International Tables for Crystallography (2013). Vol. D, ch. 3.3, pp. 413-487
https://doi.org/10.1107/97809553602060000917

Chapter 3.3. Twinning of crystals

Chapter index

A2BX4 structure type 3.3.7.2
ABX3 structure type 3.3.7.2
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
to rutile phase transition 3.3.10.6.1
anisotropy 3.3.1
annealing twins 3.3.7.1.2, 3.3.8.3
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) 3.3.6.4.3
bicrystallography 3.3.7.1.2, 3.3.8, 3.3.10.9
birefringence 3.3.1, 3.3.1, 3.3.6.1, 3.3.6.1, 3.3.6.1
boundary contrast 3.3.6.1, 3.3.10.4.2
boundary dislocations 3.3.10.8
Bravais lattice 3.3.9.1
brookite (TiO2) 3.3.2.4, 3.3.10.6.1, 3.3.10.6.1
Burgers vector 3.3.10.8, 3.3.10.8, 3.3.10.8
butterfly twin 3.3.3.1
cadmium telluride (CdTe) 3.3.6.7, 3.3.7.1.2, 3.3.8.6, 3.3.10.3.3
Cartesian coordinates 3.3.10.2
cassiterite (SnO2) 3.3.3.1, 3.3.10.6.3, 3.3.10.6.3
cell twinning 3.3.11.1
chalcopyrite 3.3.7.3
chemical bonding 3.3.8.6
chirality relation 3.3.2.1, 3.3.2.2, 3.3.2.3
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, 3.3.10.9, 3.3.10.9, 3.3.10.9
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, 3.3.6.4.4, 3.3.8, 3.3.8, 3.3.8.2, 3.3.8.2, 3.3.9.1, 3.3.11.3
coincidence-site sublattice 3.3.8, 3.3.8.1, 3.3.10.2.4
coincidence-site subset 3.3.8.1
coincidence sublattice 3.3.8.3, 3.3.8.3
colour-changing operations 3.3.5, 3.3.5
colour-preserving operations 3.3.5
colour symmetry 3.3.5, 3.3.5
compatibility relations 3.3.10.6
compatible planes 3.3.10.2
component state 3.3.2.2, 3.3.2.2
composite groups 3.3.4.4, 3.3.5
composite pseudosymmetry 3.3.6.10
conductivity
copper 3.3.10.6.5
cordierite (Mg2Al4Si5O18) 3.3.10.7.4, 3.3.10.7.4, 3.3.10.7.4, 3.3.10.7.4
corundum (Al2O3) 3.3.6.6, 3.3.10.1
coset composition 3.3.4.1
coset decomposition 3.3.4.1, 3.3.4.1, 3.3.4.1, 3.3.6.4.1, 3.3.6.4.1
Coulomb potential 3.3.10.4.1
crossed polars (Nicols) 3.3.1, 3.3.6.1, 3.3.6.1, 3.3.7.1.1, 3.3.10.7.3, 3.3.10.7.3
crystal system 3.3.7.3, 3.3.9.3
Curie principle 3.3.1
Curie temperature 3.3.9.2.1
Dauphiné–Brazil twin 3.3.6.4.3, 3.3.6.5
degeneracy 3.3.10.2.4
dichalcogenides MeX2 3.3.7.2, 3.3.9.2.4
dichromatic groups 3.3.5, 3.3.5
dielectric (or electric) polarization 3.3.10.2, 3.3.10.7.5
dielectric materials 3.3.6.14
diffraction pattern of a twinned crystal 3.3.4.1, 3.3.6.15, 3.3.8.1, 3.3.9.2.2, 3.3.11.3, 3.3.11.5.2, 3.3.11.5.2, 3.3.11.5.2, 3.3.12
diffuse scattering 3.3.10.7.3
diperiodic twins 3.3.8.1, 3.3.8.7, 3.3.9.2.4
dislocation node 3.3.10.8, 3.3.10.8
dislocation reactions 3.3.10.8
stair-rod 3.3.10.4.3
twinning 3.3.10.2.2
distorted phase 3.3.10.1
domains 3.3.12
anti-polar 3.3.10.3.1
ferroelastic 3.3.6.14, 3.3.9.3, 3.3.10.1
ferroelectric 3.3.6.14
ferroelastic 3.3.7.3
non-ferroelastic 3.3.7.3
domain texture 3.3.7.3, 3.3.7.3
domain twins 3.3.12
Druckzwillinge 3.3.7.3, 3.3.7.3
elastic energy 3.3.10.7.5
elastic strain energy 3.3.10.7.3
elbow twins 3.3.3.1, 3.3.6.10, 3.3.6.10
electrical conductivity 3.3.9.2.1, 3.3.10.3.1
electrical constraints 3.3.10.3, 3.3.10.3.3
electric field 3.3.7.3, 3.3.10.3.1
electron diffraction 3.3.10.2.1, 3.3.11
enantiomorphic groups 3.3.8.6, 3.3.11.3
enantiomorphic twin states 3.3.11.3
enantiomorphism 3.3.4, 3.3.6.4
enantiomorphous crystals 3.3.2.1, 3.3.6.1
equitranslational subgroups 3.3.7.2
Esterel twin 3.3.8.5, 3.3.8.5, 3.3.8.2
extinction position 3.3.6.1, 3.3.6.11
extinction rules 3.3.11.3
ferrobielasticity 3.3.7.3, 3.3.7.3
ferrobielastic switching 3.3.7.1.2
ferrobielastic twinning 3.3.7.3
ferrobielastic twins 3.3.6.4.1, 3.3.10.7.1
ferroelastic domains 3.3.6.14, 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 3.3.6.3, 3.3.9.1, 3.3.10.2.1, 3.3.10.2.1, 3.3.10.7.5
ferroelectric domains 3.3.6.1, 3.3.6.14, 3.3.6.16, 3.3.9.2.1
ferroelectric domain structure 3.3.6.1
ferroelectricity 3.3.6.14, 3.3.7.3
potentially 3.3.6.2
ferroelectric phase 3.3.6.14, 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
ferroic phase 3.3.12
ferromagnetic materials 3.3.10.7.5
fivefold rotation 3.3.2.4
fluorite (CaF2) 3.3.3.1, 3.3.6.7
Friedel's lattice theory 3.3.8.1, 3.3.9.2.4
gallium arsenide (GaAs) 3.3.6.7, 3.3.8.6, 3.3.10.3.3
gallium phosphate (GaPO4) 3.3.6.1, 3.3.6.4.3, 3.3.8.6
garnets 3.3.1
garnet twin 3.3.8.3
germanium 3.3.8.3, 3.3.10.6.6
glide twin 3.3.10.6.3
group–subgroup relations 3.3.10.2.2
growth defects 3.3.6.1
growth morphology 3.3.2, 3.3.7.1.2
growth-sector boundary 3.3.1, 3.3.6.1, 3.3.10.3.1
growth sectors 3.3.1, 3.3.1, 3.3.6.15
growth striations 3.3.1
growth twinning 3.3.6.1, 3.3.6.3
habit modification 3.3.7.1.2
harmotome twin 3.3.3.1, 3.3.10.7.2
high-order twins 3.3.8.3
high-temperature superconductors 3.3.7.3, 3.3.7.3
holohedral groups 3.3.6.4, 3.3.6.16, 3.3.9.1, 3.3.9.1
homogeneous shear 3.3.7.3, 3.3.10.2
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, 3.3.6.2, 3.3.7.2
indium phosphide (InP) 3.3.7.1.2
infrared spectroscopy 3.3.10.7.4
intersection group 3.3.4.3, 3.3.4.3, 3.3.4.4, 3.3.6.7, 3.3.9.1
inversion boundaries 3.3.10.4.3
inversion centre 3.3.2.3.1, 3.3.6.16, 3.3.10.4.3
iron-cross twin 3.3.3.1, 3.3.9.2.1, 3.3.10.4.1
irrational boundary 3.3.6.12
isostructural crystals 3.3.8.6, 3.3.9.2.4
Kantennormalengesetz 3.3.2.3.1, 3.3.2.3.1, 3.3.8.2, 3.3.11.2
klassengleiche subgroup 3.3.7.2
klockmannite (CuSe) 3.3.8.3
knee twin 3.3.6.10
La Gardette twins 3.3.6.4.4, 3.3.6.4.4, 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
one-dimensional 3.3.8.4
three-dimensional 3.3.8.2
two-dimensional 3.3.8.4
lattice concept of twinning 3.3.8
lattice index 3.3.8.2, 3.3.8.2
lattice pseudosymmetry 3.3.8.5, 3.3.8.5, 3.3.9.2.4
Laue class 3.3.11.3
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 3.3.6.4, 3.3.6.4
lithium formate monohydrate ([Li(CHO2)].H2O) 3.3.6.1, 3.3.6.2
lithium formate monohydrate (LiCOO·H2O) 3.3.6.1
lithium formate monohydrate [Li(CHO2).H2O] 3.3.10.2.3, 3.3.10.3.1
lithium niobate (LiNbO3) 3.3.6.1, 3.3.6.1, 3.3.10.3.1
low-energy boundaries 3.3.2.2, 3.3.8.6, 3.3.10.1, 3.3.10.2
low-symmetry phase 3.3.7.2, 3.3.11
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
magnetization 3.3.10.7.5
Mallard pseudo-cube 3.3.6.13
mechanical twinning 3.3.7.3, 3.3.7.3, 3.3.10.2, 3.3.10.2.2
Mediangesetz 3.3.2.3.1, 3.3.2.3.1
median law 3.3.2.3.1, 3.3.6.11
mériédrie réticulaire 3.3.9.1, 3.3.9.1
of translation groups (lattices) 3.3.9.1
microcline (KAlSi3O8) 3.3.6.12, 3.3.10.2.2
microtwins 3.3.6.13
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 of twins 3.3.2.4, 3.3.3, 3.3.3.1, 3.3.8
mosaic crystal 3.3.1
nanocrystalline materials 3.3.7.1.1, 3.3.8.3, 3.3.8.3, 3.3.10.6.6
needle domains 3.3.10.7.3, 3.3.10.7.3, 3.3.10.8
neutron diffraction 3.3.11
noncrystallographic symmetry 3.3.7.1.1
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
non-pyroelectric noncentrosymmetric crystals 3.3.10.3.3
optical anomaly 3.3.1, 3.3.1, 3.3.1, 3.3.6.15
optic axes 3.3.6.1
parent symmetry 3.3.10.7.3, 3.3.10.7.3
penetration trillings 3.3.6.13
pentagonal–decagonal twins 3.3.6.9
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
phase transformation (polymorphic) 3.3.7.2
phase transitions
displacive 3.3.7.2, 3.3.7.3
order–disorder 3.3.7.2, 3.3.10.2.2
phillipsite twin 3.3.3.1, 3.3.10.7.2
piezoelectricity 3.3.6.4, 3.3.6.14, 3.3.6.14
piezoelectric resonators 3.3.7.3
plagioclase twins 3.3.6.12, 3.3.10.2.2, 3.3.11.2, 3.3.6.6
planes of strain compatibility 3.3.10.2
plesiotwins 3.3.2.4, 3.3.2.4
polarization 3.3.6.1, 3.3.6.15
polarizer 3.3.6.1, 3.3.6.8
polarizing microscope 3.3.6.1
polycrystalline aggregates 3.3.10.6.4, 3.3.10.7.5
polycrystalline materials 3.3.1, 3.3.1, 3.3.7.1.2, 3.3.10.7, 3.3.10.7.5
potassium titanyl phosphate (KTP) (KTiOPO4) 3.3.6.2, 3.3.9.2.1, 3.3.10.3.1
potassium trihydrogen selenite KH3(SeO3)2 3.3.9.2.2
powder diffraction 3.3.10.7.4, 3.3.11
praeseodymium sulfide (PrS2) 3.3.9.2.3, 3.3.9.2.4, 3.3.9.2.4
prototype (or high-symmetry) phase 3.3.7.2, 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-fivefold axis 3.3.6.9
pseudo-mériédrie réticulaire 3.3.9.1
of lattice index j = 1 3.3.9.2.2
pseudo-merohedry 3.3.9.3
pseudo-threefold twin axis 3.3.2.3.2
pyrite (FeS2) 3.3.3.1, 3.3.9.2.1, 3.3.10.4.1
pyroelectric domain structures 3.3.6.1
pyroelectric materials 3.3.6.1, 3.3.6.1, 3.3.6.1
Raman spectroscopy 3.3.10.7.4
recrystallization twins 3.3.8.3, 3.3.8.3
reflection twinning 3.3.6.1
repetitive twins 3.3.3
reticular merohedry 3.3.8.5, 3.3.8.5, 3.3.9.2.4
reticular pseudo-merohedry 3.3.8.5, 3.3.9.1
rhombic section 3.3.6.12, 3.3.10.2.2
ripening process 3.3.10.7.4
Ru8Ni15Al77 3.3.6.9
saccharine 3.3.10.4.1
samarium sulfide (SmS1.9) 3.3.8.3, 3.3.9.2.3, 3.3.9.2.4, 3.3.10.1
Sapriel approach 3.3.10.2.1, 3.3.10.2.2
shear
homogeneous 3.3.7.3, 3.3.10.2
spontaneous 3.3.10.2
shear stress 3.3.7.3
Sigma gt 3 twins 3.3.8.3
silicon tricrystal 3.3.8.3
silver 3.3.10.6.5
simple twins 3.3.3, 3.3.3, 3.3.3, 3.3.4.2, 3.3.5, 3.3.5
sodium chlorate (NaClO3) 3.3.6.1
sodium lithium sulfate (NaLiSO4) 3.3.10.9
sodium nitrate (NaNO3) 3.3.7.1.1, 3.3.8.6
sodium oxalate 3.3.10.1
sodium sulfate (Na2SO4) 3.3.7.2
sphalerite (ZnS) 3.3.6.7, 3.3.8.6, 3.3.10.3.3
spontaneous nucleation 3.3.7.1.1, 3.3.8.6
spontaneous properties 3.3.12
spontaneous strain 3.3.7.3, 3.3.10.2.1, 3.3.10.2.3, 3.3.10.7.1
stacking-fault contrast 3.3.6.1, 3.3.6.1, 3.3.10.4.2
St Andrew's cross 3.3.6.13, 3.3.9.2.4, 3.3.9.2.4
structural twins 3.3.7.2
structure-factor contrast 3.3.6.1, 3.3.6.1
superconductors 3.3.7.3, 3.3.10.2.1, 3.3.10.7.3
supersaturation twins 3.3.7.1.1
tenfold rotation 3.3.2.4
tetragonal crystals 3.3.8.3, 3.3.10.2.4
transformation microcline 3.3.6.12, 3.3.10.2.2, 3.3.10.7.4
transition region 3.3.10.4.1
transition temperature 3.3.7.3, 3.3.10.7.5
translation boundary 3.3.1, 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 3.3.8.2, 3.3.9.1
translation twins (T-twins) 3.3.2.4, 3.3.7.2
triglycine sulfate (TGS) 3.3.6.1, 3.3.6.1, 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
fourfold 3.3.9.2.4
of order n gt 2 3.3.8.4
pseudo-fivefold 3.3.3.1, 3.3.10.6.6
pseudo n-fold 3.3.10.2.2
pseudo-threefold 3.3.2.3.2
sixfold 3.3.2.3.2
threefold 3.3.9.2.4, 3.3.9.2.4
with noncrystallographic multiplicities 3.3.6.9
twin component 3.3.2.1, 3.3.2.4
twin formation 3.3.2
by nucleation 3.3.7.1.1
during crystal growth 3.3.7.1.2
twin inserts 3.3.7.1.2, 3.3.7.1.2
twin lattice index 3.3.8.2, 3.3.8.2, 3.3.8.4, 3.3.8.5, 3.3.9.2
twin microstructure 3.3.10.7
twinning
by high-order merohedry 3.3.6.13
by lattice merohedry 3.3.8.2
by pseudo-merohedry 3.3.9, 3.3.9.1, 3.3.11.1, 3.3.11.5.2
by reticular pseudo-merohedry 3.3.6.13, 3.3.9.1, 3.3.11.5.2
by twin-lattice pseudo-symmetry 3.3.9
by twin-lattice symmetry 3.3.9
classification in reciprocal space 3.3.11.1
definition 3.3.2
dislocations 3.3.10.2.2, 3.3.10.8
lattice aspects of 3.3.8, 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, 3.3.10.8, 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 plane 3.3.2, 3.3.2.3.1, 3.3.2.4
twin rotations
fivefold 3.3.6.9
noncrystallographic 3.3.4.4
pseudo n-fold 3.3.2.3.2, 3.3.4.4
tenfold 3.3.6.9
twins 3.3.1
definition of 3.3.2.1
diffraction patterns of 3.3.11.1, 3.3.11.1
genetic classification 3.3.7
morphological classification 3.3.2.4, 3.3.3, 3.3.3.1
pseudo-hexagonal 3.3.11.5.2
with lattice index [j] gt 1 3.3.10.2.4
twins of twins 3.3.6.16, 3.3.6.16
twin textures 3.3.10.7
two-dimensional nucleus 3.3.7.1.2
uniaxial stress 3.3.7.3
unit-cell twinning 3.3.2.4
valence states 3.3.10.6.4
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
Σ17 twins 3.3.11.4.2
Σ19 twins 3.3.11.4.2
Σ25 twins 3.3.11.4.2
Σ27 twins 3.3.8.3, 3.3.8.3
Σ2 twins 3.3.8.3
Σ3 bicrystal boundaries 3.3.10.6.5
Σ3 twin interface 3.3.8.3, 3.3.10.6.4
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 gt 1 twins 3.3.11.5.1
Σ notation 3.3.8.2, 3.3.8.2