.9
of twin boundaries 3.3.10.8, 3.3.10.9, 3.3.10.9, 3.3.10.9
coherent interface 3.3.10.9
coincidence lattice 3.3.8.2, 3.3.8.2, 3.3.8.3, 3.3.8.3, 3.3.8.6, 3.3.9
index 3.3.8.2
coincidence
one-dimensional 3.3.8.2
three-dimensional 3.3.8.2
two-dimensional 3.3.8.2
coincidence-site lattice (CSL) 3.3.1, 3.3.2.4, 3.3.6.3.4, 3.3.8.2, 3.3.9.1
coincidence-site sublattice 3.3.8, 3.3.8.1
coincidence-site subset 3.3.8.1
colour-changing operations 3.3.5, 3.3.5
colour-preserving operations 3.3.5
colour symmetry 3.3.5, 3.3.5
compatible planes 3.3.10.2
component state 3.3.2.2, 3.3.2.2
composite pseudosymmetry 3.3.6.9
conductivity
contact relations 3.3.2.1, 3.3.2.4, 3.3.10.1, 3.3.10.5
copper 3.3.10.6.4
cordierite (Mg2Al4Si5O18) 3.3.10.7.4, 3.3.10.7.4, 3.3.10.7.4, 3.3.10.7.4
corundum (Al2O3) 3.3.6.5, 3.3.10.1
coset composition 3.3.4.1
crystal system 3.3.7.3
eightfold 3.3.6.9
sixfold 3.3.6.9
daughter phase 3.3.6.2, 3.3.7.2, 3.3.10.7.3
Dauphiné–Brazil twin 3.3.6.3.3, 3.3.6.4
dichalcogenides MeX2 3.3.7.2, 3.3.9.2.4
dichromatic groups 3.3.5, 3.3.5
diffraction pattern of a twinned crystal 3.3.4.1, 3.3.8.1, 3.3.9.2.2
diperiodic twins 3.3.8.1, 3.3.8.7, 3.3.9.2.4
dislocation node 3.3.10.8
dislocation reactions 3.3.10.8
dislocations
stair-rod 3.3.10.4.3
twinning 3.3.10.2.2
distorted phase 3.3.10.1
domains
anti-polar 3.3.10.3.1
ferroelastic 3.3.6.13, 3.3.9.3, 3.3.10.1
ferroelectric 3.3.6.13
ferroelastic 3.3.7.3
domain texture 3.3.7.3, 3.3.7.3
Druckzwillinge 3.3.7.3, 3.3.7.3
elbow twins 3.3.3.1, 3.3.6.9
electrical conductivity 3.3.10.3.1
electrical constraints 3.3.10.3
enantiomorphic groups 3.3.8.6
enantiomorphism 3.3.6.3
enantiomorphous crystals 3.3.2.1
equitranslational subgroups 3.3.7.2
Esterel twin 3.3.8.5, 3.3.8.5
Fe4Al13 3.3.10.4.1
monoclinic 3.3.7.1.1
triclinic 3.3.10.2.2
ferrobielasticity 3.3.7.3, 3.3.7.3
ferrobielastic switching 3.3.7.1.2
ferrobielastic twinning 3.3.7.3
ferrobielastic twins 3.3.6.3.1, 3.3.10.7.1
ferroelastic domains 3.3.6.13, 3.3.7.3, 3.3.9.3, 3.3.10.1
ferroelastic domain structure 3.3.7.3
ferroelastic–ferroelectric phases 3.3.7.3, 3.3.9.2.2
ferroelasticity 3.3.7.3, 3.3.7.3, 3.3.9.3, 3.3.9.3
ferroelastic phase 3.3.7.3, 3.3.10.1
potentially 3.3.7.3
ferroelastic transition 3.3.6.2, 3.3.9.1, 3.3.10.2.1, 3.3.10.2.1, 3.3.10.7.5
ferroelectric domains 3.3.6.13, 3.3.6.14, 3.3.9.2.1
ferroelectricity 3.3.6.13, 3.3.7.3
potentially 3.3.6.1
ferroelectric phase 3.3.6.13, 3.3.10.3.1, 3.3.10.4.3
ferroelectric transition 3.3.4.1, 3.3.10.2.3, 3.3.10.3.1, 3.3.10.4.3
ferromagnetic materials 3.3.10.7.5
fivefold rotation 3.3.2.4
fluorite (CaF2) 3.3.3.1, 3.3.6.6
Friedel's lattice theory 3.3.8.1
fringe contrast 3.3.10.4.2, 3.3.10.4.3
gallium arsenide (GaAs) 3.3.6.6
gallium phosphate (GaPO4) 3.3.6.3.3, 3.3.8.6
garnet twin 3.3.8.3
germanium 3.3.8.3, 3.3.10.6.5
gibbsite (Al(OH)3) 3.3.2.3.1, 3.3.4.4, 3.3.6.10, 3.3.10.1
glide twin 3.3.10.6.2
grain boundaries 3.3.1
Greek cross 3.3.6.12, 3.3.6.12
growth face 3.3.7.1.2
growth morphology 3.3.7.1.2
growth-sector boundary 3.3.1, 3.3.10.3.1
growth sectors 3.3.1
growth-sector twins 3.3.6.7, 3.3.6.7, 3.3.6.9, 3.3.6.14
habit modification 3.3.7.1.2
harmotome twin 3.3.3.1, 3.3.10.7.2
head-to-head boundaries 3.3.10.3.1, 3.3.10.3.1, 3.3.10.3.1
high-order twins 3.3.8.3
high-temperature superconductors 3.3.7.3, 3.3.7.3
holohedral groups 3.3.6.3, 3.3.6.14, 3.3.9.1
homogenous shear 3.3.7.3
hydrargillite 3.3.2.3.1, 3.3.2.3.1
hysteresis 3.3.7.3
incoherence of twin boundaries 3.3.10.8, 3.3.10.9
incoherent interfaces 3.3.10.9
index of a group–subgroup relation 3.3.4.1, 3.3.7.2
indium phosphide (InP) 3.3.7.1.2
interface energy 3.3.10.1
intergrowths 3.3.1
arbitrary 3.3.1
oriented 3.3.2.4
parallel 3.3.1
intersection group 3.3.4.3
intersection symmetry 3.3.4.2, 3.3.4.3
inversion boundaries 3.3.10.4.3
iron-cross twin 3.3.3.1, 3.3.9.2.1, 3.3.10.4.1
isostructural crystals 3.3.8.6
Kantennormalengesetz 3.3.2.3.1, 3.3.2.3.1, 3.3.8.2
klassengleiche subgroup 3.3.7.2
klockmannite (CuSe) 3.3.8.3
knee twin 3.3.6.9
La Gardette twins 3.3.6.3.4, 3.3.6.3.4, 3.3.8.5, 3.3.8.5
lamellar twinning 3.3.3.1
langbeinite [K2Mg2(SO4)3] 3.3.10.2.1
langbeinite [K2Mg2(SO4)5] 3.3.4.4
lanthanum aluminate (LaAlO3) 3.3.10.7.3
lattice coincidence 3.3.2.2, 3.3.8.2, 3.3.8.4, 3.3.9.2.4, 3.3.10.2.4
lattice concept of twinning 3.3.8
lattice index 3.3.8.2
lattice pseudosymmetry 3.3.8.5
lead barium phosphate [(PbBa)3(PO4)2] 3.3.10.7.4
lead strontium phosphate [(PbSr)3(PO4)2] 3.3.10.7.4
leucite (KAlSi2O6) 3.3.10.7.3
Liebisch twins 3.3.6.3, 3.3.6.3
lithium formate monohydrate ([Li(CHO2)].H2O) 3.3.6.1
lithium formate monohydrate [Li(CHO2).H2O] 3.3.10.2.3, 3.3.10.3.1
lithium niobate (LiNbO3) 3.3.10.3.1
low-energy boundaries 3.3.2.2, 3.3.8.6, 3.3.10.1, 3.3.10.2
macles 3.3.1, 3.3.1
dipériodiques 3.3.8, 3.3.8
monopériodiquesmaclesmonopériodiques 3.3.8
monopériodiquesmaclesmonopériodiques 3.3.8
par mériédrie 3.3.8.2, 3.3.8.2, 3.3.9, 3.3.9
par mériédrie réticulaire 3.3.8.2, 3.3.8.2, 3.3.9.2.3, 3.3.9.2.3
par pseudo-mériédrie 3.3.9, 3.3.9
par pseudo-mériédrie réticulaire 3.3.9.1, 3.3.9.1
tripériodiques 3.3.8, 3.3.8
magnetite (Fe3O4) 3.3.8.3
Mallard pseudo-cube 3.3.6.12
Mediangesetz 3.3.2.3.1, 3.3.2.3.1
median law 3.3.2.3.1, 3.3.6.10
mériédrie réticulaire 3.3.9.1, 3.3.9.1
merohedry 3.3.9.1
of translation groups (lattices) 3.3.9.1
microcline (KAlSi3O8) 3.3.10.2.2
microtwins 3.3.6.12
mimetic twins 3.3.3.1
moiré pattern 3.3.8.4
monoperiodic twins 3.3.8.1, 3.3.8.7, 3.3.9.2.4
morphological classification 3.3.3.1
mosaic crystal 3.3.1
nanocrystalline materials 3.3.7.1.1, 3.3.8.3, 3.3.8.3, 3.3.10.6.5
needle domains 3.3.10.7.3, 3.3.10.8
non-ferroelastic materials 3.3.7.3
non-ferroelastic transition 3.3.9.1, 3.3.10.7.5
non-ferroelastic twins 3.3.7.2, 3.3.7.3, 3.3.10.7.1, 3.3.10.9
non-pyroelectric acentric crystals 3.3.10.3.3
optical activity 3.3.9.2.1, 3.3.9.2.1
optical anomaly 3.3.1
orientation relation 3.3.2.1, 3.3.2.2, 3.3.2.2, 3.3.2.3
noncrystallographic 3.3.2.2
parallel-lattice twins 3.3.6.3
penetration trillings 3.3.6.12
pentagonal–decagonal twins 3.3.6.8
permissible boundaries 3.3.10.2.1, 3.3.10.2.3, 3.3.10.2.4
permissible composition planes 3.3.10.2.1
permissible domain boundaries 3.3.10.2.1
permissible domain walls 3.3.10.2.2
permissible planes 3.3.10.2
permissible twin boundaries 3.3.4.1, 3.3.10.2.2
phase transformation (polymorphic) 3.3.7.2
phase transitions
displacive 3.3.7.2, 3.3.7.3
order–disorder 3.3.7.2
phillipsite twin 3.3.3.1, 3.3.10.7.2
piezoelectricity 3.3.6.13
plagioclase 3.3.10.2.2
plagioclase twins 3.3.6.11
planes of strain compatibility 3.3.10.2
plesiotwins 3.3.2.4, 3.3.2.4
polycrystalline aggregates 3.3.10.6.3, 3.3.10.7.5
polycrystalline materials 3.3.1, 3.3.7.1.2, 3.3.10.7
potassium lithium sulfate (KLiSO4) 3.3.2.4, 3.3.6.14, 3.3.7.1.2, 3.3.9.2.1, 3.3.10.2.3, 3.3.10.3.1, 3.3.10.5.3, 3.3.10.7.3
potassium sulfate (K2SO4) 3.3.6.7, 3.3.7.2, 3.3.7.3, 3.3.9.2.4, 3.3.10.7.2
potassium titanyl phosphate (KTP) (KTiOPO4) 3.3.6.1, 3.3.9.2.1, 3.3.10.3.1
potassium trihydrogen selenite KH3(SeO3)2 3.3.9.2.2
praeseodymium sulfide (PrS2) 3.3.9.2.4
prototype (or high-symmetry) phase 3.3.7.3, 3.3.7.3, 3.3.8.7, 3.3.8.7, 3.3.10.2.2, 3.3.10.2.2
pseudo-coincidence 3.3.8.3, 3.3.8.4, 3.3.9, 3.3.9.1, 3.3.9.2.2, 3.3.9.3
pseudo-fivefold axis 3.3.6.8
pseudo-mériédrie réticulaire 3.3.9.1
of lattice index j = 1 3.3.9.2.2
pseudo-merohedry 3.3.9.3
pseudosymmetry 3.3.2.2
composite 3.3.6.9
pyrite (FeS2) 3.3.3.1, 3.3.9.2.1, 3.3.10.4.1
recrystallization twins 3.3.8.3, 3.3.8.3
repetitive twins 3.3.3
reticular merohedry 3.3.9.2.4
reticular pseudo-merohedry 3.3.9.1
rhombic section 3.3.6.11, 3.3.10.2.2
ripening process 3.3.10.7.4
Ru8Ni15Al77 3.3.6.8
saccharine 3.3.10.4.1
Samarium sulfide (SmS1.9) 3.3.9.2.4
sanidine 3.3.10.2.2
Sapriel approach 3.3.10.2.1
shear
homogenous 3.3.7.3
shear strain 3.3.10.2
Sigma gt 3 twins 3.3.8.3
silicon tricrystal 3.3.8.3
silver 3.3.10.6.4
simple twins 3.3.3, 3.3.3, 3.3.4.2, 3.3.5, 3.3.5
SmS1.9 3.3.8.3
sodium nitrate (NaNO3) 3.3.7.1.1, 3.3.8.6
sodium sulfate (Na2SO4) 3.3.7.2
sphalerite (ZnS) 3.3.6.6, 3.3.8.6
spontaneous nucleation 3.3.7.1.1
spontaneous shear 3.3.7.3, 3.3.10.2.1, 3.3.10.7.3
stacking fault contrast 3.3.10.4.2
stacking faults 3.3.1, 3.3.2.4, 3.3.8.3, 3.3.10.4.2
St Andrew's cross 3.3.6.12
stress relief 3.3.10.7.5, 3.3.10.7.5
structural twins 3.3.7.2
sublattice index 3.3.8.2
superconductors 3.3.7.3, 3.3.10.2.1, 3.3.10.7.3
supersaturation twins 3.3.7.1.1
tail-to-tail boundaries 3.3.10.3.1, 3.3.10.3.1, 3.3.10.3.1
tenfold rotation 3.3.2.4
tetragonal crystals 3.3.10.2.4
transformation microcline 3.3.6.11, 3.3.10.2.2, 3.3.10.7.4
transition region 3.3.10.4.1
translation boundary 3.3.2.4, 3.3.7.2
translation domains 3.3.1, 3.3.1, 3.3.2.4, 3.3.7.2
translationengleiche subgroups 3.3.7.2, 3.3.7.2
translation group 3.3.9.1
translation twins (T-twins) 3.3.2.4, 3.3.7.2
triglycine sulfate (TGS) 3.3.10.2.3
tropochemical cell twinning 3.3.2.4
tweed microstructure 3.3.10.7.4
twin axes 3.3.2.3.2
of order n gt 2 3.3.8.4
pseudo-fivefold 3.3.3.1
pseudo n-fold 3.3.10.2.2
sixfold 3.3.2.3.2
threefold 3.3.9.2.4
with noncrystallographic multiplicities 3.3.6.8
twin component 3.3.2.1
twin displacement vector 3.3.2.2, 3.3.2.4, 3.3.10.1, 3.3.10.4.1, 3.3.10.6.1, 3.3.10.6.2
twin elements 3.3.2.2
irrational 3.3.2.4
rational 3.3.2.4
twin formation
by nucleation 3.3.7.1.1
during crystal growth 3.3.7.1.2
twin inserts 3.3.7.1.2
twin inversion centre 3.3.2.3.1, 3.3.10.4.3
twin lattice index 3.3.8.2
twin mirror plane 3.3.2.3.1
twinning
by high-order merohedry 3.3.6.12
by lattice merohedry 3.3.8.2
by merohedry 3.3.7.3, 3.3.8.2, 3.3.9
by pseudo-merohedry 3.3.9
by reticular merohedry 3.3.8.2, 3.3.9.2.3, 3.3.9.2.4
by reticular pseudo-merohedry 3.3.6.12, 3.3.9.1
by twin-lattice pseudo-symmetry 3.3.9
by twin-lattice symmetry 3.3.9
definition 3.3.2
dislocations 3.3.10.2.2, 3.3.10.8
lattice aspects 3.3.8
mirror plane 3.3.2.4
with a change of form 3.3.7.3
without a change of form 3.3.7.3
with partial lattice coincidence (lattice index j gt 1) 3.3.9.2.3
with partial lattice pseudo-coincidence (lattice index j gt 1) 3.3.9.2.4
twinning dislocations 3.3.10.8, 3.3.10.9
twinning relation 3.3
twin obliquity 3.3.8.4, 3.3.8.5
twin pattern 3.3.10.7
twin rotations
noncrystallographic 3.3.4.4
pseudo n-fold 3.3.2.3.2, 3.3.4.4
twins 3.3.1
genetic classification 3.3.7
with inclined axes 3.3.6.3, 3.3.6.3.4
twins of twins 3.3.6.14
twin textures 3.3.10.7
twin with lattice index [j] gt 1 3.3.10.2.4
two-dimensional nucleus 3.3.7.1.2
unit-cell twinning 3.3.2.4
W′ boundary 3.3.10.2.1, 3.3.10.2.2
Young's modulus 3.3.7.3
yttrium barium copper oxide (YBaCuO) 3.3.7.3, 3.3.10.2.1, 3.3.10.7.3, 3.3.10.7.3, 3.3.10.7.4, 3.3.10.9
Zwilling 3.3.1, 3.3.1
Σ1 twins 3.3.8.3, 3.3.8.6
Σ27 twins 3.3.8.3, 3.3.8.3
Σ2 twins 3.3.8.3
Σ33 twin 3.3.8.3
Σ33 twins 3.3.10.2.4
Σ3 bicrystal boundaries 3.3.10.6.4
Σ3 twin interface 3.3.10.6.3
Σ7 twins 3.3.9.2.3
Σ81 twins 3.3.8.3, 3.3.8.3
Σ9 twins 3.3.8.3, 3.3.8.3, 3.3.8.3
Σ notation 3.3.8.2, 3.3.8.2